Complex dynamics of multiple metastases under AT and CT-MTD.

The time evolution of the total cell population in the four metastases is shown in the sub-figures for Case I. The first and second columns show the results for the initial clumped and random cell configurations in the invisible metastasis, respectively. In each sub-figure, the blue, red, yellow, and black colors show the total cell populations in metastasis 1, metastasis 2, metastasis 3, and metastasis 4, respectively; the vertical cyan lines show the emergence time (ET) of the invisible metastasis, and the red line shows the TTP. The solid and dashed lines show results under CT-MTD and AT, respectively.</p

Cell configurations at the ET and TTP under CT-MTD and AT for Case I with the clumped invisible metastasis.

The red, blue, and white dots correspond to R-cells, S-cells, and empty sites. The gray dots show the sites that are accompanied by fibroblasts.</p

Cell configurations for CAF-mediated tumor growth.

Cell configurations at different times under CT-MTD (continuous MTD therapy) for all type of fibroblast configurations. Each row shows results for one type of fibroblast configuration. The blue and orange dots show the S-cells and R-cells respectively and the purple shaded areas show the fibroblast regions. Specification of the fibroblast region is shown in the section Initial and boundary conditions.</p

Temporal change of cell configuration of different metastatic lesions for case I (Fig 11) with clumped invisible metastasis.

The red, blue, and white dots correspond to R-cells, S-cells, and empty sites respectively. The gray dots show the sites that are accompanied by CAFs. The first and second row show results for CT-MTD and AT respectively. (MP4)</p

Temporal change of cell configuration for different fibroblast distributions.

The video shows the evolution of tumor for different fibroblast structures (column wise) for clumped initial cell configuration under CT-MTD (first row) and AT (second row). The red, blue, and white dots correspond to R-cells, S-cells, and empty sites respectively. (MP4)</p

Initial cell configurations for the four cases with an invisible clumped metastasis.

The red, blue, and white dots correspond to R-cells, S-cells, and empty sites. The gray dots shows the sites accompanied by CAFs.</p

Cells’ life cycle.

Flow chart of the cells’ life cycle. In each time step, all of the cells follow the steps in the flow chart.</p

The parameter values are listed in the following table.

The parameter values are listed in the following table.</p

Consequences of CAF-mediated resistance with clumped initial R-cell distribution.

(A) The time evolution of the average of the total cell population () in the 30 simulations is shown for CT-MTD for all types of fibroblast configurations. NoF: no fibroblast, FC: fibroblast overlapping with the R-cell clump at the center of domain, FCp: fibroblast partially overlapping with the R-cell clump at the center, FSq: fibroblast completely surrounding the R-cell clump. FSp: fibroblast over a “L” shaped region, partially surrounding the R-cell clump, FR: fibroblast clumps randomly placed in the domain. (B) Boxplot of the time to progression (TTP) in the 30 realizations under CT-MTD. (C) Boxplot of the time to progression (TTP) in the 30 realizations under AT is shown. (D) Correlation of TTP with the area of impact is shown. The circles and the asterisks (the colors are similar to the legend in A) show the TTP under CT-MTD and AT respectively. The solid and dashed lines are the respective regression lines (sold line: CT-MTD, dashed line: AT). The p − values for AT and CT-MTD indicate significance of the correlation. (E) Time gain (TG) is shown as boxplots for all six types of fibroblast distributions.</p

Initial cell configurations.

Three types of initial cell configurations. Orange dots: R-cells, blue dots: S-cells, white dots: empty sites. Clumped R cells (first), random R-cells (center), and uniform R-cells (right).</p