Fig 1.
Flow diagram of the coupled in-silico cancer modelling solver.
Diagram depicting all major compartments of the multiscale, multiphysics, in-silico cancer, angiogenesis and drug modelling framework, where the interaction between the biochemical and drug delivery module, the vascular network module and the solid and fluid mechanics solver modules is illustrated using arrows. Dotted arrows denote an implicit interplay between the corresponding compartments of the multiphysics in-silico framework.
Fig 2.
IFV depends on both vessel poresize and drug affinity.
Line plots of the averaged interstitial fluid velocity (IFV) magnitude as a function of time. The 2×2 matrix of plots shows the results for two poresizes (A,B: rp = 10 nm; C,D: rp = 150 nm) and two affinities (A,C: kon = 0.005 s-1; B,D: kon = 5 s-1). Each line plot depicts the control (no drug injected), and the in-silico predictions with drug injected at day 10 (D10), day 20 (D20) or day 30 (D30). See also S2 Fig. for simulation results involving intermediate values of poresize and affinity.
Fig 3.
Tumour regression depends on vessel poresize for low affinity but not high affinity drugs.
Line plots of the relative tumour volume (V = Vol.(t)/Vol.(t = 0)−1) versus time. The 2×2 matrix of plots shows the results for two poresizes (A,B: rp = 10 nm; C,D: rp = 150 nm) and two affinities (A,C: kon = 0.005 s-1; B,D: kon = 5 s-1). Each line plot depicts the control (no drug injected), and the in-silico predictions with drug injected at day 10 (D10), day 20 (D20) or day 30 (D30). See also S4 Fig for simulation results involving intermediate values of poresize and affinity.
Fig 4.
Snapshots of tumour growth and angiogenesis over time.
Simulation results visualisation comparison of the control (centre row) versus the treated case for low poresize, rp, and two extreme affinity ratio, kon, values (0.005 s-1 and 5 s-1). From left to right, the snapshots at the second column correspond to day 11, the third column to day 21, the fourth column to day 31, and the last column to day 40. Note for low affinity (bottom three rows) the low drug concentration in the tumour, while for high affinity (top three rows), as expected, the significant concentration of the cytotoxic drug. Notably, drug distribution is very heterogeneous for early-stage injections due to the non-hierarchical structure of the immature tumour vessels, thus, supporting the argument of the the spatio-temporal variability of the vascular tree in mammary tumours. Also, comparing the top right snapshot with the bottom counterpart, the tumour is fairly more regressed for high drug affinity—see also Fig 3C and 3A respectively.
Fig 5.
THP and IFP normalisation depends on vessel poresize for low affinity but not high affinity drugs.
Line plots of (A—D) tissue hydrostatic pressure (THP), and (E—H) interstitial fluid pressure (IFP), as a function of time. Each 2×2 matrix of plots shows the results two poresizes and two affinities: rp = 10 nm or 150 nm, and kon = 0.005 s-1 or 5 s-1 respectively. Each line plot shows the in-silico predictions for the control and the treated, with drug injected at day 10 (D10), day 20 (D20) or day 30 (D30). See also S5 and S6 Figs for simulation results involving intermediate values of poresize and affinity. Negative THP in (A—D) denotes compressive stress.
Fig 6.
Vascular architecture normalisation depends on vessel poresize for low affinity but not high affinity drugs.
Line plots of (A—D) maximum distance between adjacent vessels (δmax; normalised), and (E—H) vessel distribution convexity (λ), as a function of time. Each 2×2 matrix of plots shows the in-silico predictions for two poresizes and two affinities: rp = 10 nm or 150 nm, and kon = 0.005 s-1 or 5 s-1 respectively, while each plot depicts the results for the control and the treated, with drug injected at day 10 (D10), day 20 (D20) or day 30 (D30). See also S7 and S8 Figs for simulation results involving intermediate values of poresize and affinity.
Fig 7.
Increasing drug affinity widens the window for vascular normalisation.
Contour plots of (A—D) maximum distance between adjacent vessels, δmax, and (E—H) vessel distribution convexity, λ, with respect to tumour development time and injection time. Each 2×2 matrix of contours depicts the results for two poresizes and two affinities: rp = 10 nm or 150 nm, and kon = 0.005 s-1 or 5 s-1 respectively. See also corresponding S9 and S10 Figs for simulation results involving intermediate values of poresize and affinity.
Fig 8.
High drug affinity ratio and large vessel poresize increases delivery efficacy potential.
Contour plots of the percentage of drug concentrated in the tumour, ch, as a function of vascular network structural parameters λ and δmax. Note that the common logarithm of ch is taken, as ch can vary by over a factor of 10 between the lowest and highest affinity ratios and poresize. The contours contained in the 2×2 matrix illustrates the in-silico results for two poresizes (A,B: rp = 10 nm; C,D: rp = 150 nm) and two affinities (A,C: kon = 0.005 s-1; B,D: kon = 5 s-1). See also S11 Fig for simulation results involving intermediate values of poresize and affinity.