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

Tumor proliferation and invasion are intrinsically coupled and unraveled through tunable spheroid and physics-based models

Proliferation and invasion are two key drivers of tumor growth that are traditionally considered independent multicellular processes. However, these processes are intrinsically coupled through a maximum carrying capacity, i.e., the maximum spatial cell concentration supported by the tumor volume, total cell count, nutrient access, and mechanical properties of the tissue stroma. We explored this coupling of proliferation and invasion through in vitro and in silico methods where we modulated the mechanical properties of the tumor and the surrounding extracellular matrix. E-cadherin expression and stromal collagen concentration were manipulated in a tunable breast cancer spheroid to determine the overall impacts of these tumor variables on net tumor proliferation and continuum invasion. We integrated these results into a mixed-constitutive formulation to computationally delineate the influences of cellular and extracellular adhesion, stiffness, and mechanical properties of the extracellular matrix on net proliferation and continuum invasion. This framework integrates biological in vitro data into concise computational models of invasion and proliferation to provide more detailed physical insights into the coupling of these key tumor processes and tumor growth. STATEMENT OF SIGNIFICANCE: Tumor growth involves expansion into the collagen-rich stroma through intrinsic coupling of proliferation and invasion within the tumor continuum. These processes are regulated by a maximum carrying capacity that is determined by the total cell count, tumor volume, nutrient access, and mechanical properties of the surrounding stroma. The influences of biomechanical parameters (i.e., stiffness, cell elongation, net proliferation rate and cell-ECM friction) on tumor proliferation or invasion cannot be unraveled using experimental methods alone. By pairing a tunable spheroid system with computational modeling, we delineated the interdependencies of each system parameter on tumor proliferation and continuum invasion, and established a concise computational framework for studying tumor mechanobiology.

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

Tumor Evolution Models of Phase-Field Type with Nonlocal Effects and Angiogenesis

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on diffusive interface models and follow the phase-field approach that describes the tumor as a collection of cells. Such systems are based on a multiphase approach that employs constitutive laws and balance laws for individual constituents. In mathematical oncology, numerous biological phenomena are involved, including temporal and spatial nonlocal effects, complex nonlinearities, stochasticity, and mixed-dimensional couplings. Using the models, for instance, we can express angiogenesis and cell-to-matrix adhesion effects. Finally, we offer some methods for numerically approximating the models and show simulations of the tumor's evolution in response to various biological effects.

Modeling neuron growth using isogeometric collocation based phase field method

We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. In this paper, we propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks.

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.

The calibration of agent-based models of tumor cell growth to experimental data remains a challenge in computational oncology. Besides the computational cost of modeling thousands of agents, the model’s intrinsic stochasticity demands numerous realizations of the simulations to accurately represent the statistical features of the model predictions. We developed a hybrid, multiscale, coarse-grain, agent-based model that captures the growth and decline of human breast carcinoma cells under different initial conditions. We determined the effects of coarse-graining the ABM on the multiscale model output and the number of repetitions necessary to capture the stochastic transitions present in the model. We identified the most influential parameters on the model prediction through a sensitivity analysis and selected which parameters can be fixed and which ones should be calibrated. Using Bayesian calibration, we show that the model can accurately represent the experimental data. The validation step indicates that our model can reliably predict the in vitro temporal data, depending on the choice of the training (calibration data) sets.