Tuning three-dimensional tumor progression simulations on a cluster of GPGPUs

Abstract

In the paper, we present the three-dimensional parallel simulator of tumor progression implemented for GPGPUs, together with an automatic model parameters tuning performed by evolutionary computations. We model the tumor growth by a set of Partial Differential Equations, describing the tumor density, tumor angiogenic factor, and damaged extra-cellular matrix, oxygen concentration, and a couple of auxiliary parameters, tumor pressure, tumor flux, and tumor cell sinks and sources. We also model the changes in the vasculature by the stochastic graph grammar model, expressing the angiogenesis process. We use the finite element method in the isogeometric analysis (IGA) context employing higher-order and continuity B-spline basis functions for approximation of the scalar fields modeling the tumor progression process. We show that replacing the traditional solver algorithm using the loop through elements into the alternative approach employing the loop through global basis functions enables for efficient parallelization on GPGPU. We also employ classical code optimization techniques, includes multithreading organization, memory access, and nesting and unrolling the loops. The experiments performed on the Prometheus supercomputer reported the speed-up of more than 171 times in comparison to analogous CPU simulator for the 2563 problem size. We also employ the GPGPU code for the solution of an inverse problem of identification of model parameters for patient-specific data. To achieve this goal, we synchronize three different GPGPUs simulators. We use evolutionary algorithms to find a proper model and synchronization parameters matching the prescribed medical data.