AUTHOR=Montes-Olivas Sandra , Marucci Lucia , Homer Martin 

TITLE=Mathematical Models of Organoid Cultures

JOURNAL=Frontiers in Genetics

VOLUME=Volume 10 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/genetics/articles/10.3389/fgene.2019.00873

DOI=10.3389/fgene.2019.00873

ISSN=1664-8021

ABSTRACT=Organoids are engineered three-dimensional tissue cultures derived from stem cells and capable of self-renewal and self-organization into a variety of progenitors and differentiated cell types. An organoid resembles the cellular structure of an organ and retains some of its functionalities while still being amenable to in vitro experimental study. Compared with two-dimensional cultures, the three-dimensional structure of organoids provides a more realistic environment and structural organization of in vivo organs. Similarly, organoids are better suited to reproduce signalling pathway dynamics in vitro, due to a more realistic physiological environment. As such, organoids are a valuable tool to explore the dynamics of organogenesis, and offer routes to personalized preclinical trials of cancer progression, invasion, and drug response. 
Complementary to experiments, mathematical and computational models are essential instruments in the description of spatiotemporal dynamics of organoids. Simulations of mathematical models allow the study of multiscale dynamics of organoids, at both intra- and inter-cellular levels.  Mathematical models also enable to understand the underlying mechanisms responsible for phenotypic variation, or the response to external stimulation, in a cost- and time-effective manner. 
Many recent studies have developed laboratory protocols to grow organoids resembling different organs such as intestine, brain, liver, pancreas, and mammary glands. However, the development of mathematical models specific to organoids remains comparatively underdeveloped. Here, we review the mathematical and computational approaches that exist to describe and predict organoid dynamics, the simulation frameworks used, and their strengths and limitations.