- Email: [email protected]
An additional source of error in microsphere measurement of regional blood flow
MICROVASCULAR
RESEARCH
An Additional CHARLES
21, 377-383 (1981)
Source of Error In Microsphere Regional Blood Flow’
D. MOORE, BRUCE L. GEWERTZ,~ H. THOMAS WHEELER, WILLIAM
Department
Measurement
of Surgery,
of AND
J. FRY
Southwestern Medical School, The University Center, Dallas, Texas 75235 Received November
of Texas Health
Science
3, 1980
The effects of variations in rate of microsphere injection and site and rate of reference sample withdrawal were studied to further define sources of error in microsphere measurements of regional blood flow. Anesthetized canines underwent sequential left ventricular injection of radiolabeled 25pm microspheres at slow and fast injection speeds. Simultaneous reference samples were collected from brachial and femoral artieres at slow (5 ml/min) and fast (13 ml/min) withdrawal rates. Calculated renal blood flows (RBF) were compared for each injection rate, sampling site, and withdrawal rate. Varying injection rate or withdrawal site resulted in no significant differences in RBF. RBF was influenced significantly (P < 0.005) by reference sample withdrawal (fast withdrawal 4.38 -t 1.28 ml/min. g vs slow withdrawal rate 6.87 2 2.29 ml/min. g). Data indicate that selection of an inappropriately slow rate of reference sample withdrawal results in erroneous values of regional blood flow.
INTRODUCTION The theoretical and technical constraints that limit the accuracy of microsphere measurement of regional blood flow have been extensively studied (1,5,7,8,12). The conditions that must be satisfied are: (1) microspheres must be completely trapped in the capillary bed; (2) the distribution of microspheres must be directly proportional to blood flow; and (3) an adequate number of microspheres must be present in tissue samples to minimize random deviations in sphere distribution. If these conditions are met, organ blood flow may be calculated using either of two methods. The first method calculates organ flow as a fraction of total radioactivity injected; an independent measurement of cardiac output is required (6). The second method allows calculation of regional blood flow based on a tissue with known flow or a reference sample of peripheral arterial blood. Flow to any organ is then given by (11) organ blood flow = number of microspheres in organ (ml/min) number of microspheres in reference sample
sampler:7
X
[ ,]
’ This study was supported by NIH Grant S-SO7-RR05426-18 and the Lee Hudson-Robert Penn
Professorship of the Universityof Texas Health Science Center at Dallas. 2 This work was done during Dr. Gewertz’s tenure as a teaching scholar of the American Heart Association. 377 Copyright AU rights of
0
CU262S62/81/030377-07$02.00/0 1981 by Academic Press, Inc. form reserved. Printed in U.S.A.
reproduction in any
378
MOORE
ET
AL.
Proper experimental technique is essential to obtain accurate measurements. Studies comparing different injection sites (1,7) have concluded that left atrial or left ventricular injections allow adequate central mixing of microspheres for the study of peripheral organs. If myocardial blood flow is the principal interest, atrial injections are preferred (3). The site of reference sample withdrawal does not appear to be a significant source of error if the microspheres are well mixed and evenly distributed in the peripheral arterial circulation (1). In theory, the rate of reference sample withdrawal should also have no effect on the accuracy of measurement if the number of microspheres in a sample is large enough to overcome statistical limitations. Nonetheless, despite evidence of adequate mixing (e.g., similar reference samples at two peripheral sites), some investigators have obtained erroneous measurements that cannot be easily explained (2). The current study attempts to better characterize the influence of specific techniques on the incidence and magnitude of such errors. We varied the rate of microsphere injection and simultaneously observed the effect of site and rate of reference sample withdrawal on calculated organ blood flows. All microspheres used in the experiments were 25 pm in diameter, the largest sphere in routine use. It was thought that large spheres would be more likely to demonstrate peculiar flow patterns leading to an intravascular distribution of spheres different from blood flow (9). MATERIALS
AND METHODS
Five mongrel dogs weighing 15 to 20 kg were anesthetized with intravenous sodium pentobarbital, 25 to 30 mg/kg. A catheter was palced in the right carotid artery for continuous blood pressure recording. Arterial blood gases and cardiac output (dye dilution) were monitored at regular intervals throughout the study. Microsphere injections were made through a Sones 7-French catheter placed in the left ventricle via the left carotid artery. The catheter was advanced in the artery until a left ventricular pressure tracing was observed, and then inserted an additional 3 to 4 cm into the ventricle. Placement of the catheter was checked before each isotope injection and at the end of the experiment. Sequential injections of l-ml suspension of 500,000 to 750,000 microspheres (New England Nuclear, Boston, Mass.) were made in each animal. Microspheres were suspended in saline with 0.5% Tween 80 and agitated immediately before injection. Injection rates were varied by following the 1 ml injection with a flush of 20 ml of saline injected over a period of 10 set (fast injection) or 20 set (slow injection). The sizes of microspheres were: 1251,27.2 ? 2.2 pm; 57Co, 25.2 + 2.1 pm;113Sn, 25.5 + 1.5pm;8jSr, 25.4 ? 2.1 pm; and4‘Sc, 26.6 + 2.Opm. Four dogs underwent five injections and received all isotopes except iodine. A fifth dog underwent five injections and received all five labels. The sequence of microsphere injections was randomized. Numerous studies have documented that the injection of over 2 million microspheres results in no hemodynamic effects or, in fact, any functional impairment of any organ (1,3). Both brachial and both femoral arteries were cannulated with Teflon catheters (Quik-Cath, Travenol Labs, Dearheld, Ill., i.d. 1.75 mm). Roller pumps were positioned on each side of the animal, and reference samples were obtained simultaneously from all four peripheral sites. Right brachial and right femoral
MICROSPHERE
ERROR
379
reference samples were withdrawn at a rate of approximately 5 mYmin (slow); left brachial and left femoral samples were collected at a rate of approximately 13 ml/min (fast). Sampling was begun at all four peripheral sites 10 to 15 set before microsphere injection and continued for 2 to 3 min. Reference samples were collected in a series of preweighed vials; each vial represented a 30-set collection from a sampling site. Total blood sample withdrawals never exceeded 200 ml in any animal, and withdrawals were immediately replaced with an equal volume of normal saline. The simultaneous withdrawal of all reference samples allowed paired comparisons of calculated organ flows, since the number of spheres trapped in an organ was identical for all four calculations based on the injection of a single microsphere. The only difference in each calculation of organ blood flow was the reference sample multiplier in Eq. [l] (sample withdrawal rate/number of microspheres in reference sample). Calculated renal blood flows (RBF) were selected for presentation in this manuscript. The kidney receives an abundant blood flow and is frequently studied with the microsphere technique. Furthermore, the simultaneous collection of all four reference samples from a given microsphere injection insured: (1) any observed difference would reflect only injection rate, withdrawal site, or withdrawal rate; and (2) minor changes in systemic hemodynamics would not invalidate comparisons between organ flows based on simultaneously withdrawal reference samples. For example, assuming adequate central mixing, RBF calculated from the fast femoral reference sample of a given microsphere injection should be the same as that calculated from the slow femoral reference sample irrespective of cardiac output. Following microsphere injections and sample collection, animals were sacrificed. Both kidneys were excised, cut into small sections, and placed in preweighed vials. Final tissue and blood sample weights were obtained with a digital precision balance with a resolution of 0.005 g (Brinkmann Instruments, Westbury, N.Y.). Vials were counted in a well-type gamma scintillation counter (Nuclear Chicago). Isotopes were separated by solving multiple linear equations according to Rudolph and Heymann (11). Renal blood flows (RBF) were calculated using Eq. [I], substituting disintegrations per minute for number of microspheres. Data from a given injection was excluded from analysis if a vial representing the last 30 set of a reference sample collection contained more than 2% of the total radioactivity in the reference sample. This rigorous criteria eliminated any potential artifact from incomplete collection of microspheres. Of a possible 42 paired collections, only 26 were acceptable by this criteria. It should be noted that excluding one collection on this basis also required the exclusion of its paired reference sample from analysis. Results were compared using paired t test (sampling site and collection rate) or unpaired t test (injection rate). P < 0.05 was considered significant. All results were expressed as mean + standard deviation. RESULTS Mean blood pressure at the start of the experiment was 116 t 24 mm Hg. Pressure decreased slightly to 97 * 18 mm Hg at the end of all injections. Cardiac
MOORE ET AL.
380
4
6-
.
5Right Renal blood flow (ml/min,gm)
. .
:
4 -
J
.
r= 96
1 t 1
2
3 Left
4 5 Renal Blood Flow (ml/min.gm )
6
7
0
FIG. 1. Verification of homogeneous mixing of microspheres in abdominal aorta at the level of the renal arteries. Left and right renal blood flows were calculated using the reference sample method based on fast femoral withdrawals.
output at the start of the experiments (1.97 f .79 liter/min) was nearly identical to mean cardiac output at the end of the expeirments (1.97 + .70 liter/min). The adequacy of central mixing is illustrated in Fig. 1, comparing calculated right and left renal blood flows. The concordance of these values (r = 0.98) is evidence that microspheres were adequately mixed in the abdominal aorta, and allowed us to use right renal blood flow with confidence in succeeding tabulations. Varying injection rate between 10 and 20 set per injection did not significantly affect RBF. Calculated RBF was 5.88 f 1.19 ml/mine g for slow injections and 5.22 k 2.42 ml/min g for fast injections. The effect of reference sample withdrawal site and withdrawal rate on calculated RBF is demonstrated in Fig. 2. There was no difference in RBF when slow 0 T 0
Fast withdrawal Slow withdrawal
T
N4
. BRACHIAL WITHDRAWAL
-
FEMORAL SITE
FIG. 2. Renal blood flows calculated from fast withdrawal specimens at brachial and femoralSites were lower (P < 0.005) than those calculated from slow withdrawal specimens.
MICROSPHERE ERROR
381
femoral values were compared to slow brachial values (7.00 + 2.81 vs 6.76 + 1.84 ml/mm. g) or when fast femoral values were compared to fast brachial values (4.44 ? 1.50 vs 4.32 ? 1.16 myming). RBF calculated from all fast collections was compared to RBF calculated from all slow collections. Mean RBF from fast withdrawal specimens (4.38 ? 1.28 ml/min g) was significantly less (P < 0.005) than that calculated from slow withdrawal specimens (6.87 + 2.29 ml/mine g). Mean RBF calculated from fast withdrawals is more consistent with previous data published by this laboratory and with generally accepted values for RBF in anesthetized dogs. The relationship is illustrated in Fig. 3. It should be noted that both kidneys or, for that matter, all organs demonstrated the same relationship. The reason for this is clear if Eq. [l] is considered. Any change in the reference sample multiplier (sample withdrawal rate/disintegrations per minute in reference sample) would be reflected in the same proportion in all organs. In an additional comparison, we examined the 16 pairs of reference samples that were excluded from the above analysis because greater than 2% of total radioactivity was contained in the last vial collected. In these excluded specimens, the mean radioactivity in the last vial was only 8.3 + 6.8% of total radioactivity. In addition, no correlation whatsoever existed between calculated RBF and percentage total counts in the last vial suggesting that collections were in fact complete even in these instances. Statistical analysis including all 42 pairs confirmed the effect of withdrawal rate at the P < 0.005 level. DISCUSSION The higher values for RBF calculated from reference samples withdrawn at slower rates are the result of a lower than expected number of microspheres per 13r
1’
SLOW (5 ml bin)
FAST (13mVmm)
FIG. 3. Individual values of RBF calculated from reference samples obtained simultaneously at fast and slow withdrawal rates. Results from brachial and femoral arterial samples are combined.
382
MOORE
ET AL.
unit volume of reference blood. As shown by Buckberg ef al. (1) it is unlikely that this effect is due to a smaller absolute number of microspheres in the samples. Decreasing the number of microspheres in a reference sample may increase the variability of calculated blood flow, but should not consistently elevate mean values. A relative decrease in microsphere concentration in a peripheral reference sample would occur if microspheres were present in uncollected and uncounted blood, such as that present in the collecting tubing at the end of a sample withdrawal period. This obvious source of error was avoided in our experiments by making certain that no radioactivity (less than 2% of total) was present in the last vial sampled. Since incomplete collection did not occur, the most likely explanation for our observations is related to the flow properties of microspheres in the peripheral circulation. Microsphere distribution in both large and small vessels differs from that of the red blood cell (4). Microspheres tend to be concentrated in greater than expected numbers in areas of maximal blood flow velocity such as the center of a mediumsized artery (10) or the largest vessel of a branching network, e.g., the interlobular arteries of the kidney (9). An ex vivo model of this phenomenon scaled to the capillary circulation has been developed by Yen and Fung (13). While this effect appears to diminish as the size of the microsphere approaches that of the erythrocyte, the distribution of nondeformable plastic spheres can only approximate that of deformable ellipsoid red blood cells with dimensions of 2 x 7~m. We propose that inappropriately slow withdrawal of a reference sample from a cannulated peripheral vessel induces a nonhomogeneous distribution of microspheres along velocity streamlines. Such a phenomenon will predictably result in a relative paucity of spheres in the slower channel (the reference catheter) and an increased concentration in the more proximal branches of the ligated and cannulated vessel. Although the exact relationship between vessel blood flow velocity and the amount of nonhomogeneous streaming of microspheres is not known, it would seem prudent that investigations utilizing microsphere measurement of regional blood flow carefully consider the rate of sample collection to minimize the effects of velocity mismatching on microsphere behavior. These factors would be particularly important if vessel flow rates changed appreciably in the course of the experiment. ACKNOWLEDGMENTS We gratefully acknowledge the assistance of Ann Lackey in the preparation of this manuscript.
REFERENCES 1. BUCKBERG, G., LUCK, J. C., PAYNE, D. B., HOFFMAN, J. I. E., ARCHIE, J. P., AND FIXLER,
D. E.
(1971). Some sources of error in measuring regional blood flow with radioactive microspheres. J. Appl. Physiol.
31, 598-604.
S. A. (1979). Sympathetic modulation of hypercapnic cerebral vasodilation in dogs. Circ. Res., 45, 771-785. 3. DOMENECH, R. J., HOFFMAN, J. I. E., NOBLE, M. I. M., et al. (1969). Total and regional coronary blood flow measured by radioactive microspheres in conscious and anesthetized dogs. Circ. Res., 25, 581-5%. 2. D’ALECY,
L. G., ROSE, C. J., AND SELLERS,
MICROSPHERE
ERROR
383
4. HALES, J. R. S., AND CLIFF, W. J. (1976). Direct observations of the behavior of microspheres in microvasculature. Bib/. Anat., 15, 87-91. 5. HEYMANN, M., PAYNE, B. D., HOFFMAN, J. I. E., AND RUDOLPH, A. M. (1977). Blood flow measurements with radionuclide-labeled particles. Progr. Cardiovasc. Dis., 20, 55-79. 6. KAIHARA, S., RUTHERFORD, R. B., SCHWENTRER, E. P., AND WAGNER, H. N., JR. (1%9). Distribution of cardiac output in experimental hemorrhagic shock in dogs. J. Appl. Physiol., 27, 218-222. 7. KAIHARA, S., VAN HEERDEN, P. D., MIGITA, T., AND WAGNER, H. N., JR. (1968). Measurement of distribution of cardiac output. J. Appl. Physiol., 25, 696-700. 8. MAKOWSKI, E., GIACOMO, M., DROEGEMUELLER, W., AND BA~~AGLIA, F. (1968). Measurement of umbilical arterial blood flow to the sheep placenta and fetus in utero. Circ. Res., 23,623-63 1. 9. MORKRID, L., OFSTAD, J., AND WILLASSEN, Y. (1976). Effect of steric restriction on the intracortical distribution of microspheres in the dog kidney. Circ. Res., 39, 608-615. 10. PHIBBS, R., AND DONG, L. (1970). Nonuniform distribution of microspheres in blood flowing through a medium-sized artery. Canad. .I. Physiol. Pharmacol., 48, 415-421. 11. RUDOLPH, A. M., AND HEYMANN, M. A. (1%7). Circulation of the fetus in utero: Methods for studying distribution of blood flow, cardiac output and organ blood flow. Circ. Res., 21, 163. 12. WARREN, D., AND LEDINGHAM, J. G. G. (1974). Measurement of cardiac output distribution using microspheres. Some practical and theoretical considerations. Cardiovasc. Res., 8, 570-581. 13. YEN, R. T., AND FUNG, Y. C. (1978). Effect of velocity distribution in capillary blood vessels on red cell distribution. Amer. J. Physiol., 235, H251-H257.
RESEARCH
An Additional CHARLES
21, 377-383 (1981)
Source of Error In Microsphere Regional Blood Flow’
D. MOORE, BRUCE L. GEWERTZ,~ H. THOMAS WHEELER, WILLIAM
Department
Measurement
of Surgery,
of AND
J. FRY
Southwestern Medical School, The University Center, Dallas, Texas 75235 Received November
of Texas Health
Science
3, 1980
The effects of variations in rate of microsphere injection and site and rate of reference sample withdrawal were studied to further define sources of error in microsphere measurements of regional blood flow. Anesthetized canines underwent sequential left ventricular injection of radiolabeled 25pm microspheres at slow and fast injection speeds. Simultaneous reference samples were collected from brachial and femoral artieres at slow (5 ml/min) and fast (13 ml/min) withdrawal rates. Calculated renal blood flows (RBF) were compared for each injection rate, sampling site, and withdrawal rate. Varying injection rate or withdrawal site resulted in no significant differences in RBF. RBF was influenced significantly (P < 0.005) by reference sample withdrawal (fast withdrawal 4.38 -t 1.28 ml/min. g vs slow withdrawal rate 6.87 2 2.29 ml/min. g). Data indicate that selection of an inappropriately slow rate of reference sample withdrawal results in erroneous values of regional blood flow.
INTRODUCTION The theoretical and technical constraints that limit the accuracy of microsphere measurement of regional blood flow have been extensively studied (1,5,7,8,12). The conditions that must be satisfied are: (1) microspheres must be completely trapped in the capillary bed; (2) the distribution of microspheres must be directly proportional to blood flow; and (3) an adequate number of microspheres must be present in tissue samples to minimize random deviations in sphere distribution. If these conditions are met, organ blood flow may be calculated using either of two methods. The first method calculates organ flow as a fraction of total radioactivity injected; an independent measurement of cardiac output is required (6). The second method allows calculation of regional blood flow based on a tissue with known flow or a reference sample of peripheral arterial blood. Flow to any organ is then given by (11) organ blood flow = number of microspheres in organ (ml/min) number of microspheres in reference sample
sampler:7
X
[ ,]
’ This study was supported by NIH Grant S-SO7-RR05426-18 and the Lee Hudson-Robert Penn
Professorship of the Universityof Texas Health Science Center at Dallas. 2 This work was done during Dr. Gewertz’s tenure as a teaching scholar of the American Heart Association. 377 Copyright AU rights of
0
CU262S62/81/030377-07$02.00/0 1981 by Academic Press, Inc. form reserved. Printed in U.S.A.
reproduction in any
378
MOORE
ET
AL.
Proper experimental technique is essential to obtain accurate measurements. Studies comparing different injection sites (1,7) have concluded that left atrial or left ventricular injections allow adequate central mixing of microspheres for the study of peripheral organs. If myocardial blood flow is the principal interest, atrial injections are preferred (3). The site of reference sample withdrawal does not appear to be a significant source of error if the microspheres are well mixed and evenly distributed in the peripheral arterial circulation (1). In theory, the rate of reference sample withdrawal should also have no effect on the accuracy of measurement if the number of microspheres in a sample is large enough to overcome statistical limitations. Nonetheless, despite evidence of adequate mixing (e.g., similar reference samples at two peripheral sites), some investigators have obtained erroneous measurements that cannot be easily explained (2). The current study attempts to better characterize the influence of specific techniques on the incidence and magnitude of such errors. We varied the rate of microsphere injection and simultaneously observed the effect of site and rate of reference sample withdrawal on calculated organ blood flows. All microspheres used in the experiments were 25 pm in diameter, the largest sphere in routine use. It was thought that large spheres would be more likely to demonstrate peculiar flow patterns leading to an intravascular distribution of spheres different from blood flow (9). MATERIALS
AND METHODS
Five mongrel dogs weighing 15 to 20 kg were anesthetized with intravenous sodium pentobarbital, 25 to 30 mg/kg. A catheter was palced in the right carotid artery for continuous blood pressure recording. Arterial blood gases and cardiac output (dye dilution) were monitored at regular intervals throughout the study. Microsphere injections were made through a Sones 7-French catheter placed in the left ventricle via the left carotid artery. The catheter was advanced in the artery until a left ventricular pressure tracing was observed, and then inserted an additional 3 to 4 cm into the ventricle. Placement of the catheter was checked before each isotope injection and at the end of the experiment. Sequential injections of l-ml suspension of 500,000 to 750,000 microspheres (New England Nuclear, Boston, Mass.) were made in each animal. Microspheres were suspended in saline with 0.5% Tween 80 and agitated immediately before injection. Injection rates were varied by following the 1 ml injection with a flush of 20 ml of saline injected over a period of 10 set (fast injection) or 20 set (slow injection). The sizes of microspheres were: 1251,27.2 ? 2.2 pm; 57Co, 25.2 + 2.1 pm;113Sn, 25.5 + 1.5pm;8jSr, 25.4 ? 2.1 pm; and4‘Sc, 26.6 + 2.Opm. Four dogs underwent five injections and received all isotopes except iodine. A fifth dog underwent five injections and received all five labels. The sequence of microsphere injections was randomized. Numerous studies have documented that the injection of over 2 million microspheres results in no hemodynamic effects or, in fact, any functional impairment of any organ (1,3). Both brachial and both femoral arteries were cannulated with Teflon catheters (Quik-Cath, Travenol Labs, Dearheld, Ill., i.d. 1.75 mm). Roller pumps were positioned on each side of the animal, and reference samples were obtained simultaneously from all four peripheral sites. Right brachial and right femoral
MICROSPHERE
ERROR
379
reference samples were withdrawn at a rate of approximately 5 mYmin (slow); left brachial and left femoral samples were collected at a rate of approximately 13 ml/min (fast). Sampling was begun at all four peripheral sites 10 to 15 set before microsphere injection and continued for 2 to 3 min. Reference samples were collected in a series of preweighed vials; each vial represented a 30-set collection from a sampling site. Total blood sample withdrawals never exceeded 200 ml in any animal, and withdrawals were immediately replaced with an equal volume of normal saline. The simultaneous withdrawal of all reference samples allowed paired comparisons of calculated organ flows, since the number of spheres trapped in an organ was identical for all four calculations based on the injection of a single microsphere. The only difference in each calculation of organ blood flow was the reference sample multiplier in Eq. [l] (sample withdrawal rate/number of microspheres in reference sample). Calculated renal blood flows (RBF) were selected for presentation in this manuscript. The kidney receives an abundant blood flow and is frequently studied with the microsphere technique. Furthermore, the simultaneous collection of all four reference samples from a given microsphere injection insured: (1) any observed difference would reflect only injection rate, withdrawal site, or withdrawal rate; and (2) minor changes in systemic hemodynamics would not invalidate comparisons between organ flows based on simultaneously withdrawal reference samples. For example, assuming adequate central mixing, RBF calculated from the fast femoral reference sample of a given microsphere injection should be the same as that calculated from the slow femoral reference sample irrespective of cardiac output. Following microsphere injections and sample collection, animals were sacrificed. Both kidneys were excised, cut into small sections, and placed in preweighed vials. Final tissue and blood sample weights were obtained with a digital precision balance with a resolution of 0.005 g (Brinkmann Instruments, Westbury, N.Y.). Vials were counted in a well-type gamma scintillation counter (Nuclear Chicago). Isotopes were separated by solving multiple linear equations according to Rudolph and Heymann (11). Renal blood flows (RBF) were calculated using Eq. [I], substituting disintegrations per minute for number of microspheres. Data from a given injection was excluded from analysis if a vial representing the last 30 set of a reference sample collection contained more than 2% of the total radioactivity in the reference sample. This rigorous criteria eliminated any potential artifact from incomplete collection of microspheres. Of a possible 42 paired collections, only 26 were acceptable by this criteria. It should be noted that excluding one collection on this basis also required the exclusion of its paired reference sample from analysis. Results were compared using paired t test (sampling site and collection rate) or unpaired t test (injection rate). P < 0.05 was considered significant. All results were expressed as mean + standard deviation. RESULTS Mean blood pressure at the start of the experiment was 116 t 24 mm Hg. Pressure decreased slightly to 97 * 18 mm Hg at the end of all injections. Cardiac
MOORE ET AL.
380
4
6-
.
5Right Renal blood flow (ml/min,gm)
. .
:
4 -
J
.
r= 96
1 t 1
2
3 Left
4 5 Renal Blood Flow (ml/min.gm )
6
7
0
FIG. 1. Verification of homogeneous mixing of microspheres in abdominal aorta at the level of the renal arteries. Left and right renal blood flows were calculated using the reference sample method based on fast femoral withdrawals.
output at the start of the experiments (1.97 f .79 liter/min) was nearly identical to mean cardiac output at the end of the expeirments (1.97 + .70 liter/min). The adequacy of central mixing is illustrated in Fig. 1, comparing calculated right and left renal blood flows. The concordance of these values (r = 0.98) is evidence that microspheres were adequately mixed in the abdominal aorta, and allowed us to use right renal blood flow with confidence in succeeding tabulations. Varying injection rate between 10 and 20 set per injection did not significantly affect RBF. Calculated RBF was 5.88 f 1.19 ml/mine g for slow injections and 5.22 k 2.42 ml/min g for fast injections. The effect of reference sample withdrawal site and withdrawal rate on calculated RBF is demonstrated in Fig. 2. There was no difference in RBF when slow 0 T 0
Fast withdrawal Slow withdrawal
T
N4
. BRACHIAL WITHDRAWAL
-
FEMORAL SITE
FIG. 2. Renal blood flows calculated from fast withdrawal specimens at brachial and femoralSites were lower (P < 0.005) than those calculated from slow withdrawal specimens.
MICROSPHERE ERROR
381
femoral values were compared to slow brachial values (7.00 + 2.81 vs 6.76 + 1.84 ml/mm. g) or when fast femoral values were compared to fast brachial values (4.44 ? 1.50 vs 4.32 ? 1.16 myming). RBF calculated from all fast collections was compared to RBF calculated from all slow collections. Mean RBF from fast withdrawal specimens (4.38 ? 1.28 ml/min g) was significantly less (P < 0.005) than that calculated from slow withdrawal specimens (6.87 + 2.29 ml/mine g). Mean RBF calculated from fast withdrawals is more consistent with previous data published by this laboratory and with generally accepted values for RBF in anesthetized dogs. The relationship is illustrated in Fig. 3. It should be noted that both kidneys or, for that matter, all organs demonstrated the same relationship. The reason for this is clear if Eq. [l] is considered. Any change in the reference sample multiplier (sample withdrawal rate/disintegrations per minute in reference sample) would be reflected in the same proportion in all organs. In an additional comparison, we examined the 16 pairs of reference samples that were excluded from the above analysis because greater than 2% of total radioactivity was contained in the last vial collected. In these excluded specimens, the mean radioactivity in the last vial was only 8.3 + 6.8% of total radioactivity. In addition, no correlation whatsoever existed between calculated RBF and percentage total counts in the last vial suggesting that collections were in fact complete even in these instances. Statistical analysis including all 42 pairs confirmed the effect of withdrawal rate at the P < 0.005 level. DISCUSSION The higher values for RBF calculated from reference samples withdrawn at slower rates are the result of a lower than expected number of microspheres per 13r
1’
SLOW (5 ml bin)
FAST (13mVmm)
FIG. 3. Individual values of RBF calculated from reference samples obtained simultaneously at fast and slow withdrawal rates. Results from brachial and femoral arterial samples are combined.
382
MOORE
ET AL.
unit volume of reference blood. As shown by Buckberg ef al. (1) it is unlikely that this effect is due to a smaller absolute number of microspheres in the samples. Decreasing the number of microspheres in a reference sample may increase the variability of calculated blood flow, but should not consistently elevate mean values. A relative decrease in microsphere concentration in a peripheral reference sample would occur if microspheres were present in uncollected and uncounted blood, such as that present in the collecting tubing at the end of a sample withdrawal period. This obvious source of error was avoided in our experiments by making certain that no radioactivity (less than 2% of total) was present in the last vial sampled. Since incomplete collection did not occur, the most likely explanation for our observations is related to the flow properties of microspheres in the peripheral circulation. Microsphere distribution in both large and small vessels differs from that of the red blood cell (4). Microspheres tend to be concentrated in greater than expected numbers in areas of maximal blood flow velocity such as the center of a mediumsized artery (10) or the largest vessel of a branching network, e.g., the interlobular arteries of the kidney (9). An ex vivo model of this phenomenon scaled to the capillary circulation has been developed by Yen and Fung (13). While this effect appears to diminish as the size of the microsphere approaches that of the erythrocyte, the distribution of nondeformable plastic spheres can only approximate that of deformable ellipsoid red blood cells with dimensions of 2 x 7~m. We propose that inappropriately slow withdrawal of a reference sample from a cannulated peripheral vessel induces a nonhomogeneous distribution of microspheres along velocity streamlines. Such a phenomenon will predictably result in a relative paucity of spheres in the slower channel (the reference catheter) and an increased concentration in the more proximal branches of the ligated and cannulated vessel. Although the exact relationship between vessel blood flow velocity and the amount of nonhomogeneous streaming of microspheres is not known, it would seem prudent that investigations utilizing microsphere measurement of regional blood flow carefully consider the rate of sample collection to minimize the effects of velocity mismatching on microsphere behavior. These factors would be particularly important if vessel flow rates changed appreciably in the course of the experiment. ACKNOWLEDGMENTS We gratefully acknowledge the assistance of Ann Lackey in the preparation of this manuscript.
REFERENCES 1. BUCKBERG, G., LUCK, J. C., PAYNE, D. B., HOFFMAN, J. I. E., ARCHIE, J. P., AND FIXLER,
D. E.
(1971). Some sources of error in measuring regional blood flow with radioactive microspheres. J. Appl. Physiol.
31, 598-604.
S. A. (1979). Sympathetic modulation of hypercapnic cerebral vasodilation in dogs. Circ. Res., 45, 771-785. 3. DOMENECH, R. J., HOFFMAN, J. I. E., NOBLE, M. I. M., et al. (1969). Total and regional coronary blood flow measured by radioactive microspheres in conscious and anesthetized dogs. Circ. Res., 25, 581-5%. 2. D’ALECY,
L. G., ROSE, C. J., AND SELLERS,
MICROSPHERE
ERROR
383
4. HALES, J. R. S., AND CLIFF, W. J. (1976). Direct observations of the behavior of microspheres in microvasculature. Bib/. Anat., 15, 87-91. 5. HEYMANN, M., PAYNE, B. D., HOFFMAN, J. I. E., AND RUDOLPH, A. M. (1977). Blood flow measurements with radionuclide-labeled particles. Progr. Cardiovasc. Dis., 20, 55-79. 6. KAIHARA, S., RUTHERFORD, R. B., SCHWENTRER, E. P., AND WAGNER, H. N., JR. (1%9). Distribution of cardiac output in experimental hemorrhagic shock in dogs. J. Appl. Physiol., 27, 218-222. 7. KAIHARA, S., VAN HEERDEN, P. D., MIGITA, T., AND WAGNER, H. N., JR. (1968). Measurement of distribution of cardiac output. J. Appl. Physiol., 25, 696-700. 8. MAKOWSKI, E., GIACOMO, M., DROEGEMUELLER, W., AND BA~~AGLIA, F. (1968). Measurement of umbilical arterial blood flow to the sheep placenta and fetus in utero. Circ. Res., 23,623-63 1. 9. MORKRID, L., OFSTAD, J., AND WILLASSEN, Y. (1976). Effect of steric restriction on the intracortical distribution of microspheres in the dog kidney. Circ. Res., 39, 608-615. 10. PHIBBS, R., AND DONG, L. (1970). Nonuniform distribution of microspheres in blood flowing through a medium-sized artery. Canad. .I. Physiol. Pharmacol., 48, 415-421. 11. RUDOLPH, A. M., AND HEYMANN, M. A. (1%7). Circulation of the fetus in utero: Methods for studying distribution of blood flow, cardiac output and organ blood flow. Circ. Res., 21, 163. 12. WARREN, D., AND LEDINGHAM, J. G. G. (1974). Measurement of cardiac output distribution using microspheres. Some practical and theoretical considerations. Cardiovasc. Res., 8, 570-581. 13. YEN, R. T., AND FUNG, Y. C. (1978). Effect of velocity distribution in capillary blood vessels on red cell distribution. Amer. J. Physiol., 235, H251-H257.