1
|
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.
Collapse
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
| |
Collapse
|
2
|
Nave O, Shor Y, Bar R, Segal EE, Sigron M. A new treatment for breast cancer using a combination of two drugs: AZD9496 and palbociclib. Sci Rep 2024; 14:1307. [PMID: 38225243 PMCID: PMC10789805 DOI: 10.1038/s41598-023-48305-z] [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: 06/07/2023] [Accepted: 11/24/2023] [Indexed: 01/17/2024] Open
Abstract
In this study, we examined a mathematical model of breast cancer (BC) treatment that combines an oral oestrogen receptor inhibitor, AZD9496 with Palbociclib, a selective inhibitor of cyclin- dependent kinases CDK4 and CDK6. Treatment is described by analytical functions that enable us to control the dosage and time interval of the treatment, thus personalising the treatment for each patient. Initially, we investigated the effect of each treatment separately, and finally, we investigated the combination of both treatments. By applying numerical simulations, we confirmed that the combination of AZD9496 with palbociclib was the optimal treatment for BC. The dosage of AZD9496 increased and decreased throughout the treatment period, while the intervals were constant between treatments. Palbociclib changed almost cyclically, whereas the time intervals remained constant. To investigate the mathematical model, we applied the singularly perturbed homotopy analysis method, which is a numerical algorithm. The significant advantage of this method is that the mathematical model does not have to contain a small parameter (as is standard in perturbation theory). However, it is possible to artificially introduce a small parameter into the system of equations, making it possible to study the model using asymptotic methods.
Collapse
Affiliation(s)
- Ophir Nave
- Department of Mathematics, Faculty of Science, Jerusalem College of Technology (JCT), Academic Level Centre, Jerusalem, Israel.
| | - Yehuda Shor
- Department of Computer Science, Jerusalem College of Technology (Mivchar), Jerusalem, Israel
| | - Raziel Bar
- Department of Computer Science, Jerusalem College of Technology (Mivchar), Jerusalem, Israel
| | - Eliezer Elimelech Segal
- Department of Computer Science, Jerusalem College of Technology (Mivchar), Jerusalem, Israel
| | - Moriah Sigron
- Department of Mathematics, Faculty of Science, Jerusalem College of Technology (JCT), Academic Level Centre, Jerusalem, Israel
| |
Collapse
|
3
|
Anderson HG, Takacs GP, Harris DC, Kuang Y, Harrison JK, Stepien TL. Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma. J Math Biol 2023; 88:10. [PMID: 38099947 PMCID: PMC10724342 DOI: 10.1007/s00285-023-02027-y] [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: 12/19/2022] [Revised: 08/30/2023] [Accepted: 11/05/2023] [Indexed: 12/18/2023]
Abstract
Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the approximate Bayesian computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended fourier amplitude sensitivity test. Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.
Collapse
Affiliation(s)
- Hannah G Anderson
- Department of Mathematics, University of Florida, Gainesville, FL, USA
| | - Gregory P Takacs
- Department of Pharmacology and Therapeutics, University of Florida, Gainesville, FL, USA
| | - Duane C Harris
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
| | - Jeffrey K Harrison
- Department of Pharmacology and Therapeutics, University of Florida, Gainesville, FL, USA
| | - Tracy L Stepien
- Department of Mathematics, University of Florida, Gainesville, FL, USA.
| |
Collapse
|
4
|
Sofia D, Zhou Q, Shahriyari L. Mathematical and Machine Learning Models of Renal Cell Carcinoma: A Review. Bioengineering (Basel) 2023; 10:1320. [PMID: 38002445 PMCID: PMC10669004 DOI: 10.3390/bioengineering10111320] [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: 10/17/2023] [Revised: 11/08/2023] [Accepted: 11/13/2023] [Indexed: 11/26/2023] Open
Abstract
This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients' gene expression and clinical data through a variety of techniques to predict patients' outcomes, mechanistic models focus on investigating cells' and molecules' interactions within RCC tumors. These interactions are notably centered around immune cells, cytokines, tumor cells, and the development of lung metastases. The insights gained from both machine learning and mechanistic models encompass critical aspects such as signature gene identification, sensitive interactions in the tumors' microenvironments, metastasis development in other organs, and the assessment of survival probabilities. By reviewing the models of RCC, this study aims to shed light on opportunities for the integration of machine learning and mechanistic modeling approaches for treatment optimization and the identification of specific targets, all of which are essential for enhancing patient outcomes.
Collapse
Affiliation(s)
| | | | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (D.S.); (Q.Z.)
| |
Collapse
|
5
|
Anderson HG, Takacs GP, Harris DC, Kuang Y, Harrison JK, Stepien TL. Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.15.540846. [PMID: 37292799 PMCID: PMC10245580 DOI: 10.1101/2023.05.15.540846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the Approximate Bayesian Computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended Fourier Amplitude Sensitivity Test (eFAST). Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.
Collapse
|
6
|
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] [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.
Collapse
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
| |
Collapse
|
7
|
Lavrenteva E, Theodoropoulos C, Binns M. Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy. Bioengineering (Basel) 2023; 10:bioengineering10030385. [PMID: 36978776 PMCID: PMC10045748 DOI: 10.3390/bioengineering10030385] [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: 02/13/2023] [Revised: 03/14/2023] [Accepted: 03/16/2023] [Indexed: 03/30/2023] Open
Abstract
In this study, we propose a set of nonlinear differential equations to model the dynamic growth of avascular stage tumors, considering nutrient supply from underlying tissue, innate immune response, contact inhibition of cell migration, and interactions with a chemotherapeutic agent. The model has been validated against available experimental data from the literature for tumor growth. We assume that the size of the modeled tumor is already detectable, and it represents all clinically observed existent cell populations; initial conditions are selected accordingly. Numerical results indicate that the tumor size and regression significantly depend on the strength of the host immune system. The effect of chemotherapy is investigated, not only within the malignancy, but also in terms of the responding immune cells and healthy tissue in the vicinity of a tumor.
Collapse
Affiliation(s)
- Evgeniia Lavrenteva
- Department of Chemical and Biochemical Engineering, Dongguk University-Seoul, 30 Pildong-ro 1-gil, Jung-gu, Seoul 04620, Republic of Korea
| | - Constantinos Theodoropoulos
- Department of Chemical Engineering, Biochemical and Bioprocess Engineering Group, University of Manchester, Manchester M13 9PL, UK
| | - Michael Binns
- Department of Chemical and Biochemical Engineering, Dongguk University-Seoul, 30 Pildong-ro 1-gil, Jung-gu, Seoul 04620, Republic of Korea
| |
Collapse
|
8
|
Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment. J Pers Med 2022; 12:jpm12101681. [PMID: 36294824 PMCID: PMC9605269 DOI: 10.3390/jpm12101681] [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: 08/16/2022] [Revised: 09/21/2022] [Accepted: 09/30/2022] [Indexed: 11/04/2022] Open
Abstract
The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor's growth.
Collapse
|
9
|
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: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [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.
Collapse
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
| |
Collapse
|
10
|
Sekaran R, Munnangi AK, Ramachandran M, Gandomi AH. 3D brain slice classification and feature extraction using Deformable Hierarchical Heuristic Model. Comput Biol Med 2022; 149:105990. [PMID: 36030723 DOI: 10.1016/j.compbiomed.2022.105990] [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: 05/26/2022] [Revised: 08/07/2022] [Accepted: 08/14/2022] [Indexed: 11/18/2022]
Abstract
Brain tumors are the most frequently occurring and severe type of cancer, with a life expectancy of only a few months in most advanced stages. As a result, planning the best course of therapy is critical to improve a patient's ability to fight cancer and their quality of life. Various imaging modalities, such as computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound imaging, are commonly employed to assess a brain tumor. This research proposes a novel technique for extracting and classifying tumor features in 3D brain slice images. After input images are processed for noise removal, resizing, and smoothening, features of brain tumor are extracted using Volume of Interest (VOI). The extracted features are then classified using the Deformable Hierarchical Heuristic Model-Deep Deconvolutional Residual Network (DHHM-DDRN) based on surfaces, curves, and geometric patterns. Experimental results show that proposed approach obtained an accuracy of 95%, DSC of 83%, precision of 80%, recall of 85%, and F1 score of 55% for classifying brain cancer features.
Collapse
Affiliation(s)
- Ramesh Sekaran
- Department of Information Technology, Velagapudi Ramakrishna Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India
| | - Ashok Kumar Munnangi
- Department of Information Technology, Velagapudi Ramakrishna Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India
| | | | - Amir H Gandomi
- Faculty of Engineering & Information Systems, University of Technology Sydney, Sydney, Australia.
| |
Collapse
|
11
|
Khan MS, Samreen M, Khan MA, De la Sen M. A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model. ENTROPY 2022; 24:e24070949. [PMID: 35885172 PMCID: PMC9317731 DOI: 10.3390/e24070949] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Revised: 06/27/2022] [Accepted: 06/30/2022] [Indexed: 12/29/2022]
Abstract
This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark–Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.
Collapse
Affiliation(s)
| | - Maria Samreen
- Department of Mathematics, Quaid-I-Azam University, Islamabad 44230, Pakistan;
- Correspondence: or
| | - Muhammad Asif Khan
- Department of Mathematics, Kahota-Haveli Campus, University of the Poonch Rawalakot, Rawalakot 12350, Pakistan;
| | - Manuel De la Sen
- Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Campus of Leioa, 48940 Leioa, Bizkaia, Spain;
| |
Collapse
|
12
|
Mabry PL, Pronk NP, Amos CI, Witte JS, Wedlock PT, Bartsch SM, Lee BY. Cancer systems epidemiology: Overcoming misconceptions and integrating systems approaches into cancer research. PLoS Med 2022; 19:e1004027. [PMID: 35714096 PMCID: PMC9205504 DOI: 10.1371/journal.pmed.1004027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Patricia Mabry and coauthors discuss application of systems approaches in cancer research.
Collapse
Affiliation(s)
- Patricia L. Mabry
- HealthPartners Institute, Bloomington, Minnesota, United States of America
| | - Nicolaas P. Pronk
- HealthPartners Institute, Bloomington, Minnesota, United States of America
- University of Minnesota, School of Public Health, Minneapolis, Minnesota, United States of America
| | - Christopher I. Amos
- Department of Biomedical Data Science, Geisel School of Medicine, Dartmouth College, Hanover, New Hampshire, United States of America
- Baylor College of Medicine, Institute for Clinical and Translational Research, Houston, Texas, United States of America
| | - John S. Witte
- Department of Epidemiology and Population Health, Stanford University, Stanford, California, United States of America
| | - Patrick T. Wedlock
- Center for Advanced Technology and Communication in Health (CATCH), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
- Public Health Informatics, Computational, and Operations Research (PHICOR), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
| | - Sarah M. Bartsch
- Center for Advanced Technology and Communication in Health (CATCH), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
- Public Health Informatics, Computational, and Operations Research (PHICOR), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
| | - Bruce Y. Lee
- Center for Advanced Technology and Communication in Health (CATCH), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
- Public Health Informatics, Computational, and Operations Research (PHICOR), CUNY Graduate School of Public Health and Health Policy, New York City, New York, United States of America
- * E-mail:
| |
Collapse
|
13
|
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.
Collapse
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.)
| |
Collapse
|
14
|
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.
Collapse
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:
| |
Collapse
|