Model of vascular desmoplastic multispecies tumor growth

Abstract

We present a three-dimensional nonlinear tumor growth model composed of heterogeneous cell types in a multicomponent-multispecies system, including viable, dead, healthy host, and extracellular matrix (ECM) tissue species. The model includes the capability for abnormal ECM dynamics noted in tumor development, as exemplified by pancreatic ductal adenocarcinoma, including dense desmoplasia typically characterized by a significant increase of interstitial connective tissue. An elastic energy is implemented to provide elasticity to the connective tissue. Cancer-associated fibroblasts (myofibroblasts) are modeled as key contributors to this ECM remodeling. The tumor growth is driven by growth factors released by these stromal cells as well as by oxygen and glucose provided by blood vasculature which along with lymphatics are stimulated to proliferate in and around the tumor based on pro-angiogenic factors released by hypoxic tissue regions. Cellular metabolic processes are simulated, including respiration and glycolysis with lactate fermentation. The bicarbonate buffering system is included for cellular pH regulation. This model system may be of use to simulate the complex interactions between tumor and stromal cells as well as the associated ECM and vascular remodeling that typically characterize malignant cancers notorious for poor therapeutic response.

Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm

“…To study the desmoplastic tumor microenvironment, we recently presented a tumor model (Ng and Frieboes, 2017 ) as a continuum scale multicomponent-multispecies system consisting of heterogeneous cell types and ECM. This thermodynamic mixture model, inspired by the one derived in Wise et al ( 2008 ) and Frieboes et al ( 2010 ), includes metabolic reactions, tumorigenic factors, desmoplastic response, as well as tumor-induced angiogenesis and lymphangiogenesis.…”

Simulation of a continuum tumor model using distributed computing.

“…By accounting for these additional phenomena, newer models with these compensatory equations exchange the numerical and underlying simplicity of their equations with wider applicability at the cost of mathematical complexity (Altrock, Liu, & Michor, 2015;Michor et al, 2011). The most recent of these advents is the Ng-Frieboes model that supports multispecies environments, Helmholtz energy calculations, metabolite concentrations, and vasculature in an effort to detail tumor growth in a clinically relevant manner (Ng & Frieboes, 2017. Construction of such a model yields a promising framework upon which the efficacy of drug delivery can be tested in a consistent and objective manner.…”

“…The model's key equations exhibited in Ng and Frieboes (2018) and derived in Ng and Frieboes (2017) are presented in their nondimensionalized forms below:…”

“…The tumor is more closely visualized in figure 9. While this simulated tumor is not realistic in shape, it is optimized to verify model integrity, as the observations inNg and Frieboes 2017 demonstrate. Like the openMP model they documented, the cubic tumor evolved by smoothing the corners of the cube into expanding bulbs.…”

“…Those values were compared to archived output from the older build using a SHA-256 hash. Matching hashes implied that the integrity of the solving process was not impacted by the code.All timing results were obtained using time.h clock statements and used the test scenario described inNg and Frieboes (2017). The computer used for testing has an AMD 2990WX processor with one Titan RTX GPU.…”