Biomedical Engineering Reference
In-Depth Information
e
k
i
t
(n)
e
k
e
(n)
tot
+k
i
t
(n)
i
P
(n)
ex
=
i
P
peep
e
k
e
(
t
(n)
+
(n
1)
tot
)
e
k
e
(n)
i
tot
+ e
(k
i
+k
e
)t
(n)
+k
e
(n
1)
tot
(10)
(P
peep
P
set
)
i
t
(n)
i
+
(n
1)
tot
+ e
k
e
e
k
i
t
(n)
P
(n1)
P
set
+
i
1
:
ex
This gives iteratively dened expressions for the inspiratory and expiratory
volumes and the end-expiratory pressure.
The problem is to compute V
(n)
i
(t), V
(n)
(t), P
(n)
for n = 1; 2; 3; ::: .
e
ex
This requires that we have a starting point for P
(n)
ex
, namely, P
(0)
ex
. This can
be done by letting P
(1)
= 0 and t
(0)
tot
= t
tot
= 60=f. Then equation (10)
ex
becomes:
e
k
i
t
(0)
i
e
k
i
t
(0
i
P
peep
+ e
(k
i
+k
e
)t
(0)
(P
peep
P
set
) + e
k
e
t
(0
i
P
set
P
(0)
ex
=
i
e
k
e
t
(0)
i
1
(11)
where t
(0)
= t
tot
t
(0)
, and t
(0)
i
is any number in the interval (0; t
(0)
tot
), for
e
i
example, t
(0
i
=
60
f
.
At the end of each breath, the patient's trigger pressure P
trig
is com-
pared against the end expiratory pressure P
ex
. If P
trig
> P
ex
, then the
ventilator turns \ON" for another breath. If P
trig
< P
ex
, then the ventila-
tor stays \OFF" for one breath or more until P
trig
> P
ex
. We assume that
P
trig
= P
peep
+ P
sen
, where P
sen
is the sensitivity setting of the ventilator.
In Figure 2 for illustrative purposes, we simulated our model for fteen
breaths with the following parameter values: C = 0:1 L/cmH
2
O, R
i
= R
e
=
20 cmH
2
O/L/s, P
set
= 22 cmH
2
O, P
peep
= 5 cmH
2
O, P
sen
= 15 cmH
2
O,
t
tot
= 6 s, f = 20 breaths/min, = 0:3. The ventilator sensitivity, P
sen
,
in the ICU is usually between 15 cmH
2
O. At the rst breath (n = 1),
t
tot
60
f
= 3, we calculate thaat P
ex
= 12:8 and P
trig
= P
peep
+ P
sen
=
20 > P
ex
= 12:8. Therefore, the ventilator is triggered. At the fourteenth
breath, P
ex
= 21:1 > P
trig
. Therefore, the ventilator fails to be triggered
and we have a prolonged expiration at the end of which we calculate that
P
ex
= 6:5. At the end of this long breath, P
trig
> P
ex
and P
(14)
=
= 6:5,
ex
with t
(14)
tot
=
26
f
= 6. Thus, a skipped breath has occurred at this point. In
other words, we have expiration occuring for an additional 3 seconds.
Search WWH ::
Custom Search