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Calculation of systemic blood flow with pulmonary artery thermistor probe
J
THoRAc CARDIOVASC SURG
78:576-578, 1979
Calculation of systemic blood flow with pulmonary artery thermistor probe A simple thermodilution technique is described for determining systemic blood flo II' with right atrial and left atrial catheters and a pulmonary arterial thermistor probe. Injections of cold water into the atrial catheters provide computer display readings that permit direct calculation of systemic blood jlow. The method is convenient for determining systemic blood flo II' in postoperative patients with a residual left-to-right shunt.
Robert M. Sade, M.D., Abdel Aziz Richi, M.D., and James P. Dearing, B.S., Charleston. S. C.
Measurement of cardiac output after cardiac operations has improved postoperative management by permitting evaluation of the effectiveness of hemodynamic manipulations in improving blood flow. A recent important advance is the use of afterload-reducing agents. I Evaluation of their effectiveness requires measurement of systemic vascular resistance, which in turn depends upon accurate measurement of mean arterial pressure and systemic blood flow (Qs). The most convenient way to measure cardiac output in patients undergoing cardiac operations is with a thermodilution flow probe in the pulmonary artery, 2 but this technique measures pulmonary blood flow (Qp). To calculate Qs, one must know Qp/Qs. It can be determined by the Fick equation, but oxygen content from blood samples of the right atrium, left atrium, a systemic artery, and pulmonary artery must be obtained. We recently have used an alternative method for calculating Qp/Qs which requires only right atrial and left atrial catheters and a thermodilution flow probe in the pulmonary artery. This method permits easy computation of Qs in children with residual left-to-right shunts following cardiac operations.
Method Qp is the sum of Qs and the shunt flow (Qsh): Qp = Qs + Qsh
(I)
From the Section of Pediatric Cardiac Surgery, Medical University of South Carolina, Charleston, S. C. Received for publication April 3, 1979. Accepted for publication May 29, 1979. Address for reprints: Dr. Robert M. Sade, 171 Ashley Ave., Charleston, S. C. 29403.
576
If both sides of equation 1 are divided by Qp, then I
=
(Qs :- Qsh) Qp
= ~s + ~sh Qp
Qp
(2)
Subtracting Qshz'Qp from both sides, _ Qsh Qp
(3)
or reciprocally,
(4)
_ Qsh Qp
The general equation for indicator-dilution methods of measuring flow" is . 60· I Q=-
(5)
ct
where Q is flow, I is amount of indicator, c is concentration of indicator, and t is time. In the thermodilution method, the indicator, cold water, can be injected into the right atrium or left atrium. If the amount of cold injectate is I, then all of I goes to the pulmonary artery after right atrial injection (RAI), but only a part, (Qsh/Qp) . I, goes to the pulmonary artery after left atrial injection (LAI). Thus the concentration in the pulmonary artery after RAI is I1Qp, but after LAI it is (Qsh/Qp) . I1Qp (Fig. I). Because the computer for the thermodilution system relates flow inversely to concentration, DRAI DLA1
_ -
(Qsh/Qp) . IIQp _ Qsh IIQp
- Qp
(6)
where D R A 1 is the computer's display reading after right
0022-5223/79/100576+03$00.30/0 © 1979 The C. V. Mosby Co.
Volume 78
Calculation of systemic blood flow
Number 4 October, 1979
577
atrial injection and DL\I is the display reading after left atrial injection. Although (7)
DLA 1 is not the same as Qsh. Substituting equation 6 into equation 4,
Qp
Qs
(8)
Since
Os
=
.OP.
Qp/Qs
(9)
we can substitute equations 7 and 8 into equation 9, deriving
Os
=
ORAl
III _
--
0 RAI '(1
(10)
ORAl
D LAI
Illustrative case Tetralogy of Fallot was repaired in a child with a body surface area of 0.48 m". At operation, left and right atrial, pul monary, and radial arterial catheters were placed, and a No. 2.5 Fr. pulmonary arterial thermistor probe (Edwards Laboratories, Inc., Santa Ana, Calif.) was introduced through the right ventricle. All were brought out through the epigastrium. The thermistor probe was connected to an Edwards Model 9520 cardiac output computer. A 2 ml dose of iced 5% dextrose in water was injected into the right atrial catheter twice, and the computer display readings (D R A1) were averaged. The same dose was injected twice into the left atrium, and the display readings were averaged (D LA I) . The Op/Os was derived by equation 8 and the Os by equation 10 (Table I). The same measurements were performed the morning of the first postoperative day with similar results (Table I). These results were confirmed by Fick calculations from oxygen saturation data: Op/Os 1.46 at 2 hours and 1.25 at 20 hours postoperatively. Note that D RA h which is really OP, overestimated Os by 36% at 2 hours and by 18% at 20 hours. Accurate knowledge of Os allowed appropriate management of this patient.
Discussion Calculation of Op/Os by separate injection of indicator into the right and left atria has been advocated by Krovetz and Gessner" for use in infants. Their method, however, utilized indocyanine green dye, and sampling
Fig. 1. Diagram of blood flow through the heart. Right heart chambers are to the viewer's left and left heart chambers to the right. Note the thermistor probe in the pulmonary artery, connected to the flow computer. The systemic flow (Qs} returning to the right side of the heart is augmented by the shunt flow (Osh) in the right ventricle, resulting in a pulmonary flow (Op) greater than systemic. In the left ventricle, the pulmonary venous return (Op) is partitioned into shunt flow (Qsh] and systemic flow
«».
Table I
ORAl
(= Op)
Two hours after operation
Twenty hours after operation
1.33
1.42 7.64 1.23 1.16 2.42
D LA I
5.11
Op/Os (equation 8) Os (equation 10) Systemic flow index (Qs/rrr')
1.35 0.98 2.04
Legend: Qp, Pulmonary blood flow (liters per minute). Qs, Systemic blood flow (liters per minute). DRAb Computer display after right atrial injection. DeAb Computer display after left atrial injection.
was done at a peripheral artery. The advantages of the pulmonary thermistor probe" are maintained in our method. Initial attempts with an IL 600 computer (Instrumentation Laboratories, Inc., Lexington, Mass.) to use our equation failed because the computer continues integration of the thermal curve until the temperature returns to within O. \20 C of its initial level and the rate of temperature change is less than 0.002° C/sec. The recirculation portion of the curve is therefore included in
The Journal of
578
Sade, Richi, Dearing
Thoracic and Cardiovascular Surgery
The calculation of Qp, and the result is a falsely low reading of Qp. The Edwards 9520 computer, on the other hand, stops integration when the temperature returns to 30% of base line, so that most or all of the recirculation curve is excluded and a true Qp reading is obtained. To reduce the possibility of computer error, we always record the thermal curves to verify visually the configuration of the curves after RAJ and LAI and to ascertain exclusion of the recirculation portion of the RAI curve. Since complete mixing of the injectate with venous return is necessary for accurate determination of flow, the thermistor probe should be placed distally in the pulmonary artery. In patients with a residual atrial septal defect, LAI could result in streaming toward or from the defect, which would produce an inaccurate computer reading. The method may not be valid, therefore, in measuring the size of residual atrial septal defects. The ease of placing right and left atrial catheters makes this method of deriving Qs from pulmonary flow convenient. Many surgeons routinely place atrial catheters for hemodynamic management postoperatively and need only place a pulmonary artery thermistor probe to achieve the capability of determining Qs. The simple equation 8, allowing determination of Qp/Qs, can be used at cardiac catheterization to verify
the magnitude of left-to-right shunts calculated by the Fick method. Great care must be exercised when injecting water into the left atrium to avoid introducing air or particulate matter into the systemic circulation. Detection of very low Qs and large Qp/Qs may indicate a need for reoperation. This has not occurred in our experience, but accurate knowledge of Qs (equation 10) has proved valuable to us in the pharmacologic management of patients with residual ventricular septal defect after cardiac operations.
REFERENCES Benzing G III, Helmsworth lA, Schrieber IT, Loggie J, Kaplan S: Nitroprusside after open-heart surgery. Circulation 54:467-471, 1976 2 Mathur M, Harris EA, Yarrow S, Barratt-Boyes BG: Measurement of cardiac output by thermodilution in infants and children after open-heart operations. 1 THORAC CARDIOVASC SURG 72:221-225, 1976 3 Sade RM, Cosgrove OM, Castaneda AR: Infant and Child Care in Heart Surgery, Chicago, 1977, Year book Medical Publishers, Inc., p 56. 4 Krovetz LJ, Gessner IH: A new method utilizing indicator-dilution techniques for estimation of left-to-right shunts in infants. Circulation 32:772-777, 1965
THoRAc CARDIOVASC SURG
78:576-578, 1979
Calculation of systemic blood flow with pulmonary artery thermistor probe A simple thermodilution technique is described for determining systemic blood flo II' with right atrial and left atrial catheters and a pulmonary arterial thermistor probe. Injections of cold water into the atrial catheters provide computer display readings that permit direct calculation of systemic blood jlow. The method is convenient for determining systemic blood flo II' in postoperative patients with a residual left-to-right shunt.
Robert M. Sade, M.D., Abdel Aziz Richi, M.D., and James P. Dearing, B.S., Charleston. S. C.
Measurement of cardiac output after cardiac operations has improved postoperative management by permitting evaluation of the effectiveness of hemodynamic manipulations in improving blood flow. A recent important advance is the use of afterload-reducing agents. I Evaluation of their effectiveness requires measurement of systemic vascular resistance, which in turn depends upon accurate measurement of mean arterial pressure and systemic blood flow (Qs). The most convenient way to measure cardiac output in patients undergoing cardiac operations is with a thermodilution flow probe in the pulmonary artery, 2 but this technique measures pulmonary blood flow (Qp). To calculate Qs, one must know Qp/Qs. It can be determined by the Fick equation, but oxygen content from blood samples of the right atrium, left atrium, a systemic artery, and pulmonary artery must be obtained. We recently have used an alternative method for calculating Qp/Qs which requires only right atrial and left atrial catheters and a thermodilution flow probe in the pulmonary artery. This method permits easy computation of Qs in children with residual left-to-right shunts following cardiac operations.
Method Qp is the sum of Qs and the shunt flow (Qsh): Qp = Qs + Qsh
(I)
From the Section of Pediatric Cardiac Surgery, Medical University of South Carolina, Charleston, S. C. Received for publication April 3, 1979. Accepted for publication May 29, 1979. Address for reprints: Dr. Robert M. Sade, 171 Ashley Ave., Charleston, S. C. 29403.
576
If both sides of equation 1 are divided by Qp, then I
=
(Qs :- Qsh) Qp
= ~s + ~sh Qp
Qp
(2)
Subtracting Qshz'Qp from both sides, _ Qsh Qp
(3)
or reciprocally,
(4)
_ Qsh Qp
The general equation for indicator-dilution methods of measuring flow" is . 60· I Q=-
(5)
ct
where Q is flow, I is amount of indicator, c is concentration of indicator, and t is time. In the thermodilution method, the indicator, cold water, can be injected into the right atrium or left atrium. If the amount of cold injectate is I, then all of I goes to the pulmonary artery after right atrial injection (RAI), but only a part, (Qsh/Qp) . I, goes to the pulmonary artery after left atrial injection (LAI). Thus the concentration in the pulmonary artery after RAI is I1Qp, but after LAI it is (Qsh/Qp) . I1Qp (Fig. I). Because the computer for the thermodilution system relates flow inversely to concentration, DRAI DLA1
_ -
(Qsh/Qp) . IIQp _ Qsh IIQp
- Qp
(6)
where D R A 1 is the computer's display reading after right
0022-5223/79/100576+03$00.30/0 © 1979 The C. V. Mosby Co.
Volume 78
Calculation of systemic blood flow
Number 4 October, 1979
577
atrial injection and DL\I is the display reading after left atrial injection. Although (7)
DLA 1 is not the same as Qsh. Substituting equation 6 into equation 4,
Qp
Qs
(8)
Since
Os
=
.OP.
Qp/Qs
(9)
we can substitute equations 7 and 8 into equation 9, deriving
Os
=
ORAl
III _
--
0 RAI '(1
(10)
ORAl
D LAI
Illustrative case Tetralogy of Fallot was repaired in a child with a body surface area of 0.48 m". At operation, left and right atrial, pul monary, and radial arterial catheters were placed, and a No. 2.5 Fr. pulmonary arterial thermistor probe (Edwards Laboratories, Inc., Santa Ana, Calif.) was introduced through the right ventricle. All were brought out through the epigastrium. The thermistor probe was connected to an Edwards Model 9520 cardiac output computer. A 2 ml dose of iced 5% dextrose in water was injected into the right atrial catheter twice, and the computer display readings (D R A1) were averaged. The same dose was injected twice into the left atrium, and the display readings were averaged (D LA I) . The Op/Os was derived by equation 8 and the Os by equation 10 (Table I). The same measurements were performed the morning of the first postoperative day with similar results (Table I). These results were confirmed by Fick calculations from oxygen saturation data: Op/Os 1.46 at 2 hours and 1.25 at 20 hours postoperatively. Note that D RA h which is really OP, overestimated Os by 36% at 2 hours and by 18% at 20 hours. Accurate knowledge of Os allowed appropriate management of this patient.
Discussion Calculation of Op/Os by separate injection of indicator into the right and left atria has been advocated by Krovetz and Gessner" for use in infants. Their method, however, utilized indocyanine green dye, and sampling
Fig. 1. Diagram of blood flow through the heart. Right heart chambers are to the viewer's left and left heart chambers to the right. Note the thermistor probe in the pulmonary artery, connected to the flow computer. The systemic flow (Qs} returning to the right side of the heart is augmented by the shunt flow (Osh) in the right ventricle, resulting in a pulmonary flow (Op) greater than systemic. In the left ventricle, the pulmonary venous return (Op) is partitioned into shunt flow (Qsh] and systemic flow
«».
Table I
ORAl
(= Op)
Two hours after operation
Twenty hours after operation
1.33
1.42 7.64 1.23 1.16 2.42
D LA I
5.11
Op/Os (equation 8) Os (equation 10) Systemic flow index (Qs/rrr')
1.35 0.98 2.04
Legend: Qp, Pulmonary blood flow (liters per minute). Qs, Systemic blood flow (liters per minute). DRAb Computer display after right atrial injection. DeAb Computer display after left atrial injection.
was done at a peripheral artery. The advantages of the pulmonary thermistor probe" are maintained in our method. Initial attempts with an IL 600 computer (Instrumentation Laboratories, Inc., Lexington, Mass.) to use our equation failed because the computer continues integration of the thermal curve until the temperature returns to within O. \20 C of its initial level and the rate of temperature change is less than 0.002° C/sec. The recirculation portion of the curve is therefore included in
The Journal of
578
Sade, Richi, Dearing
Thoracic and Cardiovascular Surgery
The calculation of Qp, and the result is a falsely low reading of Qp. The Edwards 9520 computer, on the other hand, stops integration when the temperature returns to 30% of base line, so that most or all of the recirculation curve is excluded and a true Qp reading is obtained. To reduce the possibility of computer error, we always record the thermal curves to verify visually the configuration of the curves after RAJ and LAI and to ascertain exclusion of the recirculation portion of the RAI curve. Since complete mixing of the injectate with venous return is necessary for accurate determination of flow, the thermistor probe should be placed distally in the pulmonary artery. In patients with a residual atrial septal defect, LAI could result in streaming toward or from the defect, which would produce an inaccurate computer reading. The method may not be valid, therefore, in measuring the size of residual atrial septal defects. The ease of placing right and left atrial catheters makes this method of deriving Qs from pulmonary flow convenient. Many surgeons routinely place atrial catheters for hemodynamic management postoperatively and need only place a pulmonary artery thermistor probe to achieve the capability of determining Qs. The simple equation 8, allowing determination of Qp/Qs, can be used at cardiac catheterization to verify
the magnitude of left-to-right shunts calculated by the Fick method. Great care must be exercised when injecting water into the left atrium to avoid introducing air or particulate matter into the systemic circulation. Detection of very low Qs and large Qp/Qs may indicate a need for reoperation. This has not occurred in our experience, but accurate knowledge of Qs (equation 10) has proved valuable to us in the pharmacologic management of patients with residual ventricular septal defect after cardiac operations.
REFERENCES Benzing G III, Helmsworth lA, Schrieber IT, Loggie J, Kaplan S: Nitroprusside after open-heart surgery. Circulation 54:467-471, 1976 2 Mathur M, Harris EA, Yarrow S, Barratt-Boyes BG: Measurement of cardiac output by thermodilution in infants and children after open-heart operations. 1 THORAC CARDIOVASC SURG 72:221-225, 1976 3 Sade RM, Cosgrove OM, Castaneda AR: Infant and Child Care in Heart Surgery, Chicago, 1977, Year book Medical Publishers, Inc., p 56. 4 Krovetz LJ, Gessner IH: A new method utilizing indicator-dilution techniques for estimation of left-to-right shunts in infants. Circulation 32:772-777, 1965