The development of glaucomous optic neuropathy prediction. Part I. Mathematical model of deformation of the lamina cribrosa and damage to nerve filaments in glaucoma
It is considered that damage to nerve filaments in glaucomous optic neuropathy primarily occurs at the level of the lamina cribrosa of the optic disc.Purpose. To develop a mathematical model for predicting damage to axons of ganglion cells at the level of the lamina cribrosa due to its deformation in the development of glaucomous optic neuropathy.Materials and methods. Twenty patients (11 women and 9 men) were diagnosed with open angle glaucoma. Patients were divided into 4 groups according to each stage of glaucoma for 5 people in each group. Studies of the morphological features of the retina and optic nerve were performed using the Swept-Source OCT (SS-OCT) method on the Topcon DRI Triton apparatus. In all cases, visualization of the lamina cribrosa of the optic nerve was available.The lamina cribrosa was modeled in the form of a solid disk with a hole in the middle. The system of equations describes the transverse and longitudinal displacements of the plate elements when deformed due to the influence of the pressure gradient on it.The curvature of nerve filaments at the level of the lamina cribrosa due to its deformation is modeled in the form of pressing a rigid cylindrical die into a thin elastic layer.Results. A quantitative criterion has been developed in which the destruction of axons of ganglion cells occurs at the level of the lamina cribrosa with the development of glaucomous optic neuropathy.Conclusions. The appearance of glaucomous optic neuropathy is a consequence of axonal damage at the level of the lamina cribrosa.It is possible to apply the developed quantitative criterion, in which there is destruction of axons of ganglion cells at the level of the lamina cribrosa, based on measurements of its parameters according to SS-OCT and daily intraocular pressure gradient for prediction of glaucomous optic neuropathy.