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Mohammad Mirzaei N, Shahriyari L. Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models. Phys Biol 2024; 21:022001. [PMID: 38330444 DOI: 10.1088/1478-3975/ad2777] [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: 10/07/2023] [Accepted: 02/08/2024] [Indexed: 02/10/2024]
Abstract
Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, United States of America
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, United States of America
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Lei W, Qian S, Zhu X, Hu J. Haemodynamic Effects on the Development and Stability of Atherosclerotic Plaques in Arterial Blood Vessel. Interdiscip Sci 2023; 15:616-632. [PMID: 37418092 DOI: 10.1007/s12539-023-00576-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2023] [Revised: 06/13/2023] [Accepted: 06/14/2023] [Indexed: 07/08/2023]
Abstract
Studying the formation and stability of atherosclerotic plaques in the hemodynamic field is essential for understanding the growth mechanism and preventive treatment of atherosclerotic plaques. In this paper, based on a multiplayer porous wall model, we established a two-way fluid-solid interaction with time-varying inlet flow. The lipid-rich necrotic core (LRNC) and stress in atherosclerotic plaque were described for analyzing the stability of atherosclerotic plaques during the plaque growth by solving advection-diffusion-reaction equations with finite-element method. It was found that LRNC appeared when the lipid levels of apoptotic materials (such as macrophages, foam cells) in the plaque reached a specified lower concentration, and increased with the plaque growth. LRNC was positively correlated with the blood pressure and was negatively correlated with the blood flow velocity. The maximum stress was mainly located at the necrotic core and gradually moved toward the left shoulder of the plaque with the plaque growth, which increases the plaque instability and the risk of the plaque shedding. The computational model may contribute to understanding the mechanisms of early atherosclerotic plaque growth and the risk of instability in the plaque growth.
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Affiliation(s)
- Weirui Lei
- School of Physics and Electronics, Hunan Normal University, Changsha, 410006, China
| | - Shengyou Qian
- School of Physics and Electronics, Hunan Normal University, Changsha, 410006, China.
| | - Xin Zhu
- Hengyang Medical School, University of South China, Hengyang, 421001, China
| | - Jiwen Hu
- School of Mathematics and Physics, University of South China, Hengyang, 421001, China.
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Schirm S, Haghikia A, Brack M, Ahnert P, Nouailles G, Suttorp N, Loeffler M, Witzenrath M, Scholz M. A biomathematical model of atherosclerosis in mice. PLoS One 2022; 17:e0272079. [PMID: 35921269 PMCID: PMC9348695 DOI: 10.1371/journal.pone.0272079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 07/12/2022] [Indexed: 11/18/2022] Open
Abstract
Atherosclerosis is one of the leading causes of death worldwide. Biomathematical modelling of the underlying disease and therapy processes might be a useful aid to develop and improve preventive and treatment concepts of atherosclerosis. We here propose a biomathematical model of murine atherosclerosis under different diet and treatment conditions including lipid modulating compound and antibiotics. The model is derived by translating known biological mechanisms into ordinary differential equations and by assuming appropriate response kinetics to the applied interventions. We explicitly describe the dynamics of relevant immune cells and lipid species in atherosclerotic lesions including the degree of blood vessel occlusion due to growing plaques. Unknown model parameters were determined by fitting the predictions of model simulations to time series data derived from mice experiments. Parameter fittings resulted in a good agreement of model and data for all 13 experimental scenarios considered. The model can be used to predict the outcome of alternative treatment schedules of combined antibiotic, immune modulating, and lipid lowering agents under high fat or normal diet. We conclude that we established a comprehensive biomathematical model of atherosclerosis in mice. We aim to validate the model on the basis of further experimental data.
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Affiliation(s)
- Sibylle Schirm
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - Arash Haghikia
- Department of Cardiology, Charité - Universitätsmedizin Berlin, Campus Benjamin Franklin, Berlin, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Berlin, Berlin, Germany
- Berlin Institute of Health (BIH), Berlin, Germany
| | - Markus Brack
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Division of Pulmonary Inflammation, Berlin, Germany
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Department of Infectious Diseases and Respiratory Medicine, Berlin, Germany
| | - Peter Ahnert
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - Geraldine Nouailles
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Division of Pulmonary Inflammation, Berlin, Germany
| | - Norbert Suttorp
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Department of Infectious Diseases and Respiratory Medicine, Berlin, Germany
| | - Markus Loeffler
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - Martin Witzenrath
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Division of Pulmonary Inflammation, Berlin, Germany
- Charité - Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Department of Infectious Diseases and Respiratory Medicine, Berlin, Germany
| | - Markus Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
- LIFE Research Center of Civilization Diseases, University of Leipzig, Leipzig, Germany
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Mohammad Mirzaei N, Tatarova Z, Hao W, Changizi N, Asadpoure A, Zervantonakis IK, Hu Y, Chang YH, Shahriyari L. A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice. J Pers Med 2022; 12:807. [PMID: 35629230 PMCID: PMC9145520 DOI: 10.3390/jpm12050807] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Revised: 05/12/2022] [Accepted: 05/12/2022] [Indexed: 02/04/2023] Open
Abstract
The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (Y.H.)
| | - Zuzana Tatarova
- Department of Radiology, Brigham & Women’s Hospital, Harvard Medical School, Boston, MA 02115, USA;
| | - Wenrui Hao
- Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA;
| | - Navid Changizi
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, MA 02747, USA; (N.C.); (A.A.)
| | - Alireza Asadpoure
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, MA 02747, USA; (N.C.); (A.A.)
| | - Ioannis K. Zervantonakis
- Department of Bioengineering, UPMC Hillman Cancer Center, University of Pittsburgh, Pittsburgh, PA 15219, USA;
| | - Yu Hu
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (Y.H.)
| | - Young Hwan Chang
- Department of Biomedical Engineering, Oregon Health & Science University, Portland, OR 97239, USA;
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (Y.H.)
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Mohammad Mirzaei N, Changizi N, Asadpoure A, Su S, Sofia D, Tatarova Z, Zervantonakis IK, Chang YH, Shahriyari L. Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model. PLoS Comput Biol 2022; 18:e1009953. [PMID: 35294447 PMCID: PMC8959189 DOI: 10.1371/journal.pcbi.1009953] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 03/28/2022] [Accepted: 02/22/2022] [Indexed: 02/07/2023] Open
Abstract
The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies. One of the outstanding challenges of the mathematical modeling of cancer progression is the existence of many unknown parameters. In this work, we develop a data-driven mathematical model of breast cancer progression by deriving a system of ordinary differential equations for the interaction networks of key cell types and molecules in breast tumors. To overcome the limitations of unknown parameters, we utilize a time course data of a PyMT mice model of breast cancer and estimate parameters using an optimization method. Although the predicted dynamics of cancer and necrotic cells using the obtained values of parameters are in good agreement with the data, the predicted values for a few other variables do not match the data. This might indicate that there are some other key interactions that have not been modeled, and/or there is a noise in the data. The sensitivity and bifurcation analyses show that the most important parameters in controlling the cancer cells population are the proliferation and death rates of cancer cells and adipocytes. These results are in agreement with some biological and clinical studies of breast cancer, which have reported a link between adipocytes and breast cancer progression.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Navid Changizi
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, Massachusetts, United States of America
| | - Alireza Asadpoure
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, Massachusetts, United States of America
| | - Sumeyye Su
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Dilruba Sofia
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Zuzana Tatarova
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, Oregon, United States of America
| | - Ioannis K. Zervantonakis
- Department of Bioengineering, UPMC Hillman Cancer Center, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Young Hwan Chang
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, Oregon, United States of America
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
- * E-mail:
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