Resumo

Goal: instead of amplitudes, latencies and power spectra traditionally measured in electrophysiology, we seek to identify and quantify the excitatory and inhibitory mechanism of the human retina in full field eletroretinogram (ERG), using new developments into the Fractal and Chaos Theory. Methods: We isolated the ON and OFF magnocellular (MC) responses in a healthy human retina using down and up sawtooth wave stimuli [Kremers, Vision Res. 33, 1997 (1993)], respectively, with a 4Hz temporal frequency on a Ganzfeld stimulator (Q450 SC Roland-Consult, Germany). The signals were analyzed using typical methods for characterizing nonlinear systems: Takens time delay reconstruction [Lect. Notes in Math. 898, 366 (1981)], Lyapunov exponents [Phys. Rev. E 65, 036702/1-10 (2002)], Kaplan-York dimension [Peitge & Walther, ‘Functional Differential Equations and Approximation of Fixed Points,’ Springer, New York (1987)] and Haussdorff fractal dimension [Physica D 124, 210-224 (1998)]. Results: Our results for the ON MC pathway, applying the Takens reconstruction over the signal, treated using a 34Hz digital RC low-pass filter, indicate the Haussdorff fractal dimension Dzero value 1.86(0.03), i.e. we may reconstruct the attractor associated with the ERG in a two-dimensional phase space. The Lyapunov exponents in two-dimension for ON MC are L1=7.2(1.2)/sec and L2=-8.6(3.4)/sec, demonstrating sensitive dependence to initial condition (chaos). Retina has memory or a feedback mechanism. The L1 and L2 results are consistent with Dzero (p=0.55), since the Kaplan-York dimension DKY, estimated from L1 and L2, value 1.84(0.37). Concerning the OFF MC pathway, we compute Dzero=1.72(0.05), L1=5.6(1.0)/sec, L2=-9.9(1.0)/sec, and DKY=1.56(0.15). Again, DKY and Dzero are the same for the OFF channel with p=0.84. Finally, Dzero of the ON MC pathway are bigger than OFF with p=0.008, indicating that the electrophysiological mechanisms of the ON and OFF MC visual processing are not the same. Conclusions: The recently development nonlinear methods are viable for the ERG signal analysis, since the ON and OFF MC electrical responses are low dimensional (small fractal dimension), i.e. these pathways could be represented by few variables. Moreover, we have one positive and one negative Lyapunov exponent associated respectively with the expansion and contraction of the phase space in chaotic systems. We conjecture that they are related with the excitatory and inhibitory process of the ganglion cells by the bipolar cells. Financial support: CNPq PDS 151011/2008-7, FAPESP 07/55125-1.