Models of venous admixture

Models of venous admixturePaul E. BigeleisenAdvan Physiol Educ 25:159-166, 2001.You might find this additional information useful...Medline items on this article's topics can be found at http://highwire.stanford.edu/lists/artbytopic.dtlon the following topics:Medicine .. Medical StudentsUpdated information and services including high-resolution figures, can be found at:http://ajpadvan.physiology.org/cgi/content/full/25/3/159Additional material and information about Advances in Physiology Education can be found at:http://www.the-aps.org/publications/advanThis information is current as of December 7, 2006 .Downloaded from ajpadvan.physiology.org on December 7, 2006Advances in Physiology Education is dedicated to the improvement of teaching and learning physiology, both in specializedcourses and in the broader context of general biology education. It is published four times a year in March, June, September andDecember by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright © 2005 by theAmerican Physiological Society. ISSN: 1043-4046, ESSN: 1522-1229. Visit our website at http://www.the-aps.org/.

I N N O V A T I O N S A N D I D E A SMODELS OF VENOUS ADMIXTUREPaul E. BigeleisenDepartment of Anesthesiology, Strong Memorial Hospital,Rochester, New York 14642Medical students, residents, and allied health professionals often have difficultyquantitating ventilation-perfusion mismatch in ill patients. Thismanuscript quantitates ventilation-perfusion mismatch using the underlyingphysiological concepts and equations that describe mismatch. In addition, clinicalproblems with diagrams and worked-out solutions are supplied to help studentsmaster these equations as well as their practical limitations.ADV PHYSIOL EDUC 25: 159–166, 2001.Key words: ventilationWhen patients have hypoxemia due to ventilationperfusionmismatch, clinicians need quantitativemethods to measure the severity of illness as afunction of time. Medical students, residents, andallied health professionals usually have some familiaritywith the virtual shunt equation, shunt nomogram,alveolar-arterial gradient, and arterial/alveolarratio. These techniques are all commonly used toassess respiratory failure. Nonetheless, students oftenhave difficulty quantitating these measures anddo not understand when these methods fail. Standardtextbooks may provide the theoretical backgroundfor the material above, but they rarely provideclinical examples to solidify these concepts (1,3, 4). This manuscript presents the derivation ofequations describing ventilation-perfusion mismatch.In addition, clinical examples with workedsolutions are provided to help students learn tomanipulate the formulas necessary to assess respiratoryfailure. The practical limitations of theseformulas are also discussed.MODELThe formal method of modeling pulmonary dysfunctionin a hypoxemic patient is the patient’s virtualshunt through his lungs. Figures 1 and 2 and Equations1-3 explain how this is done.Figure 1A shows a healthy alveolus and pulmonarycapillary. In this part of the lung, ventilation andperfusion are matched, and there is no venous admixture.Figure 1B shows a collapsed alveolus and ahealthy capillary. Here, all of the mixed venous bloodis shunted past the functional part of the lung. This iscalled venous admixture. Figure 1C shows a healthyalveolus and collapsed pulmonary capillary. This isthe definition of dead space. It is included here toavoid confusion, although it is not part of the model.Figure 2 shows how venous admixture to the systemicarterial blood can occur.Conservation of blood flow dictates that the pulmonarycapillary blood flow and shunted blood flow must equalthe total cardiac output through the lungs (Eq. 1)Q˙ T Q˙ C Q˙ S (1)where Q˙ T, Q˙ C, and Q˙ S are cardiac output, pulmonarycapillary blood flow, and shunted pulmonary capillaryblood flow, respectively.Conservation of mass dictates that the transport ofoxygen through the lung is also conserved (Eq. 2)Q˙ TCa O2 Q˙ cC c O 2 Q˙ sC v O 2 (2)Downloaded from ajpadvan.physiology.org on December 7, 20061043 - 4046 / 01 – $5.00 – COPYRIGHT © 2001 THE AMERICAN PHYSIOLOGICAL SOCIETYVOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001159

I N N O V A T I O N S A N D I D E A SFIG. 1.Oxygen and blood flow in the lung. Cap, pulmonary capillary.Downloaded from ajpadvan.physiology.org on December 7, 2006FIG. 2.Virtual shunt model.where Ca O2is the O 2 content in the systemicarterial blood (pulmonary vein), C c O 2 is theO 2 content in the pulmonary capillary, and C v O 2is the O 2 content in the shunted or mixedvenous blood. Substituting Eq. 1 into Eq. 2 andrearranging yields the familiar virtual shunt equation.Q˙ SQ˙ T C cO 2 C a O 2C c O 2 C v O 2(3)VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001160

I N N O V A T I O N S A N D I D E A SFIG. 3.Pa O2 , arterial oxygen pressure in Torr; PA O2 , alveolar oxygen pressure in Torr; isoshunt,isoshunt lines in %.To calculate shunt (Eq. 3), one must measure thepartial pressure of O 2 in the mixed venous and systemicarterial blood. In addition, one must estimatethe partial pressure of O 2 in the pulmonary capillaryby calculating the partial pressure of oxygen deliveredto the alveolus (PA O2; Eq. 3A)PA O2 PB PH 2 O FI O2 Pa CO 2R(3A)where PB is atmospheric pressure, and PH 2 Oisthepressure of water vapor in the lung. Pa CO2 is thepartial pressure of CO 2 in the systemic arterial blood,and R is the respiratory quotient, which is assumed tobe 1 in this model. The use of Eq. 3 is impractical inroutine clinical care because the mixed venous bloodis rarely sampled.This nomogram allows one to estimate the patient’svirtual shunt and follow his pulmonary dysfunction ashis FI O2and ventillatory therapy are adjusted by measuringhis Pa O2. Despite their simplicity, the isoshuntlines did not achieve popularity because pulmonarycritical care involves treating more than a single parameterand because it was impractical to carry thenomogram around.A number of years later, interest was renewed in Eq.3 with the advent of pulse oximeters and oxymetricpulmonary artery catheters. Manipulation of Eq. 3shows why. The oxygen content of blood is given byEq. 4CO 2 1.34 Hgb saturation 0.003 PO 2 (4)Downloaded from ajpadvan.physiology.org on December 7, 2006To get around this, Eq. 3 was recast in nomogramform. Nunn assumed that the C v O 2 had a constantvalue and that the hemoglobin and Pa CO2 were withincommon ranges (2). Using these assumptions, he createdthe isoshunt lines shown in Fig. 3.where PO 2 is the partial pressure of oxygen in theblood. The term (0.003 PO 2 ) represents dissolved O 2in the plasma and will be ignored here. If we assumethat the amount of dissolved oxygen is negligible,then we can substitute Eq. 4 into Eq. 3 to yield.VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001161

I N N O V A T I O N S A N D I D E A SQ˙ SQ T1.34 Hgb end-capillary sat arterial sat1.34 Hgb end-capillary sat mixed venous sat(5)With oximetry, both the arterial saturation and mixedvenous saturation could be measured continuously togive a good estimate of shunt. Unfortunately, Eq. 5still involved a cumbersome calculation and the costand morbidity of an oxymetric pulmonary artery catheter.For these reasons, Eq. 5 never achieved commonusage either. Eq. 5, however, can be simplified tomake it useful for clinicians.In patients with stable cardiac outputs who are administereda high concentration of O 2 (FI O2), the differencebetween end-capillary saturation and mixedvenous saturation is 0.25. Thus Eq. 5 becomesQ˙ SQ˙ Tend-capillary sat arterial sat0.25(6)Equation 6 is made usable by relating O 2 saturation toPa O2. Reference to the oxyhemoglobin dissociationcurve shows how this is done (Fig. 4).AtaPa O2100 Torr, the graph is nearly a flat line.Thus O 2 saturation and Pa O2are related by the formulafor a straight line (Eq. 7)O 2 saturation m Pa O2 b (7)where m is the slope of the line, and b is the intercepton the saturation axis. Substituting Eq. 7 into Eq. 6yieldsQ˙ SQ˙ T mPA O 2 Pa O2 0.25(8)where we have assumed that the PA O2is the same asPO 2 in the pulmonary capillary. Using the slope (m 1.4 10 4 saturation/Torr) on the flattest part of Fig.4 allows Eq. 8 to be recast asQ˙ SQ˙ T 1.4 104 PA O2 Pa O2 0.25(9)FIG. 4.Oxyhemoglobin dissociation curve.If we desire to use shunt fraction rather than shunt,then Eq. 9 becomesShunt fraction Q˙ SQ˙ T 100 PAO 2 PaO 218(10)Equation 10 shows that the commonly used alveolararterialgradient divided by a constant yields an easyestimate of shunt when the patient’s cardiac outputand hemoglobin are stable and when the PA O2andPa O2lie along the flat part of the oxyhemoglobindissociation curve. Using a similar approach, theshunt fraction can be estimated when the PA O2100 Torr and the Pa O2lies between 50 and 100 Torr.In this case, Eq. 10 becomesShunt fraction PAO 2 PaO 22(10A)Equations 10 and 10A are only estimates of shuntfraction and are insensitive to larger gradients in thedenominator of Eq. 5. Larger gradients in the denominatorof Eq. 5 may occur in some patients withdecreased cardiac output or significant shunt. Nonetheless,as long as cardiac output is stable, Eqs. 10 and10A will track changes in shunt fraction as the patient’spulmonary function improves or declines. Ifone wishes to account for larger gradients in Eq. 5,then the slope in Eq. 7 must be adjusted to fit Eqs. 10and 10A to clinical data.The following clinical cases below are illustrative:An 18-yr-old male with a history of asthma presents tothe emergency department in respiratory distress. Anasal cannula supplies oxygen at 28%. His blood gasshows the following values: 7.32/31/74/23, O 2 saturation95%. In this case, his alveolar O 2 (PA O2) is givenDownloaded from ajpadvan.physiology.org on December 7, 2006VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001162

I N N O V A T I O N S A N D I D E A STABLE 1FI O2 PA O2 Pa O2 A-a Gradient Virtual Shunt Estimated ShuntPatient 1 (asthma) 0.28 168 74 94 15%–20% 6%Patient 2 (surgery) 0.5 322 115 207 10%–15% 12%by Eq. 3A. Thus PA O2 (760 47) 0.28 31 168Torr. The patients’ alveolar-arterial gradient is givenby PA O2 [Pa O2] 168 74 94 Torr. Reference toFig. 3 shows the patient has a virtual shunt of 15–20%.His estimated shunt using the PA O2-Pa O2gradient (Eq.10) is6%.Now consider a very different patient. A 74-yr-oldmale with a 50-pack/yr history of cigarettes undergoesa Whipple procedure. At the end of the surgery,the patient is intubated and ventilated with an FI O2of50%. His blood gas shows the following values: 7.32/34/115/27, O 2 saturation 98%. Using the same analysisas above, we find that this patient has PA O2-Pa O2gradient of 207 Torr, a virtual shunt of 10–15%, andestimated shunt using the PA O2-Pa O2gradient (Eq. 10)of 12%. This is summarized in Table 1.Notice that patient 1 (asthma) is sicker (virtualshunt 15–20%) even though his PA O2-Pa O2gradientis smaller than patient 2. This shows the valueof the virtual shunt method, i.e., virtual shunt remainsconstant regardless of the FI O2administered.The PA O2-Pa O2gradient, however, widens as the FI O2is increased, even in the absence of increased pulmonarydysfunction. The estimated shunt of patient1 (Eq. 10) is 6%, which compares poorly withhis virtual shunt (Eq. 3). This is because his Pa O2liesalong the steep part of the oxyhemoglobin dissociationcurve. In this situation, Eq. 10 is not a goodmeasure of venous admixture. Conversely, the estimatedshunt of patient 2 (12%) is similar to hisvirtual shunt. This is because both his PA O2and Pa O2lie along the flat part of the oxyhemoglobin dissociationcurve (Fig. 4).Figure 5 shows the relationship between virtualshunt and estimated shunt. Notice that when thePa O2is greater than 100 Torr, the virtual shunt linesand estimated shunt lines have slopes and absolutevalues that are similar. Below 100 Torr, the estimatedshunt (PA O2 Pa O2) reproduces the virtualshunt poorly.Now let’s look at the problem in a different way.Suppose we consider the right heart and lungs to bean engine whose job is to convert mixed venousblood into oxygenated blood. If the engine is ideal(Fig. 6A), then the blood will be fully saturated withoxygen when it leaves the engine.If the engine is less than ideal (Fig. 6B), then theblood will be only partially oxygenated when it leavesthe heart-lung engine. We can calculate an efficiencyfor this real engine by comparing it with the idealengine (Eq. 11).Efficiency O 2 content of partially oxygenated bloodO 2 content of fully oxygenated bloodSubstituting Eq. 4 into Eq. 11 yields1.34 Hgb arterial satEfficiency 1.34 Hgb end-capillary sat(11)(12)Now, recall that on the flat part of the oxyhemoglobindissociation curve (Fig. 4), the O 2 saturation m PO 2 b (Eq. 7). Substituting Eq. 7 into Eq. 11 yieldsEfficiency PaO 2PAO 2(13)This is commonly called the a/A ratio. Our derivationshows that the a/A ratio is only a good measure ofpulmonary dysfunction (venous admixture) when thePa O2and PA O2both lie along the flat part of the oxyhemoglobindissociation curve.Figure 7 shows the graphical relationship of Pa O2/PA O2to the isoshunt lines. When the Pa O2-PA O2ratio is near1, isoshunt and Pa O2/PA O2correlate well. As the ratioDownloaded from ajpadvan.physiology.org on December 7, 2006VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001163

I N N O V A T I O N S A N D I D E A SFIG. 5.A-a gradient, estimated shunt fraction; isoshunt, isoshunt lines in percent.falls, the correlation becomes poorer because thePa O2no longer lies along the flat part of the oxyhemoglobindissociation curve.As an example, consider patients 1 and 2 again. Theefficiency of patient 1 (Pa O2/PA O2) is 0.44, whereasthat of patient 2 is 0.36. By comparing a/A ratios,patient 1 appears healthier than patient 2, althoughhis virtual shunt is greater. This is because his Pa O2liesalong the steep part of the oxyhemoglobin dissociationcurve, and the a/A ratio is less accurate in thiscase. This is summarized in Table 2.Downloaded from ajpadvan.physiology.org on December 7, 2006FIG. 6.Heart-lung engine model.VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001164

I N N O V A T I O N S A N D I D E A SSUMMARYVirtual shunt remains the best way of quantitatingvenous admixture in patients with pulmonary pathology.It is a cumbersome technique that requirespulmonary artery catheterization and data from theoxyhemoglobin dissociation curve. The isoshuntlines approximate virtual shunt when the mixedvenous saturation, hemoglobin, and Pa CO2 arewithin common ranges and are stable. Most cliniciansdo not carry this nomogram with them. TheA-a gradient and a/A ratio both give a good estimateof venous admixture when the conditions for theisoshunt lines are met and when both Pa O2and PA O2FIG. 7.a-A ratio, arterial-to-alveolar oxygen pressure ratio.lie along the flat part of the oxyhemoglobin dissociationcurve. Pa O2is easily measured, and PA O2iseasily calculated. For these reasons, they have becomethe standards in clinical care.PRACTICE PROBLEMAn 18-mo-old child presents to the emergency departmentwith respiratory distress and a chestX-ray consistent with pneumonia. A facemask suppliesoxygen at 35%. His arterial blood gas showsthe following values: 7.31/29/67/23, O 2 saturation93%.Downloaded from ajpadvan.physiology.org on December 7, 2006TABLE 2FI O2 PA O2 Pa O2 A-a Gradient Virtual Shunt Estimated Shunt a/APatient 1 (asthma) 0.28 168 74 94 15%–20% 6% 0.44Patient 2 (surgery) 0.5 322 115 207 10%–15% 12% 0.36VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001165

I N N O V A T I O N S A N D I D E A S1) Use Eq. 3A to calculate the patient’s alveolar O 2(PAO 2 ). Answer, 220 Torr.2) Calculate the patient’s alveolar arterial gradient,i.e., PAO 2 Pa O2. Answer, 153 Torr.3) Use Fig. 3 to estimate the patient’s virtual shunt.Answer, 25%.4) Now use Eq. 10 to estimate the patient’s shunt.Answer, 9%. Can you explain why Eq. 10 gives sucha poor estimate of virtual shunt? Hint, see the discussionof patient 1.5) Now use Eq. 19 to calculate the patient’s arterialalveolarratio. Answer, 0.3. Does Eq. 13 overestimateor underestimate the patient’s illness and why?Hint, see the discussion of patient 1.Address for reprint requests and other correspondence: P. E. Bigeleisen,Dept. of Anesthesiology, Box 604, Strong Memorial Hospital,601 Elmwood Ave., Rochester, NY 14642 (E-mail: Paul_Bigeleisen@urmc.rochester.edu).Received 12 November 2000; accepted in final form 4 May 2001REFERENCES1. Levitzky MG. Pulmonary Physiology. New York: McGraw-Hill,1999, p. 113–128.2. Lumb AB. Nunn’s Applied Respiratory Physiology. Oxford:Butterworth Heinemann, 2000, p. 249–298.3. Shapiro BA, Harrison A, Kacmarek RM, and Cane RD.Clinical Applications of Respiratory Care. Chicago, IL: YearBook, 1985, p. 52–61.4. West JB. Respiratory Physiology. Baltimore, MD: Williams &Wilkins, 1985, p. 49–68.Downloaded from ajpadvan.physiology.org on December 7, 2006VOLUME 25 : NUMBER 3 – ADVANCES IN PHYSIOLOGY EDUCATION – SEPTEMBER 2001166