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Figure 6 | The Journal of Mathematical Neuroscience

Figure 6

From: Exact solutions to cable equations in branching neurons with tapering dendrites

Figure 6

Comparison between the cylindrical (red) and parabolic (blue) single dendrite models. The preferred frequencies \(\varOmega^{*}\) as functions of the dendritic length \(l_{0}\) computed using the Green’s functions (78) and (79) with \(x=y=0\). Insert: The time profiles of the somatic responses to a chirp input when \(l_{0}=150 \mbox{ $\mu$m}\). The chirp current is defined to be \(I_{\mathrm{chirp}}(t)=A_{\mathrm{chirp}} \sin(\omega_{\mathrm{chirp}} t^{2})\), where \(\omega_{\mathrm{chirp}}=3\times10^{-4}\mbox{ kHz}\), \(A_{\mathrm{chirp}}=0.2\mbox{ nA}\). The geometric parameters: \(r_{c}=1 \mbox{ $\mu$m}\) for the cylindrical model, \(r_{0}=1 \mbox{ $\mu$m}\) and \(r_{1}=0 \mbox{ $\mu$m}\) for the parabolic model, \(r_{S}=12.5 \mbox{ $\mu$m}\) for both models. The electrical parameters of the dendritic and somatic membranes are the same, and identical in both models: \(C_{m}=1 \mbox{ $\mu$F $\cdot$ cm$^{-2}$}\), \(g_{l}^{-1}=2000~\varOmega\cdot \mbox{cm}^{2}\), \(R_{a}=100~\varOmega\cdot \mbox{cm}\), \(r_{\mathrm{ion}}=1000~\varOmega \cdot \mbox{cm}^{2}\), \(L_{\mathrm{ion}}=5\mbox{ H} \cdot \mbox{cm}^{2}\)

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