A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin.

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.

Designing clinical trials for patients who are not average.

The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.

Predicting response to combination evofosfamide and immunotherapy under hypoxic conditions in murine models of colon cancer.

The goal of this study is to develop a mathematical model that captures the interaction between evofosfamide, immunotherapy, and the hypoxic landscape of the tumor in the treatment of tumors. Recently, we showed that evofosfamide, a hypoxia-activated prodrug, can synergistically improve treatment outcomes when combined with immunotherapy, while evofosfamide alone showed no effects in an in vivo syngeneic model of colorectal cancer. However, the mechanisms behind the interaction between the tumor microenvironment in the context of oxygenation (hypoxic, normoxic), immunotherapy, and tumor cells are not fully understood. To begin to understand this issue, we develop a system of ordinary differential equations to simulate the growth and decline of tumors and their vascularization (oxygenation) in response to treatment with evofosfamide and immunotherapy (6 combinations of scenarios). The model is calibrated to data from in vivo experiments on mice implanted with colon adenocarcinoma cells and longitudinally imaged with [18F]-fluoromisonidazole ([18F]FMISO) positron emission tomography (PET) to quantify hypoxia. The results show that evofosfamide is able to rescue the immune response and sensitize hypoxic tumors to immunotherapy. In the hypoxic scenario, evofosfamide reduces tumor burden by $ 45.07 \pm 2.55 $%, compared to immunotherapy alone, as measured by tumor volume. The model accurately predicts the temporal evolution of five different treatment scenarios, including control, hypoxic tumors that received immunotherapy, normoxic tumors that received immunotherapy, evofosfamide alone, and hypoxic tumors that received combination immunotherapy and evofosfamide. The average concordance correlation coefficient (CCC) between predicted and observed tumor volume is $ 0.86 \pm 0.05 $. Interestingly, the model values to fit those five treatment arms was unable to accurately predict the response of normoxic tumors to combination evofosfamide and immunotherapy (CCC = $ -0.064 \pm 0.003 $). However, guided by the sensitivity analysis to rank the most influential parameters on the tumor volume, we found that increasing the tumor death rate due to immunotherapy by a factor of $ 18.6 \pm 9.3 $ increases CCC of $ 0.981 \pm 0.001 $. To the best of our knowledge, this is the first study to mathematically predict and describe the increased efficacy of immunotherapy following evofosfamide.

Investigating tumor-host response dynamics in preclinical immunotherapy experiments using a stepwise mathematical modeling strategy.

Immunotherapies such as checkpoint blockade to PD1 and CTLA4 can have varied effects on individual tumors. To quantify the successes and failures of these therapeutics, we developed a stepwise mathematical modeling strategy and applied it to mouse models of colorectal and breast cancer that displayed a range of therapeutic responses. Using longitudinal tumor volume data, an exponential growth model was utilized to designate response groups for each tumor type. The exponential growth model was then extended to describe the dynamics of the quality of vasculature in the tumors via [18F] fluoromisonidazole (FMISO)-positron emission tomography (PET) data estimating tumor hypoxia over time. By calibrating the mathematical system to the PET data, several biological drivers of the observed deterioration of the vasculature were quantified. The mathematical model was then further expanded to explicitly include both the immune response and drug dosing, so that model simulations are able to systematically investigate biological hypotheses about immunotherapy failure and to generate experimentally testable predictions of immune response. The modeling results suggest elevated immune response fractions (> 30 %) in tumors unresponsive to immunotherapy is due to a functional immune response that wanes over time. This experimental-mathematical approach provides a means to evaluate dynamics of the system that could not have been explored using the data alone, including tumor aggressiveness, immune exhaustion, and immune cell functionality.

Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas.

We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data. The calibrated digital twin is used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.

IMPLEMENTATION OF OTTAWA ANKLE RULES IN UNIVERSITY HOSPITAL EMERGENCY ROOM: PILOT STUDY.

Ankle injuries are the most common musculoskeletal injuries in emergency rooms and are associated with a great social and economic impact. The need to request additional tests for ankle sprains is based on suspicion of fracture. The Ottawa Ankle Rules (OAR) establish criteria for ordering radiographs to avoid performing unnecessary examinations. OBJECTIVE: To evaluate the implementation of the Ottawa Rules as a protocol for treating ankle sprains in the emergency department of a university hospital. METHODS: This is a retrospective observational study, conducted over a period of three months before and three months after implementation of the protocol. RESULTS: In the first phase, all patients complaining of ankle sprain underwent radiographs. In the second phase, after the application of the OAR, out of 85 patients evaluated, only 58 underwent complementary exams, showing a reduction of 31.8% in the request for imaging exams. There was no significant difference in fracture detection between the two groups (p=0.476). CONCLUSION: The OAR can be used as a tool in diagnosing ankle sprains, and their implementation reduced the request for imaging exams. Level of Evidence III, Retrospective Comparative Study.

Os traumatismos de tornozelo são as lesões musculoesqueléticas mais comuns nas salas de emergência e estão associadas a um grande impacto social e econômico. A solicitação de exames complementares para a entorse de tornozelo baseia-se na suspeita de fratura. As Regras de Ottawa para Tornozelo (ROT) estabelecem critérios para a solicitação de radiografias com o intuito de evitar a realização de exames desnecessários. Objetivo: Avaliar a implementação das ROT como protocolo de atendimento das entorses de tornozelo no pronto-socorro de um hospital universitário. Métodos: Estudo observacional retrospectivo que visou comparar a solicitação de radiografias e a presença de fraturas três meses antes e três meses após a implantação do protocolo. Resultados: Na primeira fase, todos os pacientes com queixa de entorse de tornozelo realizaram radiografias. Na segunda fase, após aplicação das ROT, de 85 pacientes avaliados, apenas 58 realizaram exames complementares, apresentando uma redução de 31,8% na solicitação dos exames de imagem. Não houve diferença na detecção de fraturas entre os dois grupos (p=0,476). Conclusão: As ROT podem ser utilizadas como ferramenta no atendimento das entorses de tornozelo e sua implantação reduziu a solicitação de exames de imagem. Nível de Evidência III, Estudo Comparativo Retrospectivo.

Bridging Scales: a Hybrid Model to Simulate Vascular Tumor Growth and Treatment Response.

Cancer is a disease driven by random DNA mutations and the interaction of many complex phenomena. To improve the understanding and ultimately find more effective treatments, researchers leverage computer simulations mimicking the tumor growth in silico. The challenge here is to account for the many phenomena influencing the disease progression and treatment protocols. This work introduces a computational model to simulate vascular tumor growth and the response to drug treatments in 3D. It consists of two agent-based models for the tumor cells and the vasculature. Moreover, partial differential equations govern the diffusive dynamics of the nutrients, the vascular endothelial growth factor, and two cancer drugs. The model focuses explicitly on breast cancer cells over-expressing HER2 receptors and a treatment combining standard chemotherapy (Doxorubicin) and monoclonal antibodies with anti-angiogenic properties (Trastuzumab). However, large parts of the model generalize to other scenarios. We show that the model qualitatively captures the effects of the combination therapy by comparing our simulation results with previously published pre-clinical data. Furthermore, we demonstrate the scalability of the model and the associated C++ code by simulating a vascular tumor occupying a volume of 400mm3 using a total of 92.5 million agents.

Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis.

The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.

Implementation of ottawa ankle rules in university hospital emergency room: pilot study / Implementação das regras de ottawa para tornozelo em pronto-socorro de hospital universitário: estudo piloto

ABSTRACT Ankle injuries are the most common musculoskeletal injuries in emergency rooms and are associated with a great social and economic impact. The need to request additional tests for ankle sprains is based on suspicion of fracture. The Ottawa Ankle Rules (OAR) establish criteria for ordering radiographs to avoid performing unnecessary examinations. Objective: To evaluate the implementation of the Ottawa Rules as a protocol for treating ankle sprains in the emergency department of a university hospital. Methods: This is a retrospective observational study, conducted over a period of three months before and three months after implementation of the protocol. Results: In the first phase, all patients complaining of ankle sprain underwent radiographs. In the second phase, after the application of the OAR, out of 85 patients evaluated, only 58 underwent complementary exams, showing a reduction of 31.8% in the request for imaging exams. There was no significant difference in fracture detection between the two groups (p=0.476). Conclusion: The OAR can be used as a tool in diagnosing ankle sprains, and their implementation reduced the request for imaging exams. Level of Evidence III, Retrospective Comparative Study.

RESUMO Os traumatismos de tornozelo são as lesões musculoesqueléticas mais comuns nas salas de emergência e estão associadas a um grande impacto social e econômico. A solicitação de exames complementares para a entorse de tornozelo baseia-se na suspeita de fratura. As Regras de Ottawa para Tornozelo (ROT) estabelecem critérios para a solicitação de radiografias com o intuito de evitar a realização de exames desnecessários. Objetivo: Avaliar a implementação das ROT como protocolo de atendimento das entorses de tornozelo no pronto-socorro de um hospital universitário. Métodos: Estudo observacional retrospectivo que visou comparar a solicitação de radiografias e a presença de fraturas três meses antes e três meses após a implantação do protocolo. Resultados: Na primeira fase, todos os pacientes com queixa de entorse de tornozelo realizaram radiografias. Na segunda fase, após aplicação das ROT, de 85 pacientes avaliados, apenas 58 realizaram exames complementares, apresentando uma redução de 31,8% na solicitação dos exames de imagem. Não houve diferença na detecção de fraturas entre os dois grupos (p=0,476). Conclusão: As ROT podem ser utilizadas como ferramenta no atendimento das entorses de tornozelo e sua implantação reduziu a solicitação de exames de imagem. Nível de Evidência III, Estudo Comparativo Retrospectivo.

Model selection for assessing the effects of doxorubicin on triple-negative breast cancer cell lines.

Doxorubicin is a chemotherapy widely used to treat several types of cancer, including triple-negative breast cancer. In this work, we use a Bayesian framework to rigorously assess the ability of ten different mathematical models to describe the dynamics of four TNBC cell lines (SUM-149PT, MDA-MB-231, MDA-MB-453, and MDA-MB-468) in response to treatment with doxorubicin at concentrations ranging from 10 to 2500 nM. Each cell line was plated and serially imaged via fluorescence microscopy for 30 days following 6, 12, or 24 h of in vitro drug exposure. We use the resulting data sets to estimate the parameters of the ten pharmacodynamic models using a Bayesian approach, which accounts for uncertainties in the models, parameters, and observational data. The ten candidate models describe the growth patterns and degree of response to doxorubicin for each cell line by incorporating exponential or logistic tumor growth, and distinct forms of cell death. Cell line and treatment specific model parameters are then estimated from the experimental data for each model. We analyze all competing models using the Bayesian Information Criterion (BIC), and the selection of the best model is made according to the model probabilities (BIC weights). We show that the best model among the candidate set of models depends on the TNBC cell line and the treatment scenario, though, in most cases, there is great uncertainty in choosing the best model. However, we show that the probability of being the best model can be increased by combining treatment data with the same total drug exposure. Our analysis points to the importance of considering multiple models, built on different biological assumptions, to capture the observed variations in tumor growth and treatment response.

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology.

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

Impacto de la Telesalud en los Sistemas de Salud Andinos, durante la pandemia por COVID-19 / Impact of Telehealth on Andean Health Systems, during the COVID-19 pandemic

Webinar N° 102 del ORAS-CONHU, realizado el 25 de enero de 2022, se realizó un webinar sobre el impacto de la Telesalud en las atenciones de salud en el contexto de la pandemia por COVID-19 en Bolivia, Colombia y Perú. Como reto en nuestra región se resalta: Expandir los avances de la telesalud al campo de la Salud Digital, que permita materializar los ocho principios rectores de la transformación digital del sector de la salud. Conferencistas del webinar: Ernesto Lima, Responsable del Programa de Telesalud, Ministerio de Salud y Deportes de Bolivia, Sandra Gallegos, equipo de la Dirección de Prestación de Servicios y Atención Primaria Ministerio de Salud y Protección Social de Colombia; Bernardette Cotrina, Directora General de Telesalud, Referencia y Urgencias, Ministerio de Salud de Perú.

Optimizing combination therapy in a murine model of HER2+ breast cancer.

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

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

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.

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

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.

Mathematical modeling of COVID-19 in 14.8 million individuals in Bahia, Brazil.

COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase in R0. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology.

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.