Biomedical Engineering Reference
In-Depth Information
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Figure 4.1:
Construction of a cable from patches of membrane.
or more compactly,
φ
i
2
φ
i
φ
i
−
+
=
i
m
(4.3)
dx
2
·
r
i
φ
e
−
2
φ
e
+
φ
e
=−
i
m
(4.4)
dx
2
·
r
e
where
i
m
is defined as the passive circuit:
dV
m
dt
V
m
r
m
i
m
=
c
m
−
(4.5)
rearranging Eqs. (4.3) and (4.4)
φ
i
φ
i
2
φ
i
−
+
=
r
i
·
i
m
(4.6)
dx
2
φ
e
−
2
φ
e
+
φ
e
=−
r
e
·
i
m
(4.7)
dx
2
and then subtracting Eq. (4.7) from Eq. (4.6)
(φ
i
2
(φ
i
(φ
i
φ
3
)
φ
e
)
φ
e
)
−
−
−
+
−
=
(r
i
−
r
e
)i
m
(4.8)
dx
2
V
m
−
2
V
m
+
V
m
=
(r
i
−
r
e
)i
m
(4.9)
dx
2
