Linear interactions between intraocular, intracranial pressure, and retinal vascular pulse amplitude in the fourier domain
Authors: Abdul-Rahman Anmar , Morgan William , Jo Khoo Ying , Lind Christopher , Kermode Allan , Carroll William , Yu Dao-Yi 
Published: June 2022

Purpose
To compare the retinal vascular pulsatile characteristics in subjects with normal (ICPn) and high (ICPh) intracranial pressure and quantify the interactions between intraocular pressure, intracranial pressure, and retinal vascular pulse amplitude in the Fourier domain.

Materials and methods
Twenty-one subjects were examined using modified photoplethysmography with simultaneous ophthalmodynamometry. A harmonic regression model was fitted to each pixel in the time-series, and used to quantify the retinal vascular pulse wave parameters including the harmonic regression wave amplitude (HRWa). The pulse wave attenuation was measured under different ranges of induced intraocular pressure (IOPi), as a function of distance along the vessel (VDist). Intracranial pressure (ICP) was measured using lumbar puncture. A linear mixed-effects model was used to estimate the correlations between the Yeo-Johnson transformed harmonic regression wave amplitude (HRWa-YJt) with the predictors (IOPi, VDist and ICP). A comparison of the model coefficients was done by calculating the weighted Beta (βx) coefficients.

Results
The median HRWa in the ICPn group was higher in the retinal veins (4.563, interquartile range (IQR) = 3.656) compared to the retinal arteries (3.475, IQR = 2.458), p<0.0001. In contrast, the ICPh group demonstrated a reduction in the median venous HRWa (3.655, IQR = 3.223) and an elevation in the median arterial HRWa (3.616, IQR = 2.715), p<0.0001. Interactions of the pulsation amplitude with ICP showed a significant disordinal interaction and the loss of a main effect of the Fourier sine coefficient (bn1) in the ICPh group, suggesting that this coefficient reflects the retinal vascular response to ICP wave. The linear mixed-effects model (LME) showed the decay in the venous (HRWa-YJt) was almost twice that in the retinal arteries (−0.067±0.002 compared to −0.028±0.0021 respectively, p<0.00001). The overall interaction models had a total explanatory power of (conditional R2) 38.7%, and 42% of which the fixed effects explained 8.8%, and 5.8% of the variance (marginal R2) for the venous and arterial models respectively. A comparison of the damping effect of VDist and ICP showed that ICP had less influence on pulse decay than distance in the retinal arteries (βICP = -0.21, se = ±0.017 compared to βVDist=-0.26, se = ±0.019), whereas the mean value was equal for the retinal veins (venous βVDist=-0.42, se = ±0.015, βICP = -0.42, se = ±0.019).

Conclusion
The retinal vascular pulsation characteristics in the ICPh group showed high retinal arterial and low venous pulsation amplitudes. Interactions between retinal vascular pulsation amplitude and ICP suggest that the Fourier sine coefficient bn1 reflects the retinal vascular response to the ICP wave. Although a matrix of regression lines showed high linear characteristics, the low model explanatory power precludes its use as a predictor of ICP. These results may guide future predictive modelling in non-invasive estimation of ICP using modified photoplethysmography.