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Marino S, Menna G, Bilgin L, Mattogno PP, Gaudino S, Quaranta D, Caraglia N, Olivi A, Berger MS, Doglietto F, Della Pepa GM. "False friends" in Language Subcortical Mapping: A Systematic Literature Review. World Neurosurg 2024:S1878-8750(24)01132-X. [PMID: 38968990 DOI: 10.1016/j.wneu.2024.06.156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2024] [Revised: 06/27/2024] [Accepted: 06/28/2024] [Indexed: 07/07/2024]
Abstract
BACKGROUND Subcortical brain mapping in awake glioma surgery might optimize the extent of resection while minimizing neurological morbidity, but it requires a correct interpretation of responses evoked during surgery. To define, with a systematic review: 1) a comprehensive 'map' of the principal white matter bundles involved in awake surgery on language-related networks, describing the most employed tests and the expected responses; 2) In linguistics, a false friend is a word in a different language that looks or sounds like a word in given language but differs significantly in meaning. Similarly, our aim is to give the surgeons a comprehensive review of potentially misleading responses, namely "false friends", in subcortical language mapping. METHODS Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines were followed. Standardized data extraction was conducted. RESULTS Out of a total of 224 initial papers, 67 were included for analysis. Expected responses, common tests, and potential "false friends" were recorded for each of the following white matter bundles: frontal aslant tract, superior and inferior longitudinal fascicles, arcuate fascicle, inferior fronto-occipital fascicle, uncinate fascicle. Practical examples are discussed to underline the risk of intraoperative fallouts ("false friends") that might lead to an early interruption (false positive) or a risky surgical removal (false negative). CONCLUSIONS This paper represents a critical review of the present status of subcortical awake mapping and underlines practical "false-friend" in mapping critical crossroads in language-related networks.
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Affiliation(s)
- Salvatore Marino
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy
| | - Grazia Menna
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy
| | - Lal Bilgin
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy
| | - Pier Paolo Mattogno
- Neurosurgery Unit, Department of Neurosciences, Fondazione Policlinico Universitario Agostino Gemelli, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Roma, Italy
| | - Simona Gaudino
- Diagnostic Neuroradiology Unit, Department of Radiological and Hematological Sciences, Fondazione Policlinico Universitario Agostino Gemelli, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Rome, Italy
| | - Davide Quaranta
- Neurology Unit, Neurorehabilitation and Neuropsychology Service, Fondazione Policlinico Universitario "A. Gemelli", Istituto di Ricovero e Cura a Carattere Scientifico, San Giovanni Rotondo, Italy
| | - Naike Caraglia
- Neurology Unit, Neurorehabilitation and Neuropsychology Service, Fondazione Policlinico Universitario "A. Gemelli", Istituto di Ricovero e Cura a Carattere Scientifico, San Giovanni Rotondo, Italy
| | - Alessandro Olivi
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy; Neurosurgery Unit, Department of Neurosciences, Fondazione Policlinico Universitario Agostino Gemelli, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Roma, Italy
| | - Mitchel S Berger
- Department of Neurological Surgery, University of California, San Francisco, California, USA
| | - Francesco Doglietto
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy; Neurosurgery Unit, Department of Neurosciences, Fondazione Policlinico Universitario Agostino Gemelli, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Roma, Italy
| | - Giuseppe Maria Della Pepa
- Neurosurgery Unit, Department of Neurosciences, Catholic University School of Medicine, Rome, Italy; Neurosurgery Unit, Department of Neurosciences, Fondazione Policlinico Universitario Agostino Gemelli, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Roma, Italy.
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Simpson MJ, Maclaren OJ. Making Predictions Using Poorly Identified Mathematical Models. Bull Math Biol 2024; 86:80. [PMID: 38801489 PMCID: PMC11129983 DOI: 10.1007/s11538-024-01294-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 04/10/2024] [Indexed: 05/29/2024]
Abstract
Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub . Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.
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Affiliation(s)
- Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
| | - Oliver J Maclaren
- Department of Engineering Science and Biomedical Engineering, University of Auckland, Auckland, New Zealand
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3
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Zhang S, Yu T, Zhang G, Chen M, Yin D, Zhang C. Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field. Biomech Model Mechanobiol 2024:10.1007/s10237-024-01858-y. [PMID: 38801615 DOI: 10.1007/s10237-024-01858-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Accepted: 04/28/2024] [Indexed: 05/29/2024]
Abstract
Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.
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Affiliation(s)
- Shilong Zhang
- Institute for Special Environmental Biophysics, Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, People's Republic of China
- Department of Bioinformatics, College of Life Sciences, Zhejiang University, Hangzhou, 310058, People's Republic of China
| | - Tongyao Yu
- Institute for Special Environmental Biophysics, Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, People's Republic of China
| | - Ge Zhang
- Institute for Special Environmental Biophysics, Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, People's Republic of China
| | - Ming Chen
- Department of Bioinformatics, College of Life Sciences, Zhejiang University, Hangzhou, 310058, People's Republic of China
| | - Dachuan Yin
- Institute for Special Environmental Biophysics, Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, People's Republic of China.
| | - Chenyan Zhang
- Institute for Special Environmental Biophysics, Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, People's Republic of China.
- Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, 518063, People's Republic of China.
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4
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Simpson MJ, Murphy KM, McCue SW, Buenzli PR. Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion. ROYAL SOCIETY OPEN SCIENCE 2024; 11:240126. [PMID: 39076824 PMCID: PMC11286127 DOI: 10.1098/rsos.240126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 02/22/2024] [Indexed: 07/31/2024]
Abstract
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.
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Affiliation(s)
- Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Keeley M. Murphy
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Scott W. McCue
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Pascal R. Buenzli
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
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5
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Wang L, Wang H, D’Angelo F, Curtin L, Sereduk CP, Leon GD, Singleton KW, Urcuyo J, Hawkins-Daarud A, Jackson PR, Krishna C, Zimmerman RS, Patra DP, Bendok BR, Smith KA, Nakaji P, Donev K, Baxter LC, Mrugała MM, Ceccarelli M, Iavarone A, Swanson KR, Tran NL, Hu LS, Li J. Quantifying intra-tumoral genetic heterogeneity of glioblastoma toward precision medicine using MRI and a data-inclusive machine learning algorithm. PLoS One 2024; 19:e0299267. [PMID: 38568950 PMCID: PMC10990246 DOI: 10.1371/journal.pone.0299267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 02/06/2024] [Indexed: 04/05/2024] Open
Abstract
BACKGROUND AND OBJECTIVE Glioblastoma (GBM) is one of the most aggressive and lethal human cancers. Intra-tumoral genetic heterogeneity poses a significant challenge for treatment. Biopsy is invasive, which motivates the development of non-invasive, MRI-based machine learning (ML) models to quantify intra-tumoral genetic heterogeneity for each patient. This capability holds great promise for enabling better therapeutic selection to improve patient outcome. METHODS We proposed a novel Weakly Supervised Ordinal Support Vector Machine (WSO-SVM) to predict regional genetic alteration status within each GBM tumor using MRI. WSO-SVM was applied to a unique dataset of 318 image-localized biopsies with spatially matched multiparametric MRI from 74 GBM patients. The model was trained to predict the regional genetic alteration of three GBM driver genes (EGFR, PDGFRA and PTEN) based on features extracted from the corresponding region of five MRI contrast images. For comparison, a variety of existing ML algorithms were also applied. Classification accuracy of each gene were compared between the different algorithms. The SHapley Additive exPlanations (SHAP) method was further applied to compute contribution scores of different contrast images. Finally, the trained WSO-SVM was used to generate prediction maps within the tumoral area of each patient to help visualize the intra-tumoral genetic heterogeneity. RESULTS WSO-SVM achieved 0.80 accuracy, 0.79 sensitivity, and 0.81 specificity for classifying EGFR; 0.71 accuracy, 0.70 sensitivity, and 0.72 specificity for classifying PDGFRA; 0.80 accuracy, 0.78 sensitivity, and 0.83 specificity for classifying PTEN; these results significantly outperformed the existing ML algorithms. Using SHAP, we found that the relative contributions of the five contrast images differ between genes, which are consistent with findings in the literature. The prediction maps revealed extensive intra-tumoral region-to-region heterogeneity within each individual tumor in terms of the alteration status of the three genes. CONCLUSIONS This study demonstrated the feasibility of using MRI and WSO-SVM to enable non-invasive prediction of intra-tumoral regional genetic alteration for each GBM patient, which can inform future adaptive therapies for individualized oncology.
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Affiliation(s)
- Lujia Wang
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America
| | - Hairong Wang
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America
| | - Fulvio D’Angelo
- Institute for Cancer Genetics, Columbia University Medical Center, New York City, New York, United States of America
| | - Lee Curtin
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Christopher P. Sereduk
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Gustavo De Leon
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Kyle W. Singleton
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Javier Urcuyo
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Andrea Hawkins-Daarud
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Pamela R. Jackson
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Chandan Krishna
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Richard S. Zimmerman
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Devi P. Patra
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Bernard R. Bendok
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Kris A. Smith
- Department of Neurosurgery, Barrow Neurological Institute—St. Joseph’s Hospital and Medical Center, Phoenix, Arizona, United States of America
| | - Peter Nakaji
- Department of Neurosurgery, Barrow Neurological Institute—St. Joseph’s Hospital and Medical Center, Phoenix, Arizona, United States of America
| | - Kliment Donev
- Department of Pathology, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Leslie C. Baxter
- Department of Neuropsychology, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Maciej M. Mrugała
- Department of Neuro-Oncology, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Michele Ceccarelli
- Department of Electrical Engineering and Information Technology, University of Naples “Federico II”, Naples, Italy
| | - Antonio Iavarone
- Institute for Cancer Genetics, Columbia University Medical Center, New York City, New York, United States of America
| | - Kristin R. Swanson
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Nhan L. Tran
- Department of Neurosurgery, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
- Department of Cancer Biology, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Leland S. Hu
- Department of Radiology, Mayo Clinic Arizona, Phoenix, Arizona, United States of America
| | - Jing Li
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, United States of America
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6
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Simpson MJ, Murphy RJ, Maclaren OJ. Modelling count data with partial differential equation models in biology. J Theor Biol 2024; 580:111732. [PMID: 38218530 DOI: 10.1016/j.jtbi.2024.111732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Revised: 12/03/2023] [Accepted: 01/08/2024] [Indexed: 01/15/2024]
Abstract
Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.
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Affiliation(s)
- Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
| | - Ryan J Murphy
- School of Mathematics and Statistics, The University of Melbourne, Victoria, Australia
| | - Oliver J Maclaren
- Department of Engineering Science and Biomedical Engineering, University of Auckland, Auckland, New Zealand
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7
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Leander R, Owanga G, Nelson D, Liu Y. A Mathematical Model of Stroma-Supported Allometric Tumor Growth. Bull Math Biol 2024; 86:38. [PMID: 38446260 DOI: 10.1007/s11538-024-01265-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 01/29/2024] [Indexed: 03/07/2024]
Abstract
Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.
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Affiliation(s)
- Rachel Leander
- Department of Mathematical Sciences, Middle Tennessee State University, MTSU Box 34, Murfreesboro, TN, 37132, USA.
| | - Greg Owanga
- Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL, 32306, USA
| | - David Nelson
- Department of Biology, Middle Tennessee State University, MTSU Box 60, Murfreesboro, TN, 610101, USA
| | - Yeqian Liu
- Department of Mathematical Sciences, Middle Tennessee State University, MTSU Box 34, Murfreesboro, TN, 37132, USA
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8
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Hassan J, Saeed SM, Deka L, Uddin MJ, Das DB. Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges. Pharmaceutics 2024; 16:260. [PMID: 38399314 PMCID: PMC10892549 DOI: 10.3390/pharmaceutics16020260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 01/29/2024] [Accepted: 02/07/2024] [Indexed: 02/25/2024] Open
Abstract
The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.
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Affiliation(s)
- Jasmin Hassan
- Drug Delivery & Therapeutics Lab, Dhaka 1212, Bangladesh; (J.H.); (S.M.S.)
| | | | - Lipika Deka
- Faculty of Computing, Engineering and Media, De Montfort University, Leicester LE1 9BH, UK;
| | - Md Jasim Uddin
- Department of Pharmaceutical Technology, Faculty of Pharmacy, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Diganta B. Das
- Department of Chemical Engineering, Loughborough University, Loughborough LE11 3TU, UK
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9
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Urcuyo JC, Curtin L, Langworthy JM, De Leon G, Anderies B, Singleton KW, Hawkins-Daarud A, Jackson PR, Bond KM, Ranjbar S, Lassiter-Morris Y, Clark-Swanson KR, Paulson LE, Sereduk C, Mrugala MM, Porter AB, Baxter L, Salomao M, Donev K, Hudson M, Meyer J, Zeeshan Q, Sattur M, Patra DP, Jones BA, Rahme RJ, Neal MT, Patel N, Kouloumberis P, Turkmani AH, Lyons M, Krishna C, Zimmerman RS, Bendok BR, Tran NL, Hu LS, Swanson KR. Image-localized biopsy mapping of brain tumor heterogeneity: A single-center study protocol. PLoS One 2023; 18:e0287767. [PMID: 38117803 PMCID: PMC10732423 DOI: 10.1371/journal.pone.0287767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 06/13/2023] [Indexed: 12/22/2023] Open
Abstract
Brain cancers pose a novel set of difficulties due to the limited accessibility of human brain tumor tissue. For this reason, clinical decision-making relies heavily on MR imaging interpretation, yet the mapping between MRI features and underlying biology remains ambiguous. Standard (clinical) tissue sampling fails to capture the full heterogeneity of the disease. Biopsies are required to obtain a pathological diagnosis and are predominantly taken from the tumor core, which often has different traits to the surrounding invasive tumor that typically leads to recurrent disease. One approach to solving this issue is to characterize the spatial heterogeneity of molecular, genetic, and cellular features of glioma through the intraoperative collection of multiple image-localized biopsy samples paired with multi-parametric MRIs. We have adopted this approach and are currently actively enrolling patients for our 'Image-Based Mapping of Brain Tumors' study. Patients are eligible for this research study (IRB #16-002424) if they are 18 years or older and undergoing surgical intervention for a brain lesion. Once identified, candidate patients receive dynamic susceptibility contrast (DSC) perfusion MRI and diffusion tensor imaging (DTI), in addition to standard sequences (T1, T1Gd, T2, T2-FLAIR) at their presurgical scan. During surgery, sample anatomical locations are tracked using neuronavigation. The collected specimens from this research study are used to capture the intra-tumoral heterogeneity across brain tumors including quantification of genetic aberrations through whole-exome and RNA sequencing as well as other tissue analysis techniques. To date, these data (made available through a public portal) have been used to generate, test, and validate predictive regional maps of the spatial distribution of tumor cell density and/or treatment-related key genetic marker status to identify biopsy and/or treatment targets based on insight from the entire tumor makeup. This type of methodology, when delivered within clinically feasible time frames, has the potential to further inform medical decision-making by improving surgical intervention, radiation, and targeted drug therapy for patients with glioma.
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Affiliation(s)
- Javier C Urcuyo
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Lee Curtin
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Jazlynn M. Langworthy
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Gustavo De Leon
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Barrett Anderies
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Kyle W. Singleton
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Andrea Hawkins-Daarud
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Pamela R. Jackson
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Kamila M. Bond
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Sara Ranjbar
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Yvette Lassiter-Morris
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Kamala R. Clark-Swanson
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Lisa E. Paulson
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Chris Sereduk
- Department of Cancer Biology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Maciej M. Mrugala
- Department of Neurology, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Oncology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Alyx B. Porter
- Department of Neurology, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Oncology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Leslie Baxter
- Department of Neurophysiology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Marcela Salomao
- Department of Pathology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Kliment Donev
- Department of Pathology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Miles Hudson
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Jenna Meyer
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Qazi Zeeshan
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Mithun Sattur
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Devi P. Patra
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Breck A. Jones
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Rudy J. Rahme
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Matthew T. Neal
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Naresh Patel
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Pelagia Kouloumberis
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Ali H. Turkmani
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Mark Lyons
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Chandan Krishna
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Richard S. Zimmerman
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Bernard R. Bendok
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Nhan L. Tran
- Department of Cancer Biology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Leland S. Hu
- Department of Radiology, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Kristin R. Swanson
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Cancer Biology, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Radiation Oncology, Mayo Clinic, Phoenix, Arizona, United States of America
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10
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Guillevin R, Naudin M, Fayolle P, Giraud C, Le Guillou X, Thomas C, Herpe G, Miranville A, Fernandez-Maloigne C, Pellerin L, Guillevin C. Diagnostic and Therapeutic Issues in Glioma Using Imaging Data: The Challenge of Numerical Twinning. J Clin Med 2023; 12:7706. [PMID: 38137775 PMCID: PMC10744312 DOI: 10.3390/jcm12247706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 11/28/2023] [Accepted: 12/11/2023] [Indexed: 12/24/2023] Open
Abstract
Glial tumors represent the leading etiology of primary brain tumors. Their particularities lie in (i) their location in a highly functional organ that is difficult to access surgically, including for biopsy, and (ii) their rapid, anisotropic mode of extension, notably via the fiber bundles of the white matter, which further limits the possibilities of resection. The use of mathematical tools enables the development of numerical models representative of the oncotype, genotype, evolution, and therapeutic response of lesions. The significant development of digital technologies linked to high-resolution NMR exploration, coupled with the possibilities offered by AI, means that we can envisage the creation of digital twins of tumors and their host organs, thus reducing the use of physical sampling.
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Affiliation(s)
- Rémy Guillevin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Mathieu Naudin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Pierre Fayolle
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Clément Giraud
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Xavier Le Guillou
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
- Department of Genetic, University Hospital Center of Poitiers, 86000 Poitiers, France
| | - Clément Thomas
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Guillaume Herpe
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Alain Miranville
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | | | - Luc Pellerin
- IRMETIST Laboratory, INSERM U1313, University of Poitiers and University Hospital Center of Poitiers, 86000 Poitiers, France
| | - Carole Guillevin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
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11
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Mohammed S, Kurtek S, Bharath K, Rao A, Baladandayuthapani V. Tumor radiogenomics in gliomas with Bayesian layered variable selection. Med Image Anal 2023; 90:102964. [PMID: 37797481 PMCID: PMC10653647 DOI: 10.1016/j.media.2023.102964] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 12/09/2022] [Accepted: 07/03/2023] [Indexed: 10/07/2023]
Abstract
We propose a statistical framework to analyze radiological magnetic resonance imaging (MRI) and genomic data to identify the underlying radiogenomic associations in lower grade gliomas (LGG). We devise a novel imaging phenotype by dividing the tumor region into concentric spherical layers that mimics the tumor evolution process. MRI data within each layer is represented by voxel-intensity-based probability density functions which capture the complete information about tumor heterogeneity. Under a Riemannian-geometric framework these densities are mapped to a vector of principal component scores which act as imaging phenotypes. Subsequently, we build Bayesian variable selection models for each layer with the imaging phenotypes as the response and the genomic markers as predictors. Our novel hierarchical prior formulation incorporates the interior-to-exterior structure of the layers, and the correlation between the genomic markers. We employ a computationally-efficient Expectation-Maximization-based strategy for estimation. Simulation studies demonstrate the superior performance of our approach compared to other approaches. With a focus on the cancer driver genes in LGG, we discuss some biologically relevant findings. Genes implicated with survival and oncogenesis are identified as being associated with the spherical layers, which could potentially serve as early-stage diagnostic markers for disease monitoring, prior to routine invasive approaches. We provide a R package that can be used to deploy our framework to identify radiogenomic associations.
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Affiliation(s)
- Shariq Mohammed
- Department of Biostatistics, Boston University, 801 Massachusetts Ave, Boston, MA 02118, United States; Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48103, United States; Department of Computational Medicine and Bioinformatics, University of Michigan, 100 Washtenaw Avenue, Ann Arbor, MI 48109, United States.
| | - Sebastian Kurtek
- Department of Statistics, The Ohio State University, 1958 Neil Avenue, Columbus, OH 43210, United States
| | - Karthik Bharath
- School of Mathematical Sciences, University Park, Nottingham, NG7 2RD, United Kingdom
| | - Arvind Rao
- Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48103, United States; Department of Computational Medicine and Bioinformatics, University of Michigan, 100 Washtenaw Avenue, Ann Arbor, MI 48109, United States; Department of Radiation Oncology, University of Michigan, 1500 E Medical Center Dr, Ann Arbor, MI 48109, United States
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12
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Hillen T, Loy N, Painter KJ, Thiessen R. Modelling microtube driven invasion of glioma. J Math Biol 2023; 88:4. [PMID: 38015257 PMCID: PMC10684558 DOI: 10.1007/s00285-023-02025-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Revised: 10/20/2023] [Accepted: 10/29/2023] [Indexed: 11/29/2023]
Abstract
Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.
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Affiliation(s)
- Thomas Hillen
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada.
| | - Nadia Loy
- Department of Mathematical Sciences (DISMA), Politecnico di Torino, Turin, Italy
| | - Kevin J Painter
- Interuniversity Department of Regional and Urban Studies and Planning (DIST), Politecnico di Torino, Turin, Italy
| | - Ryan Thiessen
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
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13
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Nowicka Z, Rentzeperis F, Beck R, Tagal V, Pinto AF, Scanu E, Veith T, Cole J, Ilter D, Viqueira WD, Teer JK, Maksin K, Pasetto S, Abdalah MA, Fiandaca G, Prabhakaran S, Schultz A, Ojwang M, Barnholtz-Sloan JS, Farinhas JM, Gomes AP, Katira P, Andor N. Interactions between ploidy and resource availability shape clonal interference at initiation and recurrence of glioblastoma. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.10.17.562670. [PMID: 37905142 PMCID: PMC10614845 DOI: 10.1101/2023.10.17.562670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
Glioblastoma (GBM) is the most aggressive form of primary brain tumor. Complete surgical resection of GBM is almost impossible due to the infiltrative nature of the cancer. While no evidence for recent selection events have been found after diagnosis, the selective forces that govern gliomagenesis are strong, shaping the tumor's cell composition during the initial progression to malignancy with late consequences for invasiveness and therapy response. We present a mathematical model that simulates the growth and invasion of a glioma, given its ploidy level and the nature of its brain tissue micro-environment (TME), and use it to make inferences about GBM initiation and response to standard-of-care treatment. We approximate the spatial distribution of resource access in the TME through integration of in-silico modelling, multi-omics data and image analysis of primary and recurrent GBM. In the pre-malignant setting, our in-silico results suggest that low ploidy cancer cells are more resistant to starvation-induced cell death. In the malignant setting, between first and second surgery, simulated tumors with different ploidy compositions progressed at different rates. Whether higher ploidy predicted fast recurrence, however, depended on the TME. Historical data supports this dependence on TME resources, as shown by a significant correlation between the median glucose uptake rates in human tissues and the median ploidy of cancer types that arise in the respective tissues (Spearman r = -0.70; P = 0.026). Taken together our findings suggest that availability of metabolic substrates in the TME drives different cell fate decisions for cancer cells with different ploidy and shapes GBM disease initiation and relapse characteristics.
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Affiliation(s)
- Zuzanna Nowicka
- Department of Biostatistics and Translational Medicine, Medical University of Łódź, Łódź, Poland
| | | | - Richard Beck
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Vural Tagal
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Ana Forero Pinto
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Elisa Scanu
- Queen Mary University of London, London, United Kingdom
| | - Thomas Veith
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
- Cancer Biology PhD Program, University of South Florida, Tampa, FL, USA
| | - Jackson Cole
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Didem Ilter
- Department of Molecular Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | | | - Jamie K. Teer
- Biostatistics and Bioinformatics, Moffitt Cancer Center, Tampa, FL, USA
| | | | - Stefano Pasetto
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | | | - Giada Fiandaca
- Department of Cellular, Computational and Integrative Biology, University of Trento, Tento, Italy
| | - Sandhya Prabhakaran
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Andrew Schultz
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Maureiq Ojwang
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Jill S. Barnholtz-Sloan
- Center for Biomedical Informatics & Information Technology and Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, USA
| | | | - Ana P. Gomes
- Department of Molecular Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Parag Katira
- Department of Mechanical Engineering, San Diego State University, San Diego, CA, USA
| | - Noemi Andor
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
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14
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Buckwar E, Conte M, Meddah A. A stochastic hierarchical model for low grade glioma evolution. J Math Biol 2023; 86:89. [PMID: 37147527 PMCID: PMC10163130 DOI: 10.1007/s00285-023-01909-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 03/17/2023] [Accepted: 03/22/2023] [Indexed: 05/07/2023]
Abstract
A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker-Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.
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Affiliation(s)
- Evelyn Buckwar
- Institute of Stochastics, Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria
- Centre for Mathematical Sciences, Lund University, 221 00, Lund, Sweden
| | - Martina Conte
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
| | - Amira Meddah
- Institute of Stochastics, Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria.
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15
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Yen CH, Lai YC, Wu KA. Morphological instability of solid tumors in a nutrient-deficient environment. Phys Rev E 2023; 107:054405. [PMID: 37329102 DOI: 10.1103/physreve.107.054405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Accepted: 04/24/2023] [Indexed: 06/18/2023]
Abstract
A phenomenological reaction-diffusion model that includes a nutrient-regulated growth rate of tumor cells is proposed to investigate the morphological instability of solid tumors during the avascular growth. We find that the surface instability could be induced more easily when tumor cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed for tumor cells in a nutrient-rich environment due to the nutrient-regulated proliferation. In addition, the surface instability is shown to be influenced by the growth moving speed of tumor rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability. A nourished length that represents the proximity is defined to illustrate its close relation to the surface instability.
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Affiliation(s)
- Chien-Han Yen
- Department of Physics, National Tsing Hua University, 30013 Hsinchu, Taiwan
| | - Yi-Chieh Lai
- Department of Physics, National Tsing Hua University, 30013 Hsinchu, Taiwan
| | - Kuo-An Wu
- Department of Physics, National Tsing Hua University, 30013 Hsinchu, Taiwan
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16
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Ghannoum S, Fantini D, Zahoor M, Reiterer V, Phuyal S, Leoncio Netto W, Sørensen Ø, Iyer A, Sengupta D, Prasmickaite L, Mælandsmo GM, Köhn-Luque A, Farhan H. A combined experimental-computational approach uncovers a role for the Golgi matrix protein Giantin in breast cancer progression. PLoS Comput Biol 2023; 19:e1010995. [PMID: 37068117 PMCID: PMC10159355 DOI: 10.1371/journal.pcbi.1010995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 05/04/2023] [Accepted: 03/04/2023] [Indexed: 04/18/2023] Open
Abstract
Our understanding of how speed and persistence of cell migration affects the growth rate and size of tumors remains incomplete. To address this, we developed a mathematical model wherein cells migrate in two-dimensional space, divide, die or intravasate into the vasculature. Exploring a wide range of speed and persistence combinations, we find that tumor growth positively correlates with increasing speed and higher persistence. As a biologically relevant example, we focused on Golgi fragmentation, a phenomenon often linked to alterations of cell migration. Golgi fragmentation was induced by depletion of Giantin, a Golgi matrix protein, the downregulation of which correlates with poor patient survival. Applying the experimentally obtained migration and invasion traits of Giantin depleted breast cancer cells to our mathematical model, we predict that loss of Giantin increases the number of intravasating cells. This prediction was validated, by showing that circulating tumor cells express significantly less Giantin than primary tumor cells. Altogether, our computational model identifies cell migration traits that regulate tumor progression and uncovers a role of Giantin in breast cancer progression.
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Affiliation(s)
- Salim Ghannoum
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Damiano Fantini
- Department of Urology, Northwestern University, Chicago, Illinois, United States of America
| | - Muhammad Zahoor
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Veronika Reiterer
- Institute of Pathophysiology, Medical University of Innsbruck, Innsbruck, Austria
| | - Santosh Phuyal
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Waldir Leoncio Netto
- Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo, Oslo, Norway
| | - Øystein Sørensen
- Center for Lifespan Changes in Brain and Cognition, Department of Psychology, University of Oslo, Oslo, Norway
| | - Arvind Iyer
- Department of Computational Biology, University of Lausanne (UNIL), Lausanne, Switzerland
| | - Debarka Sengupta
- Department of Computational Biology, Indraprastha Institute of Information Technology, New Delhi, India
- Centre for Artificial Intelligence, Indraprastha Institute of Information Technology, Delhi, India
| | - Lina Prasmickaite
- Department of Tumor Biology, Institute for Cancer Research, Oslo University Hospital, The Norwegian Radium Hospital, Oslo, Norway
| | - Gunhild Mari Mælandsmo
- Department of Tumor Biology, Institute for Cancer Research, Oslo University Hospital, The Norwegian Radium Hospital, Oslo, Norway
- Department of Medical Biology, UiT-The Arctic University of Norway, Tromsø, Norway
| | - Alvaro Köhn-Luque
- Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo, Oslo, Norway
| | - Hesso Farhan
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
- Institute of Pathophysiology, Medical University of Innsbruck, Innsbruck, Austria
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17
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Tursynkozha A, Kashkynbayev A, Shupeyeva B, Rutter EM, Kuang Y. Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION 2023; 118:107008. [PMID: 36582429 PMCID: PMC9794186 DOI: 10.1016/j.cnsns.2022.107008] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.
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Affiliation(s)
- Aisha Tursynkozha
- Department of Mathematics, Nazarbayev University, 010000 Astana, Kazakhstan
| | - Ardak Kashkynbayev
- Department of Mathematics, Nazarbayev University, 010000 Astana, Kazakhstan
| | - Bibinur Shupeyeva
- Department of Mathematics, Nazarbayev University, 010000 Astana, Kazakhstan
| | - Erica M. Rutter
- Department of Applied Mathematics, University of California, Merced, 5200 North Lake Rd., Merced, CA, 95343, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
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18
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Yan Z, Tang J, Ge H, Liu D, Liu Y, Liu H, Zou Y, Hu X, Yang K, Chen J. Synergistic structural and functional alterations in the medial prefrontal cortex of patients with high-grade gliomas infiltrating the thalamus and the basal ganglia. Front Neurosci 2023; 17:1136534. [PMID: 37051149 PMCID: PMC10083262 DOI: 10.3389/fnins.2023.1136534] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 02/28/2023] [Indexed: 03/28/2023] Open
Abstract
BackgroundHigh-grade gliomas (HGGs) are characterized by a high degree of tissue invasion and uncontrolled cell proliferation, inevitably damaging the thalamus and the basal ganglia. The thalamus exhibits a high level of structural and functional connectivity with the default mode network (DMN). The present study investigated the structural and functional compensation within the DMN in HGGs invading the thalamus along with the basal ganglia (HITBG).MethodsA total of 32 and 22 healthy controls were enrolled, and their demographics and neurocognition (digit span test, DST) were assessed. Of the 32 patients, 18 patients were involved only on the left side, while 15 of them were involved on the right side. This study assessed the amplitude of low-frequency fluctuation (ALFF), regional homogeneity (ReHo), gray matter (GM) volume, and functional connectivity (FC) within the DMN and compared these measures between patients with left and right HITBG and healthy controls (HCs).ResultThe medial prefrontal cortex (mPFC) region existed in synchrony with the significant increase in ALFF and GM volume in patients with left and right HITBG compared with HCs. In addition, patients with left HITBG exhibited elevated ReHo and GM precuneus volumes, which did not overlap with the findings in patients with right HITBG. The patients with left and right HITBG showed decreased GM volume in the contralateral hippocampus without any functional variation. However, no significant difference in FC values was observed in the regions within the DMN. Additionally, the DST scores were significantly lower in patients with HITBG, but there was no significant correlation with functional or GM volume measurements.ConclusionThe observed pattern of synchrony between structure and function was present in the neuroplasticity of the mPFC and the precuneus. However, patients with HITBG may have a limited capacity to affect the connectivity within the regions of the DMN. Furthermore, the contralateral hippocampus in patients with HITBG exhibited atrophy. Thus, preventing damage to these regions may potentially delay the progression of neurological function impairment in patients with HGG.
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Affiliation(s)
- Zheng Yan
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Jun Tang
- Department of Neurosurgery, Yixing Hospital of Traditional Chinese Medicine, Yixing, China
| | - Honglin Ge
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Dongming Liu
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Yong Liu
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Hongyi Liu
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Yuanjie Zou
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Xinhua Hu
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
| | - Kun Yang
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- *Correspondence: Kun Yang
| | - Jiu Chen
- Department of Neurosurgery, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Institute of Brain Functional Imaging, The Affiliated Brain Hospital of Nanjing Medical University, Nanjing, Jiangsu, China
- Jiu Chen
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Hussain A, Muthuvalu MS, Faye I, Zafar M, Inc M, Afzal F, Iqbal MS. Numerical investigation of treated brain glioma model using a two-stage successive over-relaxation method. Comput Biol Med 2023; 153:106429. [PMID: 36587570 DOI: 10.1016/j.compbiomed.2022.106429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 11/17/2022] [Accepted: 12/13/2022] [Indexed: 12/31/2022]
Abstract
A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18-76.34% faster than the TSGS and GS methods.
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Affiliation(s)
- Abida Hussain
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Intelligent Signal and Imaging Research, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mohana Sundaram Muthuvalu
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Ibrahima Faye
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Intelligent Signal and Imaging Research, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mudasar Zafar
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Research in Enhanced Oil Recovery, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mustafa Inc
- Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey; Department of Medical Research, China Medical University, Taichung, Taiwan.
| | - Farkhanda Afzal
- Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology (NUST), Islamabad, Pakistan
| | - Muhammad Sajid Iqbal
- Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology (NUST), Islamabad, Pakistan
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20
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Meaney C, Das S, Colak E, Kohandel M. Deep learning characterization of brain tumours with diffusion weighted imaging. J Theor Biol 2023; 557:111342. [PMID: 36368560 DOI: 10.1016/j.jtbi.2022.111342] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 10/19/2022] [Accepted: 10/30/2022] [Indexed: 11/09/2022]
Abstract
Glioblastoma multiforme (GBM) is one of the most deadly forms of cancer. Methods of characterizing these tumours are valuable for improving predictions of their progression and response to treatment. A mathematical model called the proliferation-invasion (PI) model has been used extensively in the literature to model the growth of these tumours, though it relies on known values of two key parameters: the tumour cell diffusivity and proliferation rate. Unfortunately, these parameters are difficult to estimate in a patient-specific manner, making personalized tumour forecasting challenging. In this paper, we develop and apply a deep learning model capable of making accurate estimates of these key GBM-characterizing parameters while simultaneously producing a full prediction of the tumour progression curve. Our method uses two sets of multi sequence MRI in order to produce estimations and relies on a preprocessing pipeline which includes brain tumour segmentation and conversion to tumour cellularity. We first apply our deep learning model to synthetic tumours to showcase the model's capabilities and identify situations where prediction errors are likely to occur. We then apply our model to a clinical dataset consisting of five patients diagnosed with GBM. For all patients, we derive evidence-based estimates for each of the PI model parameters and predictions for the future progression of the tumour, along with estimates of the parameter uncertainties. Our work provides a new, easily generalizable method for the estimation of patient-specific tumour parameters, which can be built upon to aid physicians in designing personalized treatments.
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Affiliation(s)
- Cameron Meaney
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.
| | - Sunit Das
- Division of Neurosurgery, Li Ka Shing Knowledge Institute, St. Michael's Hospital, Toronto, Canada; Faculty of Medicine, University of Toronto, Toronto, Canada
| | - Errol Colak
- Faculty of Medicine, University of Toronto, Toronto, Canada; Department of Medical Imaging and Li Ka Shing Knowledge Institute, St. Michael's Hospital, Toronto, Canada; Odette Professorship in Artificial Intelligence for Medical Imaging, St. Michael's Hospital, Toronto, Canada
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
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21
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Buti G, Shusharina N, Ajdari A, Sterpin E, Bortfeld T. Exploring trade-offs in treatment planning for brain tumor cases with a probabilistic definition of the clinical target volume. Med Phys 2023; 50:410-423. [PMID: 36354283 DOI: 10.1002/mp.16097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Revised: 10/20/2022] [Accepted: 10/26/2022] [Indexed: 11/12/2022] Open
Abstract
PURPOSE This study demonstrates how a novel probabilistic clinical target volume (CTV) concept-the clinical target distribution (CTD)-can be used to navigate the trade-off between target coverage and organ sparing with a semi-interactive treatment planning approach. METHODS Two probabilistic treatment planning methods are presented that use tumor probabilities to balance tumor control with organ-at-risk (OAR) sparing. The first method explores OAR dose reduction by systematically discarding x % $x\%$ of CTD voxels with an unfavorable dose-to-probability ratio from the minimum dose coverage objective. The second method sequentially expands the target volume from the GTV edge, calculating the CTD coverage versus OAR sparing trade-off after dosing each expansion. Each planning method leads to estimated levels of tumor control under specific statistical models of tumor infiltration: an independent tumor islets model and contiguous circumferential tumor growth model. The methods are illustrated by creating proton therapy treatment plans for two glioblastoma patients with the clinical goal of sparing the hippocampus and brainstem. For probabilistic plan evaluation, the concept of a dose-expected-volume histogram is introduced, which plots the dose to the expected tumor volume ⟨ v ⟩ $\langle v \rangle$ considering tumor probabilities. RESULTS Both probabilistic planning approaches generate a library of treatment plans to interactively navigate the planning trade-offs. In the first probabilistic approach, a significant reduction of hippocampus dose could be achieved by excluding merely 1% of CTD voxels without compromising expected tumor control probability (TCP) or CTD coverage: the hippocampus D 2 % $D_{2\%}$ dose reduces with 9.5 and 5.3 Gy for Patient 1 and 2, while the TCP loss remains below 1%. Moreover, discarding up to 10% of the CTD voxels does not significantly diminish the expected CTD dose, even though evaluation with a binary volume suggests poor CTD coverage. In the second probabilistic approach, the expected CTD D ⟨ 98 % ⟩ $D_{\langle 98\%\rangle }$ and TCP depend more strongly on the extent of the high-dose region: the target volume margin cannot be reduced by more than 2 mm if one aims at keeping the expected CTD D ⟨ 98 % ⟩ $D_{\langle 98\%\rangle }$ loss and TCP loss under 1 Gy and 2%, respectively. Therefore, there is less potential for improved OAR sparing without compromising TCP or expected CTD coverage. CONCLUSIONS This study proposes and implements treatment planning strategies to explore trade-offs using tumor probabilities.
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Affiliation(s)
- Gregory Buti
- Institute of Experimental and Clinical Research, Center of Molecular Imaging, Radiotherapy and Oncology, Brussels, Belgium.,Massachusetts General Hospital and Harvard Medical School, Department of Radiation Oncology, Division of Radiation Biophysics, Boston, Massachusetts, USA
| | - Nadya Shusharina
- Massachusetts General Hospital and Harvard Medical School, Department of Radiation Oncology, Division of Radiation Biophysics, Boston, Massachusetts, USA
| | - Ali Ajdari
- Massachusetts General Hospital and Harvard Medical School, Department of Radiation Oncology, Division of Radiation Biophysics, Boston, Massachusetts, USA
| | - Edmond Sterpin
- Institute of Experimental and Clinical Research, Center of Molecular Imaging, Radiotherapy and Oncology, Brussels, Belgium.,KU Leuven, Department of Oncology, Laboratory of Experimental Radiotherapy, Leuven, Belgium
| | - Thomas Bortfeld
- Massachusetts General Hospital and Harvard Medical School, Department of Radiation Oncology, Division of Radiation Biophysics, Boston, Massachusetts, USA
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22
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Zhang Y, Liu PX, Hou W. Modeling of glioma growth using modified reaction-diffusion equation on brain MR images. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 227:107233. [PMID: 36375418 DOI: 10.1016/j.cmpb.2022.107233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 11/02/2022] [Accepted: 11/04/2022] [Indexed: 06/16/2023]
Abstract
BACKGROUND AND OBJECTIVE Modeling of glioma growth and evolution is of key importance for cancer diagnosis, predicting clinical progression and improving treatment outcomes of neurosurgery. However, existing models are unable to characterize spatial variations of the proliferation and infiltration of tumor cells, making it difficult to achieve accurate prediction of tumor growth. METHODS In this paper, a new growth model of brain tumor using a reaction-diffusion equation on brain magnetic resonance images is proposed. Both the heterogeneity of brain tissue and the density of tumor cells are used to estimate the proliferation and diffusion coefficients of brain tumor cells. The diffusion coefficient that characterizes tumor diffusion and infiltration is calculated based on the ratio of tissues (white and gray matter), while the proliferation coefficient is evaluated using the spatial gradient of tumor cells. In addition, a parameter space is constructed using inverse distance weighted interpolation to describe the spatial distribution of proliferation coefficient. RESULTS The glioma growth predicted by the proposed model were tested by comparing with the real magnetic resonance images of the patients. Experiments and simulation results show that the proposed method achieves accurate modeling of glioma growth. The interpolation-based growth model has higher average dice score of 0.0647 and 0.0545, and higher average Jaccard index of 0.0673 and 0.0573, respectively, compared to the uniform- and gradient-based growth models. CONCLUSIONS The experimental results demonstrate the feasibility of calculating the proliferation and diffusion coefficients of the growth model based on patient-specific anatomy. The parameter space that characterizes spatial distribution of proliferation and diffusion coefficients is established and incorporated into the simulation of glioma growth. It enables to obtain patient-specific models about glioma growth by estimating and calibrating only a few model parameters.
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Affiliation(s)
- Yanying Zhang
- School of Information Science and Engineering Zhejiang Sci-Tech University, Hangzhou,Zhejiang, China
| | - Peter X Liu
- School of Information Science and Engineering Zhejiang Sci-Tech University, Hangzhou,Zhejiang, China; Department of Systems and Computer Engineering Carleton University,Ottawa,ON KIS 5B6, Canada.
| | - Wenguo Hou
- Shenzhen Institute of Advanced Technology Chinese Academy of Sciences,Shenzhen, Guangdong,China.
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23
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Paul GC, Tauhida, Kumar D. Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology. Heliyon 2022; 8:e10773. [PMID: 36217488 PMCID: PMC9547222 DOI: 10.1016/j.heliyon.2022.e10773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 06/04/2022] [Accepted: 09/22/2022] [Indexed: 11/28/2022] Open
Abstract
In this paper, the homotopy analysis method, a powerful analytical technique, is applied to obtain analytical solutions to the Fisher-KPP equation in studying the spatial spreading of invasive species in ecology and to extract the nature of the spatial spreading of invasive cell populations in biology. The effect of the proliferation rate of the model of interest on the entire population is studied. It is observed that the invasive cell or the invasive population is decreased within a short time with the minimum proliferation rate. The homotopy analysis method is found to be superior to other analytical methods, namely the Adomian decomposition method, the homotopy perturbation method, etc. because of containing an auxiliary parameter, which provides us with a convenient way to adjust and control the region of convergence of the series solution. Graphical representation of the approximate series solutions obtained by the homotopy analysis method, the Adomian decomposition method, and the Homotopy perturbation method is illustrated, which shows the superiority of the homotopy analysis method. The method is examined on several examples, which reveal the ingenuousness and the effectiveness of the method of interest. Closed-form solutions are obtained for the Fisher-KPP equation through the Homotopy analysis method. The effect of the proliferation rate of the model of interest on the entire population is studied. The invasive cell or the invasive population decreases in short time with the minimum proliferation rate. The Homotopy analysis method is found superior over other analytical methods.
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24
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El-Hachem M, McCue SW, Simpson MJ. Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2022; 39:226-250. [PMID: 35818827 DOI: 10.1093/imammb/dqac004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Revised: 01/27/2022] [Accepted: 04/25/2022] [Indexed: 06/15/2023]
Abstract
The Fisher-Kolmogorov-Petrovsky-Piskunov (KPP) model, and generalizations thereof, involves simple reaction-diffusion equations for biological invasion that assume individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate $\lambda $. For the Fisher-KPP model, biologically relevant initial conditions lead to long-time travelling wave solutions that move with speed $c=2\sqrt {\lambda D}$. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically relevant initial conditions lead to travelling waves that move with speed $c=2\sqrt {\lambda D}> 0$. This means that, for biologically relevant initial data, the Fisher-KPP model cannot be used to study invasion with $c \ne 2\sqrt {\lambda D}$, or retreating travelling waves with $c < 0$. Here, we reformulate the Fisher-KPP model as a moving boundary problem and show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front that can propagate with any wave speed, $-\infty < c < \infty $. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub.
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Affiliation(s)
- Maud El-Hachem
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, 4000, Australia
| | - Scott W McCue
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, 4000, Australia
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, 4000, Australia
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25
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Bortfeld T, Buti G. Modeling the propagation of tumor fronts with shortest path and diffusion models—implications for the definition of the clinical target volume. Phys Med Biol 2022; 67. [PMID: 35817046 PMCID: PMC9388053 DOI: 10.1088/1361-6560/ac8043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 07/11/2022] [Indexed: 11/11/2022]
Abstract
Abstract
Objective. The overarching objective is to make the definition of the clinical target volume (CTV) in radiation oncology less subjective and more scientifically based. The specific objective of this study is to investigate similarities and differences between two methods that model tumor spread beyond the visible gross tumor volume (GTV): (1) the shortest path model, which is the standard method of adding a geometric GTV-CTV margin, and (2) the reaction-diffusion model. Approach. These two models to capture the invisible tumor ‘fire front’ are defined and compared in mathematical terms. The models are applied to example cases that represent tumor spread in non-uniform and anisotropic media with anatomical barriers. Main results. The two seemingly disparate models bring forth traveling waves that can be associated with the front of tumor growth outward from the GTV. The shape of the fronts is similar for both models. Differences are seen in cases where the diffusive flow is reduced due to anatomical barriers, and in complex spatially non-uniform cases. The diffusion model generally leads to smoother fronts. The smoothness can be controlled with a parameter defined by the ratio of the diffusion coefficient and the proliferation rate. Significance. Defining the CTV has been described as the weakest link of the radiotherapy chain. There are many similarities in the mathematical description and the behavior of the common geometric GTV-CTV expansion method, and the definition of the CTV tumor front via the reaction-diffusion model. Its mechanistic basis and the controllable smoothness make the diffusion model an attractive alternative to the standard GTV-CTV margin model.
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26
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Cell-Level Spatio-Temporal Model for a Bacillus Calmette–Guérin-Based Immunotherapy Treatment Protocol of Superficial Bladder Cancer. Cells 2022; 11:cells11152372. [PMID: 35954213 PMCID: PMC9367543 DOI: 10.3390/cells11152372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 07/25/2022] [Accepted: 07/29/2022] [Indexed: 02/04/2023] Open
Abstract
Bladder cancer is one of the most widespread types of cancer. Multiple treatments for non-invasive, superficial bladder cancer have been proposed over the last several decades with a weekly Bacillus Calmette–Guérin immunotherapy-based therapy protocol, which is considered the gold standard today. Nonetheless, due to the complexity of the interactions between the immune system, healthy cells, and cancer cells in the bladder’s microenvironment, clinical outcomes vary significantly among patients. Mathematical models are shown to be effective in predicting the treatment outcome based on the patient’s clinical condition at the beginning of the treatment. Even so, these models still have large errors for long-term treatments and patients that they do not fit. In this work, we utilize modern mathematical tools and propose a novel cell-level spatio-temporal mathematical model that takes into consideration the cell–cell and cell–environment interactions occurring in a realistic bladder’s geometric configuration in order to reduce these errors. We implement the model using the agent-based simulation approach, showing the impacts of different cancer tumor sizes and locations at the beginning of the treatment on the clinical outcomes for today’s gold-standard treatment protocol. In addition, we propose a genetic-algorithm-based approach to finding a successful and time-optimal treatment protocol for a given patient’s initial condition. Our results show that the current standard treatment protocol can be modified to produce cancer-free equilibrium for deeper cancer cells in the urothelium if the cancer cells’ spatial distribution is known, resulting in a greater success rate.
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27
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Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model. Biomech Model Mechanobiol 2022; 21:1483-1509. [PMID: 35908096 PMCID: PMC9626445 DOI: 10.1007/s10237-022-01602-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 06/17/2022] [Indexed: 11/29/2022]
Abstract
Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.
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28
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Ismail M, Prasanna P, Bera K, Statsevych V, Hill V, Singh G, Partovi S, Beig N, McGarry S, Laviolette P, Ahluwalia M, Madabhushi A, Tiwari P. Radiomic Deformation and Textural Heterogeneity (R-DepTH) Descriptor to Characterize Tumor Field Effect: Application to Survival Prediction in Glioblastoma. IEEE TRANSACTIONS ON MEDICAL IMAGING 2022; 41:1764-1777. [PMID: 35108202 PMCID: PMC9575333 DOI: 10.1109/tmi.2022.3148780] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The concept of tumor field effect implies that cancer is a systemic disease with its impact way beyond the visible tumor confines. For instance, in Glioblastoma (GBM), an aggressive brain tumor, the increase in intracranial pressure due to tumor burden often leads to brain herniation and poor outcomes. Our work is based on the rationale that highly aggressive tumors tend to grow uncontrollably, leading to pronounced biomechanical tissue deformations in the normal parenchyma, which when combined with local morphological differences in the tumor confines on MRI scans, will comprehensively capture tumor field effect. Specifically, we present an integrated MRI-based descriptor, radiomic-Deformation and Textural Heterogeneity (r-DepTH). This descriptor comprises measurements of the subtle perturbations in tissue deformations throughout the surrounding normal parenchyma due to mass effect. This involves non-rigidly aligning the patients' MRI scans to a healthy atlas via diffeomorphic registration. The resulting inverse mapping is used to obtain the deformation field magnitudes in the normal parenchyma. These measurements are then combined with a 3D texture descriptor, Co-occurrence of Local Anisotropic Gradient Orientations (COLLAGE), which captures the morphological heterogeneity and infiltration within the tumor confines, on MRI scans. In this work, we extensively evaluated r-DepTH for survival risk-stratification on a total of 207 GBM cases from 3 different cohorts (Cohort 1 ( n1 = 53 ), Cohort 2 ( n2 = 75 ), and Cohort 3 ( n3 = 79 )), where each of these three cohorts was used as a training set for our model separately, and the other two cohorts were used for testing, independently, for each training experiment. When employing Cohort 1 for training, r-DepTH yielded Concordance indices (C-indices) of 0.7 and 0.65, hazard ratios (HR) and Confidence Intervals (CI) of 10 (6 - 19) and 5 (3 - 8) on Cohorts 2 and 3, respectively. Similarly, training on Cohort 2 yielded C-indices of 0.6 and 0.7, HR and CI of 1 (0.7 - 2) and 3 (2 - 5) on Cohorts 1 and 3, respectively. Finally, training on Cohort 3 yielded C-indices of 0.75 and 0.63, HR and CI of 24 (10 - 57) and 12 (6 - 21) on Cohorts 1 and 2, respectively. Our results show that r-DepTH descriptor may serve as a comprehensive and a robust MRI-based prognostic marker of disease aggressiveness and survival in solid tumors.
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29
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The early infiltrative phase of GBM hypothesis: are molecular glioblastomas histological glioblastomas in the making? A preliminary multicenter study. J Neurooncol 2022; 158:497-506. [PMID: 35699848 DOI: 10.1007/s11060-022-04040-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 05/17/2022] [Indexed: 10/18/2022]
Abstract
PURPOSE The presence of necrosis or microvascular proliferation was previously the hallmark for glioblastoma (GBM) diagnosis. The 2021 WHO classification now considers IDH-wildtype diffuse astrocytic tumors without the histological features of glioblastoma (that would have otherwise been classified as grade 2 or 3) as molecular GBM (molGBM) if they harbor any of the following molecular abnormalities: TERT promoter mutation, EGFR amplification, or chromosomal + 7/-10 copy changes. We hypothesize that these tumors are early histological GBM and will eventually develop the classic histological features. METHODS Medical records from 65 consecutive patients diagnosed with molGBM at three tertiary-care centers from our institution were retrospectively reviewed from November 2017-October 2021. Only patients who underwent reoperation for tumor recurrence and whose tissue at initial diagnosis and recurrence was available were included in this study. The detailed clinical, histopathological, and radiographic scenarios are presented. RESULTS Five patients were included in our final cohort. Three (60%) patients underwent reoperation for recurrence in the primary site and 2 (40%) underwent reoperation for distal recurrence. Microvascular proliferation and pseudopalisading necrosis were absent at initial diagnosis but present at recurrence in 4 (80%) patients. Radiographically, all tumors showed contrast enhancement, however none of them showed the classic radiographic features of GBM at initial diagnosis. CONCLUSIONS In this manuscript we present preliminary data for a hypothesis that molGBMs are early histological GBMs diagnosed early in their natural history of disease and will eventually develop necrosis and microvascular proliferation. Further correlative studies are needed in support of this hypothesis.
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30
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Tripathi S, Vivas-Buitrago T, Domingo RA, Biase GD, Brown D, Akinduro OO, Ramos-Fresnedo A, Sherman W, Gupta V, Middlebrooks EH, Sabsevitz DS, Porter AB, Uhm JH, Bendok BR, Parney I, Meyer FB, Chaichana KL, Swanson KR, Quiñones-Hinojosa A. IDH-wild-type glioblastoma cell density and infiltration distribution influence on supramarginal resection and its impact on overall survival: a mathematical model. J Neurosurg 2022; 136:1567-1575. [PMID: 34715662 PMCID: PMC9248269 DOI: 10.3171/2021.6.jns21925] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 06/18/2021] [Indexed: 12/14/2022]
Abstract
OBJECTIVE Recent studies have proposed resection of the T2 FLAIR hyperintensity beyond the T1 contrast enhancement (supramarginal resection [SMR]) for IDH-wild-type glioblastoma (GBM) to further improve patients' overall survival (OS). GBMs have significant variability in tumor cell density, distribution, and infiltration. Advanced mathematical models based on patient-specific radiographic features have provided new insights into GBM growth kinetics on two important parameters of tumor aggressiveness: proliferation rate (ρ) and diffusion rate (D). The aim of this study was to investigate OS of patients with IDH-wild-type GBM who underwent SMR based on a mathematical model of cell distribution and infiltration profile (tumor invasiveness profile). METHODS Volumetric measurements were obtained from the selected regions of interest from pre- and postoperative MRI studies of included patients. The tumor invasiveness profile (proliferation/diffusion [ρ/D] ratio) was calculated using the following formula: ρ/D ratio = (4π/3)2/3 × (6.106/[VT21/1 - VT11/1])2, where VT2 and VT1 are the preoperative FLAIR and contrast-enhancing volumes, respectively. Patients were split into subgroups based on their tumor invasiveness profiles. In this analysis, tumors were classified as nodular, moderately diffuse, or highly diffuse. RESULTS A total of 101 patients were included. Tumors were classified as nodular (n = 34), moderately diffuse (n = 34), and highly diffuse (n = 33). On multivariate analysis, increasing SMR had a significant positive correlation with OS for moderately and highly diffuse tumors (HR 0.99, 95% CI 0.98-0.99; p = 0.02; and HR 0.98, 95% CI 0.96-0.99; p = 0.04, respectively). On threshold analysis, OS benefit was seen with SMR from 10% to 29%, 10% to 59%, and 30% to 90%, for nodular, moderately diffuse, and highly diffuse, respectively. CONCLUSIONS The impact of SMR on OS for patients with IDH-wild-type GBM is influenced by the degree of tumor invasiveness. The authors' results show that increasing SMR is associated with increased OS in patients with moderate and highly diffuse IDH-wild-type GBMs. When grouping SMR into 10% intervals, this benefit was seen for all tumor subgroups, although for nodular tumors, the maximum beneficial SMR percentage was considerably lower than in moderate and highly diffuse tumors.
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Affiliation(s)
- Shashwat Tripathi
- 1Department of Neurosurgery, Mayo Clinic, Jacksonville, Florida
- 10Feinberg School of Medicine, Northwestern University, Chicago, Illinois; and
| | - Tito Vivas-Buitrago
- 1Department of Neurosurgery, Mayo Clinic, Jacksonville, Florida
- 11Department of Health Sciences, School of Medicine, Universidad de Santander UDES, Bucaramanga, Colombia
| | | | | | - Desmond Brown
- 2Department of Neurosurgery, Mayo Clinic, Rochester, Minnesota
| | | | | | - Wendy Sherman
- 1Department of Neurosurgery, Mayo Clinic, Jacksonville, Florida
- 7Department of Neurology, Division of Neuro-Oncology, Mayo Clinic, Jacksonville
| | - Vivek Gupta
- 8Department of Radiology, Mayo Clinic, Jacksonville
| | - Erik H Middlebrooks
- 1Department of Neurosurgery, Mayo Clinic, Jacksonville, Florida
- 8Department of Radiology, Mayo Clinic, Jacksonville
| | - David S Sabsevitz
- 1Department of Neurosurgery, Mayo Clinic, Jacksonville, Florida
- 9Department of Psychology, Mayo Clinic, Jacksonville, Florida
| | - Alyx B Porter
- 5Department of Neurology, Division of Neuro-Oncology, Mayo Clinic, Phoenix, Arizona
| | - Joon H Uhm
- 6Department of Neurology, Division of Neuro-Oncology, Mayo Clinic, Rochester, Minnesota
| | | | - Ian Parney
- 2Department of Neurosurgery, Mayo Clinic, Rochester, Minnesota
| | - Fredric B Meyer
- 2Department of Neurosurgery, Mayo Clinic, Rochester, Minnesota
| | | | - Kristin R Swanson
- 3Department of Neurosurgery, Mayo Clinic, Phoenix
- 4Mathematical Neuro-Oncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix
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31
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Lv K, Cao X, Wang R, Du P, Fu J, Geng D, Zhang J. Neuroplasticity of Glioma Patients: Brain Structure and Topological Network. Front Neurol 2022; 13:871613. [PMID: 35645982 PMCID: PMC9136300 DOI: 10.3389/fneur.2022.871613] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 04/26/2022] [Indexed: 11/19/2022] Open
Abstract
Glioma is the most common primary malignant brain tumor in adults. It accounts for about 75% of such tumors and occurs more commonly in men. The incidence rate has been increasing in the past 30 years. Moreover, the 5-year overall survival rate of glioma patients is < 35%. Different locations, grades, and molecular characteristics of gliomas can lead to different behavioral deficits and prognosis, which are closely related to patients' quality of life and associated with neuroplasticity. Some advanced magnetic resonance imaging (MRI) technologies can explore the neuroplasticity of structural, topological, biochemical metabolism, and related mechanisms, which may contribute to the improvement of prognosis and function in glioma patients. In this review, we summarized the studies conducted on structural and topological plasticity of glioma patients through different MRI technologies and discussed future research directions. Previous studies have found that glioma itself and related functional impairments can lead to structural and topological plasticity using multimodal MRI. However, neuroplasticity caused by highly heterogeneous gliomas is not fully understood, and should be further explored through multimodal MRI. In addition, the individualized prediction of functional prognosis of glioma patients from the functional level based on machine learning (ML) is promising. These approaches and the introduction of ML can further shed light on the neuroplasticity and related mechanism of the brain, which will be helpful for management of glioma patients.
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Affiliation(s)
- Kun Lv
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
| | - Xin Cao
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
- Institute of Functional and Molecular Medical Imaging, Fudan University, Shanghai, China
- Center for Shanghai Intelligent Imaging for Critical Brain Diseases Engineering and Technology Reasearch, Shanghai, China
- Institute of Intelligent Imaging Phenomics, International Human Phenome Institutes (Shanghai), Shanghai, China
| | - Rong Wang
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
- Institute of Functional and Molecular Medical Imaging, Fudan University, Shanghai, China
- Center for Shanghai Intelligent Imaging for Critical Brain Diseases Engineering and Technology Reasearch, Shanghai, China
- Institute of Intelligent Imaging Phenomics, International Human Phenome Institutes (Shanghai), Shanghai, China
| | - Peng Du
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
| | - Junyan Fu
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
| | - Daoying Geng
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
- Institute of Functional and Molecular Medical Imaging, Fudan University, Shanghai, China
- Center for Shanghai Intelligent Imaging for Critical Brain Diseases Engineering and Technology Reasearch, Shanghai, China
- Institute of Intelligent Imaging Phenomics, International Human Phenome Institutes (Shanghai), Shanghai, China
- *Correspondence: Daoying Geng
| | - Jun Zhang
- Department of Radiology, Huashan Hospital, Fudan University, Shanghai, China
- Institute of Functional and Molecular Medical Imaging, Fudan University, Shanghai, China
- Center for Shanghai Intelligent Imaging for Critical Brain Diseases Engineering and Technology Reasearch, Shanghai, China
- Institute of Intelligent Imaging Phenomics, International Human Phenome Institutes (Shanghai), Shanghai, China
- Jun Zhang
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32
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Simulating the behaviour of glioblastoma multiforme based on patient MRI during treatments. J Math Biol 2022; 84:44. [PMID: 35482133 DOI: 10.1007/s00285-022-01747-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Revised: 03/31/2022] [Accepted: 04/01/2022] [Indexed: 10/18/2022]
Abstract
Glioblastoma multiforme is a brain cancer that still shows poor prognosis for patients despite the active research for new treatments. In this work, the goal is to model and simulate the evolution of tumour associated angiogenesis and the therapeutic response to glioblastoma multiforme. Multiple phenomena are modelled in order to fit different biological pathways, such as the cellular cycle, apoptosis, hypoxia or angiogenesis. This leads to a nonlinear system with 4 equations and 4 unknowns: the density of tumour cells, the [Formula: see text] concentration, the density of endothelial cells and the vascular endothelial growth factor concentration. This system is solved numerically on a mesh fitting the geometry of the brain and the tumour of a patient based on a 2D slice of MRI. We show that our numerical scheme is positive, and we give the energy estimates on the discrete solution to ensure its existence. The numerical scheme uses nonlinear control volume finite elements in space and is implicit in time. Numerical simulations have been done using the different standard treatments: surgery, chemotherapy and radiotherapy, in order to conform to the behaviour of a tumour in response to treatments according to empirical clinical knowledge. We find that our theoretical model exhibits realistic behaviours.
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33
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Kaur G, Rana PS, Arora V. State-of-the-art techniques using pre-operative brain MRI scans for survival prediction of glioblastoma multiforme patients and future research directions. Clin Transl Imaging 2022; 10:355-389. [PMID: 35261910 PMCID: PMC8891433 DOI: 10.1007/s40336-022-00487-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 02/15/2022] [Indexed: 11/28/2022]
Abstract
Objective Glioblastoma multiforme (GBM) is a grade IV brain tumour with very low life expectancy. Physicians and oncologists urgently require automated techniques in clinics for brain tumour segmentation (BTS) and survival prediction (SP) of GBM patients to perform precise surgery followed by chemotherapy treatment. Methods This study aims at examining the recent methodologies developed using automated learning and radiomics to automate the process of SP. Automated techniques use pre-operative raw magnetic resonance imaging (MRI) scans and clinical data related to GBM patients. All SP methods submitted for the multimodal brain tumour segmentation (BraTS) challenge are examined to extract the generic workflow for SP. Results The maximum accuracies achieved by 21 state-of-the-art different SP techniques reviewed in this study are 65.5 and 61.7% using the validation and testing subsets of the BraTS dataset, respectively. The comparisons based on segmentation architectures, SP models, training parameters and hardware configurations have been made. Conclusion The limited accuracies achieved in the literature led us to review the various automated methodologies and evaluation metrics to find out the research gaps and other findings related to the survival prognosis of GBM patients so that these accuracies can be improved in future. Finally, the paper provides the most promising future research directions to improve the performance of automated SP techniques and increase their clinical relevance.
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Affiliation(s)
- Gurinderjeet Kaur
- Computer Science and Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab India
| | - Prashant Singh Rana
- Computer Science and Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab India
| | - Vinay Arora
- Computer Science and Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab India
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34
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El-Hachem M, McCue SW, Simpson MJ. A Continuum Mathematical Model of Substrate-Mediated Tissue Growth. Bull Math Biol 2022; 84:49. [PMID: 35237899 PMCID: PMC8891221 DOI: 10.1007/s11538-022-01005-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 02/09/2022] [Indexed: 11/30/2022]
Abstract
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model, which we call the substrate model, involves a partial differential equation describing the density of tissue, \documentclass[12pt]{minimal}
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\begin{document}$${\hat{u}}(\hat{{\mathbf {x}}},{\hat{t}})$$\end{document}u^(x^,t^) that is coupled to the concentration of an immobile extracellular substrate, \documentclass[12pt]{minimal}
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\begin{document}$${\hat{s}}(\hat{{\mathbf {x}}},{\hat{t}})$$\end{document}s^(x^,t^). Cell migration is modelled with a nonlinear diffusion term, where the diffusive flux is proportional to \documentclass[12pt]{minimal}
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\begin{document}$${\hat{s}}$$\end{document}s^, while a logistic growth term models cell proliferation. The extracellular substrate \documentclass[12pt]{minimal}
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\begin{document}$${\hat{s}}$$\end{document}s^ is produced by cells and undergoes linear decay. Preliminary numerical simulations show that this mathematical model is able to recapitulate key features of recent tissue growth experiments, including the formation of sharp fronts. To provide a deeper understanding of the model we analyse travelling wave solutions of the substrate model, showing that the model supports both sharp-fronted travelling wave solutions that move with a minimum wave speed, \documentclass[12pt]{minimal}
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\begin{document}$$c = c_{\mathrm{min}}$$\end{document}c=cmin, as well as smooth-fronted travelling wave solutions that move with a faster travelling wave speed, \documentclass[12pt]{minimal}
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\begin{document}$$c > c_{\mathrm{min}}$$\end{document}c>cmin. We provide a geometric interpretation that explains the difference between smooth and sharp-fronted travelling wave solutions that is based on a slow manifold reduction of the desingularised three-dimensional phase space. In addition, we also develop and test a series of useful approximations that describe the shape of the travelling wave solutions in various limits. These approximations apply to both the sharp-fronted and smooth-fronted travelling wave solutions. Software to implement all calculations is available at GitHub.
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Affiliation(s)
- Maud El-Hachem
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Scott W McCue
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
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35
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Jafari Nivlouei S, Soltani M, Shirani E, Salimpour MR, Travasso R, Carvalho J. A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach. Cell Prolif 2022; 55:e13187. [PMID: 35132721 PMCID: PMC8891571 DOI: 10.1111/cpr.13187] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 12/09/2021] [Accepted: 01/03/2022] [Indexed: 12/17/2022] Open
Abstract
OBJECTIVES Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies. MATERIALS AND METHODS A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network. RESULTS Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens. CONCLUSIONS Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.
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Affiliation(s)
- Sahar Jafari Nivlouei
- Department of Mechanical Engineering, Isfahan University of Technology, Isafahan, Iran.,Department of Physics, CFisUC, University of Coimbra, Coimbra, Portugal
| | - Madjid Soltani
- Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran.,Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada.,Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, ON, Canada.,Advanced Bioengineering Initiative Center, Computational Medicine Center, K. N. Toosi University of Technology, Tehran, Iran.,Cancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, Iran
| | - Ebrahim Shirani
- Department of Mechanical Engineering, Isfahan University of Technology, Isafahan, Iran.,Department of Mechanical Engineering, Foolad Institute of Technology, Fooladshahr, Iran
| | | | - Rui Travasso
- Department of Physics, CFisUC, University of Coimbra, Coimbra, Portugal
| | - João Carvalho
- Department of Physics, CFisUC, University of Coimbra, Coimbra, Portugal
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36
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Azimzade Y. Invasion front dynamics of interactive populations in environments with barriers. Sci Rep 2022; 12:826. [PMID: 35039586 PMCID: PMC8764055 DOI: 10.1038/s41598-022-04806-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 01/03/2022] [Indexed: 11/20/2022] Open
Abstract
Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as [Formula: see text] describing invasion front position. We then obtained how [Formula: see text] and [Formula: see text] depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as [Formula: see text]. Similar to the 1D case, we calculate how [Formula: see text] and [Formula: see text] respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, [Formula: see text], depends on both population interaction and environmental barrier intensity. Saturated interface width, [Formula: see text], versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran, 14395-547, Iran.
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37
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Gomez J, Holmes N, Hansen A, Adhikarla V, Gutova M, Rockne RC, Cho H. Mathematical modeling of therapeutic neural stem cell migration in mouse brain with and without brain tumors. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:2592-2615. [PMID: 35240798 PMCID: PMC8958926 DOI: 10.3934/mbe.2022119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Neural stem cells (NSCs) offer a potential solution to treating brain tumors. This is because NSCs can circumvent the blood-brain barrier and migrate to areas of damage in the central nervous system, including tumors, stroke, and wound injuries. However, for successful clinical application of NSC treatment, a sufficient number of viable cells must reach the diseased or damaged area(s) in the brain, and evidence suggests that it may be affected by the paths the NSCs take through the brain, as well as the locations of tumors. To study the NSC migration in brain, we develop a mathematical model of therapeutic NSC migration towards brain tumor, that provides a low cost platform to investigate NSC treatment efficacy. Our model is an extension of the model developed in Rockne et al. (PLoS ONE 13, e0199967, 2018) that considers NSC migration in non-tumor bearing naive mouse brain. Here we modify the model in Rockne et al. in three ways: (i) we consider three-dimensional mouse brain geometry, (ii) we add chemotaxis to model the tumor-tropic nature of NSCs into tumor sites, and (iii) we model stochasticity of migration speed and chemosensitivity. The proposed model is used to study migration patterns of NSCs to sites of tumors for different injection strategies, in particular, intranasal and intracerebral delivery. We observe that intracerebral injection results in more NSCs arriving at the tumor site(s), but the relative fraction of NSCs depends on the location of injection relative to the target site(s). On the other hand, intranasal injection results in fewer NSCs at the tumor site, but yields a more even distribution of NSCs within and around the target tumor site(s).
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Affiliation(s)
- Justin Gomez
- Department of Mathematics, University of California, Riverside, Riverside, CA 92521, USA
| | - Nathanael Holmes
- Department of Mathematics, University of California, Riverside, Riverside, CA 92521, USA
| | - Austin Hansen
- Department of Mathematics, University of California, Riverside, Riverside, CA 92521, USA
| | - Vikram Adhikarla
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Margarita Gutova
- Department of Stem Cell Biology and Regenerative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Russell C. Rockne
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA 91010, USA
| | - Heyrim Cho
- Department of Mathematics, University of California, Riverside, Riverside, CA 92521, USA
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38
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Ebrahimi Zade A, Shahabi Haghighi S, Soltani M. Deep Neural Networks for Neuro-oncology: Towards Patient Individualized Design of Chemo-Radiation Therapy for Glioblastoma Patients. J Biomed Inform 2022; 127:104006. [DOI: 10.1016/j.jbi.2022.104006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Revised: 01/04/2022] [Accepted: 01/25/2022] [Indexed: 11/28/2022]
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39
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Comparing the effects of linear and one-term Ogden elasticity in a model of glioblastoma invasion. BRAIN MULTIPHYSICS 2022. [DOI: 10.1016/j.brain.2022.100050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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40
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Maini PK, Chaplain MAJ, Lewis MA, Sherratt JA. Special Collection: Celebrating J.D. Murray's Contributions to Mathematical Biology. Bull Math Biol 2021; 84:13. [PMID: 34865189 DOI: 10.1007/s11538-021-00955-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
| | - Mark A J Chaplain
- School of Mathematics and Statistics, Mathematical Institute, University of St Andrews, St Andrews, KY16 9SS, UK
| | - Mark A Lewis
- Department of Mathematical and Statistical Sciences, CAB 545B, University of Alberta, Edmonton, AB, T6G 2G1, Canada
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41
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Seow P, Hernowo AT, Narayanan V, Wong JHD, Bahuri NFA, Cham CY, Abdullah NA, Kadir KAA, Rahmat K, Ramli N. Neural Fiber Integrity in High- Versus Low-Grade Glioma using Probabilistic Fiber Tracking. Acad Radiol 2021; 28:1721-1732. [PMID: 33023809 DOI: 10.1016/j.acra.2020.09.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 09/05/2020] [Accepted: 09/07/2020] [Indexed: 02/02/2023]
Abstract
RATIONALE AND OBJECTIVES Gliomatous tumors are known to affect neural fiber integrity, either by displacement or destruction. The aim of this study is to investigate the integrity and distribution of the white matter tracts within and around the glioma regions using probabilistic fiber tracking. MATERIAL AND METHODS Forty-two glioma patients were subjected to MRI using a standard tumor protocol with diffusion tensor imaging (DTI). The tumor and peritumor regions were delineated using snake model with reference to structural and diffusion MRI. A preprocessing pipeline of the structural MRI image, DTI data, and tumor regions was implemented. Tractography was performed to delineate the white matter (WM) tracts in the selected tumor regions via probabilistic fiber tracking. DTI indices were investigated through comparative mapping of WM tracts and tumor regions in low-grade gliomas (LGG) and high-grade gliomas (HGG). RESULTS Significant differences were seen in the planar tensor (Cp) in peritumor regions; mean diffusivity, axial diffusivity and pure isotropic diffusion in solid-enhancing tumor regions; and fractional anisotropy, axial diffusivity, pure anisotropic diffusion (q), total magnitude of diffusion tensor (L), relative anisotropy, Cp and spherical tensor (Cs) in solid nonenhancing tumor regions for affected WM tracts. In most cases of HGG, the WM tracts were not completely destroyed, but found intact inside the tumor. DISCUSSION Probabilistic fiber tracking revealed the existence and distribution of WM tracts inside tumor core for both LGG and HGG groups. There were more DTI indices in the solid nonenhancing tumor region, which showed significant differences between LGG and HGG.
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42
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Khajanchi S, Nieto JJ. Spatiotemporal dynamics of a glioma immune interaction model. Sci Rep 2021; 11:22385. [PMID: 34789751 PMCID: PMC8599515 DOI: 10.1038/s41598-021-00985-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 10/20/2021] [Indexed: 12/20/2022] Open
Abstract
We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.
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Affiliation(s)
- Subhas Khajanchi
- Department of Mathematics, Presidency University, 86/1 College Street, Kolkata, 700073, India.
| | - Juan J Nieto
- Instituto de Matem\acute{a}ticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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43
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Collet S, Guillamo JS, Berro DH, Chakhoyan A, Constans JM, Lechapt-Zalcman E, Derlon JM, Hatt M, Visvikis D, Guillouet S, Perrio C, Bernaudin M, Valable S. Simultaneous Mapping of Vasculature, Hypoxia, and Proliferation Using Dynamic Susceptibility Contrast MRI, 18F-FMISO PET, and 18F-FLT PET in Relation to Contrast Enhancement in Newly Diagnosed Glioblastoma. J Nucl Med 2021; 62:1349-1356. [PMID: 34016725 PMCID: PMC8724903 DOI: 10.2967/jnumed.120.249524] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 01/14/2021] [Indexed: 11/16/2022] Open
Abstract
Conventional MRI plays a key role in the management of patients with high-grade glioma, but multiparametric MRI and PET tracers could provide further information to better characterize tumor metabolism and heterogeneity by identifying regions having a high risk of recurrence. In this study, we focused on proliferation, hypervascularization, and hypoxia, all factors considered indicative of poor prognosis. They were assessed by measuring uptake of 18F-3'-deoxy-3'-18F-fluorothymidine (18F-FLT), relative cerebral blood volume (rCBV) maps, and uptake of 18F-fluoromisonidazole (18F-FMISO), respectively. For each modality, the volumes and high-uptake subvolumes (hot spots) were semiautomatically segmented and compared with the contrast enhancement (CE) volume on T1-weighted gadolinium-enhanced (T1w-Gd) images, commonly used in the management of patients with glioblastoma. Methods: Dynamic susceptibility contrast-enhanced MRI (31 patients), 18F-FLT PET (20 patients), or 18F-FMISO PET (20 patients), for a total of 31 patients, was performed on preoperative glioblastoma patients. Volumes and hot spots were segmented on SUV maps for 18F-FLT PET (using the fuzzy locally adaptive bayesian algorithm) and 18F-FMISO PET (using a mean contralateral image + 3.3 SDs) and on rCBV maps (using a mean contralateral image + 1.96 SDs) for dynamic susceptibility contrast-enhanced MRI and overlaid on T1w-Gd images. For each modality, the percentages of the peripheral volumes and the peripheral hot spots outside the CE volume were calculated. Results: All tumors showed highly proliferated, hypervascularized, and hypoxic regions. The images also showed pronounced heterogeneity of both tracers regarding their uptake and rCBV maps, within each individual patient. Overlaid volumes on T1w-Gd images showed that some proliferative, hypervascularized, and hypoxic regions extended beyond the CE volume but with marked differences between patients. The ranges of peripheral volume outside the CE volume were 1.6%-155.5%, 1.5%-89.5%, and 3.1%-78.0% for 18F-FLT, rCBV, and 18F-FMISO, respectively. All patients had hyperproliferative hot spots outside the CE volume, whereas hypervascularized and hypoxic hot spots were detected mainly within the enhancing region. Conclusion: Spatial analysis of multiparametric maps with segmented volumes and hot spots provides valuable information to optimize the management and treatment of patients with glioblastoma.
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Affiliation(s)
- Solène Collet
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
- Radiophysics Department, Centre François Baclesse, Caen, France
| | - Jean-Sébastien Guillamo
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
- Department of Neurology, CHU de Caen, Caen, France
- Department of Neurology, CHU de Nimes, Nimes, France
| | - David Hassanein Berro
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
- Department of Neurosurgery, CHU de Caen, Caen, France
| | - Ararat Chakhoyan
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
| | - Jean-Marc Constans
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
- Department of Neuroradiology, CHU de Caen, Caen, France
| | - Emmanuèle Lechapt-Zalcman
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
- Department of Pathology, CHU de Caen, Caen, France
- Department of Neuropathology, GHU Paris Psychiatry and Neuroscience, Paris, France
| | - Jean-Michel Derlon
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
| | - Mathieu Hatt
- LaTIM, INSERM, UMR 1101, University of Brest, Brest, France; and
| | | | - Stéphane Guillouet
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/LDM-TEP Group, GIP Cyceron, Caen, France
| | - Cécile Perrio
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/LDM-TEP Group, GIP Cyceron, Caen, France
| | - Myriam Bernaudin
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France
| | - Samuel Valable
- Normandie University, UNICAEN, CEA, CNRS, ISTCT/CERVOxy Group, GIP Cyceron, Caen, France;
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Revilla-Pacheco F, Rodríguez-Salgado P, Barrera-Ramírez M, Morales-Ruiz MP, Loyo-Varela M, Rubalcava-Ortega J, Herrada-Pineda T. Extent of resection and survival in patients with glioblastoma multiforme: Systematic review and meta-analysis. Medicine (Baltimore) 2021; 100:e26432. [PMID: 34160432 PMCID: PMC8238332 DOI: 10.1097/md.0000000000026432] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 06/04/2021] [Indexed: 01/04/2023] Open
Abstract
BACKGROUND Glioblastoma multiforme (GBM) owes an ominous prognosis: its mean overall survival is 14 months. The extent of surgical resection (ESR) highlights among factors in which an association has been found to a somewhat better prognosis. However, the association between greater ESR and prolonged overall (OS) survival is not a constant finding nor a proven cause-and-effect phenomenon. To our objective is to establish the strength of association between ESR and OS in patients with GBM through a systematic review and meta-analysis. METHODS In accordance with PRISMA-P recommendations, we conducted a systematic literature search; we included studies with adult patients who had undergone craniotomy for GBM. Our primary outcome is overall postoperative survival at 12 and 24 months. We reviewed 180 studies, excluded 158, and eliminated 8; 14 studies that suited our requirements were analyzed. RESULTS The initial level of evidence of all studies is low, and it may be degraded to very low according to GRADE criteria because of design issues. The definition of different levels of the extent of resection is heterogeneous and poorly defined. We found a great amount of variation in the methodology of the operation and the adjuvant treatment protocol. The combined result for relative risk (RR) for OS for 12 months analysis is 1.25 [95% confidence interval (95% CI) 1.14-1.36, P < .01], absolute risk reduction (ARR) of 15.7% (95% CI 11.9-19.4), relative risk reduction (RRR) of 0.24 (95% CI 0.18-0.31), number needed to treat (NNT) 6; for 24-month analysis RR is 1.59 (95% CI 1.11-2.26, P < .01) ARR of 11.5% (95% CI 7.7-15.1), relative risk reduction (RRR) of 0.53 (95% CI 0.33-0.76), (NNT) 9. In each term analysis, the proportion of alive patients who underwent more extensive resection is significantly higher than those who underwent subtotal resection. CONCLUSION Our results sustain a weak but statistically significant association between the ESR and OS in patients with GBM obtained from observational studies with a very low level of evidence according to GRADE criteria. As a consequence, any estimate of effect is very uncertain. Current information cannot sustain a cause-and-effect relationship between these variables.
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Falco J, Agosti A, Vetrano IG, Bizzi A, Restelli F, Broggi M, Schiariti M, DiMeco F, Ferroli P, Ciarletta P, Acerbi F. In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case. J Clin Med 2021; 10:2169. [PMID: 34067871 PMCID: PMC8156762 DOI: 10.3390/jcm10102169] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/24/2021] [Accepted: 05/14/2021] [Indexed: 01/28/2023] Open
Abstract
Glioblastoma extensively infiltrates the brain; despite surgery and aggressive therapies, the prognosis is poor. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of glioblastoma evolution in every single patient, with the aim of tailoring therapeutic weapons. In particular, the ultimate goal of biomathematics for cancer is the identification of the most suitable theoretical models and simulation tools, both to describe the biological complexity of carcinogenesis and to predict tumor evolution. In this report, we describe the results of a critical review about different mathematical models in neuro-oncology with their clinical implications. A comprehensive literature search and review for English-language articles concerning mathematical modelling in glioblastoma has been conducted. The review explored the different proposed models, classifying them and indicating the significative advances of each one. Furthermore, we present a specific case of a glioblastoma patient in which our recently proposed innovative mechanical model has been applied. The results of the mathematical models have the potential to provide a relevant benefit for clinicians and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. Further prospective comparative trials, however, are still necessary to prove the impact of mathematical neuro-oncology in clinical practice.
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Affiliation(s)
- Jacopo Falco
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Abramo Agosti
- MOX, Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy; (A.A.); (P.C.)
| | - Ignazio G. Vetrano
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Alberto Bizzi
- Department of Neuroradiology, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy;
| | - Francesco Restelli
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Morgan Broggi
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Marco Schiariti
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Francesco DiMeco
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
- Department of Pathophysiology and Transplantation, Università degli Studi di Milano, 20122 Milan, Italy
- Department of Neurological Surgery, Johns Hopkins Medical School, Baltimora, MD 21205, USA
| | - Paolo Ferroli
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Pasquale Ciarletta
- MOX, Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy; (A.A.); (P.C.)
| | - Francesco Acerbi
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
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Chulián S, Martinez-Rubio Á, Gandarias ML, Rosa M. Lie point symmetries for generalised Fisher's equations describing tumour dynamics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:3291-3312. [PMID: 34198386 DOI: 10.3934/mbe.2021164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.
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Affiliation(s)
- Salvador Chulián
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | - Álvaro Martinez-Rubio
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | | | - María Rosa
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
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Azimzade Y, Saberi AA, Gatenby RA. Superlinear growth reveals the Allee effect in tumors. Phys Rev E 2021; 103:042405. [PMID: 34005934 DOI: 10.1103/physreve.103.042405] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Accepted: 03/16/2021] [Indexed: 12/17/2022]
Abstract
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran and Institut für Theoretische Physik, Universitat zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
| | - Robert A Gatenby
- Cancer Biology and Evolution Program, Integrated Mathematical Oncology Department, and Diagnostic Imaging Department, Moffitt Cancer Center, Tampa, Florida 33612, USA
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A novel mathematical model of heterogeneous cell proliferation. J Math Biol 2021; 82:34. [PMID: 33712945 DOI: 10.1007/s00285-021-01580-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Revised: 10/21/2020] [Accepted: 02/14/2021] [Indexed: 12/22/2022]
Abstract
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two cellular processes, asymmetric cell division and induced switching between proliferative states, which are important determinants for the heterogeneity of a cell population. As motivation for our model we provide experimental data that illustrate the induced-switching process. Our model consists of a system of two coupled delay differential equations with distributed time delays and the cell densities as functions of time. The distributed delays are bounded and allow for the choice of delay kernel. We analyse the model and prove the nonnegativity and boundedness of solutions, the existence and uniqueness of solutions, and the local stability characteristics of the equilibrium points. We find that the parameters for induced switching are bifurcation parameters and therefore determine the long-term behaviour of the model. Numerical simulations illustrate and support the theoretical findings, and demonstrate the primary importance of transient dynamics for understanding the evolution of many experimental cell populations.
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Invading and Receding Sharp-Fronted Travelling Waves. Bull Math Biol 2021; 83:35. [PMID: 33611673 DOI: 10.1007/s11538-021-00862-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Accepted: 01/20/2021] [Indexed: 02/03/2023]
Abstract
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade vacant regions, is routinely studied using partial differential equation models based upon the classical Fisher-KPP equation. While the Fisher-KPP model and extensions have been successfully used to model a range of invasive phenomena, including ecological and cellular invasion, an often-overlooked limitation of the Fisher-KPP model is that it cannot be used to model biological recession where the spatial extent of the population decreases with time. In this work, we study the Fisher-Stefan model, which is a generalisation of the Fisher-KPP model obtained by reformulating the Fisher-KPP model as a moving boundary problem. The nondimensional Fisher-Stefan model involves just one parameter, [Formula: see text], which relates the shape of the density front at the moving boundary to the speed of the associated travelling wave, c. Using numerical simulation, phase plane and perturbation analysis, we construct approximate solutions of the Fisher-Stefan model for both slowly invading and receding travelling waves, as well as for rapidly receding travelling waves. These approximations allow us to determine the relationship between c and [Formula: see text] so that commonly reported experimental estimates of c can be used to provide estimates of the unknown parameter [Formula: see text]. Interestingly, when we reinterpret the Fisher-KPP model as a moving boundary problem, many overlooked features of the classical Fisher-KPP phase plane take on a new interpretation since travelling waves solutions with [Formula: see text] are normally disregarded. This means that our analysis of the Fisher-Stefan model has both practical value and an inherent mathematical value.
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A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors. PLoS Comput Biol 2021; 17:e1008266. [PMID: 33566821 PMCID: PMC7901744 DOI: 10.1371/journal.pcbi.1008266] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 02/23/2021] [Accepted: 01/16/2021] [Indexed: 12/12/2022] Open
Abstract
Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.
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