We construct a three-dimensional anatomically accurate multicellular model of a parotid gland acinus to investigate the influence that the topology of its lumen has on primary fluid secretion. Our model consists of seven individual cells, coupled via a common lumen and intercellular signalling. Each cell is equipped with the intracellular calcium ( $$\mathrm{Ca}^{2+}$$ Ca 2 + )-signalling model developed by Pages et al, Bull Math Biol 81: 1394–1426, 2019. https://doi.org/10.1007/s11538-018-00563-z and the secretion model constructed by Vera-Sigüenza et al., Bull Math Biol 81: 699–721, 2019. https://doi.org/10.1007/s11538-018-0534-z . The work presented here is a continuation of these studies. While previous mathematical research has proven invaluable, to the best of our knowledge, a multicellular modelling approach has never been implemented. Studies have hypothesised the need for a multiscale model to understand the primary secretion process, as acinar cells do not operate on an individual basis. Instead, they form racemous clusters that form intricate water and protein delivery networks that join the acini with the gland’s ducts-questions regarding the extent to which the acinus topology influences the efficiency of primary fluid secretion to persist. We found that (1) The topology of the acinus has almost no effect on fluid secretion. (2) A multicellular spatial model of secretion is not necessary when modelling fluid flow. Although the inclusion of intercellular signalling introduces vastly more complex dynamics, the total secretory rate remains fundamentally unchanged. (3) To obtain an acinus, or better yet a gland flow rate estimate, one can multiply the output of a well-stirred single-cell model by the total number of cells required.

中文翻译：

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腮腺初级唾液分泌的多细胞模型

我们构建了腮腺腺泡的三维解剖学准确多细胞模型，以研究其腔的拓扑结构对初级液体分泌的影响。我们的模型由七个单独的细胞组成，通过共同的管腔和细胞间信号传导耦合。每个细胞都配备有由 Pages 等人开发的细胞内钙 ( $$\mathrm{Ca}^{2+}$$ Ca 2 + )-信号模型，Bull Math Biol 81: 1394–1426, 2019. https:/ /doi.org/10.1007/s11538-018-00563-z 和 Vera-Sigüenza 等人构建的分泌模型，Bull Math Biol 81: 699–721, 2019. https://doi.org/10.1007/s11538- 018-0534-z。这里介绍的工作是这些研究的延续。虽然以前的数学研究已被证明是无价的，但据我们所知，多细胞建模方法从未实施过。研究假设需要一个多尺度模型来了解初级分泌过程，因为腺泡细胞不是在个体基础上运作的。相反，它们形成总状簇，形成复杂的水和蛋白质输送网络，将腺泡与腺体的导管连接起来——关于腺泡拓扑结构影响初级液体分泌效率的程度的问题持续存在。我们发现（1）腺泡的拓扑结构对液体分泌几乎没有影响。(2) 在模拟流体流动时，不需要分泌的多细胞空间模型。尽管包含细胞间信号传导引入了更加复杂的动力学，但总分泌率从根本上保持不变。(3) 为了获得腺泡，或者更好的腺体流速估计值，