Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations under suitable assumptions on the domain velocity. Moreover, we quantify the associated modelling errors by establishing a-priori estimates in evolving Bochner spaces. In particular, we show that the modelling error decreases with the characteristic vessel diameter and thus vanishes for infinitely slender vessels. Numerical tests in idealized geometries corroborate and extend upon our theoretical findings.

翻译：从全维度溶质输运模型出发，我们推导并分析了脉动血管与血管周网络中及周围区域的时间依赖对流、扩散和交换的多维度模型。这些模型广泛适用于模拟血管化组织、脑部血管周间隙、维管植物及类似环境中的输运过程。我们在对区域速度施加适当假设的条件下，证明了全维度和多维度方程解的存在性与唯一性。此外，通过在演化Bochner空间中建立先验估计，我们量化了相关联的建模误差。特别地，研究表明建模误差随特征血管直径减小而降低，并在血管无限细长时趋近于零。在理想化几何构型中的数值试验验证并拓展了我们的理论发现。