95
in the network. This could be assessed with the bar light stimulus by dividing the voltage
response by the equivalent photocurrent generated, but would require making several as-
sumptions.
A plot of the network impedance vs 7 = Rc∣Rm for a ID and 2D network is shown
in figure 5.7 B. As the Rc∣Rm grows, the network becomes essentially uncoupled, and the
input impedance approaches Rm. The impedance in the one-dimensional network is greater
because there are fewer paths for the current to take.
Figure 5.7 A shows the normalized length constant D∕λ as a function of Rc∣Rm. The
length constant decreases as Rc∣Rm increases because it becomes increasingly difficult for
current to flow laterally. For the ID steady-state solution, the length constant describes an
exponential decay as in equation 5.4. Although the 2D steady-state solution (equation 5.7
involves a Bessel function, the discrete solution is well approximated by an exponential decay
with length constant λ2D> shown in figure 5.5. Figure 5.4 C shows the relationship between
length constant and cell input impedance. This is a useful relationship because the length
constant can be measured experimentally, whereas 7 cannot.
5.4.6 Network impulse response and frequency response
Figure 5.8 B shows the impulse response (Green’s function) for a 2D network with Rm =
- 0.7 GΩ, Rc = 0.9 GΩ, and C = 50 ■ IO-3 nF. The corresponding frequency responses of
the indicated cells are shown in figure 5.8 C. The cutoff frequency in the Origninating rod
(0,0) is around 1 Hz. The cutroff frequency in more distant rods decreases further from the