JOURNAL
OF SURGICAL
RESEARCH
26, 1-9 (1979)
Effect of Flow Rate and Vessel Calibre WESLEY SMOORE, Department
of Surgery
M.D.,FACS,2
on Critical
AND JAMES
Arterial
M. MALONE,
of the University of Arizona, College of Medicine,
Stenosis1
M.D.
Tucson, Arizona
85724
Submitted for publication March 28, 1978 Critical arterial stenosis, the decrease in lumenal cross-sectional area which is associated with a 10% decrease in flow rate, is not a fixed number but varies directly with the size (cross-sectional area) of the artery and inversely with the flow rate for each vessel being evaluated. Percent changes in blood pressure distal to the lumenal stenosis were found to correlate exactly with percent changes in blood flow. In other words, measurement of distal extremity blood pressure provides a statistically reliable assessment of changes in distal extremity blood flow. The value of arteriography as the sole criterion in the assessment of significant atherosclerotic lesions is limited. The utilization of noninvasive vascular diagnostic equipment is emphasized based upon the demonstration that distal extremity blood pressure is a statistically significant predictor of distal extremity blood flow.
lumenal cross-sectional area [4]. This pressure-flow relationship was also demonstrated in experimental studies by Killen and Oh [2] and more recently by Flanigan et ul. [I]. The previously published pressure-flow studies were performed with external arterial constriction, in contrast to clinical atherosclerosis which produces interlumenal narrowing. We have previously reported data suggesting a relationship between flow rate, arterial calibre, and critical stenosis [7, 91. The purpose of this report is to describe an experimental mode in which the pressure-flow relationships of progressive arterial narrowing could be studied using intralumenal stenotic lesions and to determine whether critical arterial stenosis is a fixed value or is variable depending upon anatomic location, vessel calibre, and flow-rate demand.
In 1938, Mann and co-workers demonstrated that a significant reduction in the cross-sectional area of a carotid artery could occur before there was a reduction in blood flow [3]. The cross-sectional area of the lumen could be reduced as much as 50% without any change in blood flow, and as much as 90% before a 50% reduction of blood flow occurred. However, once the reduction in lumenal cross-sectional area approached “critical stenosis,” any small increment of narrowing produced a precipitous drop in flow. More recently, May and co-workers demonstrated that critical arterial stenosis was also influenced by the rate of baseline flow through the artery being studied. These authors also studied the pressure-flow relationship with progressive arterial stenosis accomplished by external constriction. They confirmed Mann’s original findings and also demonstrated that the curves for percentage change in distal blood pressure followed the curves for percentage change in flow when compared to the effective
MATERIALS
AND METHODS
Twenty-two mongrel dogs, with an average weight of 18 kg, were anesthetized with intravenous pentobarbital, and intubated, but allowed to breathe spontaneously. The dogs were divided into two groups of 11 dogs each. Group 1 was used
’ This study is supported in part by research funds from the Veterans Administration. 2 Address correspondence to Wesley S. Moore, M.D., Professor and Head, Section of Vascular Surgery, Arizona Health Sciences Center, Tucson, Arizona 85724. 1
0022-4804/79/010001-09$01.00/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
2
JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY
Aorta
I I
JI
Renal A.
I Iliac A.
FIG. 1. An artist’s conception of the experimental pressure-flow model employing the abdominal aorta. This graphically demonstrates the coupling insertion permitting the addition of intralumenal stenoses. The positions of the flow probe, pressure catheters, and arteriovenous fistulae for selectively increasing flow rates are also demonstrated.
to study the pressure-flow relationships of progressive intralumenal arterial stenosis of the abdominal aorta. Group 2 was used to study the same parameters in the iliac artery. GROUP 1: ABDOMINAL
AORTA
Through a midline abdominal incision, the aorta was mobilized from the renal arteries to the aortic trifurcation. The inferior mesenteric artery and all lumbar branches were divided and ligated. The left renal artery was divided and its proximal portion cannulated with a PE 190 polyethylene catheter which was used to record the proximal aortic arterial pressure. The internal iliac and middle sacral vessels were divided and ligated. A second PE 190 catheter was inserted into the proximal portion of one of the divided internal iliac arteries and was utilized to monitor distal aortic arterial pressure. Both arterial catheters were connected to Statham arterial pressure transducers and
1979
the transducer outputs were recorded on a Grass Model 8 polygraph. All animals were systemically heparinized (l-2 mg/kg) prior to the insertion of the pressure cannulas. In order to provide a method for increasing flow rates through the same artery (an exercise analog), three distal arteriovenous fistulae were established between the following vessels: the right iliac artery and vein, the left iliac artery and vein, and the middle sacral artery and vena cava. The arteriovenous fistulae were constructed by interconnecting the appropriate artery and vein with polyethylene cannulas. Flow rates through the abdominal aorta could then be increased in three increments by opening first one, then two, and finally all three arteriovenous fistulae (Fig. 1). The abdominal aorta was next divided, a short length resected, and a coupling fitting was inserted into both the proximal and distal ends of the aorta. The coupling fittings were secured in place with external ligatures. The couplings were machined from solid Teflon, and both the cross-sectional area and the wall thickness were carefully designed so that no narrowing of the abdominal aortic lumen was produced by the coupling device. The outer end of each coupling fitting could be bridged by inserting a Teflon tube held in place by friction. By changing the series of bridging tubes with tubes of progressively diminishing crosssectional area, stepwise lumenal stenosis of the abdominal aorta could be created (Figs. 2a-c). Blood flows through the abdominal aorta were measured with a Biotronics alternating square-wave electromagnetic flowmeter. The noncannulating flow probe was placed proximal to the coupling device on the abdominal aorta. Following calibration by occlusive zero, baseline flows and proximal and distal aortic blood pressures were obtained at each of three increasingly larger flow rates. The three flow rates were produced by opening one, two, and then three of our artificial arteriovenous fistulae. Once a stable baseline was obtained for each flow condition being analyzed, a series of pro-
FIG. 2. (a) A close-up view of the arterial coupling device bridged by a Teflon tube. (b) The appearance of the coupling device separated from the Teflon tube. (c) This illustrates the progression of Teflon tubes simulating intralumenal stenosis.
of the abdominal aorta, including the internal iliac and middle sacral vessels, were divided and ligated. The right femoral artery and vein were exposed through a vertical inguinal incision. The inguinal ligament was transected and the femoral artery was mobilized proximally until it was in free continuity with the abdominally exposed portion of the external iliac artery. A proximal arterial pressure line was placed through a divided lumbar artery. A distal arterial pressure line was inserted into a lateral branch of the external iliac artery in a manner so as not to obstruct blood flow in the main vessel. The right external iliac artery was then divided in its midportion and a short segment of artery excised so that a coupling fitting, which was similar in design to the aortic model but appropriate in size GROUP 2: ILIAC ARTERY to the iliac artery, could be inserted. A In this group of experimental animals, the Biotronics electromagnetic flow probe was aortoiliac system was mobilized. All branches then placed on the external iliac artery disgressively smaller tubes were inserted into the aortic coupling device so as to simulate intralumenal stenosis. Flow readings were continued until the flow rate fell to zero. Each of the three conditions of flow were studied in an identical manner. Following completion of the flow measurements, a cast of the abdominal aorta was made using plastic foam in order to obtain an accurate measurement of the cross-sectional lumenal area of the abdominal aorta. The percentage of stenosis to aortic flow that each bridging tube represented was determined by expressing the cross-sectional area of the bridging tube as a percentage of the crosssectional area of the aorta of each experimental animal.
4
JOURNAL
OF SURGICAL
RESEARCH:
VOL. 26, NO. 1, JANUARY
1979
Flow Probe
“.~W...‘,
ligament \\ \i fern0 Arte -V Fistula b
Vein
y
FIG. 3 (a) This is an intraoperative photograph showing the iliac artery stenosis model. The coupling device has been placed, the pressure cannulas are located proximal and distal to the stenosis, and an arterial flow probe, connected to a flowmeter, is visualized. (b) An artist’s conception of the experimental model used to demonstrate pressure-flow relationships in the iliac artery with progressive intrahtmenal stenoses. The locations of the pressure cannulas, arteriovenous fistula, and flow probe are demonstrated.
tal to the coupling device. As with the Group I animals, changes in the cross-sectional diameter of the coupling bridge tubes simu-
lated external iliac artery stenoses. A distal arteriovenous fistula was created by interconnecting the lateral branch of the femoral
FIG. 4. This is a foam cast removed from the lumen of the iliac artery which was used to measure the intralumenal cross-sectional area of the vessel. A series of indentations on the cast were done to demonstrate the effect of various contours of the vessel.
MOORE AND MALONE: CRITICAL ARTERIAL
5
STENOSIS
AORTA - 2 A-V FISTULAS
80 3
70 -
m 0\o 3020 15’ 100 90
’ ’ 80 70
’ 60
’ 50
40
30
20
IO
0
% CROSS SECTIONAL AREA FIG. 5. This graph presents the percentage of baseline flow on the ordinate as a function of diminishing crosssectional area represented on the abscissa. The curve fitted to the scattergram and method of calculating critical arterial stenosis corresponding to a 10% reduction in blood flow are illustrated.
artery and a corresponding branch of the fitted to each set of data. Critical arterial femoral vein with a polyethylene catheter stenosis was defined as occurring when (Figs. 3a and b). This system was then pro- there was a 10%drop in blood flow. The pervided for two flow rates through the iliac centage of available lumen (unobstructed artery, which consisted of a baseline flow lumenal cross-sectional area) at which this and an augmented flow rate that was provided with the addition of the distal arterioILIAC ARTERY venous fistula. The sequence of measurements was identical to the aortic series and loom Too upon completion of each experiment, a cast 90 of the iliac artery was made to ascertain 60 PRESSURE% its lumenal cross-sectional area (Fig. 4). 70 2 FLOW . . . . . . . . . . .
1 60
METHODS
OF DATA ANALYSIS
For each of the three aortic flow rates and each of the two iliac flow rates, both percentage change in distal blood pressure and percentage change in blood flow were plotted as a function of decreasing percentage of unobstructed lumenal cross-sectional area. The data ‘for each of the five given flow rates were pooled from each individual experiment, and the resulting graphic plots produced scattergrams. Each scattergram for each respective flow rate was carefully analyzed, and a curve was visually
50
: 40
f
30 t 20 ,5 I 100 90
8 2 m .\"
ii 30
I I I I I I 60 70 60 50 40 30
I I 20 IO
; 20 ,5 0
% CROSS SECTIONAL AREA
6. This is a composite graph .illustrating the effect of reducing cross-sectional area on the percentage of baseline flow and the percentage of systemic pressure. It should be noted that the blood-pressure curve exactly .coincides with the blood-flow curve, indicating that critical arterial stenosis has an identical effect on pressure drop, as well as on blood flow, in the iliac artery model. FIG.
6
JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY AORTA - 3 A-V FISTULAS 100.
8 g
60-
g so0 d 40$
30-
100 SO 60 70 60 50 40 30 20 IO 0 % CROSS SECTIONAL
AREA
1979
peared to be linearly related. This relationship was then further defined by plotting the percentage drop in distal blood pressure as a function of the percentage drop in flow for the pooled experimental data for each flow rate and specific artery. These pressure-flow curves were then subjected to a t test analysis for linear correlation and determination of the slope of the regression line. RESULTS
The mean internal diameter of 11 iliac arteries was 5.24 mm (SD = 0.57). The pressure-flow relationship as a function of cross-sec- mean internal diameter of 11 aortas was 7.76 tional area in the aortic model with maximum flow employing three arteriovenous fistulae. It should be noted mm (SD = 0.73). The percentage of lumenal stenosis that that critical arterial stenosis occurs with less-comproresulted in a 10% reduction of blood flow mised cross-sectional area in this high-flow situation and that the configuration of the pressure curve is and a 10% drop in distal arterial blood presidentical to the flow curve, once again indicating that sure for each condition of flow in the aorta critical arterial stenosis can be inferred and that the extent of blood flow compromised can be measured by and iliac arteries is summarized in Table 1. The value of critical arterial stenosis under the distal blood pressure drop. each set of flow conditions was found to be flow rate occurred was determined by evalu- identical, whether calculated by pressure ating our data with distal pressure and distal gradient or change in blood flow. Not only blood flow plotted simultaneously as a func- did critical stenosis as measured by pertion of decreasing unobstructed lumenal centage change in blood flow or percentage cross-sectional area. Extension of a per- change in distal blood pressure coincide for pendicular line from the 90% flow rate to a specific point, but the curves for percentthe abscissa, which represented percentage age change in a blood flow vs. lumenal of unobstructed lumenal cross-sectional stenosis are identical for each flow rate area, resulted in a determination of a numeri- and artery studied (Figs. 6 and 7). This cal value for critical arterial stenosis. An linear correlation suggested that percentage example of this process is shown in Fig. 5. In of compromise in blood flow could be ina similar manner, the percentage of critical TABLE 1 arterial stenosis which resulted in a 10% DETERMINATION OF CRITICAL STENOSIS drop inflow was measured for each flow rate in each of the two arteries studied. Critical stenosis Critical stenosis In order to evaluate the relationship beAVWSp determinedby detemtinedby 10%dmp blood 10%drop tween percentage change in distal blood Conditionof Row in flow in pressure pressure and percentage change in distal meaS”rement (mUmin) Pm Pa blood flow with respect to progressive lu144 Iliac artery 8s 86 menal stenosis, both percentage change in Iliac artcry + one A-V distal blood pressure and percentage change 456 75 74 fistula in blood flow were plotted simultaneously Aorta + one A-V tistuh 314 86 86 as a function of decreasing percentage of Aorta + two unobstructed lumenal cross-sectional area 79 A-V fistulae 593 79 (Figs. 6 and 7). The percentage changes in Aorta + thme A-V fistulae 886 73 73 distal blood pressure and in blood flow apFIG. 7. This is a compound graph presenting the
MOORE
AND MALONE:
CRITICAL
ARTERIAL
STENOSIS
7
area (,rrr2) is an exponential function of the radius, it would be expected that small COMPARISON OF THE PERCENTAGE CHANGE OF BLOOD changes in diameter would cause signifiPRESSURE DECREASE AS A FUNCTION OF BLOOD-FLOW DECREASE cantly larger changes in cross-sectional area. From Table 1 it can be seen that at PerCentage of confidence flow rates of 144 and 314 ml/min for the Slopeof f Value of linear for Conditionof regression iliac artery and aorta, respectively, that the correlation linearity line lttG3S”EItle”t critical stenosis for both arteries was 85 to 99.9 1.01 27.8 Iliac artery 86%. Since the aortic flow rate is 2.2 times Iliac artery the comparable iliac flow rate, one would + one A-V 43.0 99.9 I .25 fistula expect the aortic critical stenosis to be less Aorta + one than 85 to 86%, since critical stenosis varies 30.8 99.9 0.74 A-V listula Aorta + two inversely with flow rate. However, the aorta 99.9 22.7 0.85 A-V fistulae has 1.48 times the mean diameter of the Aorta + three 19.7 99.9 0.90 A-V fist&e iliac artery, and therefore 2.2 times the effective cross-sectional area of the compaferred by measuring the percentage reduc- rable iliac artery. The increase in effective tion of the distal blood pressure. In order aortic cross-sectional diameter (2.2 times to test this hypothesis, the percentage pres- the comparable iliac artery diameter) is sure reduction was graphically plotted as a exactly matched by the increased aortic function of percentage flow reduction for flow compared to the iliac artery flow (aortic each of the five conditions of vessel size flow is 2.2 times the comparable iliac flow). and flow. These data were subjected to linear regression analysis; the slope for each DISCUSSION line was measured, and a t test as a measThe results of the study indicate that urement of linear correlation was determined. These data are summarized in Table critical arterial stenosis is not a constant number but varies directly with the effec2. The percentage of confidence for linearity for each pair of data exceeded 99.9%, and tive cross-sectional area of the artery and the slopes of the five lines approached unity, inversely with the flow rate. This is of particindicating that a one-to-one relationship be- ular clinical importance in trying to recontween percentage flow reduction and per- cile lesions demonstrated by angiography centage blood-pressure drop existed. There- with symptoms of arterial insufficiency. fore, percentage change in distal arterial Thus, a lesion producing a particular reducpressure is a statistically accurate predictor tion in cross-sectional area for a large artery may not result in any compromise of percentage change in blood flow. The value for critical arterial stenosis in blood flow, but the same percentage rewithin the same vessel changed for each duction in cross-sectional area of a smaller separate flow rate and was found to be in- vessel may exceed the critical stenosis level versely proportional to flow rate. As the for that artery. Similarly, with augmented flow rate increased, the amount of lumenal flows through a specified artery such as cross-sectional area reduction required to might occur with exercise, a stenosis that produce a critical stenosis decreased (Table was insignificant at basal flows may become 1). For example, with a baseline flow aver- quite significant at the higher flow demand aging 314 ml/min, the critical stenosis was and result in symptoms of arterial insuf86% for the abdominal aorta; however, ficiency. Our data support those of Young when the aortic flow was increased to 886 et al. who reach similar conclusions remYmin, the critical stenosis was decreased garding the relationships of blood flow and clinical arterial stenoses [lo]. to 73%. Since the numerical value of critical arSince the calculation of cross-sectional TABLE
2
8
JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY
terial stenosis varies with both lumenal cross-sectional area and flow rate, the use of angiography as a sole criterion for judging the physiological significance of any arterial lesion would appear to be quite limited. This limitation of angiography has been partially improved upon by the utilization of two plane angiography. However, since symptoms of arterial insufficiency are often exercise-induced and therefore related to the dynamics of blood flow, any static test such as angiography has only limited value. Nonetheless, two-plane angiography is mandatory both to visually identify lesions in the arterial tree and to plan appropriate reconstructive procedures. Clearly, the best method for evaluating the significance of a lesion or a series of lesions in the arterial tree would be the actual measurements of flow rates, not only at rest, but also under conditions requiring augmented flows, such as exercise. Since these measurements cannot be performed with noninvasive methods such testing is not practical. A solution to this dilemma can be found in the linear relationship of distal blood pressure response to changes in distal blood flow as demonstrated in this study. Percentage change in distal blood pressure was shown to be a statistically reliable predictor of percentage change in distal blood flow. Therefore, noninvasive measurement of distal blood pressure at the malleolar level, both at rest and following exercise, together with measurement of systemic blood pressure at the brachial artery level, will allow calculation of the percentage pressure drop in the legs, both at rest and after exercise. According to this study, the percentage pressure drop is equal to the percentage reduction in arterial flow. Distal ankle pressure measurement is of additional value since the pressure-flow correlation is valid not only at basal conditions, but also under conditions requiring augmented blood flow (exercise). On occasion it may be difficult to evaluate the contribution of lesions proximal to the common femoral artery when it is known that stenotic lesions also exist distal to the
1979
common femoral artery. Either proximal or distal lesion or the combined lesions in series may result in a blood pressure drop measured at the malleolar level. Discrimination of the individual lesions contributing to blood-flow reduction can be ascertained by utilizing direct femoral pressure studies with exercise. This technique, which we have previously described, would help to differentiate the significance of proximal vs distal lesions and would influence the clinical decision of whether or not a proximal reconstructive procedure should be performed prior to or instead of a distal arterial repair [6]. However, due to the fact that direct femoral pressure measurement is an invasive procedure, its usefulness as a practical clinical tool is limited. Another approach to the evaluation of proximal lesions is the utilization of the Doppler flowmeter to record femoral artery wave forms at rest and after exercise. There is an accumulating body of evidence which suggests that some type of arterial waveform analysis or other noninvasive parameter may permit separation of proximal obstructing arterial lesions from distal lesions in evaluating overall hemodynamic compromise [8]. Obviously, distal repairs such as femoral-popliteal bypass done in the presence of aortoiliac disease are at higher risk for thrombosis. It is usually recommended that inflow problems be corrected prior to repair or reconstruction of more distal lesions. REFERENCES Flanigan D. P., Tullis, J. P., Streeten, V. L., et al. Multiple subcritical arterial stenoses: Effect on poststenotic pressure and flow. Ann. Surg. 186: 663-668, 1977. Killen, D. A., and Oh, S. U. Quantitation of the severity of arterial stenosis by pressure gradient measurement. Amer. Surg. 34: 341-349, 1968. Mann, F. C., Herrick, J. F., Essex, H. E., and Baldes, E. J. Effect on blood flow of decreasing lumen of blood vessel. Surgery 4: 249-252, 1938. May, A. G., DeWeese, J. A., and Rob, C. G. Hemodynamic effects of arterial stenosis. Surgery 53: 513-524, 1963.
MOORE AND MALONE: CRITICAL ARTERIAL 5. May, A. G., Van De Berg, L. V., DeWeese, J. A., and Rob, C. G. Critical arterial stenosis. Surgery 54: 250-259, 1963. 6. Moore, W. S., and Hall, A. D. Unrecognized aortoiliac stenosis: A physiologic approach to the diagnosis. Arch. Surg. 103: 633-638, 1971. 7. Moore, W. S., Sydorak, G. H., Newcomb, L., and Campagna, G. Blood pressure gradient to estimate flow changes with progressive arterial stenosis. Surg. Forum 24; 248-250, 1973. 8. Rutherford, R. B., Hiatt, W. R., and Kreutzer,
STENOSIS
9
E. W. The use of velocity wave form analysis in the diagnosis of carotid artery occlusive disease. Surgery 82: 695-702, 1977. 9. Sydorak, G. R., Moore, W. S., Newcomb, L., et al. Effect of increasing flow rates and arterial caliber on critical arterial stenoses. Surg. Forum 23: 243-244, 1972. 10. Young, D. F., Cholvin, N. R., and Roth, A. C. Pressure drop across artificially induced stenoses in the femoral arteries of dogs. Circ. Res. 36: 735-743, 1975.
OF SURGICAL
RESEARCH
26, 1-9 (1979)
Effect of Flow Rate and Vessel Calibre WESLEY SMOORE, Department
of Surgery
M.D.,FACS,2
on Critical
AND JAMES
Arterial
M. MALONE,
of the University of Arizona, College of Medicine,
Stenosis1
M.D.
Tucson, Arizona
85724
Submitted for publication March 28, 1978 Critical arterial stenosis, the decrease in lumenal cross-sectional area which is associated with a 10% decrease in flow rate, is not a fixed number but varies directly with the size (cross-sectional area) of the artery and inversely with the flow rate for each vessel being evaluated. Percent changes in blood pressure distal to the lumenal stenosis were found to correlate exactly with percent changes in blood flow. In other words, measurement of distal extremity blood pressure provides a statistically reliable assessment of changes in distal extremity blood flow. The value of arteriography as the sole criterion in the assessment of significant atherosclerotic lesions is limited. The utilization of noninvasive vascular diagnostic equipment is emphasized based upon the demonstration that distal extremity blood pressure is a statistically significant predictor of distal extremity blood flow.
lumenal cross-sectional area [4]. This pressure-flow relationship was also demonstrated in experimental studies by Killen and Oh [2] and more recently by Flanigan et ul. [I]. The previously published pressure-flow studies were performed with external arterial constriction, in contrast to clinical atherosclerosis which produces interlumenal narrowing. We have previously reported data suggesting a relationship between flow rate, arterial calibre, and critical stenosis [7, 91. The purpose of this report is to describe an experimental mode in which the pressure-flow relationships of progressive arterial narrowing could be studied using intralumenal stenotic lesions and to determine whether critical arterial stenosis is a fixed value or is variable depending upon anatomic location, vessel calibre, and flow-rate demand.
In 1938, Mann and co-workers demonstrated that a significant reduction in the cross-sectional area of a carotid artery could occur before there was a reduction in blood flow [3]. The cross-sectional area of the lumen could be reduced as much as 50% without any change in blood flow, and as much as 90% before a 50% reduction of blood flow occurred. However, once the reduction in lumenal cross-sectional area approached “critical stenosis,” any small increment of narrowing produced a precipitous drop in flow. More recently, May and co-workers demonstrated that critical arterial stenosis was also influenced by the rate of baseline flow through the artery being studied. These authors also studied the pressure-flow relationship with progressive arterial stenosis accomplished by external constriction. They confirmed Mann’s original findings and also demonstrated that the curves for percentage change in distal blood pressure followed the curves for percentage change in flow when compared to the effective
MATERIALS
AND METHODS
Twenty-two mongrel dogs, with an average weight of 18 kg, were anesthetized with intravenous pentobarbital, and intubated, but allowed to breathe spontaneously. The dogs were divided into two groups of 11 dogs each. Group 1 was used
’ This study is supported in part by research funds from the Veterans Administration. 2 Address correspondence to Wesley S. Moore, M.D., Professor and Head, Section of Vascular Surgery, Arizona Health Sciences Center, Tucson, Arizona 85724. 1
0022-4804/79/010001-09$01.00/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
2
JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY
Aorta
I I
JI
Renal A.
I Iliac A.
FIG. 1. An artist’s conception of the experimental pressure-flow model employing the abdominal aorta. This graphically demonstrates the coupling insertion permitting the addition of intralumenal stenoses. The positions of the flow probe, pressure catheters, and arteriovenous fistulae for selectively increasing flow rates are also demonstrated.
to study the pressure-flow relationships of progressive intralumenal arterial stenosis of the abdominal aorta. Group 2 was used to study the same parameters in the iliac artery. GROUP 1: ABDOMINAL
AORTA
Through a midline abdominal incision, the aorta was mobilized from the renal arteries to the aortic trifurcation. The inferior mesenteric artery and all lumbar branches were divided and ligated. The left renal artery was divided and its proximal portion cannulated with a PE 190 polyethylene catheter which was used to record the proximal aortic arterial pressure. The internal iliac and middle sacral vessels were divided and ligated. A second PE 190 catheter was inserted into the proximal portion of one of the divided internal iliac arteries and was utilized to monitor distal aortic arterial pressure. Both arterial catheters were connected to Statham arterial pressure transducers and
1979
the transducer outputs were recorded on a Grass Model 8 polygraph. All animals were systemically heparinized (l-2 mg/kg) prior to the insertion of the pressure cannulas. In order to provide a method for increasing flow rates through the same artery (an exercise analog), three distal arteriovenous fistulae were established between the following vessels: the right iliac artery and vein, the left iliac artery and vein, and the middle sacral artery and vena cava. The arteriovenous fistulae were constructed by interconnecting the appropriate artery and vein with polyethylene cannulas. Flow rates through the abdominal aorta could then be increased in three increments by opening first one, then two, and finally all three arteriovenous fistulae (Fig. 1). The abdominal aorta was next divided, a short length resected, and a coupling fitting was inserted into both the proximal and distal ends of the aorta. The coupling fittings were secured in place with external ligatures. The couplings were machined from solid Teflon, and both the cross-sectional area and the wall thickness were carefully designed so that no narrowing of the abdominal aortic lumen was produced by the coupling device. The outer end of each coupling fitting could be bridged by inserting a Teflon tube held in place by friction. By changing the series of bridging tubes with tubes of progressively diminishing crosssectional area, stepwise lumenal stenosis of the abdominal aorta could be created (Figs. 2a-c). Blood flows through the abdominal aorta were measured with a Biotronics alternating square-wave electromagnetic flowmeter. The noncannulating flow probe was placed proximal to the coupling device on the abdominal aorta. Following calibration by occlusive zero, baseline flows and proximal and distal aortic blood pressures were obtained at each of three increasingly larger flow rates. The three flow rates were produced by opening one, two, and then three of our artificial arteriovenous fistulae. Once a stable baseline was obtained for each flow condition being analyzed, a series of pro-
FIG. 2. (a) A close-up view of the arterial coupling device bridged by a Teflon tube. (b) The appearance of the coupling device separated from the Teflon tube. (c) This illustrates the progression of Teflon tubes simulating intralumenal stenosis.
of the abdominal aorta, including the internal iliac and middle sacral vessels, were divided and ligated. The right femoral artery and vein were exposed through a vertical inguinal incision. The inguinal ligament was transected and the femoral artery was mobilized proximally until it was in free continuity with the abdominally exposed portion of the external iliac artery. A proximal arterial pressure line was placed through a divided lumbar artery. A distal arterial pressure line was inserted into a lateral branch of the external iliac artery in a manner so as not to obstruct blood flow in the main vessel. The right external iliac artery was then divided in its midportion and a short segment of artery excised so that a coupling fitting, which was similar in design to the aortic model but appropriate in size GROUP 2: ILIAC ARTERY to the iliac artery, could be inserted. A In this group of experimental animals, the Biotronics electromagnetic flow probe was aortoiliac system was mobilized. All branches then placed on the external iliac artery disgressively smaller tubes were inserted into the aortic coupling device so as to simulate intralumenal stenosis. Flow readings were continued until the flow rate fell to zero. Each of the three conditions of flow were studied in an identical manner. Following completion of the flow measurements, a cast of the abdominal aorta was made using plastic foam in order to obtain an accurate measurement of the cross-sectional lumenal area of the abdominal aorta. The percentage of stenosis to aortic flow that each bridging tube represented was determined by expressing the cross-sectional area of the bridging tube as a percentage of the crosssectional area of the aorta of each experimental animal.
4
JOURNAL
OF SURGICAL
RESEARCH:
VOL. 26, NO. 1, JANUARY
1979
Flow Probe
“.~W...‘,
ligament \\ \i fern0 Arte -V Fistula b
Vein
y
FIG. 3 (a) This is an intraoperative photograph showing the iliac artery stenosis model. The coupling device has been placed, the pressure cannulas are located proximal and distal to the stenosis, and an arterial flow probe, connected to a flowmeter, is visualized. (b) An artist’s conception of the experimental model used to demonstrate pressure-flow relationships in the iliac artery with progressive intrahtmenal stenoses. The locations of the pressure cannulas, arteriovenous fistula, and flow probe are demonstrated.
tal to the coupling device. As with the Group I animals, changes in the cross-sectional diameter of the coupling bridge tubes simu-
lated external iliac artery stenoses. A distal arteriovenous fistula was created by interconnecting the lateral branch of the femoral
FIG. 4. This is a foam cast removed from the lumen of the iliac artery which was used to measure the intralumenal cross-sectional area of the vessel. A series of indentations on the cast were done to demonstrate the effect of various contours of the vessel.
MOORE AND MALONE: CRITICAL ARTERIAL
5
STENOSIS
AORTA - 2 A-V FISTULAS
80 3
70 -
m 0\o 3020 15’ 100 90
’ ’ 80 70
’ 60
’ 50
40
30
20
IO
0
% CROSS SECTIONAL AREA FIG. 5. This graph presents the percentage of baseline flow on the ordinate as a function of diminishing crosssectional area represented on the abscissa. The curve fitted to the scattergram and method of calculating critical arterial stenosis corresponding to a 10% reduction in blood flow are illustrated.
artery and a corresponding branch of the fitted to each set of data. Critical arterial femoral vein with a polyethylene catheter stenosis was defined as occurring when (Figs. 3a and b). This system was then pro- there was a 10%drop in blood flow. The pervided for two flow rates through the iliac centage of available lumen (unobstructed artery, which consisted of a baseline flow lumenal cross-sectional area) at which this and an augmented flow rate that was provided with the addition of the distal arterioILIAC ARTERY venous fistula. The sequence of measurements was identical to the aortic series and loom Too upon completion of each experiment, a cast 90 of the iliac artery was made to ascertain 60 PRESSURE% its lumenal cross-sectional area (Fig. 4). 70 2 FLOW . . . . . . . . . . .
1 60
METHODS
OF DATA ANALYSIS
For each of the three aortic flow rates and each of the two iliac flow rates, both percentage change in distal blood pressure and percentage change in blood flow were plotted as a function of decreasing percentage of unobstructed lumenal cross-sectional area. The data ‘for each of the five given flow rates were pooled from each individual experiment, and the resulting graphic plots produced scattergrams. Each scattergram for each respective flow rate was carefully analyzed, and a curve was visually
50
: 40
f
30 t 20 ,5 I 100 90
8 2 m .\"
ii 30
I I I I I I 60 70 60 50 40 30
I I 20 IO
; 20 ,5 0
% CROSS SECTIONAL AREA
6. This is a composite graph .illustrating the effect of reducing cross-sectional area on the percentage of baseline flow and the percentage of systemic pressure. It should be noted that the blood-pressure curve exactly .coincides with the blood-flow curve, indicating that critical arterial stenosis has an identical effect on pressure drop, as well as on blood flow, in the iliac artery model. FIG.
6
JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY AORTA - 3 A-V FISTULAS 100.
8 g
60-
g so0 d 40$
30-
100 SO 60 70 60 50 40 30 20 IO 0 % CROSS SECTIONAL
AREA
1979
peared to be linearly related. This relationship was then further defined by plotting the percentage drop in distal blood pressure as a function of the percentage drop in flow for the pooled experimental data for each flow rate and specific artery. These pressure-flow curves were then subjected to a t test analysis for linear correlation and determination of the slope of the regression line. RESULTS
The mean internal diameter of 11 iliac arteries was 5.24 mm (SD = 0.57). The pressure-flow relationship as a function of cross-sec- mean internal diameter of 11 aortas was 7.76 tional area in the aortic model with maximum flow employing three arteriovenous fistulae. It should be noted mm (SD = 0.73). The percentage of lumenal stenosis that that critical arterial stenosis occurs with less-comproresulted in a 10% reduction of blood flow mised cross-sectional area in this high-flow situation and that the configuration of the pressure curve is and a 10% drop in distal arterial blood presidentical to the flow curve, once again indicating that sure for each condition of flow in the aorta critical arterial stenosis can be inferred and that the extent of blood flow compromised can be measured by and iliac arteries is summarized in Table 1. The value of critical arterial stenosis under the distal blood pressure drop. each set of flow conditions was found to be flow rate occurred was determined by evalu- identical, whether calculated by pressure ating our data with distal pressure and distal gradient or change in blood flow. Not only blood flow plotted simultaneously as a func- did critical stenosis as measured by pertion of decreasing unobstructed lumenal centage change in blood flow or percentage cross-sectional area. Extension of a per- change in distal blood pressure coincide for pendicular line from the 90% flow rate to a specific point, but the curves for percentthe abscissa, which represented percentage age change in a blood flow vs. lumenal of unobstructed lumenal cross-sectional stenosis are identical for each flow rate area, resulted in a determination of a numeri- and artery studied (Figs. 6 and 7). This cal value for critical arterial stenosis. An linear correlation suggested that percentage example of this process is shown in Fig. 5. In of compromise in blood flow could be ina similar manner, the percentage of critical TABLE 1 arterial stenosis which resulted in a 10% DETERMINATION OF CRITICAL STENOSIS drop inflow was measured for each flow rate in each of the two arteries studied. Critical stenosis Critical stenosis In order to evaluate the relationship beAVWSp determinedby detemtinedby 10%dmp blood 10%drop tween percentage change in distal blood Conditionof Row in flow in pressure pressure and percentage change in distal meaS”rement (mUmin) Pm Pa blood flow with respect to progressive lu144 Iliac artery 8s 86 menal stenosis, both percentage change in Iliac artcry + one A-V distal blood pressure and percentage change 456 75 74 fistula in blood flow were plotted simultaneously Aorta + one A-V tistuh 314 86 86 as a function of decreasing percentage of Aorta + two unobstructed lumenal cross-sectional area 79 A-V fistulae 593 79 (Figs. 6 and 7). The percentage changes in Aorta + thme A-V fistulae 886 73 73 distal blood pressure and in blood flow apFIG. 7. This is a compound graph presenting the
MOORE
AND MALONE:
CRITICAL
ARTERIAL
STENOSIS
7
area (,rrr2) is an exponential function of the radius, it would be expected that small COMPARISON OF THE PERCENTAGE CHANGE OF BLOOD changes in diameter would cause signifiPRESSURE DECREASE AS A FUNCTION OF BLOOD-FLOW DECREASE cantly larger changes in cross-sectional area. From Table 1 it can be seen that at PerCentage of confidence flow rates of 144 and 314 ml/min for the Slopeof f Value of linear for Conditionof regression iliac artery and aorta, respectively, that the correlation linearity line lttG3S”EItle”t critical stenosis for both arteries was 85 to 99.9 1.01 27.8 Iliac artery 86%. Since the aortic flow rate is 2.2 times Iliac artery the comparable iliac flow rate, one would + one A-V 43.0 99.9 I .25 fistula expect the aortic critical stenosis to be less Aorta + one than 85 to 86%, since critical stenosis varies 30.8 99.9 0.74 A-V listula Aorta + two inversely with flow rate. However, the aorta 99.9 22.7 0.85 A-V fistulae has 1.48 times the mean diameter of the Aorta + three 19.7 99.9 0.90 A-V fist&e iliac artery, and therefore 2.2 times the effective cross-sectional area of the compaferred by measuring the percentage reduc- rable iliac artery. The increase in effective tion of the distal blood pressure. In order aortic cross-sectional diameter (2.2 times to test this hypothesis, the percentage pres- the comparable iliac artery diameter) is sure reduction was graphically plotted as a exactly matched by the increased aortic function of percentage flow reduction for flow compared to the iliac artery flow (aortic each of the five conditions of vessel size flow is 2.2 times the comparable iliac flow). and flow. These data were subjected to linear regression analysis; the slope for each DISCUSSION line was measured, and a t test as a measThe results of the study indicate that urement of linear correlation was determined. These data are summarized in Table critical arterial stenosis is not a constant number but varies directly with the effec2. The percentage of confidence for linearity for each pair of data exceeded 99.9%, and tive cross-sectional area of the artery and the slopes of the five lines approached unity, inversely with the flow rate. This is of particindicating that a one-to-one relationship be- ular clinical importance in trying to recontween percentage flow reduction and per- cile lesions demonstrated by angiography centage blood-pressure drop existed. There- with symptoms of arterial insufficiency. fore, percentage change in distal arterial Thus, a lesion producing a particular reducpressure is a statistically accurate predictor tion in cross-sectional area for a large artery may not result in any compromise of percentage change in blood flow. The value for critical arterial stenosis in blood flow, but the same percentage rewithin the same vessel changed for each duction in cross-sectional area of a smaller separate flow rate and was found to be in- vessel may exceed the critical stenosis level versely proportional to flow rate. As the for that artery. Similarly, with augmented flow rate increased, the amount of lumenal flows through a specified artery such as cross-sectional area reduction required to might occur with exercise, a stenosis that produce a critical stenosis decreased (Table was insignificant at basal flows may become 1). For example, with a baseline flow aver- quite significant at the higher flow demand aging 314 ml/min, the critical stenosis was and result in symptoms of arterial insuf86% for the abdominal aorta; however, ficiency. Our data support those of Young when the aortic flow was increased to 886 et al. who reach similar conclusions remYmin, the critical stenosis was decreased garding the relationships of blood flow and clinical arterial stenoses [lo]. to 73%. Since the numerical value of critical arSince the calculation of cross-sectional TABLE
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JOURNAL OF SURGICAL RESEARCH: VOL. 26, NO. 1, JANUARY
terial stenosis varies with both lumenal cross-sectional area and flow rate, the use of angiography as a sole criterion for judging the physiological significance of any arterial lesion would appear to be quite limited. This limitation of angiography has been partially improved upon by the utilization of two plane angiography. However, since symptoms of arterial insufficiency are often exercise-induced and therefore related to the dynamics of blood flow, any static test such as angiography has only limited value. Nonetheless, two-plane angiography is mandatory both to visually identify lesions in the arterial tree and to plan appropriate reconstructive procedures. Clearly, the best method for evaluating the significance of a lesion or a series of lesions in the arterial tree would be the actual measurements of flow rates, not only at rest, but also under conditions requiring augmented flows, such as exercise. Since these measurements cannot be performed with noninvasive methods such testing is not practical. A solution to this dilemma can be found in the linear relationship of distal blood pressure response to changes in distal blood flow as demonstrated in this study. Percentage change in distal blood pressure was shown to be a statistically reliable predictor of percentage change in distal blood flow. Therefore, noninvasive measurement of distal blood pressure at the malleolar level, both at rest and following exercise, together with measurement of systemic blood pressure at the brachial artery level, will allow calculation of the percentage pressure drop in the legs, both at rest and after exercise. According to this study, the percentage pressure drop is equal to the percentage reduction in arterial flow. Distal ankle pressure measurement is of additional value since the pressure-flow correlation is valid not only at basal conditions, but also under conditions requiring augmented blood flow (exercise). On occasion it may be difficult to evaluate the contribution of lesions proximal to the common femoral artery when it is known that stenotic lesions also exist distal to the
1979
common femoral artery. Either proximal or distal lesion or the combined lesions in series may result in a blood pressure drop measured at the malleolar level. Discrimination of the individual lesions contributing to blood-flow reduction can be ascertained by utilizing direct femoral pressure studies with exercise. This technique, which we have previously described, would help to differentiate the significance of proximal vs distal lesions and would influence the clinical decision of whether or not a proximal reconstructive procedure should be performed prior to or instead of a distal arterial repair [6]. However, due to the fact that direct femoral pressure measurement is an invasive procedure, its usefulness as a practical clinical tool is limited. Another approach to the evaluation of proximal lesions is the utilization of the Doppler flowmeter to record femoral artery wave forms at rest and after exercise. There is an accumulating body of evidence which suggests that some type of arterial waveform analysis or other noninvasive parameter may permit separation of proximal obstructing arterial lesions from distal lesions in evaluating overall hemodynamic compromise [8]. Obviously, distal repairs such as femoral-popliteal bypass done in the presence of aortoiliac disease are at higher risk for thrombosis. It is usually recommended that inflow problems be corrected prior to repair or reconstruction of more distal lesions. REFERENCES Flanigan D. P., Tullis, J. P., Streeten, V. L., et al. Multiple subcritical arterial stenoses: Effect on poststenotic pressure and flow. Ann. Surg. 186: 663-668, 1977. Killen, D. A., and Oh, S. U. Quantitation of the severity of arterial stenosis by pressure gradient measurement. Amer. Surg. 34: 341-349, 1968. Mann, F. C., Herrick, J. F., Essex, H. E., and Baldes, E. J. Effect on blood flow of decreasing lumen of blood vessel. Surgery 4: 249-252, 1938. May, A. G., DeWeese, J. A., and Rob, C. G. Hemodynamic effects of arterial stenosis. Surgery 53: 513-524, 1963.
MOORE AND MALONE: CRITICAL ARTERIAL 5. May, A. G., Van De Berg, L. V., DeWeese, J. A., and Rob, C. G. Critical arterial stenosis. Surgery 54: 250-259, 1963. 6. Moore, W. S., and Hall, A. D. Unrecognized aortoiliac stenosis: A physiologic approach to the diagnosis. Arch. Surg. 103: 633-638, 1971. 7. Moore, W. S., Sydorak, G. H., Newcomb, L., and Campagna, G. Blood pressure gradient to estimate flow changes with progressive arterial stenosis. Surg. Forum 24; 248-250, 1973. 8. Rutherford, R. B., Hiatt, W. R., and Kreutzer,
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9
E. W. The use of velocity wave form analysis in the diagnosis of carotid artery occlusive disease. Surgery 82: 695-702, 1977. 9. Sydorak, G. R., Moore, W. S., Newcomb, L., et al. Effect of increasing flow rates and arterial caliber on critical arterial stenoses. Surg. Forum 23: 243-244, 1972. 10. Young, D. F., Cholvin, N. R., and Roth, A. C. Pressure drop across artificially induced stenoses in the femoral arteries of dogs. Circ. Res. 36: 735-743, 1975.
