Non-linear interactions between intraocular, intracranial pressure and the retinal vascular pulse amplitude in the Fourier domain

The low explanatory power of a mixed effects linear model in evaluating interactions between retinal vascular pulse amplitude, intraocular pressure, and intracranial pressure suggests that these interactions are driven by non-linear dynamics. However, mathematical models inherently balance interpretability with predictive capability, and models explaining substantial variance may compromise interpretive clarity, a well-recognized limitation of artificial intelligence models, known as the black box problem. To explore these interactions, a generalized additive mixed model (GAMM) was applied to retinal venous and arterial pulse amplitude data in relation to intraocular and intracranial pressures. Each GAMM, constrained to prioritize interpretability, utilized 51 basis functions, and successfully achieved convergence. Partial effect plots and three-dimensional interaction visualizations were generated, revealing the geometric nature of these physiological relationships. The arterial and venous GAMMs explained 49.21 and 62.96% of the deviance respectively, describing a complex three-dimensional surface with pronounced curvature at intracranial pressures exceeding 25 cm water. Consistent with findings from a previously reported linear mixed-effects model, elevated intracranial pressure had an antipodal effect on the vascular pulse amplitude manifest as a reduction in venous and augmentation of the arterial pulse amplitudes.