1
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Nguyen K, Rutter EM, Flores KB. Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data. Bull Math Biol 2023; 85:62. [PMID: 37268762 DOI: 10.1007/s11538-023-01162-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 05/03/2023] [Indexed: 06/04/2023]
Abstract
Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.
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Affiliation(s)
- Kyle Nguyen
- Biomathematics Graduate Program, North Carolina State University, Raleigh, NC, USA
- Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, USA
| | - Erica M Rutter
- Department of Applied Mathematics, University of California, Merced, Merced, CA, USA
| | - Kevin B Flores
- Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, USA.
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA.
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2
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Phillips CM, Lima EABF, Gadde M, Jarrett AM, Rylander MN, Yankeelov TE. Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis. PLoS Comput Biol 2023; 19:e1009499. [PMID: 36652468 PMCID: PMC9886306 DOI: 10.1371/journal.pcbi.1009499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Revised: 01/30/2023] [Accepted: 12/13/2022] [Indexed: 01/19/2023] Open
Abstract
The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.
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Affiliation(s)
- Caleb M. Phillips
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Texas Advanced Computing Center, The University of Texas at Austin, Austin, Texas, United States of America
- * E-mail:
| | - Manasa Gadde
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
| | - Angela M. Jarrett
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, Texas, United States of America
| | - Marissa Nichole Rylander
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
| | - Thomas E. Yankeelov
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Oncology, The University of Texas at Austin, Austin, Texas, United States of America
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Imaging Physics, The University of Texas at Austin, MD Anderson Cancer Center, Houston, Texas, United States of America
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3
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Lorenzo G, di Muzio N, Deantoni CL, Cozzarini C, Fodor A, Briganti A, Montorsi F, Pérez-García VM, Gomez H, Reali A. Patient-specific forecasting of postradiotherapy prostate-specific antigen kinetics enables early prediction of biochemical relapse. iScience 2022; 25:105430. [DOI: 10.1016/j.isci.2022.105430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2022] [Revised: 09/04/2022] [Accepted: 10/19/2022] [Indexed: 11/06/2022] Open
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4
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Luo MC, Nikolopoulou E, Gevertz JL. From Fitting the Average to Fitting the Individual: A Cautionary Tale for Mathematical Modelers. Front Oncol 2022; 12:793908. [PMID: 35574407 PMCID: PMC9097280 DOI: 10.3389/fonc.2022.793908] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 03/09/2022] [Indexed: 11/13/2022] Open
Abstract
An outstanding challenge in the clinical care of cancer is moving from a one-size-fits-all approach that relies on population-level statistics towards personalized therapeutic design. Mathematical modeling is a powerful tool in treatment personalization, as it allows for the incorporation of patient-specific data so that treatment can be tailor-designed to the individual. Herein, we work with a mathematical model of murine cancer immunotherapy that has been previously-validated against the average of an experimental dataset. We ask the question: what happens if we try to use this same model to perform personalized fits, and therefore make individualized treatment recommendations? Typically, this would be done by choosing a single fitting methodology, and a single cost function, identifying the individualized best-fit parameters, and extrapolating from there to make personalized treatment recommendations. Our analyses show the potentially problematic nature of this approach, as predicted personalized treatment response proved to be sensitive to the fitting methodology utilized. We also demonstrate how a small amount of the right additional experimental measurements could go a long way to improve consistency in personalized fits. Finally, we show how quantifying the robustness of the average response could also help improve confidence in personalized treatment recommendations.
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Affiliation(s)
- Michael C Luo
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, United States
| | - Elpiniki Nikolopoulou
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States
| | - Jana L Gevertz
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, United States
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5
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Ruiz-Garcia H, Middlebrooks EH, Trifiletti DM, Chaichana KL, Quinones-Hinojosa A, Sheehan JP. The Extent of Resection in Gliomas-Evidence-Based Recommendations on Methodological Aspects of Research Design. World Neurosurg 2022; 161:382-395.e3. [PMID: 35505558 DOI: 10.1016/j.wneu.2021.08.140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 08/30/2021] [Indexed: 12/14/2022]
Abstract
OBJECTIVE Modern neurosurgery has established maximal safe resection as a cornerstone in the management of diffuse gliomas. Evaluation of the extent of resection (EOR), and its association with certain outcomes or interventions, heavily depends on an adequate methodology to draw strong conclusions. We aim to identify weaknesses and limitations that may threaten the internal validity and generalizability of studies involving the EOR in patients with glioma and to suggest methodological recommendations that may help mitigate these threats. METHODS A systematic search was performed by querying PubMed, Web of Science, and Scopus since inception to April 30, 2021 using PICOS/PRISMA guidelines. Articles were then screened to identify high-impact studies evaluating the EOR in patients diagnosed with diffuse gliomas in accordance with predefined criteria. We identify common weakness and limitations during the evaluation of the EOR in the selected studies and then delineate potential methodological recommendations for future endeavors dealing with the EOR. RESULTS We identified 31 high-impact studies and found several research design issues including inconsistencies regarding EOR terminology, measurement, data collection, analysis, and reporting. Although some of these issues were related to now outdated reporting standards, many were still present in recent publications and deserve attention in contemporary and future research. CONCLUSIONS There is a current need to focus more attention to the methodological aspects of glioma research. Methodological inconsistencies may introduce weaknesses into the internal validity of the studies and hamper comparative analysis of cohorts from different institutions. We hope our recommendations will eventually help develop stronger methodological designs in future research endeavors.
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Affiliation(s)
- Henry Ruiz-Garcia
- Department of Neurological Surgery, Mayo Clinic, Jacksonville, Florida, USA; Department of Radiation Oncology, Mayo Clinic, Jacksonville, Florida, USA; Robert D. and Patricia E. Kern Center for the Science of Health Care Delivery, Mayo Clinic, Jacksonville, Florida, USA
| | - Erik H Middlebrooks
- Department of Neurological Surgery, Mayo Clinic, Jacksonville, Florida, USA; Department of Radiology, Mayo Clinic, Jacksonville, Florida, USA
| | - Daniel M Trifiletti
- Department of Neurological Surgery, Mayo Clinic, Jacksonville, Florida, USA; Department of Radiation Oncology, Mayo Clinic, Jacksonville, Florida, USA
| | | | | | - Jason P Sheehan
- Department of Neurological Surgery, University of Virginia, Charlottesville, Virginia, USA.
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6
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Lipková J, Menze B, Wiestler B, Koumoutsakos P, Lowengrub JS. Modelling glioma progression, mass effect and intracranial pressure in patient anatomy. J R Soc Interface 2022; 19:20210922. [PMID: 35317645 PMCID: PMC8941421 DOI: 10.1098/rsif.2021.0922] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Accepted: 02/21/2022] [Indexed: 02/06/2023] Open
Abstract
Increased intracranial pressure is the source of most critical symptoms in patients with glioma, and often the main cause of death. Clinical interventions could benefit from non-invasive estimates of the pressure distribution in the patient's parenchyma provided by computational models. However, existing glioma models do not simulate the pressure distribution and they rely on a large number of model parameters, which complicates their calibration from available patient data. Here we present a novel model for glioma growth, pressure distribution and corresponding brain deformation. The distinct feature of our approach is that the pressure is directly derived from tumour dynamics and patient-specific anatomy, providing non-invasive insights into the patient's state. The model predictions allow estimation of critical conditions such as intracranial hypertension, brain midline shift or neurological and cognitive impairments. A diffuse-domain formalism is employed to allow for efficient numerical implementation of the model in the patient-specific brain anatomy. The model is tested on synthetic and clinical cases. To facilitate clinical deployment, a high-performance computing implementation of the model has been publicly released.
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Affiliation(s)
- Jana Lipková
- Department of Pathology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | - Bjoern Menze
- Department of Informatics, Technical University of Munich, Munich, Germany
- Department of Quantitative Biomedicine, University of Zürich, Zürich, Switzerland
- Department of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Benedikt Wiestler
- Department of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Petros Koumoutsakos
- Computational Science and Engineering Lab, ETH Zürich, Zürich, Switzerland
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - John S. Lowengrub
- Department of Mathematics, University of California, Irvine, CA, USA
- Department of Biomedical Engineering, University of California, Irvine, CA, USA
- Center for Complex Biological Systems, Chao Family Comprehensive Cancer Center, University of California, Irvine, CA, USA
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7
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Hu LS, Brat DJ, Bloch O, Ramkissoon S, Lesser GJ. The Practical Application of Emerging Technologies Influencing the Diagnosis and Care of Patients With Primary Brain Tumors. Am Soc Clin Oncol Educ Book 2020; 40:1-12. [PMID: 32324425 DOI: 10.1200/edbk_280955] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Over the past decade, a variety of new and innovative technologies has led to important advances in the diagnosis and management of patients with primary malignant brain tumors. New approaches to surgical navigation and tumor localization, advanced imaging to define tumor biology and treatment response, and the widespread adoption of a molecularly defined integrated diagnostic paradigm that complements traditional histopathologic diagnosis continue to impact the day-to-day care of these patients. In the neuro-oncology clinic, discussions with patients about the role of tumor treating fields (TTFields) and the incorporation of next-generation sequencing (NGS) data into therapeutic decision-making are now a standard practice. This article summarizes newer applications of technology influencing the pathologic, neuroimaging, neurosurgical, and medical management of patients with malignant primary brain tumors.
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Affiliation(s)
- Leland S Hu
- Neuroradiology Section, Department of Radiology, Mayo Clinic, Phoenix, AZ
| | - Daniel J Brat
- Department of Pathology, Northwestern University Feinberg School of Medicine, Chicago, IL
| | - Orin Bloch
- Department of Neurologic Surgery, UC Davis Comprehensive Cancer Center, Sacramento, CA
| | - Shakti Ramkissoon
- Foundation Medicine, Inc., Morrisville, NC.,Comprehensive Cancer Center, Wake Forest Baptist Health, Winston-Salem, NC.,Department of Pathology, Wake Forest School of Medicine, Winston-Salem, NC
| | - Glenn J Lesser
- Comprehensive Cancer Center, Wake Forest Baptist Health, Winston-Salem, NC
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8
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Nardini JT, Lagergren JH, Hawkins-Daarud A, Curtin L, Morris B, Rutter EM, Swanson KR, Flores KB. Learning Equations from Biological Data with Limited Time Samples. Bull Math Biol 2020; 82:119. [PMID: 32909137 PMCID: PMC8409251 DOI: 10.1007/s11538-020-00794-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 08/16/2020] [Indexed: 01/25/2023]
Abstract
Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.
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Affiliation(s)
- John T Nardini
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA.
- The Statistical and Applied Mathematical Sciences Institute, Durham, NC, USA.
| | - John H Lagergren
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Andrea Hawkins-Daarud
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Lee Curtin
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Bethan Morris
- Centre for Mathematical Medicine and Biology, University of Nottingham, Nottingham, UK
| | - Erica M Rutter
- Department of Applied Mathematics, University of California, Merced, Merced, CA, USA
| | - Kristin R Swanson
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Kevin B Flores
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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9
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Morris B, Curtin L, Hawkins-Daarud A, Hubbard ME, Rahman R, Smith SJ, Auer D, Tran NL, Hu LS, Eschbacher JM, Smith KA, Stokes A, Swanson KR, Owen MR. Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2020; 17:4905-4941. [PMID: 33120534 PMCID: PMC8382158 DOI: 10.3934/mbe.2020267] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute to disappointing clinical trial results. Image-localized biopsy techniques allow multiple biopsies to be taken during surgery and provide information that identifies regions where particular sub-populations occur within an individual GBM, thus providing insight into their regional genetic variability. These sub-populations may also interact with one another in a competitive or cooperative manner; it is important to ascertain the nature of these interactions, as they may have implications for responses to targeted therapies. We combine genetic information from biopsies with a mechanistic model of interacting GBM sub-populations to characterise the nature of interactions between two commonly occurring GBM sub-populations, those with EGFR and PDGFRA genes amplified. We study population levels found across image-localized biopsy data from a cohort of 25 patients and compare this to model outputs under competitive, cooperative and neutral interaction assumptions. We explore other factors affecting the observed simulated sub-populations, such as selection advantages and phylogenetic ordering of mutations, which may also contribute to the levels of EGFR and PDGFRA amplified populations observed in biopsy data.
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Affiliation(s)
- Bethan Morris
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
| | - Lee Curtin
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, 85054, USA
| | | | - Matthew E. Hubbard
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
| | - Ruman Rahman
- School of Medicine and Health Sciences, University of Nottingham, Nottingham, NG7 2UH, UK
| | - Stuart J. Smith
- School of Medicine and Health Sciences, University of Nottingham, Nottingham, NG7 2UH, UK
| | - Dorothee Auer
- School of Medicine and Health Sciences, University of Nottingham, Nottingham, NG7 2UH, UK
| | - Nhan L. Tran
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, 85054, USA
- Department of Cancer Biology, Mayo Clinic, Phoenix, Arizona 85054, USA
| | - Leland S. Hu
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, 85054, USA
- Department of Radiology, Mayo Clinic, Phoenix, Arizona 85054, USA
| | - Jennifer M. Eschbacher
- Department of Pathology, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
| | - Kris A. Smith
- Department of Neurosurgery, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
| | - Ashley Stokes
- Department of Imaging Research, Barrow Neurological Institute - St. Joseph’s Hospital and Medical Center, Phoenix, Arizona 85013, USA
| | - Kristin R. Swanson
- Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, 85054, USA
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona 85054, USA
| | - Markus R. Owen
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
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Hu LS, Swanson KR. Roadmap for the clinical integration of radiomics in neuro-oncology. Neuro Oncol 2020; 22:743-745. [PMID: 32227184 DOI: 10.1093/neuonc/noaa078] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Leland S Hu
- Department of Radiology, Mayo Clinic Arizona, Phoenix, Arizona
| | - Kristin R Swanson
- Mathematical NeuroOncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic Arizona, Phoenix, Arizona
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12
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Hu LS, Hawkins-Daarud A, Wang L, Li J, Swanson KR. Imaging of intratumoral heterogeneity in high-grade glioma. Cancer Lett 2020; 477:97-106. [PMID: 32112907 DOI: 10.1016/j.canlet.2020.02.025] [Citation(s) in RCA: 59] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Revised: 02/17/2020] [Accepted: 02/19/2020] [Indexed: 12/19/2022]
Abstract
High-grade glioma (HGG), and particularly Glioblastoma (GBM), can exhibit pronounced intratumoral heterogeneity that confounds clinical diagnosis and management. While conventional contrast-enhanced MRI lacks the capability to resolve this heterogeneity, advanced MRI techniques and PET imaging offer a spectrum of physiologic and biophysical image features to improve the specificity of imaging diagnoses. Published studies have shown how integrating these advanced techniques can help better define histologically distinct targets for surgical and radiation treatment planning, and help evaluate the regional heterogeneity of tumor recurrence and response assessment following standard adjuvant therapy. Application of texture analysis and machine learning (ML) algorithms has also enabled the emerging field of radiogenomics, which can spatially resolve the regional and genetically distinct subpopulations that coexist within a single GBM tumor. This review focuses on the latest advances in neuro-oncologic imaging and their clinical applications for the assessment of intratumoral heterogeneity.
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Affiliation(s)
- Leland S Hu
- Department of Radiology, Mayo Clinic Arizona, 5777 E Mayo Blvd, Phoenix, AZ, 85054, USA.
| | - Andrea Hawkins-Daarud
- Mathematical NeuroOncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 East Mayo Blvd, Support, Services Building Suite 2-700, Phoenix, AZ, 85054, USA.
| | - Lujia Wang
- School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, 699 S Mill Ave, Tempe, AZ, 85281, USA.
| | - Jing Li
- School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, 699 S Mill Ave, Tempe, AZ, 85281, USA.
| | - Kristin R Swanson
- Mathematical NeuroOncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic, 5777 East Mayo Blvd, Support, Services Building Suite 2-700, Phoenix, AZ, 85054, USA.
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13
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Singleton KW, Porter AB, Hu LS, Johnston SK, Bond KM, Rickertsen CR, De Leon G, Whitmire SA, Clark-Swanson KR, Mrugala MM, Swanson KR. Days gained response discriminates treatment response in patients with recurrent glioblastoma receiving bevacizumab-based therapies. Neurooncol Adv 2020; 2:vdaa085. [PMID: 32864609 PMCID: PMC7447137 DOI: 10.1093/noajnl/vdaa085] [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] [Indexed: 11/13/2022] Open
Abstract
Abstract
Background
Accurate assessments of patient response to therapy are a critical component of personalized medicine. In glioblastoma (GBM), the most aggressive form of brain cancer, tumor growth dynamics are heterogenous across patients, complicating assessment of treatment response. This study aimed to analyze days gained (DG), a burgeoning model-based dynamic metric, for response assessment in patients with recurrent GBM who received bevacizumab-based therapies.
Methods
DG response scores were calculated using volumetric tumor segmentations for patients receiving bevacizumab with and without concurrent cytotoxic therapy (N = 62). Kaplan–Meier and Cox proportional hazards analyses were implemented to examine DG prognostic relationship to overall (OS) and progression-free survival (PFS) from the onset of treatment for recurrent GBM.
Results
In patients receiving concurrent bevacizumab and cytotoxic therapy, Kaplan–Meier analysis showed significant differences in OS and PFS at DG cutoffs consistent with previously identified values from newly diagnosed GBM using T1-weighted gadolinium-enhanced magnetic resonance imaging (T1Gd). DG scores for bevacizumab monotherapy patients only approached significance for PFS. Cox regression showed that increases of 25 DG on T1Gd imaging were significantly associated with a 12.5% reduction in OS hazard for concurrent therapy patients and a 4.4% reduction in PFS hazard for bevacizumab monotherapy patients.
Conclusion
DG has significant meaning in recurrent therapy as a metric of treatment response, even in the context of anti-angiogenic therapies. This provides further evidence supporting the use of DG as an adjunct response metric that quantitatively connects treatment response and clinical outcomes.
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Affiliation(s)
- Kyle W Singleton
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
| | - Alyx B Porter
- Division of Neuro-Oncology, Department of Neurology, Mayo Clinic, Phoenix, AZ
| | - Leland S Hu
- Department of Radiology, Mayo Clinic, Phoenix, Arizona
| | - Sandra K Johnston
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
- Department of Radiology, University of Washington, Seattle, Washington
| | - Kamila M Bond
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
- Mayo Clinic Alix School of Medicine, Mayo Clinic, Rochester, Minnesota
| | - Cassandra R Rickertsen
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
| | - Gustavo De Leon
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
| | - Scott A Whitmire
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
| | - Kamala R Clark-Swanson
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
| | - Maciej M Mrugala
- Division of Neuro-Oncology, Department of Neurology, Mayo Clinic, Phoenix, AZ
| | - Kristin R Swanson
- Mathematical NeuroOncology Lab, Precision NeuroTherapeutics Innovation Program, Mayo Clinic, Phoenix, Arizona
- Department of Neurosurgery, Mayo Clinic, Phoenix, Arizona
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15
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Lipkova J, Angelikopoulos P, Wu S, Alberts E, Wiestler B, Diehl C, Preibisch C, Pyka T, Combs SE, Hadjidoukas P, Van Leemput K, Koumoutsakos P, Lowengrub J, Menze B. Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans, and Bayesian Inference. IEEE TRANSACTIONS ON MEDICAL IMAGING 2019; 38:1875-1884. [PMID: 30835219 PMCID: PMC7170051 DOI: 10.1109/tmi.2019.2902044] [Citation(s) in RCA: 60] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Glioblastoma (GBM) is a highly invasive brain tumor, whose cells infiltrate surrounding normal brain tissue beyond the lesion outlines visible in the current medical scans. These infiltrative cells are treated mainly by radiotherapy. Existing radiotherapy plans for brain tumors derive from population studies and scarcely account for patient-specific conditions. Here, we provide a Bayesian machine learning framework for the rational design of improved, personalized radiotherapy plans using mathematical modeling and patient multimodal medical scans. Our method, for the first time, integrates complementary information from high-resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in GBM patients. The Bayesian framework quantifies imaging and modeling uncertainties and predicts patient-specific tumor cell density with credible intervals. The proposed methodology relies only on data acquired at a single time point and, thus, is applicable to standard clinical settings. An initial clinical population study shows that the radiotherapy plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard radiotherapy protocols. Moreover, the inferred regions of high tumor cell densities coincide with the tumor radioresistant areas, providing guidance for personalized dose-escalation. The proposed integration of multimodal scans and mathematical modeling provides a robust, non-invasive tool to assist personalized radiotherapy design.
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Rockne RC, Hawkins-Daarud A, Swanson KR, Sluka JP, Glazier JA, Macklin P, Hormuth DA, Jarrett AM, Lima EABF, Tinsley Oden J, Biros G, Yankeelov TE, Curtius K, Al Bakir I, Wodarz D, Komarova N, Aparicio L, Bordyuh M, Rabadan R, Finley SD, Enderling H, Caudell J, Moros EG, Anderson ARA, Gatenby RA, Kaznatcheev A, Jeavons P, Krishnan N, Pelesko J, Wadhwa RR, Yoon N, Nichol D, Marusyk A, Hinczewski M, Scott JG. The 2019 mathematical oncology roadmap. Phys Biol 2019; 16:041005. [PMID: 30991381 PMCID: PMC6655440 DOI: 10.1088/1478-3975/ab1a09] [Citation(s) in RCA: 97] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
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Affiliation(s)
- Russell C Rockne
- Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA 91010, United States of America. Author to whom any correspondence should be addressed
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