Modeling tumor growth with peridynamics

A morpho-viscoelasticity theory for growth in proliferating aggregates

Despite significant research efforts in the continuum modeling of biological growth, certain aspects have been overlooked. For instance, numerous investigations have examined the influence of morphogenetic cell behaviors, like division and intercalation, on the mechanical response of passive (non-growing) tissues. Yet, their impact on active growth dynamics remains inadequately explored. A key reason for this inadequacy stems from challenges in the continuum treatment of cell-level processes. While some coarse-grained models have been proposed to address these shortcomings, a focus on cell division and cell expansion has been missing, rendering them unusable when it comes to modeling growth. Moreover, existing studies are limited to two-dimensional tissues and are yet to be formally extended to three-dimensional multicellular systems. To address these limitations, we here present a generalized multiscale model for three-dimensional aggregates that accounts for complex morphogenetic movements that include division, expansion, and intercalation. The proposed continuum theory thus allows for a comprehensive exploration into the growth and dissipation mechanics of proliferating aggregates, such as spheroids and organoids.

Computing whole embryo strain maps during gastrulation

Gastrulation is a critical process during embryonic development that transforms a single-layered blastula into a multilayered embryo with distinct germ layers, which eventually give rise to all the tissues and organs of the organism. Studies across species have uncovered the mechanisms underlying the building blocks of gastrulation movements, such as localized in-plane and out-of-plane epithelial deformations. The next challenge is to understand dynamics on the scale of the embryo: this requires quantifying strain tensors, which rigorously describe the differences between the deformed configurations taken on by local clusters of cells at time instants of observation and their reference configuration at an initial time. We present a systematic strategy for computing such tensors from the local dynamics of cell clusters, which are chosen across the embryo from several regions whose morphogenetic fate is central to viable gastrulation. As an application of our approach, we demonstrate a strategy of identifying distinct Drosophila morphological domains using strain tensors.

Quantifying the relationship between cell division angle and morphogenesis through computational modeling

When biological cells divide, they divide on a given angle. It has been shown experimentally that the orientation of cell division angle for a single cell can be described by a probability density function. However, the way in which the probability density function underlying cell division orientation influences population or tissue scale morphogenesis is unknown. Here we show that a computational approach, with thousands of stochastic simulations modeling growth and division of a population of cells, can be used to investigate this unknown. In this paper we examine two potential forms of the probability density function: a wrapped normal distribution and a binomial distribution. Our results demonstrate that for the wrapped normal distribution the standard deviation of the division angle, potentially interpreted as biological noise, controls the degree of tissue scale anisotropy. For the binomial distribution, we demonstrate a mechanism by which direction and degree of tissue scale anisotropy can be tuned via the probability of each division angle. We anticipate that the method presented in this paper and the results of these simulations will be a starting point for further investigation of this topic.