Vol. 274, Issue 2, H694-H700, February 1998
MODELING IN PHYSIOLOGY
Theoretical optimization of pulmonary-to-systemic flow ratio after
a bidirectional cavopulmonary anastomosis
William P.
Santamore1,
Ofer
Barnea2,
Christopher J.
Riordan1,
Mitchell P.
Ross3, and
Erle H.
Austin1
1 Department of Surgery,
University of Louisville, Louisville, Kentucky 40292;
2 Biomedical Engineering
Department, Tel Aviv University, Tel Aviv, Israel 69978; and
3 Department of Pediatrics, Kosair
Children's Hospital, Louisville, Kentucky 40292
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ABSTRACT |
A univentricle
with parallel pulmonary and systemic circulations is inherently
inefficient because mixing of pulmonary and systemic venous return
occurs. Thus a cavopulmonary anastomosis is used as a staged palliative
procedure to reduce volume overload in patients with cyanotic
congenital heart disease. On the basis of oxygen uptake and
consumption, an equation was derived that related cardiac output,
pulmonary venous oxygen saturation, upper body oxygen consumption, and
superior-to-inferior vena caval blood flow ratio
(QSVC/QIVC)
to oxygen delivery. The primary findings were as follows.
1) As
QSVC/QIVC
increases, total body oxygen delivery and arterial and superior vena
caval oxygen saturations increase.
2) As
QSVC/QIVC
increases, lower body oxygen delivery and inferior vena caval oxygen
saturation initially increase, then peak, and then decrease.
3) As the percentage of lower body oxygen consumption increases, oxygen delivery and saturation decrease. 4) A cavopulmonary anastomosis
decreases the required cardiac output for a given oxygen delivery. Thus
we concluded that a high systemic arterial oxygen saturation after
cavopulmonary anastomosis requires a high percentage of upper body
oxygen consumption and a high
QSVC/QIVC
and that the cavopulmonary anastomosis reduces the volume load on the
single ventricle.
hypoplastic left heart syndrome; pulmonary blood flow; aortic blood
flow; computer models; infants
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INTRODUCTION |
HYPOPLASTIC LEFT HEART syndrome is currently the most
common cardiac malformation that results in death of the newborn infant (17). Without treatment, 95% of these infants die during the first
month of life and none survive beyond 4 mo (23). The management of
neonates with hypoplastic left heart syndrome is complex. Palliative surgery, developed by Norwood, involves several staged operations (6,
19). The first surgery stabilizes the univentricular circulation by
attaching the right ventricular outflow to the aorta and placing an
aorta-to-pulmonary artery shunt. With this approach, survival beyond
the first few weeks became possible (19).
Definitive long-term palliation requires a modified Fontan procedure,
in which the aorta-to-pulmonary artery shunt is closed and
venous blood flows directly into the pulmonary artery, completely bypassing the right heart. Because of an observed high mortality rate
from the Fontan operation for hypoplastic left heart syndrome, a
bidirectional cavopulmonary anastomosis or Glenn shunt procedure is now
often performed before the Fontan operation (5, 8, 11, 12, 20). This
procedure, in which the superior vena cava is anastomosed to the
pulmonary artery, is thought to diminish the effects of volume overload
on the single ventricle.
Because natural animal models of this heart defect do not exist,
management of infants with hypoplastic left heart syndrome has been
derived primarily from clinical experience, determined by trial and
error. Thus we previously developed a theoretical analysis to determine
the effect of blood flow distribution between the two circulations on
systemic oxygen delivery (4). In the present study, we performed a
similar theoretical analysis to determine the effects of a
bidirectional cavopulmonary anastomosis in the univentricular
circulation on systemic oxygen delivery and on the required cardiac
output to provide this systemic oxygen delivery.
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METHODS |
A model of this circulation is shown in Fig.
1. After the Glenn shunt, the blood that
normally drains into the right atrium from the superior vena cava is
redirected via an anastomosis to the pulmonary artery and flows
passively through the pulmonary circulation. Oxygenated pulmonary
venous blood is routed from the left atrium via an interatrial septal
defect to the right atrium, where it mixes with systemic venous blood.
Note that with hypoplastic left heart syndrome, the right ventricle
does all the pumping of blood. The right ventricular outflow goes into a reconstructed aorta, where it is divided into flow to the upper and
lower systemic circulations. In effect, this forms a parallel circulation: the combined upper systemic circulation and pulmonary circulation is in parallel with lower systemic circulation. Note that
although Fig. 1 and the analysis below are for hypoplastic left heart syndrome, the analysis also is applicable to the other univentricular conditions.
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Fig. 1.
A model of the hypoplastic left heart circulation after a cavopulmonary
anastomosis. P is pulmonary circulation;
SL and
SU are lower and upper systemic
circulations, respectively; QP (or
QSVC),
QIVC, and CO are pulmonary flow
(upper systemic or superior vena caval flow), slower systemic flow
(inferior vena caval flow), and right ventricular output (cardiac
output), respectively;
CPVO2,
CSVCO2,
CIVCO2,
and CaO2 are oxygen content (ml
O2/ml blood) in pulmonary venous
blood, superior vena caval blood, inferior vena caval blood, and mixed
blood ejected from right ventricle, respectively.
 O2 L
is the rate of oxygen supply or uptake in the lungs and
O2 is whole body oxygen
consumption. RV, right ventricle; RA, right atrium; LA, left atrium;
SVC-PA anastomosis, superior vena cava-to-pulmonary artery anastomosis;
Ao, aorta; k, fraction of whole body
oxygen consumption used by the upper body.
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The analysis is based on movement of oxygen into the pulmonary
circulation (uptake) and out of the systemic circulation (consumption). The basic equations are as follows
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(1)
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Equation 1 states that whole body oxygen consumption
(O2, in ml
O2/min) is divided between the
upper body [blood draining into the superior vena cava
(QSVC)] oxygen consumption
(k · O2) and lower body oxygen consumption [(1 
k)O2],
where k is the fraction of whole body
oxygen consumption used by the upper body. For the lower systemic
circulation
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(2)
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Equation 2 states that the oxygen flow rate into the lower
systemic circulation is a product of arterial oxygen content
(CaO2, in ml
O2/ml blood) and lower body blood
flow [blood draining into the inferior vena cava
(QIVC)]. This oxygen flow
rate into the lower systemic circulation is reduced by the lower body
oxygen consumed (ml
O2/min), leaving the
reduced oxygen flow rate returning to the right atrium
(CIVCO2 · QIVC),
where
CIVCO2 is the oxygen content of the inferior vena caval blood. Similarly
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(3)
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Equation 3 states that the oxygen flow rate into the upper
systemic circulation
(CaO2 · QSVC)
is reduced by the upper body oxygen consumed
(k · O2),
leaving the reduced oxygen flow rate returning to the
superior vena cava and then to the pulmonary artery
(CSVCO2 · QSVC),
where
CSVCO2is
the oxygen content of the superior vena caval blood
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(4a)
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(4b)
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Equation 4a states that pulmonary artery blood flow
(QP) is equal to blood flow to
the upper systemic circulation, i.e.,
QSVC. Equation 4b states that the oxygen flow rate into the pulmonary circulation
(CSVCO2 · QSVC)
plus the oxygen uptake in the lungs
(O2, L) gives the
oxygen flow rate returning to the atrium from the pulmonary circulation
(CPVO2 · QP),
where CPVO2
is the oxygen content of the superior vena cava blood.
Equation 5 relates blood flow in the
upper and lower systemic circulations to total cardiac output (CO)
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(5)
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The analysis assumes a steady-state condition. At the cellular level,
on the basis of the law of mass conservation, oxygen uptake and oxygen
consumption must be equal. Therefore
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(6)
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By replacing
CSVCO2 · QSVC
in Eq. 4b with Eq. 3 and replacing QP
with QSVC by using
Eq. 4a, and then using
Eq. 6, we obtain
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(7)
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Using
Eq. 5 gives
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(8)
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Using Eqs. 3,
4b, and
5, note that
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(9)
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Combining Eqs.
8 and 9, systemic arterial oxygen
delivery
(CaO2 · CO)
equals
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(10)
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Thus systemic oxygen delivery is a complex function of
cardiac output, pulmonary venous blood oxygen content, lower body oxygen consumption [(1 k) · O2],
and
QSVC/QIVC.
Using a Compaq computer (Deskpro 486 66dx, Compaq Computer, Houston,
TX), we studied this relationship by altering each variable individually while considering the following constraints. The relevant
physiological and physical constraints were that the arterial oxygen
content cannot be less than zero and that blood flow rates
(QSVC and
QIVC) must be positive, i.e., in
the direction of the QSVC and
QIVC arrows in Fig.
1. In RESULTS, blood
oxygen content was converted to percent oxygen saturation by assuming a
hemoglobin concentration ([Hb]) of 15 g/dl,
giving an oxygen capacity of 22 ml
O2/dl blood (1.38 × 15[Hb]).
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RESULTS |
Figure 2A
shows oxygen delivery (top) and
saturations (bottom) as a function
of the ratio
QSVC/QIVC.
In this example, the whole body oxygen consumption was set to 9 ml
O2 · min
1 · kg1,
which represents a normal mean value for infants and young children (18). The percentage of oxygen consumed by the upper body,
k, was set to 60%. Figure
2A, top, shows that as
QSVC/QIVC
increases, lower body systemic oxygen delivery initially increases.
This is because QSVC, which is
equal to pulmonary flow, increases. However, as
QSVC/QIVC
increases further, lower body systemic oxygen delivery reaches a
maximum and then decreases. This decrease is due to the decrease in
QIVC. At the peak of the lower
body oxygen delivery, the optimal value for
QSVC/QIVC
is <1 (i.e., QIVC > QSVC or
QP). In contrast, upper body and
whole body (total) systemic oxygen delivery increase continuously as
QSVC/QIVC
increases.
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Fig. 2.
Glenn shunt circulation. A:
semilogarithmic plots of oxygen delivery
(top) and oxygen saturation
(bottom) vs.
QSVC/QIVC.
B: plots of superior (SVC) and
inferior vena caval (IVC) oxygen saturations vs.
QSVC/QIVC.
Solid lines, k = 60%; dashed lines,
k = 30%. For
A and
B, pulmonary venous oxygen saturation
(SPVO2) = 98%; CO = 200 ml · min1 · kg1.
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Figure 2A, bottom, shows the
relationship of oxygen saturations vs.
QSVC/QIVC.
As
QSVC/QIVC
increases, systemic arterial
(SaO2) and
superior vena caval oxygen saturation
(SSVCO2)
continually increase. The changes in inferior vena caval oxygen
saturation (SIVCO2)
resemble the changes in lower body systemic oxygen delivery: as
QSVC/QIVC
increases,
SIVCO2
initially increases, reaches a
maximum, and then decreases.
In Fig. 2A,
top and
bottom, there are two vertical dashed
lines. These lines represent the effects of early development. The line
on the right has a
QSVC/QIVC
of 1.56, which was the average value found in children (mean age 2.95 yr) after a Glenn shunt procedure (21). The line on the left has a
QSVC/QIVC
of 0.65, which is the average value for 6-yr-old children (21). As the child develops, the lower body grows proportionately more than the
upper body. Thus
QSVC/QIVC
will decrease. Thus normal early growth will decrease upper body oxygen
delivery and SaO2.
Figure 2B plots
SSVCO2
and
SIVCO2
vs.
QSVC/QIVC.
The solid lines were obtained with the percentage of oxygen consumed by
the upper body, k, set to 60%,
whereas for the dashed lines k was set
to 30%.
SIVCO2
is affected by this percentage. Lowering the percentage of oxygen
consumed by the upper body (or conversely increasing the percentage of
oxygen consumed by the lower body) decreases
SIVCO2.
However,
SSVCO2 is only minimally affected by the percentage of oxygen consumed by the
upper body. The decrease in upper body oxygen consumption and the
decrease in arterial oxygen content tend to cancel each other, leading
to only minimal changes in
SSVCO2.
Also note in Fig. 2B the points of
intersection at which superior and inferior oxygen saturations are
equal
(SSVCO2 = SIVCO2). At these points, blood flow is matched to oxygen demands
[QSVC/QIVC = k/(1 k)]. When
SSVCO2 > SIVCO2,
the superior vena cava blood flow is disproportionately higher than
oxygen demands and/or inferior vena cava blood flow is
disproportionately lower than oxygen demands. Conversely, when
SSVCO2 < SIVCO2,
the superior vena caval blood flow is disproportionately lower than
oxygen demands and/or inferior vena caval blood flow is
disproportionately higher than oxygen demands. Note in Fig. 2A we plotted
QSVC/QIVC
from 0.1 to 4 on a logarithmic scale to show the complete theoretical
response. However, after the Glenn shunt, ratios >4 are uncommon.
Figure 3 plots the maximum systemic oxygen
delivery possible at any given cardiac output. The results are shown
for the present Glenn shunt simulation, for our previously published
hypoplastic left heart syndrome circulation simulation (4), and for the nonfenestrated Fontan circulation. Figure 3 shows the equations used to
calculate the maximal systemic oxygen delivery. For the Glenn shunt,
because there is no obvious peak oxygen delivery, we tied
QSVC/QIVC
to the ratio of upper to lower body oxygen consumption [QSVC/QIVC = k/(1 k)].
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Fig. 3.
Plot of maximal oxygen delivery for any given CO. Curves are shown for
hypoplastic left heart syndrome (HLHS), univentricular plus Glenn
shunt, and nonfenestrated Fontan (nf-Fontan) circulations.
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For all circulations, a higher peak systemic oxygen delivery requires a
higher cardiac output. In the nonfenestrated Fontan circulation,
deoxygenated blood is not recirculated, and thus this is the most
efficient circulation. For the same oxygen delivery, the nonfenestrated
Fontan circulation requires considerably less cardiac output than the
hypoplastic left heart syndrome circulation does. The Glenn shunt is
between the nonfenestrated Fontan and the hypoplastic left heart
syndrome circulations. The slope of oxygen delivery vs. cardiac output
is the same for the Glenn shunt and the nonfenestrated Fontan
circulation. The improvement in oxygen delivery after the Glenn shunt
operation depends on the k value: the
higher the percentage of oxygen consumed by the upper body, the lower
the cardiac output required for the same systemic oxygen delivery. Both
early development, with its relative increase in lower body size
compared with the upper body, and exercise (walking, running) will
decrease k and thereby decrease the
efficiency of the Glenn shunt circulation.
Figure 4,
A and
B, plots whole body oxygen delivery
and arterial and venous oxygen saturations, respectively. These
variables are plotted against k.
Again, we tied
QSVC/QIVC
to the ratio of upper to lower body oxygen consumption
[QSVC/QIVC = k/(1 k)]. As the percentage of
upper body oxygen consumption decreases, whole body oxygen delivery and
arterial and venous oxygen saturations decrease. Exercise (walking,
running) will increase lower body oxygen consumption and thus reduce
k. In younger children, growth will
increase the relative size of the lower body and thus reduce k. Both of these factors (exercise and
growth) are additive. Hence, early development and exercise, by
themselves, will decrease oxygen delivery and decrease blood gases.
This situation is depicted in Fig. 4,
A and
B. As the infant grows (dashed
line A to dashed line B), oxygen delivery and
arterial and venous oxygen saturations will decrease. If the child
starts to walk or run (dashed line B to dashed line
C), oxygen delivery and arterial and venous oxygen saturations
will decrease further.
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Fig. 4.
Effects of growth and exercise on oxygen delivery and oxygen
saturation. A: whole body oxygen
delivery vs. k (in %).
B: arterial
(SaO2) and venous oxygen
saturations
(SvO2) vs.
k (in %). Growth period, dashed
line A to dashed line B; exercise period, dashed
line B to dashed line
C.
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Figure 5 plots the ratio of Glenn to
nonfenestrated Fontan circulation cardiac output
(COGlenn/COnf-Fontan)
vs. k.
COGlenn/COnf-Fontan indicates how much extra cardiac output is required in the Glenn shunt
circulation for the same oxygen delivery as in the nonfenestrated Fontan or normal circulation. A ratio of 2 would indicate that the
Glenn shunt circulation would require twice the nonfenestrated Fontan
cardiac output for the same oxygen delivery. Figure 5 plots these
relationships for resting conditions (CO = 200 ml · min1 · kg1)
and for mild exercise (CO = 400 ml · min1 · kg1).
As k decreases, the efficiency of the
Glenn circulation decreases. However, this decrease is not linear. For
k 
50%, the efficiency decreases
rapidly. Figure 5 also shows the effects of early development and
exercise on efficiency. As the infant grows (dashed line A to dashed line B), efficiency decreases. If the child
starts to walk or run now (dashed line B to dashed
line C), efficiency will decrease further.
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Fig. 5.
Ratio of Glenn to nonfenestrated Fontan circulation cardiac outputs
(COGlenn/COnf-Fontan)
vs. k (in %). Note that as
k decreases, the Glenn shunt
circulation requires considerably more CO for the same systemic oxygen
delivery compared with the nonfenestrated Fontan circulation. Curves:
CO = 200 and 400 ml · min1 · kg1.
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DISCUSSION |
The present analysis examined the balance between pulmonary and lower
body systemic blood flows in univentricular circulation after a
bidirectional cavopulmonary anastomosis. The model was based on the
flow of oxygen uptake in the lungs and of whole body oxygen
consumption. The analysis developed an equation relating the key
variables of cardiac output, pulmonary venous oxygen saturation, lower
body oxygen consumption, and
QSVC/QIVC
to systemic oxygen delivery.
The key findings are as follows. 1)
As
QSVC/QIVC
increases, upper body and total oxygen delivery increases along with
systemic SaO2 and
SSVCO2.
2) As
QSVC/QIVC
increases, lower body oxygen delivery and
SIVCO2
initially increase, then peak, and then decrease.
3) For a high systemic
SaO2 after a bidirectional cavopulmonary
anastomosis, a low percentage of oxygen consumed by the lower body and
a high
QSVC/QIVC
are needed. 4) As the percentage of
oxygen consumed by the lower body increases with early development or
exercise, whole body oxygen delivery and
SaO2 decrease.
5) A bidirectional cavopulmonary
anastomosis greatly decreases the required cardiac output to achieve
the same oxygen delivery as the univentricular circulation.
6)
SSVCO2
and
SIVCO2 are different.
Review of literature and clinical implications.
Salim et al. (21) examined the pulmonary-to-systemic flow ratios
(QP/QS)
in 29 children (mean age 2.95 yr) studied 1.25 yr after cavopulmonary
anastomosis. They found the following mean values:
SaO2 = 84%,
SSVCO2 = 61%,
SIVCO2 = 65%, QP/QS = 0.61, and cardiac index = 4.10 l · min1 · m2.
Gross et al. (10) reported similar values for
SaO2 (86%), QP/QS
(0.69), and cardiac index (3.1 l · min1 · m2).
On the basis of our theoretical analysis, for a high
SaO2 after the Glenn shunt operation, a
high pulmonary venous oxygen saturation (SPVO2),
a high
QSVC/QIVC,
and a high k value are required for
SaO2 to exceed 80%. In our controls, we
set pulmonary venous oxygen saturation at 98%, the same value reported
by Salim et al. (98%) (21). Cardiac output was set to
200 ml · min1 · kg1
in our analysis. Assuming that a 4-kg baby has a height of 53 cm for a
body surface area of 0.19 m2, this
gives a cardiac output of 4.2 l · min1 · m2,
similar to the value reported by Salim et al. (21). As
per QP/QS,
note that we calculated this as pulmonary flow divided by inferior vena
caval flow and not as pulmonary flow divided by total systemic flow
[QSVC/(QSVC + QIVC)]. Thus a
QP/QS
of 0.61 would equal a
QP/QS
of 1.56, and
QP/QS
can never be >1.
In our controls, we set the percentage of upper body oxygen consumption
to 60%, close to the value estimated from the data of Salim et al.
(21). The mixing of the systemic venous blood and
pulmonary venous blood lowers the resulting arterial oxygen tension. If
the lower body uses more oxygen, systemic venous return oxygen tension
decreases, thereby lowering the subsequent systemic arterial oxygen
tension. Conversely, upper body oxygen consumption does not affect
systemic arterial oxygen tension: the deoxygenated blood from the upper
body flows from the superior vena cava into the lungs and is
reoxygenated in the lungs. This is the advantage of the Glenn shunt.
Cardiac output and oxygen delivery.
In the normal circulation, all the deoxygenated blood flows through the
lungs, and only oxygenated blood is supplied to the systemic
circulation. In the hypoplastic left heart circulation, the systemic
and pulmonary circulations are in parallel. Thus, for the same systemic
oxygen delivery, the univentricular circulation requires almost twice
the normal cardiac output. The Glenn shunt is between the
nonfenestrated Fontan and hypoplastic left heart circulations. The
blood flow to the upper body is in series with the pulmonary
circulation. The deoxygenated blood flows into the lungs, similar to
the normal circulation. Thus there is no wasted energy or decreased
efficiency in the upper circulation. However, the deoxygenated blood
from the lower body is mixed with the oxygenated blood from the
pulmonary veins, thereby reducing systemic oxygen saturation. This is
the wasted energy in the Glenn shunt. Although physiologically
impossible, the extremes provide insight. With no upper body oxygen
consumption, the Glenn shunt becomes the hypoplastic left heart
circulation again. With no lower body oxygen consumption, the Glenn
shunt becomes a nonfenestrated Fontan circulation.
The analysis indicates that the Glenn shunt is more efficient than the
hypoplastic left heart circulation but less efficient than the
nonfenestrated Fontan circulation. This implies that the systemic
ventricle will decrease in size after the Glenn shunt operation but
will still be larger than normal. Consistent with these ideas, several
clinical studies have reported a significant decrease in the systemic
ventricular volume after the Glenn operation. In patients with
tricuspid atresia, LaCorte et al. (14) reported that two patients with
a Glenn shunt had the least abnormal values for volumes and ejection
fraction. Graham et al. (9) reported that three patients with a Glenn
shunt had the smallest volumes among the patients with postshunt
tricuspid atresia. Kobayashi et al. (13) showed that the systemic
ventricular end-diastolic volume index decreased significantly, from
141 ml/m2 before to 98 ml/m2,
1 mo after bidirectional cavopulmonary shunt. Similarly, Allgood et al.
(2) showed a significant decrease in the ventricular volume with the
bidirectional Glenn shunt procedure.
Effects of early development and exercise.
As stated above, the reduction in arterial oxygen tension is caused by
lower body oxygen consumption. This is the extra cardiac output
required in the univentricular circulation after the Glenn shunt. Thus
anything that increases the percentage of lower body oxygen consumption
will decrease systemic oxygen delivery and necessitate a higher cardiac
output. Our analysis would predict that with walking or running or
after a meal, the percentage of upper body oxygen
consumption will decrease and SaO2 will
also decrease. We know of no studies that have measured
SaO2 with the child active. Another
important and uncontrollable cause for increases in lower body oxygen
consumption is early development or growth. As the child becomes older,
the lower body grows proportionately more than the upper body (16).
This will decrease the proportion of upper body oxygen consumption and
result in a decrease in SaO2.
Several clinical studies and observations are consistent with these
predictions. The Glenn shunt palliation appears to be good for the
first 5-7 yr and deteriorates after 7 yr (3, 7, 9, 15) with
progressive cyanosis. Cyanosis may be due to collaterals between the
superior and inferior vena cava system, due to a
pulmonary arteriovenous shunt, and due to ventricular dysfunction.
Independent of these effects, age also may be a factor. Gross et al.
(10) analyzed the data from 45 patients with univentricular congenital
heart disease after a bidirectional cavopulmonary anastomosis. They
found that the patient's age and body surface area were associated with postoperative desaturation independently of other known causes of
cyanosis. Likewise, Allgood et al. (2) showed age to be independently
associated with the ventricular volume status before and late after the
Glenn procedure and with the early postoperative ventricular mass. Thus
older age may be a risk factor for cyanosis, perhaps because of a
smaller proportion of blood return from the superior vena cava relative
to the inferior vena cava. For example, in the study of Gross et al.
(10),
QP/QS
was 0.69 for younger children (2.8 yr) but only 0.44 in the older
children (9.6 yr). In 145 healthy children, Salim et al. (22) observed
that the superior vena caval flow accounted for 49% of cardiac output
in newborn infants, reached a maximum of 55% at age 2.5 yr, and then gradually decreased to the adult value of 35% by 6.6 yr. Obviously, additional clinical observations are needed to verify these theoretical predictions.
In this model, both declines in
SPVO2
and increases in oxygen consumption were associated with significant
declines in systemic oxygen saturation, and these effects were
additive. Alteration in
SPVO2
related to intrapulmonary shunting of blood results in a lowering of
the absolute ceiling for systemic oxygenation due to incomplete
oxygenation of upper body systemic blood return. In contrast, given a
fixed
SPVO2,
an increase in oxygen consumption will only influence the lower body
contribution to systemic oxygenation (the second term on the right side
of Eq. 10); therefore,
the influence of increased oxygen consumption will be greatest if the
percentage of oxygen consumed by the upper body is small. This
influence will be greater as the child grows (decreasing
k) and will be accentuated by
physical activity such as running.
Timing of Fontan operation.
The analysis also provides some insight into when to perform the Fontan
operation. Assuming blood flow and oxygen demands are matched
[QSVC/QIVC = k/(1 k)], our analysis shows that
as QSVC/QIVC
decreases, the advantages of the Glenn shunt decrease: i.e., mechanical
efficiency, systemic oxygen delivery, and arterial and venous oxygen
saturations all decrease. In healthy children, QSVC/ QIVC = 0.96 in newborn infants, reaches a maximum of 1.22 at age 2.5 yr, and
then gradually decreases to the adult value of 0.54 by 6.6 yr (22).
This would suggest that 2.5-3 yr of age would be the age to start
to consider the Fontan procedure. Because these flow ratios were
determined in normal children, another approach, if possible, would be
to directly measure
QSVC/QIVC in the patient. When this ratio is 1
(QSVC QIVC), the Fontan operation
should be considered. Obviously, many factors need to be considered.
This analysis only considers the effects of
QSVC/QIVC and the percentage of lower body oxygen consumption. Thus the suggested
age may be too early when all the other relevant factors are taken into
consideration.
Limitations.
In Figs. 3-5, we assumed that blood flow and oxygen consumption
were linearly related. If the upper body consumed 60% of total body
oxygen, then QSVC equaled 60% of
total cardiac output. This assumption allowed us to plot oxygen
delivery and oxygen saturations vs. k
and relate this to changes in growth and exercise. If the upper body
had a disproportionately higher flow
(QSVC) compared with its oxygen
consumption, the effects of growth and exercise would be less than
shown in Figs. 3-5. Conversely, if the lower body
had a higher flow (QIVC)
compared with its oxygen consumption, then the effects of growth and
exercise would be greater. Without any data available from the
literature on responses during exercise, the exact relationship between
flow and oxygen consumption is impossible to determine. Thus we used a
linear assumption.
Whether
QSVC/QIVC
can be acutely changed after Glenn shunt operation is unknown. One view
is that because upper body systemic vascular resistance is in series
with the pulmonary vascular resistance and because the upper body
systemic vascular resistance is so much greater than pulmonary vascular
resistance, small changes in pulmonary vascular resistance will have
only minimal effects on
QSVC/QIVC.
We believe that the systemic upper body vascular resistance is like a
waterfall. The pulmonary circulation is downstream from the systemic
arterial capillary waterfall. Thus pulmonary blood flow is not affected
by systemic arterial pressure (by the height of the waterfall). Rather,
pulmonary blood flow is passively controlled by pulmonary artery
pressure and pulmonary vascular resistance. If these ideas are correct,
then changes in pulmonary vascular resistance will have a large effect
on
QSVC/QIVC
and will also elevate superior vena caval pressure. The development of
the superior vena caval syndrome and an increase in mortality after the
Glenn shunt procedure in patients with elevated pulmonary vascular
resistance have been well described clinically (1). Experimental
studies and further clinical observations will be necessary to resolve
this issue.
| |
FOOTNOTES |
Address for reprint requests: W. P. Santamore, Dept. of Surgery,
Division of Thoracic and Cardiovascular Surgery, Univ. of Louisville,
Louisville, KY 40292.
Received 31 January 1997; accepted in final form 22 September
1997.
| |
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