Figure 4

Numerical simulation of secreted TGFβ1 diffusion in the chip system. (A) Schematic diagram showing 3-dimensional and side views of DOI for a simulation scenario where an empty hole is situated near eight neighboring holes occupied by cancer cells. (B) Distributions of the concentration difference of TGFβ1 (\({{\rm{\Delta }}C}_{\text{TGF}\beta 1})\) in the fibroblast region with respect to time. (C) Time evolution of \({{\rm{\Delta }}C}_{\text{TGF}\beta 1}\) at selected positions: (a) the center of the hole containing a single cancer cell, (b) the middle position between an empty hole and a tumor-occupied hole, and (c) the center of the empty hole. (D) Distribution of \({{\rm{\Delta }}C}_{\text{TGF}\beta 1}\) along the path (a-c) from a cancer cell-occupied hole to an empty hole for various time. (E) Hyperbolic curve fitting (solid lines) to determine exposure condition. The minimum amount of TGFβ1 exposure for highly probable autophagy activation was determined as the upper bound (red symbols) and the maximum amount of TGFβ1 exposure that is unlikely to induce autophagy was determined as the lower bound (black symbols). (F) Contour plot of the TGFβ1 exposure (\({{\rm{J}}}_{\text{TGF}{\rm{\beta }}1}\)) in (distance, exposure time)-space, where the numerical simulation was conducted. Based on \({{\rm{J}}}_{\text{TGF}\beta 1}={\int }_{0}^{{\rm{T}}}({{\rm{\Delta }}C}_{\text{TGF}\beta 1}+{\rm{b}}){\rm{d}}{\rm{t}}\), the exposure condition space can be divided into high, intermediate, and low probable regimes for autophagy activation. The optimized exposure time, which is sufficiently short so as not to affect autophagy induction via TGFβ1 diffusion from neighbor tumors and sufficiently long to induce autophagy activation at their own position, can be decided by the contour plot.