Biomedical Engineering Reference
In-Depth Information
Eq. (13.9) is true whenever o
d
T
p
¼
n
p
:
The time to peak amplitude is the smallest value that
p
o
d
¼
p
p
1
:
To determine y(
satisfies Eq. (13.9), which is
n
¼
1. Thus,
T
p
¼
T
p
), note that
z
2
o
n
o
d
t
þ
c
¼
p
þ
c, and
2
4
3
5
p
1
zp
1
y
T
p
¼
z
2
g
K
þ
e
p
1
cos p þ c
ð
Þ
z
2
2
4
3
5
zp
1
p
1
q
1
z
2
g
K
þ
e
ð
13
:
10
Þ
z
2
¼
1
p
z
2
!
pz
1
p
g
K
z
2
¼
1
þ
e
An important aid in examining the suitability of a model is to study the model predic-
tions and data estimates of higher-order derivatives. If there are problems with the model,
these problems are amplified when comparing estimates of the higher-order derivatives
with model predictions. For the Westheimer model, maximum velocity is found from
@
t
¼
T
mv
¼
2
y
@
t
0, where
is the time at peak velocity. Using the solution given by
T
mv
2
Eq. (13.6), we next compute
2
4
3
5
@
2
y
@
t
2
¼
@
g
K
e
zo
n
t
1
p
f
zo
n
cos o
d
t
þ
ð
c
Þ þ
o
d
sin
ð
o
d
t
þ
c
Þ
g
@
t
z
2
g
ð
13
:
11
Þ
zo
n
e
zo
n
t
zo
n
¼
p
1
½
ð
cos o
d
t
þ
ð
c
Þ þ
o
d
sin o
d
t
þ
ð
c
Þ
Þ
z
2
K
¼
þ
e
zo
n
t
o
2
d
zo
n
o
d
sin o
d
t
þ
ð
c
Þ þ
cos o
d
t
þ
ð
c
Þ
0
After taking the second derivative in Eq. (13.11), we find that
p
1
!
z
2
1
w
d
tan
1
T
mv
¼
ð
13
:
12
Þ
z
y(
T
m
v
) can be evaluated using
T
mv
.
