IOl
Figure 4.1: Schematic of the strong-weak model for a uniform fiber, along with its spatial
discretization to illustrate the ordering of compartments
absolute and relative voltages at the transition point:
Vτ(t) = Vs(xτ,t) = Vw(xτ,t), υτ(t) = Vτ(t) - Vτ.
(4.1)
It will be computationally advantageous to work with voltages with respect to rest.
The strong fiber obeys the nonlinear cable equation, while the weak fiber obeys
the quasi-active version of this PDE. Hence, using the cable equation from §2.3.1, we
write the strong-weak system as
ɪ c Fc
GjCrric)fVs _ ɑ ∂χχXs G Gsc(x)(vs Ec ) ɪɪ scf Is(Vs> ^∙> t)
0 < X < xτ, 0 < t,
∂twscf
G) cf ,oo('ʊ s) 'G'scf
xτ < x < P, 0 < t,
(4.2)
(4.3)
(4.4)
where vw and ω,,jc denote the linearized weak voltage and gating variables, Φ denotes
the ionic current function, Is and denotes the inputs to the strong fiber, Iw denotes
the linearized inputs to the weak fiber, and Qw is the quasi-active operator, as in