Mathematical Model of Tumour Spheroid Experiments with Real-Time Cell Cycle Imaging

Abstract

Three-dimensional (3D) in vitro tumour spheroid experiments are an important tool for studying cancer progression and potential drug therapies. Standard experiments involve growing and imaging spheroids to explore how different experimental conditions lead to different rates of spheroid growth. These kinds of experiments, however, do not reveal any information about the spatial distribution of the cell cycle within the expanding spheroid. Since 2008, a new experimental technology called fluorescent ubiquitination-based cell cycle indicator (FUCCI), has enabled

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

“…However, a more biologically realistic and meaningful model would incorporate a three-dimensional (3D) environment (e.g. [51]). By constraining our model to a 2D hexagonal lattice, we ultimately omit realistically modelling: the spatial supply of oxygen, nutrients and drugs; the orientation in 3D space; and interactions with the extracellular matrix [19,52].…”

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

“…Using the IBM we are able to describe the spatial and temporal densities of living agents in various phases of the cell cycle (G1, eS and S/G2/M) as well as G1-arrested agents. We plot each density profile as a function of the distance from the periphery as this allows us to compare various profiles as the size of the spheroid increases [9, 37].…”

“…Continuum mathematical models of tumour spheroids have been developed, analysed, and deployed for over 50 years [10][11][12][13][14][15][16][17][18], and these developments have included very recent adaptations of classical models so that they can be used to study tumour spheroids with FUCCI [9]. However, continuum modelling approaches lack the ability to track individual cells within the growing population, and typically neglect heterogeneity and stochasticity within the population.…”

“…Late time growth is characterised by the formation of a central necrotic region, indicated by a complete absence of fluorescence. FUCCI allows us to identify both the position of individual cells within the growing spheroid in three spatial dimensions, as well as identifying cell cycle status, giving rise to the notion of a four-dimensional (4D) tumour spheroid [9]. Assuming spherical symmetry, we can characterise the geometry of 4D spheroids by three radii: r o ( t ) > 0 is the outer radius, r a ( t ) ≥ 0 is the arrested radius, and r n ( t ) ≥ 0 is the necrotic radius, with r o ( t ) > r a ( t ) ≥ r n ( t ).…”

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using Approximate Bayesian Computation

“…However, a more biologically realistic and meaningful model would incorporate a three-dimensional (3D) environment (e.g. Jin et al, 2021). By constraining our model to a 2D hexagonal lattice, we ultimately omit realistically modelling: the spatial supply of oxygen, nutrients and drugs; the orientation in 3D space; and interactions with the extracellular matrix (Beaumont et al, 2014;Smalley et al, 2006).…”