World J. Surg., 2, 621--629, 1978

Hemodynamics of Arterial Stenosis Bok Y. Lee, M.D., Cyrus Assadi, M.D., John L. Madden, M.D., David Kavner, D.Eng., Frieda S. Trainor, Ph.D., and William J. McCann, M.D. Departments of Medicineand Surgery,U.S. VeteransAdministrationHospital, Castle Pointand New York MedicalCollege,New York, and Departmentof Surgery,New RochelleHospital-MedicalCenter, New Rochelle,New York

strated the significance of the pulsatile component of blood flow as an indicator of the quality of perfusion [11]. Similarly, many of the noninvasive diagnostic techniques, such as ultrasonic Doppler flowmetry, segmental pneumatic plethysmography, electrical impedance plethysmography, and strain gauge measurements, yield an output related to the pulsatile component of arterial blood flow. The objective of this study was to establish the quantitative relationships for both the mean and the pulsatile components of blood flow and the pressure variations in models having a wide range of induced stenoses. An in vitro mechanical simulation of the arterial circulation was constructed to demonstrate the parameters in a controlled environment, and animal experiments were done to reproduce the results in a living organism.

In order to derive a better understanding of the effect of varying degrees of stenosis on arterial pulsatile waveforms, an in vitro model was constructed and in vivo studies were done in dogs to observe and record the changes in the pulsatile and steady arterial blood flow components. Blood flow measurements were made using the electromagnetic blood flowmeter proximal and distal to the stenosis. The data show that as the degree of stenosis increases, the decreases in the pulsatile components of flow and distal pressure occur earlier and to a much greater degree than changes in mean flow.

The hemodynamics of arterial stenosis continue to be of interest to both physiologists and vascular surgeons. The phenomenon of a rapidly decreasing blood flow when the intraluminal cross-sectional area of an artery is reduced greater than 80% has been noted since the report of Mann et al. [1] in 1938. Since then, the concept of "critical stenosis" has been subjected to considerable scrutiny by many investigators [1-9]. Our interest in arterial stenosis stems from our experience with the use of the electromagnetic flowmeter in the operating room for blood flow measurements during reconstructive vascular procedures [ 10], and from the use of noninvasive tests for the evaluation of vascular disease. We have demon-

Methods

In Vitro

An experimental simulation of the peripheral arterial circulation was devised to investigate the effects of lumen stenosis on those pulsatile flow and pressure parameters that may occur in living organisms. The experimental apparatus, shown in Fig. 1, consisted of a pulsatile flow pump and various lengths and grades of elastic tubing. The fluid used was normal saline. The pump fed into a compliant " a o r t i c "

Presented at the XXVIIth Congress of the Soci6t6 Internationale de Chirurgie, Kyoto, Japan, September 3-8, 1977. Reprint requests: Bok Y. Lee, M.D., Chief, Surgical Service, U.S. Veterans Administration Hospital, Castle Point, New York 12511, U.S.A.

0364-2313/78/0002-0621 $01.80 9 1978 Soci6t6 Internationale de Chirurgie 621

622

World J. Surg. Vol. 2, No. 5, September, 1978

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Fig. 1. Apparatus used to simulate the peripheral arterial circulation for in vitro studies section of tubing at a rate of 60 strokes/min with a stroke volume of 20 cc. Of the total flow, 90% was shunted through a partially occluding clamp and provided sufficient control to maintain both the central mean and pulse pressure within physiologic range (the " b o d y " ) . The remaining 10% of the flow was directed through a 1 m length of a small-diameter tubing (the " li m b" ) and emerged via a throttling valve that simulated a local peripheral vascular resistance. An in-line electromagnetic flow probe was situated 20 cm from the proximal end of the long tube. Pressure measurements were obtained at the proximal end o f the tube and at the site of the flow probe for the distal pressure. A set of graded stenoses was made from 6.35 mm (outside diameter) Teflon | rod; 1 cm length segments were bored using various size drill bits. These segments were then implanted in the peripheral tube and centered between the proximal end and the flow probe. Pressure and flow were recorded and analyzed according to the procedures outlined in the method of the in vivo experiment.

In Vivo

The effect on blood flow of varying grades of stenosis was studied using beagle dogs. Following anesthesia, the abdominal aorta was exposed from below the left renal artery down to the lower end of the aorta. Right and left internal and external iliac arteries and the median sacral artery were exposed. An indwelling catheter was passed through the median sacral artery up to the end of the abdominal aorta for measurement of proximal pressures. A catheter for measurement of distal pressures was passed through the deep femoral artery, cranial femoral artery, or saphenous artery to the distal end of the external iliac artery or the proximal end of the femoral artery. Each catheter was connected by a

Location of probes for canineexperiments

transducer

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/ To distal pressure transducer Fig. 2. Placement of the flow probe, "loop stenosis," and pressure catheters in dogs. 20 cm length of large-bore rigid polyethylene tubing to a calibrated pressure transducer (Fig. 2). Varying degrees of stenosis were produced by using a loop of nylon monofilament thread wrapped around the external iliac artery. One end of the loop was fastened to a fixed point in a threaded acrylic tube. The other end was attached to a bolt the linear position o f which could be adjusted by turning the bolt. The threads of the bolt were .79 mm apart. Thus, a single full turn of the bolt would reduce the arterial circumference by 0.794 mm. The initial out-

B.Y. Lee et al.- Hemodynamies of Arterial Stenosis

623

experiment

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side circumference was measured and the wall thickness was estimated using the length of the loop at full occlusion. The % stenosis was computed as 100 (1-As/Ao), where As/Ao is the ratio of the stenosis to the open-lumen cross-sectional area. Blood flow measurements were made using the square-wave electromagnetic blood flowmeter. The probe was placed approximately 2 cm distal to the stenosis. Pulsatile flow was measured using a 10 msec electronic damping factor. Pulsatile flow, mean flow, proximal pressures, and distal pressures were recorded simultaneously on a multichannel stripchart recorder and a 4-channel instrumentation tape recorder. Following each complete experiment, the data that were stored on magnetic tape were analyzed using a minicomputer with analog to digital capability. Ten seconds of data for each stenosis was played into the computer and sampled at a rate of 100/sec per channel. The mean blood flows and

pressures were computed using straight-time averaging of the respective signals. Pulsatile parameters were defined as a range from minimum to maximum flow or pressure during a single cardiac cycle and the values reported were 10-sec averages. Both flow and pressure data were reported as the normalized fraction of the open vessel. Each data run consisted of about 12 discrete stenoses ranging from 0% (fully open vessel) to 100% (occluded). There were from 4 to 10 data runs on each of 4 animals, giving a total of 25 complete data runs or data for approximately 300 separate stenoses to be analyzed.

Results Typical s tripchart recordings obtained from the dog experiments are shown in Figs. 3A and B. These 4 tracings, recorded at increasing degrees of stenosis,

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624

World J. Surg. Vol. 2, No. 5, September, 1978

Canine experiment Blood flow vs. % stenosis 81% stenosis

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0 Fig. 3. Stripchart recordings from dog experiments continued. B. Mean blood flow, pulsatile blood flow, and distal pressure at 74% and 81% stenosis. Pulsatile blood flow and distal pressure continue to show marked decreases at 74% and 81% stenosis. Mean flow shows a slight decrease at 74% stenosis with marked changes not appearing until 81% stenosis. Table 2. Table 1.

Flow reduction during stenosis in dog experi-

ments. % stenosisa

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0 14 25 35 46 55 62 68 73 77 83 88 92 97 100

1.00 0.98 1.01 0.99 0.98 0.94 0.92 0.88 0.87 0.79 0:75 0.64 0.39 0.20 0.00

1.00 0.95 0.91 0.85 0.74 0.62 0.56 0.46 0.31 0.27 0.18 0.10 0.03 0.01 0.00

-+ 0.000 (25) -+ 0.033 (15) -+ 0.043 (15) -+ 0.061 (20) -+ 0.042 (17) -+ 0.045 (27) -+ 0.025 (13) -+ 0.049 (21) -+ 0.067 (18) -_ 0.070 (18) _+ 0.100 (21) -+ 0.076 (19) -+ 0.109 (19) +_ 0 . 0 5 9 ( 8 ) -+ 0.000 (25)

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(25) (12) (16) (23) (14) (23) (16) (14) (13) (18) (17) (25) (17) (11) (25)

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Stenosis ratio.

% stenosisa

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1.00 _+ 0.000 0.99 - 0.035 0.95 -+ 0.050 0.92 -+ 0.052 0.85 -+ 0.077 0.72 _+ 0.106 0.68 +-_ 0.087 0.58 - 0.350 0.36 -+ 0.203 0.36 - 0.169 0.25 _+ 0.386 0.12 +- 0.170 0.05 -+ 0.682 0 . 0 6+ - 0.159 0.00 -+ 0.000

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(25) (15) (13) (18) (24) (31) (18) (19) (18) (19) (23) (18) (18) (9) (25)

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aPercent reduction of lumen cross-sectional area. b(Ap - AP100%)/(AP~ - AP10o%). ~Distal systolic pressure minus diastolic pressure divided by initial distal pulse pressure.

B.Y.

Lee et al.: H e m o d y n a m i c s o f Arterial Stenosis

625

Fraction of initial pressure vs. % stenosis

Canine experiment Fraction of original flow vs. % stenosis 1.0

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demonstrate the dramatic decrease in the pulsatile c o m p o n e n t o f blood flow as compared to the decrease in mean flow. The entire 25 data runs for the 4 dogs are summarized in Tables 1 and 2. The flow ratios are defined as the flow through the stenosis divided by the unobstructed flow. The standard deviation and the number of data points in the sample are also included. In Table 2, the differential pressure ratio was c o m p u t e d as the pressure drop across the stenosis minus the full occlusion pressure drop divided by the difference between the initial drop minus the occlusion pressure drop. This

Table 3.

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Fig. 5. Graphic representation of the pressure data obtained in vivo as tabulated in Table 2.

formulation was used to obtain a representative value going from unity at 0% stenosis to 0 at full occlusion. Figs. 4 and 5 are graphs of the data presented in these tables. The results indicate the quite different response o f the pulsatile c o m p o n e n t s o f flow and pressure as compared to their mean values. The 2 graphs of flow and pressure are apparently similar in nature. A correlation o f the differential pressure ratio with the mean flow ratio is shown in Fig. 6A. The correlation coelficient was high, indicating that the pressure drop across an obstruction can be directly related to the reduction in mean blood flow.

Flow and pressure ratio data obtained in the in vitro experiment.

% stenosis a

Mean flow ratio b

Pulsatile flow ratio e

Differential pressure ratio d

Distal pulse pressure ratioe

0 11.1 19.6 41.1 54.8 66.6 77.5 88.1 92.6 96.1 100.0

1.00 1.00 1.01 0.99 0.95 0.88 0.75 0.52 0.40 0.21 0.00

1.00 0.99 0.95 0.86 0.65 0.36 0.11 0.01 0.00 0.03 0.00

1.00 1.00 0.99 0.97 0.92 0.78 0.58 0.27 0.15 0.01 0.00

1.00 0.98 0.96 0.56 0.27 0.10 0.27 - 0.08 0.05 0.60 0.00

apercent reduction of lumen cross-sectional area. bMean flow divided by flow at 0 stenosis, ePulsatile flow divided by flow at 0 stenosis, d(AP - AP100%)/(AP0% - APt00% ). eDistal systolic pressure minus diastolic pressure divided by distal pulse pressure.

626

World J. Surg. Vol. 2, No. 5, September, 1978

Correlation of pressurewith flow reduction-canine experiments Differential pressureratio

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