Spelman T A, Stewart P S
School of Mathematics and Statistics, Mathematics and Statistics Building, University of Glasgow, Glasgow G12 8QW, UK.
Proc Math Phys Eng Sci. 2020 Feb;476(2234):20190269. doi: 10.1098/rspa.2019.0269. Epub 2020 Feb 12.
Retinal haemorrhage is often observed following brain injury. The retinal circulation is supplied (drained) by the central retinal artery (vein) which enters (leaves) the eye through the optic nerve at the optic disc; these vessels penetrate the nerve immediately after passing through a region of cerebrospinal fluid (CSF). We consider a theoretical model for the blood flow in the central retinal vessels, treating each as multi-region collapsible tubes, where we examine how a sudden change in CSF pressure (mimicking an injury) drives a large amplitude pressure perturbation towards the eye. In some cases, this wave can steepen to form a shock. We show that the region immediately proximal to the eye (within the optic nerve where the vessels are strongly confined by the nerve fibres) can significantly reduce the amplitude of the pressure wave transmitted into the eye. When the length of this region is consistent with clinical measurements, the CSF pressure perturbation generates a wave of significantly lower amplitude than the input, protecting the eye from damage. We construct an analytical framework to explain this observation, showing that repeated rapid propagation and reflection of waves along the confined section of the vessel distributes the perturbation over a longer lengthscale.
脑损伤后常可见视网膜出血。视网膜循环由视网膜中央动脉（静脉）供应（引流），该动脉（静脉）通过视神经在视盘处进入（离开）眼睛；这些血管在穿过脑脊液（CSF）区域后立即穿透神经。我们考虑一个视网膜中央血管内血流的理论模型，将每个血管视为多区域可塌陷管，在此模型中我们研究脑脊液压力的突然变化（模拟损伤）如何向眼睛驱动大幅度压力扰动。在某些情况下，此波会陡化形成冲击波。我们表明，紧邻眼睛的区域（在视神经内，血管被神经纤维紧密包裹）可显著降低传入眼睛的压力波幅度。当该区域的长度与临床测量结果一致时，脑脊液压力扰动产生的波幅明显低于输入波幅，从而保护眼睛免受损伤。我们构建了一个分析框架来解释这一现象，表明波在血管受限段的反复快速传播和反射会使扰动分布在更长的长度尺度上。
