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Meeting Abstracts  |   August 1995
Theoretical Analysis of Cerebral Venous Blood Hemoglobin Oxygen Saturation as an Index of Cerebral Oxygenation during Hypothermic Cardiopulmonary Bypass: A Counterproposal to the "Luxury Perfusion" Hypothesis
Author Notes
  • (Dexter) Assistant Professor.
  • (Hindman) Associate Professor.
  • Received from the Department of Anesthesia, University of Iowa College of Medicine, Iowa City, Iowa. Submitted for publication January 17, 1995. Accepted for publication April 29, 1995. Supported in part by National Institute of Health grant HL47159.
  • Reprints will not be available.
  • Address correspondence to Dr. Dexter: Department of Anesthesia, University of Iowa College of Medicine, 200 Hawkins Drive, Iowa City, Iowa 52242-1079. Address electronic mail to: franklin-dexter@uiowa.edu.
Article Information
Meeting Abstracts   |   August 1995
Theoretical Analysis of Cerebral Venous Blood Hemoglobin Oxygen Saturation as an Index of Cerebral Oxygenation during Hypothermic Cardiopulmonary Bypass: A Counterproposal to the "Luxury Perfusion" Hypothesis
Anesthesiology 8 1995, Vol.83, 405-412.. doi:
Anesthesiology 8 1995, Vol.83, 405-412.. doi:
Methods: We developed a theoretical model of cerebral oxygen consumption and blood-brain oxygen transfer. Our model included the temperature dependence of blood and brain oxygen solubility; the temperature, age, and acid-base dependence of hemoglobin oxygen dissociation; and the temperature and age dependence of CMRO2. We simulated cerebral blood flow reductions that decreased SvO2and CMRO2.
Results: Our model predicts the relation between CMRO2and SvO2to be dependent on temperature, because of a shift of the oxygen partial pressure at which hemoglobin oxygen saturation equals 0.50. For example, during normothermic CPB, SvO2can decrease to 30% before CMRO2will decrease to less than 90% of normal. In contrast, for alpha-stat management of infants at 17 degrees Celsius, Sv sub O2must be maintained at greater than 95% to maintain CMROsub 2 at greater than 90% of its temperature appropriate value.
Conclusions: High SvO2observed during hypothermic CPB may indicate impaired oxygen transfer from hemoglobin to brain, not "luxury perfusion." The relation between SvO2and CMRO2depends dramatically on the temperature of the patient. SvO2per se may not be a reliable index of normal CMRO2during hypothermic CPB.
Key words: Brain: cerebral venous blood hemoglobin oxygen saturation; metabolic rate. Mathematical model: oxygen transport. Temperature: hypothermia.
DESPITE advances in surgical technique, cardiopulmonary bypass (CPB), and anesthesia, neurologic and neuropsychologic abnormalities remain comparatively common occurrences after cardiac surgery and CPB. To assess the adequacy of cerebral oxygenation during CPB, many groups now advocate monitoring cerebral venous blood hemoglobin oxygen saturation (Sv sub O2). This is done directly, by sampling jugular venous blood, [1] or indirectly, by near-infrared spectroscopy. [2] A normal SvOsub 2 ([nearly equal] 60%) is usually interpreted as indicating that cerebral blood flow is adequate relative to the cerebral metabolic rate for oxygen (CMRO2), and that CMRO2is being adequately maintained. [3] Studies during hypothermic CPB uniformly find SvOsub 2 to be considerably greater than "normal" (i.e., > 60%). This finding has been interpreted as indicating that CMRO2is reduced to a greater extent by hypothermia than is cerebral blood flow. [1,3,4] In other words, hypothermia is believed to create a state of "luxury perfusion" [1,3,4] (i.e., CMRO2is being preserved with a relative excess of cerebral blood flow).
Although hypothermia decreases cerebral oxygen consumption, it also increases hemoglobin oxygen affinity. As temperature decreases, increased hemoglobin oxygen affinity may impair oxygen transfer from hemoglobin to the brain. If so, the increased SvO2observed during hypothermic CPB might actually be the result of impaired oxygen transfer from hemoglobin to brain. In contrast to current thinking, SvO2would be increased not because of excessive cerebral blood flow, but because oxygen would not be easily transferred from arterial blood to brain. If this were the case, then SvO2would not be a reliable index of whether or not normal CMRO2was being maintained during hypothermic CPB.
To investigate this issue, we developed a mathematical model of cerebral oxygen consumption and blood-brain oxygen transfer during CPB. Our goal was to characterize the relation between SvO2and CMR sub O2over the range of temperatures used during CPB.
Materials and Methods
Oxygen Solubility in Brain and Blood
In this model, we assume blood and brain are in thermal equilibrium. Our earlier simulation studies have shown that this assumption will limit this analysis to times other than the initial periods of cooling and rewarming. [5] Thus, temperature T refers to both blood and brain temperature (degree Celsius).
Oxygen solubility in blood (alphabl) (ml O2*symbol* 100 ml sup -1 *symbol* mmHg sup -1) depends on hemoglobin concentration and temperature. [6] Let H = hemoglobin concentration (g *symbol* 100 ml sup -1). Then, Equation 1. We use H = 8 g *symbol* 100 ml sup -1 in the calculation of alphablduring CPB.
(Equation 1) gives alphabl= 2.9 *symbol* 10 sup -3 ml O sub 2 *symbol* 100 ml sup -1 *symbol* mmHg sup -1 for H = 15 g *symbol* 100 ml sup -1 and T = 37 degrees Celsius. This value is virtually identical to oxygen solubility in brain tissue (3.0 *symbol* 10 sup -3 ml O2*symbol* 100 ml sup -1 *symbol* mmHg sup -1). [7] Thus, we use Equation 1with H = 15 g *symbol* 100 ml sup -1 to predict oxygen solubility in brain as a function of temperature. [6] .
Hemoglobin Oxygen Dissociation Curve
The hemoglobin oxygen dissociation curve is described by the Hill equation [6] : Equation 2SO2(unitless) = fractional hemoglobin oxygen saturation and PO2(mmHg) = oxygen partial pressure. The unitless Hill coefficient (2.8) gives the hemoglobin oxygen dissociation curve its sigmoid shape. P50(mmHg) = the oxygen partial pressure at which hemoglobin oxygen saturation equals 0.50. Over the clinically relevant range of temperatures, diffusion primarily limits oxygen transfer from hemoglobin to brain. [8] Therefore, the mathematical model does not include chemical reaction kinetics. Equation 2is inaccurate for saturations less than 0.30. To ensure this inaccuracy does not affect our results, we did not perform simulations for which hemoglobin oxygen saturation is less than 0.30. We also use the inverse of Equation 2in the calculations, Equation 3.
Currently, two different hypothermic acid-base strategies are used during CPB, alpha-stat and pH-stat. With the pH-stat technique, arterial blood carbon dioxide partial pressure (PaCO2) is maintained at approximately 40 mmHg when corrected to temperature in vivo. With alpha-stat technique, PaCO2is maintained at approximately 40 mmHg when measured at 37 degrees Celsius. As temperature decreases, differences in PaCO2between techniques increases. Hemoglobin P sub 50 decreases with decreasing temperature, but increases with increasing PaCO2. Therefore, two equations are needed to describe the effect of temperature on P50, depending on whether alpha-stat or pH-stat blood gas management is used [6] : Equation 4where Page50equals the P50at T = 37 degrees Celsius that is age appropriate.
Changes in Equation 2as a function of temperature can be predicted from Equation 4, because the Hill coefficient does not change with temperature. [8,9] To include fetal hemoglobin in our model, [9,10] Equation 5.
(Equation 2, Equation 3, Equation 4, Equation 5), were not developed using data from CPB. However, it is reasonable to assume they apply during CPB, because CPB per se does not affect P50. [11] Indeed, P50values predicted by Equation 4agree with available data from studies in humans. Coetzee and Swanepoel found P50to equal 11.6 mmHg in adults undergoing CPB at 25.4 degrees Celsius (alpha-stat management). [11] This value to close to the P50= 12.0 mmHg predicted by Equation 4.
Oxygen Diffusion
Net oxygen transport from blood to tissue is described using Fick's law of diffusion for a parallel plane-layer geometric configuration [6,12] Equation 6where CMRO2is given in ml O2*symbol* 100 ml sup -1 *symbol* mmHg sup -1; alphabr= oxygen solubility in brain (ml O2*symbol* 100 ml sup -1 *symbol* mmHg sup -1); PvOsub 2 (mmHg) = cerebral venous blood oxygen partial pressure; PinOsub 2 (mmHg) = interstitial oxygen partial pressure; and D (cm2*symbol* min sup -1) = the net oxygen diffusion coefficient in the blood and tissue. Equation 6assumes PvO2equals the cerebral end capillary oxygen partial pressure. The 11,400 cm2*symbol* 100 g sup -1 term equals the sum of arteriole, capillary, and venule surface areas available for oxygen exchange. [6,13] The 27 *symbol* 10 sup -4 cm term specifies the sum of capillary and tissue thicknesses. [6,12] The 13 (unitless) is a correction for the increase in oxygen diffusivity that Schacterle and colleagues showed was necessary for Fick's law to attain the level of oxygen transport measured experimentally. [14] We recognize this correction factor, determined at normothermia, could decrease with decreasing temperature. The implications of this possibility are considered in the Discussion section, below. The equation for D is [15] Equation 7.
Cerebral Oxygen Transport
At all temperatures, CMRO2can be determined by mass balance for oxygen [6] : Equation 8where CBF = regional cerebral blood flow (ml *symbol* g sup -1 *symbol* min sup -1); SaO2(unitless) = arterial blood hemoglobin oxygen saturation; PaO2(mmHg) = arterial blood oxygen partial pressure; and SvO2is unitless. We use PaO2= 300 mmHg in all simulations.
Cerebral Oxygen Consumption
At normothermia, cerebral oxygen consumption varies with the interstitial oxygen partial pressure (PinO2) [14] : Equation 9where 2.0 mmHg specifies the interstitial oxygen partial pressure at which CMRO2is 50% of the maximal (i.e., normal) value (CMRO2max). Thus, as the interstitial oxygen partial pressure increases, CMRO2asymptotically approaches its maximal (normal) value. Recently, Back and colleagues, using microelectrodes in normothermic rats, found cerebral interstitial oxygen partial pressure to equal 28 mmHg. [16] Substituting this value into Equation 9, at an interstitial oxygen partial pressure of 28 mmHg, CMRO2is predicted to be 93% of its maximal (normal) value. We consider 93% to be a value clinically indistinguishable from normal.
An important issue is how the relation described in Equation 9changes with temperature. It is well known CMRO2, and therefore CMRO2max, decreases with decreasing temperature. For all simulations, CMRO2max is that appropriate for temperature. Specifically, the relation between CMRO2and temperature in adults and infants during CPB can be described by [1,3,6] Equation 10. In both cases, CMRO2was determined under steady-state, "high-flow" conditions. Hence, we assume these CMRO2measurements represent maximal normal values.
In contrast, the 2.0 mmHg term in Equation 9does not change with temperature. It represents the oxygen partial pressure that needs to be maintained at the cerebral mitochondria. As analyzed by Willford and colleagues, [6] the intracellular oxygen gradient needed to maintain mitochondrial oxygenation probably does not depend on temperature. In brief, neither the interstitial-intracellular surface area for diffusion nor the distance over which oxygen diffusion occurs are likely to depend on temperature. Furthermore, a decreased oxygen diffusion rate proportionately compensates for an increased solubility for oxygen at lower temperatures.
Numerical Methods
The algebraic equations (1-10) were solved simultaneously using the Systat (Evanston, IL) statistics program implementation of the Simplex direct-search method. [17] Solutions for CMRO2were constrained to be less than or equal to CMRO2max with a penalty function. [17] In particular, a nearly infinite value was added to the cost function whenever the constraint was not satisfied. Iterations were continued until CMRO2and SvO2were calculated to within 0.01%. Cerebral blood flow was varied to achieve different CMRO2.
Simplified Mathematical Model
The least reliable parts of the mathematical model are the oxygen solubility in brain, oxygen diffusion (Equation 6and Equation 7), and cerebral oxygen transport (Equation 8). We therefore repeated our analysis using a simplified model that did not include these terms. We assume that oxygen diffusion and transport are sufficient for PvO2= PinO2. Then, solving Equation 9for PinO2and substituting the result into Equation 2, Equation 11. This simplified model predicts the relation between SvO2and the temperature-appropriate CMRO2without including oxygen diffusion, transport, or solubility in brain.
Results
We simulated relations between temperature-appropriate normal CMRO2versus SvO2for adults and infants undergoing CPB at 37 degrees Celsius, 27 degrees Celsius, or 17 degrees Celsius, with alpha-stat or pH-stat acid-base management. In each case, to create a decreasing SvO2, cerebral blood flow was varied (decreased). Figure 1shows the complete CMRO2versus SvO2relation during three common CPB scenarios: 37 degrees Celsius adult, 27 degrees Celsius (alpha-stat) adult, and 17 degrees Celsius (alpha-stat) infant. Table 1shows predicted SvO2values below which CMR sub O2will decrease to less than 90% of temperature-appropriate normal CMRO2, under all simulated conditions. The results are nearly identical using the simplified mathematical model (Table 1), which omitted terms for oxygen diffusion, transport, and solubility in brain. Collectively, these simulations show that as temperature and P50decrease, SvO2must be maintained at progressively greater values to maintain temperature-appropriate CMRO2. Limitation of oxygen transfer from hemoglobin to brain becomes a progressively more important determinant of CMRO2as temperature decreases.
Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
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Table 1. Effect of Temperature and Acid-Base Management on Hemoglobin P sub 50 and SvO2Required to Maintain CMRO2at 90% of Its Normal Temperature-appropriate Value
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Table 1. Effect of Temperature and Acid-Base Management on Hemoglobin P sub 50 and SvO2Required to Maintain CMRO2at 90% of Its Normal Temperature-appropriate Value
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During normothermic CPB, decreasing cerebral blood flow results in decreasing SvO2. Nevertheless, Figure 1shows CMRO2remains nearly normal until SvO2approaches very low values. During normothermic CPB, SvO2could decrease to less than 30% before CMRO2would be significantly reduced (i.e., to < 90% of normal CMRO2) (see Comments).
In stark contrast, the CMRO2versus SvO2relation is markedly different during CPB at 17 degrees Celsius (alpha-stat). Decreasing cerebral blood flow results in decreasing SvO2. However, in contrast to normothermia, CMRO2significantly decreases. At 17 degrees Celsius, CMRO2varies with SvO2in an almost linear fashion once SvO2is less than 95%. Thus, during profoundly hypothermic CPB, impaired transfer of oxygen from hemoglobin limits oxygen availability to the brain. At 17 degrees Celsius, to maintain cerebral aerobic metabolism, cerebral blood flow must be maintained at values that preserve high SvO2.
Discussion
Appropriate Interpretation of Cerebral Venous Blood Hemoglobin Oxygen Saturation during Hypothermic Bypass
SvO2(measured by jugular venous catheters or near-infrared spectroscopy) is commonly used as an index of the adequacy of cerebral oxygenation during CPB. It is widely believed that SvO2values greater than the normal (normothermic) value of 60% [3,18] indicate that, during hypothermic CPB, CMRO2is being preserved with a relative excess of cerebral blood flow. [1,3,4] Our results suggest that this interpretation may be wrong. The CMRO2versus SvO2relation changes with temperature. To maintain CMRO2at temperature-appropriate values, the interstitial oxygen partial pressure must remain essentially constant at all temperatures. Consequently, the cerebral venous oxygen partial pressure must also remain essentially constant. However, hemoglobin Phosphorus50decreases with temperature. As a result, to maintain constant cerebral venous oxygen partial pressure, SvO2must be maintained at progressively greater values as temperature decreases. Thus, appropriate clinical interpretation of SvO2during hypothermic CPB depends dramatically on the temperature of the patient.
Cerebral Metabolic Rate for Oxygen versus Cerebral Venous Blood Hemoglobin Oxygen Saturation
During Normothermic ("Warm") Bypass. Our model predicts, that during normothermia, decreases in cerebral blood flow can be compensated for by increased oxygen transfer from hemoglobin to brain. This increased extraction can maintain CMRO2until SvO2decreases to very low levels (< 30%). This prediction has been verified in a non-CPB baboon model of focal cerebral ischemia. [19] A 46% reduction of cerebral blood flow was associated with a decrease in SvO2from 60% to approximately 30%. However, CMRO2did not change. Recently, Mutch and colleagues used graded CPB pump flow reductions in normothermic dogs to reduce cerebral blood flow (from 74 to 57 ml *symbol* 100 g sup -1 min sup -1). [20] SvO2decreased from 0.66 to 0.56, without a change in CMRO2. [20] Thus, during normothermic CPB, increased oxygen off-loading from hemoglobin can compensate for significant decreases in cerebral blood flow. Within bounds, at normothermia, increased extraction can maintain normal cerebral oxygen metabolism.
During Moderately Hypothermic Bypass. During moderately hypothermic CPB, SvO2equals roughly 75% with alpha-stat management. [3] This greater than normal SvO2has been interpreted as indicating an excess of cerebral blood flow compared with metabolism (i.e., "luxury perfusion"). [3] On the other hand, the literature consistently shows that cerebral autoregulation is fairly well maintained under alpha-stat conditions at 27 degrees Celsius. [20,21] Teleologically, it seems strange the brain would autoregulate and maintain cerebral blood flow at an "excessive" level. Our model predicts the relatively high SvO2does not indicate the presence of "luxury perfusion." At 27 degrees Celsius, maintenance of an SvO2around 75% is, in fact, necessary to maintain CMRO2at nearly (i.e., > 90%) its temperature-appropriate norm. Greater SvO2simply reflect a decreased Phosphorus50and impaired oxygen transfer from hemoglobin to brain.
Nevertheless, within the customary range of systemic pressures and flows maintained during moderately hypothermic CPB, impairment of oxygen transfer is probably not clinically significant. Fedderson and colleagues decreased cerebral blood flow during hypothermic CPB (28 degrees Celsius) by decreasing mean arterial pressure. [22] SvOsub 2 was reduced from 71% to 55%. The model predicts that, at an SvO2of 55%, CMRO2should be approximately 95% of the value of that with an SvO2of 71% (Figure 1). As predicted, Fedderson and colleagues found CMRO2decreased from 1.0 to 0.9 ml O2*symbol* 100 g sup -1 *symbol* min sup -1. [22] Thus, at 27 degrees Celsius, it appears oxygen off-loading from hemoglobin is sufficient to maintain CMRO2at temperature-appropriate values. This applies even when cerebral blood flow and SvO2are significantly decreased. Consequently, the 3 mmHg increase in hemoglobin Phosphorus50resulting from pH-stat management is unlikely to meaningfully improve oxygen off-loading or increase CMRO2under standard, moderately hypothermic CPB. Consistent with this latter hypothesis, both rabbit [23] and human [21] studies have found CMR sub O2to be equivalent under alpha-stat and pH-stat conditions at 27 degrees Celsius.
During Profoundly Hypothermic Bypass. During full-flow CPB at profound hypothermia (15-20 degrees Celsius), SvO2is typically 85% or greater. [1,2] This has been interpreted as indicating a state of "luxury perfusion." [1] However, our model predicts SvO2must be in this range to maintain CMRO2at temperature-appropriate norms (Figure 1and Table 1). Profound hypothermia induces a decrease in hemoglobin Phosphorus50, which causes marked impairment of oxygen off-loading from hemoglobin. Thus, only a relatively small amount of oxygen is transported from arterial blood to brain. Therefore, to maintain CMRO2, SvO2must be relatively high, and cerebral blood flow must be large compared with CMR sub O2. This has been observed in both human infants [1] and baboons. [24] Cerebral blood flow to CMRO2ratios were three to four times greater during profound hypothermia than during normothermia.
Suppose cerebral blood flow were, in fact, truly "luxurious" at profound hypothermia. Then, one would expect large reductions in cerebral blood flow to not affect CMRO2. This does not seem to be the case. Kern and colleagues, studying infants at 22 degrees Celsius, decreased CPB flow to decrease cerebral blood flow. [4] SvO2decreased from 70% to 63%. Our model would predict a small ([nearly equal] 4%) decrease in CMRO2based solely on this change in SvOsub 2 (Figure 1). In contrast, Kern and colleagues found CMRO2decreased by 45%. This suggests that in vivo, there may be an even greater limitation of oxygen transfer from hemoglobin to brain than predicted from this model.
Canine data at 20 degrees Celsius also suggest that actual Sv sub O2values required to preserve CMRO2are probably greater than predicted. Miyamoto and colleagues [25] decreased CPB flow to decrease cerebral blood flow. SvO2decreased from 83% to 37%. Our model would predict a 12% decrease in CMRO2based solely on this change in SvO2. In contrast, these investigators found CMR sub O2decreased by 35%. Therefore, SvO2is probably an even less accurate index of the cerebral blood flow and CMRO2relation during hypothermic CPB than our model predicts. We discuss possible reasons for the discrepancy in the Limitations of the Model section, below. Nevertheless, the point is clear: although cerebral blood flow and SvO2are relatively high during profound hypothermia, there is probably a significant limitation in oxygen transfer. High SvO2values cannot be considered as indicating "luxury perfusion." Sv sub O2is probably not a reliable index of CMRO2during hypothermic CPB.
One might anticipate pH-stat management, by increasing Phosphorus50, might allow a greater CMRO2for a given Sv sub O2during profound hypothermia. However, at 17 degrees Celsius, the effect of pH-stat management to increase fetal hemoglobin Phosphorus sub 50 ([nearly equal] 2 mmHg) is negligible compared with the overwhelming effect of hypothermia to decrease it (Table 1). Thus, pH-stat management seems unlikely to better preserve CMRO2.
Our simulations show that, during profoundly hypothermic CPB, impaired oxygen transfer from hemoglobin to brain can greatly affect cerebral oxygen metabolism (Figure 1and Table 1). However, this impairment is likely to be clinically important only during low flow CPB (i.e., when cerebral blood flow is very low). [4] An issue of current controversy is the lower limit of systemic perfusion necessary to provide adequate cerebral perfusion during profoundly hypothermic CPB. Monitoring SvO2, by jugular bulb saturation or near-infrared spectroscopy, may be a way to assess whether cerebral oxygen requirements are being met. However, what our simulations show are that a "normal" SvO2(i.e., [nearly equal] 60%) does not indicate an adequate (i.e., normal) CMRO2during profound hypothermia. The SvO2must be maintained at high levels (i.e., > 90%) to fully support cerebral oxygen consumption at 17 degrees Celsius.
Cerebral Venous Blood Hemoglobin O Desaturation during Rewarming
SvO2desaturation (to < 50%) occurs commonly during rewarming after both moderately [18,26] and profoundly [1] hypothermic CPB. This desaturation has been interpreted as showing a pathologic mismatch between cerebral blood flow and CMRO2. [26] Simultaneous measurements of CMRO2and cerebral blood flow show SvO2desaturations can, at times, reflect inadequate cerebral oxygen delivery. [26] However, the increase in Phosphorus50with rewarming might also result in SvO2reduction, simply because of increased ease of oxygen transfer from hemoglobin to brain (Table 1).
Limitations of the Model
The extreme simplicity of the mathematical model is both its strength and weakness. Our model only considers the temperature and age dependence of cerebral metabolism and hemoglobin Phosphorus50(Table 1). The advantage of this simplicity is the simulation results can be easily interpreted. The drawback is many important physiologic processes (e.g., shunt and capillary recruitment) are necessarily excluded. Therefore, it is important to appreciate predicted SvO2at given levels of CMR sub O2(Figure 1and Table 1) should be considered as rough estimates only. It appears that our model underestimates the limitation of oxygen transfer from hemoglobin to brain during profound hypothermia. Actual SvO2values required to preserve CMRO2may be higher than those given in Table 1for profoundly hypothermic CPB. However, determination of these estimates was not the goal of the study. Instead, our aim was to determine the effect of hypothermia on the relation between CMRO2and SvO2. By limiting our model, we could examine the pure effect of temperature on cerebral metabolism and hemoglobin oxygen dissociation.
The greatest simplification and potential limitation in our model concerns net oxygen diffusion from blood to brain. Both experimental results and theoretical analyses of cerebral oxygen transport are (almost exclusively) limited to the case of the normothermic adult. Therefore, we could not make this part of our model more realistic. [6] Nevertheless, we can make some predictions about how model error might affect our results. In the complex model, we assumed cerebral venous oxygen partial pressure equals the cerebral end capillary oxygen partial pressure. In the simplified model, we assumed the cerebral venous oxygen partial pressure also equals the cerebral interstitial oxygen partial pressure. Results from the detailed and simplified models closely matched (Table 1). Therefore, the detailed model essentially assumed that oxygen diffusion and transport are sufficient for cerebral venous oxygen partial pressure to equal the interstitial oxygen partial pressure. The quantitative model discrepancy at profound hypothermia suggests that under these conditions cerebral venous oxygen partial pressure probably exceeds interstitial oxygen partial pressure.
The discrepancy may relate to the diffusivity of oxygen in vivo. For example, as described in Materials and Methods, above, researchers have found it necessary to increase the oxygen diffusion term (13-fold) to match the level of oxygen transport measured experimentally at normothermia. [14] Suppose this correction term for oxygen diffusivity in vivo were to decrease with decreasing temperature. Then, for a given decrease in SvO2, CMRO2would be less than those predicted in Figure 1and Table 1. However, there are several other explanations. For example, examining Equation 1and Equation 6, the model relation for the temperature dependence of oxygen solubility in brain could overestimate the solubility during profound hypothermia. Alternatively, nonequilibrium chemical reactions in erythrocytes [27] may limit oxygen delivery during profound hypothermia. Nevertheless, both models indicate that oxygen transfer from blood to brain is impaired during profound hypothermia. That clinical and experimental studies show that oxygen transfer may be worse than predicted only substantiates the model conclusions that luxury perfusion may not exist during hypothermic CPB.
Experimental Verification of Model Predictions
Our model shows that hemoglobin Phosphorus50strongly influences the relation between cerebral blood flow and metabolism. Consequently, experiments to test predictions of this model should consider differences between animals and humans in baseline Phosphorus50and in the effect of temperature on Phosphorus50. For example, the pig is commonly used in studies of cerebral physiology under profoundly hypothermic conditions. However, both normothermic Phosphorus50, and the temperature dependence of Phosphorus50, differ dramatically from that of humans. [28] Porcine Phosphorus50decreases much less with temperature than does human Phosphorus50. For example, predicted Phosphorus50for adult humans at 17 degrees Celsius under pH-stat conditions equals 9.3 mmHg. At comparable conditions in pigs, Phosphorus50equals 17.1 mmHg. [28] This latter value exceeds human Phosphorus50at 27 degrees Celsius (Table 1), where, as we have discussed, impairment of oxygen off-loading from hemoglobin is probably not significant. Therefore, the relation between CMRO2and cerebral blood flow under hypothermic conditions probably differs significantly between pigs and humans. Species, such as the pig, with values for hemoglobin Phosphorus sub 50 and/or Phosphorus50temperature dependencies that differ from that of humans are not appropriate to test the predictions of this model.
Summary
We used computer simulation to predict the relation between changes in SvO2and CMRO2. The relation is temperature dependent. SvO2per se may not be an accurate measure of CMRO2during hypothermic CPB. Investigators of cerebral physiology during hypothermic CPB should consider these limitations when interpreting SvO2data.
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Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
Figure 1. Relation between cerebral metabolic rate for oxygen (CMRO2) and cerebral venous blood hemoglobin oxygen saturation (SvOsub 2) during cardiopulmonary bypass. CMRO2is shown on the vertical axis as a percentage of the temperature-appropriate normal CMR sub O2. Three conditions are plotted: 37 degrees Celsius adult, 27 degrees Celsius alpha-stat adult, and 17 degrees Celsius alpha-stat infant. We decreased cerebral blood flow to create decreasing SvO2and CMRO2.
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Table 1. Effect of Temperature and Acid-Base Management on Hemoglobin P sub 50 and SvO2Required to Maintain CMRO2at 90% of Its Normal Temperature-appropriate Value
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Table 1. Effect of Temperature and Acid-Base Management on Hemoglobin P sub 50 and SvO2Required to Maintain CMRO2at 90% of Its Normal Temperature-appropriate Value
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