CASE CONFERENCES The Clinical Physiologist Section Editor: John Kreit, M.D.
Lie Down and Breathe Sean Agbor-Enoh1,2 and Henry E. Fessler1 1 Division of Pulmonary and Critical Care Medicine, Johns Hopkins Hospital, Baltimore, Maryland; and 2Division of Critical Care Medicine, National Institutes of Health, Bethesda, Maryland
In Brief A 56-year-old man with alcoholic and hepatitis C–induced cirrhosis presented to the emergency department with a 2-month history of progressive dyspnea without worsening symptoms of ascites or volume overload. His evaluation was remarkable for dyspnea and hypoxemia in the erect position that improved when supine. This orthostatic hypoxemia in patients with cirrhosis is quite characteristic and guided the investigations leading to diagnosis and management.
The Clinical Challenge A 56-year-old man with cirrhosis (ChildPugh C) due to alcohol and hepatitis C presented with 2 months of worsening dyspnea. The dyspnea had initially occurred only with activity but had progressed to dyspnea at rest. The patient had noted that his dyspnea improved when recumbent, and he had been spending much of the day in bed. He had chronic ascites and leg edema, which had been stable on spironolactone and furosemide. The patient denied cough, sputum production, fever, chills, and weight loss. Examination of the lungs revealed no dullness to percussion, crackles, or wheezes. There was no jugular venous distention, heart sounds were normal, and there were no murmurs or gallops. The patient’s abdomen was distended, and shifting dullness was present. He had
Questions
ascites or hepatic hydrothorax or by comorbid diseases, such as chronic obstructive pulmonary disease, heart failure, or pulmonary embolism. The patient’s history, physical examination, laboratory testing, and radiographic imaging were not consistent with any of these disorders. Portopulmonary hypertension was also unlikely given the clinical presentation. Because of the patient’s significant postural changes in dyspnea and PaO2, we considered hepatopulmonary syndrome (HPS) to be the most likely diagnosis. HPS is defined as the triad of liver disease, hypoxemia, and intrapulmonary shunt. Pathologically, there are two characteristic abnormalities of the pulmonary microvasculature: arteriovenous malformations and markedly dilated pulmonary capillaries and arteries. The diagnosis of HPS is made by demonstrating a significant intrapulmonary right-to-left shunt in a hypoxemic patient with liver disease.
What is the cause of this patient’s dyspnea and hypoxemia?
The Clinical Solution
mild, symmetric leg edema. Laboratory evaluation was notable for a stable hemoglobin concentration of 8.5 g/dl, a platelet count of 79,000/L, total bilirubin of 2.1 mg/dl, albumin of 2.5 g/dl, and an international normalized ratio of 1.6. A chest radiograph demonstrated normal lung volumes without pulmonary infiltrates, pleural effusion, or cardiomegaly, and computed tomography angiography showed no evidence of acute or chronic pulmonary embolism. While breathing room air, arterial blood gas measurements performed while seated showed a pH of 7.39, a PaCO2 of 35 mm Hg, a PaO2 of 52 mm Hg, and an SaO2 of 88%. When supine, the patient’s PaO2 increased to 64 mm Hg with an increase in SaO2 to 92%. Using a 1 (absent) to 10 (severe) dyspnea scale, the patient reported a score of 7 while seated and 3 when supine.
What is the significance of this patient’s platypnea and orthodeoxia? What is the diagnosis?
Clinical Reasoning Dyspnea and hypoxemia in patients with cirrhosis are usually caused by massive
While in the upright position breathing 100% oxygen, the patient’s PaO2 was 68 mm Hg and his calculated shunt fraction was 37% of the cardiac output. Contrastenhanced transthoracic echocardiography using intravenously injected agitated saline demonstrated microbubbles in the left atrium after five cardiac cycles. This confirmed both the presence of an
(Received in original form February 19, 2014; accepted in final form July 14, 2014 ) Correspondence and requests for reprints should be addressed to Sean Agbor-Enoh, M.D., Ph.D., Johns Hopkins Hospital, Pulmonary and Critical Care Medicine, 1830 East Monument Street, Baltimore, MD 21287. E-mail: [email protected] Ann Am Thorac Soc Vol 11, No 7, pp 1155–1158, Sep 2014 Copyright © 2014 by the American Thoracic Society DOI: 10.1513/AnnalsATS.201402-073CC Internet address: www.atsjournals.org
Case Conferences: The Clinical Physiologist
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CASE CONFERENCES intrapulmonary shunt and the diagnosis of HPS. The patient was subsequently referred for liver transplant evaluation.
The Science behind the Solution Hypoxemia in the HPS
In general, there are five mechanisms of arterial hypoxemia: low barometric pressure (i.e., high: altitude), : hypoventilation, V=Q mismatch, rightto-left shunt, and diffusion limitation. In patients with HPS, the latter two predominate and are caused by two characteristic vascular abnormalities— dilated pulmonary capillaries and arteriovenous malformations (Figure 1).
As shown in Figure 1A, the small diameter of the normal pulmonary capillaries forces red blood cells (RBCs) to squeeze through in “single file” (1). This minimizes the diffusion distance for oxygen and carbon dioxide and allows rapid equilibration of alveolar and capillary PO2 and PCO2. In healthy individuals, RBCs require only about one-third of their normal 0.75-s transit time to become fully saturated with oxygen. In HPS, dilated capillaries, which may reach 10 times the normal diameter, increase diffusion distance, which prevents equilibration and reduces PaO2 (Figure 1B). As in other disorders that impair diffusion, such as emphysema and interstitial lung disease, an exertion-induced increase in cardiac output worsens arterial hypoxemia by speeding
A
RBC transit and further decreasing the time available for equilibration. Figure 1B also shows precapillary arteriovenous connections, which produce a right-to-left shunt and allow mixed venous blood to directly enter the systemic circulation (1). The resulting hypoxemia correlates with the shunt fraction, which is the proportion of the cardiac output that bypasses the alveolar capillaries. In patients with HPS, dilated capillaries and arteriovenous malformations occur primarily at the lung bases (Figure 2). When patients sit or stand, gravity forces more blood through these abnormal vessels, which reduces the PaO2 and increases dyspnea. When patients are supine, pulmonary blood flow is more evenly distributed, the PaO2 rises, and dyspnea decreases. These postural effects on dyspnea and PaO2 are referred to as platypnea and orthodeoxia, respectively, and are characteristic of the HPS. The Quantification of Shunt Fraction
Alveolus Deoxygenated blood
O2
O2 O2
O2
Because blood passing through arteriovenous malformations is not exposed to alveolar oxygen, an important characteristic of shunt-induced hypoxemia is that there is relatively little improvement in PaO2 even at high FIO2. This can be used to distinguish shuntinduced hypoxemia from : : impaired oxygenation due to V=Q mismatching and diffusion limitation, which resolves with high FIO2. When a patient receives an FIO2 of 1.0 through a tight-fitting facemask or mouthpiece, the shunt fraction, or the ratio : of blood flow through the shunt (QS) to : total cardiac output (Q T ), can be calculated. : : Qs Q t ¼ ðCcO2 2 CaO2 Þ ðCcO2 2 CvO2 Þ
Oxygenated blood
Blood flow
B
Dilated intrapulmonary vessel
Alveolus O2 O2
O2
O2
Partially oxygenated blood
ð1Þ Blood flow
Arteriovenous bypass Figure 1. Vascular malformations in the hepatopulmonary syndrome. (A) Normal alveolar–capillary interface. Deoxygenated blood (blue) is completely oxygenated (red) as it flows through the capillary. (B) Effect of dilated capillaries and arteriovenous malformations in a patient with hepatopulmonary syndrome. Mixed venous blood (blue) is added directly to the systemic circulation through arteriovenous connections and incompletely oxygenated as it flows through the dilated capillaries. Reprinted by permission from Reference 1.
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A step-by-step derivation of the shunt equation can be found in Appendix 1. In Equation 1, CcO2, CaO2, and CvO2 represent the oxygen content of endcapillary, arterial, and mixed venous blood, respectively. Oxygen content (CO2) is the total volume of oxygen in the blood and is conventionally expressed as milliliters of O2 per deciliter of blood. The vast majority of oxygen is combined with hemoglobin, and this is calculated by multiplying the hemoglobin concentration (Hb) by the
AnnalsATS Volume 11 Number 7 | September 2014
CASE CONFERENCES alveolar PO2 (PaO2) calculated using the alveolar gas equation. PaO2 ¼ ðPB 2 PH2O Þ 3 FiO2 2 PaCO2 =R ð6 Þ In Equation 6, PB is the barometric pressure, PH2O is the partial pressure of water in the conducting airways and alveoli, and R is the respiratory quotient, or the ratio of CO2 to O2 exchanged at the alveolar–capillary interface. If FIO2 is 1.0 and we make the additional assumptions that PB is 760 mm Hg, PH2O is 47 mm Hg, and R is 1, Equation 6 can be simplified to
ð7 Þ
PaO2 ¼ 713 2 PaCO2
The oxygen content of end-capillary blood can then be calculated as CcO2 ¼ ð1:34 3 Hb 3 1:0Þ 1 ðPaO2 3 0:003Þ
ð8Þ Figure 2. Distribution of vascular malformations in the hepatopulmonary syndrome. Coronal section of a chest computed tomography image showing that dilated pulmonary vessels predominate at the lung bases.
fractional hemoglobin saturation (SO2/100) and 1.34, which is the volume of oxygen carried by 1 g of fully saturated hemoglobin. A much smaller volume is dissolved in the plasma and RBCs, and this is the product of the PO2 and the solubility of oxygen in blood. CO2 ðml=dlÞ ¼ 1:34 ðml=gÞ 3 Hb ðg=dlÞ 3 So2 =100 1 Po2 ðmm HgÞ 3 0:003 ðml=dl=mm HgÞ ð2Þ
CcO2, CaO2, and CvO2 are calculated as: CcO2 ¼ ð1:34 3 Hb 3 ScO2 =100Þ 1 ðPcO2 3 0:003Þ
ð3Þ
CaO2 ¼ ð1:34 3 Hb 3 SaO2 =100Þ 1 ðPaO2 3 0:003Þ
ð4Þ CvO2 ¼ ð1:34 3 Hb 3 SvO2 =100Þ 1 ðPvO2 3 0:003Þ
ð5Þ
Although CaO2 can be easily calculated from arterial blood gas measurements, a number of assumptions must be made to determine the oxygen content of endcapillary and mixed venous blood. First, it is assumed that at an FIO2 of 1, ScO2 is 100%. Also, if there is no diffusion impairment, the PcO2 is equal to the
Although mixed venous oxygen content is ideally calculated by measuring the PO2 and SO2 of pulmonary arterial blood, this is not routinely done in clinical practice. Instead, CvO2 is calculated from CaO2 by assuming that there is a normal arteriovenous oxygen content difference of 5 ml/dl.
ð9Þ
CvO2 ¼ CaO2 2 5 In the patient described here, these calculations yielded an estimated shunt fraction of 0.37, or 37% of the cardiac output. n
Author disclosures are available with the text of this article at www.atsjournals.org. Acknowledgment: The authors thank Dr. Elizabeth Weihe for her assistance preparing the radiologic images.
Reference 1 Grace JA, Angus PW. Hepatopulmonary syndrome: update on recent advances in pathophysiology, investigation, and treatment. J Gastroenterol Hepatol 2013;28:213–219.
Case Conferences: The Clinical Physiologist
1157
CASE CONFERENCES :
Derivation of shunt equation : The cardiac output (Q T) is the sum of blood flow through: the pulmonary capillaries (QC) and shunt (Q S). :
:
Q t ¼ Qc 1 Qs :
:
Qc ¼ Q t 2 Qs
Rearranging Equation 15 gives :
ð13Þ
Do2 ¼ Do2C 3 Do2S
:
:
Q t 3 CaO2 ¼ Q t 3 CcO2 2Qs 3 CcO2 : 1 Qs 3 CvO2
Oxygen delivery is also the sum of the oxygen delivered by the shunted (DO2S) and the nonshunted (DO2C) blood.
ð10Þ
:
:
:
ð11Þ
The volume of oxygen delivered to the tissues (oxygen delivery [DO2]) is the product of cardiac output and arterial oxygen content (CaO2)*. *Oxygen content is the product of the hemoglobin concentration (Hb), the fractional hemoglobin saturation of the blood (SO2/100), and 1.34, which is the volume of oxygen carried by 1 g of fully saturated hemoglobin.
:
:
ð14Þ Substituting Equation 11 into Equation 14 gives :
:
1 Qs 3 CvO2
: : Qs 3 CcO2 2 CvO2 ¼ Q t 3 CcO2 2 CaO2
ð18Þ Equation 18 can then be rearranged to yield the shunt fraction equation. :
Q t 3 CaO2 ¼ Q t 2 Qs 3 CcO2 :
:
ð17 Þ
Q t 3 CaO2 ¼ Qc 3 CcO2 3 Qs 3 CvO2
:
ð16 Þ
Qs 3 CcO2 2 Qs 3 CvO2 ¼ Q t 3 CcO2 2 Q t 3 CaO2
Equation 13 can be rewritten as
Rearranging Equation 10 gives
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ð12Þ
Do2 ¼ Q t 3 CaO2
Appendix 1
Qs
ð15Þ
:
Qt
¼
ðCcO2 2 CaO2 Þ ðCcO2 2 CvO2 Þ
ð19Þ
AnnalsATS Volume 11 Number 7 | September 2014
Lie Down and Breathe Sean Agbor-Enoh1,2 and Henry E. Fessler1 1 Division of Pulmonary and Critical Care Medicine, Johns Hopkins Hospital, Baltimore, Maryland; and 2Division of Critical Care Medicine, National Institutes of Health, Bethesda, Maryland
In Brief A 56-year-old man with alcoholic and hepatitis C–induced cirrhosis presented to the emergency department with a 2-month history of progressive dyspnea without worsening symptoms of ascites or volume overload. His evaluation was remarkable for dyspnea and hypoxemia in the erect position that improved when supine. This orthostatic hypoxemia in patients with cirrhosis is quite characteristic and guided the investigations leading to diagnosis and management.
The Clinical Challenge A 56-year-old man with cirrhosis (ChildPugh C) due to alcohol and hepatitis C presented with 2 months of worsening dyspnea. The dyspnea had initially occurred only with activity but had progressed to dyspnea at rest. The patient had noted that his dyspnea improved when recumbent, and he had been spending much of the day in bed. He had chronic ascites and leg edema, which had been stable on spironolactone and furosemide. The patient denied cough, sputum production, fever, chills, and weight loss. Examination of the lungs revealed no dullness to percussion, crackles, or wheezes. There was no jugular venous distention, heart sounds were normal, and there were no murmurs or gallops. The patient’s abdomen was distended, and shifting dullness was present. He had
Questions
ascites or hepatic hydrothorax or by comorbid diseases, such as chronic obstructive pulmonary disease, heart failure, or pulmonary embolism. The patient’s history, physical examination, laboratory testing, and radiographic imaging were not consistent with any of these disorders. Portopulmonary hypertension was also unlikely given the clinical presentation. Because of the patient’s significant postural changes in dyspnea and PaO2, we considered hepatopulmonary syndrome (HPS) to be the most likely diagnosis. HPS is defined as the triad of liver disease, hypoxemia, and intrapulmonary shunt. Pathologically, there are two characteristic abnormalities of the pulmonary microvasculature: arteriovenous malformations and markedly dilated pulmonary capillaries and arteries. The diagnosis of HPS is made by demonstrating a significant intrapulmonary right-to-left shunt in a hypoxemic patient with liver disease.
What is the cause of this patient’s dyspnea and hypoxemia?
The Clinical Solution
mild, symmetric leg edema. Laboratory evaluation was notable for a stable hemoglobin concentration of 8.5 g/dl, a platelet count of 79,000/L, total bilirubin of 2.1 mg/dl, albumin of 2.5 g/dl, and an international normalized ratio of 1.6. A chest radiograph demonstrated normal lung volumes without pulmonary infiltrates, pleural effusion, or cardiomegaly, and computed tomography angiography showed no evidence of acute or chronic pulmonary embolism. While breathing room air, arterial blood gas measurements performed while seated showed a pH of 7.39, a PaCO2 of 35 mm Hg, a PaO2 of 52 mm Hg, and an SaO2 of 88%. When supine, the patient’s PaO2 increased to 64 mm Hg with an increase in SaO2 to 92%. Using a 1 (absent) to 10 (severe) dyspnea scale, the patient reported a score of 7 while seated and 3 when supine.
What is the significance of this patient’s platypnea and orthodeoxia? What is the diagnosis?
Clinical Reasoning Dyspnea and hypoxemia in patients with cirrhosis are usually caused by massive
While in the upright position breathing 100% oxygen, the patient’s PaO2 was 68 mm Hg and his calculated shunt fraction was 37% of the cardiac output. Contrastenhanced transthoracic echocardiography using intravenously injected agitated saline demonstrated microbubbles in the left atrium after five cardiac cycles. This confirmed both the presence of an
(Received in original form February 19, 2014; accepted in final form July 14, 2014 ) Correspondence and requests for reprints should be addressed to Sean Agbor-Enoh, M.D., Ph.D., Johns Hopkins Hospital, Pulmonary and Critical Care Medicine, 1830 East Monument Street, Baltimore, MD 21287. E-mail: [email protected] Ann Am Thorac Soc Vol 11, No 7, pp 1155–1158, Sep 2014 Copyright © 2014 by the American Thoracic Society DOI: 10.1513/AnnalsATS.201402-073CC Internet address: www.atsjournals.org
Case Conferences: The Clinical Physiologist
1155
CASE CONFERENCES intrapulmonary shunt and the diagnosis of HPS. The patient was subsequently referred for liver transplant evaluation.
The Science behind the Solution Hypoxemia in the HPS
In general, there are five mechanisms of arterial hypoxemia: low barometric pressure (i.e., high: altitude), : hypoventilation, V=Q mismatch, rightto-left shunt, and diffusion limitation. In patients with HPS, the latter two predominate and are caused by two characteristic vascular abnormalities— dilated pulmonary capillaries and arteriovenous malformations (Figure 1).
As shown in Figure 1A, the small diameter of the normal pulmonary capillaries forces red blood cells (RBCs) to squeeze through in “single file” (1). This minimizes the diffusion distance for oxygen and carbon dioxide and allows rapid equilibration of alveolar and capillary PO2 and PCO2. In healthy individuals, RBCs require only about one-third of their normal 0.75-s transit time to become fully saturated with oxygen. In HPS, dilated capillaries, which may reach 10 times the normal diameter, increase diffusion distance, which prevents equilibration and reduces PaO2 (Figure 1B). As in other disorders that impair diffusion, such as emphysema and interstitial lung disease, an exertion-induced increase in cardiac output worsens arterial hypoxemia by speeding
A
RBC transit and further decreasing the time available for equilibration. Figure 1B also shows precapillary arteriovenous connections, which produce a right-to-left shunt and allow mixed venous blood to directly enter the systemic circulation (1). The resulting hypoxemia correlates with the shunt fraction, which is the proportion of the cardiac output that bypasses the alveolar capillaries. In patients with HPS, dilated capillaries and arteriovenous malformations occur primarily at the lung bases (Figure 2). When patients sit or stand, gravity forces more blood through these abnormal vessels, which reduces the PaO2 and increases dyspnea. When patients are supine, pulmonary blood flow is more evenly distributed, the PaO2 rises, and dyspnea decreases. These postural effects on dyspnea and PaO2 are referred to as platypnea and orthodeoxia, respectively, and are characteristic of the HPS. The Quantification of Shunt Fraction
Alveolus Deoxygenated blood
O2
O2 O2
O2
Because blood passing through arteriovenous malformations is not exposed to alveolar oxygen, an important characteristic of shunt-induced hypoxemia is that there is relatively little improvement in PaO2 even at high FIO2. This can be used to distinguish shuntinduced hypoxemia from : : impaired oxygenation due to V=Q mismatching and diffusion limitation, which resolves with high FIO2. When a patient receives an FIO2 of 1.0 through a tight-fitting facemask or mouthpiece, the shunt fraction, or the ratio : of blood flow through the shunt (QS) to : total cardiac output (Q T ), can be calculated. : : Qs Q t ¼ ðCcO2 2 CaO2 Þ ðCcO2 2 CvO2 Þ
Oxygenated blood
Blood flow
B
Dilated intrapulmonary vessel
Alveolus O2 O2
O2
O2
Partially oxygenated blood
ð1Þ Blood flow
Arteriovenous bypass Figure 1. Vascular malformations in the hepatopulmonary syndrome. (A) Normal alveolar–capillary interface. Deoxygenated blood (blue) is completely oxygenated (red) as it flows through the capillary. (B) Effect of dilated capillaries and arteriovenous malformations in a patient with hepatopulmonary syndrome. Mixed venous blood (blue) is added directly to the systemic circulation through arteriovenous connections and incompletely oxygenated as it flows through the dilated capillaries. Reprinted by permission from Reference 1.
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A step-by-step derivation of the shunt equation can be found in Appendix 1. In Equation 1, CcO2, CaO2, and CvO2 represent the oxygen content of endcapillary, arterial, and mixed venous blood, respectively. Oxygen content (CO2) is the total volume of oxygen in the blood and is conventionally expressed as milliliters of O2 per deciliter of blood. The vast majority of oxygen is combined with hemoglobin, and this is calculated by multiplying the hemoglobin concentration (Hb) by the
AnnalsATS Volume 11 Number 7 | September 2014
CASE CONFERENCES alveolar PO2 (PaO2) calculated using the alveolar gas equation. PaO2 ¼ ðPB 2 PH2O Þ 3 FiO2 2 PaCO2 =R ð6 Þ In Equation 6, PB is the barometric pressure, PH2O is the partial pressure of water in the conducting airways and alveoli, and R is the respiratory quotient, or the ratio of CO2 to O2 exchanged at the alveolar–capillary interface. If FIO2 is 1.0 and we make the additional assumptions that PB is 760 mm Hg, PH2O is 47 mm Hg, and R is 1, Equation 6 can be simplified to
ð7 Þ
PaO2 ¼ 713 2 PaCO2
The oxygen content of end-capillary blood can then be calculated as CcO2 ¼ ð1:34 3 Hb 3 1:0Þ 1 ðPaO2 3 0:003Þ
ð8Þ Figure 2. Distribution of vascular malformations in the hepatopulmonary syndrome. Coronal section of a chest computed tomography image showing that dilated pulmonary vessels predominate at the lung bases.
fractional hemoglobin saturation (SO2/100) and 1.34, which is the volume of oxygen carried by 1 g of fully saturated hemoglobin. A much smaller volume is dissolved in the plasma and RBCs, and this is the product of the PO2 and the solubility of oxygen in blood. CO2 ðml=dlÞ ¼ 1:34 ðml=gÞ 3 Hb ðg=dlÞ 3 So2 =100 1 Po2 ðmm HgÞ 3 0:003 ðml=dl=mm HgÞ ð2Þ
CcO2, CaO2, and CvO2 are calculated as: CcO2 ¼ ð1:34 3 Hb 3 ScO2 =100Þ 1 ðPcO2 3 0:003Þ
ð3Þ
CaO2 ¼ ð1:34 3 Hb 3 SaO2 =100Þ 1 ðPaO2 3 0:003Þ
ð4Þ CvO2 ¼ ð1:34 3 Hb 3 SvO2 =100Þ 1 ðPvO2 3 0:003Þ
ð5Þ
Although CaO2 can be easily calculated from arterial blood gas measurements, a number of assumptions must be made to determine the oxygen content of endcapillary and mixed venous blood. First, it is assumed that at an FIO2 of 1, ScO2 is 100%. Also, if there is no diffusion impairment, the PcO2 is equal to the
Although mixed venous oxygen content is ideally calculated by measuring the PO2 and SO2 of pulmonary arterial blood, this is not routinely done in clinical practice. Instead, CvO2 is calculated from CaO2 by assuming that there is a normal arteriovenous oxygen content difference of 5 ml/dl.
ð9Þ
CvO2 ¼ CaO2 2 5 In the patient described here, these calculations yielded an estimated shunt fraction of 0.37, or 37% of the cardiac output. n
Author disclosures are available with the text of this article at www.atsjournals.org. Acknowledgment: The authors thank Dr. Elizabeth Weihe for her assistance preparing the radiologic images.
Reference 1 Grace JA, Angus PW. Hepatopulmonary syndrome: update on recent advances in pathophysiology, investigation, and treatment. J Gastroenterol Hepatol 2013;28:213–219.
Case Conferences: The Clinical Physiologist
1157
CASE CONFERENCES :
Derivation of shunt equation : The cardiac output (Q T) is the sum of blood flow through: the pulmonary capillaries (QC) and shunt (Q S). :
:
Q t ¼ Qc 1 Qs :
:
Qc ¼ Q t 2 Qs
Rearranging Equation 15 gives :
ð13Þ
Do2 ¼ Do2C 3 Do2S
:
:
Q t 3 CaO2 ¼ Q t 3 CcO2 2Qs 3 CcO2 : 1 Qs 3 CvO2
Oxygen delivery is also the sum of the oxygen delivered by the shunted (DO2S) and the nonshunted (DO2C) blood.
ð10Þ
:
:
:
ð11Þ
The volume of oxygen delivered to the tissues (oxygen delivery [DO2]) is the product of cardiac output and arterial oxygen content (CaO2)*. *Oxygen content is the product of the hemoglobin concentration (Hb), the fractional hemoglobin saturation of the blood (SO2/100), and 1.34, which is the volume of oxygen carried by 1 g of fully saturated hemoglobin.
:
:
ð14Þ Substituting Equation 11 into Equation 14 gives :
:
1 Qs 3 CvO2
: : Qs 3 CcO2 2 CvO2 ¼ Q t 3 CcO2 2 CaO2
ð18Þ Equation 18 can then be rearranged to yield the shunt fraction equation. :
Q t 3 CaO2 ¼ Q t 2 Qs 3 CcO2 :
:
ð17 Þ
Q t 3 CaO2 ¼ Qc 3 CcO2 3 Qs 3 CvO2
:
ð16 Þ
Qs 3 CcO2 2 Qs 3 CvO2 ¼ Q t 3 CcO2 2 Q t 3 CaO2
Equation 13 can be rewritten as
Rearranging Equation 10 gives
1158
ð12Þ
Do2 ¼ Q t 3 CaO2
Appendix 1
Qs
ð15Þ
:
Qt
¼
ðCcO2 2 CaO2 Þ ðCcO2 2 CvO2 Þ
ð19Þ
AnnalsATS Volume 11 Number 7 | September 2014
