School of Mathematics and Statistics, University of Melbourne, Australia.
School of Mathematics and Statistics, University of Melbourne, Australia; Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Australia.
J Theor Biol. 2023 Sep 21;573:111592. doi: 10.1016/j.jtbi.2023.111592. Epub 2023 Aug 7.
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.
人们越来越认识到在组织内模拟病毒传播的空间动力学模型的实用性。多细胞模型将细胞表示为与病毒密度表面相连的离散空间区域，是捕获这些动力学的一种流行方法。传统上，通过离散化病毒表面并根据病毒扩散的速度和其他考虑因素来模拟此类模型，可以使用更精细或更粗糙的离散化。尚未研究这种选择对系统行为的影响。在这里，我们证明在现实的参数范围内 - 在病毒扩散足够小以支持形成熟悉的环形感染斑块的情况下 - 病毒表面的空间离散化选择可以定性地改变关键模型结果，包括感染的时间尺度。重要的是，我们表明，将病毒传播实现为细胞级过程还是高分辨率收敛 PDE 可以产生不同的模型结果，这就提出了关于支撑模型空间结构的假设强度的重要概念问题。我们研究了这些离散化伪影的驱动机制，它们可能对模型预测的影响，并提供了有关设计和实施病毒动力学的空间和特别是多细胞模型的指导。我们使用最简单的 TIV 结构来获取病毒动力学的结果，因此预计我们描述的重要影响也将影响病毒-细胞-免疫系统相互作用的更复杂模型的预测。这种分析将有助于构建稳健且具有生物学现实性的模型进行推理。
