Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology

Kazerouni, Anum S.; Gadde, Manasa; Gardner, Andrea; Hormuth, David A.; Jarrett, Angela M.; Johnson, Kaitlyn E.; Lima, Ernesto A. B. F.; Lorenzo, Guillermo; Phillips, Caleb M.; Brock, Amy; Yankeelov, Thomas E.

doi:10.1016/j.isci.2020.101807

Cited by 23 publications

(23 citation statements)

References 146 publications

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“…However, our mathematical models could be made readily applicable to tumor cell spheroid data. In particular, our models could be extended to a set of partial differential equations, accounting for tumor cell mobility and spatially-resolved parameters and variables, which would allow for a spatiotemporal description of spheroid growth in both in vitro and in vivo settings [30], [70]. Indeed, these extended models could incorporate other spatially-varying mechanisms beyond tumor cell dynamics, such as drug diffusion, mechanics, and angiogenesis, which have also been recognized as key components of chemoresistance and drug action [70]- [74].…”

Section: Discussionmentioning

confidence: 99%

“…In particular, our models could be extended to a set of partial differential equations, accounting for tumor cell mobility and spatially-resolved parameters and variables, which would allow for a spatiotemporal description of spheroid growth in both in vitro and in vivo settings [30], [70]. Indeed, these extended models could incorporate other spatially-varying mechanisms beyond tumor cell dynamics, such as drug diffusion, mechanics, and angiogenesis, which have also been recognized as key components of chemoresistance and drug action [70]- [74]. Finally, we acknowledge the limitations in modeling subpopulation dynamics with total tumor cell data, and that our study thus lacks methods for specifically validating the proposed mathematical description of drug-resistant and drug-sensitive tumor cell dynamics.…”

Section: Discussionmentioning

confidence: 99%

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Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

Yang

Howard

Brock

et al. 2021

Preprint

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The development of chemoresistance remains a significant cause of treatment failure in breast cancer. We posit that a mathematical understanding of chemoresistance could assist in developing successful treatment strategies. Towards that end, we have developed a model that describes the effects of the standard chemotherapeutic drug doxorubicin on the MCF-7 breast cancer cell line. We assume that the tumor is composed of two subpopulations: drug-resistant cells, which continue proliferating after treatment, and drug-sensitive cells, which gradually transition from proliferating to treatment-induced death. The model is fit to experimental data including variations in drug concentration, inter-treatment interval, and number of doses. Our model recapitulates tumor growth dynamics in all these scenarios (as quantified by the concordance correlation coefficient, CCC > 0.95). In particular, superior tumor control is observed with higher doxorubicin concentrations, shorter inter-treatment intervals, and a higher number of doses (p < 0.05). Longer inter-treatment intervals require adapting the model parameterization after each doxorubicin dose, suggesting the promotion of chemoresistance. Additionally, we propose promising empirical formulas to describe the variation of model parameters as functions of doxorubicin concentration (CCC > 0.78). Thus, we conclude that our mathematical model could deepen our understanding of the effects of doxorubicin and could be used to explore practical drug regimens achieving optimal tumor control.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

Yang

Howard

Brock

et al. 2021

Preprint

Self Cite

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“…Phillips et al [ 18 , 79 , 100 ] have proposed integrating confocal microscopy data from an in vitro vascularized tumor platform [ 117 ] with an agent-based mathematical model of tumor angiogenesis [ 100 ]. In their framework, time-resolved confocal measurements of individual angiogenic sprouts are used to calibrate and validate a multiscale agent-based model.…”

Section: Approaches For Modeling Tumor Vasculature At the Cell Scalementioning

confidence: 99%

“…Given such a theory, one could identify, through systematic, in silico evaluations, therapeutic regimens that are personalized to optimize treatment outcomes for each individual patient [ 17 ]. While the literature is filled with numerous theoretical studies characterizing tumor-associated vasculature from the cell to tissue scale, there is a lack of research that explicitly links theory with quantitative experimental studies [ 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Hormuth

Phillips

et al. 2021

Cancers

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Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2–3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

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“…This approach is known as “coarse-graining” in particle simulations of chemical or physical processes whereby several physical particles are lumped into a single simulation agent (or bead) to substantially reduce the degrees of freedom (see, e.g., [ 44 ]). Additionally, improving the predictive utility of hybrid ABMs in cancer requires the integration of data and models through a systematic model calibration and validation scheme that rigorously handles uncertainties in data and parameter calibration [ 25 , 45 , 46 ] as well as parameter inference methods that cope with the inherent stochasticity of the model [ 47 , 48 ].…”

Section: Introductionmentioning

confidence: 99%

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth

et al. 2021

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Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.

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Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology

Cited by 23 publications

References 146 publications

Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth

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