Biomedical Engineering Reference
In-Depth Information
Fig. 6 a A typical MIGET plot obtained from a normal subject, which illustrates the distribution
of ventilation and perfusion in the lung (reproduced from [
88
] with kind permission from
Springer Science and Business Media). b Shows a simulated distribution of ventilation and
perfusion in a normal subject obtained using the models of Clark et al. [
17
] and Swan et al. [
55
].
The two distributions compare well
1
dp
cO
2
dt
¼
D
O
2
V
c
r
1
þ
4Hb
r
dS
ð
p
cO
2
Þ
dp
cO
2
ð
p
AO
2
p
cO
2
Þ
;
ð
8
Þ
where D
O2
is the diffusion capacity (transfer factor) of oxygen between air and
blood, V
c
is capillary blood volume, r is the solubility of oxygen in blood, Hb is
the hemoglobin concentration in whole blood, and S(p
cO2
) is the hemoglobin
saturation function. This function can be fit to experimental data or derived from
models of the chemical interactions between oxygen and hemoglobin. If one
assumes equilibration between air and blood gases, the ODE given by Eq.
8
can be
reduced to a system of algebraic equations which explicitly depend on capillary
blood flow rates (Q
c
) and predict end-expired oxygen levels. The equation for
oxygen is (e.g. [
85
])
V
I
p
IO
2
V
E
p
AO
2
¼
Q
C
k
ð
C
cO
2
C
vO
2
Þ
;
ð
9
Þ
where V
I
is inspired ventilation into the unit, p
IO2
is inspired oxygen partial
pressure, V
E
is expired ventilation out of the unit, Q
c
is the rate of capillary blood
flow, C
cO2
is the oxygen content in end-capillary blood, C
vO2
is oxygen content
entering the lungs from mixed venous blood, k is a constant factor that accounts
for differences between body temperature and pressure and inspired air tempera-
ture and pressure as well as allowing consistency between the units of the left and
right hand side of Eq.
9
. Content (in mol l-1) is related to partial pressure by
C
O
2
¼
rp
O
2
þ
4HbS
ð
p
O
2
Þ
:
ð
10
Þ
Critically, each of Eqs.
8
and
9
is dependent on capillary blood pressures and
blood flow rates, which are both spatially and temporally variable (note that the
parameter V
c
in Eq.
8
is variable with Q
c
as capillaries are elastic). Whilst previous
modeling studies assessing the function of the pulmonary circulation had focused
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