Phase transition-related parameters.

As a powerful but computationally intensive method, hybrid computational models study the dynamics of multicellular systems by evolving discrete cells in reacting and diffusing extracellular microenvironments. As the scale and complexity of studied biological systems continuously increase, the exploding computational cost starts to limit large-scale cell-based simulations. To facilitate the large-scale hybrid computational simulation and make it feasible on easily accessible computational devices, we develop Gell (GPU Cell), a fast and memory-efficient open-source GPU-based hybrid computational modeling platform for large-scale system modeling. We fully parallelize the simulations on GPU for high computational efficiency and propose a novel voxel sorting method to further accelerate the modeling of massive cell-cell mechanical interaction with negligible additional memory footprint. As a result, Gell efficiently handles simulations involving tens of millions of cells on a personal computer. We compare the performance of Gell with a state-of-the-art paralleled CPU-based simulator on a hanging droplet spheroid growth task and further demonstrate Gell with a ductal carcinoma in situ (DCIS) simulation. Gell affords ~150X acceleration over the paralleled CPU method with one-tenth of the memory requirement.</div

HDS simulation with altered phenotype.

The 60-um thick central slices of simulated spheroids with various cellular mechanical properties. All the spheroids start with a small cluster of 2347 randomly placed cells, and the cultivation duration is 450 hours. (a) The reference spheroid ends up with 0.9 million cells and a diameter of 1.87 mm. (b) Spheroid of tumor cells with no swelling during early necrosis, with 0.9 million cells and a diameter of 1.8 mm. (c) Spheroid of tumor cells with the cell-cell adhesion suppressed, with 1.0 million cells and a diameter of 1.97 mm. (d) Spheroid of tumor cells with the cell-cell adhesion enhanced, with 0.66 million cells and a diameter of 1.53 mm.</p

Simulation results of DCIS development.

(a) Ductal carcinoma in situ simulation with duct radius of 150 μm. (b) Linear DCIS growth under various duct radius conditions.</p

Cell volume growth related parameters.

As a powerful but computationally intensive method, hybrid computational models study the dynamics of multicellular systems by evolving discrete cells in reacting and diffusing extracellular microenvironments. As the scale and complexity of studied biological systems continuously increase, the exploding computational cost starts to limit large-scale cell-based simulations. To facilitate the large-scale hybrid computational simulation and make it feasible on easily accessible computational devices, we develop Gell (GPU Cell), a fast and memory-efficient open-source GPU-based hybrid computational modeling platform for large-scale system modeling. We fully parallelize the simulations on GPU for high computational efficiency and propose a novel voxel sorting method to further accelerate the modeling of massive cell-cell mechanical interaction with negligible additional memory footprint. As a result, Gell efficiently handles simulations involving tens of millions of cells on a personal computer. We compare the performance of Gell with a state-of-the-art paralleled CPU-based simulator on a hanging droplet spheroid growth task and further demonstrate Gell with a ductal carcinoma in situ (DCIS) simulation. Gell affords ~150X acceleration over the paralleled CPU method with one-tenth of the memory requirement.</div

HDS simulation result after 450 hours.

(a) Cell cluster generated by Gell. (b) 60 μm thick central slice of the HDS simulation result shows the microstructure of the necrotic core of Gell simulation. (c) central slice of PhysiCell showing identical microstructure. Both spheroids have a radius of 1.87 mm.</p

Performance scaling of Gell.

As a powerful but computationally intensive method, hybrid computational models study the dynamics of multicellular systems by evolving discrete cells in reacting and diffusing extracellular microenvironments. As the scale and complexity of studied biological systems continuously increase, the exploding computational cost starts to limit large-scale cell-based simulations. To facilitate the large-scale hybrid computational simulation and make it feasible on easily accessible computational devices, we develop Gell (GPU Cell), a fast and memory-efficient open-source GPU-based hybrid computational modeling platform for large-scale system modeling. We fully parallelize the simulations on GPU for high computational efficiency and propose a novel voxel sorting method to further accelerate the modeling of massive cell-cell mechanical interaction with negligible additional memory footprint. As a result, Gell efficiently handles simulations involving tens of millions of cells on a personal computer. We compare the performance of Gell with a state-of-the-art paralleled CPU-based simulator on a hanging droplet spheroid growth task and further demonstrate Gell with a ductal carcinoma in situ (DCIS) simulation. Gell affords ~150X acceleration over the paralleled CPU method with one-tenth of the memory requirement.</div

Melanoma cell line spheroids.

Two spheroids of the same melanoma cell line (A2508) show distinct pattern differences in necrotic core microstructures due to differences in cell treatment. Images are adapted from [33], and treatment details are not mentioned in the original literature. (a) A pimonidazole stained spheroid. (b) A hematoxylin and eosin stained spheroid. Adapted from [33] with permission.</p

Gell simulation speedup with respect to PhysiCell.

Gell simulation speedup with respect to PhysiCell with varying cell numbers (a), domain voxel numbers (b), and PhysiCell CPU thread numbers (c with logarithmic x scale).</p

The execution time cost of each simulation module in Gell.

The execution time cost of each simulation module in Gell.</p

Simulation result analysis of Gell.

(a) Whole tumor radius and necrotic core radius change over the HDS growth. (b) Number change of total tumor cells and necrotic tumor cells over the HDS growth.</p