Cardiac shunt calculations made easy: A casebased ...

Catheterization and Cardiovascular Interventions 76:137–142 (2010)

Cardiac Shunt Calculations Made Easy: A Case-based Approach Mario Go¨ssl,

MD

and Charanjit S. Rihal,*

MD

On the basis of an interesting case of a 40-year-old lady with an atrial septal defect, we describe a simple approach for complex shunt volume calculations based on the Fick principle using hemodynamic data obtained in the catheterization laboratory. Understanding Fick’s principle allows determination of all relevant flows, flow ratio, and resistances without having to resort to memorization of complex formulae. Those findings significantly impact the managements of patients like ours with hemodynamically and clinically relevant shunting. VC 2010 Wiley-Liss, Inc. Key words: atrial septal defect; shunt; Fick’s principle; right heart catheterization

INTRODUCTION

Shunt calculations derived from data obtained in the catheterization laboratory appear complex and nonintuitive. We therefore sought to describe a simplified approach of calculating shunt volumes based upon the Fick principle without having to memorize complicated formulae that is readily applicable to patients. CASE

A 40-year-old woman with a history of a 1.7-cm atrial septal defect (ASD) complicated by severe pulmonary hypertension with bidirectional shunt presented for a follow-up visit. She had stable dyspnea (NYHA I-II) and was able to walk 534 m on a standardized 6min-walk test. Her medical regimen consisted of coumadin, lasix, spironolactone, bosentan, and sildenafil. Physical examination revealed normal jugular venous pressure and carotid upstrokes. Her lungs were clear to auscultation. She had a 1þ left sternal heave with a palpable pulmonary closure sound. The first heart sound was normal in intensity. The second heart sound was narrowly split with an ejection click and a loud pulmonary closure sound. There was a grade 1 systolic murmur followed by a diastolic murmur at the left upper sternal border. There was no gallop rhythm appreciated. Her extremities showed no edema, clubbing, or cyanosis, and her distal pulses were normal. The transthoracic echocardiogram showed improvement in her Doppler derived right ventricular systolic C 2010 Wiley-Liss, Inc. V

pressure (RVSP) with an estimated RVSP of 65 mm Hg (compared to a systolic blood pressure of 100 mm Hg). Her prior documented RVSP was 110 mm Hg by echocardiogram a year ago and 90 mm Hg by cardiac catheterization 5 years ago. Also noted was an atrial septal aneurysm and large atrial septal defect with bidirectional shunt, moderate right ventricular enlargement with severe hypertrophy but only mildly decreased right ventricular systolic function. The main pulmonary artery was dilated (36 mm), there was mild pulmonary valve regurgitation. Her left ventricular chamber size was normal with normal systolic function, ejection fraction 75%. Because of her chest pain and improvement in her pulmonary hemodynamics, she was referred for cardiac catheterization. Hemodynamic data were collected during right heart catheterization on room air and subsequently with 100% oxygen delivered via a nonrebreathing mask.

Division of Cardiovascular Diseases, Mayo Clinic College of Medicine, Rochester, Minnesota Conflict of interest: Nothing to report. *Correspondence to: Charanjit S. Rihal, MD, Division of Cardiovascular Diseases, Mayo Clinic College of Medicine, Rochester, MN. E-mail: [email protected] Received 29 December 2009; Revision accepted 20 January 2010 DOI 10.1002/ccd.22471 Published online 1 June 2010 in Wiley InterScience (www. interscience.wiley.com).

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TABLE I. Definitions and Calculations Oxygen consumption (VO2, ml/min; measured) Arterial oxygen content (FAO2, ml/l) Mixed venous oxygen saturation (%) Mixed venous oxygen content (MVO2) Pulmonary vein oxygen content (PVO2) Pulmonary artery oxygen content (PVO2) Cardiac output (Fick; CO l/min) Systemic flow (Qs) Pulmonary flow (Qp) Effective flow (Qe) Pulmonary arteriolar resistance index (PARI): normal: 150–250 dyn. s/cm5/m2 Recirculated pulmonary flow Recirculated systemic flow

1.36 Hb 10 arterial oxygen saturation ((3 SVC oxygen saturation þ 1 IVC oxygen saturation)/4) 1.36 Hb 10 mixed venous oxygen saturation 1.36 Hb 10 pulmonary vein oxygen saturation 1.36 Hb 10 pulmonary artery oxygen saturation VO2 (ml/min)/[(arterial O2 sat – venous O2 sat) 1.36 Hb (g/dl) 10], or VO2 (ml/min)/(arterial oxygen content – venous oxygen content) VO2/[(FAO2 – MVO2) 1.36 Hb 10] VO2/[(PVO2 – PAO2) 1.36 Hb 10] VO2/[(PVO2 – MVO2) 1.36 Hb 10] [(Mean pulmonary arterial pressure – mean left atrial pressure)/CO] 80/BSA

Qp – Qe (pulmonary flow – effective flow) Qs – Qe (systemic flow – effective flow)

How would you approach the complex shunt calculations in this patient with an ASD with bidirectional shunting using the actual values obtained during the right heart catheterization? First, we must understand Fick’s principle. Fick’s principle describes the relationship between uptake or production of an indicator substance, flow through a system, and the concentration of the indicator entering and exiting the system. The Fick equation is a method of determining cardiac output (or indeed any flow or consumption in the body such as renal blood flow, bronchial blood flow, myocardial substrate uptake and output). The inverse of the reverse Fick principle can be used to determine oxygen consumption if CO is determined by the thermodilution method. Adolf Fick (1829–1901) was an influential German physiologist who besides inventing the contact lens was the first to develop a method to measure cardiac output in 1870. The method was not used in humans until 1940 when cardiac catheterization became a clinical diagnostic tool. Fick’s principle relates input and output concentrations of a substance to its rate of consumption. Knowing these values, flow rates can be determined. As an analogy, consider a coal train carrying coal into a city. If the city has a coal consumption of 200 tons/day and trains with 10 tons of coal/train would come and leave with 8 tons/train, the question ‘‘how many trains would have to come into the city to cover the daily coal consumption’’ can be asked. The answer, of course, is 100 trains per day (200/2 ¼ 100). In this analogy, the daily coal consumption corresponds to the patient’s oxygen consumption, the in- and outgoing trains represent the arterial and mixed venous blood oxygen contents and the number of trains needed to cover the city’s coal needs represent the cardiac output. Therefore, to calculate cardiac output, the difference between arterial and mixed venous oxygen content (oxygen content in the

Fig. 1. Right and left oxygen saturations on room air. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

right atrium, right ventricle or pulmonary artery) is divided into the oxygen consumption of the body (VO2), see Table I. Understanding the Fick principle is the first, crucial step in understanding complex shunts. RIGHT HEART CATHETERIZATION ON ROOM AIR

Measurements made on room air is shown in Fig. 1. In addition, we obtained the following data that are needed for our subsequent calculations:

Catheterization and Cardiovascular Interventions DOI 10.1002/ccd. Published on behalf of The Society for Cardiovascular Angiography and Interventions (SCAI).

Cardiac Shunt Calculations Made Easy

Oxygen consumption 346 ml/min. Oxygen consumption is either estimated from the patient’s weight or directly measured by gas exchange as in this case. It has been shown previously that estimated values of oxygen consumption do not correlate well with measured data, often differing by 25% [1]. Thus, direct measurement is generally preferred over estimation, particularly since we are interested in calculating absolute flows, not just relative flows. If, however, direct measurement is not readily available, the equations of LaFarge and Miettinen [2] have shown the closest approximation to the measured data and their use is recommended in preference to values predicted from basal metabolic rate studies. Our laboratory uses the MedGraphics Ultima CPX (Medical Graphics Corporation, St. Paul, MN) for direct measurement of oxygen consumption. The method used by this device has been described by Beaver et al. [3]. In brief, the breathing apparatus consists of a two-way valve, a pneumotachygraph in the expiration arm connected to a differential pressure transducer. Small lumen sampling lines connected to the mouthpiece lead to a fast responding oxygen analyzer and a carbon dioxide analyzer which are connected through the standard input couplers of an oscillographic recorder. The flow signal together with oxygen and carbon dioxide partial pressures are sampled during both inspiration and expiration. After calibration (and application of correction factors for respiratory gas exchange ratio, water vapor, and breathing valve dead space), gas concentrations and flow are appropriately in phase and can be multiplied and integrated at each sample interval to give oxygen uptake and carbon dioxide production for each breath. After reaching a steady state (usually after 3–4 min), oxygen consumption is recorded. CBC With Hemoglobin Concentration 14.2 mg/dl is directly relevant since each gram of hemoglobin (Hb) can typically (assuming a structurally and functionally normal Hb molecule) carry 1.36 ml of oxygen per dl, or 13.6 ml O2/l. Arterial oxygen saturation was 89%, hence arterial oxygen content calculates as 1.36 Hb (14.2) 10 0.89 ¼ 172 ml/l. SVC oxygen saturation was 72%, her IVC oxygen saturation was 73%. A weighted average (three parts SVC, one part IVC) gives a mixed venous oxygen saturation ((3 72% þ 1 73%)/4): 72.25%. Mixed venous (MV) oxygen content is therefore 1.36 Hb (14.2) 10 0.7225 ¼ 140 ml/l. Directly measured pulmonary vein oxygen saturation was 95% (we accessed one of her pulmonary veins through the large ASD). Hence, her pulmonary vein oxygen content calculates as 1.36 Hb (14.2) 10 0.95 ¼ 183 ml/l. Her pulmonary artery oxygen saturation was 72% and the corresponding pulmonary artery oxygen content 1.36 Hb 10 0.72 ¼ 139 ml/l.

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FICK EQUATION AND CARDIAC OUTPUT

Using the coal train analogy and the data we calculated above, the cardiac output is: 346 ml/min/(172 ml/ l – 140 ml/l) ¼ 10.7 l/min. The relative contribution of oxygen dissolved in the blood that is not bound to Hb is assumed to be minimal. This is a valid assumption as long as the patient is not anemic. The higher the FiO2, the larger this contribution becomes, for example if the patient is breathing 100% O2. In that case each liter of blood can absorb an additional 0.03 ml of oxygen. INTRACARDIAC SHUNTS

Intracardiac shunts invalidate the concept of a single cardiac output. In the presence of intracardiac shunts, it is more precise to speak in terms of systemic blood flow (SBF) and pulmonary blood flow (PBF) for the reason that inflow and outflow oxygen content varies depending on the site of sampling, the location of the shunt, and the direction of the shunt. As such, cardiac output becomes difficult to define as there are different flows across the systemic and pulmonary circulations. Thinking in terms of SBF and PBF then allows precise calculation of shunt flows, either left to right, right to left, or both, using Fick’s Principle. USING THE FICK EQUATION WITH INTRACARDIAC SHUNTS

The Fick equation is the cornerstone of understanding the hemodynamics and flows of intracardiac shunts. Using Fick’s Principle, three key Fick equations can be quickly defined to use in the setting of a shunt. With these three equations, all important hemodynamic shunt parameters can be determined. Systemic Flow Systemic flow (Qs) is the total flow across the systemic circulation, specifically between the femoral artery and the right atrium (Table I). Mixed venous oxygen content (MVO2) is calculated based on venous blood return to the right side of the heart before it actually enters the heart using the formula shown in Table I. In our patient: Systemic flow:

• Questions to ask: What goes into the system and what comes out? • Into the system: arterial oxygen content ¼ 172 ml/l. • Out of the system: mixed venous oxygen content ¼ 140 ml/l.


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• therefore systemic blood flow: 346/ (172 – 140) ¼ 10.7 l/min. Pulmonary Flow

Pulmonary flow (Qp) is total flow across the pulmonary circulation, more precisely between the pulmonary artery and pulmonary veins (Table I). In our patient: Pulmonary flow: • Questions to ask: What goes into the lungs and what comes out? • Into the lungs: pulmonary artery oxygen content ¼ 139 ml/l. • Out of the lungs: pulmonary vein oxygen content ¼ 183 ml/l. • therefore pulmonary blood flow: 346/(183 – 139) ¼ 7.79 l/min.

Effective Forward Flow This is the theoretical flow of unshunted blood through the entire circulatory system. In the presence of a shunt, this of course is a theoretical value. The flow allows calculation of exact shunt flows by answering the question ‘‘what would blood flow be if there were no shunts?’’ Qe is calculated by using sites of oxygen sampling that are taken upstream to any shunting such as pulmonary vein oxygen content and the mixed venous oxygen content (for calculation see Table I). In our patient:

• Question to ask: What is the theoretical amount of blood that would flow through the system if no shunt existed? • Pulmonary vein oxygen content ¼ 183 ml/l. • Mixed venous oxygen content ¼ 140 ml/l. • therefore effective flow: 346/(183 – 140) ¼ 7.88 l/ min.

Shunt Flow Recirculated pulmonary flow represents the amount of left to right shunting. It is the fully saturated blood that is shunted to the right side of the heart without passing through the systemic capillaries (Table I for calculation). Recirculated systemic flow represents the amount of right to left shunting. It is the desaturated mixed venous blood that is shunted to the left side of the heart without being oxygenated by the lungs (Table I for calculation). In our patient:

• With the above information you can easily calculate the differential contribution of a R/L and L/R shunt. Remember that in a system with no shunts effective flow ¼ systemic flow ¼ pulmonary flow. • Is there a R/L shunt OR is the effective flow lower than the calculated systemic flow due to a R/L shunt? • Systemic flow – effective flow: 10.7 – 7.88 ¼ 2.82 l/ min ¼ the absolute right to left shunt. • Similarly, is there a L/R shunt OR is the effective flow lower than the pulmonary flow due to a L/R shunt? Pulmonary blood flow – effective flow: 7.79 – 7.88 ¼ –0.09 l/min (no left to right shunt at rest). • Baseline summary: This patient has a right to left shunt of almost 3 l/min on room air. PULMONARY ARTERIOLAR RESISTANCE

Pulmonary arteriolar resistance (PAR) is the total resistance through the pulmonary arterial circuit (Table I) and influences the degree and direction of shunting. It is usually indexed to body surface area. In the absence of pulmonary venous hypertension, pulmonary capillary wedge pressure can be substituted for left atrial pressure. In our patient: • PAP mean: 40 mm Hg, PCW mean: 6 mm Hg, BSA: 2.17 m2. • [(PAP mean – PCW mean)/CO] 80/2.17 ¼ 117 dyn sec/cm5/m2.

RIGHT HEART CATHETERIZATION ON 100% O2 VIA NON-REBREATHING MASK

Initial calculations and measurements were performed on room air. Repeating the measurements and calculations on 100% oxygen allows one to determine if a change in pulmonary arterial resistance occurs with a change in shunt flow direction and/or volume. This has implications for subsequent therapeutic decisions. Figure 2 gives measurements obtained from the right heart catheterization under 100% oxygen. We will now try to answer the following question using the calculations described above: What hemodynamic changes occurred on 100% oxygen? a. Nothing changes, the patient has still a 3 l/min R/L shunt. b. The shunt reverses into a L/R shunt. c. The R/L shunt increases. d. There is no shunt on 100% oxygen.


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• Into the lungs: pulmonary artery oxygen content ¼ 164 ml/l. • Out of the lungs: pulmonary vein oxygen content ¼ 191 ml/l. • Pulmonary flow: 346/(191 – 164) ¼ 12.81 l/min. Effective flow • Question to ask: What is the theoretical amount of blood that would flow through the system if no shunt existed. • Pulmonary vein oxygen content ¼ 191 ml/l. • Mixed venous oxygen content ¼ 155 ml/l. • Effective flow: 346/ (191 – 155) ¼ 9.61 l/min. Is there a R/L shunt? • No, systemic flow – effective flow: 9.68 – 9.68 ¼ 0 l/min. • Is there a L/R shunt? • Pulmonary flow – effective flow: 12.8 – 9.68 ¼ 3.12 l/min. • Answer: Our patient now has a L/R shunt of about 3 l/min on 100% oxygen. Fig. 2. Right and left heart oxygen saturations on 100% oxygen via nasal canula. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Basic calculations: • Arterial oxygen content: 1.36 Hb 10 0.99 ¼ 191 ml/l. • Mixed venous oxygen saturation ((3 SVC þ 1 IVC)/4): 80.5%. • Mixed venous oxygen content: 1.36 Hb 10 0.805 ¼ 155 ml/l. • Pulmonary vein oxygen content: 1.36 Hb 10 0.99 ¼ 191 ml/l. • Pulmonary artery oxygen content: 1.36 Hb 10 0.85 ¼ 164 ml/l. • Cardiac output: 346/(191 – 155) ¼ 9.61 l/min. Systemic flow • Questions to ask: What goes into the system and what comes out? • Into the system: arterial oxygen content ¼ 191 ml/l. • Out of the system: mixed venous oxygen content ¼ 155 ml/l. • Systemic flow: 346/(191 – 155) ¼ 9.61 l/min Pulmonary flow • Questions to ask: What goes into the lungs and what comes out?

Pulmonary arteriolar resistance index (PARI): • PAP mean: 36 mm Hg, PCW mean: 6 mm Hg, BSA: 2.17 m2. • [(PAP mean – PCW mean)/CO] 80/2.17 ¼ 115 dyn sec/cm5/m2. Thus, changing pulmonary arteriolar resistance with 100% O2 has reversed the intracardiac shunt from right to left at baseline to a left to right shunt. This indicates the pulmonary hypertension is not irreversible and that the patient may still benefit from surgical closure of the ASD. Qp/Qs (Ratio of Pulmonary Flow and Systemic Flow)

In presence of pulmonary hypertension, the Qp/Qs ratio is a major determinant of candidacy for ASD closure. Traditionally, a residual Qp/Qs > 1.5, indicating a left to right shunt, after drug interventions (100% oxygen, Flolan, NO) is considered a very favorable response of the pulmonary circulation and that the pulmonary hypertension is not irreversible. Such finding suggests that repair of the ASD might not be contraindicated. Irreversible pulmonary hypertension is a contraindication to closure. If pulmonary hypertension is present, vasodilators must reduce the mean pulmonary arterial pressure by 10 mm Hg to an absolute value of 40 mm Hg or PAR must be reduced to