Biomedical Engineering Reference
In-Depth Information
Inspiration
dV
(n)
i
dt
+
V
(n)
+ P
(n1)
= P
set
;
(n1)
tot
t
(n1)
+ t
(n)
i
R
i
i
C
ex
tot
(1)
V
(n)
i
(0) = 0
Expiration
dV
(n)
e
dt
+
V
(n)
+ P
(n)
ex
= P
peep
;
(n1)
+ t
(n)
i
t
(n)
R
e
e
C
tot
tot
(2)
V
(n)
(t
(n)
tot
) = 0
e
where is either 1 or 2 and n = 1; 2;. V
(n)
i
(t) denotes the inspiratory
lung volume during nth breath, V
(n)
(t) the expiratory lung volume during
e
nth breath, P
(n)
ex
the end expiratory pressure at the end of nth breath, t
(n)
i
the length of inspiratory time of nth breath, t
(n
e
the length of expiratory
time of nth breath, P
set
the applied ventilator pressure during inspiration,
P
peep
the applied ventilator pressure during expiration, R
i
the inspiratory
resistance, R
e
the expiratory resistance, D the inspiratory time fraction,
D =
t
tot
, and f the number of breaths per minute. Here
(n)
t
i
tot
, n = 1; 2; :::
is the actual time at the end of the nth breath. That is, we assume that
each breath is of length t
(n)
tot
= 60k=f, where k is a positive integer, and
t
(n)
i
+ t
(n)
= t
(n)
tot
. In this notation,
e
(n)
tot
= t
(1)
tot
+ t
(2)
tot
+ ::: + t
(n)
tot
:
In the expression, t
(n)
tot
= 60k=f, if k > 1, then this indicates skipped
breaths. If there are no skipped breaths during the nth
breath, then
t
(n)
tot
= 60=f. If there is one skipped breath during the nth
breath, then
t
(n)
tot
= 120=f; if two skipped breaths, then t
(n)
tot
= 180=f; etc.
dV
(n)
i
dt
In equations (1) and (2), the resistive pressure, P
resistive
, is R
i
, respectively, the elastic pressure, P
elastic
, is
V
(n)
dV
(n)
e
dt
and
V
(n)
and R
e
,
i
C
e
C
the residual pressure, P
residual
, is the end-expiratory pressure, P
(k)
ex
, k =
n1; n. The ventilator pressure, P
vent
, is the applied ventilator pressure.
That is,
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