Analyzing rheoophthalmic signals in glaucoma by nonlinear dynamics methods

Abstract

We assess the possibility to analyze signals of transpalpebral rheoophthalmography (TP ROG) by methods of nonlinear dynamics and find out how informative this technique is in examining patients with various stages of primary open-angle glaucoma (POAG). The technique was verified on the basis of TP ROG signals obtained in examining 4 groups of subjects: (1) control group (10 eyes with no ocular pathology), (2) stage I of POAG (15 non-operated eyes), (3) stage II of POAG (7 eyes), and (4) stage III of POAG (4 eyes). In all, 36 eyes of 28 subjects aged 25–84 (average age 62.1 ± 7.1 years) were examined. The analysis of TP ROG signals included determining the rheographic index (RI), calculating the RI average in each group, and finding out how RI depends on POAG stage. Alternatively, we used the nonlinear dynamics method with the signal’s attractor reconstruction, where we chose the time delay, determined the embedding dimension, and constructed the attractor in the space of the chosen coordinates. After the barycenters of each reconstructed attractor were found, we analyzed TP ROG signals graphically in the attractors’ representation plane. The analysis of TP ROG signals by nonlinear dynamics methods demonstrated that a more distinct differentiation of POAG stages as compared to traditional signal processing becomes possible. As the stage of the diseases advances, the location of the barycenter of the reconstructed attractor is changing significantly. It shifts rightward and upward in the space of the chosen coordinates. Due to this fact, it becomes possible to separate TP ROG signals into POAG stages by simple geometric figures and to increase the accuracy of the diagnosis at early stages of the disease, which may be used for further study of the link between the hemodynamic state of the eye and glaucoma stages.