**4.1 The Fick principle**

The Fick principle states that 'The total uptake or release of any substance by an organ is the product of blood flow to the organ and the arteriovenous concentration difference of the substance.' (Fick 1870).

Accurate Measurement of Systemic

Case et al. (1995):

**circulation** 

pulmonary artery shunt. Therefore:

Oxygen Consumption in Ventilated Children with Congenital Heart Disease 305

 DO2 = CO × CaO2 (13) where CaO2, CvO2, and CpvO2 are systemic arterial and venous, and pulmonary venous oxygen contents; and MaP, MvP, and MpvP are mean systemic arterial, venous, and pulmonary venous pressures. ERO2 is calculated as in the normal circulation (Equation 8).

CO= VO2×(CpvO2 – CivcO2) /[(CpvO2 – CsvcO2)×(CaO2 – CivcO2)] (17)

where CaO2, CivcO2, CsvcO2, and CpvO2 are arterial, inferior and superior vena cava and pulmonary venous oxygen contents; MaP, MivcP, MsvcP, and MpvP are mean systemic arterial, inferior and superior vena cava, and pulmonary venous pressures. DO2 and ERO2

**4.5 In single ventricular circulation: Hypoplastic left heart syndrome and the Norwood** 

In functionally single ventricular circulation, a single outlet from the heart provides both systemic and pulmonary circulations via an interposed B-T shunt or right ventricle to

are calculated as in the normal circulation (Equations 7 & 8).

**4.4 In one-and-a-half ventricular circulation: Bidirectional cavopulmonary shunt**  In bidirectional cavopulmonary shunt circulation, the blood from the superior vena cava is directed to the pulmonary arteries, passing through the pulmonary circulation (Qp) and becomes oxygenated before it reaches the systemic circulation. Once in the systemic circulation, the blood from the superior vena cava mixes with systemic venous blood from the inferior vena cava (Qivc) to form total cardiac output (CO). Therefore, as stated by Salim,

SVR = (MaP – MsvcP)/Qs (11)

PVR = (MpaP – MpvP)/Qp (12)

Qsvc = Qp (14)

CO = Qp + Qivc (15)

Qivc = CO – Qp (18)

CO = Qs + Qp (21)

Qs = VO2 / (CaO2-CvO2) (22)

Qp = VO2 / (CpvO2-CaO2) (23)

SVR = (MaP – MsvcP)/Qs (24)

SVR = (MaP – MivcP)/Qs (19)

PVR = (MsvcP – MpvP)/Qp (20)

Qp = VO2 / (CpvO2 – CsvcO2) (16)

The Fick principle implies that if the flow in a system cannot be measured directly, then it can be measured using an indicator, provided that the indicator is removed at a known rate. Fick described the theory of a method to calculate cardiac output but never actually measured it himself. He argued: 'It is astonishing that no one has arrived at the following obvious method by which the amount of blood ejected by the ventricle of the heart with each systole may be determined directly, at least in animals. One measures how much oxygen an animal absorbs from the air in a given time. During the experiment one obtains a sample of arterial and venous blood; in both the oxygen content is measured. The difference in oxygen content tells how much oxygen each cubic centimeter of blood takes up in its passage through the lungs. As one knows the total quantity of oxygen absorbed in a given time one can calculate how many cubic centimeters of blood passed through the lungs in this time.' (Vandam and Fox 1998).

Verification of the Fick principle in humans was initially accomplished in 1930, through the daring exploits of Baumann and Grollman at a time when cardiac catheterization had yet to be established as a clinical tool. They obtained samples of mixed venous blood by inserting a spinal tap needle just to the right of the sternum; the needle entered the right ventricular chamber by puncturing its wall (Grollman 1932).

The direct Fick principle using VO2 is one of the oldest methods of measuring systemic and pulmonary blood flows, but nonetheless remains the gold standard. It can be used in simple biventricular and varied complex circulations in congenital heart defects, before or after surgical repair palliations. Relevant equations are provided in the following sections.

#### **4.2 In normal circulation**

The direct Fick method measures cardiac output (CO, which is systemic blood flow, Qs, and is equal to pulmonary blood flow, Qp) with VO2 according to the following equation:

$$\text{'CO} = \text{VO}\_2 \text{ / (CaO}\_2\text{-CvO}\_2\text{)}\tag{4}$$

where CaO2 and CvO2 are arterial and the mixed venous oxygen contents, respectively. Then:

$$\text{SNR} \equiv \text{(MaP - MsvC)} / \text{CO} \tag{5}$$

$$\text{PVR} = (\text{MpaP} - \text{MpvP}) / \text{CO} \tag{6}$$

$$\text{DO}\_2 = \text{CO} \times \text{CaO}\_2 \tag{7}$$

$$\text{ERO}\_2 = \text{VO}\_2 / \text{DO}\_2 \tag{8}$$

where MaP, MsvcP, MpaP, and MpvP are mean systemic arterial, superior vena cava, pulmonary arterial, and pulmonary venous pressures; CaO2 is systemic arterial oxygen content.

#### **4.3 In biventricular circulation with shunt**

In a biventricular circulation, the left to right, right to left, or bidirectional shunt may be present at the atrial, ventricular, or great vessel levels, such as in atrial septal defect, ventricular septal defect, patent arterial duct, or tetrology of Fallot.

$$\text{Qs} = \text{VO}\_2 \text{ / (CaO}\_2\text{-CvO}\_2\text{)}\tag{9}$$

$$\text{Qp} = \text{VO}\_2 \mid \text{(CpvO}\_2\text{-CpaO}\_2\text{)}\tag{10}$$

The Fick principle implies that if the flow in a system cannot be measured directly, then it can be measured using an indicator, provided that the indicator is removed at a known rate. Fick described the theory of a method to calculate cardiac output but never actually measured it himself. He argued: 'It is astonishing that no one has arrived at the following obvious method by which the amount of blood ejected by the ventricle of the heart with each systole may be determined directly, at least in animals. One measures how much oxygen an animal absorbs from the air in a given time. During the experiment one obtains a sample of arterial and venous blood; in both the oxygen content is measured. The difference in oxygen content tells how much oxygen each cubic centimeter of blood takes up in its passage through the lungs. As one knows the total quantity of oxygen absorbed in a given time one can calculate how many cubic centimeters of blood passed through the lungs in

Verification of the Fick principle in humans was initially accomplished in 1930, through the daring exploits of Baumann and Grollman at a time when cardiac catheterization had yet to be established as a clinical tool. They obtained samples of mixed venous blood by inserting a spinal tap needle just to the right of the sternum; the needle entered the right ventricular

The direct Fick principle using VO2 is one of the oldest methods of measuring systemic and pulmonary blood flows, but nonetheless remains the gold standard. It can be used in simple biventricular and varied complex circulations in congenital heart defects, before or after surgical repair palliations. Relevant equations are provided in the following sections.

The direct Fick method measures cardiac output (CO, which is systemic blood flow, Qs, and

where CaO2 and CvO2 are arterial and the mixed venous oxygen contents, respectively. Then:

DO2 = CO × CaO2 (7)

 ERO2 = VO2 / DO2 (8) where MaP, MsvcP, MpaP, and MpvP are mean systemic arterial, superior vena cava, pulmonary arterial, and pulmonary venous pressures; CaO2 is systemic arterial oxygen

In a biventricular circulation, the left to right, right to left, or bidirectional shunt may be present at the atrial, ventricular, or great vessel levels, such as in atrial septal defect,

CO = VO2 / (CaO2 – CvO2) (4)

SVR = (MaP – MsvcP)/CO (5)

PVR = (MpaP – MpvP)/CO (6)

Qs = VO2 / (CaO2-CvO2) (9)

Qp = VO2 / (CpvO2-CpaO2) (10)

is equal to pulmonary blood flow, Qp) with VO2 according to the following equation:

this time.' (Vandam and Fox 1998).

**4.2 In normal circulation** 

content.

chamber by puncturing its wall (Grollman 1932).

**4.3 In biventricular circulation with shunt** 

ventricular septal defect, patent arterial duct, or tetrology of Fallot.

$$\text{SVR} \equiv \text{(MaP - MsvcP)}/\text{Qs} \tag{11}$$

$$\text{PVR} \equiv \text{(MpaP - MpvP)}/\text{Qp} \tag{12}$$

$$\text{DO}\_2 = \text{CO} \times \text{CaO}\_2 \tag{13}$$

where CaO2, CvO2, and CpvO2 are systemic arterial and venous, and pulmonary venous oxygen contents; and MaP, MvP, and MpvP are mean systemic arterial, venous, and pulmonary venous pressures. ERO2 is calculated as in the normal circulation (Equation 8).

#### **4.4 In one-and-a-half ventricular circulation: Bidirectional cavopulmonary shunt**

In bidirectional cavopulmonary shunt circulation, the blood from the superior vena cava is directed to the pulmonary arteries, passing through the pulmonary circulation (Qp) and becomes oxygenated before it reaches the systemic circulation. Once in the systemic circulation, the blood from the superior vena cava mixes with systemic venous blood from the inferior vena cava (Qivc) to form total cardiac output (CO). Therefore, as stated by Salim, Case et al. (1995):

$$\mathbf{Q} \mathbf{s} \mathbf{v} \mathbf{c} = \mathbf{Q} \mathbf{p} \tag{14}$$

$$\text{CO} = \text{Qp} + \text{Qivc} \tag{15}$$

$$\text{Qp} = \text{VO}\_2 \mid \text{(CpvO}\_2\text{--CsvCO}\_2\text{)}\tag{16}$$

$$\text{CO=VO} \times \text{(CpvO\_2-CivO\_2)} / \left[ \text{(CpvO\_2-CsvO\_2)} \times \text{(CaO\_2-CivO\_2)} \right] \tag{17}$$

$$\text{Qivc} = \text{CO} - \text{Qp} \tag{18}$$

$$\text{SVR} \triangleq \langle \text{MaP} - \text{MivcP} \rangle / \text{Qs} \tag{19}$$

$$\text{PVR} \equiv \left( \text{MsvcP} - \text{MpvP} \right) / \text{Qp} \tag{20}$$

where CaO2, CivcO2, CsvcO2, and CpvO2 are arterial, inferior and superior vena cava and pulmonary venous oxygen contents; MaP, MivcP, MsvcP, and MpvP are mean systemic arterial, inferior and superior vena cava, and pulmonary venous pressures. DO2 and ERO2 are calculated as in the normal circulation (Equations 7 & 8).

#### **4.5 In single ventricular circulation: Hypoplastic left heart syndrome and the Norwood circulation**

In functionally single ventricular circulation, a single outlet from the heart provides both systemic and pulmonary circulations via an interposed B-T shunt or right ventricle to pulmonary artery shunt. Therefore:

$$\text{CO} = \text{Qs} + \text{Qp} \tag{21}$$

$$\text{Qs} = \text{VO}\_2 \mid \text{(CaO}\_2\text{-CvO}\_2\text{)}\tag{2}$$

$$\text{Qp} = \text{VO}\_2 \text{ / (CpvO}\_2\text{-CaO}\_2\text{)}\tag{23}$$

$$\text{SVR} \equiv \langle \text{MaP}-\text{MsvcpP} \rangle / \text{Qs} \tag{24}$$

Accurate Measurement of Systemic

in the modified Norwood procedure.

Oxygen Consumption in Ventilated Children with Congenital Heart Disease 307

systemic hemodynamics and oxygen transport. Use of actual values has significantly improved our understanding of the Norwood physiology and its postoperative management.

Previous studies used assumptions for VO2 of 160 or 180 mL/min/m2 to calculate hemodynamics (Charpie, Dekeon et al. 2001; Hoffman, Ghanayem et al. 2000; Maher, Pizarro et al. 2003; Tweddell, Hoffman et al. 1999)**.** Those values are much higher than the directly measured VO2 in our patients, which ranged from 45 to 152 mL/min/m2 (Figure 8).

Fig. 8. The changes in oxygen consumption (VO2), oxygen delivery (DO2) and oxygen extraction ration (ERO2) in neonates in the first 72 hours after the Norwood procedure.

Dotted lines indicate individual patients; solid line indicates the mean.

**5.1 Profiles of hemodynamics and oxygen transport after the Norwood procedure**  The Norwood physiology is an ideal model for understanding oxygen transport, since it is characterized by profound hemodynamic instability and oxygen transport imbalance (Li, Zhang et al. 2007). Wide, unstable, inter-individual and intra-individual variations in all the elements of hemodynamics and oxygen transport are observed, particularly on the systemic side (including systemic vascular resistant and blood flow). Pulmonary vascular resistance and blood flow are less variable, due to the mechanical limitation of the Blalock-Taussig shunt in the classic Norwood procedure or to the right ventricle to pulmonary artery shunt

**5.2 VO2 and its contribution to the balance of oxygen transport** 

'PVR' = (MaP – MpvP)/Qp (25)

(including the shunt)

$$\text{DO}\_2 = \text{Qs} \times \text{CaO}\_2 \tag{26}$$

Where CaO2, CvO2 and CpvO2 are systemic arterial, superior vena caval and pulmonary venous oxygen contents; MaP, MsvcP, and MpvP are mean systemic arterial, superior vena cava, and pulmonary venous pressures; 'PVR' is pulmonary vascular resistance including the shunt in the classic Norwood procedure (Li, Zhang et al. 2006; Li, Zhang et al. 2007). ERO2 is calculated as in the normal circulation (Equation 8).

In this Chapter, the Norwood circulation is used as the model to understand the balance of oxygen transport and the factors affecting it. This is an ideal model to understand the concept of oxygen transport, since the Norwood physiology is characterized by profound hemodynamic instability and oxygen transport imbalance, and represents the most challenging group of children for postoperative management after CPB. Data presented in this chapter were obtained in neonates after the classic Norwood procedure with the Blalock-Taussig shunt, but the basic physiology of the classic Norwood procedure is largely the same as the modified procedure with the right ventricle to pulmonary artery conduit, i.e., a single neonatal ventricle provides the parallel pulmonary and systemic circulations.

### **5. Improved understanding of the Norwood physiology and postoperative management using direct measurement of VO2**

The Norwood procedure for hypoplastic left heart syndrome, and similar anatomic variants, continues to have significant morbidity, and a mortality rate that ranges from 6% to 25% (Azakie, Merklinger et al. 2001; Gaynor, Mahle et al. 2002; Ohye, Sleeper et al. 2010; Sano, Huang et al. 2009). Despite advances in surgical and postoperative management, these infants have little hemodynamic reserve. Instability following repair is inherent in the neonatal single ventricle supplying parallel pulmonary and systemic circulations, and is compounded by the variable effects of CPB and ischemia and reperfusion injury. Our understanding of the Norwood physiology has been based on theoretical studies using computational models (Barnea, Austin et al. 1994; Migliavacca, Pennati et al. 2001), and on animal models (Kitaichi, Chikugo et al. 2003). Necessarily, these models do not reflect the true functionally single ventricular physiology. In previous studies in humans, arterial superior vena caval oxygen saturations, and their derivations were most commonly used as surrogates of DO2 (Charpie, Dekeon et al. 2001; Hoffman, Ghanayem et al. 2000; Maher, Pizarro et al. 2003; Tweddell, Hoffman et al. 1999). In some human studies, derived values of pulmonary and systemic blood flows have been obtained, but are based on the key assumption of a fixed VO2 of 160 or 180 mL/min/m2 (Charpie, Dekeon et al. 2001; Hoffman, Ghanayem et al. 2000; Maher, Pizarro et al. 2003; Tweddell, Hoffman et al. 1999). However, as demonstrated above in section 2.1.1 (Figure 2), postoperative VO2 has wide inter- and intra-patient variability in children (Li, Schulze-Neick et al. 2000; Li, Zhang et al. 2006; Li, Zhang et al. 2007; Li, Zhang et al. 2008). Thus, significant errors may be introduced in the calculation of hemodynamic and oxygen transport indices incorporating fixed values of VO2. The introduction of such errors has greatly limited our understanding of postoperative hemodynamics and oxygen transport in these patients.

The adaptation of the respiratory mass spectrometer (AMIS2000, Innovision A/S, Demark) to continuously measure VO2 allows the measurement of actual values for each element of

(including the shunt)

 DO2 = Qs × CaO2 (26) Where CaO2, CvO2 and CpvO2 are systemic arterial, superior vena caval and pulmonary venous oxygen contents; MaP, MsvcP, and MpvP are mean systemic arterial, superior vena cava, and pulmonary venous pressures; 'PVR' is pulmonary vascular resistance including the shunt in the classic Norwood procedure (Li, Zhang et al. 2006; Li, Zhang et al. 2007).

In this Chapter, the Norwood circulation is used as the model to understand the balance of oxygen transport and the factors affecting it. This is an ideal model to understand the concept of oxygen transport, since the Norwood physiology is characterized by profound hemodynamic instability and oxygen transport imbalance, and represents the most challenging group of children for postoperative management after CPB. Data presented in this chapter were obtained in neonates after the classic Norwood procedure with the Blalock-Taussig shunt, but the basic physiology of the classic Norwood procedure is largely the same as the modified procedure with the right ventricle to pulmonary artery conduit, i.e., a single neonatal ventricle provides the parallel pulmonary and systemic circulations.

**5. Improved understanding of the Norwood physiology and postoperative** 

The Norwood procedure for hypoplastic left heart syndrome, and similar anatomic variants, continues to have significant morbidity, and a mortality rate that ranges from 6% to 25% (Azakie, Merklinger et al. 2001; Gaynor, Mahle et al. 2002; Ohye, Sleeper et al. 2010; Sano, Huang et al. 2009). Despite advances in surgical and postoperative management, these infants have little hemodynamic reserve. Instability following repair is inherent in the neonatal single ventricle supplying parallel pulmonary and systemic circulations, and is compounded by the variable effects of CPB and ischemia and reperfusion injury. Our understanding of the Norwood physiology has been based on theoretical studies using computational models (Barnea, Austin et al. 1994; Migliavacca, Pennati et al. 2001), and on animal models (Kitaichi, Chikugo et al. 2003). Necessarily, these models do not reflect the true functionally single ventricular physiology. In previous studies in humans, arterial superior vena caval oxygen saturations, and their derivations were most commonly used as surrogates of DO2 (Charpie, Dekeon et al. 2001; Hoffman, Ghanayem et al. 2000; Maher, Pizarro et al. 2003; Tweddell, Hoffman et al. 1999). In some human studies, derived values of pulmonary and systemic blood flows have been obtained, but are based on the key assumption of a fixed VO2 of 160 or 180 mL/min/m2 (Charpie, Dekeon et al. 2001; Hoffman, Ghanayem et al. 2000; Maher, Pizarro et al. 2003; Tweddell, Hoffman et al. 1999). However, as demonstrated above in section 2.1.1 (Figure 2), postoperative VO2 has wide inter- and intra-patient variability in children (Li, Schulze-Neick et al. 2000; Li, Zhang et al. 2006; Li, Zhang et al. 2007; Li, Zhang et al. 2008). Thus, significant errors may be introduced in the calculation of hemodynamic and oxygen transport indices incorporating fixed values of VO2. The introduction of such errors has greatly limited our understanding of postoperative

The adaptation of the respiratory mass spectrometer (AMIS2000, Innovision A/S, Demark) to continuously measure VO2 allows the measurement of actual values for each element of

ERO2 is calculated as in the normal circulation (Equation 8).

**management using direct measurement of VO2** 

hemodynamics and oxygen transport in these patients.

'PVR' = (MaP – MpvP)/Qp (25)

systemic hemodynamics and oxygen transport. Use of actual values has significantly improved our understanding of the Norwood physiology and its postoperative management.

#### **5.1 Profiles of hemodynamics and oxygen transport after the Norwood procedure**

The Norwood physiology is an ideal model for understanding oxygen transport, since it is characterized by profound hemodynamic instability and oxygen transport imbalance (Li, Zhang et al. 2007). Wide, unstable, inter-individual and intra-individual variations in all the elements of hemodynamics and oxygen transport are observed, particularly on the systemic side (including systemic vascular resistant and blood flow). Pulmonary vascular resistance and blood flow are less variable, due to the mechanical limitation of the Blalock-Taussig shunt in the classic Norwood procedure or to the right ventricle to pulmonary artery shunt in the modified Norwood procedure.
