(Circulation. 1999;100:2198.)
© 1999 American Heart Association, Inc.
Basic Science Reports |
Oxygenation in Patients With a Functionally Univentricular Circulation and Complete Mixing of Blood
Are Saturation and Flow Interchangeable?
From the Department of Cardiology (D.P.F., S.A.T., L.C.D., A.J.S.C.) and the Biomedical Engineering Research Unit (K.W.), Royal Brompton Hospital, and the National Heart and Lung Institute, Imperial College of Science, Technology, and Medicine (D.P.F., S.A.T., L.C.D., A.J.S.C.), London, UK.
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Abstract |
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 Top Abstract IntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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Background—Perioperative management of patients with complete mixing of pulmonary and systemic blood centers on approximately equating pulmonary (Qp) and systemic (Qs) blood flow (Qp/Qs
1). This empirically derived
target is opposed by theoretical studies advocating a target Qp/Qs well
below 1. We studied the cause of this persistent discrepancy. Methods and Results—Classic theoretical studies have concentrated on maximizing 1 of many potential combination parameters of arterial oxygen content (CaO2) and systemic blood flow: total oxygen delivery (DO2)=CaO2xQs. We defined "useful" oxygen delivery as the amount of oxygen above a notional saturation threshold (SatThresh): D(u)O2=carrying capacityx(SaO2-SatThresh)xQs. Whereas DO2 peaks at Qp/Qs ratios <1, D(u)O2 peaks at higher Qp/Qs ratios, nearer to (or exceeding) 1. Systemic venous saturation (which mirrors tissue oxygen tension) peaks at Qp/Qs=1.
Conclusions—First, the standard model of single-ventricle physiology can be reexpressed in a form allowing analysis by differential calculus, which allows broader conclusions to be drawn than does computer modeling alone. Second, the classic measure DO2 fails to reflect the fact that proportional changes in saturation and flow are not clinically equivalent. Recognizing this asymmetry by using D(u)O2 can give a target Qp:Qs balance that better represents clinical experience. Finally, to avoid an arbitrary choice of SatThresh, systemic venous oxygen saturation (SsvO2) may be a useful parameter to maximize: this occurs at a Qp/Qs ratio of 1. Attempts to increase DO2 by altering Qp/Qs away from this value will inevitably reduce SsvO2 and therefore tissue oxygenation. Oxygen delivery is far from synonymous with tissue oxygen status.
Key Words: oxygen • circulation • blood flow
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Introduction |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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Patients with complete mixing of pulmonary and systemic blood present a difficult clinical problem,1 particularly in the delicate perioperative period, when mortality can be very high.2 3 Given a limited cardiac output, clinicians on the critical care unit modify filling pressures and vary the administration of oxygen (a pulmonary vasodilator), carbon dioxide (a peripheral vasodilator), and inotropic and vasoactive agents to affect the relative flows through the systemic and pulmonary circulations.3
A clinical target of an approximately equal division of flow between
pulmonary (Qp) and systemic (Qs) arms of the circulation
(Qp/Qs1) is a common one1 4 that has been developed
largely by trial and error.
Theoretical studies5 6 have considered the effects of different Qp/Qs ratios with the aim of forming an analytical basis for the clinical manipulations. However, the standard mathematical model has persistently yielded target Qp/Qs ratios of <1.
We set out to study the reason for this discrepancy and consider possible ways of unifying theory and practice.
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Choice of Variable to Maximize and Implicit Choice of Relative Merits of Flow and Saturation |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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Tissue oxygenation is difficult to measure directly. It is intuitively obvious that for any given peripheral blood flow Qs, the situation of the tissues would be improved if the arterial oxygen content (CaO2) were to rise. Likewise for any given arterial oxygen content, an increase in Qs would clearly be beneficial. This much is not in contention.
In principle, one aims to combine these 2 variables into a single parameter that can be maximized theoretically and clinically in the hope of thus optimizing the clinical state of the patient. However, a wide variety of combination parameters are conceivable that demonstrate an increase when either CaO2 or Qs alone increases. The combination parameters differ in the way they interpret the balance of benefit and harm when (for example) Qs increases while CaO2 falls.
Recent theoretical studies have chosen the product of the 2 as the combination parameter. This is known as oxygen delivery: DO2=CaO2 · Qs. Alongside this explicit selection, there is therefore an implicit assumption that any change in 1 variable, if it were accompanied by a reciprocal change in the other, would lead to zero net clinical effect. For example, by choosing to use DO2 as our combination parameter, we are saying that a fall in arterial oxygen saturation from 80% to 40% would have no net clinical effect if Qs could somehow be doubled from 0.3 to 0.6 L · min-1 · kg-1.
How can we have arrived at such an untenable result? The answer lies in the choice of combination parameter. DO2 recognizes no special nature in saturation that distinguishes it from flow: it in effect considers them to be interchangeable.
What if they are not interchangeable? The question arises because not all the O2 molecules that arrive in the systemic circulation are of equal value. The first molecules to be removed from the oxygenated blood are unloaded at a high capillary PO2. Once these valuable molecules are transferred into the tissue, those that remain are of lower value, because they will only pass into tissue of low PO2.
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Total Delivery or Useful Delivery? |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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Any given total delivery is more helpful to the tissue (ie, demands a less severe tissue hypoxia for the transfer to occur) if it is delivered as a smaller quantity of high-saturation blood than if it is delivered as a large quantity of low-saturation blood. Assessment of DO2 (which treats flow and saturation symmetrically) unfortunately does not recognize this fact. One simple solution is to assert an arbitrary saturation threshold, SatThresh, below which we consider the tissues to be "scraping the bottom of the barrel." The modified parameter, which we propose to call "useful oxygen delivery" (D(u)O2), can be calculated by a simple modification of the formula for DO2.
We placed a notional threshold in capillary oxygen saturation
(SatThresh) below which any further oxygen
remaining (carrying capacityxSatThresh) should
be considered not useful for maintaining normal function. The amount of
oxygen being delivered in a useful form to the body could therefore be
considered to be not
DO2=CaO2
· Qs but rather
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Capillary Contents: Quantity or Quality? |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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The term "oxygen delivery" may itself be a misnomer, because its formula represents the total amount of oxygen that passes through the systemic capillary tree. Not all of this is actually delivered into the tissues: indeed, true delivery into tissues must equal total tissue utilization of oxygen (
O2). Using the measurable values of blood oxygen saturations, the closest we can get to determining tissue oxygen levels is to examine the blood that was in equilibrium with it most recently, ie, mixed blood in the systemic veins. Thus, systemic venous O2 saturation may be our best available capillary indicator of mean systemic capillary O2 saturation and thus capillary PO2 and, indirectly, tissue PO2.
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Methods |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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A standard model of the univentricular circulation was used, as shown in Figure 1
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A single functioning ventricle receives blood from both the
pulmonary and systemic veins and pumps this mixture into both
pulmonary and systemic circulations. The content of oxygen is
the same (CaO2, measured in L
O2 per L blood) in both pulmonary and
systemic arteries, whereas in venous blood the contents differ
(CpvO2 and
CsvO2, respectively). The
cardiac output is divided between the pulmonary and systemic
circulations, with flow rates of Qp and Qs, respectively (in L/min). At
steady state, metabolic utilization of oxygen must be
matched by pulmonary oxygen uptake, so both can be
represented by the symbol
O2, measured in L/min. In both
systemic and pulmonary circulations, oxygen transfer rate is by
definition blood flow multiplied by the arteriovenous difference in
oxygen content.
 | (1) |
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The main free variable is therefore the balance of distribution of the limited cardiac output between pulmonary and systemic circulations (Qp:Qs balance). We used 2 independent methods to study the effect of changes in this balance.
Computer Model
We formed a model of the system described above using commercial
mathematical modeling software (Matlab, Mathworks) to assess the effect
of changes in distribution of cardiac output (Qp:Qs) on the value of
DO2 and
D(u)O2, as well as the ability of
CaO2 and
CsvO2 to predict the peak levels of
DO2 and
D(u)O2.
In the acute postsurgical situation of neonates, clinical work7 has suggested a cardiac output of 0.3 L · min-1 · kg-1 and an oxygen consumption of 0.009 L · min-1 · kg-1 as suitable approximations, although it should not be forgotten that patients with single-ventricle physiology may develop the ability to survive on even lower oxygen consumption rates. Oxygen-carrying capacity of blood was taken as 0.207 L O2/L blood, based on 1.38x10-3 L O2/g hemoglobin and a hemoglobin concentration of 150 g/L. We studied the effects of SatThresh values of 10%, 20%, 30%, 40%, and 50% on the behavior of D(u)O2 in relation to changes in balance between Qp and Qs.
Calculus Analysis
Differential calculus provides simple and well-validated methods
for analyzing the behavior of such systems of equations without the aid
(and restrictions) of a computer. Entirely independently of the
computer model, we applied differential calculus to the formulas above
to seek to understand the relationships between Qp:Qs distribution and
DO2,
D(u)O2, and systemic venous oxygen
saturation. The avoidance of computer modeling enabled us to consider
these relationships independently of any particular oxygen consumption
or cardiac output.
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Results |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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Computer Model of Total and Useful Oxygen Delivery: Impact of O2 Saturation Threshold
We studied the effect of varying Qp:Qs balance on both total DO2 (Figures 2
and 3, thick line, marked 0%) and
useful delivery D(u)O2 (thin lines).
We examined the impact of different notional minimal acceptable
capillary O2 saturation thresholds
(SatThresh): 10%, 20%, 30%, 40%, and 50%
(thin lines). Crosses mark the points at which Qp=Qs, that is, half of
the cardiac output goes to each part of the circulation.
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In Figure 2
, we can see that total oxygen delivery (thick line)
peaks at a Qp/Qs ratio of clearly <1. However, considering useful
oxygen delivery instead reveals 2 interesting facts. First,
D(u)O2 is of course less than
DO2: the absolute difference is
greatest at low Qp/Qs ratios. Second, the peak in
D(u)O2 occurs at higher Qp/Qs ratios
than the peak in DO2. Indeed, so
great is this shift in optimal Qp/Qs that it becomes >1 at higher
SatThresh values.
The effect can be seen more clearly by eliminating the distorting
nonlinearity introduced by the Qp/Qs ratio and considering instead Qp
itself (with Qs understood to be CO-Qp), as shown in Figure 3.
More striking is the implication for the interpretation of
arterial blood gases. In Figure 4, we show the relationship of useful
oxygen delivery to arterial oxygen saturation. At Qp/Qs=1
(crosses on graph), arterial saturation is 60%. Clearly,
total oxygen delivery peaks at an oxygen saturation at which Qp/Qs is
<1 (to the left of the cross on the thick line). However, evaluation
of useful oxygen delivery reveals that its maximum coincides with
higher oxygen saturations than those of maximum total
DO2. Note also that for a
SatThresh of 30% (central thin line), useful
oxygen delivery falls to zero when arterial saturation is
30%, because below this threshold, blood flow (however vigorous)
cannot contribute oxygen above SatThresh.
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In Figure 5, we can see that systemic
venous saturation levels peak at a Qp/Qs ratio of 1 (as shown in the
previous section). What is interesting is that 1 particular venous
saturation may indicate 2 completely different
DO2 values and similarly, 2 different
D(u)O2 values, even when the same
SatThresh is used. The only exception is when
systemic venous saturation is maximal, which corresponds to a unique
Qp/Qs ratio of 1, and consequently an unambiguous
DO2 or
D(u)O2.
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Maximizing DO2 and
D(u)O2 by Altering Qp:Qs Balance: Results From
Application of Differential Calculus
To determine the flow balance at which
DO2 or
D(u)O2 reaches its peak, we can
exploit the fact that Qp+Qs=CO:
 | (2) |
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Of course, total DO2 is simply
the special case of D(u)O2 at which
SatThresh=0, and so it need not be considered
separately at this stage. To identify the Qp at which
D(u)O2 is maximal, we
differentiate:
 | (3) |
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The maximum value of D(u)O2 is
obtained when this expression is zero, ie, when
 | (4) |
Perhaps the most important result of all is that useful oxygen
delivery D(u)O2 is maximal when the
pulmonary flow fraction is
 | (5) |
In contrast, traditional total oxygen delivery
DO2 is maximal at this flow
fraction:
 | (6) |
D(u)O2 clearly peaks at a
different Qp:Qs balance than does
DO2. The effect of choosing
successively higher putative minimal useful oxygen saturation
thresholds (SatThresh) is to progressively raise
the Qp/CO ratio at which D(u)O2 is
maximal. The target Qp/CO will reach one half (and therefore target
Qp/Qs will reach 1) when a SatThresh of
is selected, which for our case is 37%. Above this value of
SatThresh, a Qp/Qs ratio of >1 will be necessary
to maximize D(u)O2.
Impact of Qp:Qs Balance on Systemic Arterial and
Venous Saturations
Leaving aside the derived variables
DO2 and
D(u)O2, we turned to address the
relationship of Qp:Qs balance on the systemic arterial and
venous saturations, which are more concrete physical variables.
Using Equation 1, we studied the effect of changing Qp:Qs balance on
arterial and systemic venous saturations (Figure 6). Cardiac output (Qs+Qp) was kept
constant at 0.3 L · min-1 ·
kg-1, as was
O2 at 0.009 L ·
min-1 · kg-1.
Pulmonary venous O2 saturation was taken
as 95%.
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As can be seen from the equation
and the graph, at high Qp, CaO2 is
only slightly below CpvO2. However,
the consequence of a high Qp with a limited CO is that Qs is small.
Hence, from the equation
or the graph, it can be seen that
CsvO2 is forced considerably below
the arterial level.
In contrast, at low Qp, CaO2 is a long way below CpvO2, but CsvO2 is not far below that level. Either extreme of flow distribution leads to a low CsvO2.
What flow balance gives the highest
CsvO2? From Equations 1, we
derive
 | (7) |
.
These relationships all hold true regardless of the level of
O2 or CO. |
Discussion |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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In the management of patients with complete mixing of systemic and pulmonary blood, the clinical management has focused on attaining a Qp/Qs ratio of
1. Existing theoretical analyses
have studied the relationship of controllable parameters
(such as the pulmonary-to-systemic flow ratio, Qp/Qs) and
measurable parameters (such as arterial and
systemic venous saturations). One particular parameter that
combines information about flow and saturation is
DO2. This variable has
been shown6 to peak at Qp/Qs ratios distinctly <1. It has not been clear how to reconcile this with the often-used clinical target of Qp/Qs=1. Our observation is that not every molecule of oxygen passing through the systemic circulation is of equal value: those traveling in blood at higher saturations are able to be delivered at higher tissue partial pressures and are therefore more beneficial to tissue metabolism. Blood containing oxygen at lower saturations is of less value, even if the flow rate is correspondingly larger. The impact of these considerations on optimal Qp/Qs ratios and saturation measurements has not previously been assessed in detail.
Theoretical optimization of hemodynamics using DO2 alone can lead to some perverse choices when saturation is significantly <100%. We believe that this contradiction between theory and clinical judgment is due to the insidious effect of choosing a simple (and at first sight, plausible) combination parameter for blood flow and arterial oxygen content. We believe that the tissue pressure at which the oxygen is made available is important rather than irrelevant.
These considerations are not purely academic, because the choice of parameter to optimize has a significant effect on the direction in which clinicians might attempt to influence changeable hemodynamic parameters such as Qp:Qs balance.
Factors Affecting Arterial and Systemic Venous
Saturations
Blood draining from the pulmonary veins undergoes 2
downward steps in oxygen content (Figure 7). First, at the time of mixing in the
ventricle, it falls by O2/Qp
from CpvO2 to
CaO2. Blood traveling to the systemic
circulation then transfers an amount of oxygen
O2/Qs to the tissues and ends
up with oxygen content CsvO2.
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High cardiac outputs allow large Qp and Qs to coexist, and so there are only small drops in oxygen content and consequently CsvO2 is not very low. However, given a limited total cardiac output, there is a trade-off between the pulmonary-venous–to-arterial drop and the arterial-to–systemic-venous drop, because any change in Qp results in a concomitant contrary change in Qs.
Maximal Attainable Systemic Venous Saturation
It can be seen from inspection of Equation 7 or Figure 6, or by application of calculus, that the situation that
maximizes CsvO2 for any given cardiac
output is Qp=Qs=CO/2. The maximal systemic venous saturation that can
be attained
is
,
which neatly summarizes the possible modalities (other than equalizing
flow in systemic and pulmonary circulation) by which the
oxygenation of such patients may be improved.
SpvO2 can often not be safely
increased because this would lead to a fall in pulmonary
vascular resistance and therefore an adverse change in Qp:Qs balance.
O2 is not under the
clinician’s direct control. It only remains to maximize the
product of carrying capacity and cardiac output while realizing
that if the carrying capacity is made too high by excessive blood
transfusion, the increase in blood viscosity can impede flow and thus
reduce cardiac output.
Quantity Flowing Past or Quality at Point of Delivery?
Oxygen delivery has been the center point of a variety of
proposals for a choice of parameter to optimize: maximizing
DO2 (Reference 66 ); maximizing
DO2/O2
(also called 
)8 ; or minimizing
O2/DO2
(also called oxygen extraction ratio).9
Given a constant metabolic rate
(O2), we can see from Equation 5 that all of these targets are met simultaneously when the
proportion of cardiac output sent to the pulmonary circulation
is
.
For our case of O2=0.009
L · min-1 ·
kg-1, CO=0.3 L ·
min-1 · kg-1, and
CpvO2=0.95x0.207=0.197 L
O2/L blood, this optimal flow balance is 39%
pulmonary, 61% systemic. This accords with the findings of the
graph from the computer model. In fact, from the algebraic formulas,
DO2 maximization will continue to
recommend Qp/Qs<1 unless cardiac output rises above
,
ie, 0.065 L · min-1 ·
kg-1.
All suffer from the limitation that the quality-blind parameter DO2 is used, rather than a quality-conscious one such as D(u)O2, and so lower arterial saturation, however severe, is considered to be able to be compensated for simply by proportionately higher flows. Yet computation of D(u)O2 rather than DO2 is not a panacea: it involves an arbitrary saturation threshold and still retains assumptions of a linear relationship of useful delivery to flow and saturation. The model could be refined further, although at the cost of substantially increased complexity.
The problem is that in tissues, oxygen extraction continues until metabolic requirements are met, even if this means that tissue oxygen tension is too low for satisfactory organ function. The oxygen tension in the tissue is determined not by the tension prevailing when the first molecule of O2 is unloaded but rather by the tension at which the last molecule is transferred: this in turn is intimately related to SsvO2 by the hemoglobin dissociation curve.
Maximizing DO2 and maximizing
SsvO2 will lead to different
SsvO2 values and hence different
tissue oxygen tensions. The magnitude of the difference (shown
in Figure 8) is small, at 3 to 8
percentage points in saturation, corresponding to <0.4 kPa in terms of
PO2. Yet it may be clinically
important in the intensive care setting, given that it may
represent a 10% difference in
PO2 and that the patients may be
poised unstably at the extreme of physiological
endurance.
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Determination of SsvO2 is difficult
and can be subject to measurement error,10 but the
substitution of SsvO2-derived
parameters such as DO2,
DO2/O2,
and
O2/DO2
cannot ameliorate this. From a clinical point of view, it is often
remarked that the venous sample is taken from a vein containing a
biased sample of venous blood and therefore does not show true mixed
venous saturation. However, it is likely that the difference in
saturation between this sample and true mixed venous saturation is
stable, so that maximizing the measured saturation is likely to
maximize true mixed venous saturation. We suggest that adding,
subtracting, multiplying, or dividing by other parameters,
alone or together, cannot generate a parameter that more
closely reflects changes in tissue oxygenation than
does SsvO2.
Indeed, clinical outcome studies in perioperative patients with hypoplastic left heart syndrome support a relationship between gradual elevation in SsvO2 and survival.3 Particularly interesting is the observation in stable congenital heart disease patients11 that with low SsvO2 values, oxygen extraction can no longer be increased (because tissue PO2 values are too low) and consequently, aerobic metabolism becomes restricted.
The considerations outlined in this article are applicable not only to the neonatal patient but also to any patient with a functionally univentricular circulation and complete mixing of blood.
In patients without congenital cardiac disease who are undergoing supportive care in the intensive care unit, attempts have been made to maximize DO2, with conflicting results.12 13 Nor has maximization of mixed venous oxygen saturation14 been successful in conferring survival benefit among adults with normally connected hearts. However, their situation clearly is markedly different from that of the neonate with complete mixing, because the clinician is not adjusting the balance between pulmonary and systemic blood flow and trading off flow against saturation.
Conclusions
We contend that an excessive focus on quantity of delivered
oxygen, as occurs in attempts to maximize
DO2, necessarily involves depriving
the body of quality of oxygen delivery. Instinct would prevent a
clinician from believing the implication from
DO2 calculations that a fall in
SaO2 from 90% to 15% could be
adequately compensated for by an increase in blood flow from 0.15 to
0.90 L · kg-1 ·
min-1. When more subtle changes are involved,
however, clinical judgment is less able to help.
We propose that maximizing D(u)O2 is a more logical target than maximizing total DO2 and show how it gives a result that accords more closely with clinical judgment. We demonstrate the potential loss of capillary saturation, and hence tissue oxygen tension, that can arise from undue attention to DO2 despite a falling SsvO2. Yet even D(u)O2 cannot be said to be a perfect quantifier of oxygen traveling to tissues. A notional "perfect" parameter, taking into account the curvilinear nature of hemoglobin-oxygen dissociation and the potential for tissue metabolism to vary with oxygen delivery, may in the end closely mirror the simple parameter SsvO2 or its partial-pressure counterpart.
We speculate that in these critically ill patients with complete mixing, it is tissue oxygenation, and hence SsvO2, that we should be attempting to maximize. We show why apportioning blood flow equally between pulmonary and systemic circulations leads to this outcome.
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Acknowledgments |
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Dr Francis was supported by the estate of the late Mabel Grace Parker and by the British Heart Foundation (FS 98005). Dr Davies was supported by the Robert Luff Fellowship. Prof Coats was supported by the Viscount Royston Trust. Dr Thorne was supported by the British Heart Foundation.
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Footnotes |
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Reprint requests to Dr D.P. Francis, Heart Function Unit, Department of Cardiology, Royal Brompton Hospital, Sydney St, London SW3 6LY, UK.
Received December 2, 1998; revision received July 2, 1999; accepted July 2, 1999.
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References |
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TopAbstractIntroductionChoice of Variable to...Total Delivery or Useful...Capillary Contents: Quantity or...MethodsResultsDiscussionReferences |
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