CM. Rodkiewicz
On the Subclavian Steal Syndrome In Vitro Studies
Fellow ASME. 1
J. Centkowski
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8
S. Zajac Polish Medical Academy, Warsaw, Poland
An elastic model of the arterial system has been used in which a specially designed pumping unit simulated the heart action. Physiological pressures and normal geometry, size, and flow distribution together with the normal cardiac output and use of prosthetic heart valves are the features of the system. Atherosclerosis was simulated by introducing blockages of known cross-section at specific sites of predilection. It has been shown that, for some specific occlusion magnitude in the left or right subclavian, or in the brachycephalic arteries, the stagnant no blood flow condition will appear in the left vertebral, or the right vertebral, or right common carotid, or the right internal carotid arteries. For larger occlusions the blood flow in these arteries reverses its direction, i.e., the "stealsyndrome" appears. It is shown that besides the known single steal syndrome there exists also a double steal syndrome, i.e., blood reverses its flow direction simultaneously in two arteries, both on the right side of the arterial system. This blood is taken from the circle of Willis, which at the same time is significantly supplemented by the increased blood flow through the other arteries leading into the circle of Willis.
Introduction The subclavian steal syndrome is the effect of occlusion of the subclavian artery proximal to the origin of the vertebral (Berger et al., 1967; Moran et al., 1988). This occlusion causes reduction in the vertebral blood flow (which is intended for cerebral circulation) and in the subclavian. Furthermore, when degenerative vascular disease causes lumen of the occluded artery to become sufficiently small, or totally blocked, the flow of blood in the vertebral is reversed, i.e., some blood is detoured into the obstructed artery (Reivich et al., 1961). Most of the research carried out on the subclavian steal syndrome was concentrated on the causes of the disorder and the biological and pathological changes associated with its development. However, though the disorder appears to be strongly associated with the fluid flow principles, no work has been done which would simulate the subclavian steal syndrome in a fluid mechanics laboratory. It is hoped that the presently reported work will fill the gap, and it is believed that it brings, for the benefit of the medical profession, additional and useful information. The effect of atherosclerotic lesions on the blood mass flow distribution was first studied by Rodkiewicz et al. (1979), when a rigid model of the aortic arch, with only the primary branches, was used. The experiments were carried out for steady flow and a set of blockage combinations was tested. The Reynolds number, at entrance to the aorta, was kept around 1300 during the experiments. In the present analysis an elastic model has been developed 'On leave from the Polish Academy of Sciences, Gdansk. Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division July 24, 1991; revised manuscript received March 4, 1992. Associate Technical Editor: L. Talbot.
and used. Prosthetic heart valves were used in the experiments and pulsatile flow was maintained with a flow time course similar to that actually produced by a human heart. The main objective of the study was to determine the amount of blood flowing at different stages of atherosclerotic formations, to the arms directly and via the circle of Willis. This also gave the opportunity to obtain important information regarding correlated variations in the blood delivery to the brain. Model of the Arterial System The model of the arterial system included all main branches which are directly or indirectly responsible for blood supply to the brain. In the lower region, however, only the iliacs and the renals were modeled, together with a supplementary artery that represented all the other arteries branching off the abdominal aorta, which are considered not important from the point of view of the present analysis. The fact that the geometry and size of the aorta and its different branches varies from individual to individual posed great difficulty in selecting the most suitable values for the model. However, the final geometry was selected by considering the information provided by Haque (1982). The shape of the modelled arteries together with some relevant dimensions is shown in Fig. 1. The model was made in parts with sections made at locations where blockages had to be placed. These are also shown in Fig. 1 as location A, B, or C. A part of the made model was the elastic aortic arch. It was manufactured so that it reflected the natural twist of approximately 15 deg (Rodkiewicz et al., 1985). The dilatation of each artery depends on the wall thickness, expressed as a strain, it globally averaged 6.3 percent (based NOVEMBER 1992, Vol. 114 / 527
Journal of Biomechanical Engineering
Copyright © 1992 by ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
on the diameter) at the normal pulse rate and average pressure of 120 mm Hg. The importance of the wall elasticity, when considering the blood flow distribution, has been indicated in the work of Doo et al. (1984) where tests were performed by using elastic model. It was found that the rigidity of the modelled arterial walls has an effect on the flow distribution. This effect gave maximum difference of 4.9 percent. Apparatus The experimental setup consists of the pulsatile unit, a frame holding the model, and the measuring system. The schematic arrangement of these parts is shown in Fig. 2. The pulsatile unit is powered by a single phase, a.c. motor having a shaft Right Internal Carotid A.
Left Internal Carotid A. 2%
Right Vertebral Artery \ 1 \/
.Right Common
Right Subclavian A.
Brachiocephalic A.
-Internal Diameter [mm)
Common Iliac A
Fig. 1 Geometry of the modeled arteries and the normal flow distribution
speed of 3450 rpm. The speed is reduced by using a standard gear box followed by an adjustable gear train. The groove cam driven by the motor is cut according to the sum of the first five harmonics which closely approximates the flow time course found at the entrance to the aorta (Haque, 1982; Centkowski et al., 1982). A piston and cylinder arrangement follows the cam and this is further followed by the model of the left ventricle. A surgical diaphragm divides the ventricle into two parts so that the working fluid does not mix with the fluid in direct contact with the piston (water). The further side of the ventricle has the inlet and outlet ports fitted with prosthetic ball-type heart valves. It should be noted that although the cam was designed from a physiological profile and the motion of the ball of the prosthetic aortic valve is generated by this cam, there is a difference in the flow passage relative to the normal physiological situation, which somewhat modifies the velocity profile in the aorta. The extent of this variation was not investigated. However, it was indicated by Rodkiewicz et al. (1985) that blood flow distribution of the aortic arch is insensitive to the wave form. The flow from all branches was let to the measuring arrangement by hard-walled tygon tubing. Arteries leading to the brain were connected with a volume representing circle of Willis (CW). The flow from various terminal branches was directed to separate tubes and was taken to a height of 100 cm where it was discharged into a series of measuring tanks. Each tube has an independent regulating valve near the discharge level to set the reference flow distribution. The working fluid was an aqueous-glycerol mixture with 36.7 percent glycerol content by volume. The density was 1.1 g/cm3 and the absolute viscosity was 4.08 cP at the temperature of 20°C. This Newtonian mixture was used to model the flow of blood. However, it was appreciated that recently published arguments (Rodkiewicz et al., 1990) indicate that blood predominantly behaves as a non-Newtonian fluid. The selected, made of brass, arterial blockages (at A, B, or C) were 50, 75, 85, 90, 95, and 100 percent by area. Geometric shape of these is shown as an insert, in Fig. 1. Lower sizes were not used because for less severe flow restrictions the arterial flow distribution appears to be insensitive (Rodkiewicz et al., 1979). In Fig. 1 locations of blockages are indicated. These were used in turn. Experimental Procedure For each case the flow distribution was recorded at heart rates of 70 beats per minute which was considered to be the
CW LS Manometers -^d
||
Measurement Tanks
Acqueous-Glycerol Mixture
CAM
Prosthetic Heart Valves
/Motor
^Pulsatile Unit
Fig. 2 Schematic of the apparatus
528 / Vol. 114, NOVEMBER 1992
Transactions of the ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
CW
Fig. 4
LS
Dividing element of CW
oase A
;QLS = 3 % Q T
100%!
QLS
o ^ * * ^
—r-xioo Fig. 3
Schematic of the measurement arrangement
normal case. The Reynolds number at the entrance to the aortic arch was equal to 1200. The corresponding normal total cardiac output QT was approximately 6.1 liters/minute, i.e., about 87.1 ml per beat. Each result was reproduced within a tolerance limit of ±1.5 percent. The flow was collected over a period of time and averaged for flow per minute; the results were reproducible within close limits. As a first phase of the experiments, no blockages were introduced and the flow was recorded when the arterial system was connected by simple connectors. By adjusting the regulating valves, a normal reference flow distribution was obtained as in round numbers given in Fig. 1. The valves were sealed at this reference position after reproducing the results several times. Next, for each occlusion location A, B, or C (see Fig. 1), measurements were made in two steps. Consider, for example, caseAofthe left side. It is shown in Fig. 3. In step one precision valve XL was closed, precision valve YL was fully open, and ON/OFF clump ZL was open. This arrangement produced a gauge pressure at the CW and at the left subclavian (LS) and their difference Ah. These quantities were maintained constant throughout testing of case A. (Identical procedure for the right side, i.e., cases B and C, involved corresponding valves XR, YR, and ZR.) The measured quantity QTLS was the sum of the "steal" component Qs and the quantity QLS which passed through the blockage. In the second step, for every bloackage setting, ON/OFF clump was closed and valves XL and YL were adjusted so that pressures in CW and in LS and the differential pressure Ah returned to their original values. This produced flow through valve XL which was the required quantity Qs and quantity QLS through valve YL. It should be noted that redirecting Qs via XL did not change rates of discharge in the outer controlled outlets. The "steal" quantity Q s was decreasing with increasing lumen of the blockages, and there were difficulties in determining exactly the stagnant vertebral condition (the flow reversal condition). This state of no blood movement in the vertebral should also be of interest to the medical profession (Rodkiewicz, 1975; Rodkiewicz and Kalita, 1977). In order to find this Journal of Biomechanical Engineering
QLS
100%
80%
60%
40%
0%
Case B
;C^S = 3 % Q ' T
X100
20%.
o^^ 95% ,
100%
80%
; q ; s = 3%
60%
40%
20%
0%
Case C
Q'T
100%
•X100 95%
100%
80%
60%
40%
20%
Blockage in Per Cent Fig. 5
Flow in the left and right subclavian
condition it was decided to obtain a few experimental points with the vertebral forward flow and then interpolate with the data for the vertebral backward flow. This was achieved by using additional apparatus modification shown in Fig. 4. In effect, a movable dividing element was used in the CW volume which isolated flow from the vertebral artery. Required flow rate was obtained when pressure on each side of the dividing element became the same. Results Before commencing with the result presentation it may be helpful to quote the following extract from Editorial (1961): "In 1 human patient it was possible to measure the amount NOVEMBER 1992, Vol. 114/529
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
Case A
; q; R = i 4 % o ' T '
X100
•
Q8R=14%QT
X100
i
100%
.
i
80%
On the Subclavian Steal Syndrome In Vitro Studies
Fellow ASME. 1
J. Centkowski
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8
S. Zajac Polish Medical Academy, Warsaw, Poland
An elastic model of the arterial system has been used in which a specially designed pumping unit simulated the heart action. Physiological pressures and normal geometry, size, and flow distribution together with the normal cardiac output and use of prosthetic heart valves are the features of the system. Atherosclerosis was simulated by introducing blockages of known cross-section at specific sites of predilection. It has been shown that, for some specific occlusion magnitude in the left or right subclavian, or in the brachycephalic arteries, the stagnant no blood flow condition will appear in the left vertebral, or the right vertebral, or right common carotid, or the right internal carotid arteries. For larger occlusions the blood flow in these arteries reverses its direction, i.e., the "stealsyndrome" appears. It is shown that besides the known single steal syndrome there exists also a double steal syndrome, i.e., blood reverses its flow direction simultaneously in two arteries, both on the right side of the arterial system. This blood is taken from the circle of Willis, which at the same time is significantly supplemented by the increased blood flow through the other arteries leading into the circle of Willis.
Introduction The subclavian steal syndrome is the effect of occlusion of the subclavian artery proximal to the origin of the vertebral (Berger et al., 1967; Moran et al., 1988). This occlusion causes reduction in the vertebral blood flow (which is intended for cerebral circulation) and in the subclavian. Furthermore, when degenerative vascular disease causes lumen of the occluded artery to become sufficiently small, or totally blocked, the flow of blood in the vertebral is reversed, i.e., some blood is detoured into the obstructed artery (Reivich et al., 1961). Most of the research carried out on the subclavian steal syndrome was concentrated on the causes of the disorder and the biological and pathological changes associated with its development. However, though the disorder appears to be strongly associated with the fluid flow principles, no work has been done which would simulate the subclavian steal syndrome in a fluid mechanics laboratory. It is hoped that the presently reported work will fill the gap, and it is believed that it brings, for the benefit of the medical profession, additional and useful information. The effect of atherosclerotic lesions on the blood mass flow distribution was first studied by Rodkiewicz et al. (1979), when a rigid model of the aortic arch, with only the primary branches, was used. The experiments were carried out for steady flow and a set of blockage combinations was tested. The Reynolds number, at entrance to the aorta, was kept around 1300 during the experiments. In the present analysis an elastic model has been developed 'On leave from the Polish Academy of Sciences, Gdansk. Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division July 24, 1991; revised manuscript received March 4, 1992. Associate Technical Editor: L. Talbot.
and used. Prosthetic heart valves were used in the experiments and pulsatile flow was maintained with a flow time course similar to that actually produced by a human heart. The main objective of the study was to determine the amount of blood flowing at different stages of atherosclerotic formations, to the arms directly and via the circle of Willis. This also gave the opportunity to obtain important information regarding correlated variations in the blood delivery to the brain. Model of the Arterial System The model of the arterial system included all main branches which are directly or indirectly responsible for blood supply to the brain. In the lower region, however, only the iliacs and the renals were modeled, together with a supplementary artery that represented all the other arteries branching off the abdominal aorta, which are considered not important from the point of view of the present analysis. The fact that the geometry and size of the aorta and its different branches varies from individual to individual posed great difficulty in selecting the most suitable values for the model. However, the final geometry was selected by considering the information provided by Haque (1982). The shape of the modelled arteries together with some relevant dimensions is shown in Fig. 1. The model was made in parts with sections made at locations where blockages had to be placed. These are also shown in Fig. 1 as location A, B, or C. A part of the made model was the elastic aortic arch. It was manufactured so that it reflected the natural twist of approximately 15 deg (Rodkiewicz et al., 1985). The dilatation of each artery depends on the wall thickness, expressed as a strain, it globally averaged 6.3 percent (based NOVEMBER 1992, Vol. 114 / 527
Journal of Biomechanical Engineering
Copyright © 1992 by ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
on the diameter) at the normal pulse rate and average pressure of 120 mm Hg. The importance of the wall elasticity, when considering the blood flow distribution, has been indicated in the work of Doo et al. (1984) where tests were performed by using elastic model. It was found that the rigidity of the modelled arterial walls has an effect on the flow distribution. This effect gave maximum difference of 4.9 percent. Apparatus The experimental setup consists of the pulsatile unit, a frame holding the model, and the measuring system. The schematic arrangement of these parts is shown in Fig. 2. The pulsatile unit is powered by a single phase, a.c. motor having a shaft Right Internal Carotid A.
Left Internal Carotid A. 2%
Right Vertebral Artery \ 1 \/
.Right Common
Right Subclavian A.
Brachiocephalic A.
-Internal Diameter [mm)
Common Iliac A
Fig. 1 Geometry of the modeled arteries and the normal flow distribution
speed of 3450 rpm. The speed is reduced by using a standard gear box followed by an adjustable gear train. The groove cam driven by the motor is cut according to the sum of the first five harmonics which closely approximates the flow time course found at the entrance to the aorta (Haque, 1982; Centkowski et al., 1982). A piston and cylinder arrangement follows the cam and this is further followed by the model of the left ventricle. A surgical diaphragm divides the ventricle into two parts so that the working fluid does not mix with the fluid in direct contact with the piston (water). The further side of the ventricle has the inlet and outlet ports fitted with prosthetic ball-type heart valves. It should be noted that although the cam was designed from a physiological profile and the motion of the ball of the prosthetic aortic valve is generated by this cam, there is a difference in the flow passage relative to the normal physiological situation, which somewhat modifies the velocity profile in the aorta. The extent of this variation was not investigated. However, it was indicated by Rodkiewicz et al. (1985) that blood flow distribution of the aortic arch is insensitive to the wave form. The flow from all branches was let to the measuring arrangement by hard-walled tygon tubing. Arteries leading to the brain were connected with a volume representing circle of Willis (CW). The flow from various terminal branches was directed to separate tubes and was taken to a height of 100 cm where it was discharged into a series of measuring tanks. Each tube has an independent regulating valve near the discharge level to set the reference flow distribution. The working fluid was an aqueous-glycerol mixture with 36.7 percent glycerol content by volume. The density was 1.1 g/cm3 and the absolute viscosity was 4.08 cP at the temperature of 20°C. This Newtonian mixture was used to model the flow of blood. However, it was appreciated that recently published arguments (Rodkiewicz et al., 1990) indicate that blood predominantly behaves as a non-Newtonian fluid. The selected, made of brass, arterial blockages (at A, B, or C) were 50, 75, 85, 90, 95, and 100 percent by area. Geometric shape of these is shown as an insert, in Fig. 1. Lower sizes were not used because for less severe flow restrictions the arterial flow distribution appears to be insensitive (Rodkiewicz et al., 1979). In Fig. 1 locations of blockages are indicated. These were used in turn. Experimental Procedure For each case the flow distribution was recorded at heart rates of 70 beats per minute which was considered to be the
CW LS Manometers -^d
||
Measurement Tanks
Acqueous-Glycerol Mixture
CAM
Prosthetic Heart Valves
/Motor
^Pulsatile Unit
Fig. 2 Schematic of the apparatus
528 / Vol. 114, NOVEMBER 1992
Transactions of the ASME
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
CW
Fig. 4
LS
Dividing element of CW
oase A
;QLS = 3 % Q T
100%!
QLS
o ^ * * ^
—r-xioo Fig. 3
Schematic of the measurement arrangement
normal case. The Reynolds number at the entrance to the aortic arch was equal to 1200. The corresponding normal total cardiac output QT was approximately 6.1 liters/minute, i.e., about 87.1 ml per beat. Each result was reproduced within a tolerance limit of ±1.5 percent. The flow was collected over a period of time and averaged for flow per minute; the results were reproducible within close limits. As a first phase of the experiments, no blockages were introduced and the flow was recorded when the arterial system was connected by simple connectors. By adjusting the regulating valves, a normal reference flow distribution was obtained as in round numbers given in Fig. 1. The valves were sealed at this reference position after reproducing the results several times. Next, for each occlusion location A, B, or C (see Fig. 1), measurements were made in two steps. Consider, for example, caseAofthe left side. It is shown in Fig. 3. In step one precision valve XL was closed, precision valve YL was fully open, and ON/OFF clump ZL was open. This arrangement produced a gauge pressure at the CW and at the left subclavian (LS) and their difference Ah. These quantities were maintained constant throughout testing of case A. (Identical procedure for the right side, i.e., cases B and C, involved corresponding valves XR, YR, and ZR.) The measured quantity QTLS was the sum of the "steal" component Qs and the quantity QLS which passed through the blockage. In the second step, for every bloackage setting, ON/OFF clump was closed and valves XL and YL were adjusted so that pressures in CW and in LS and the differential pressure Ah returned to their original values. This produced flow through valve XL which was the required quantity Qs and quantity QLS through valve YL. It should be noted that redirecting Qs via XL did not change rates of discharge in the outer controlled outlets. The "steal" quantity Q s was decreasing with increasing lumen of the blockages, and there were difficulties in determining exactly the stagnant vertebral condition (the flow reversal condition). This state of no blood movement in the vertebral should also be of interest to the medical profession (Rodkiewicz, 1975; Rodkiewicz and Kalita, 1977). In order to find this Journal of Biomechanical Engineering
QLS
100%
80%
60%
40%
0%
Case B
;C^S = 3 % Q ' T
X100
20%.
o^^ 95% ,
100%
80%
; q ; s = 3%
60%
40%
20%
0%
Case C
Q'T
100%
•X100 95%
100%
80%
60%
40%
20%
Blockage in Per Cent Fig. 5
Flow in the left and right subclavian
condition it was decided to obtain a few experimental points with the vertebral forward flow and then interpolate with the data for the vertebral backward flow. This was achieved by using additional apparatus modification shown in Fig. 4. In effect, a movable dividing element was used in the CW volume which isolated flow from the vertebral artery. Required flow rate was obtained when pressure on each side of the dividing element became the same. Results Before commencing with the result presentation it may be helpful to quote the following extract from Editorial (1961): "In 1 human patient it was possible to measure the amount NOVEMBER 1992, Vol. 114/529
Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jbendy/25891/ on 02/16/2017 Terms of Use: http://www.asme.org/abo
Case A
; q; R = i 4 % o ' T '
X100
•
Q8R=14%QT
X100
i
100%
.
i
80%
![[Carotid-subclavian steal syndrome].](/assets/img/hold.png)
