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A. Messias, H. Jaegle, F. Gekeler, R. Jorge, R. C. Siqueira, E. Zrenner; Dark-Adapted b-Wave Luminance Function: Comparison of Two Mathematical Models in Normal Subjects and in Patients With Retinal Dystrophy. Invest. Ophthalmol. Vis. Sci. 2010;51(13):1500.
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© ARVO (1962-2015); The Authors (2016-present)
The relationship between b-wave amplitude and stimulus luminance has been described by a hyperbolic function [Vmax.I/(I+k)]. But at high luminance levels, where this model shows saturation, a second increase appears in response amplitude. In this work, we propose a model to describe this "limb" and investigate how the new model fits data from normal subjects and patients with cone and cone-rod dystrophy.
Data from 27 normally sighted subjects (54 eyes; CTRL), 3 patients with cone-dystrophy (10 eyes; CD), 2 patients with cone-dystrophy and supernormal rod ERG (4 eyes; CDS), and 5 patients with early stages (recordable dark-adapted ERG) of rod-cone dystrophy (10 eyes; CRD) were analyzed. Dark-adapted ERGs were recorded using DTL electrodes in a Ganzfeld-system (Espion E2 system; Diagnosys LLC) using an extended ISCEV protocol including 9 steps of increasing flash luminance (0.0001 to 10 cd.s/m2). The classical hyperbolic function (model A) and a simple sum of two hyperbolic saturation functions [Vmax.I/(I+k) + Vmax2.I/(I+k2)] (model B - designed by John Robson, pers.comm) were used to fit the data by means of a nonlinear model fit using JMP 7.0.2.
As expected, the mean sum of residuals was lower with model B for all eyes. However, in 40 out of 75 eyes (24 CTRL’s and 16 patients’) the parameters Vmax2 and k2 were not statistically significantly determined, indicating that the limb could not be identified due to data variability. Parameter Vmax from models A and B was significantly reduced in CDR, and higher in CDS. Mean ± SD Vmax (µV) for model A: was 470.3 ± 140.7; 417.6 ± 67.3; 171.1 ± 72.5; and 883.9 ± 166; and for model B: 527.5 ± 160.5; 193.2 ± 73.3; 435.7 ± 85.4; 884.1 ± 166.1; for CTRL, CD, CRD, and CDS respectively. Parameter k from model A was approximately 1 log cd.s/m2 higher in CDS than in CTRL, but no difference was observed in other groups; the same has been observed in k from model B.
Model B describes the b-wave intensity function better than the classical hyperbolic function as indicated by lower residuals. However, values for Vmax2 were statistically significant in only 47% of the cases, indicating that the second limb is often not identified.
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