Mathematical Model of Cataract Evolution and Its Solution in Quadratures
https://doi.org/10.1134/S2304487X20020157
Abstract
A heuristic mathematical model of cataract evolution has been proposed on the basis of a simplified physiological model. The process is presented as a non-stationary Neumann problem for the Poisson equation. Its initial conditions are the solution of the stationary problem corresponding to a healthy eye. According to the crystalline lens degradation concept, the feeding agent is being transported inside the boundary and naturally consumed. Its lack results in opacification of the crystalline lens tissue. The crystalline lens is considered as a biconvex lens-like body constrained within intersecting spheres of different radii. The Green’s function for the area has been built by the reflection method. A finite number of reflections occur if the spheres are orthogonal; this circumstance, together with the height and thickness of the crystalline lens, uniquely determines the geometry of the problem. The model describes the nuclear, subcapsular, and cortical cataract. The behavior of solutions in each case is discussed. The physiological meaning of an arbitrary constant in the Neumann problem solution is interpreted. A necessity to reach some agreement with respect to the threshold value of the feeding agent concentration that enables one to distinguish between healthy and unhealthy regimes of the eye functioning is emphasized. Extended names of cataract types are offered with adding the etymological feature to the morphological one: diffuse–nuclear, sclerotic–subcapsular, and sclerotic–cortical, respectively.
About the Authors
M. V. Vigdorowitsch
Angara GmbH
Germany
Germany
40599
Düsseldorf
E. V. Evdokimova
Local Health Supervisory Body for Tambov region
Russian Federation
Russian Federation
392030
Tambov
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Review
For citations:
Vigdorowitsch M.V., Evdokimova E.V. Mathematical Model of Cataract Evolution and Its Solution in Quadratures. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):147-154. (In Russ.) https://doi.org/10.1134/S2304487X20020157
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