RGC damage may elevate neural noise due to associated neuronal dysfunction in the retina or/and the cortex, but also may reduce spatial sampling at the retinal level (i.e., a reduction in the RGC density). Equivalent input noise is often viewed as internal noise in the visual system, whereas calculation efficiency (also termed as sampling efficiency
79) is known to represent the efficiency with which the human observer samples the available information relative to an ideal observer. For this reason, undersampling due to neuronal loss (e.g., a loss of RGCs) has been associated with a reduction in calculation efficiency.
52,80,81 However, here we demonstrated that retinal undersampling resulting from ganglion cell damage may predominantly affect equivalent input noise. To evaluate the effect of retinal undersampling, we incorporated an RGC sampling module into the LAM. As illustrated in the top panel of
Figure 5, in the LAM, the human visual system is assumed to consist of additive internal noise and the calculation that transforms the stimulus (i.e., signal plus external noise) and internal noise into a decision variable. Now we introduce the undersampling at the retinal level to mimic a loss of RGCs in glaucomatous eyes. We first partitioned internal noise into two stages: the early stage of internal noise (
Neq1) arising from optical properties, and the late stage of internal noise (
Neq2) resulting from neuronal properties. The RGC sampling module was then inserted between the two stages of internal noise (the bottom panel of
Fig. 5). Let us denote the resulting effect of RGC sampling on signal as
s1and its resulting effect on either external noise (
Next) or the early internal noise (
Neq1) as
s2. Then we can express Equation
1 as follows:
\begin{equation}{s_1}E = \frac{{{{\left( {d^{\prime} + \sqrt {0.5} } \right)}^2}}}{J} \times \left( {{s_2}{N_{ext}} + {s_2}{N_{eq1}} + {N_{eq2}}} \right),\end{equation}
which is equal to
\begin{equation}E = \frac{{{{\left( {d^{\prime} + \sqrt {0.5} } \right)}^2}}}{{\left( {\frac{{{s_1}}}{{{s_2}}}} \right)J}} \times \left( {{N_{ext}} + {N_{eq1}} + \frac{{{N_{eq2}}}}{{{s_2}}}} \right).\end{equation}
When we let
\(\;{N_{eq}}^{\prime} = {N_{eq1}} + \frac{{{N_{eq2}}}}{{{s_2}}}\) and
\(J^{\prime} = ( {\frac{{{s_1}}}{{{s_2}}}} )J\), we can express Equation
5 in the form of Equation
1 as follows:
\begin{equation}E = \frac{{{{\left( {d^{\prime} + \sqrt {0.5} } \right)}^2}}}{{J^{\prime}}} \times {\rm{\;}}\left( {{N_{ext}} + {N_{eq}}{\rm{^{\prime}}}} \right),\end{equation}
where
\({N_{eq}}^{\prime}\) represents the sum of the early internal noise and the late internal noise scaled by
s2, and
J′ represents the calculation efficiency scaled by
\(\frac{{{s_1}}}{{{s_2}}}\), the relative effect of RGC sampling on signal and external noise.