A Simplified Model of Activation and Deactivation of Human Rod Phototransduction-An Electroretinographic Study.

Purpose: To test the hypothesis that a simple model having properties consistent with activation and deactivation in the rod approximates the whole time course of the photoresponse. Methods: Routinely, an exponential of the form f = α·(1 - exp(-(τ·(t - teff)s-1))), with amplitude α, rate constant τ (often scaled by intensity), irreducible delay teff, and time exponent s-1, is fit to the early period of the flash electroretinogram. Notably, s (an integer) represents the three integrating stages in the rod amplification cascade (rhodopsin isomerization, transducin activation, and cGMP hydrolysis). The time course of the photoresponse to a 0.17 cd·s·m-2 conditioning flash (CF) was determined in 21 healthy eyes by presenting the CF plus a bright probe flash (PF) in tandem, separated by interstimulus intervals (ISIs) of 0.01 to 1.4 seconds, and calculating the proportion of the PF a-wave suppressed by the CF at each ISI. To test if similar kinetics describe deactivation, difference of exponential (DoE) functions with common α and teff parameters, respective rate constants for the initiation (I) and quenching (Q) phases of the response, and specified values of s (sI, sQ), were compared to the photoresponse time course. Results: As hypothesized, the optimal values of sI and sQ were 3 and 2, respectively. Mean ± SD α was 0.80 ± 0.066, I was 7700 ± 2400 m2·cd-1·s-3, and Q was 1.4 ± 0.47 s-1. Overall, r2 was 0.93. Conclusions: A method, including a DoE model with just three free parameters (α, I, Q), that robustly captures the magnitude and time-constants of the complete rod response, was produced. Only two steps integrate to quench the rod photoresponse.

Modelling eye lengths and refractions in the periphery.

PURPOSE: To create a simplified model of the eye by which we can specify a key optical characteristic of the crystalline lens, namely its power. METHODS: Cycloplegic refraction and axial length were obtained in 60 eyes of 30 healthy subjects at eccentricities spanning 40° nasal to 40° temporal and were fitted with a three-dimensional parabolic model. Keratometric values and geometric distances to the cornea, lens and retina from 45 eyes supplied a numerical ray tracing model. Posterior lens curvature (PLC) was found by optimising the refractive data using a fixed lens equivalent refractive index ( n eq ). Then, n eq was found using a fixed PLC. RESULTS: Eccentric refractive errors were relatively hyperopic in eyes with central refractions ≤-1.44 D but relatively myopic in emmetropes and hyperopes. Posterior lens power, which cannot be measured directly, was derived from the optimised model lens. There was a weak, negative association between derived PLC and central spherical equivalent refraction. Regardless of refractive error, the posterior retinal curvature remained fixed. CONCLUSIONS: By combining both on- and off-axis refractions and eye length measurements, this simplified model enabled the specification of posterior lens power and captured off-axis lenticular characteristics. The broad distribution in off-axis lens power represents a notable contrast to the relative stability of retinal curvature.