Designing and interpreting 4D tumour spheroid experiments

Abstract

Tumour spheroid experiments are routinely used to study cancer progression and treatment. Various and inconsistent experimental designs are used, leading to challenges in interpretation and reproducibility. Using multiple experimental designs, live-dead cell staining, and real-time cell cycle imaging, we measure necrotic and proliferation-inhibited regions in over 1000 4D tumour spheroids (3D space plus cell cycle status). By intentionally varying the initial spheroid size and temporal sampling frequencies across multiple cell lines, we collect an abundance of measurements of internal spheroid structure. These data are difficult to compare and interpret. However, using an objective mathematical modelling framework and statistical identifiability analysis we quantitatively compare experimental designs and identify design choices that produce reliable biological insight. Measurements of internal spheroid structure provide the most insight, whereas varying initial spheroid size and temporal measurement frequency is less important. Our general framework applies to spheroids grown in different conditions and with different cell types.

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

“…By contrast, the spheroid in figure 6 is larger with rofalse(0false)=274 μm and we see a clear necrotic core at t=3 days. This highlights the importance of taking great care with measurements at the beginning of the experiment [17].

Figure 7Modelling results for the population growth of different spheroid populations, averaged over 10 simulations with ( a ) identical initial conditions for each realization and ( b ) introduced experimental variability in initial spheroid radius and population, with the agent density held constant and initial radius rofalse(tfalse)∈false[232.75,235.47,238.97,242.19,244.89,247.76,247.93,251.23,251.48,260.13false] μm.

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“…We now compare and analyse images and measurements from a range of in vitro experiments and in silico simulations. All experiments use the WM793B melanoma cell line, which takes approximately 4 days to form spheroids after the initial seeding in the experiments [17]. This means that t=0 days corresponds to 4 days after seeding to give the experimental spheroids sufficient time to form.…”

“…We use definitions in electronic supplementary material, §S1 (Confocal imaging) to identify the lower and upper cross sections in both the experimental and simulation images. While previous studies have often compared model predictions with experimental observations at a single cross section [17,22], we aim to provide more comprehensive information about the internal structure of the spheroid by making comparisons at multiple locations. At the beginning of the experiment, in all cross sections (in vitro and in silico), we see the population is relatively uniform, with an even distribution of colours, suggesting the entire spheroid is composed of freely cycling cells.…”

“…By contrast, the spheroid in figure 6 is larger with r o ð0Þ ¼ 274 mm and we see a clear necrotic core at t ¼ 3 days. This highlights the importance of taking great care with measurements at the beginning of the experiment [17].…”

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