Fig 1.
Schematic of TME computational domain with different scales including tissue, cellular, and molecular scales.
Vessels sprout form the circular "mother vessel" at the periphery of the domain. A tumor is seeded at the center. The hybrid approach follows the dynamics of cells, vessels, growth factors, oxygen and nutrients in the growing tumor and surrounding normal tissue.
Fig 2.
Computational flowchart of the TME model including molecular (green), cellular (red) and tissue-size (blue) scales.
The spatiotemporal distributions of molecular agents, along with cellular properties, are calculated within the continuous domain of the model using the finite difference method (FDM). This approach enables the determination of cellular phenotypes and dynamics, which collectively contribute to the formation of tissue-scale accumulations. At the tissue scale, a hybrid continuous-discrete method is employed to integrate the discrete agents, such as tumor and endothelial cells, with the continuous fields of the tissue, including hemodynamics and interstitial fluid flow. This approach enables the simultaneous modeling and interaction of discrete cellular entities within the continuous environment of the tissue.
Fig 3.
Simulated time course of tumor growth and vascularization without treatment.
The side and top views show the three-dimensional tumor and vascular supply for days 36, 39, 42, 45, and 48. The contour plots show the distributions of cell types including proliferative (green), quiescent (orange), and necrotic (yellow) cancer cells along with normal tissue (blue) at the middle cross-section of the domain. We use the well-vascularized tumor from day 36 as the initial condition for testing drug regimens. Stochastic events in the model result in heterogenous tumor growth, angiogenesis and cell phenotype, which influence the delivery and efficacy of drugs.
Fig 4.
Dose schedules of anti-cancer and anti-angiogenesis drugs.
We simulate a maximum tolerated dose (MTD) of the anti-cancer drug, Cisplatin (half-life: 30 min) on day 36 (A), metronomic therapy with Cisplatin, applying daily doses (20% MTD [89]) starting on day 36 (B). We then combined anti-angiogenesis (AA) with MTD (C, “AA+MTD α-Cancer”) or metronomic anti-cancer treatment (D, “AA+M α-Cancer”), both starting on day 36. Red solid lines are the normalized anti-cancer drug concentration in the plasma, and blue dashed-lines are the normalized anti-angiogenic drug plasma concentration.
Fig 5.
Spatial maps of interstitial fluid pressure (IFP, top panels) and anti-cancer drug distribution in the tumor and surrounding tissue (bottom panels).
The gray lines in the anti-cancer drug maps delineate the tumor. Treatment with anti-VEGF decreases vessel permeability, preserving the transvascular pressure that drives blood plasma perfusion and interstitial fluid flow. The drug administration schedules are shown below each panel (blue: Anti-angiogenic (AA) drug; red: cisplatin). Note that the metronomic and anti-VEGF treatments can decrease tumor IFP, and that there are differences in drug exposure to the tumor and normal tissues with the various treatments.
Fig 6.
Drug delivery is affected by treatment.
Drug concentration in the tumor (A) and normal tissue (B) during different chemotherapy regimens (MTD anti-cancer "MTD," metronomic anti-cancer "M", combination anti-angiogenesis and MTD treatment "AA+MTD", and combination anti-angiogenic and metronomic, "AA+M"). the drug concentrations are normalized with the MTD injection dose. C) Drug delivery factor (calculated by integrating drug concentration over the viable cancer cells over time, normalized by the total number of live cancer cells) for different chemotherapy approaches. D) Spatial average of tumor IFP during different therapeutic regimens.
Fig 7.
Simulated tumor growth and angiogenesis before and during different treatment regimens.
Treatment schedules are detailed in Fig 4) Each top row shows the three-dimensional morphology of the tumor and angiogenic vessels, and the corresponding lower panels show the central cross-section of the tumor in the y-z plane (side view) or x-y plane (top view). Various cell phenotypes are indicated by the contour plot colors: normal tissue around tumor (blue), proliferating cancer cells (green), quiescent cancer cells (orange), and necrotic cancer cells (yellow). The various treatments result in dramatic differences in tumor morphology and viability status.
Fig 8.
Effect of various treatment regimens on cancer cell viability.
A) viable cancer cell number (proliferating plus quiescent), B) number of necrotic cells, C) total number of cancer cells (live and dead) in the tumor. The violet dashed line in panel A shows the maximum allowable tumor size for the simulations; beyond this size, the untreated (control) tumor outgrows the domain at day 48 (the last day of the untreated tumor).
Fig 9.
Hypoxic ratio (A) and hypoglycemic ratio (B) of the tumor under different chemotherapy approaches (MTD, M, AA+MTD, AA+M). MTD therapy results in the largest variation in hypoxia and hypoglycemia in the tumor because of transport limitations in the TME.
Fig 10.
Distribution of tumor clusters with different sizes at day 78 (number of cells in each cluster) for tumors treated with MTD (A), AA+MTD (B), M (C), AA+M (D). The width of each bar is proportional to the number of clusters of that size at a given location. Note the larger dispersion of the clusters in A and B, and the more localized clustering in C and D.