Biomedical Engineering Reference
In-Depth Information
Thus, the time constant τ
d
equals
1
β
β
β
t t
Vt
Vt
−
τ=
05
025
(9.14)
d
( )
()
Tt
Tt
025
025
025 05
ln
05
05
05 025
By Equation (9.8), the proportional coefficient
K
is
Vt
()
t
K
=
025
025
(9.15)
β
025
−
t
T
F
e
τ
025
025
d
0
It is clear that once the stretching exponent β is known, τ
d
and
K
are
obtained. Moreover, similar equations to Equations (9.14) and (9.15) can be
obtained from the ratios of the other equations. To distinguish the param-
eters calculated from other ratios, τ
d
and
K
in the preceding equations are
replaced by τ
d
12
and
K
12
. Thus, Equations (9.14) and (9.15) can be rewritten as
1
β
β
β
t
−
t
05
025
τ=
d
12
(9.16)
Vt
Vt
()
()
Tt
Tt
025
025
025 05
ln
05
05
05 025
Vt
025
(
025
)
K
=
(9.17)
12
β
t
025
12
t
T
−
F
025
025
e
τ
d
0
S i m i l a rly, τ
d
23
,
K
23
, τ
d
31
, and
K
31
can be defined as
1
β
ββ
t t
Vt
Vt
−
1
05
τ=
d
23
(9.18)
()
()
Tt
Tt
05 05
11
05 1
105
ln
Vt
(9.19)
05
(
05
)
K
=
23
β
t
05
23
t
T
−
F
05
e
τ
d
0
05
