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Christgen M, Caetano RA, Eisenburger M, Traulsen A, Altrock PM. Deficient cell-cell cohesion is linked with lobular localization in simplified models of lobular carcinoma in situ (LCIS). Math Biosci 2024; 380:109369. [PMID: 39694324 DOI: 10.1016/j.mbs.2024.109369] [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: 06/26/2024] [Revised: 12/12/2024] [Accepted: 12/15/2024] [Indexed: 12/20/2024]
Abstract
Lobular carcinoma in situ (LCIS) is a precursor of invasive lobular carcinoma of the breast. LCIS cells lack cell-cell cohesion due to the loss of E-cadherin. LCIS cells grow in mammary lobules rather than in ducts. The etiology of this pattern, especially its dependence on cellular cohesion, is incompletely understood. We simulated passive intra-glandular scattering of carcinoma in situ (CIS) cells in an ultra-simplified hollow mold tissue replica (HMTR) and a discrete-time mathematical model featuring particles of variable sizes representing single cells (LCIS-like particles) or groups of cohesive carcinoma cells (DCIS-like particles). The HMTR features structures reminiscent of a mammary duct with associated lobules. The discrete mathematical model characterizes spatial redistribution over time and includes transition probabilities between ductal or lobular localizations. Redistribution of particles converged toward an equilibrium depending on particle size. Strikingly, equilibrium proportions depended on particle properties, which we also confirm in a continuous-time mathematical model that considers controlling lobular properties such as crowding. Particles of increasing size, representing CIS cells with proficient cohesion, showed increasingly higher equilibrium ductal proportions. Our investigations represent two conceptual abstractions implying a link between loss of cell-cell cohesion and lobular localization of LCIS, which provide a much-needed logical foundation for studying the connections between collective cell behavior and cancer development in breast tissues. In light of the findings from our simplified modeling approach, we discuss multiple avenues for near-future research that can address and evaluate the redistribution hypothesis mathematically and empirically.
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Affiliation(s)
- Matthias Christgen
- Institute of Pathology, Hannover Medical School, Carl-Neuberg-Str. 1, Hannover 30625, Germany.
| | - Rodrigo A Caetano
- Departamento de Física, Universidade Federal do Paraná, Curitiba, Brazil
| | - Michael Eisenburger
- Clinic for Prosthetic Dentistry and Biomedical Material Science, Hannover Medical School, Germany
| | - Arne Traulsen
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön 24306, Germany
| | - Philipp M Altrock
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön 24306, Germany.
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2
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Crouch SA, Krause J, Dandekar T, Breitenbach T. DataXflow: Synergizing data-driven modeling with best parameter fit and optimal control - An efficient data analysis for cancer research. Comput Struct Biotechnol J 2024; 23:1755-1772. [PMID: 38707537 PMCID: PMC11068525 DOI: 10.1016/j.csbj.2024.04.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 04/04/2024] [Accepted: 04/05/2024] [Indexed: 05/07/2024] Open
Abstract
Building data-driven models is an effective strategy for information extraction from empirical data. Adapting model parameters specifically to data with a best fitting approach encodes the relevant information into a mathematical model. Subsequently, an optimal control framework extracts the most efficient targets to steer the model into desired changes via external stimuli. The DataXflow software framework integrates three software pipelines, D2D for model fitting, a framework solving optimal control problems including external stimuli and JimenaE providing graphical user interfaces to employ the other frameworks lowering the barriers for the need of programming skills, and simultaneously automating reoccurring modeling tasks. Such tasks include equation generation from a graph and script generation allowing also to approach systems with many agents, like complex gene regulatory networks. A desired state of the model is defined, and therapeutic interventions are modeled as external stimuli. The optimal control framework purposefully exploits the model-encoded information by providing those external stimuli that effect the desired changes most efficiently. The implementation of DataXflow is available under https://github.com/MarvelousHopefull/DataXflow. We showcase its application by detecting specific drug targets for a therapy of lung cancer from measurement data to lower proliferation and increase apoptosis. By an iterative modeling process refining the topology of the model, the regulatory network of the tumor is generated from the data. An application of the optimal control framework in our example reveals the inhibition of AURKA and the activation of CDH1 as the most efficient drug target combination. DataXflow paves the way to an agile interplay between data generation and its analysis potentially accelerating cancer research by an efficient drug target identification, even in complex networks.
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Affiliation(s)
| | | | - Thomas Dandekar
- Department of Bioinformatics, Biocenter, University of Würzburg, Am Hubland 97074, Würzburg, Germany
| | - Tim Breitenbach
- Department of Bioinformatics, Biocenter, University of Würzburg, Am Hubland 97074, Würzburg, Germany
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3
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Kunz LV, Bosque JJ, Nikmaneshi M, Chamseddine I, Munn LL, Schuemann J, Paganetti H, Bertolet A. AMBER: A Modular Model for Tumor Growth, Vasculature and Radiation Response. Bull Math Biol 2024; 86:139. [PMID: 39460828 DOI: 10.1007/s11538-024-01371-4] [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: 04/09/2024] [Accepted: 10/09/2024] [Indexed: 10/28/2024]
Abstract
Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.
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Affiliation(s)
- Louis V Kunz
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Jesús J Bosque
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Mohammad Nikmaneshi
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Ibrahim Chamseddine
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Lance L Munn
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Jan Schuemann
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Harald Paganetti
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA
| | - Alejandro Bertolet
- Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA.
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4
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Lange S, Schmied J, Willam P, Voss-Böhme A. Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth. J Theor Biol 2024; 592:111882. [PMID: 38944379 DOI: 10.1016/j.jtbi.2024.111882] [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: 03/12/2024] [Revised: 06/04/2024] [Accepted: 06/14/2024] [Indexed: 07/01/2024]
Abstract
Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition. We discuss how our approach enables the introduction of effective bio-mechanical interactions in a CA framework for future studies.
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Affiliation(s)
- Steffen Lange
- DataMedAssist Group, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany; OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, 01307, Germany.
| | - Jannik Schmied
- DataMedAssist Group, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany; Faculty of Informatics/Mathematics, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany
| | - Paul Willam
- DataMedAssist Group, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany
| | - Anja Voss-Böhme
- DataMedAssist Group, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany; Faculty of Informatics/Mathematics, HTW Dresden-University of Applied Sciences, Dresden, 01069, Germany
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5
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Singh D, Paquin D. Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:6659-6693. [PMID: 39176414 DOI: 10.3934/mbe.2024292] [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: 08/24/2024]
Abstract
Tumor growth dynamics serve as a critical aspect of understanding cancer progression and treatment response to mitigate one of the most pressing challenges in healthcare. The in silico approach to understanding tumor behavior computationally provides an efficient, cost-effective alternative to wet-lab examinations and are adaptable to different environmental conditions, time scales, and unique patient parameters. As a result, this paper explored modeling of free tumor growth in cancer, surveying contemporary literature on continuum, discrete, and hybrid approaches. Factors like predictive power and high-resolution simulation competed against drawbacks like simulation load and parameter feasibility in these models. Understanding tumor behavior in different scenarios and contexts became the first step in advancing cancer research and revolutionizing clinical outcomes.
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Affiliation(s)
- Dashmi Singh
- Stanford University Online High School, 415 Broadway Academy Hall, Floor 2, 8853,415 Broadway, Redwood City, CA 94063, USA
| | - Dana Paquin
- Stanford University Online High School, 415 Broadway Academy Hall, Floor 2, 8853,415 Broadway, Redwood City, CA 94063, USA
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6
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Miti T, Desai B, Miroshnychenko D, Basanta D, Marusyk A. Dissecting the Spatially Restricted Effects of Microenvironment-Mediated Resistance on Targeted Therapy Responses. Cancers (Basel) 2024; 16:2405. [PMID: 39001467 PMCID: PMC11240540 DOI: 10.3390/cancers16132405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2024] [Revised: 06/16/2024] [Accepted: 06/26/2024] [Indexed: 07/16/2024] Open
Abstract
The response of tumors to anti-cancer therapies is defined not only by cell-intrinsic therapy sensitivities but also by local interactions with the tumor microenvironment. Fibroblasts that make tumor stroma have been shown to produce paracrine factors that can strongly reduce the sensitivity of tumor cells to many types of targeted therapies. Moreover, a high stroma/tumor ratio is generally associated with poor survival and reduced therapy responses. However, in contrast to advanced knowledge of the molecular mechanisms responsible for stroma-mediated resistance, its effect on the ability of tumors to escape therapeutic eradication remains poorly understood. To a large extent, this gap of knowledge reflects the challenge of accounting for the spatial aspects of microenvironmental resistance, especially over longer time frames. To address this problem, we integrated spatial inferences of proliferation-death dynamics from an experimental animal model of targeted therapy responses with spatial mathematical modeling. With this approach, we dissected the impact of tumor/stroma distribution, magnitude and distance of stromal effects. While all of the tested parameters affected the ability of tumor cells to resist elimination, spatial patterns of stroma distribution within tumor tissue had a particularly strong impact.
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Affiliation(s)
- Tatiana Miti
- Department of Integrative Mathematical Oncology, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL 33612, USA;
| | - Bina Desai
- Department of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL 33612, USA (D.M.)
- Cancer Biology Ph.D. Program, University of South Florida, Tampa, FL 33620, USA
| | - Daria Miroshnychenko
- Department of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL 33612, USA (D.M.)
| | - David Basanta
- Department of Integrative Mathematical Oncology, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL 33612, USA;
| | - Andriy Marusyk
- Department of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL 33612, USA (D.M.)
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7
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De Carli A, Kapelyukh Y, Kursawe J, Chaplain MAJ, Wolf CR, Hamis S. Simulating BRAFV600E-MEK-ERK signalling dynamics in response to vertical inhibition treatment strategies. NPJ Syst Biol Appl 2024; 10:51. [PMID: 38750040 PMCID: PMC11096323 DOI: 10.1038/s41540-024-00379-9] [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: 12/13/2023] [Accepted: 04/29/2024] [Indexed: 05/18/2024] Open
Abstract
In vertical inhibition treatment strategies, multiple components of an intracellular pathway are simultaneously inhibited. Vertical inhibition of the BRAFV600E-MEK-ERK signalling pathway is a standard of care for treating BRAFV600E-mutated melanoma where two targeted cancer drugs, a BRAFV600E-inhibitor, and a MEK inhibitor, are administered in combination. Targeted therapies have been linked to early onsets of drug resistance, and thus treatment strategies of higher complexities and lower doses have been proposed as alternatives to current clinical strategies. However, finding optimal complex, low-dose treatment strategies is a challenge, as it is possible to design more treatment strategies than are feasibly testable in experimental settings. To quantitatively address this challenge, we develop a mathematical model of BRAFV600E-MEK-ERK signalling dynamics in response to combinations of the BRAFV600E-inhibitor dabrafenib (DBF), the MEK inhibitor trametinib (TMT), and the ERK-inhibitor SCH772984 (SCH). From a model of the BRAFV600E-MEK-ERK pathway, and a set of molecular-level drug-protein interactions, we extract a system of chemical reactions that is parameterised by in vitro data and converted to a system of ordinary differential equations (ODEs) using the law of mass action. The ODEs are solved numerically to produce simulations of how pathway-component concentrations change over time in response to different treatment strategies, i.e., inhibitor combinations and doses. The model can thus be used to limit the search space for effective treatment strategies that target the BRAFV600E-MEK-ERK pathway and warrant further experimental investigation. The results demonstrate that DBF and DBF-TMT-SCH therapies show marked sensitivity to BRAFV600E concentrations in silico, whilst TMT and SCH monotherapies do not.
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Affiliation(s)
- Alice De Carli
- School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, UK
| | - Yury Kapelyukh
- School of Medicine, Jacqui Wood Cancer Centre, Ninewells Hospital and Medical School, University of Dundee, Dundee, Scotland, UK
| | - Jochen Kursawe
- School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, UK
| | - Mark A J Chaplain
- School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, UK
| | - C Roland Wolf
- School of Medicine, Jacqui Wood Cancer Centre, Ninewells Hospital and Medical School, University of Dundee, Dundee, Scotland, UK
| | - Sara Hamis
- School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, UK.
- Tampere Institute for Advanced Study, Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland.
- Department of Information Technology, Uppsala University, Uppsala, Sweden.
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8
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Ojwang' AME, Bazargan S, Johnson JO, Pilon-Thomas S, Rejniak KA. Histology-guided mathematical model of tumor oxygenation: sensitivity analysis of physical and computational parameters. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.03.05.583363. [PMID: 38496532 PMCID: PMC10942376 DOI: 10.1101/2024.03.05.583363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
A hybrid off-lattice agent-based model has been developed to reconstruct the tumor tissue oxygenation landscape based on histology images and simulated interactions between vasculature and cells with microenvironment metabolites. Here, we performed a robustness sensitivity analysis of that model's physical and computational parameters. We found that changes in the domain boundary conditions, the initial conditions, and the Michaelis constant are negligible and, thus, do not affect the model outputs. The model is also not sensitive to small perturbations of the vascular influx or the maximum consumption rate of oxygen. However, the model is sensitive to large perturbations of these parameters and changes in the tissue boundary condition, emphasizing an imperative aim to measure these parameters experimentally.
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Affiliation(s)
- Awino Maureiq E Ojwang'
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Sarah Bazargan
- Department of Immunology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Joseph O Johnson
- Analytic Microscopy Core, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Shari Pilon-Thomas
- Department of Immunology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Katarzyna A Rejniak
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
- Department of Oncologic Sciences, Morsani College of Medicine, University of South Florida, Tampa, FL, USA
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9
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Kusch L, Diaz-Pier S, Klijn W, Sontheimer K, Bernard C, Morrison A, Jirsa V. Multiscale co-simulation design pattern for neuroscience applications. Front Neuroinform 2024; 18:1156683. [PMID: 38410682 PMCID: PMC10895016 DOI: 10.3389/fninf.2024.1156683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 01/19/2024] [Indexed: 02/28/2024] Open
Abstract
Integration of information across heterogeneous sources creates added scientific value. Interoperability of data, tools and models is, however, difficult to accomplish across spatial and temporal scales. Here we introduce the toolbox Parallel Co-Simulation, which enables the interoperation of simulators operating at different scales. We provide a software science co-design pattern and illustrate its functioning along a neuroscience example, in which individual regions of interest are simulated on the cellular level allowing us to study detailed mechanisms, while the remaining network is efficiently simulated on the population level. A workflow is illustrated for the use case of The Virtual Brain and NEST, in which the CA1 region of the cellular-level hippocampus of the mouse is embedded into a full brain network involving micro and macro electrode recordings. This new tool allows integrating knowledge across scales in the same simulation framework and validating them against multiscale experiments, thereby largely widening the explanatory power of computational models.
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Affiliation(s)
- Lionel Kusch
- Institut de Neurosciences des Systèmes (INS), UMR1106, Aix-Marseille Université, Marseilles, France
| | - Sandra Diaz-Pier
- Simulation and Data Lab Neuroscience, Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation, JARA, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Wouter Klijn
- Simulation and Data Lab Neuroscience, Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation, JARA, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Kim Sontheimer
- Simulation and Data Lab Neuroscience, Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation, JARA, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Christophe Bernard
- Institut de Neurosciences des Systèmes (INS), UMR1106, Aix-Marseille Université, Marseilles, France
| | - Abigail Morrison
- Simulation and Data Lab Neuroscience, Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation, JARA, Forschungszentrum Jülich GmbH, Jülich, Germany
- Forschungszentrum Jülich GmbH, IAS-6/INM-6, JARA, Jülich, Germany
- Computer Science 3 - Software Engineering, RWTH Aachen University, Aachen, Germany
| | - Viktor Jirsa
- Institut de Neurosciences des Systèmes (INS), UMR1106, Aix-Marseille Université, Marseilles, France
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Matin HN, Setayeshi S. A computational tumor growth model experience based on molecular dynamics point of view using deep cellular automata. Artif Intell Med 2024; 148:102752. [PMID: 38325930 DOI: 10.1016/j.artmed.2023.102752] [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: 05/28/2023] [Revised: 11/01/2023] [Accepted: 12/22/2023] [Indexed: 02/09/2024]
Abstract
Cancer, as identified by the World Health Organization, stands as the second leading cause of death globally. Its intricate nature makes it challenging to study solely based on biological knowledge, often leading to expensive research endeavors. While tremendous strides have been made in understanding cancer, gaps remain, especially in predicting tumor behavior across various stages. The integration of artificial intelligence in oncology research has accelerated our insights into tumor behavior, right from its genesis to metastasis. Nevertheless, there's a pressing need for a holistic understanding of the interactions between cancer cells, their microenvironment, and their subsequent interplay with the broader body environment. In this landscape, deep learning emerges as a potent tool with its multifaceted applications in diverse scientific challenges. Motivated by this, our study presents a novel approach to modeling cancer tumor growth from a molecular dynamics' perspective, harnessing the capabilities of deep-learning cellular automata. This not only facilitates a microscopic examination of tumor behavior and growth but also delves deeper into its overarching behavioral patterns. Our work primarily focused on evaluating the developed tumor growth model through the proposed network, followed by a rigorous compatibility check with traditional mathematical tumor growth models using R and Matlab software. The outcomes notably aligned with the Gompertz growth model, accentuating the robustness of our approach. Our validated model stands out by offering adaptability to diverse tumor growth datasets, positioning itself as a valuable tool for predictions and further research.
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Affiliation(s)
- Hossein Nikravesh Matin
- Institute for Cognitive Sciences Studies, Tehran, Iran; Medical Radiation Eng. Department, Faculty of Physics and Energy Eng., Amirkabir University of Technology, (Tehran Polytechnics), Tehran, Iran
| | - Saeed Setayeshi
- Institute for Cognitive Sciences Studies, Tehran, Iran; Medical Radiation Eng. Department, Faculty of Physics and Energy Eng., Amirkabir University of Technology, (Tehran Polytechnics), Tehran, Iran.
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11
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Dimitriou NM, Demirag E, Strati K, Mitsis GD. A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2024; 243:107920. [PMID: 37976612 DOI: 10.1016/j.cmpb.2023.107920] [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: 06/23/2023] [Revised: 10/27/2023] [Accepted: 11/05/2023] [Indexed: 11/19/2023]
Abstract
BACKGROUND AND OBJECTIVE The validation of mathematical models of tumour growth is frequently hampered by the lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates. METHODS The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance. RESULTS The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) yielded the best fit for the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles. CONCLUSIONS Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved.
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Affiliation(s)
| | - Ece Demirag
- Department of Biological Sciences, University of Cyprus, Nicosia, 2109, Cyprus
| | - Katerina Strati
- Department of Biological Sciences, University of Cyprus, Nicosia, 2109, Cyprus
| | - Georgios D Mitsis
- Department of Bioengineering, McGill University, Montreal, H3A 0E9, QC, Canada.
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12
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Abbas E, Fanni SC, Bandini C, Francischello R, Febi M, Aghakhanyan G, Ambrosini I, Faggioni L, Cioni D, Lencioni RA, Neri E. Delta-radiomics in cancer immunotherapy response prediction: A systematic review. Eur J Radiol Open 2023; 11:100511. [PMID: 37520768 PMCID: PMC10371799 DOI: 10.1016/j.ejro.2023.100511] [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: 05/10/2023] [Revised: 07/11/2023] [Accepted: 07/12/2023] [Indexed: 08/01/2023] Open
Abstract
Background The new immunotherapies have not only changed the oncological therapeutic approach but have also made it necessary to develop new imaging methods for assessing the response to treatment. Delta radiomics consists of the analysis of radiomic features variation between different medical images, usually before and after therapy. Purpose This review aims to evaluate the role of delta radiomics in the immunotherapy response assessment. Methods A systematic search was performed in PubMed, Scopus, and Web Of Science using "delta radiomics AND immunotherapy" as search terms. The included articles' methodological quality was measured using the Radiomics Quality Score (RQS) tool. Results Thirteen articles were finally included in the systematic review. Overall, the RQS of the included studies ranged from 4 to 17, with a mean RQS total of 11,15 ± 4,18 with a corresponding percentage of 30.98 ± 11.61 %. Eleven articles out of 13 performed imaging at multiple time points. All the included articles performed feature reduction. No study carried out prospective validation, decision curve analysis, or cost-effectiveness analysis. Conclusions Delta radiomics has been demonstrated useful in evaluating the response in oncologic patients undergoing immunotherapy. The overall quality was found law, due to the lack of prospective design and external validation. Thus, further efforts are needed to bring delta radiomics a step closer to clinical implementation.
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Affiliation(s)
- Engy Abbas
- The Joint Department of Medical Imaging, University of Toronto, University Health Network, Sinai Health System, Women’s College Hospital, 610 University Ave, Toronto, ON, Canada M5G 2M9
| | | | - Claudio Bandini
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Roberto Francischello
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Maria Febi
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Gayane Aghakhanyan
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Ilaria Ambrosini
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Lorenzo Faggioni
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | - Dania Cioni
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
| | | | - Emanuele Neri
- The Joint Department of Medical Imaging, University of Toronto, University Health Network, Sinai Health System, Women’s College Hospital, 610 University Ave, Toronto, ON, Canada M5G 2M9
- Department of Translational Research, Academic Radiology, University of Pisa, Pisa, Italy
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13
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Cai Y, Zhao Z, Zhuge C. The spatial dynamics of immune response upon virus infection through hybrid dynamical computational model. Front Immunol 2023; 14:1257953. [PMID: 38022575 PMCID: PMC10657891 DOI: 10.3389/fimmu.2023.1257953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Accepted: 10/10/2023] [Indexed: 12/01/2023] Open
Abstract
Introduction The immune responses play important roles in the course of disease initiation and progression upon virus infection such as SARS-CoV-2. As the tissues consist of spatial structures, the spatial dynamics of immune responses upon viral infection are essential to the outcome of infection. Methods A hybrid computational model based on cellular automata coupled with partial differential equations is developed to simulate the spatial patterns and dynamics of the immune responses of tissue upon virus infection with several different immune movement modes. Results Various patterns of the distribution of virus particles under different immune strengths and movement modes of immune cells are obtained through the computational models. The results also reveal that the directed immune cell wandering model has a better immunization effect. Several other characteristics, such as the peak level of virus density and onset time and the onset of the diseases, are also checked with different immune and physiological conditions, for example, different immune clearance strengths, and different cell-to-cell transmission rates. Furthermore, by the Lasso analysis, it is identified that the three main parameters had the most impact on the rate of onset time of disease. It is also shown that the cell-to-cell transmission rate has a significant effect and is more important for controlling the diseases than those for the cell-free virus given that the faster cell-to-cell transmission than cell-free transmission the rate of virus release is low. Discussion Our model simulates the process of viral and immune response interactions in the alveola repithelial tissues of infected individuals, providing insights into the viral propagation of viruses in two dimensions as well as the influence of immune response patterns and key factors on the course of infection.
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Affiliation(s)
| | | | - Changjing Zhuge
- Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China
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14
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Terragni F, Martinson WD, Carretero M, Maini PK, Bonilla LL. Soliton approximation in continuum models of leader-follower behavior. Phys Rev E 2023; 108:054407. [PMID: 38115402 DOI: 10.1103/physreve.108.054407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/17/2023] [Indexed: 12/21/2023]
Abstract
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.
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Affiliation(s)
- F Terragni
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - W D Martinson
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - M Carretero
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - P K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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15
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Romero-Arias JR, González-Castro CA, Ramírez-Santiago G. A multiscale model of the role of microenvironmental factors in cell segregation and heterogeneity in breast cancer development. PLoS Comput Biol 2023; 19:e1011673. [PMID: 37992135 DOI: 10.1371/journal.pcbi.1011673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Revised: 12/06/2023] [Accepted: 11/08/2023] [Indexed: 11/24/2023] Open
Abstract
We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cell proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors.
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Affiliation(s)
- J Roberto Romero-Arias
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Ciudad de México, Mexico
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16
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Eftimie R, Rolin G, Adebayo OE, Urcun S, Chouly F, Bordas SPA. Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives. Bull Math Biol 2023; 85:117. [PMID: 37855947 DOI: 10.1007/s11538-023-01222-8] [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: 04/19/2023] [Accepted: 10/02/2023] [Indexed: 10/20/2023]
Abstract
Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.
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Affiliation(s)
- R Eftimie
- Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25000, Besançon, France.
| | - G Rolin
- INSERM CIC-1431, CHU Besançon, F-25000, Besançon, France
- EFS, INSERM, UMR 1098 RIGHT, Université de Franche-Comté, F-25000, Besançon, France
| | - O E Adebayo
- Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25000, Besançon, France
| | - S Urcun
- Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, Luxembourg
| | - F Chouly
- Institut de Mathématiques de Bourgogne, Université de Franche-Comté, 21078, Dijon, France
- Center for Mathematical Modelling and Department of Mathematical Engineering, University of Chile and IRL 2807 - CNRS, Santiago, Chile
- Departamento de Ingeniería Matemática, CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile
| | - S P A Bordas
- Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, Luxembourg
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17
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Verma J, Warsame C, Seenivasagam RK, Katiyar NK, Aleem E, Goel S. Nanoparticle-mediated cancer cell therapy: basic science to clinical applications. Cancer Metastasis Rev 2023; 42:601-627. [PMID: 36826760 PMCID: PMC10584728 DOI: 10.1007/s10555-023-10086-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 01/16/2023] [Indexed: 02/25/2023]
Abstract
Every sixth person in the world dies due to cancer, making it the second leading severe cause of death after cardiovascular diseases. According to WHO, cancer claimed nearly 10 million deaths in 2020. The most common types of cancers reported have been breast (lung, colon and rectum, prostate cases), skin (non-melanoma) and stomach. In addition to surgery, the most widely used traditional types of anti-cancer treatment are radio- and chemotherapy. However, these do not distinguish between normal and malignant cells. Additional treatment methods have evolved over time for early detection and targeted therapy of cancer. However, each method has its limitations and the associated treatment costs are quite high with adverse effects on the quality of life of patients. Use of individual atoms or a cluster of atoms (nanoparticles) can cause a paradigm shift by virtue of providing point of sight sensing and diagnosis of cancer. Nanoparticles (1-100 nm in size) are 1000 times smaller in size than the human cell and endowed with safer relocation capability to attack mechanically and chemically at a precise location which is one avenue that can be used to destroy cancer cells precisely. This review summarises the extant understanding and the work done in this area to pave the way for physicians to accelerate the use of hybrid mode of treatments by leveraging the use of various nanoparticles.
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Affiliation(s)
- Jaya Verma
- School of Engineering, London South Bank University, London, SE10AA UK
| | - Caaisha Warsame
- School of Engineering, London South Bank University, London, SE10AA UK
| | | | | | - Eiman Aleem
- School of Applied Sciences, Division of Human Sciences, Cancer Biology and Therapy Research Group, London South Bank University, London, SE10AA UK
| | - Saurav Goel
- School of Engineering, London South Bank University, London, SE10AA UK
- Department of Mechanical Engineering, University of Petroleum and Energy Studies, Dehradun, 248007 India
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18
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Lewinsohn MA, Bedford T, Müller NF, Feder AF. State-dependent evolutionary models reveal modes of solid tumour growth. Nat Ecol Evol 2023; 7:581-596. [PMID: 36894662 PMCID: PMC10089931 DOI: 10.1038/s41559-023-02000-4] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 01/26/2023] [Indexed: 03/11/2023]
Abstract
Spatial properties of tumour growth have profound implications for cancer progression, therapeutic resistance and metastasis. Yet, how spatial position governs tumour cell division remains difficult to evaluate in clinical tumours. Here, we demonstrate that faster division on the tumour periphery leaves characteristic genetic patterns, which become evident when a phylogenetic tree is reconstructed from spatially sampled cells. Namely, rapidly dividing peripheral lineages branch more extensively and acquire more mutations than slower-dividing centre lineages. We develop a Bayesian state-dependent evolutionary phylodynamic model (SDevo) that quantifies these patterns to infer the differential division rates between peripheral and central cells. We demonstrate that this approach accurately infers spatially varying birth rates of simulated tumours across a range of growth conditions and sampling strategies. We then show that SDevo outperforms state-of-the-art, non-cancer multi-state phylodynamic methods that ignore differential sequence evolution. Finally, we apply SDevo to single-time-point, multi-region sequencing data from clinical hepatocellular carcinomas and find evidence of a three- to six-times-higher division rate on the tumour edge. With the increasing availability of high-resolution, multi-region sequencing, we anticipate that SDevo will be useful in interrogating spatial growth restrictions and could be extended to model non-spatial factors that influence tumour progression.
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Affiliation(s)
- Maya A Lewinsohn
- Department of Genome Sciences, University of Washington, Seattle, WA, USA.
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA.
| | - Trevor Bedford
- Department of Genome Sciences, University of Washington, Seattle, WA, USA
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA
- Howard Hughes Medical Institute, Seattle, WA, USA
| | - Nicola F Müller
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA.
| | - Alison F Feder
- Department of Genome Sciences, University of Washington, Seattle, WA, USA.
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19
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Gonçalves IG, García-Aznar JM. Hybrid computational models of multicellular tumour growth considering glucose metabolism. Comput Struct Biotechnol J 2023; 21:1262-1271. [PMID: 36814723 PMCID: PMC9939553 DOI: 10.1016/j.csbj.2023.01.044] [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: 12/01/2022] [Revised: 01/30/2023] [Accepted: 01/30/2023] [Indexed: 02/04/2023] Open
Abstract
Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.
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Key Words
- ABM, agent-based model
- ATP, adenosine triphosphate
- CA, cellular automata
- CPM, cellular Potts model
- ECM, extracellular matrix
- FBA, Flux Balance Analysis
- FDG-PET, [18F]-fluorodeoxyglucose-positron emission tomography
- MCTS, multicellular tumour spheroids
- ODEs, ordinary differential equations
- PDEs, partial differential equations
- SBML, Systems Biology Markup Language
- Warburg effect
- agent-based models
- glucose metabolism
- hybrid modelling
- multicellular simulations
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Affiliation(s)
- Inês G. Gonçalves
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
| | - José Manuel García-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
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20
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Alexiou A, Tsagkaris C, Chatzichronis S, Koulouris A, Haranas I, Gkigkitzis I, Zouganelis G, Mukerjee N, Maitra S, Jha NK, Batiha GES, Kamal MA, Nikolaou M, Ashraf GM. The Fractal Viewpoint of Tumors and Nanoparticles. Curr Med Chem 2023; 30:356-370. [PMID: 35927901 DOI: 10.2174/0929867329666220801152347] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Revised: 04/02/2022] [Accepted: 04/19/2022] [Indexed: 02/08/2023]
Abstract
Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.
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Affiliation(s)
- Athanasios Alexiou
- Department of Science and Engineering, Novel Global Community Educational Foundation, Hebersham, NSW 2770, Australia.,AFNP Med, 1030 Wien, Austria
| | - Christos Tsagkaris
- Department of Science and Engineering, Novel Global Community Educational Foundation, Hebersham, NSW 2770, Australia.,European Student Think Tank, Public Health and Policy Working Group, 1058, Amsterdam, Netherlands
| | - Stylianos Chatzichronis
- Department of Science and Engineering, Novel Global Community Educational Foundation, Hebersham, NSW 2770, Australia
| | - Andreas Koulouris
- Thoracic Oncology Center, Theme Cancer, Karolinska University Hospital, 17177 Stockholm, Sweden.,Faculty of Medicine, University of Crete, 70013 Heraklion, Greece
| | - Ioannis Haranas
- Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, ON, N2L-3C5, Canada
| | - Ioannis Gkigkitzis
- NOVA Department of Mathematics, 8333 Little River Turnpike, Annandale, VA 22003 USA
| | - Georgios Zouganelis
- Human Sciences Research Centre, College of Life and Natural Sciences, University of Derby, East Midlands, DE22 1GB England, UK
| | - Nobendu Mukerjee
- Department of Science and Engineering, Novel Global Community Educational Foundation, Hebersham, NSW 2770, Australia.,Department of Microbiology; Ramakrishna Mission Vivekananda Centenary College, Akhil Mukherjee Rd, Chowdhary Para, Rahara, Khardaha, West Bengal, Kolkata- 700118, India
| | - Swastika Maitra
- Department of Microbiology, Adamas University, Kolkata, India
| | - Niraj Kumar Jha
- Department of Biotechnology, School of Engineering & Technology, Sharda University, Greater Noida, Uttar Pradesh, 201310, India.,Department of Biotechnology, School of Applied & Life Sciences (SALS), Uttaranchal University, Dehradun 248007, India.,Department of Biotechnology Engineering and Food Technology, Chandigarh University, Mohali, 140413, India
| | - Gaber El-Saber Batiha
- Department of Pharmacology and Therapeutics, Faculty of Veterinary Medicine, Damanhour University, Damanhour 22511, AlBeheira, Egypt
| | - Mohammad Amjad Kamal
- Institutes for Systems Genetics, Frontiers Science Center for Disease-related Molecular Network, West China Hospital, Sichuan University, Chengdu, China.,King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia.,Department of Pharmacy, Faculty of Allied Health Sciences, Daffodil International University, Dhaka, Bangladesh.,Enzymoics, 7 Peterlee place, Hebersham, NSW 2770; Novel Global Community Educational Foundation, Australia
| | - Michail Nikolaou
- 1st Oncology Department, "Saint Savas" Anticancer, Oncology Hospital, 11522 Athens, Greece
| | - Ghulam Md Ashraf
- Pre-Clinical Research Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia.,Department of Medical Laboratory Technology, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
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21
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Delgado-Campos A, Cuetos A. Influence of homeostatic mechanisms of bacterial growth and division on structural properties of microcolonies: A computer simulation study. Phys Rev E 2022; 106:034402. [PMID: 36266836 DOI: 10.1103/physreve.106.034402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
Abstract
Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in growing bacteria remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is not entirely determined. In this work, computer simulations using an agent-based model are used to study the effect of these homeostatic mechanisms on the geometrical and structural properties of the developing microcolonies, focusing on the early stages of its development. Also, we examine the effect of linear or exponential dependence with the time of cellular growth on these properties. From our study, we deduce that these mechanisms do not have a noticeable impact on the properties studied, which could be due to the importance that stochastic factors play in the cell division and growth process. In addition, we discuss how competition between cell growth and diffusion is a key aspect in explaining the structure and geometry of developing bacterial microcolonies. The results of the study will help to clarify which processes and parameters should be considered relevant when designing simulation models.
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Affiliation(s)
- Andrés Delgado-Campos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Seville, Spain
| | - Alejandro Cuetos
- Department of Physical, Chemical and Natural Systems, Pablo de Olavide University, 41013 Seville, Spain
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22
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Lapin A, Perfahl H, Jain HV, Reuss M. Integrating a dynamic central metabolism model of cancer cells with a hybrid 3D multiscale model for vascular hepatocellular carcinoma growth. Sci Rep 2022; 12:12373. [PMID: 35858953 PMCID: PMC9300625 DOI: 10.1038/s41598-022-15767-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Accepted: 06/29/2022] [Indexed: 11/09/2022] Open
Abstract
We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.
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Affiliation(s)
- Alexey Lapin
- Stuttgart Research Center Systems Biology, University Stuttgart, Stuttgart, Germany
- Institute of Chemical Process Engineering, University Stuttgart, Stuttgart, Germany
| | - Holger Perfahl
- Stuttgart Research Center Systems Biology, University Stuttgart, Stuttgart, Germany
| | - Harsh Vardhan Jain
- Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN, USA
| | - Matthias Reuss
- Stuttgart Research Center Systems Biology, University Stuttgart, Stuttgart, Germany.
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23
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Bonforti A, Solé R. Unicellular-multicellular evolutionary branching driven by resource limitations. J R Soc Interface 2022; 19:20220018. [PMID: 35642429 DOI: 10.1098/rsif.2022.0018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Multicellular life forms have evolved many times on our planet, suggesting that this is a common evolutionary innovation. Multiple advantages have been proposed for the emergence of multicellularity (MC). In this paper, we address the problem of how the first precondition for MC, namely 'stay together', might have occurred under spatially limited resources exploited by a population of unicellular agents. Using a minimal model of evolved cell-cell adhesion among growing and dividing cells that exploit a localized resource with a given size, we show that a transition occurs at a critical resource size separating a phase of evolved multicellular aggregates from a phase where unicellularity (UC) is favoured. The two phases are separated by an intermediate domain where both UC and MC can be selected by evolution. This model provides a minimal approach to the early stages that were required to transition from individuality to cohesive groups of cells associated with a physical cooperative effect: when resources are present only in a localized portion of the habitat, MC is a desirable property as it helps cells to keep close to the available local nutrients.
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Affiliation(s)
- Adriano Bonforti
- ICREA-Complex Systems Lab, UPF-PRBB, Dr. Aiguader 80, 08003 Barcelona, Spain.,Institut de Biologia Evolutiva, CSIC-UPF, Passeig Maritim de la Barceloneta 37, 08003 Barcelona, Spain
| | - Ricard Solé
- ICREA-Complex Systems Lab, UPF-PRBB, Dr. Aiguader 80, 08003 Barcelona, Spain.,Institut de Biologia Evolutiva, CSIC-UPF, Passeig Maritim de la Barceloneta 37, 08003 Barcelona, Spain.,Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
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24
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Bekker RA, Kim S, Pilon-Thomas S, Enderling H. Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system. Neoplasia 2022; 28:100796. [PMID: 35447601 PMCID: PMC9043662 DOI: 10.1016/j.neo.2022.100796] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 03/27/2022] [Accepted: 04/01/2022] [Indexed: 11/01/2022]
Abstract
Radiotherapy is a primary therapeutic modality widely utilized with curative intent. Traditionally tumor response was hypothesized to be due to high levels of cell death induced by irreparable DNA damage. However, the immunomodulatory aspect of radiation is now widely accepted. As such, interest into the combination of radiotherapy and immunotherapy is increasing, the synergy of which has the potential to improve tumor regression beyond that observed after either treatment alone. However, questions regarding the timing (sequential vs concurrent) and dose fractionation (hyper-, standard-, or hypo-fractionation) that result in improved anti-tumor immune responses, and thus potentially enhanced tumor inhibition, remain. Here we discuss the biological response to radiotherapy and its immunomodulatory properties before giving an overview of pre-clinical data and clinical trials concerned with answering these questions. Finally, we review published mathematical models of the impact of radiotherapy on tumor-immune interactions. Ranging from considering the impact of properties of the tumor microenvironment on the induction of anti-tumor responses, to the impact of choice of radiation site in the setting of metastatic disease, these models all have an underlying feature in common: the push towards personalized therapy.
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de Melo Quintela B, Hervas-Raluy S, Manuel Garcia Aznar J, Walker D, Wertheim KY, Viceconti M. A Theoretical Analysis of the Scale Separation in a Model to Predict Solid Tumour Growth. J Theor Biol 2022; 547:111173. [DOI: 10.1016/j.jtbi.2022.111173] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Revised: 03/27/2022] [Accepted: 05/19/2022] [Indexed: 11/27/2022]
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Liu F, Heiner M, Gilbert D. Hybrid modelling of biological systems: current progress and future prospects. Brief Bioinform 2022; 23:6555400. [PMID: 35352101 PMCID: PMC9116374 DOI: 10.1093/bib/bbac081] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Revised: 02/12/2022] [Accepted: 02/16/2022] [Indexed: 11/15/2022] Open
Abstract
Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.
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Affiliation(s)
- Fei Liu
- School of Software Engineering, South China University of Technology, Guangzhou 510006, P.R. China
- Corresponding author: Fei Liu, School of Software Engineering, South China University of Technology, Guangzhou 510006, P.R. China. E-mail:
| | - Monika Heiner
- Department of Computer Science, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus 03046, Germany
| | - David Gilbert
- Department of Computer Science, Brunel University London, Middlesex UB8 3PH, UK
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de los Reyes AA, Kim Y. Optimal regulation of tumour-associated neutrophils in cancer progression. ROYAL SOCIETY OPEN SCIENCE 2022; 9:210705. [PMID: 35127110 PMCID: PMC8808100 DOI: 10.1098/rsos.210705] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Accepted: 11/19/2021] [Indexed: 06/14/2023]
Abstract
In a tumour microenvironment, tumour-associated neutrophils could display two opposing differential phenotypes: anti-tumour (N1) and pro-tumour (N2) effector cells. Converting N2 to N1 neutrophils provides innovative therapies for cancer treatment. In this study, a mathematical model for N1-N2 dynamics describing the cancer survival and immune inhibition in response to TGF-β and IFN-β is considered. The effects of exogenous intervention of TGF-β inhibitor and IFN-β are examined in order to enhance N1 recruitment to combat tumour progression. Our approach employs optimal control theory to determine drug infusion protocols that could minimize tumour volume with least administration cost possible. Four optimal control scenarios corresponding to different therapeutic strategies are explored, namely, TGF-β inhibitor control only, IFN-β control only, concomitant TGF-β inhibitor and IFN-β controls, and alternating TGF-β inhibitor and IFN-β controls. For each scheme, different initial conditions are varied to depict different pathophysiological condition of a cancer patient, leading to adaptive treatment schedule. TGF-β inhibitor and IFN-β drug dosages, total drug amount, infusion times and relative cost of drug administrations are obtained under various circumstances. The control strategies achieved could guide in designing individualized therapeutic protocols.
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Affiliation(s)
- Aurelio A. de los Reyes
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines
| | - Yangjin Kim
- Department of Mathematics, Konkuk University, Seoul 05029, Republic of Korea
- Mathematical Biosciences Institute, Columbus, OH 43210, USA
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Italia M, Dercole F, Lucchetti R. Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model. Phys Biol 2022; 19. [PMID: 35100568 DOI: 10.1088/1478-3975/ac509c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 01/31/2022] [Indexed: 11/12/2022]
Abstract
Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.
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Affiliation(s)
- Matteo Italia
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Fabio Dercole
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Roberto Lucchetti
- Mathematics, Politecnico di Milano, Via Edoardo Bonardi, 9, Milano, 20133, ITALY
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Mathias S, Coulier A, Hellander A. CBMOS: a GPU-enabled Python framework for the numerical study of center-based models. BMC Bioinformatics 2022; 23:55. [PMID: 35100968 PMCID: PMC8805507 DOI: 10.1186/s12859-022-04575-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 01/11/2022] [Indexed: 11/24/2022] Open
Abstract
BACKGROUND Cell-based models are becoming increasingly popular for applications in developmental biology. However, the impact of numerical choices on the accuracy and efficiency of the simulation of these models is rarely meticulously tested. Without concrete studies to differentiate between solid model conclusions and numerical artifacts, modelers are at risk of being misled by their experiments' results. Most cell-based modeling frameworks offer a feature-rich environment, providing a wide range of biological components, but are less suitable for numerical studies. There is thus a need for software specifically targeted at this use case. RESULTS We present CBMOS, a Python framework for the simulation of the center-based or cell-centered model. Contrary to other implementations, CBMOS' focus is on facilitating numerical study of center-based models by providing access to multiple ordinary differential equation solvers and force functions through a flexible, user-friendly interface and by enabling rapid testing through graphics processing unit (GPU) acceleration. We show-case its potential by illustrating two common workflows: (1) comparison of the numerical properties of two solvers within a Jupyter notebook and (2) measuring average wall times of both solvers on a high performance computing cluster. More specifically, we confirm that although for moderate accuracy levels the backward Euler method allows for larger time step sizes than the commonly used forward Euler method, its additional computational cost due to being an implicit method prohibits its use for practical test cases. CONCLUSIONS CBMOS is a flexible, easy-to-use Python implementation of the center-based model, exposing both basic model assumptions and numerical components to the user. It is available on GitHub and PyPI under an MIT license. CBMOS allows for fast prototyping on a central processing unit for small systems through the use of NumPy. Using CuPy on a GPU, cell populations of up to 10,000 cells can be simulated within a few seconds. As such, it will substantially lower the time investment for any modeler to check the crucial assumption that model conclusions are independent of numerical issues.
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Affiliation(s)
- Sonja Mathias
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Adrien Coulier
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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Gondal MN, Chaudhary SU. Navigating Multi-Scale Cancer Systems Biology Towards Model-Driven Clinical Oncology and Its Applications in Personalized Therapeutics. Front Oncol 2021; 11:712505. [PMID: 34900668 PMCID: PMC8652070 DOI: 10.3389/fonc.2021.712505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 10/26/2021] [Indexed: 12/19/2022] Open
Abstract
Rapid advancements in high-throughput omics technologies and experimental protocols have led to the generation of vast amounts of scale-specific biomolecular data on cancer that now populates several online databases and resources. Cancer systems biology models built using this data have the potential to provide specific insights into complex multifactorial aberrations underpinning tumor initiation, development, and metastasis. Furthermore, the annotation of these single- and multi-scale models with patient data can additionally assist in designing personalized therapeutic interventions as well as aid in clinical decision-making. Here, we have systematically reviewed the emergence and evolution of (i) repositories with scale-specific and multi-scale biomolecular cancer data, (ii) systems biology models developed using this data, (iii) associated simulation software for the development of personalized cancer therapeutics, and (iv) translational attempts to pipeline multi-scale panomics data for data-driven in silico clinical oncology. The review concludes that the absence of a generic, zero-code, panomics-based multi-scale modeling pipeline and associated software framework, impedes the development and seamless deployment of personalized in silico multi-scale models in clinical settings.
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Affiliation(s)
- Mahnoor Naseer Gondal
- Biomedical Informatics Research Laboratory, Department of Biology, Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences, Lahore, Pakistan
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI, United States
| | - Safee Ullah Chaudhary
- Biomedical Informatics Research Laboratory, Department of Biology, Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences, Lahore, Pakistan
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Quantifying ERK activity in response to inhibition of the BRAFV600E-MEK-ERK cascade using mathematical modelling. Br J Cancer 2021; 125:1552-1560. [PMID: 34621046 PMCID: PMC8608797 DOI: 10.1038/s41416-021-01565-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 09/06/2021] [Accepted: 09/21/2021] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND Simultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanism of how vertical inhibition synergistically suppresses intracellular ERK activity, and consequently cell proliferation, are yet to be fully elucidated. METHODS We develop a mechanistic mathematical model that describes how the mutant BRAF inhibitor, dabrafenib, and the MEK inhibitor, trametinib, affect BRAFV600E-MEK-ERK signalling. The model is based on a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations that are parameterised by in vitro data and solved numerically to obtain the temporal evolution of cascade component concentrations. RESULTS The model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E-mutant melanoma cells. The model elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated BRAF concentrations generate drug resistance to dabrafenib and trametinib. The computational simulations further suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. CONCLUSIONS The model can be used to systematically motivate which dabrafenib-trametinib dose combinations, for treating BRAFV600E-mutated melanoma, warrant experimental investigation.
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Modeling codelivery of CD73 inhibitor and dendritic cell-based vaccines in cancer immunotherapy. Comput Biol Chem 2021; 95:107585. [PMID: 34610532 DOI: 10.1016/j.compbiolchem.2021.107585] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 07/16/2021] [Accepted: 09/23/2021] [Indexed: 11/21/2022]
Abstract
Dendritic cells (DCs) are the dominant class of antigen-presenting cells in humans; therefore, a range of DC-based approaches have been established to promote an immune response against cancer cells. The efficacy of DC-based immunotherapeutic approaches is markedly affected by the immunosuppressive factors related to the tumor microenvironment, such as adenosine. In this paper, based on immunological theories and experimental data, a hybrid model is designed that offers some insights into the effects of DC-based immunotherapy combined with adenosine inhibition. The model combines an individual-based model for describing tumor-immune system interactions with a set of ordinary differential equations for adenosine modeling. Computational simulations of the proposed model clarify the conditions for the onset of a successful immune response against cancer cells. Global and local sensitivity analysis of the model highlights the importance of adenosine blockage for strengthening effector cells. The model is used to determine the most effective suppressive mechanism caused by adenosine, proper vaccination time, and the appropriate time interval between injections.
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Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs. Bull Math Biol 2021; 83:103. [PMID: 34459993 PMCID: PMC8405495 DOI: 10.1007/s11538-021-00935-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 08/10/2021] [Indexed: 11/26/2022]
Abstract
We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.
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Truong VT, Baverel PG, Lythe GD, Vicini P, Yates JWT, Dubois VFS. Step-by-step comparison of ordinary differential equation and agent-based approaches to pharmacokinetic-pharmacodynamic models. CPT-PHARMACOMETRICS & SYSTEMS PHARMACOLOGY 2021; 11:133-148. [PMID: 34399036 PMCID: PMC8846629 DOI: 10.1002/psp4.12703] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Revised: 04/28/2021] [Accepted: 05/14/2021] [Indexed: 12/03/2022]
Abstract
Mathematical models in oncology aid in the design of drugs and understanding of their mechanisms of action by simulation of drug biodistribution, drug effects, and interaction between tumor and healthy cells. The traditional approach in pharmacometrics is to develop and validate ordinary differential equation models to quantify trends at the population level. In this approach, time‐course of biological measurements is modeled continuously, assuming a homogenous population. Another approach, agent‐based models, focuses on the behavior and fate of biological entities at the individual level, which subsequently could be summarized to reflect the population level. Heterogeneous cell populations and discrete events are simulated, and spatial distribution can be incorporated. In this tutorial, an agent‐based model is presented and compared to an ordinary differential equation model for a tumor efficacy model inhibiting the pERK pathway. We highlight strengths, weaknesses, and opportunities of each approach.
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Affiliation(s)
- Van Thuy Truong
- Clinical Pharmacology and Quantitative Pharmacology, Clinical Pharmacology and Safety Sciences, AstraZeneca, Aaron Klug Building, Granta Park, Cambridge, CB21 6GH, UK.,Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom
| | - Paul G Baverel
- Clinical Pharmacology and Quantitative Pharmacology, Clinical Pharmacology and Safety Sciences, AstraZeneca, Aaron Klug Building, Granta Park, Cambridge, CB21 6GH, UK.,Roche Pharma Research and Early Development, Clinical Pharmacology, Pharmaceutical Sciences, Roche Innovation Center Basel F. Hoffmann-La Roche Ltd, Switzerland
| | - Grant D Lythe
- Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom
| | - Paolo Vicini
- Clinical Pharmacology and Quantitative Pharmacology, Clinical Pharmacology and Safety Sciences, AstraZeneca, Aaron Klug Building, Granta Park, Cambridge, CB21 6GH, UK.,Confo Therapeutics, Technologiepark 94, 9052, Ghent (Zwijnaarde), Belgium
| | | | - Vincent F S Dubois
- Clinical Pharmacology and Quantitative Pharmacology, Clinical Pharmacology and Safety Sciences, AstraZeneca, Aaron Klug Building, Granta Park, Cambridge, CB21 6GH, UK
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In-Silico Modeling of Tumor Spheroid Formation and Growth. MICROMACHINES 2021; 12:mi12070749. [PMID: 34202262 PMCID: PMC8303756 DOI: 10.3390/mi12070749] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Revised: 06/21/2021] [Accepted: 06/22/2021] [Indexed: 12/20/2022]
Abstract
Mathematical modeling has significant potential for understanding of biological models of cancer and to accelerate the progress in cross-disciplinary approaches of cancer treatment. In mathematical biology, solid tumor spheroids are often studied as preliminary in vitro models of avascular tumors. The size of spheroids and their cell number are easy to track, making them a simple in vitro model to investigate tumor behavior, quantitatively. The growth of solid tumors is comprised of three main stages: transient formation, monotonic growth and a plateau phase. The last two stages are extensively studied. However, the initial transient formation phase is typically missing from the literature. This stage is important in the early dynamics of growth, formation of clonal sub-populations, etc. In the current work, this transient formation is modeled by a reaction–diffusion partial differential equation (PDE) for cell concentration, coupled with an ordinary differential equation (ODE) for the spheroid radius. Analytical and numerical solutions of the coupled equations were obtained for the change in the radius of tumor spheroids over time. Human glioblastoma (hGB) cancer cells (U251 and U87) were spheroid cultured to validate the model prediction. Results of this study provide insight into the mechanism of development of solid tumors at their early stage of formation.
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BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration. PLoS Comput Biol 2021; 17:e1009066. [PMID: 34129639 PMCID: PMC8232544 DOI: 10.1371/journal.pcbi.1009066] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Revised: 06/25/2021] [Accepted: 05/11/2021] [Indexed: 11/19/2022] Open
Abstract
Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments. Pattern formation during embryonic development and pathological tissue dynamics, such as cancer invasion, emerge from individual intercellular interactions. In order to study the impact of single cell dynamics and cell-cell interactions on tissue behaviour, one needs to develop space-time-dependent on- or off-lattice agent-based models (ABMs), which consider the behaviour of individual cells. However, classical on-lattice agent-based models also known as cellular automata fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. Here, we present the rule- and lattice-based BIO-LGCA modelling class which allows for (i) rigorous derivation of rules from biophysical laws and/or experimental data, (ii) mathematical analysis of collective migration, and (iii) computationally efficient simulations.
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Schölzel C, Blesius V, Ernst G, Dominik A. Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: a software engineering perspective. NPJ Syst Biol Appl 2021; 7:27. [PMID: 34083542 PMCID: PMC8175692 DOI: 10.1038/s41540-021-00182-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Accepted: 04/19/2021] [Indexed: 02/06/2023] Open
Abstract
Reuse of mathematical models becomes increasingly important in systems biology as research moves toward large, multi-scale models composed of heterogeneous subcomponents. Currently, many models are not easily reusable due to inflexible or confusing code, inappropriate languages, or insufficient documentation. Best practice suggestions rarely cover such low-level design aspects. This gap could be filled by software engineering, which addresses those same issues for software reuse. We show that languages can facilitate reusability by being modular, human-readable, hybrid (i.e., supporting multiple formalisms), open, declarative, and by supporting the graphical representation of models. Modelers should not only use such a language, but be aware of the features that make it desirable and know how to apply them effectively. For this reason, we compare existing suitable languages in detail and demonstrate their benefits for a modular model of the human cardiac conduction system written in Modelica.
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Affiliation(s)
- Christopher Schölzel
- Technische Hochschule Mittelhessen - University of Applied Sciences, Giessen, Germany.
| | - Valeria Blesius
- Technische Hochschule Mittelhessen - University of Applied Sciences, Giessen, Germany
| | - Gernot Ernst
- Vestre Viken Hospital Trust, Kongsberg, Norway
- University of Oslo, Oslo, Norway
| | - Andreas Dominik
- Technische Hochschule Mittelhessen - University of Applied Sciences, Giessen, Germany
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38
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Gradeci D, Bove A, Vallardi G, Lowe AR, Banerjee S, Charras G. Cell-scale biophysical determinants of cell competition in epithelia. eLife 2021; 10:e61011. [PMID: 34014166 PMCID: PMC8137148 DOI: 10.7554/elife.61011] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Accepted: 04/23/2021] [Indexed: 11/25/2022] Open
Abstract
How cells with different genetic makeups compete in tissues is an outstanding question in developmental biology and cancer research. Studies in recent years have revealed that cell competition can either be driven by short-range biochemical signalling or by long-range mechanical stresses in the tissue. To date, cell competition has generally been characterised at the population scale, leaving the single-cell-level mechanisms of competition elusive. Here, we use high time-resolution experimental data to construct a multi-scale agent-based model for epithelial cell competition and use it to gain a conceptual understanding of the cellular factors that governs competition in cell populations within tissues. We find that a key determinant of mechanical competition is the difference in homeostatic density between winners and losers, while differences in growth rates and tissue organisation do not affect competition end result. In contrast, the outcome and kinetics of biochemical competition is strongly influenced by local tissue organisation. Indeed, when loser cells are homogenously mixed with winners at the onset of competition, they are eradicated; however, when they are spatially separated, winner and loser cells coexist for long times. These findings suggest distinct biophysical origins for mechanical and biochemical modes of cell competition.
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Affiliation(s)
- Daniel Gradeci
- Department of Physics and Astronomy, University College LondonLondonUnited Kingdom
- London Centre for Nanotechnology, University College LondonLondonUnited Kingdom
| | - Anna Bove
- London Centre for Nanotechnology, University College LondonLondonUnited Kingdom
- Department of Cell and Developmental Biology, University College LondonLondonUnited Kingdom
| | - Giulia Vallardi
- Institute for Structural and Molecular Biology, University College LondonLondonUnited Kingdom
| | - Alan R Lowe
- London Centre for Nanotechnology, University College LondonLondonUnited Kingdom
- Institute for Structural and Molecular Biology, University College LondonLondonUnited Kingdom
- Institute for the Physics of Living Systems, University College LondonLondonUnited Kingdom
| | - Shiladitya Banerjee
- Department of Physics and Astronomy, University College LondonLondonUnited Kingdom
- Institute for the Physics of Living Systems, University College LondonLondonUnited Kingdom
- Department of Physics, Carnegie Mellon UniversityPittsburghUnited States
| | - Guillaume Charras
- London Centre for Nanotechnology, University College LondonLondonUnited Kingdom
- Department of Cell and Developmental Biology, University College LondonLondonUnited Kingdom
- Institute for the Physics of Living Systems, University College LondonLondonUnited Kingdom
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39
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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: 1.5] [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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Miller AK, Brown JS, Basanta D, Huntly N. What Is the Storage Effect, Why Should It Occur in Cancers, and How Can It Inform Cancer Therapy? Cancer Control 2021; 27:1073274820941968. [PMID: 32723185 PMCID: PMC7658723 DOI: 10.1177/1073274820941968] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Intratumor heterogeneity is a feature of cancer that is associated with progression, treatment resistance, and recurrence. However, the mechanisms that allow diverse cancer cell lineages to coexist remain poorly understood. The storage effect is a coexistence mechanism that has been proposed to explain the diversity of a variety of ecological communities, including coral reef fish, plankton, and desert annual plants. Three ingredients are required for there to be a storage effect: (1) temporal variability in the environment, (2) buffered population growth, and (3) species-specific environmental responses. In this article, we argue that these conditions are observed in cancers and that it is likely that the storage effect contributes to intratumor diversity. Data that show the temporal variation within the tumor microenvironment are needed to quantify how cancer cells respond to fluctuations in the tumor microenvironment and what impact this has on interactions among cancer cell types. The presence of a storage effect within a patient’s tumors could have a substantial impact on how we understand and treat cancer.
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Affiliation(s)
- Anna K Miller
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Joel S Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - David Basanta
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Nancy Huntly
- Ecology Center & Department of Biology, Utah State University, Logan, UT, USA
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Comparative analysis of continuum angiogenesis models. J Math Biol 2021; 82:21. [PMID: 33619643 PMCID: PMC7900093 DOI: 10.1007/s00285-021-01570-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 12/07/2020] [Accepted: 01/17/2021] [Indexed: 11/06/2022]
Abstract
Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.
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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: 1.5] [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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Rodriguez-Brenes IA, Wodarz D, Komarova NL. Beyond the pair approximation: Modeling colonization population dynamics. Phys Rev E 2021; 101:032404. [PMID: 32289892 DOI: 10.1103/physreve.101.032404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Accepted: 01/02/2020] [Indexed: 11/07/2022]
Abstract
The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.
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Affiliation(s)
| | - Dominik Wodarz
- Department of Population Health and Disease Prevention, University of California, Irvine, California 92617, USA
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, California 92697, USA
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A New Mathematical Model for Controlling Tumor Growth Based on Microenvironment Acidity and Oxygen Concentration. BIOMED RESEARCH INTERNATIONAL 2021; 2021:8886050. [PMID: 33575354 PMCID: PMC7857879 DOI: 10.1155/2021/8886050] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Revised: 12/29/2020] [Accepted: 01/08/2021] [Indexed: 12/12/2022]
Abstract
Hypoxia and the pH level of the tumor microenvironment have a great impact on the treatment of tumors. Here, the tumor growth is controlled by regulating the oxygen concentration and the acidity of the tumor microenvironment by introducing a two-dimensional multiscale cellular automata model of avascular tumor growth. The spatiotemporal evolution of tumor growth and metabolic variations is modeled based on biological assumptions, physical structure, states of cells, and transition rules. Each cell is allocated to one of the following states: proliferating cancer, nonproliferating cancer, necrotic, and normal cells. According to the response of the microenvironmental conditions, each cell consumes/produces metabolic factors and updates its state based on some stochastic rules. The input parameters are compatible with cancer biology using experimental data. The effect of neighborhoods during mitosis and simulating spatial heterogeneity is studied by considering multicellular layer structure of tumor. A simple Darwinist mutation is considered by introducing a critical parameter (Nmm) that affects division probability of the proliferative tumor cells based on the microenvironmental conditions and cancer hallmarks. The results show that Nmm regulation has a significant influence on the dynamics of tumor growth, the growth fraction, necrotic fraction, and the concentration levels of the metabolic factors. The model not only is able to simulate the in vivo tumor growth quantitatively and qualitatively but also can simulate the concentration of metabolic factors, oxygen, and acidity graphically. The results show the spatial heterogeneity effects on the proliferation of cancer cells and the rest of the system. By increasing Nmm, tumor shrinkage and significant increasing in the oxygen concentration and the pH value of the tumor microenvironment are observed. The results demonstrate the model's ability, providing an essential tool for simulating different tumor evolution scenarios of a patient and reliable prediction of spatiotemporal progression of tumors for utilizing in personalized therapy.
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Liebisch T, Drusko A, Mathew B, Stelzer EHK, Fischer SC, Matthäus F. Cell fate clusters in ICM organoids arise from cell fate heredity and division: a modelling approach. Sci Rep 2020; 10:22405. [PMID: 33376253 PMCID: PMC7772343 DOI: 10.1038/s41598-020-80141-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 12/17/2020] [Indexed: 01/13/2023] Open
Abstract
During the mammalian preimplantation phase, cells undergo two subsequent cell fate decisions. During the first decision, the trophectoderm and the inner cell mass are formed. Subsequently, the inner cell mass segregates into the epiblast and the primitive endoderm. Inner cell mass organoids represent an experimental model system, mimicking the second cell fate decision. It has been shown that cells of the same fate tend to cluster stronger than expected for random cell fate decisions. Three major processes are hypothesised to contribute to the cell fate arrangements: (1) chemical signalling; (2) cell sorting; and (3) cell proliferation. In order to quantify the influence of cell proliferation on the observed cell lineage type clustering, we developed an agent-based model accounting for mechanical cell-cell interaction, i.e. adhesion and repulsion, cell division, stochastic cell fate decision and cell fate heredity. The model supports the hypothesis that initial cell fate acquisition is a stochastically driven process, taking place in the early development of inner cell mass organoids. Further, we show that the observed neighbourhood structures can emerge solely due to cell fate heredity during cell division.
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Affiliation(s)
- Tim Liebisch
- Faculty of Biological Sciences and Frankfurt Institute for Advanced Studies (FIAS), Goethe Universität Frankfurt am Main, Ruth-Moufang-Straße 1, 60438, Frankfurt, Germany.
| | - Armin Drusko
- Faculty of Biological Sciences and Frankfurt Institute for Advanced Studies (FIAS), Goethe Universität Frankfurt am Main, Ruth-Moufang-Straße 1, 60438, Frankfurt, Germany
| | - Biena Mathew
- Faculty of Biological Sciences and Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, Max-von-Laue Str. 15, 60438, Frankfurt, Germany
| | - Ernst H K Stelzer
- Faculty of Biological Sciences and Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, Max-von-Laue Str. 15, 60438, Frankfurt, Germany
| | - Sabine C Fischer
- Center for Computational and Theoretical Biology (CCTB), Julius-Maximilians-Universität Würzburg, Campus Hubland Nord 32, 97074, Würzburg, Germany
| | - Franziska Matthäus
- Faculty of Biological Sciences and Frankfurt Institute for Advanced Studies (FIAS), Goethe Universität Frankfurt am Main, Ruth-Moufang-Straße 1, 60438, Frankfurt, Germany
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Martinson WD, Byrne HM, Maini PK. Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling. Phys Rev E 2020; 102:062417. [PMID: 33466087 DOI: 10.1103/physreve.102.062417] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 11/18/2020] [Indexed: 06/12/2023]
Abstract
Branched networks constitute a ubiquitous structure in biology, arising in plants, lungs, and the circulatory system; however, the mechanisms behind their creation are not well understood. A commonly used model for network morphogenesis proposes that sprouts develop through interactions between leader (tip) cells and follower (stalk) cells. In this description, tip cells emerge from existing structures, travel up chemoattractant gradients, and form new networks by guiding the movement of stalk cells. Such dynamics have been mathematically represented by continuum "snail-trail" models in which the tip cell flux contributes to the stalk cell proliferation rate. Although snail-trail models constitute a classical depiction of leader-follower behavior, their accuracy has yet to be evaluated in a rigorous quantitative setting. Here, we extend the snail-trail modeling framework to two spatial dimensions by introducing a novel multiplicative factor to the stalk cell rate equation, which corrects for neglected network creation in directions other than that of the migrating front. Our derivation of this factor demonstrates that snail-trail models are valid descriptions of cell dynamics when chemotaxis dominates cell movement. We confirm that our snail-trail model accurately predicts the dynamics of tip and stalk cells in an existing agent-based model (ABM) for network formation [Pillay et al., Phys. Rev. E 95, 012410 (2017)10.1103/PhysRevE.95.012410]. We also derive conditions for which it is appropriate to use a reduced, one-dimensional snail-trail model to analyze ABM results. Our analysis identifies key metrics for cell migration that may be used to anticipate when simple snail-trail models will accurately describe experimentally observed cell dynamics in network formation.
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Affiliation(s)
- W Duncan Martinson
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Helen M Byrne
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Philip K Maini
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
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Buttenschön A, Edelstein-Keshet L. Bridging from single to collective cell migration: A review of models and links to experiments. PLoS Comput Biol 2020; 16:e1008411. [PMID: 33301528 PMCID: PMC7728230 DOI: 10.1371/journal.pcbi.1008411] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.
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Affiliation(s)
- Andreas Buttenschön
- Department of Mathematics, University of British Columbia, Vancouver, Canada
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Kara E, Rahman A, Aulisa E, Ghosh S. Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies. Phys Rev E 2020; 102:062425. [PMID: 33466110 DOI: 10.1103/physreve.102.062425] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 11/23/2020] [Indexed: 11/07/2022]
Abstract
In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.
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Affiliation(s)
- Erdi Kara
- Department of Mathematics and Statistics, Texas Tech University, Lubbock TX
| | - Aminur Rahman
- Department of Applied Mathematics, University of Washington, Seattle WA
| | - Eugenio Aulisa
- Department of Mathematics and Statistics, Texas Tech University, Lubbock TX
| | - Souparno Ghosh
- Department of Statistics, University of Nebraska - Lincoln, Lincoln NB
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49
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Mathias S, Coulier A, Bouchnita A, Hellander A. Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models. Bull Math Biol 2020; 82:132. [PMID: 33025278 PMCID: PMC7538447 DOI: 10.1007/s11538-020-00810-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Accepted: 09/21/2020] [Indexed: 12/17/2022]
Abstract
Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.
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Affiliation(s)
- Sonja Mathias
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Adrien Coulier
- Department of Information Technology, Uppsala University, Uppsala, Sweden
| | - Anass Bouchnita
- Department of Information Technology, Uppsala University, Uppsala, Sweden
- Present Address: Ecole Centrale Casablanca, Bouskoura, Morocco
| | - Andreas Hellander
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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50
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Ruiz-Arrebola S, Tornero-López AM, Guirado D, Villalobos M, Lallena AM. An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids. Phys Med 2020; 77:194-203. [PMID: 32882615 DOI: 10.1016/j.ejmp.2020.07.026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/23/2020] [Accepted: 07/19/2020] [Indexed: 11/26/2022] Open
Abstract
PURPOSE To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools. METHODS Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters. RESULTS Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings. CONCLUSIONS The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.
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Affiliation(s)
- S Ruiz-Arrebola
- Servicio de Oncología Radioterápica, Hospital Universitario Marqués de Valdecilla, E-39008 Santander, Spain
| | - A M Tornero-López
- Servicio de Radiofísica y Protección Radiológica, Hospital Universitario Dr. Negrín, E-35010 Gran Canaria, Spain
| | - D Guirado
- Unidad de Radiofísica, Hospital Universitario San Cecilio, E-18016 Granada, Spain; Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain
| | - M Villalobos
- Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain; Departamento de Radiología y Medicina Física, Universidad de Granada, E-18071 Granada, Spain; Instituto de Biopatología y Medicina Regenerativa (IBIMER), Universidad de Granada, E-18071 Granada, Spain
| | - A M Lallena
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada, Spain; Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain.
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