Mathematical Models of Organoid Cultures

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 functionality, 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 signaling 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 valuable instruments in the description of spatiotemporal dynamics of organoids. Simulations of mathematical models allow the study of multiscale dynamics of organoids, at both the intracellular and intercellular levels. Mathematical models also enable us to understand the underlying mechanisms responsible for phenotypic variation and 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 the 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 proposed so far to describe and predict organoid dynamics, reporting the simulation frameworks used and the models’ strengths and limitations.

Mathematical modelling reveals cellular dynamics within tumour spheroids

“…A wide range of models have been developed to describe the growth and mechanical properties of tumour spheroids [ 6 – 8 ] and organoids [ 9 , 10 ] and their response to treatment [ 11 , 12 ]. The simplest models, which include logistic growth and Gompertzian growth, recapitulate the characteristic sigmoid curve describing how the total spheroid volume changes over time [ 13 – 15 ].…”

Long-term live imaging of epithelial organoids and corresponding multiscale analysis reveal high heterogeneity and identify core regulatory principles

“…They can be used to predict organoid behaviour in conditions that are challenging to implement in experiments or when perturbations of normal conditions occur (Dahl-Jensen et al, 2017; Eils et al, 2013). However, only relatively few models for organoid systems have been developed (Montes-Olivas et al, 2019).…”

“…In summary, the simulation of epithelial organoid growth predicts organoid behaviour and helps to understand the intrinsic mechanisms responsible for the organoid phenotype. Further, it is straightforward to generate a cost- and time-effective tool to predict possible outcomes of external stimuli like drug treatments for instance (Montes-Olivas et al, 2019).…”

Toward Engineering Biosystems With Emergent Collective Functions

“…In contrast to simple logic circuits, the complexity of the molecular interactions and mechanical forces underpinning these processes motivate the use of multi-agent modeling to better understand how developmental programs work in morphogenetic systems. In particular, multi-agent models are able to capture the role of cellular heterogeneity, proliferation and morphology, mechanical and environmental cues, movement of cells as well as the integration of multiple processes at diverse scales and the feedback between these ( Montes-Olivas et al, 2019 ). Such models have helped deepen our understanding of early mammalian embryogenesis ( Godwin et al, 2017 ), as well as the formation of vascular networks ( Perfahl et al, 2017 ) and other complex structures and organs, including the skin, lung ( Stopka et al, 2019 ), kidney ( Lambert et al, 2018 ), and brain ( Caffrey et al, 2014 ).…”