The Effect of Natural and Surgically Constructed Aortopulmonary Shunts on Hernodynamic Function in Tetralogy of Fallot A. Thomas Look, Jr., M.D., and Thomas R. Bates, Jr., Ph.D. ABSTRACT A hernodynamic model has been developed for the patient with tetralogy of Fallot. Equations representing the circulatory flow pattern and oxygen balance in this disease were incorporated into a computer program. With the computer model it is possible to simulate the effect of natural and surgically constructed aortopulmonary shunt flow on hemodynamic function in tetralogy of Fallot. Graphic representationsof the computer output are presented which show how aortopulmonary shunt flow influences the physiology of exercise and hypoxic episodes. An explanation is advanced for the lack of correlation between resting arterial oxygen saturation and the incidence of hypoxic episodes. The model demonstrates the effect of surgical aortopulmonary shunts in eliminating hypoxic spells.
K
irklin and Karp [9] pointed out in their monograph that it is worthwhile to limit the morphological definition of tetralogy of Fallot to those patients with a large ventricular septa1 defect “approximating the size of the aortic valvular orifice” and pulmonary stenosis severe enough to cause right-to-left shunting. A key compensatory response that occurs in patients with this syndrome is an increase in aortopulmonary (A-P) collateral circulation. This A-P shunt flow is described as consisting of both an enlargement of the normal precapillary anastomoses and the presence of small or medium-sized vessels joining the aorta to large branches of the pulmonary arteries. Collateral flow has been measured directly for patients with tetralogy of Fallot during complete cardiopulmonary bypass operations. Moffitt, Kirklin, and Theye [ 113 reported an average A-P shunt flow of 22% of the total cardiac output; Kirklin and Karp [9] found a range of 5 to 40%. Aortopulmonary shunt flow rates in the same range were also determined by indirect physiological studies in earlier work by Bing and associates [ 11. The Blalock-Taussig and Potts-Gibson-Smith procedures for palliation of patients with tetralogy of Fallot are surgical extensions of the natural compensa-
From the University of Michigan Medical School and the Department of Mechanical Engineering, the University of Michigan, Ann Arbor, Mich. Supported in part by the Departments of Mechanical Engineering and Pediatrics, University of Michigan, and by the University of Michigan Medical School. Accepted for publication Apr. 23, 1975. Address reprint requests to Dr. Look, Department of Pediatrics, F-2230 Mott Hospital, Ann Arbor, Mich. 48104. VOL. 20, NO. 5, NOVEMBER, 1975
571
LOOK AND BATES tory response. Artificially constructed shunts increase systemic-to-pulmonary flow beyond the capacity of enlarged bronchopulmonary anastomoses. Thus, the abnormal circulatory pattern in tetralogy of Fallot contains two types of shunts between the systemic and pulmonary circulations: the inherent right-to-left intracardiac shunt across the ventricular septa1 defect and the systemic-to-pulmonary A-P shunts of natural or surgical origin. Because of these shunts, it is impossible to quantify the systemic and pulmonary blood flow rates in tetralogy of Fallot based on classic cardiac catheterization data and the Fick principle [ 11. In this paper a computer model is described that simulates the hemodynamic system in tetralogy of Fallot. With the computer simulation it is possible to show the effect of flow through an A-P shunt, whether natural or surgically constructed, on the physiological capabilities of a patient with tetralogy of Fallot. Level of cyanosis, exercise tolerance, and susceptibility to hypoxic crises are examined as functions of A-P shunt flow rate both before and after palliative operation.
Description
of the Model
A schematic diagram outlining the hemodynamic system in tetralogy of Fallot is presented in Figure 1. A series of simultaneous equations have been derived relating blood flow rates, hemodynamic resistances, and pressure drops for tetralogy of Fallot. Oxygen balance equations have been written to relate the systemic and pulmonary percent hemoglobin saturation with total oxygen consumption. The equations describing flow rates and oxygen saturations have been incorporated into a computer program written in Fortran IV and loaded into a Fortran G compiler [3]. This computer simulation of a patient with tetralogy of Fallot permits individual variables to be manipulated to simulate the physiological phenomena characteristic of the disease.*
Results BASELINE MODEL PARAMETERS
In order to use the computer model derived for tetralogy of Fallot, it is necessary to include baseline model parameters. For this analysis, a cardiac catheterization data set for a typical child with tetralogy of Fallot is taken from Kirklin and Karp [91 (Table 1). The fraction of the cardiac output that returns to the pulmonary circuit through the hypertrophied aortopulmonary collaterals (the A-P shunt fraction) is the one patient-specific variable that cannot be extracted from cardiac catheterization studies. For this analysis the hypothetical patient is modeled at 5,22, and 40% natural A-P shunt fractions. These values represent the mean, high, and low values determined by Moffitt and colleagues [ l l ] and Kirklin and Karp [9] as previously described. *A detailed analysis with equations and computer printout is available from the authors on request.
572
T H E ANNALS OF THORACIC SURGERY
Haodynamic Model fn-Tetralogy .fFallot
PULMONARY VASCULAR /SYSTEM
PULMONARY VALVE AND INFUNDIBULUM VENTRICULAR SEPTAL DEFECT
VASCULAR SYSTEM
FIG. 1 . Hmodynamic system in tetralogy of Fallot. PARTIAL FACTORIAL ANALYSIS BASED O N T H E COMPUTER MODEL
The hemodynamic model variables are divided into dependent and independent variables. The dependent variables for this analysis are blood flow rates and blood oxygen saturations, the variables generated by computer simulation of the physiological phenomena in tetralogy of Fallot. The independent variables are the A-P shunt fraction, pressure drops across the right and left heart, hemodynamic resistances, and oxygen consumption. Variations in the key independent variables are specified in the computer program in order to simulate the physiology of exercise and hypoxic crises. For this analysisthe variables that are changed from the resting state in order to reproduce this physiological state are A-P shunt fraction, oxygen consumption, total peripheral systemic resistance, and resistance across the stenosed pulmonary valve. The other independent variables remain essentially constant for the computer simulations, based on the available physiological data [2, 6, 8, 9, 141. T H E PALLIATIVE SYSTEMIC-TO-PULMONARY S H U N T OPERATION MODEL
In order to model the revised circulatory pattern that accompaniesa palliative operation, the following changes are made in the baseline parameters for our hypothetical patient: A-P shunt fraction is increased to 75%; pulmonary artery VOL. 20, NO. 5, NOVEMBER, 1975
5 73
LOOK AND BATES TABLE 1. DATA FROM CARDIAC CATHETERIZATION OF A “PATIENT” WITH TETRALOGY OF FALLOT
Catheter Position
svc
IVC RA RV sinus Infundibulum PA LA LV Aorta
O2 Levels (% sat) 54 66 61 67 70
6
10210
5015
.. . 95 87 81
20110
6
-
102162
0, capacity = 18.02 voVl00 ml O2consumption 158 cdmin SVC = superior vena cava; IVC = inferior vena cava; RA = right atrium; RV = right ventricle; PA = pulmonary artery; LA = left atrium; LV. = left ventricle. Reproduced with permission from Kirklin and Karp, Tetralogy OfFallot, p 62 [91.
pressure is raised to 30 mm Hg; and arterial, mixed venous, and pulmonary infundibular oxygen saturations are increased to 91,71, and 84.6%,respectively. These data are based on a study of 24 patients by Crawford and associates [41 after palliative shunting operations. GRAPHIC REPRESENTATION OF THE COMPUTER SJMULATION
The computer simulation of exercise qnd hypoxic crisis in tetralogy of Fallot accurately reproduces the known effects oq arterial oxygen saturation before and after palliative operation. In addition, it is possible using partial factorial analysis to demonstrate the individual effect of each key independent variable. Graphic representations of the computer output show the partial effects of individual variables for exercise and hypoxic crisis (see Figs. 2-6).
Comment EXERCISE
The individual with tetralogy of Fallot has a tendency toward decreased arterial oxygen saturation with exercise as well as a diminished overall ability to increase his oxygen consumption. These effects are the result of normal physiological responses to exercise combined with the abnormal anatomical relationships in tetralogy of Fallot. Through partial factorial analysis based on the computer patient model, it is possible to deaonstrate how these deleterious effects occur. The key blood flow rates predicted by the computer for the patient model with a natural A-P shunt flow of 22%are illustrated in Figure 2. The flow rates for the patient model during exercise correspond to the values for decreasing systemic resistance. This analysis is based on the fact that the most important cause of increased cardiac output with exercise is direct vasodilation of vessels supplying 574
THE ANNALS OF THORACIC SURGERY
Hemodynamic Model fm Tetralogy
I
FIG. 2 . Distribution .f cardiac output with exercisefor patient model with 22 76 natural A P J,h..,t Kin*., I ~ U I ' I J YVLU.
I L I
I
.2
I
.4
1
.6
of Fallot
1
.%
0
RE iTING Ll VEL
2
SYSTEMIC RESISTANCE
(in multides of the restinq level)
metabolically active muscle tissue. Figure 2 illustrates that with increasing exercise, blood flow through the peripheral system and ventricular septa1 defect increases markedly. In contrast, flow through the lungs remains relatively constant. Therefore, decreasing the systemic resistance causes a selective increase in blood supply to the tissues without the corresponding normal increase in flow through the pulmonary circuit. Oxygen consumption increases during exercise due to the increased metabolic rate of active muscle tissue. Figure 3 shows arterial oxygen saturation for the patient model with a 22% natural A-P shunt flow at levels of exercise determined by increased oxygen consumption and decreased systemic resistance. The solid curves for constant oxygen consumption represent the physiological range of arterial oxygen saturation, and the dashed lines indicate the range where the corresponding mixed venous saturation is below equilibrium [S]. Based on point B in Figure 3, it is apparent that the patient model is able to achieve increased oxygen consumptiqn with decreased systemic resistance. This is because the systemic flow increases as systemic resistance decreases (see Fig. 2), which allows greater oxygen transpdrt. The most important point illustrated by Figure 3 is the significant decrease in arterial oxygen saturation that occurs when the patient with tetralogy of Fallot increases his oxygen consumption and decreases his systemic resistance during exercise. The physiological limit of increased oxygen consumption with exercise predicted by the computer simulation is approximately three times resting oxygen consumption at a corresponding arterial oxygen saturation of 45% (see VOL. 20, NO. 5, NOVEMBER, 1975
575
LOOK AND BATES
2x
OXYGEN
C_O_NMPTION 4x
I
I
.2
EXERCISE I
.4
I
.6
I
.8
I
1.0
RESTING LEVEL
I
1.2
SYSTEMIC RESISTANCE (in multiples of the resting level)
FIG. 3 . Variation in arterial oxygen saturation with exercise,22 96 natural A-P shuntflow.
point B in Fig. 3). This result predicted by the model correlates well with published cardiac catheterization data for patients with tetralogy of Fallot during exercise [ l , 4, 5, 121. HYPOXIC EPISODES
The clinical phenomenon of hypoxic episodes in patients with tetralogy of Fallot was well described by Morgan and associates [ 131 based on a retrospective study of 190 patients. Thirty-eight percent of the patients with tetralogy had well-documented histories of hypoxic episodes “characterized by paroxysmal hyperpnea and increased cyanosis.” The spells were found to occur most often in the morning, associated with activities such as feeding, bowel movements, and crying. The spells generally did not appear to occur after severe exercise. They were found to last “from less than a minute to several hours, with a majority lasting 15 to 60 minutes” [ 131. In general, patients recover from the episode, but increasing cyanosis can occur in spite of the greater respiratory effort. The patient then develops dulling of the senses, progressing to unconsciousness, convulsions, and sometimes death. Apparently the susceptibility of an individual patient to hypoxic spells does not correlate well with the severity of disease as indicated by resting arterial oxygen saturation. Morgan and co-workers [ 131 concluded: “The most surprising finding was the lack of correlation of hyperpneic spells with resting arterial desaturation, although all arterial saturations obtained during attacks were quite low. Two patients with observed, typical paroxysms had arterial saturations under
576
THE ANNALS OF THORACIC SURGERY
Hemodynamic Model fm Tetralogy of Fallot
sedation of 93 and 98 percent, in contrast to a patient with a 44 percent saturation who had no spells.” Physiological data available from cardiac catheterization studies during hypoxic crises further define this condition. Morgan and co-workers [13] reported arterial oxygen saturations of 15, 24, and 33% in patients tested during hypoxic spells. Wood [ 141 found an average arterial oxygen saturation of 20% in 5 patients with hypoxic crises studied during cardiac catheterization. In the same study Wood found that systemic blood pressure remains unchanged during the attacks. Hyperventilation is known to decrease systemic resistance by about 20% in normal individuals [6]. The application of this decrease to patients with tetralogy of Fallot is supported by Wood’s observation that heart rate increases at constant blood pressure during hypoxic crises. The computer model of tetralogy of Fallot provides a means to investigate the mechanism of hypoxic episodes. Wide ranges of systemic, A-P shunt, and pulmonary valve resistance have been investigated through computer simulation in an attempt to duplicate the physiological variables during hypoxic crises. The results of the analysis support the hypothesis first advanced by Wood [ 141 that hypoxic crises are caused by a sudden increase in resistance in the outflow tract of the right ventricle. An increase in resistance across the pulmonary valve is the only factor that reproduces the physiological conditions of hypoxic crisis in the computer simulation. The left panel in Figure 4 illustrates the effect of increasing the resistance across the pulmonary valve for the patient model with a 5% natural A-P shunt flow. Based on hemodynamic conditions during hyperventilation described ear’
.
!
PULMONARY INFUNDIBULAR SPASM
1
PULMONARY INFUNDIBULAR SPA%
j I
A. Oxygen Consumption=.5x
. i
i
B. Oxygen Consumption = I x
[
C. Oxygen Consumption = 2 x
/
(the resting level)
PULMONARY INFUNDIBULAR SPASM
PULMONARY VALVE RESISTANCE (in multiples of the resting level) FIG. 4 . Variation in arterial oxygen saturation with increased pulmonary valve resistance at (left) 5%, (middle)22%, and (right)40% natural A-P shuntflow.
VOL. 20, NO. 5, NOVEMBER, 1975
577
LOOK AND BATES 90 -
-8
-
z
9
A.
3
B. OXYGEN CONSUMPTION= 2x
ta
4
E YX
50-
C.
OXYGEN CONSUMPTION= In (RESTING LEVEL)
OXYGEN CONSUMPTlON = 3 x
D. OXYGEN
CONSUMPTION= 4 x
0 -I
9 a W
k U
.+
10 -
-
.2
EXERCISE
.4
.6
.8
1.0
RESTING LEVEL
1.2
SYSTEMIC RESISTANCE (in multiples of the resting level)
FIG. 5. Variation in arterial oxwen saturation with exercisefollowingpalliat& A-P shunt operation.
lier, systemic blood pressure is held constant at resting values and systemic resistance is reduced 20% for this analysis. This portion of Figure 4 clearly demonstrates that the arterial oxygen saturations of approximately 20% observed during hypoxic crises are caused by increased resistance of the pulmonary valve. It is also evident that increased pulmonary resistance limits oxygen consumption to less than resting capacity. This is due to the marked decrease in blood flow through the lungs. The limitation of oxygen consumption by circulatory flow rates points out the ineffectiveness of hyperventilation during hypoxic crises. In fact, the mechanical work of hyperventilation has been shown to increase oxygen demand above resting levels [ 101. Therefore, the response of hyperventilation to the anoxia in hypoxic crisis adversely affects the patient’s overall oxygen balance. Unless the pulmonary outflow resistance is reduced naturally or with drugs, arterial oxygen saturation decreases until vital centers are compromised. The middle and right panels of Figure 4 show the effect of increasing pulmonary valve resistance for the patient model with 22 and 40% natural A-P shunt flows, respectively. In these instances a sudden increase in pulmonary valve resistance does not induce the low arterial oxygen saturations found in hypoxic crisis. In other words, for patients with identical resting oxygen saturations, the patient with a relatively large pulmonary infundibulum and small natural A-P
578
T H E ANNALS OF THORACIC SURGERY
Hemodynamic Model fw Tetralogy of Fallot
A.
lot
1 I
FIG. 6 . Variation in arterial oxygen saturation with increased pulmonary ualue resistancefollowingpalliatiue A-P shunt operation.
OXYGEN CONSUMPTION = I x (RESTING LEVEL)
B. OXYGEN
CONSUMPTION = 2 x
C. OXYGEN
CONSUMPTION=3x
PULMONARY INFUNDIBULAR SPA&
RESTING LEVEL
5
10
PULMONARY VALVE RESISTANCE (in multiples of the resting level)
shunt flow (Fig. 4, left panel) would be susceptible to hypoxic crises, while the patient with more severe infundibular restriction and larger shunt flow would not (Fig. 4, right panel). EFFECT OF PALLIATIVE OPERATIONS
Based on data from Crawford and associates [4] it is possible to create a computer model of the hypothetical patient after he has received a surgical systemic-to-pulmonary artery shunt. The baseline determinations for the patient with a 5% shunt are used since this patient is the most prone to hypoxic crises. Figures 5 and 6 show the effects of decreased systemic resistance and increased pulmonary outflow tract resistance forthe patient model after a palliative operation. Figure 5 shows that the patient has significantly increased exercise tolerance following the operation. The graphs predict that he will still have a significant fall in arterial oxygen saturation at maximum oxygen consumption. The magnitudes of both oxygen consumption and arterial oxygen saturation predicted in Figure 6 from the computer simulation correlate well with data from studies of patients after shunting procedures [4].Figure 6 shows that after surgical palliation the patient is no longer susceptible to hypoxic episodes caused by increased resistance across the pulmonary outflow tract. This graph corresponds to the patient with the worst prognosis in the preceding section, as shown in the left panel of Figure 4.
VOL. 20, NO. 5, NOVEMBER, 1975
579
LOOK AND BATES
References 1. Bing, R. J., Vandam, L. D., and Bray, F. D., Jr. Physiological studies in congenital heart disease. Bull Johns Hopkins Hosp 80:107, 1947. 2. Brotmacher, L. Haemodynamic effects of squatting during repose and haemodynamic effects of squatting during recovery from exertion. Br HeartJ 19:567, 1957. 3. Carnahan, B., and Wilkes, J. 0. Digital Computing, Fortran IV, Wa@v, and MTS. Ann Arbor: University of Michigan Press, 1973. 4. Crawford, D. W., Simpson, E., and McIlroy, M. B. Cardiopulmonary function in Fallot’s tetralogy after palliative shunting operations. Am Heart J 74:463, 1967. 5 . Davison, P. H., Armitage, G. H., and Arnott, W. M. The mechanisms of adaptation to a central venous-arterial shunt. Br Heart J 15:2 1, 1953. 6. Guntheroth, W. G., Morgan, B. C., and Mullins, G. L. Physiologic studies of paroxysmal hyperpnea in cyanotic congenital heart disease. Circulation 3 1 :70, 1965. 7. Guntheroth, W. G., Morgan, B. C., Mullins, G. L., and Baum, D. Venous return with knee-chest position and squatting in tetralogy of Fallot. Am Heart J 75:313, 1968. 8. Guyton, A. C. Textbook ofMedical Physiology (4th ed). Philadelphia: Saunders, 1971. 9. Kirklin, J. W., and Karp, R. B. The Tetralogy ofFallot, From a Surgical Viewpoint. Philadelphia: Saunders, 1970. 10. McKerrow, C. B., and Otis, A. B. Oxygen cost of hyperventilation. Trans Assoc Am Phys 67:375, 1954. 1 1 . Moffitt, E. A., Kirklin,J. W., and Theye, R. A. Physiologic studiesduringwhole-body perfusion in tetralogy of Fallot.J Thorac Cardiovasc Surg 44:180, 1962. 12. Montgomery, G. E., Jr., Geraci, J. E., Parker, R. L., and Wood, E. H. The arterial oxygen saturation in cyanotic types of congenital heart disease.Circulation 3 1 :66,1965. 13. Morgan, B. C., Guntheroth, W. G., Bloom, R. S., and Fyler, D. C. A clinical profile of paroxysmal hyperpnea in cyanotic congenital heart disease. Circulation 3 1 :66, 1965. 14. Wood, P. Symposium on congenital heart disease: Attacks of deeper cyanosis and loss of cons$ousness (syncope) in Fallot’s tetralogy. Br Heart J 20:282, 1959.
580
THE ANNALS OF THORACIC SURGERY
K
irklin and Karp [9] pointed out in their monograph that it is worthwhile to limit the morphological definition of tetralogy of Fallot to those patients with a large ventricular septa1 defect “approximating the size of the aortic valvular orifice” and pulmonary stenosis severe enough to cause right-to-left shunting. A key compensatory response that occurs in patients with this syndrome is an increase in aortopulmonary (A-P) collateral circulation. This A-P shunt flow is described as consisting of both an enlargement of the normal precapillary anastomoses and the presence of small or medium-sized vessels joining the aorta to large branches of the pulmonary arteries. Collateral flow has been measured directly for patients with tetralogy of Fallot during complete cardiopulmonary bypass operations. Moffitt, Kirklin, and Theye [ 113 reported an average A-P shunt flow of 22% of the total cardiac output; Kirklin and Karp [9] found a range of 5 to 40%. Aortopulmonary shunt flow rates in the same range were also determined by indirect physiological studies in earlier work by Bing and associates [ 11. The Blalock-Taussig and Potts-Gibson-Smith procedures for palliation of patients with tetralogy of Fallot are surgical extensions of the natural compensa-
From the University of Michigan Medical School and the Department of Mechanical Engineering, the University of Michigan, Ann Arbor, Mich. Supported in part by the Departments of Mechanical Engineering and Pediatrics, University of Michigan, and by the University of Michigan Medical School. Accepted for publication Apr. 23, 1975. Address reprint requests to Dr. Look, Department of Pediatrics, F-2230 Mott Hospital, Ann Arbor, Mich. 48104. VOL. 20, NO. 5, NOVEMBER, 1975
571
LOOK AND BATES tory response. Artificially constructed shunts increase systemic-to-pulmonary flow beyond the capacity of enlarged bronchopulmonary anastomoses. Thus, the abnormal circulatory pattern in tetralogy of Fallot contains two types of shunts between the systemic and pulmonary circulations: the inherent right-to-left intracardiac shunt across the ventricular septa1 defect and the systemic-to-pulmonary A-P shunts of natural or surgical origin. Because of these shunts, it is impossible to quantify the systemic and pulmonary blood flow rates in tetralogy of Fallot based on classic cardiac catheterization data and the Fick principle [ 11. In this paper a computer model is described that simulates the hemodynamic system in tetralogy of Fallot. With the computer simulation it is possible to show the effect of flow through an A-P shunt, whether natural or surgically constructed, on the physiological capabilities of a patient with tetralogy of Fallot. Level of cyanosis, exercise tolerance, and susceptibility to hypoxic crises are examined as functions of A-P shunt flow rate both before and after palliative operation.
Description
of the Model
A schematic diagram outlining the hemodynamic system in tetralogy of Fallot is presented in Figure 1. A series of simultaneous equations have been derived relating blood flow rates, hemodynamic resistances, and pressure drops for tetralogy of Fallot. Oxygen balance equations have been written to relate the systemic and pulmonary percent hemoglobin saturation with total oxygen consumption. The equations describing flow rates and oxygen saturations have been incorporated into a computer program written in Fortran IV and loaded into a Fortran G compiler [3]. This computer simulation of a patient with tetralogy of Fallot permits individual variables to be manipulated to simulate the physiological phenomena characteristic of the disease.*
Results BASELINE MODEL PARAMETERS
In order to use the computer model derived for tetralogy of Fallot, it is necessary to include baseline model parameters. For this analysis, a cardiac catheterization data set for a typical child with tetralogy of Fallot is taken from Kirklin and Karp [91 (Table 1). The fraction of the cardiac output that returns to the pulmonary circuit through the hypertrophied aortopulmonary collaterals (the A-P shunt fraction) is the one patient-specific variable that cannot be extracted from cardiac catheterization studies. For this analysis the hypothetical patient is modeled at 5,22, and 40% natural A-P shunt fractions. These values represent the mean, high, and low values determined by Moffitt and colleagues [ l l ] and Kirklin and Karp [9] as previously described. *A detailed analysis with equations and computer printout is available from the authors on request.
572
T H E ANNALS OF THORACIC SURGERY
Haodynamic Model fn-Tetralogy .fFallot
PULMONARY VASCULAR /SYSTEM
PULMONARY VALVE AND INFUNDIBULUM VENTRICULAR SEPTAL DEFECT
VASCULAR SYSTEM
FIG. 1 . Hmodynamic system in tetralogy of Fallot. PARTIAL FACTORIAL ANALYSIS BASED O N T H E COMPUTER MODEL
The hemodynamic model variables are divided into dependent and independent variables. The dependent variables for this analysis are blood flow rates and blood oxygen saturations, the variables generated by computer simulation of the physiological phenomena in tetralogy of Fallot. The independent variables are the A-P shunt fraction, pressure drops across the right and left heart, hemodynamic resistances, and oxygen consumption. Variations in the key independent variables are specified in the computer program in order to simulate the physiology of exercise and hypoxic crises. For this analysisthe variables that are changed from the resting state in order to reproduce this physiological state are A-P shunt fraction, oxygen consumption, total peripheral systemic resistance, and resistance across the stenosed pulmonary valve. The other independent variables remain essentially constant for the computer simulations, based on the available physiological data [2, 6, 8, 9, 141. T H E PALLIATIVE SYSTEMIC-TO-PULMONARY S H U N T OPERATION MODEL
In order to model the revised circulatory pattern that accompaniesa palliative operation, the following changes are made in the baseline parameters for our hypothetical patient: A-P shunt fraction is increased to 75%; pulmonary artery VOL. 20, NO. 5, NOVEMBER, 1975
5 73
LOOK AND BATES TABLE 1. DATA FROM CARDIAC CATHETERIZATION OF A “PATIENT” WITH TETRALOGY OF FALLOT
Catheter Position
svc
IVC RA RV sinus Infundibulum PA LA LV Aorta
O2 Levels (% sat) 54 66 61 67 70
6
10210
5015
.. . 95 87 81
20110
6
-
102162
0, capacity = 18.02 voVl00 ml O2consumption 158 cdmin SVC = superior vena cava; IVC = inferior vena cava; RA = right atrium; RV = right ventricle; PA = pulmonary artery; LA = left atrium; LV. = left ventricle. Reproduced with permission from Kirklin and Karp, Tetralogy OfFallot, p 62 [91.
pressure is raised to 30 mm Hg; and arterial, mixed venous, and pulmonary infundibular oxygen saturations are increased to 91,71, and 84.6%,respectively. These data are based on a study of 24 patients by Crawford and associates [41 after palliative shunting operations. GRAPHIC REPRESENTATION OF THE COMPUTER SJMULATION
The computer simulation of exercise qnd hypoxic crisis in tetralogy of Fallot accurately reproduces the known effects oq arterial oxygen saturation before and after palliative operation. In addition, it is possible using partial factorial analysis to demonstrate the individual effect of each key independent variable. Graphic representations of the computer output show the partial effects of individual variables for exercise and hypoxic crisis (see Figs. 2-6).
Comment EXERCISE
The individual with tetralogy of Fallot has a tendency toward decreased arterial oxygen saturation with exercise as well as a diminished overall ability to increase his oxygen consumption. These effects are the result of normal physiological responses to exercise combined with the abnormal anatomical relationships in tetralogy of Fallot. Through partial factorial analysis based on the computer patient model, it is possible to deaonstrate how these deleterious effects occur. The key blood flow rates predicted by the computer for the patient model with a natural A-P shunt flow of 22%are illustrated in Figure 2. The flow rates for the patient model during exercise correspond to the values for decreasing systemic resistance. This analysis is based on the fact that the most important cause of increased cardiac output with exercise is direct vasodilation of vessels supplying 574
THE ANNALS OF THORACIC SURGERY
Hemodynamic Model fm Tetralogy
I
FIG. 2 . Distribution .f cardiac output with exercisefor patient model with 22 76 natural A P J,h..,t Kin*., I ~ U I ' I J YVLU.
I L I
I
.2
I
.4
1
.6
of Fallot
1
.%
0
RE iTING Ll VEL
2
SYSTEMIC RESISTANCE
(in multides of the restinq level)
metabolically active muscle tissue. Figure 2 illustrates that with increasing exercise, blood flow through the peripheral system and ventricular septa1 defect increases markedly. In contrast, flow through the lungs remains relatively constant. Therefore, decreasing the systemic resistance causes a selective increase in blood supply to the tissues without the corresponding normal increase in flow through the pulmonary circuit. Oxygen consumption increases during exercise due to the increased metabolic rate of active muscle tissue. Figure 3 shows arterial oxygen saturation for the patient model with a 22% natural A-P shunt flow at levels of exercise determined by increased oxygen consumption and decreased systemic resistance. The solid curves for constant oxygen consumption represent the physiological range of arterial oxygen saturation, and the dashed lines indicate the range where the corresponding mixed venous saturation is below equilibrium [S]. Based on point B in Figure 3, it is apparent that the patient model is able to achieve increased oxygen consumptiqn with decreased systemic resistance. This is because the systemic flow increases as systemic resistance decreases (see Fig. 2), which allows greater oxygen transpdrt. The most important point illustrated by Figure 3 is the significant decrease in arterial oxygen saturation that occurs when the patient with tetralogy of Fallot increases his oxygen consumption and decreases his systemic resistance during exercise. The physiological limit of increased oxygen consumption with exercise predicted by the computer simulation is approximately three times resting oxygen consumption at a corresponding arterial oxygen saturation of 45% (see VOL. 20, NO. 5, NOVEMBER, 1975
575
LOOK AND BATES
2x
OXYGEN
C_O_NMPTION 4x
I
I
.2
EXERCISE I
.4
I
.6
I
.8
I
1.0
RESTING LEVEL
I
1.2
SYSTEMIC RESISTANCE (in multiples of the resting level)
FIG. 3 . Variation in arterial oxygen saturation with exercise,22 96 natural A-P shuntflow.
point B in Fig. 3). This result predicted by the model correlates well with published cardiac catheterization data for patients with tetralogy of Fallot during exercise [ l , 4, 5, 121. HYPOXIC EPISODES
The clinical phenomenon of hypoxic episodes in patients with tetralogy of Fallot was well described by Morgan and associates [ 131 based on a retrospective study of 190 patients. Thirty-eight percent of the patients with tetralogy had well-documented histories of hypoxic episodes “characterized by paroxysmal hyperpnea and increased cyanosis.” The spells were found to occur most often in the morning, associated with activities such as feeding, bowel movements, and crying. The spells generally did not appear to occur after severe exercise. They were found to last “from less than a minute to several hours, with a majority lasting 15 to 60 minutes” [ 131. In general, patients recover from the episode, but increasing cyanosis can occur in spite of the greater respiratory effort. The patient then develops dulling of the senses, progressing to unconsciousness, convulsions, and sometimes death. Apparently the susceptibility of an individual patient to hypoxic spells does not correlate well with the severity of disease as indicated by resting arterial oxygen saturation. Morgan and co-workers [ 131 concluded: “The most surprising finding was the lack of correlation of hyperpneic spells with resting arterial desaturation, although all arterial saturations obtained during attacks were quite low. Two patients with observed, typical paroxysms had arterial saturations under
576
THE ANNALS OF THORACIC SURGERY
Hemodynamic Model fm Tetralogy of Fallot
sedation of 93 and 98 percent, in contrast to a patient with a 44 percent saturation who had no spells.” Physiological data available from cardiac catheterization studies during hypoxic crises further define this condition. Morgan and co-workers [13] reported arterial oxygen saturations of 15, 24, and 33% in patients tested during hypoxic spells. Wood [ 141 found an average arterial oxygen saturation of 20% in 5 patients with hypoxic crises studied during cardiac catheterization. In the same study Wood found that systemic blood pressure remains unchanged during the attacks. Hyperventilation is known to decrease systemic resistance by about 20% in normal individuals [6]. The application of this decrease to patients with tetralogy of Fallot is supported by Wood’s observation that heart rate increases at constant blood pressure during hypoxic crises. The computer model of tetralogy of Fallot provides a means to investigate the mechanism of hypoxic episodes. Wide ranges of systemic, A-P shunt, and pulmonary valve resistance have been investigated through computer simulation in an attempt to duplicate the physiological variables during hypoxic crises. The results of the analysis support the hypothesis first advanced by Wood [ 141 that hypoxic crises are caused by a sudden increase in resistance in the outflow tract of the right ventricle. An increase in resistance across the pulmonary valve is the only factor that reproduces the physiological conditions of hypoxic crisis in the computer simulation. The left panel in Figure 4 illustrates the effect of increasing the resistance across the pulmonary valve for the patient model with a 5% natural A-P shunt flow. Based on hemodynamic conditions during hyperventilation described ear’
.
!
PULMONARY INFUNDIBULAR SPASM
1
PULMONARY INFUNDIBULAR SPA%
j I
A. Oxygen Consumption=.5x
. i
i
B. Oxygen Consumption = I x
[
C. Oxygen Consumption = 2 x
/
(the resting level)
PULMONARY INFUNDIBULAR SPASM
PULMONARY VALVE RESISTANCE (in multiples of the resting level) FIG. 4 . Variation in arterial oxygen saturation with increased pulmonary valve resistance at (left) 5%, (middle)22%, and (right)40% natural A-P shuntflow.
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LOOK AND BATES 90 -
-8
-
z
9
A.
3
B. OXYGEN CONSUMPTION= 2x
ta
4
E YX
50-
C.
OXYGEN CONSUMPTION= In (RESTING LEVEL)
OXYGEN CONSUMPTlON = 3 x
D. OXYGEN
CONSUMPTION= 4 x
0 -I
9 a W
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.+
10 -
-
.2
EXERCISE
.4
.6
.8
1.0
RESTING LEVEL
1.2
SYSTEMIC RESISTANCE (in multiples of the resting level)
FIG. 5. Variation in arterial oxwen saturation with exercisefollowingpalliat& A-P shunt operation.
lier, systemic blood pressure is held constant at resting values and systemic resistance is reduced 20% for this analysis. This portion of Figure 4 clearly demonstrates that the arterial oxygen saturations of approximately 20% observed during hypoxic crises are caused by increased resistance of the pulmonary valve. It is also evident that increased pulmonary resistance limits oxygen consumption to less than resting capacity. This is due to the marked decrease in blood flow through the lungs. The limitation of oxygen consumption by circulatory flow rates points out the ineffectiveness of hyperventilation during hypoxic crises. In fact, the mechanical work of hyperventilation has been shown to increase oxygen demand above resting levels [ 101. Therefore, the response of hyperventilation to the anoxia in hypoxic crisis adversely affects the patient’s overall oxygen balance. Unless the pulmonary outflow resistance is reduced naturally or with drugs, arterial oxygen saturation decreases until vital centers are compromised. The middle and right panels of Figure 4 show the effect of increasing pulmonary valve resistance for the patient model with 22 and 40% natural A-P shunt flows, respectively. In these instances a sudden increase in pulmonary valve resistance does not induce the low arterial oxygen saturations found in hypoxic crisis. In other words, for patients with identical resting oxygen saturations, the patient with a relatively large pulmonary infundibulum and small natural A-P
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T H E ANNALS OF THORACIC SURGERY
Hemodynamic Model fw Tetralogy of Fallot
A.
lot
1 I
FIG. 6 . Variation in arterial oxygen saturation with increased pulmonary ualue resistancefollowingpalliatiue A-P shunt operation.
OXYGEN CONSUMPTION = I x (RESTING LEVEL)
B. OXYGEN
CONSUMPTION = 2 x
C. OXYGEN
CONSUMPTION=3x
PULMONARY INFUNDIBULAR SPA&
RESTING LEVEL
5
10
PULMONARY VALVE RESISTANCE (in multiples of the resting level)
shunt flow (Fig. 4, left panel) would be susceptible to hypoxic crises, while the patient with more severe infundibular restriction and larger shunt flow would not (Fig. 4, right panel). EFFECT OF PALLIATIVE OPERATIONS
Based on data from Crawford and associates [4] it is possible to create a computer model of the hypothetical patient after he has received a surgical systemic-to-pulmonary artery shunt. The baseline determinations for the patient with a 5% shunt are used since this patient is the most prone to hypoxic crises. Figures 5 and 6 show the effects of decreased systemic resistance and increased pulmonary outflow tract resistance forthe patient model after a palliative operation. Figure 5 shows that the patient has significantly increased exercise tolerance following the operation. The graphs predict that he will still have a significant fall in arterial oxygen saturation at maximum oxygen consumption. The magnitudes of both oxygen consumption and arterial oxygen saturation predicted in Figure 6 from the computer simulation correlate well with data from studies of patients after shunting procedures [4].Figure 6 shows that after surgical palliation the patient is no longer susceptible to hypoxic episodes caused by increased resistance across the pulmonary outflow tract. This graph corresponds to the patient with the worst prognosis in the preceding section, as shown in the left panel of Figure 4.
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References 1. Bing, R. J., Vandam, L. D., and Bray, F. D., Jr. Physiological studies in congenital heart disease. Bull Johns Hopkins Hosp 80:107, 1947. 2. Brotmacher, L. Haemodynamic effects of squatting during repose and haemodynamic effects of squatting during recovery from exertion. Br HeartJ 19:567, 1957. 3. Carnahan, B., and Wilkes, J. 0. Digital Computing, Fortran IV, Wa@v, and MTS. Ann Arbor: University of Michigan Press, 1973. 4. Crawford, D. W., Simpson, E., and McIlroy, M. B. Cardiopulmonary function in Fallot’s tetralogy after palliative shunting operations. Am Heart J 74:463, 1967. 5 . Davison, P. H., Armitage, G. H., and Arnott, W. M. The mechanisms of adaptation to a central venous-arterial shunt. Br Heart J 15:2 1, 1953. 6. Guntheroth, W. G., Morgan, B. C., and Mullins, G. L. Physiologic studies of paroxysmal hyperpnea in cyanotic congenital heart disease. Circulation 3 1 :70, 1965. 7. Guntheroth, W. G., Morgan, B. C., Mullins, G. L., and Baum, D. Venous return with knee-chest position and squatting in tetralogy of Fallot. Am Heart J 75:313, 1968. 8. Guyton, A. C. Textbook ofMedical Physiology (4th ed). Philadelphia: Saunders, 1971. 9. Kirklin, J. W., and Karp, R. B. The Tetralogy ofFallot, From a Surgical Viewpoint. Philadelphia: Saunders, 1970. 10. McKerrow, C. B., and Otis, A. B. Oxygen cost of hyperventilation. Trans Assoc Am Phys 67:375, 1954. 1 1 . Moffitt, E. A., Kirklin,J. W., and Theye, R. A. Physiologic studiesduringwhole-body perfusion in tetralogy of Fallot.J Thorac Cardiovasc Surg 44:180, 1962. 12. Montgomery, G. E., Jr., Geraci, J. E., Parker, R. L., and Wood, E. H. The arterial oxygen saturation in cyanotic types of congenital heart disease.Circulation 3 1 :66,1965. 13. Morgan, B. C., Guntheroth, W. G., Bloom, R. S., and Fyler, D. C. A clinical profile of paroxysmal hyperpnea in cyanotic congenital heart disease. Circulation 3 1 :66, 1965. 14. Wood, P. Symposium on congenital heart disease: Attacks of deeper cyanosis and loss of cons$ousness (syncope) in Fallot’s tetralogy. Br Heart J 20:282, 1959.
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