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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Mohammad Mirzaei N, Hao W, Shahriyari L. Investigating the spatial interaction of immune cells in colon cancer. iScience 2023; 26:106596. [PMID: 37168560 PMCID: PMC10165418 DOI: 10.1016/j.isci.2023.106596] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Revised: 02/28/2023] [Accepted: 04/03/2023] [Indexed: 05/13/2023] Open
Abstract
The intricate network of interactions between cells and molecules in the tumor microenvironment creates a heterogeneous ecosystem. The proximity of the cells and molecules to their activators and inhibitors is essential in the progression of tumors. Here, we develop a system of partial differential equations coupled with linear elasticity to investigate the effects of spatial interactions on the tumor microenvironment. We observe interesting cell and cytokine distribution patterns, which are heavily affected by macrophages. We also see that cytotoxic T cells get recruited and suppressed at the site of macrophages. Moreover, we observe that anti-tumor macrophages reorganize the patterns in favor of a more spatially restricted cancer and necrotic core. Furthermore, the adjoint-based sensitivity analysis indicates that the most sensitive model's parameters are directly related to macrophages. The results emphasize the widely acknowledged effect of macrophages in controlling cancer cells population and spatially arranging cells in the tumor microenvironment.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, 01003 MA, USA
| | - Wenrui Hao
- Department of Mathematics, Pennsylvania State University, University Park, 16802 PA, USA
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, 01003 MA, USA
- Corresponding author
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Hu Y, Mohammad Mirzaei N, Shahriyari L. Bio-Mechanical Model of Osteosarcoma Tumor Microenvironment: A Porous Media Approach. Cancers (Basel) 2022; 14:cancers14246143. [PMID: 36551627 PMCID: PMC9777270 DOI: 10.3390/cancers14246143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Revised: 12/05/2022] [Accepted: 12/08/2022] [Indexed: 12/14/2022] Open
Abstract
Osteosarcoma is the most common malignant bone tumor in children and adolescents with a poor prognosis. To describe the progression of osteosarcoma, we expanded a system of data-driven ODE from a previous study into a system of Reaction-Diffusion-Advection (RDA) equations and coupled it with Biot equations of poroelasticity to form a bio-mechanical model. The RDA system includes the spatio-temporal information of the key components of the tumor microenvironment. The Biot equations are comprised of an equation for the solid phase, which governs the movement of the solid tumor, and an equation for the fluid phase, which relates to the motion of cells. The model predicts the total number of cells and cytokines of the tumor microenvironment and simulates the tumor's size growth. We simulated different scenarios using this model to investigate the impact of several biomedical settings on tumors' growth. The results indicate the importance of macrophages in tumors' growth. Particularly, we have observed a high co-localization of macrophages and cancer cells, and the concentration of tumor cells increases as the number of macrophages increases.
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Stahlberg EA, Abdel-Rahman M, Aguilar B, Asadpoure A, Beckman RA, Borkon LL, Bryan JN, Cebulla CM, Chang YH, Chatterjee A, Deng J, Dolatshahi S, Gevaert O, Greenspan EJ, Hao W, Hernandez-Boussard T, Jackson PR, Kuijjer M, Lee A, Macklin P, Madhavan S, McCoy MD, Mohammad Mirzaei N, Razzaghi T, Rocha HL, Shahriyari L, Shmulevich I, Stover DG, Sun Y, Syeda-Mahmood T, Wang J, Wang Q, Zervantonakis I. Exploring approaches for predictive cancer patient digital twins: Opportunities for collaboration and innovation. Front Digit Health 2022; 4:1007784. [PMID: 36274654 PMCID: PMC9586248 DOI: 10.3389/fdgth.2022.1007784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2022] [Accepted: 08/30/2022] [Indexed: 01/26/2023] Open
Abstract
We are rapidly approaching a future in which cancer patient digital twins will reach their potential to predict cancer prevention, diagnosis, and treatment in individual patients. This will be realized based on advances in high performance computing, computational modeling, and an expanding repertoire of observational data across multiple scales and modalities. In 2020, the US National Cancer Institute, and the US Department of Energy, through a trans-disciplinary research community at the intersection of advanced computing and cancer research, initiated team science collaborative projects to explore the development and implementation of predictive Cancer Patient Digital Twins. Several diverse pilot projects were launched to provide key insights into important features of this emerging landscape and to determine the requirements for the development and adoption of cancer patient digital twins. Projects included exploring approaches to using a large cohort of digital twins to perform deep phenotyping and plan treatments at the individual level, prototyping self-learning digital twin platforms, using adaptive digital twin approaches to monitor treatment response and resistance, developing methods to integrate and fuse data and observations across multiple scales, and personalizing treatment based on cancer type. Collectively these efforts have yielded increased insights into the opportunities and challenges facing cancer patient digital twin approaches and helped define a path forward. Given the rapidly growing interest in patient digital twins, this manuscript provides a valuable early progress report of several CPDT pilot projects commenced in common, their overall aims, early progress, lessons learned and future directions that will increasingly involve the broader research community.
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Affiliation(s)
- Eric A. Stahlberg
- Cancer Data Science Initiatives, Frederick National Laboratory for Cancer Research, Frederick, MD, United States
| | - Mohamed Abdel-Rahman
- Department of Ophthalmology and Visual Sciences, The Ohio State University Wexner Medical Center and James Comprehensive Cancer Center, Columbus, OH, United States
| | - Boris Aguilar
- Institute for Systems Biology, Seattle, WA, United States
| | - Alireza Asadpoure
- Department of Civil and Environmental Engineering, University of Massachusetts Amherst, Amherst, MA, United States
| | - Robert A. Beckman
- Innovation Center for Biomedical Informatics, Georgetown University, Washington DC, United States
| | - Lynn L. Borkon
- Cancer Data Science Initiatives, Frederick National Laboratory for Cancer Research, Frederick, MD, United States
| | - Jeffrey N. Bryan
- Department of Veterinary Medicine and Surgery, University of Missouri, Columbia, MO, United States
| | - Colleen M. Cebulla
- Department of Ophthalmology and Visual Sciences, The Ohio State University Wexner Medical Center and James Comprehensive Cancer Center, Columbus, OH, United States
| | - Young Hwan Chang
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, OR, United States
| | - Ansu Chatterjee
- School of Statistics, University of Minnesota, Minneapolis, MN, United States
| | - Jun Deng
- Department of Therapeutic Radiology, Yale University School of Medicine, Yale University, New Haven, CT, United States
| | - Sepideh Dolatshahi
- Department of Biomedical Engineering, University of Virginia, Charlottesville VA, United States
| | - Olivier Gevaert
- Stanford Center for Biomedical Informatics Research (BMIR), Department of Medicine and Department of Biomedical Data Science, Stanford University, Stanford, CA, United States
| | - Emily J. Greenspan
- Center for Biomedical Informatics and Information Technology, National Cancer Institute, National Institutes of Health, Bethesda, MD, United States
| | - Wenrui Hao
- Department of Mathematics, The Pennsylvania State University, University Park, PA, United States
| | - Tina Hernandez-Boussard
- Stanford Center for Biomedical Informatics Research (BMIR), Department of Medicine and Department of Biomedical Data Science, Stanford University, Stanford, CA, United States
| | - Pamela R. Jackson
- Mathematical NeuroOncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic Arizona, Phoenix, AZ, United States
| | - Marieke Kuijjer
- Computational Biology and Systems Medicine Group, Centre for Molecular Medicine Norway University of Oslo, Oslo, Norway
| | - Adrian Lee
- Department of Pharmacology and Chemical Biology, University of Pittsburgh, Pittsburgh, PA, United States
| | - Paul Macklin
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, United States
| | - Subha Madhavan
- Innovation Center for Biomedical Informatics, Georgetown University, Washington DC, United States
| | - Matthew D. McCoy
- Innovation Center for Biomedical Informatics, Georgetown University, Washington DC, United States
| | - Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, United States
| | - Talayeh Razzaghi
- School of Industrial and Systems Engineering, The University of Oklahoma, Norman, OK, United States
| | - Heber L. Rocha
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, United States
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, United States
| | | | - Daniel G. Stover
- Division of Medical Oncology and Department of Medicine, The Ohio State University Comprehensive Cancer Center, Columbus, OH, United States
| | - Yi Sun
- Department of Mathematics, University of South Carolina, Columbia, SC, United States
| | | | - Jinhua Wang
- Institute for Health Informatics and the Masonic Cancer Center, University of Minnesota, Minneapolis, MN, United States
| | - Qi Wang
- Department of Mathematics, University of South Carolina, Columbia, SC, United States
| | - Ioannis Zervantonakis
- Department of Bioengineering, UPMC Hillman Cancer Center, University of Pittsburgh, Pittsburgh, PA, United States
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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] [What about the content of this article? (0)] [Affiliation(s)] [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] [What about the content of this article? (0)] [Affiliation(s)] [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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Mohammad Mirzaei N, Su S, Sofia D, Hegarty M, Abdel-Rahman MH, Asadpoure A, Cebulla CM, Chang YH, Hao W, Jackson PR, Lee AV, Stover DG, Tatarova Z, Zervantonakis IK, Shahriyari L. A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration. J Pers Med 2021; 11:jpm11101031. [PMID: 34683171 PMCID: PMC8540934 DOI: 10.3390/jpm11101031] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 10/12/2021] [Indexed: 01/03/2023] Open
Abstract
Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.
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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.); (S.S.); (D.S.); (M.H.)
| | - Sumeyye Su
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (S.S.); (D.S.); (M.H.)
| | - Dilruba Sofia
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (S.S.); (D.S.); (M.H.)
| | - Maura Hegarty
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (S.S.); (D.S.); (M.H.)
| | - Mohamed H. Abdel-Rahman
- Department of Ophthalmology, Ohio State University Comprehensive Cancer Center, Columbus, OH 43210, USA; (M.H.A.-R.); (C.M.C.); (D.G.S.)
| | - Alireza Asadpoure
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, MA 02747, USA;
| | - Colleen M. Cebulla
- Department of Ophthalmology, Ohio State University Comprehensive Cancer Center, Columbus, OH 43210, USA; (M.H.A.-R.); (C.M.C.); (D.G.S.)
| | - Young Hwan Chang
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, OR 97239, USA; (Y.H.C.); (Z.T.)
| | - Wenrui Hao
- Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA;
| | - Pamela R. Jackson
- Mathematical NeuroOncology Lab, Precision Neurotherapeutics Innovation Program, Mayo Clinic Arizona, Phoenix, AZ 85054, USA;
| | - Adrian V. Lee
- Department of Pharmacology and Chemical Biology, University of Pittsburgh, Pittsburgh, PA 15219, USA;
| | - Daniel G. Stover
- Department of Ophthalmology, Ohio State University Comprehensive Cancer Center, Columbus, OH 43210, USA; (M.H.A.-R.); (C.M.C.); (D.G.S.)
| | - Zuzana Tatarova
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, OR 97239, USA; (Y.H.C.); (Z.T.)
| | - Ioannis K. Zervantonakis
- Department of Bioengineering, UPMC Hillman Cancer Center, University of Pittsburgh, Pittsburgh, PA 15219, USA;
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (N.M.M.); (S.S.); (D.S.); (M.H.)
- Correspondence:
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Mohammad Mirzaei N, Weintraub WS, Fok PW. An integrated approach to simulating the vulnerable atherosclerotic plaque. Am J Physiol Heart Circ Physiol 2020; 319:H835-H846. [PMID: 32795179 PMCID: PMC7654660 DOI: 10.1152/ajpheart.00174.2020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Revised: 08/04/2020] [Accepted: 08/12/2020] [Indexed: 11/22/2022]
Abstract
Analyses of individual atherosclerotic plaques are mostly descriptive, relying, for example, on histological classification by spectral analysis of ultrasound waves or staining and observing particular cellular components. Such passive methods have proved useful for characterizing the structure and vulnerability of plaques but have little quantitative predictive power. Our aim is to introduce and discuss a computational framework to provide insight to clinicians and help them visualize internal plaque dynamics. We use partial differential equations (PDEs) with macrophages, necrotic cells, oxidized lipids, oxygen concentration, and platelet-derived growth factor (PDGF) as primary variables coupled to a biomechanical model to describe vessel growth. The model is deterministic, providing mechanical, morphological, and histological characteristics of an atherosclerotic vessel at any desired future time point. We use our model to create computer-generated animations of a plaque evolution that are in qualitative agreement with published serial ultrasound images and hypothesize possible atherogenic mechanisms. A systems biology model consisting of five differential equations is able to capture the morphology of necrotic cores residing within vulnerable atherosclerotic plaque. In the context of the model, the distribution of oxidized low-density lipoprotein (Ox-LDL) particles, endothelial inflammation, plaque oxygenation (via the presence of vasa vasora), and intimal oxygenation are four important factors that drive changes in core morphology.NEW & NOTEWORTHY In this article, we propose a quantitative framework to describe the evolution of atherosclerotic plaque. We use partial differential equations (PDEs) with macrophages, necrotic cells, oxidized lipids, oxygen concentration, and PDGF as primary variables coupled to a biomechanical model to describe vessel growth. A feature of our method is that it outputs color-coded vessel sections corresponding to regions of the plaque that are necrotic and fibrous, qualitatively similar to images generated by enhanced intravascular ultrasound.
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Affiliation(s)
| | - William S Weintraub
- MedStar Heart and Vascular Institute, MedStar Washington Hospital Center, Washington, District of Columbia
| | - Pak-Wing Fok
- Department of Mathematical Sciences, University of Delaware, Newark, Delaware
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Mohammad Mirzaei N, Fok PW. Simple model of atherosclerosis in cylindrical arteries: impact of anisotropic growth on Glagov remodeling. Math Med Biol 2020; 38:59-82. [PMID: 32814945 DOI: 10.1093/imammb/dqaa011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Revised: 07/08/2020] [Accepted: 07/21/2020] [Indexed: 01/14/2023]
Abstract
In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth.
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Affiliation(s)
| | - Pak-Wing Fok
- Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
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