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Miniere HJM, Lima EABF, Lorenzo G, Hormuth II DA, Ty S, Brock A, Yankeelov TE. A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin. Cancer Biol Ther 2024; 25:2321769. [PMID: 38411436 PMCID: PMC11057790 DOI: 10.1080/15384047.2024.2321769] [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: 05/11/2023] [Accepted: 02/18/2024] [Indexed: 02/28/2024] Open
Abstract
Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.
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Affiliation(s)
- Hugo J. M. Miniere
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Guillermo Lorenzo
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Department of Civil Engineering and Architecture, University of Pavia, Lombardy, Italy
| | - David A. Hormuth II
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
| | - Sophia Ty
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
| | - Thomas E. Yankeelov
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, USA
- Department of Oncology, The University of Texas at Austin, Austin, USA
- Division of Diagnostic Imaging, The University of Texas M.D. Anderson Cancer Center, Houston, USA
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Cotner M, Meng S, Jost T, Gardner A, De Santiago C, Brock A. Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics. Am J Physiol Cell Physiol 2023; 324:C247-C262. [PMID: 36503241 PMCID: PMC9886359 DOI: 10.1152/ajpcell.00185.2022] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Revised: 11/21/2022] [Accepted: 11/21/2022] [Indexed: 12/15/2022]
Abstract
Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.
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Affiliation(s)
- Michael Cotner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Sarah Meng
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Tyler Jost
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Andrea Gardner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Carolina De Santiago
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
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3
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Johnson KE, Howard GR, Morgan D, Brenner EA, Gardner AL, Durrett RE, Mo W, Al’Khafaji A, Sontag ED, Jarrett AM, Yankeelov TE, Brock A. Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer. Phys Biol 2020; 18:016001. [PMID: 33215611 PMCID: PMC8156495 DOI: 10.1088/1478-3975/abb09c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.
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Affiliation(s)
- Kaitlyn E Johnson
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Grant R Howard
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Daylin Morgan
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Eric A Brenner
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - Andrea L Gardner
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Russell E Durrett
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - William Mo
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Aziz Al’Khafaji
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - Eduardo D Sontag
- Department of Electrical and Computer Engineering,
Northeastern University, Boston, MA, 02115, United States of America
- Department of Bioengineering, Northeastern University,
Boston, MA, 02115, United States of America
- Laboratory of Systems Pharmacology, Program in Therapeutics
Science, Harvard Medical School, Boston, MA, 02115, United States of America
| | - Angela M Jarrett
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Oden Institute for Computational Engineering and Sciences,
The University of Texas at Austin
| | - Thomas E Yankeelov
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Oden Institute for Computational Engineering and Sciences,
The University of Texas at Austin
- Department of Diagnostic Medicine, The University of Texas
at Austin, Austin, TX, 78712, United States of America
- Department of Oncology, The University of Texas at Austin,
Austin, TX, 78712, United States of America
- Department of Imaging Physics, The MD Anderson Cancer
Center Houston, TX, 77030, United States of America
| | - Amy Brock
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
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Lima EABF, Ghousifam N, Ozkan A, Oden JT, Shahmoradi A, Rylander MN, Wohlmuth B, Yankeelov TE. Calibration of Multi-Parameter Models of Avascular Tumor Growth Using Time Resolved Microscopy Data. Sci Rep 2018; 8:14558. [PMID: 30266911 PMCID: PMC6162291 DOI: 10.1038/s41598-018-32347-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 09/04/2018] [Indexed: 12/24/2022] Open
Abstract
Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.
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Affiliation(s)
- E A B F Lima
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712, USA.
| | - N Ghousifam
- Department of Mechanical Engineering, The University of Texas at Austin, Austin, 78712, USA
| | - A Ozkan
- Department of Mechanical Engineering, The University of Texas at Austin, Austin, 78712, USA
| | - J T Oden
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712, USA
| | - A Shahmoradi
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712, USA
- Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, 78712, USA
| | - M N Rylander
- Department of Mechanical Engineering, The University of Texas at Austin, Austin, 78712, USA
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712, USA
| | - B Wohlmuth
- Department of Mathematics, Technical University of Munich, Garching, 85748, Germany
| | - T E Yankeelov
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712, USA
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712, USA
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, 78712, USA
- Department of Oncology, The University of Texas at Austin, Austin, 78712, USA
- Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, 78712, USA
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