Roberts Paul A, Gaffney Eamonn A, Luthert Philip J, Foss Alexander J E, Byrne Helen M
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK; Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
J Theor Biol. 2017 Jul 21;425:53-71. doi: 10.1016/j.jtbi.2017.05.006. Epub 2017 May 6.
The group of genetically mediated diseases, known collectively as retinitis pigmentosa (RP), cause retinal degeneration and, hence, loss of vision. The most common inherited retinal degeneration, RP is currently untreatable. The retina detects light using cells known as photoreceptors, of which there are two types: rods and cones. In RP, genetic mutations cause patches of photoreceptors to degenerate and typically directly affect either rods or cones, but not both. During disease progression, degenerate patches spread and the unaffected photoreceptor type also begins to degenerate. The cause underlying these phenomena is currently unknown. The oxygen toxicity hypothesis proposes that secondary photoreceptor loss is due to hyperoxia (toxically high oxygen levels), which results from the decrease in oxygen uptake following the initial loss of photoreceptors. In this paper, we construct mathematical models, formulated as 1D systems of partial differential equations, to investigate this hypothesis. Using a combination of numerical simulations, asymptotic analysis and travelling wave analysis, we find that degeneration may spread due to hyperoxia, and generate spatio-temporal patterns of degeneration similar to those seen in vivo. We determine the conditions under which a degenerate patch will spread and show that the wave speed of degeneration is a monotone decreasing function of the local photoreceptor density. Lastly, the effects of treatment with antioxidants and trophic factors, and of capillary loss, upon the dynamics of photoreceptor loss and recovery are considered.
这组统称为色素性视网膜炎（RP）的基因介导疾病会导致视网膜变性，进而导致视力丧失。RP是最常见的遗传性视网膜变性疾病，目前无法治愈。视网膜利用称为光感受器的细胞来检测光线，光感受器有两种类型：视杆细胞和视锥细胞。在RP中，基因突变会导致部分光感受器退化，通常直接影响视杆细胞或视锥细胞，但不会同时影响两者。在疾病进展过程中，退化区域会扩散，未受影响的光感受器类型也会开始退化。目前尚不清楚这些现象背后的原因。氧毒性假说认为，继发性光感受器丧失是由于高氧（有毒的高氧水平）引起的，高氧是由于最初光感受器丧失后氧摄取减少所致。在本文中，我们构建了以一维偏微分方程组形式表示的数学模型，以研究这一假说。通过数值模拟、渐近分析和行波分析相结合的方法，我们发现退化可能由于高氧而扩散，并产生与体内所见相似的退化时空模式。我们确定了退化区域扩散的条件，并表明退化的波速是局部光感受器密度的单调递减函数。最后，考虑了抗氧化剂和营养因子治疗以及毛细血管丧失对光感受器丧失和恢复动态的影响。
