Stromal Reactivity Differentially Drives Tumor Cell Evolution and Prostate Cancer Progression

New Results

Ziv Frankenstein,  View ORCID ProfileDavid Basanta, Omar E. Franco, Yan Gao, Rodrigo A. Javier, Douglas W. Strand, MinJae Lee,  View ORCID ProfileSimon W. Hayward, Gustavo Ayala,  View ORCID ProfileAlexander R. A. Anderson

doi: https://doi.org/10.1101/159616 

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Abstract

We implemented a hybrid multiscale model of carcinogenesis that merges data from biology and pathology on the microenvironmental regulation of prostate cancer (PCa) cell behavior. It recapitulates the biology of stromal influence in prostate cancer progression. Our data indicate that the interactions between the tumor cells and reactive stroma shape the evolutionary dynamics of PCa cells and explain overall tumor aggressiveness. We show that the degree of stromal reactivity, when coupled with the current clinical biomarkers, significantly improves PCa prognostication, both for death and recurrence, that may alter treatment decisions. We also show that stromal reactivity correlates directly with tumor growth but inversely modulates tumor evolution. This suggests that the aggressive stromal independent PCa may be an inevitable evolutionary result of poor stromal reactivity. It also suggests that purely tumor centric metrics of aggressiveness may be misleading in terms on clinical outcome.

http://www.biorxiv.org/content/early/2017/08/21/159616

A High-Performance Cellular Automaton Model of Tumor Growth with Dynamically Growing Domains

Jan Poleszczuk, Heiko Enderling

(Submitted on 24 Sep 2013)

Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but computing performance often counterbalances simplicity. Computationally convenient simulation times can be achieved by choosing appropriate data structures, memory and cell handling as well as domain setup. We propose a cellular automaton model of tumor growth with a domain that expands dynamically as the tumor population increases. We discuss memory access, data structures and implementation techniques that yield high-performance multi-scale Monte Carlo simulations of tumor growth. We present simulation results of the tumor growth model and discuss tumor properties that favor the proposed high-performance design.

link: http://arxiv.org/abs/1309.6015

A recent physical approach to angiogenesis modeling: mixture models

Angiogenesis modeling has generally tended towards (1) discrete models of individual sprout tip cells (cellular automata, Plank-Sleeman free-swimming models, etc.), or (2) continuum models of the evolving blood vessel density. At the Mathways into Cancer II workshop last week, I learned of a new approach using mixture (or phase field) models: computational voxels are treated as a conserved mixture of water, matrix, and endothelial cells. Applying conservation laws to each of these phases, plus an energy formulation of how the phases mix, leads to fourth-order Cahn-Hilliard equations for the mixture components. These require some fairly tricky numerics to solve correctly, but the results can be beautiful. And notably, it allows the inclusion of sophisticated cell and tissue mechanics.

Without further ado, I present two papers (by two different groups) on this new approach to angiogenesis modeling, combined as hybrid models with "traditional" sprout tip agents:

Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis
Guillermo Vilanova, Ignasi Colominas, Hector Gomez

Abstract: Tumor angiogenesis, the growth of new capillaries from preexisting ones promoted by the starvation and hypoxia of cancerous cell, creates complex biological patterns. These patterns are captured by a hybrid model that involves high-order partial differential equations coupled with mobile, agent-based components. The continuous equations of the model rely on the phase-field method to describe the intricate interfaces between the vasculature and the host tissue. The discrete equations are posed on a cellular scale and treat tip endothelial cells as mobile agents. Here, we put the model into a coherent mathematical and algorithmic framework and introduce a numerical method based on isogeometric analysis that couples the discrete and continuous descriptions of the theory. Using our algorithms, we perform numerical simulations that show the development of the vasculature around a tumor. The new method permitted us to perform a parametric study of the model. Furthermore, we investigate different initial configurations to study the growth of the new capillaries. The simulations illustrate the accuracy and efficiency of our numerical method and provide insight into the dynamics of the governing equations as well as into the underlying physical phenomenon.

Preprint / advance copy: http://dx.doi.org/10.1002/cnm.2552

(AFAIK) The first work using this approach was by Rui Travasso and colleagues in 2011, with a focus on the role of mechanistic modeling in driving biological hypotheses:

Tumor Angiogenesis and Vascular Patterning: A Mathematical Model
Rui D. M. Travasso et al.

Abstract: Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools.

Open access: http://dx.doi.org/10.1371/journal.pone.0019989