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

Abstract

A fully adaptive non-linear full multigrid (FMG) algorithm is implemented to computationally simulate a model of multispecies desmoplastic tumor growth in three spatial dimensions. The algorithm solves a thermodynamic mixture model employing a diffuse interface approach with Cahn-Hilliard-type fourth-order equations that are coupled, non-linear, and numerically stiff. The tumor model includes extracellular matrix (ECM) as a major component with elastic energy contribution in its chemical potential term. Blood and lymphatic vasculatures are simulated via continuum representations. The model employs advection-reaction-diffusion partial differential equations (PDEs) for the cell, ECM, and vascular components, and reaction-diffusion PDEs for the elements diffusing from the vessels. This study provides the details of the numerical solution obtained by applying the fully adaptive non-linear FMG algorithm with finite difference method to solve this complex system of PDEs. The results indicate that this type of computational model can simulate the extracellular matrix-rich desmoplastic tumor microenvironment typical of fibrotic tumors, such as pancreatic adenocarcinoma.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

“…Mathematical modeling and computational analysis are actively being pursued in several aspects of oncology to personalize and improve therapeutic outcomes (e.g., Ibrahim-Hashim et al, 2017 ). In particular, tissue structure and transport in liver ( Rani et al, 2006 ; Hoehme et al, 2007 ; Campbell et al, 2008 ; Hoehme et al, 2010 , 2017 , 2018 ; Holzhutter et al, 2012 ; Drasdo et al, 2014 ; Dutta-Moscato et al, 2014 ; Lettmann and Hardtke-Wolenski, 2014 ; Schliess et al, 2014 ; Siggers et al, 2014 ; Bethge et al, 2015 ; Ricken et al, 2015 ; Schwen et al, 2015 ; Nishii et al, 2016 ; Sluka et al, 2016 ; White et al, 2016 ; Friedman and Hao, 2017 ; Hudson et al, 2017 , 2019 ; Meyer et al, 2017 ; Fu et al, 2018 ; Mahlbacher et al, 2018 ; Clendenon et al, 2019 ; Van Liedekerke et al, 2020 ) as well as pancreas ( Haeno et al, 2012 ; Louzoun et al, 2014 ; Ng and Frieboes, 2017 , 2018 ; Roy and Finley, 2017 ; Yamamoto et al, 2017 ; Chen et al, 2020 ; Dogra et al, 2020b ) have been modeled. While numerous studies have simulated tumor growth and angiogenesis [see recent reviews and related work ( Cristini et al, 2008 ; Edelman et al, 2010 ; Lowengrub et al, 2010 ; Osborne et al, 2010 ; Rejniak and McCawley, 2010 ; Vineis et al, 2010 ; Andasari et al, 2011 ; Chaplain, 2011 ; Deisboeck et al, 2011 ; Frieboes et al, 2011 ; Michor et al, 2011 ; Rejniak and Anderson, 2011 ; Swanson et al, 2011 )] including metastatic conditions ( Campbell et al, 2008 ; Haeno et al, 2012 ; …”

An in-silico study of cancer cell survival and spatial distribution within a 3D microenvironment

“…These results were fundamental for hypothesizing the cause of cell death in the initial experiment and identify which aspect of the experimental protocol could be changed to address this issue. This feature sets SALSA apart from other relevant hybrid models in cancer research 15,22 that mostly rely on theoretical models that are more difficult to incorporate with experimental analysis.…”

Simulation of a continuum tumor model using distributed computing.

“…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 coupled nature of the Ng-Frieboes model and previous models has led to numerical solution methods (Frieboes et al, 2010;Ng & Frieboes, 2018). The numerical solution for the model stems from Multigrid based on previous work by Lowengrub and coworkers (Lowengrub et al, 2010).…”

“…The numerical solution for the model stems from Multigrid based on previous work by Lowengrub and coworkers (Lowengrub et al, 2010). The algorithm is given in Ng and Frieboes (2018): (Reiter, Vogel, Heppner, Rupp, & Wittum, 2013). This also means that every node on a previous level must operate on the final level Lmax.…”