BackgroundInflux and clearance of substances in the brain parenchyma occur by a combination of diffusion and convection, but the relative importance of these mechanisms is unclear. Accurate modeling of tracer distributions in the brain relies on parameters that are partially unknown and with literature values varying by several orders of magnitude. In this work, we rigorously quantified the variability of tracer distribution in the brain resulting from uncertainty in diffusion and convection model parameters.MethodsUsing the convection–diffusion–reaction equation, we simulated tracer distribution in the brain parenchyma after intrathecal injection. Several models were tested to assess the uncertainty both in type of diffusion and velocity fields and also the importance of their magnitude. Our results were compared with experimental MRI results of tracer enhancement.ResultsIn models of pure diffusion, the expected amount of tracer in the gray matter reached peak value after 15 h, while the white matter did not reach peak within 24 h with high likelihood. Models of the glymphatic system were similar qualitatively to the models of pure diffusion with respect to expected time to peak but displayed less variability. However, the expected time to peak was reduced to 11 h when an additional directionality was prescribed for the glymphatic circulation. In a model including drainage directly from the brain parenchyma, time to peak occured after 6–8 h for the gray matter.ConclusionEven when uncertainties are taken into account, we find that diffusion alone is not sufficient to explain transport of tracer deep into the white matter as seen in experimental data. A glymphatic velocity field may increase transport if a large-scale directional structure is included in the glymphatic circulation.

中文翻译：

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使用随机扩散和对流速度场对实质示踪剂分布的不确定性量化

背景物质在脑实质中的流入和清除是通过扩散和对流的组合发生的，但这些机制的相对重要性尚不清楚。大脑中示踪剂分布的准确建模依赖于部分未知的参数，并且文献值有几个数量级的变化。在这项工作中，我们严格量化了由扩散和对流模型参数的不确定性导致的大脑中示踪剂分布的可变性。方法使用对流-扩散-反应方程，我们模拟了鞘内注射后脑实质中的示踪剂分布。测试了几个模型以评估扩散和速度场类型的不确定性以及它们的重要性。我们的结果与示踪剂增强的实验MRI结果进行了比较。结果在纯扩散模型中，灰质中示踪剂的预期量在15小时后达到峰值，而白质在24小时内未达到峰值的可能性很高。就预期达到峰值的时间而言，glymphatic 系统的模型在性质上与纯扩散模型相似，但显示的变异性较小。然而，当为 glymphatic 循环规定了额外的方向性时，预期达到峰值的时间减少到 11 小时。在包括直接从脑实质引流的模型中，灰质达到峰值的时间在 6-8 小时后出现。结论即使考虑到不确定性，我们发现单独的扩散不足以解释示踪剂深入白质的传输，如实验数据所示。如果类淋巴循环中包含大规模定向结构，则类淋巴速度场可能会增加运输。