Stefan Engblom, Uppsala Universitet
This presentation explores some stochastic modeling approaches for
spatially extended biological processes. The motivation is drawn from
diverse scenarios such as wound healing, gradient sensing in migrating
cells, colon crypt development, and quorum sensing mechanisms. A
significant modeling challenge lies in efficiently capturing dynamic
cell-to-cell communication within evolving cell populations.
Beginning with a brief review of our work in the reaction-diffusion
master equation framework, ideal for highly resolved models of
individual cells, we then shift our focus to the cell population. We
present a dedicated computational framework designed to address the
scale separation intrinsic to such applications, thus emphasizing
In a concrete example of modeling cancer research, we tackle the
recurring theme of avascular tumor growth, often expressed through
PDEs borrowed from fluid dynamics. We propose a discrete stochastic
model and derive an approximate mean-field PDE, facilitating a
comprehensive analysis of the model’s behavior and the impact of key
parameters and responses of interest.
 E. Blom and S. Engblom, Morphological stability for in silico models of
avascular tumors (preprint 2023), http://arxiv.org/abs/2309.07889
 S. Engblom, Stochastic simulation of pattern formation in growing
tissue: a multilevel approach, Bull. Math. Biol. (2018).
 S. Engblom, D. B. Wilson, and R. E. Baker, Scalable
population-level modeling of biological cells incorporating
mechanics and kinetics in continuous time, Roy. Soc. Open
Sci. 5(8) (2018).
 A. Chevallier, and S. Engblom, Pathwise error bounds in Multiscale
variable splitting methods for spatial stochastic kinetics, SIAM
J. Numer. Anal. 56(1):469–498 (2018).
 S. Engblom, Strong convergence for split-step methods in
stochastic jump kinetics, SIAM J. Numer. Anal. 53(6):2655–2676