Multiscale Parallel Simulation of Malignant Pleural Mesothelioma via Adaptive Domain Partitioning -- an Efficiency Analysis Study

TL;DR

The study tackles the computational burden of multiscale malignant pleural mesothelioma simulations by coupling a Cellular Potts Model with diffusion–reaction PDEs on a CT-derived pleural-space geometry. It introduces adaptive domain partitioning with a dynamic bounding box and a parallel FiPy-based PDE solver invoked via mpi4py to confine computation to the region of interest and balance load. Performance metrics such as $T_{Serial}$, $T_{Parallel}$, $S_p = T_{Serial}/T_{Parallel}$, and $E_p = S_p/p$ reveal speedups up to about $S_p \approx 1.8$–$1.95$ on 4 cores for domain sizes $100^3$ to $200^3$, with diminishing returns at higher core counts due to communication overhead; the dynamic bounding box significantly reduces memory usage and enables PC-scale execution. The work provides a scalable framework for large-scale MPM simulations, with proposed future enhancements including automated core allocation, scalability assessments to larger domains, and adaptive meshing to further optimize speed and memory usage.

Abstract

A novel parallel efficiency analysis on a framework for simulating the growth of Malignant Pleural Mesothelioma (MPM) tumours is presented. Proliferation of MPM tumours in the pleural space is simulated using a Cellular Potts Model (CPM) coupled with partial differential equations (PDEs). Using segmented lung data from CT scans, an environment is set up with artificial tumour data in the pleural space, representing the simulation domain, onto which a dynamic bounding box is applied to restrict computations to the region of interest, dramatically reducing memory and CPU overhead. This adaptive partitioning of the domain enables efficient use of computational resources by reducing the three-dimensional (3D) domain over which the PDEs are to be solved. The PDEs, representing oxygen, nutrients, and cytokines, are solved using the finite-volume method with a first-order implicit Euler scheme. Parallelization is realized using the public Python library mpi4py in combination with LinearGMRESSolver and PETSc for efficient convergence. Performance analyses have shown that parallelization achieves a reduced solving time compared to serial computation. Also, optimizations enable efficient use of available memory and improved load balancing amongst the cores.

Figures (7)

• Figure 1: Flowchart depicting the multiscale modelling workflow, starting from organ-level CT segmentation and progressing through tissue-level domain definition, cell-level CPM dynamics and parallel continuum-level PDE computations. Everything takes place in the Compucell3D Steppables with exception of the Parallel execution.
• Figure 2: Computational domain generated from CT scans. (A) Zoomed in MPM tumour. (B) Visceral pleura extracted from CT scan segmentation. (C) Tumour in the pleural space. For visualization purposes the parietal pleura is not shown. (D) Bounding box around the tumour, used to reduce the computational demand.
• Figure 3: PDE solver computational time per time step for three different domain sizes using different number of cores
• Figure 4: Parallel speedup for various numbers of cores for the three respective domain sizes.
• Figure 5: Parallel efficiency for various numbers of cores for the three respective domain sizes.