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Flow patterns at the major T-junctions of the dog descending aorta
FLOW
PATTERNS AT THE MAJOR T-JUNCTIONS DOG DESCENDING AORTA MINEO
TAKESHI KARINO;
McGill University Medical
MOTOMIYA
OF THE
and HARRY L. GOLDSMITH
Clinic. Montreal General Hospital, Quebec H3G 1A4, Canada
1650 Cedar Avenue. Montreal,
Abstnet-Using a novel technique developed in our own laboratory. an isolated transparent arterial segment containing the whole descending aorta and its four major branches was prepared from a dog The flow patterns at each aortic T-junction were studied in detail under the conditions of steady flow by means of flow visualization and cinemicrographic techniques. It was found that a standing recirculation zone consisting of a pair of thin-layered spiral secondary flows located symmetrically about the common median plane of the aorta and side branches was formed at each T-junction over a wide range of flow conditions including the time-averaged estimated mean values of physiological flow rates and flow rate ratios. The resultssupport the recent in riro findings by other investigators that Row reversal occurs at some junctionsof the dog abdominal aorta during each cardiac cycle. The flow patterns at the aortic T-junctions were very much similar to those previously observed in various glass model T-junctions. However. due to the particular anatomical structure of the vessel wail at each branching site (the curvature of the wall was very sharp at the flow divider. but gently rounded at the bend opposite to it) no recirculation zone was formed III the side branches. At a given flow rate ratio, the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher in aortic T-junctions than those in glass model T-junctions having equivalent branching angles and diameter ratios. These results indicate that, in the circulation. conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows.
1978; Schcttlcr
NWIENCLATURE
Thcorctically, parent vessel diameter inllow rate outllow rate critical Reynolds number inflow Reynolds number inflow mean lluid velocity side branch diameter viscosity of suspending fluid density of suspending fluid density of tracer microsphsrcs
tional
various channels,
relatively
it has now
(11 ul.,
1988).
of computa-
bccomc
possible
but the analysis is still limited
those vessels having over-simplified perimentally.
due to the difiicultics
have been conducted arteries (Bharadvaj
Ex-
in visualizing
the
ill airro using various models of
CI N/.. 1982; Moravec
and Liepsch,
1983; Fukushima
zt ul.. 19871 and arterial
molds
et ul.,
(Walburn
Rayman
large arteries by the progressive thickening
quality day,
1981; Deters
ct (I/.. 1985). However, casting and molding
it is still
casts and
et cl.,
1984;
even with the high
techniques available
not easy to precisely
duplicate
complex geometry of the vessel lumen encountered various regions of the circulation.
and
post-mortem
atherosclerotic randomly,
plaques rich in cholesterol. indicate
in the circulation,
localized sites in the arterial
the entrances
of bifurcations
To solve the problem,
that
lesions on the vessel wall develop not
and not everywhere
at particular
studies
but
prepare
we developed
transparent
natural
from animals and humans post-mortem Motomiya,
tree such as
and T-junctions,
isolated
curved segments of arteries where the blood flow is
various regions of the circulation
disturbed
and photographing
and eddies are likely to form. Therefore.
elucidate the possible connection and
the
localized
atherosclerosis.
genesis
a considerable
to
between blood flow
and
dcvclopmcnt
amount
of work,
cluding
studies from our own laboratory,
carried
out in recent years (Goldsmith
of in-
has been
and Karino.
particles
(Karino
and
of the flow in
by directly observing
the behavior of suspended tracer
and hardened
we have previously through
venous
(Karino
and
blood cells flowing
through
bifurcation
bogenesis sites. 537
and
studied the detailed flow patterns valves
Motomiya,
1984), in connection
jorm
to
vessels
normal and diseased vessels. Using the above method,
artery
Received in final 6 Sepremher 1989. *To whom correspondence should be addressed.
in
1983). This has, for the first time, enabled
us to study in detail the characteristics
and
a method blood
tothe
formation Clinical
to
gcomctrics.
and eventual hardening of the vessel wall through the ofatheromatous
to
dctailcd Row patterns in oiuo. most of the flow studies
disease which affects
is a degenerative
techniques.
1983; Yoshida the dcvclopmcnt
simulate the steady or pulsatilc tlow of blood through
INTRODUCTIOK Atherosclerosis
cr ul.. through
in
dog
saphenous
veins
1984) and at the carotid
in man (Motomiya
and
Karino.
with the high incidence of throm-
atherogenesis
respectively,
at
these
538
T. KARISO cr al.
The present paper extends the work to a study of the detailed flow patterns at arterial T-junctions in the descending aorta of the dog. The groundwork for this study was carried out earlier using glass models of T-junctions having various branching angles and diameter ratios (Karino et al.. 1979; Karino and Goldsmith, 1985). Using dilute, neutrally buoyant suspensions of polystyrene microspheres, we showed that when flow entered the main tube, paired spiral secondary flows and recirculation zones symmetrical about the common median plane were formed at the entrances of the main and side daughter vessels as illustrated in Fig. 1 for 60” and 135” uniform 3 mm diameter Tjunctions. Such disturbed Row was observed over a wide range of inflow Reynolds numbers and flow rate ratios in the two daughter vessels. Moreover, as shown in the figure, the side and main recirculation zones
were connected through a part of the stray flow from the main recirculation zone which traveled backward along the vessel wall, crossed above and below the mainstream encircling it, and then entered the comer recirculation zone at the leading edge of the side branch. It was also shown that, at a given Reynolds number and Row rate ratio (side/parent vessel), a decrease in branching angle and side tube diameter resulted in a decrease in the size of both the main and side recirculation zones. The formation of the complex spiral secondary flows and recirculation zones was largely determined by the flow rate ratios in the daughter vessels, the curvature of the walls at the flow divider, and the bend opposite to it. Whenever such disturbed flows were created, they were always formed as a paired structure in both the main and side daughter vessels, but were never in the form of a closed
Re,,=llO d/D= 1.0 i&=127mms-’ 0,/Q, = 1.0
Re.=l47 d/D= 1.0 lJo=9D9mms-’ Q,/Q = 0.25
Fig. I. Flow patterns obscrvcd in the common median plane of 3 mm diameter 6O’(uppcr) and 135”(lower) glass model T-junctions as traced from the paths of polystyrene microsphercs in 25% aqueous glycerol. The junctions. which had a very small radius orcurvsturc at the bend, were made by fitting and glueing together lengths of thin-walled glass tubing. The solid lines represent paths of tracer microsphcres in or close IO the median plane. the dashed lines paths which arc far out or the median plane. some of which round their ways from the main to the side recirculation zone encircling the mainstream. The arrows at S and R indicate the respective separation and reattachment points of the flow in the recirculation zones. The numbers indicate particle velocities in mm s-‘. (From Karino and Goldsmith. 1985.)
Row patterns in vortex as predicted for two-dimensional
the dog descending
bifurcations
and T-junctions (Hung and Naff, 1969; Kawaguchi and Hamano, 1979). The present study was designed to test whether these findings hold true in natural arterial T-junctions where the geometrical structure at the branching site is far more complex than in the glass models used in our previous investigations.
METHODS
Preparation of a transparent
40rtlI
An isolated transparent segment of the descending aorta containing branches of the celiac, superior mesenteric and right and left renal arteries was prepared from a dog by the method described by Karino and Motomiya (1983). A 22 cm long arterial segment which included a 12 cm long portion of the thoracic aorta proximal to the branch of the celiac artery was obtained from a IS kg dog sacrificed at the end of experiments carried out for other purposes. After rinsing the vessel with isotonic saline and clearing the excesstissue. the aorta and its four major branches (the celiac, superior mesenteric and right and left renal arteries) were cannulated with thin-walled stainless steel pipes, glass tubes and polystyrene tubing which fitted lo the vessels.All the intercostal arteries and other smaller vessels were occluded by ligating and coagulating rhem with a fulgurator. The aorta was mounted on a three-dimensional supporting frame while keeping a physiological time mean trnnsmural pressure of 100 mm Hg. Special care was taken lo maintain the lengths (measured in situ) and the three-dimensional configuration of the aorta and side branches as close as possible to those observed prior 10 dissecting out the aorta. The vesselwas then fixed for 5 h by perfusing it with a mixture of 2% glutaraldehyde and 4% formaldehyde in normal saline under a physiological mean perfusion pressure of 100 mm Hg and, at the same time, immersing the whole segment in the same fixing solution. The arterial segment was dehydrated over 2-3 days by perfusing it with. and immersing it in, ethanol-saline mixtures of progressively increasing ethanol concentration under the same perfusion pressure, and finally suspending it in pure ethanol. The vessel segment was then encased firmly in a glass chamber. Finally, the arterial segment and the glass chamber were filled with methyl salicylate (oil of wintergreen), containing 5% ethanol, under the physiological mean perfusion pressure, to render the vesselsegment transparent. Two transparent vesselswere prepared by this method. Out of these, the better prepared one was used for flow studies. The aorta lost its elasticity during the process of fixing, dehydrating and rendering it transparent. However, the exact three-dimensional configuration of the natural blood vesselwas preserved.The greatest
539
aorta
advantage of this method was that the vesselbecame transparent without any optical distortion, allowing one to make observations and measurements of the Bow from any desired direction without the refraction errors inevitable when glass models and plastic casts are used. Experimental
procedure
and analysis
The transparent aorta in the glass chamber was vertically positioned with the iniet at the, bottom and firmly installed on the vertically mounted stage of a microscope. The aorta and its branches were then connected via 6.4 and 2.7 mm inner diameter plastic tubing to a head tank and collecting reservoirs, providing steady flow rates over the desired range from 90-1500 ml min-I. The areas of interest on the vessel were trans-illuminated with condensed parallel light provided by a Reichert Binolux twin-lamp assembly supplying either low intensity light from a tungsten filament lamp, or high intensity light from a 200 W d.c. mercury arc lamp with a blue filter to eliminate ultraviolet illumination. Dilute suspensions of a mixture of 15. 100 and 200 Mm diameter polystyrene microspheres (density p,=l.l6gcm-‘) in oil of wintergreen containing 5% ethanol (density I’= 1.18 gem-‘, viscosity q= 3.0 mPa s, refractive index n = 1.53) were subjected to steady flow through the transparent aorta. The behavior of individual suspendedtracer particles flowing through various regions of the aorta were observed through a low magnification microscope (2.5 x -15 x ) or a zoom lens (1 x -5 x ) attached to a tine camera, and photographed on 16 mm tine films (Kodak double X-negative) using a Locam 16 mm tine camera (Red Lake Labs, Santa Clara, CA) at film speedsfrom 300 to 500 pictures per second. The developed films were subsequently projected onto a drafting table and the movements of individual tracer particles were analyzed frame by frame with Ihe aid of a stop-motion 16 mm movie analyzer (Vanguard Instrument Corp., Melville, NY) lo obtain the detailed flow patterns and velocity distributions.
RESULTS
Geometrical
structure
of the oortic
T-junctions
As previously described for glass model T-junctions (Karino ef ol., 1979; Karino and Goldsmith, 1985). geometrical factors play an important role in determining the flow patterns and distribution of the fluid into the main and side branches at the junction. Thus, it is first necessaryto describe the geometrical features of the dog aortic T-junctions. Figure 2 shows a photograph of the isolated transparent dog descending aorta used in the present investigation. The internal diameter of the aorta measured at locations proximal lo each branching site varied from 7.3 to 5.6 mm. The celiac and superior mesenteric arteries were located on the ventral side of the aorta almost on
the same diametrical plane which bisected the aorta and the spinal column. The branching angle was slightly smaller than 90’ for both arteries as shown in Figs t-4. The branching interval (axial distance between the epices of flow dividers of two branches) for these arteries was about IOmm. The right and left renal arteries were located on the ventral half of the aorta. They branched off the aorta almost tangentially relative to the circumference of the cylindrical vessel and almost symmetrically about the plane bisecting the celiac, superior mesenteric arteries, aorta and spinal column. The branching angle was smaller than 45” for both arteries and the branching intervals were approximately 17 mm for the superior mesenteric artery and the right renal artery, and 6 mm for the right and left renal arteries. In addition. it was noted that, at each junction, the curvature of the vessel wall was very sharp (<90”) at the flow divider, but gently rounded at the bend opposite to it. This was true also for the other vessel, which was not used for flow studies due to some artifacts in geometrical arrangements of branches. Furthermore. there was a sudden decrease in the aortic diameter distal to each branch as indicated by the values given in Fig. 2 and the outlines of the vessel wall drawn in Figs 3 and 4. From the results obtained in glass model T-junctions ( Karino ct al., 1979; Karino and Goldsmith, 1985) one would predict that such vesselgeometry represents the optimum condition for minimizing the size of both the main and side recirculation tones. and hence the dcgrce of flow disturbance at the aorlic T-junctions. Drtuiked /low puttrrns and /low chuructrristics A series of flow expcrimcnts were carried out over wide ranges of inflow Reynolds numbers, Re,= D, ij#p/q (D, and u0 being the respective vessel diameter and mean fluid velocity in the aorta measured at the narrowest point proximal to each branch), and flow ratio, Q,/Qu (outflow/inflow in the aorta), at each junction. To relate the results to those obtained in glass model T-junctions (Karino et ol., 1979; Karino and Goldsmith, 1985). experiments were first conducted by opening only one side branch at a time. For this reason, the inflow Reynolds numbers were evaluated independently at each junction. Quasi-parabolic flow was chosen as the entrance flow to the arterial segment. This was based on the velocity profiles measured at various locations along the aorta of dogs obtained by Shultz (1972) using a hot-film anemometer. The Row patterns observed at each branching site were, in general. similar to those previously observed in various glass model T-junctions. Figures 3 and 4 illustrate the detailed flow patterns observed at the aorto-celiac and aorto-superior mesenteric artery junctions respectively in steady flow at the geometrical flow rate ratio. This was defined as the flow rate ratio calculated by assuming that the flow in the parent vessel is distributed into the two daughter vesselsin
proportion to their cross-sectional areas assessedat the flow divider. As shown in these figures.a recirculation zone consisting of a pair of thin-layered spiral secondary Rows located symmetrically on both sides of the common median plane of the aorta and side branches were formed in the aorta at each branching site. Particles located on streamlines slightly away from the common median plane were deflected sideways at the flow divider, and traveled laterally and very slowly along the vesselwall on both sides of the common median plane almost at right angles to and encircling the undisturbed parallel-streamlined mainstream. They then changed direction, some in the outer orbits trailing along the vesselwall in the aorta, and others moving backward along the lateral wall of the aorta describing spiral orbits of increasing diameter, then changing direction again and approaching the proximal leading edge of the side branch close to the common median plane and entering the branch. The streamline which divided the inflow into the side branch from that in the aorta was located close to the ventral wall (upper wall in the figure) of the aorta on the common median plane. However, moving further away from the common median plane, the location of the dividing streamline gradually shifted towards the dorsal (lower) wall forming paired thin-layered slow flow located symmetrically on either side of the common median plane adjacent to the vessel wall. As a result, fluid was drawn into the side branch even from the dorsal wall of the aorta proximal to the junction. At the geometrical flow rate ratio. formation of paired spiral secondary tlows was observed at all four major junctions in the descending aorta. However, as predicted above from the anatomical structure of the aortic T-junctions. no recirculation zone was formed in the side branches. At a given Re,,, the size of the recirculation zone increased with decreasing Q,/Q,. To identify the regions of high and low wall shear stressin the area of the junction, velocity distributions in the common median plane were measured for the flow at the aorto-celiac artery junction shown in Fig. 3. The results are shown in Fig. 5. As is evident from the figure, velocity distributions are skewed towards the ventral wall (upper wall in the figure) in the aorta and towards the inner wall of the T-junction in the side branch, indicating that regions of high wall shear stress are located along the inner walls of the T-junction just distal to the flow divider. Factors aficting thefirmution oortic T-jrnctions
of recirculation zones at
As described earlier, a recirculation zone which consisted of a pair of spiral secondary flows was formed at each junction of the four major arteries which branch off the descending aorta. The formation and the size of the recirculation zone were largely dependent on two major factors, the flow rate ratio, Q,/Qm and the inflow Reynolds number, Re,. To investigate the effectsof these factors, measurements of the critical Reynolds number, Re,, for the formation of
Fig. 2. Photograph or the segment of transparent dog aorta used in the present experiments showing the geometrical arrangement of the celiac, sqcrior mesenteric and left renal branches ( from top lo bottom). The numbers indicate the internal diameter of the aorta in mm. Note the gentle curvature of the outer wall at each branching site in Contras1 to the very sharp curvature of the wall al the flow divider. Also, there is a marked decrease in aortic diameter distal to each hrwzh.
Flow patterns in the dog descending aorta
Rev=609 d/D=4_QiZ2 ij,=21Smm5e’ Q/Q* -0.72
Fig. 3. Detailed flow patterns at the aorto-celiac artery junction of the aorta shown in Fig. 2 at Ru, =609 and geometrical Row rate ratio. Q,/Q,,=O.?Z (72% of the flow leaving through the aorta). Shown are tracings of the paths of polystyrene microspheres. the solid lines being paths along the mainstream in the median plane of the aorta and branch. the dashed lines paths on the secondary flow and recirculation zones lying out or the median plane. Note the gentle curvature of the wall at the bendoppositethe flow dividerin contrast to the sharp curvature ol the wall at the flow divider. The numbers indicate the particle velocities in mm s - ‘.
Re,=1,002 d/D= 3.9/&S
ij,= 395 mm s-’ Q,/Q,
il
= 0.64
artery
Abdominal
oorto
Fig. 4. Flow patterns, as in Fig. 3. at the aorto-superior mcscnteric junction at Re,== 1002 and geometrical Row raft ratio, Q,/Qu -0.64 (44% of the flow leaving through the aorta). The cehac artery was occluded. Here, the sudden decrease in aortic diameter distal to the flow divider is particularly noticeable.
recirculation zones and fully developed disturbed Bows at each T-junction were carried out. This was done by observing through a microscope the motion of the smallest (I5 pm) diameter tracer polystyrene microspheres located near the lateral and outer (lower) walls of the T-junctions as a function ofQ, /Q,,. Here again, in order to compare the results with those obtained in glass model T-junctions. experiments were
carried out by opening only one side branch of interest at a time. The results are shown as a plot of Re, vs Q,/Qo for each junction in Figs 6-8. In these figures, critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed Row which was de&ted as the Re, at which the largest spiral orbit reached the dorsal (outer) wall, are indicated respectively by the dashed and solid lines drawn
T. KARINO et al.
Re,= 609 d/D-407.2 &=215mms-’ Q, IQ. = 0.72
Ql
Abdaminal oorto Fig. 5. Distribution of fluid velocity in the common median plane of the aorta and celiac artery at the geometrical flow rate ratio as obtained from the measured velocities of tracer polystyrene microspheres when the superior mesenteric artery was occluded. The numbers indicate the maximum velocities of the spheres in mm s - I.
through the points of measured values. At the norto-celiac artery junction, as illustrated in Fig. 6 at the value of Q, /Q,, -0.72 corresponding to the geometrical tlow rate ratio (indicated by the vertical dashed line), spiral secondary flows first appeared at RP, -290, grew in size with increasing Ree, and at Rc,c930. the largest spiral orbit reached the dorsal (outer) wall of the descending aorta. At this point, the paired thin-layered spiral secondary flows completely encircled the undisturbed parallel-streamlined mainflow situated close to the common median plane. Beyond the critical Reynolds number for the formation of fully developed disturbed flows, a further increase in Re, resulted in an increase of the longitudinal length and intensity of the spiral secondary flows. No turbulent flow was observed at aortic T-junctions under any flow conditions covered in the present investigation. At the aorto-superior mesenteric artery junction (cf. Fig. 7). the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher than those for the aorto-celiac artery junction. This may reflect the particular anatomical structure of this Tjunction, i.e. the sudden reduction of aortic diameter distal to the flow divider described earlier, which favors the distribution of the aortic inflow into the side branch. At the aorto-left renal artery junction (cf. Fig. 8). spiral secondary flows were formed at Re, much lower than those for the aorto-superior mesenteric artery junction. However, within the range of Re, covered in the present study, the formation of fully developed disturbed Rows was not observed at the geometrical flow rate ratio (Q,/Qc=O.69). Presumably, this is due to the fact that both the diameter
ratios, d/D, (side/parent vessel)and branching angles for both right and left renal arteries are much smaller than those for the other two arteries. The formation of recirculation zones and fully developed disturbed flows at aortic T-junctions were also observed when all the branches were opened and the aortic inflow was distributed to the distal aorta and the four side branches in proportion to their crosssectional areas evaluated at each flow divider. However. due to the technical diliiculties encountered in illuminating areas wide enough to cover two adjacent branches as well as recording on 16 mm tine films the movements of tracer microspheres at high magnification sufficient for film analysis, it was not possible to study or demonstrate the details of the interactions of the two recirculation zones which formed at any two adjacent branches, such as the celiac and superior mesenteric arteries and the right and left renal arteries. DISCUSSION
We have studied the flow patterns at aortic Tjunctions in detail using a segment of dog descending aorta rendered transparent, and analyzed the threedimensional structure and characteristics of the recirculation flows which formed around the flow divider of each branching site. The experiments were carried out using a rigid-walled vessel and under conditions of steady flow. The results may therefore not be directly applicable to the real situation in vitro where the vesselwall is elastic and the flow is pulsatile. In light of this, caution should be exercised in applying the present results to pulsatile flow in uivo. The fact that paired recirculation flows were formed at Re =300-600, which are much lower than estimated
Flow patterns in the dog descending aorta
545
1.600
Aorta-Cek
Aorto-hperior
junetiem
Mesenterie.
junction
1.000
v *
Reo
. 800
600
I
400
200
I -_6~_-_o~,_-o.d-.
. -
0.8 ::
Fig. 6. Plot of the inflow Reynolds number for the aorto-celiac artery junction showing the measured critical Reynolds numbers for the formation of spiral secondary flows (open circles) and fully developeddisturbed flows (closedcircles)asa functionof the flow rate ratio et/Q,,. The vertical dashed line indicates the gcomctrical flow rate ratio for this T-junction.
0
_“_.o~2
. .._
,.-o.,_.‘-&2’_
o*a
_L.__~,
% Fig. 7. Plot of the inflow Reynolds number for the aorto-superior mesenteric artcry junction showing the measured critical Reynolds numbers for the formation of spiral secondary flows (opn circles) and fully dcvclopcd disturbed flows (closed circles) as a function of the flow rate ratio Q,/Q,,. The vertical dashed line indicates the geometrical flow rate ratio for this T-junction,
physiological time-averaged Re (Attinger, 1964), and The results demonstrated convincingly that the that the changes in the cross-sectional area of the dog formation of paired spiral secondary flows, previously observed in various glass model T-junctions, does descending aorta during a cardiac cycle is only f 3% (Pate1 et al., 1964). makes it most likely that there is no occur in natural vessels.The fact that such disturbed significant digerence in general flow patterns between flows were formed at Reynolds numbers much lower the flow in rigid models and elastic natural vessels. than those prevailing in uiuo (Attinger, 1964; Lutz er However, it is possible that critical Re for the onset of al., 1975) makes it plausible that spiral secondary flows recirculation and fully developed disturbed flows is are formed at aortic T-junctions under normal physiosomewhat lower in elastic than rigid vessels since logical conditions even if only for a short period some in vitro experiments have shown that the comduring the cardiac cycle. The results by Hutchison et pliance of vessel walls has an etTect in reducing the al. (1988) who measured velocity contours at the aostic intensity of turbulence (Stein and Sabbah, 1980). junctions in anesthetized dogs using pulsed Doppler The major purpose of the present investigation was ultrasound techniques provide full support to our to extend our previous studies with various glass present observation. In the aortic junctions, however, model T-junctions (Karino et ol., 1979; Karino and due to the particular anatomical structure of the vessel Goldsmith, 1985) to natural vesselsin order to confirm wall at each branching site, i.e. the sharp curvature of our findings on the formation of recirculation zones, the wall at the Row divider, the gentle round curvature and to compare the differences in various anatomical at the bend opposite to it, and the sudden step-wise decrease in the aortic diameter distal to each branch, and flow characteristics between the model and natuno recirculation zone was formed in the side branches ral vessels.
T. KARINO er al.
546
1.400~
1.200
-
1.000
-
fb 800.
600.
400.
200.
0 -,-
0.2
*--!l--1-
A-O.6 0.4
08
-I
1.0
ii:
Fig. 8. Plot of the inflow Reynolds number for the aorlo-left renal artery junction showing the measured critical Reynolds numhcrs for the formation of spiral secondary flows (open circles) and lully develoPed disturhcd flows (closed circles) as a function of the flow catc ratio Q,/Q,,. fhc vertical dashed line indicates the geometrical flow rate ratio for this Tjunction.
at the geometrical flow rate ratios. At a given flow rate ratio, Q,/Qo, the measured critical Reynolds numbers, Res. for the formation of fully developed disturbed flows were much higher in aortic T-junctions than those obtained in glass model T-junctions having equivalent branching angles and diameter ratios, d/D, (side/parent vessel). For example, in the aorto-celiac and aorto-superior mesenteric artery junctions, Re, at their geometrical
flow rate ratios was approximately
whereas Re, in the corresponding glass model T-junctions was approximately 400 and 300 respectively. These data indicate that, in the circulation, conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows. However, even in such well designed natural arteries, there were some regions where flow was locally disturbed and both the fluid elements and suspended particles behaved in a manner different from that in the mainstream. As previously observed in glass model T-junctions, a standing recirculation 900 and 1400 respectively,
zone consisting of a pair of thin-layered spiral secondary flows was formed at the flow divider of each branching site in the dog descendingaorta over a wide range of flow conditions including the time-averaged estimated mean values of the physiological flow rates and flow rate ratios (Attinger. 1964; Lutz er al., 1975). Thus, at each major branching site of the dog descending aorta, the behavior of plasma and cells located in the vicinity of the vessel wall was completely different from those in the core ROW. Due to the particular flow patterns described above, vascular endothelial cells at aortic T-junctions will experience shear stresses in different directions depending on their locations. Since it is known that these endothelial cells are susceptible to flow and exhibit certain morphological changes corresponding to the direction and magnitude of fluid shear stress( Flaherty et al., 1972; Reidy and Bowyer. 1971; Dewey et al.. 1981; Levesqueet al.. 1986). it is likely that, at aorticTjunctions. endothelial cells located within the regions ofspiral secondary flows are elongated in the direction of the local flows which, in some regions, are completely different from those in the mainstream. In the present paper, we have shown that velocity distributions in the common median plane arc skewed toward the inner walls at each tlow divider. It is possible to calculate the local wall shear stresses from these velocity distributions, although WCdid not do this for the following reason. The common median plane is a very special plant bccausc it is not only a plane of symmetry of the vcssclwall, but also of the flow field. Thus, the intcrscction between the common median plane and the inner walls downstream of the flow divider in both the aorta and side branch acts as a line of stagnation on either side of which flow is deflected and spiral secondary flows are formed. It is likely that the wall shear stresses calculated along the lines of stagnation do not provide the maximum or representative values prevailing around the flow divider. In fact, the results from a model mass transfer experiment by Adamson and Roach (1981) indicate that, at T-junctions, the regions of high wall shear stressare located not on the common median plane (line of stagnation) but in a paired arrangement, symmetrically on both sides of it in a pattern similar to the spiral secondary flows shown earlier in Figs 3 and 4 in the present paper. Due to the large variation in the magnitude of wall shear stressin the recirculation zone, as well as in the mainstream proximal to the leading edge of the side branches and distal to each flow divider, the degree ofelongation of individual endothelial cells will also be diRerent from region to region, the highest being around the flow divider and the lowest along the outer orbits of the spiral secondary flows in the backflow region and at the leading edge of the side branch opposite to the flow divider. Such large variations in wall shear stress and the morphology of endothelial cells, as well as the particular flow pattern itself, may atTecttransport phenomena at the bloodvessel wall boundary although no visible atheroscler-
Flow patterns in the dog descending aorta
otic lesion was found at such sites in dog aortas prepared in the present study. Presumably, this was due to the relatively shorter life span of dogs compared to that of humans. Recently, we have looked at some human aortas and found that the anatomical structure of the vesselwall at major junctions is very much similar to that observed in dog aortas, i.e. the curvature of the vesselwall is very sharp at the flow divider and gently rounded opposite it. Thus, it is possible that similar flow patterns exist at the major junctions of human descending aorta where atherosclerotic lesions were found in most autopsy specimens. Although no direct correlation has been established so far between flow patterns, spatial distribution of wall shear stressand the sites of atheromatous plaques and atherosclerotic wall thickenings along the wall of the human aorta, the existing data indicate that preferential areas for the formation ofatherosclerotic lesionsin man lie around the proximal leading edge and lateral sides of the orifices of side branches (Murphy et al.. 1962; Caro et al., 1971; Zarins. 1986). In light of our present findings, these correspond to the regions of slow flow, hence low wall shear stress.where endothelial cells are likely to be minimally elongated. In such regions, it is possible that because of the much lower translational velocity and shear stressprevailing there, platelets and lipids have more opportunity to interact for longer periods with the vesselwall than anywhere else. This, in turn, may enhance the deposition of platelets. if activated, on the vessel wall and increase the uptake of lipids by the endothelial cells existing in such regions. What is not clear at present is how much the uptake of atherogenic lipoproteins by endothelial cells is aflected by the magnitude of the local wall shear stressand the nature of the individual ceils located in different regions of the vesselwall at arterial branching sites. In this regard, there have been several interesting reports which indicate that cell turnover is enhanced in regions of round-shaped endothclial cells (Caplan and Schwartz, 1973), that exposure ofendothelial cells to moderate to high shear stress prevents atherosclerosis in monkeys (Zarins et 01.. 1981). enhances the production of prostacyclin by the cells ( Frangos et al., 1985). and that vesicular pinocytosis in endothelial cells is enhanced by a change in the level of shear stress (Davies et al., 1984). However, it is still not clear how these individual effects are incorporated in the long process of localized genesis and development of atherosclerotic lesions in the circulation. To find a full explanation for the localization of atherosclerosis in the human arterial tree, it is necessary to further investigate the erect of disturbed flows on the transport and uptake of atherogenic lipoproteins by endothelial cells, and the effects of high and low shear stresseson the morphology and functions of endothelial cells under various flow conditions. AcknowledgemenfrThis work was supported by Grant HL29502 from the National Heart, Lung and Blood Institute. N.I.H., U.S.A.. Grant MT-7084 and MT-1835 from the
s4-l
Medical ResearchCouncil of Canada.and a grant from the Quebec Heart Foundation. The authors thank C. Artigas and M. Sgro for their technical assistance and D. Bessofor typing the manuscript.
REFERESCES
Adamson.S. L. and Roach, M. R. (1981) Measurement of wall shear stress in a glass model renal bifurcation by a technique that monitors the rate of erosion of an opaque coating layer. Biorheology IS, 9-21. Attinger, E 0. (1964) The cardiovascular system. In P&utile Blood Flow (Edited by Attinger. E. 0.). p. 3. McGraw-Hill, New York. Bharadvaj. B. K.. Mabon. R. F. and Giddcns, D. P. (1982) Steady Row in a model of the human carotid bifurcation. Part I-flow visualization. J. Biomechonics l&349-378. Caplan. B. R. and SchwartL C. J. (1973) Increased endothelial all turnover in areas of in t+ro Evans blue uptake in the pig. At/teroxlerosis 17, 401417. Caro. C. G., Fitz-Gerald, J. M. and Schroter. R. C. (1971) Arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Pm. R. SW Lmd. Bl77.360-374. Davies, P. F.. Dewey. C. F. Jr. Bussolari. S. R.. Gordon. E. J. and Gimbronc. M. A. Jr (1984) Influcna of hemodynamic forces on vascular cndo~helial function. In cjirro studies of shear stress and pinocytosis in bovine aorlic cells. J. c/in. Inoesf. 73. 1121-l 129. Deters, 0. J.. Mark, F. F.. Bcrgcron, C. B.. Friedman, M. H. and Hutchins. G. M. (1984) Comparison of steady and pulsalilc flow near the ventral and dorsal walls of casts of human aorlic bifurcations. J. hiomech. Enyng 106, 79-82. Dewey, C. F. Jr, Bussolari. S. R.. Gimbronc. M. A. Jr and Davies. P. F. (1981) The dynamic response of vascular cndolhclial alls to fluid shear stress. 1. biumech. Enyng 103. 177-185. Flahcrly. J. T.. Picra. J. E.. Fcrrans. V. J.. Patcl, D. J.,Tuckcr. W. K. and Frv. D. L. (1972) Endolhclial nuclear oaItcrns in the canine ar&ial tree wiih particular re&ren& to hcmodynamic events. Circ. Res. 30. 23-33. Frangos. J. A., Eskin. S. G.. McIntyre. L. V. and Ives. C. L. (1985) Flow tffccts on prostacylin production by cullurcd human endolhclial fells. Science 277. 1477-1479. Fukushima, T., Homma. T.. Azuma, T. and Harakawa. K. (1987) Characteristics of secondary flow in steady and pulsatilc flows through a symmetrical bifurcation. Biorheology 24. 3-12. Goldsmith, H. L. and Karino. T. (1978) Mechanically induccd thromboemboli. In Quonrilurice Cordioooxular Studies-Clinical and Rrseurch Applicorions o/Engineering hinciples (Edited by Hwang. N. H. C.. Gross, D. R. and Patcl. D. J.), pp. 289-351. University Park Press, Baltimore. Hung, T. K. and NaA; S. A. (1969) A mathematical model of systolic blood flow through a bifurcation. Proc. 8th IN. Confi Med. Biorny.. Chicago, IL. Hulchison. K. J.. Karpinski, E.. Campbell, J. D. and Potemkowski, A. P. (1988) Aortic velocity contours at abdominal branches in anesthetized dogs. J. Biomechanics 21, 277-286. Karino. 7. and Goldsmith. H. L. (1985) Particle flow behavior in mod& of branchina vessels.11. Effects of branching angle and diameter ratio on flow patterns. Biorheology 22.87-104. Karino. T.. Kwong, H. M. and Goldsmith. H. L. (1979) Particlc llow behavior in models of branching vessels. I. Vortices in 90” T-junctions. Biorheology 16. 231-248. Karino, T. and Motomiya. M. (1983) Flow visualization in isolated transparent natural blood vessels.&rheology 20, 119-127.
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Karino. T. and Motomiya M. (1984) Flow through a venous valve and its implication in thrombus formation. Thromb. Res. 34, 245-257. Kawaguchi M. and Hamano, A. (1979) Numerical study on bifurcating flow ofa viscous fluid. J. physiol. Sot. Jopon 46. 1X0-1365. Levesquc. M. J.. Liepsch, D., Moravec. S. and Nerem R. M. (1986) Correlation of cndothelial cell shape and wall shear stress in a stenosed dog aorta. Atherosclerosis 6. 220-229. Luy R. J, Cannon. J. N.. BischotT, K. B., Dedrich. R. L.. Stiles. R. K. and Frv. D. L. (1975) Wall shear stress distribution in a model canine artery’during steady flow. Circ. Res. 41. 393-399. Moravec. S. and Liepsch, D. (1983) Flow visualization in a model of three-dimensional human artery with Newtonian and non-Newtonian fluids, Part I. Riorheology 20, 745-759. Motomiya. M. and Karino, T. (1984) Flow patterns in the human carotid artery bifurcation. Stroke 15, 50-56. Murphy, E. A., Rowsell. H. C., Downie. H. G.. Robinson, G. A. and Mustard, J. F. (1962) Encrustations and atherosclerosis: the analogy between early in riro lesions and deposits which occur in extracorporeal circuits. Can. med. Ass. J. 87, 259-274.
Patel. D. J.. Greenfield. J. C. Jr and Fry, D. L. (1964) In viuo pressure-length-radius relationship of certain blood vessels in man and dog In PulsutiC Blood Flow (Edited by Attinger. E. 0.). pp. 293-305. McGraw-Hill. New York.
Rayman, R, Kratky. R. G. and Roach, M. R. (1985) Steady Row visualization in a rigid canine aortic cast. 1. Bit+ mechanics 18, 863-875. Reidy. M. A. and Bowyer, D. E. (1977) Scanning electron microscopy of arteries. The morphology of aortic endothclium in hemodynamically stressed areas associated with branches Atherosclerosis 26, 181-194. Schettler. G, Ncrem. R. M., Schmid-Schiinbein, H, M&l. H. and Diehm, C. (1983) Fluid Dynamics as a Localizing Fuctorfir Atherogenesis. Springer, Heidelberg. Shultt D. L. (1972) Pressure and Row in lame arteries. In Cclrdiovasc&r F&d Dynamics (Edited By Beergel.D. H.). pp. 287-314. Academic Press, London. Stein, P. D. and Sabbah. N. H. (1980) Hemorheology of turbulence. Biorheology 17, 301-319. Walburn. F. J.. Sabbah. H. N. and Stein. P. D. (1981) Flow visualization in a mold of an atherosclerotic human abdominal aorta. J. biomech. Engng 103, 168-170. Yoshida. Y.. Yamaguchi. T.. Caro, C. G., Glagov. S. and Nerem, R. M. (1988) Role o/Blood Flow in Arherogenesis. Springer, Tokyo. Zarins, C. K. (1986) Hemodvnamics in atherogenesis. In Vascular Surgery-A Comprehensit~e Rerirw (2nd Edition) (Edited by Moore, W.). pp. 97-l IS. Grune and Stratton, Orlando. Zarins. C. K., Bomberger. R. A. and Glagov. S. (1981) Local effects of stenoses: Increased flow velocity inhibits atherogenesis. Circulation 64, 22 l-227.
PATTERNS AT THE MAJOR T-JUNCTIONS DOG DESCENDING AORTA MINEO
TAKESHI KARINO;
McGill University Medical
MOTOMIYA
OF THE
and HARRY L. GOLDSMITH
Clinic. Montreal General Hospital, Quebec H3G 1A4, Canada
1650 Cedar Avenue. Montreal,
Abstnet-Using a novel technique developed in our own laboratory. an isolated transparent arterial segment containing the whole descending aorta and its four major branches was prepared from a dog The flow patterns at each aortic T-junction were studied in detail under the conditions of steady flow by means of flow visualization and cinemicrographic techniques. It was found that a standing recirculation zone consisting of a pair of thin-layered spiral secondary flows located symmetrically about the common median plane of the aorta and side branches was formed at each T-junction over a wide range of flow conditions including the time-averaged estimated mean values of physiological flow rates and flow rate ratios. The resultssupport the recent in riro findings by other investigators that Row reversal occurs at some junctionsof the dog abdominal aorta during each cardiac cycle. The flow patterns at the aortic T-junctions were very much similar to those previously observed in various glass model T-junctions. However. due to the particular anatomical structure of the vessel wail at each branching site (the curvature of the wall was very sharp at the flow divider. but gently rounded at the bend opposite to it) no recirculation zone was formed III the side branches. At a given flow rate ratio, the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher in aortic T-junctions than those in glass model T-junctions having equivalent branching angles and diameter ratios. These results indicate that, in the circulation. conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows.
1978; Schcttlcr
NWIENCLATURE
Thcorctically, parent vessel diameter inllow rate outllow rate critical Reynolds number inflow Reynolds number inflow mean lluid velocity side branch diameter viscosity of suspending fluid density of suspending fluid density of tracer microsphsrcs
tional
various channels,
relatively
it has now
(11 ul.,
1988).
of computa-
bccomc
possible
but the analysis is still limited
those vessels having over-simplified perimentally.
due to the difiicultics
have been conducted arteries (Bharadvaj
Ex-
in visualizing
the
ill airro using various models of
CI N/.. 1982; Moravec
and Liepsch,
1983; Fukushima
zt ul.. 19871 and arterial
molds
et ul.,
(Walburn
Rayman
large arteries by the progressive thickening
quality day,
1981; Deters
ct (I/.. 1985). However, casting and molding
it is still
casts and
et cl.,
1984;
even with the high
techniques available
not easy to precisely
duplicate
complex geometry of the vessel lumen encountered various regions of the circulation.
and
post-mortem
atherosclerotic randomly,
plaques rich in cholesterol. indicate
in the circulation,
localized sites in the arterial
the entrances
of bifurcations
To solve the problem,
that
lesions on the vessel wall develop not
and not everywhere
at particular
studies
but
prepare
we developed
transparent
natural
from animals and humans post-mortem Motomiya,
tree such as
and T-junctions,
isolated
curved segments of arteries where the blood flow is
various regions of the circulation
disturbed
and photographing
and eddies are likely to form. Therefore.
elucidate the possible connection and
the
localized
atherosclerosis.
genesis
a considerable
to
between blood flow
and
dcvclopmcnt
amount
of work,
cluding
studies from our own laboratory,
carried
out in recent years (Goldsmith
of in-
has been
and Karino.
particles
(Karino
and
of the flow in
by directly observing
the behavior of suspended tracer
and hardened
we have previously through
venous
(Karino
and
blood cells flowing
through
bifurcation
bogenesis sites. 537
and
studied the detailed flow patterns valves
Motomiya,
1984), in connection
jorm
to
vessels
normal and diseased vessels. Using the above method,
artery
Received in final 6 Sepremher 1989. *To whom correspondence should be addressed.
in
1983). This has, for the first time, enabled
us to study in detail the characteristics
and
a method blood
tothe
formation Clinical
to
gcomctrics.
and eventual hardening of the vessel wall through the ofatheromatous
to
dctailcd Row patterns in oiuo. most of the flow studies
disease which affects
is a degenerative
techniques.
1983; Yoshida the dcvclopmcnt
simulate the steady or pulsatilc tlow of blood through
INTRODUCTIOK Atherosclerosis
cr ul.. through
in
dog
saphenous
veins
1984) and at the carotid
in man (Motomiya
and
Karino.
with the high incidence of throm-
atherogenesis
respectively,
at
these
538
T. KARISO cr al.
The present paper extends the work to a study of the detailed flow patterns at arterial T-junctions in the descending aorta of the dog. The groundwork for this study was carried out earlier using glass models of T-junctions having various branching angles and diameter ratios (Karino et al.. 1979; Karino and Goldsmith, 1985). Using dilute, neutrally buoyant suspensions of polystyrene microspheres, we showed that when flow entered the main tube, paired spiral secondary flows and recirculation zones symmetrical about the common median plane were formed at the entrances of the main and side daughter vessels as illustrated in Fig. 1 for 60” and 135” uniform 3 mm diameter Tjunctions. Such disturbed Row was observed over a wide range of inflow Reynolds numbers and flow rate ratios in the two daughter vessels. Moreover, as shown in the figure, the side and main recirculation zones
were connected through a part of the stray flow from the main recirculation zone which traveled backward along the vessel wall, crossed above and below the mainstream encircling it, and then entered the comer recirculation zone at the leading edge of the side branch. It was also shown that, at a given Reynolds number and Row rate ratio (side/parent vessel), a decrease in branching angle and side tube diameter resulted in a decrease in the size of both the main and side recirculation zones. The formation of the complex spiral secondary flows and recirculation zones was largely determined by the flow rate ratios in the daughter vessels, the curvature of the walls at the flow divider, and the bend opposite to it. Whenever such disturbed flows were created, they were always formed as a paired structure in both the main and side daughter vessels, but were never in the form of a closed
Re,,=llO d/D= 1.0 i&=127mms-’ 0,/Q, = 1.0
Re.=l47 d/D= 1.0 lJo=9D9mms-’ Q,/Q = 0.25
Fig. I. Flow patterns obscrvcd in the common median plane of 3 mm diameter 6O’(uppcr) and 135”(lower) glass model T-junctions as traced from the paths of polystyrene microsphercs in 25% aqueous glycerol. The junctions. which had a very small radius orcurvsturc at the bend, were made by fitting and glueing together lengths of thin-walled glass tubing. The solid lines represent paths of tracer microsphcres in or close IO the median plane. the dashed lines paths which arc far out or the median plane. some of which round their ways from the main to the side recirculation zone encircling the mainstream. The arrows at S and R indicate the respective separation and reattachment points of the flow in the recirculation zones. The numbers indicate particle velocities in mm s-‘. (From Karino and Goldsmith. 1985.)
Row patterns in vortex as predicted for two-dimensional
the dog descending
bifurcations
and T-junctions (Hung and Naff, 1969; Kawaguchi and Hamano, 1979). The present study was designed to test whether these findings hold true in natural arterial T-junctions where the geometrical structure at the branching site is far more complex than in the glass models used in our previous investigations.
METHODS
Preparation of a transparent
40rtlI
An isolated transparent segment of the descending aorta containing branches of the celiac, superior mesenteric and right and left renal arteries was prepared from a dog by the method described by Karino and Motomiya (1983). A 22 cm long arterial segment which included a 12 cm long portion of the thoracic aorta proximal to the branch of the celiac artery was obtained from a IS kg dog sacrificed at the end of experiments carried out for other purposes. After rinsing the vessel with isotonic saline and clearing the excesstissue. the aorta and its four major branches (the celiac, superior mesenteric and right and left renal arteries) were cannulated with thin-walled stainless steel pipes, glass tubes and polystyrene tubing which fitted lo the vessels.All the intercostal arteries and other smaller vessels were occluded by ligating and coagulating rhem with a fulgurator. The aorta was mounted on a three-dimensional supporting frame while keeping a physiological time mean trnnsmural pressure of 100 mm Hg. Special care was taken lo maintain the lengths (measured in situ) and the three-dimensional configuration of the aorta and side branches as close as possible to those observed prior 10 dissecting out the aorta. The vesselwas then fixed for 5 h by perfusing it with a mixture of 2% glutaraldehyde and 4% formaldehyde in normal saline under a physiological mean perfusion pressure of 100 mm Hg and, at the same time, immersing the whole segment in the same fixing solution. The arterial segment was dehydrated over 2-3 days by perfusing it with. and immersing it in, ethanol-saline mixtures of progressively increasing ethanol concentration under the same perfusion pressure, and finally suspending it in pure ethanol. The vessel segment was then encased firmly in a glass chamber. Finally, the arterial segment and the glass chamber were filled with methyl salicylate (oil of wintergreen), containing 5% ethanol, under the physiological mean perfusion pressure, to render the vesselsegment transparent. Two transparent vesselswere prepared by this method. Out of these, the better prepared one was used for flow studies. The aorta lost its elasticity during the process of fixing, dehydrating and rendering it transparent. However, the exact three-dimensional configuration of the natural blood vesselwas preserved.The greatest
539
aorta
advantage of this method was that the vesselbecame transparent without any optical distortion, allowing one to make observations and measurements of the Bow from any desired direction without the refraction errors inevitable when glass models and plastic casts are used. Experimental
procedure
and analysis
The transparent aorta in the glass chamber was vertically positioned with the iniet at the, bottom and firmly installed on the vertically mounted stage of a microscope. The aorta and its branches were then connected via 6.4 and 2.7 mm inner diameter plastic tubing to a head tank and collecting reservoirs, providing steady flow rates over the desired range from 90-1500 ml min-I. The areas of interest on the vessel were trans-illuminated with condensed parallel light provided by a Reichert Binolux twin-lamp assembly supplying either low intensity light from a tungsten filament lamp, or high intensity light from a 200 W d.c. mercury arc lamp with a blue filter to eliminate ultraviolet illumination. Dilute suspensions of a mixture of 15. 100 and 200 Mm diameter polystyrene microspheres (density p,=l.l6gcm-‘) in oil of wintergreen containing 5% ethanol (density I’= 1.18 gem-‘, viscosity q= 3.0 mPa s, refractive index n = 1.53) were subjected to steady flow through the transparent aorta. The behavior of individual suspendedtracer particles flowing through various regions of the aorta were observed through a low magnification microscope (2.5 x -15 x ) or a zoom lens (1 x -5 x ) attached to a tine camera, and photographed on 16 mm tine films (Kodak double X-negative) using a Locam 16 mm tine camera (Red Lake Labs, Santa Clara, CA) at film speedsfrom 300 to 500 pictures per second. The developed films were subsequently projected onto a drafting table and the movements of individual tracer particles were analyzed frame by frame with Ihe aid of a stop-motion 16 mm movie analyzer (Vanguard Instrument Corp., Melville, NY) lo obtain the detailed flow patterns and velocity distributions.
RESULTS
Geometrical
structure
of the oortic
T-junctions
As previously described for glass model T-junctions (Karino ef ol., 1979; Karino and Goldsmith, 1985). geometrical factors play an important role in determining the flow patterns and distribution of the fluid into the main and side branches at the junction. Thus, it is first necessaryto describe the geometrical features of the dog aortic T-junctions. Figure 2 shows a photograph of the isolated transparent dog descending aorta used in the present investigation. The internal diameter of the aorta measured at locations proximal lo each branching site varied from 7.3 to 5.6 mm. The celiac and superior mesenteric arteries were located on the ventral side of the aorta almost on
the same diametrical plane which bisected the aorta and the spinal column. The branching angle was slightly smaller than 90’ for both arteries as shown in Figs t-4. The branching interval (axial distance between the epices of flow dividers of two branches) for these arteries was about IOmm. The right and left renal arteries were located on the ventral half of the aorta. They branched off the aorta almost tangentially relative to the circumference of the cylindrical vessel and almost symmetrically about the plane bisecting the celiac, superior mesenteric arteries, aorta and spinal column. The branching angle was smaller than 45” for both arteries and the branching intervals were approximately 17 mm for the superior mesenteric artery and the right renal artery, and 6 mm for the right and left renal arteries. In addition. it was noted that, at each junction, the curvature of the vessel wall was very sharp (<90”) at the flow divider, but gently rounded at the bend opposite to it. This was true also for the other vessel, which was not used for flow studies due to some artifacts in geometrical arrangements of branches. Furthermore. there was a sudden decrease in the aortic diameter distal to each branch as indicated by the values given in Fig. 2 and the outlines of the vessel wall drawn in Figs 3 and 4. From the results obtained in glass model T-junctions ( Karino ct al., 1979; Karino and Goldsmith, 1985) one would predict that such vesselgeometry represents the optimum condition for minimizing the size of both the main and side recirculation tones. and hence the dcgrce of flow disturbance at the aorlic T-junctions. Drtuiked /low puttrrns and /low chuructrristics A series of flow expcrimcnts were carried out over wide ranges of inflow Reynolds numbers, Re,= D, ij#p/q (D, and u0 being the respective vessel diameter and mean fluid velocity in the aorta measured at the narrowest point proximal to each branch), and flow ratio, Q,/Qu (outflow/inflow in the aorta), at each junction. To relate the results to those obtained in glass model T-junctions (Karino et ol., 1979; Karino and Goldsmith, 1985). experiments were first conducted by opening only one side branch at a time. For this reason, the inflow Reynolds numbers were evaluated independently at each junction. Quasi-parabolic flow was chosen as the entrance flow to the arterial segment. This was based on the velocity profiles measured at various locations along the aorta of dogs obtained by Shultz (1972) using a hot-film anemometer. The Row patterns observed at each branching site were, in general. similar to those previously observed in various glass model T-junctions. Figures 3 and 4 illustrate the detailed flow patterns observed at the aorto-celiac and aorto-superior mesenteric artery junctions respectively in steady flow at the geometrical flow rate ratio. This was defined as the flow rate ratio calculated by assuming that the flow in the parent vessel is distributed into the two daughter vesselsin
proportion to their cross-sectional areas assessedat the flow divider. As shown in these figures.a recirculation zone consisting of a pair of thin-layered spiral secondary Rows located symmetrically on both sides of the common median plane of the aorta and side branches were formed in the aorta at each branching site. Particles located on streamlines slightly away from the common median plane were deflected sideways at the flow divider, and traveled laterally and very slowly along the vesselwall on both sides of the common median plane almost at right angles to and encircling the undisturbed parallel-streamlined mainstream. They then changed direction, some in the outer orbits trailing along the vesselwall in the aorta, and others moving backward along the lateral wall of the aorta describing spiral orbits of increasing diameter, then changing direction again and approaching the proximal leading edge of the side branch close to the common median plane and entering the branch. The streamline which divided the inflow into the side branch from that in the aorta was located close to the ventral wall (upper wall in the figure) of the aorta on the common median plane. However, moving further away from the common median plane, the location of the dividing streamline gradually shifted towards the dorsal (lower) wall forming paired thin-layered slow flow located symmetrically on either side of the common median plane adjacent to the vessel wall. As a result, fluid was drawn into the side branch even from the dorsal wall of the aorta proximal to the junction. At the geometrical flow rate ratio. formation of paired spiral secondary tlows was observed at all four major junctions in the descending aorta. However, as predicted above from the anatomical structure of the aortic T-junctions. no recirculation zone was formed in the side branches. At a given Re,,, the size of the recirculation zone increased with decreasing Q,/Q,. To identify the regions of high and low wall shear stressin the area of the junction, velocity distributions in the common median plane were measured for the flow at the aorto-celiac artery junction shown in Fig. 3. The results are shown in Fig. 5. As is evident from the figure, velocity distributions are skewed towards the ventral wall (upper wall in the figure) in the aorta and towards the inner wall of the T-junction in the side branch, indicating that regions of high wall shear stress are located along the inner walls of the T-junction just distal to the flow divider. Factors aficting thefirmution oortic T-jrnctions
of recirculation zones at
As described earlier, a recirculation zone which consisted of a pair of spiral secondary flows was formed at each junction of the four major arteries which branch off the descending aorta. The formation and the size of the recirculation zone were largely dependent on two major factors, the flow rate ratio, Q,/Qm and the inflow Reynolds number, Re,. To investigate the effectsof these factors, measurements of the critical Reynolds number, Re,, for the formation of
Fig. 2. Photograph or the segment of transparent dog aorta used in the present experiments showing the geometrical arrangement of the celiac, sqcrior mesenteric and left renal branches ( from top lo bottom). The numbers indicate the internal diameter of the aorta in mm. Note the gentle curvature of the outer wall at each branching site in Contras1 to the very sharp curvature of the wall al the flow divider. Also, there is a marked decrease in aortic diameter distal to each hrwzh.
Flow patterns in the dog descending aorta
Rev=609 d/D=4_QiZ2 ij,=21Smm5e’ Q/Q* -0.72
Fig. 3. Detailed flow patterns at the aorto-celiac artery junction of the aorta shown in Fig. 2 at Ru, =609 and geometrical Row rate ratio. Q,/Q,,=O.?Z (72% of the flow leaving through the aorta). Shown are tracings of the paths of polystyrene microspheres. the solid lines being paths along the mainstream in the median plane of the aorta and branch. the dashed lines paths on the secondary flow and recirculation zones lying out or the median plane. Note the gentle curvature of the wall at the bendoppositethe flow dividerin contrast to the sharp curvature ol the wall at the flow divider. The numbers indicate the particle velocities in mm s - ‘.
Re,=1,002 d/D= 3.9/&S
ij,= 395 mm s-’ Q,/Q,
il
= 0.64
artery
Abdominal
oorto
Fig. 4. Flow patterns, as in Fig. 3. at the aorto-superior mcscnteric junction at Re,== 1002 and geometrical Row raft ratio, Q,/Qu -0.64 (44% of the flow leaving through the aorta). The cehac artery was occluded. Here, the sudden decrease in aortic diameter distal to the flow divider is particularly noticeable.
recirculation zones and fully developed disturbed Bows at each T-junction were carried out. This was done by observing through a microscope the motion of the smallest (I5 pm) diameter tracer polystyrene microspheres located near the lateral and outer (lower) walls of the T-junctions as a function ofQ, /Q,,. Here again, in order to compare the results with those obtained in glass model T-junctions. experiments were
carried out by opening only one side branch of interest at a time. The results are shown as a plot of Re, vs Q,/Qo for each junction in Figs 6-8. In these figures, critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed Row which was de&ted as the Re, at which the largest spiral orbit reached the dorsal (outer) wall, are indicated respectively by the dashed and solid lines drawn
T. KARINO et al.
Re,= 609 d/D-407.2 &=215mms-’ Q, IQ. = 0.72
Ql
Abdaminal oorto Fig. 5. Distribution of fluid velocity in the common median plane of the aorta and celiac artery at the geometrical flow rate ratio as obtained from the measured velocities of tracer polystyrene microspheres when the superior mesenteric artery was occluded. The numbers indicate the maximum velocities of the spheres in mm s - I.
through the points of measured values. At the norto-celiac artery junction, as illustrated in Fig. 6 at the value of Q, /Q,, -0.72 corresponding to the geometrical tlow rate ratio (indicated by the vertical dashed line), spiral secondary flows first appeared at RP, -290, grew in size with increasing Ree, and at Rc,c930. the largest spiral orbit reached the dorsal (outer) wall of the descending aorta. At this point, the paired thin-layered spiral secondary flows completely encircled the undisturbed parallel-streamlined mainflow situated close to the common median plane. Beyond the critical Reynolds number for the formation of fully developed disturbed flows, a further increase in Re, resulted in an increase of the longitudinal length and intensity of the spiral secondary flows. No turbulent flow was observed at aortic T-junctions under any flow conditions covered in the present investigation. At the aorto-superior mesenteric artery junction (cf. Fig. 7). the measured critical Reynolds numbers for the formation of spiral secondary flows and fully developed disturbed flows were much higher than those for the aorto-celiac artery junction. This may reflect the particular anatomical structure of this Tjunction, i.e. the sudden reduction of aortic diameter distal to the flow divider described earlier, which favors the distribution of the aortic inflow into the side branch. At the aorto-left renal artery junction (cf. Fig. 8). spiral secondary flows were formed at Re, much lower than those for the aorto-superior mesenteric artery junction. However, within the range of Re, covered in the present study, the formation of fully developed disturbed Rows was not observed at the geometrical flow rate ratio (Q,/Qc=O.69). Presumably, this is due to the fact that both the diameter
ratios, d/D, (side/parent vessel)and branching angles for both right and left renal arteries are much smaller than those for the other two arteries. The formation of recirculation zones and fully developed disturbed flows at aortic T-junctions were also observed when all the branches were opened and the aortic inflow was distributed to the distal aorta and the four side branches in proportion to their crosssectional areas evaluated at each flow divider. However. due to the technical diliiculties encountered in illuminating areas wide enough to cover two adjacent branches as well as recording on 16 mm tine films the movements of tracer microspheres at high magnification sufficient for film analysis, it was not possible to study or demonstrate the details of the interactions of the two recirculation zones which formed at any two adjacent branches, such as the celiac and superior mesenteric arteries and the right and left renal arteries. DISCUSSION
We have studied the flow patterns at aortic Tjunctions in detail using a segment of dog descending aorta rendered transparent, and analyzed the threedimensional structure and characteristics of the recirculation flows which formed around the flow divider of each branching site. The experiments were carried out using a rigid-walled vessel and under conditions of steady flow. The results may therefore not be directly applicable to the real situation in vitro where the vesselwall is elastic and the flow is pulsatile. In light of this, caution should be exercised in applying the present results to pulsatile flow in uivo. The fact that paired recirculation flows were formed at Re =300-600, which are much lower than estimated
Flow patterns in the dog descending aorta
545
1.600
Aorta-Cek
Aorto-hperior
junetiem
Mesenterie.
junction
1.000
v *
Reo
. 800
600
I
400
200
I -_6~_-_o~,_-o.d-.
. -
0.8 ::
Fig. 6. Plot of the inflow Reynolds number for the aorto-celiac artery junction showing the measured critical Reynolds numbers for the formation of spiral secondary flows (open circles) and fully developeddisturbed flows (closedcircles)asa functionof the flow rate ratio et/Q,,. The vertical dashed line indicates the gcomctrical flow rate ratio for this T-junction.
0
_“_.o~2
. .._
,.-o.,_.‘-&2’_
o*a
_L.__~,
% Fig. 7. Plot of the inflow Reynolds number for the aorto-superior mesenteric artcry junction showing the measured critical Reynolds numbers for the formation of spiral secondary flows (opn circles) and fully dcvclopcd disturbed flows (closed circles) as a function of the flow rate ratio Q,/Q,,. The vertical dashed line indicates the geometrical flow rate ratio for this T-junction,
physiological time-averaged Re (Attinger, 1964), and The results demonstrated convincingly that the that the changes in the cross-sectional area of the dog formation of paired spiral secondary flows, previously observed in various glass model T-junctions, does descending aorta during a cardiac cycle is only f 3% (Pate1 et al., 1964). makes it most likely that there is no occur in natural vessels.The fact that such disturbed significant digerence in general flow patterns between flows were formed at Reynolds numbers much lower the flow in rigid models and elastic natural vessels. than those prevailing in uiuo (Attinger, 1964; Lutz er However, it is possible that critical Re for the onset of al., 1975) makes it plausible that spiral secondary flows recirculation and fully developed disturbed flows is are formed at aortic T-junctions under normal physiosomewhat lower in elastic than rigid vessels since logical conditions even if only for a short period some in vitro experiments have shown that the comduring the cardiac cycle. The results by Hutchison et pliance of vessel walls has an etTect in reducing the al. (1988) who measured velocity contours at the aostic intensity of turbulence (Stein and Sabbah, 1980). junctions in anesthetized dogs using pulsed Doppler The major purpose of the present investigation was ultrasound techniques provide full support to our to extend our previous studies with various glass present observation. In the aortic junctions, however, model T-junctions (Karino et ol., 1979; Karino and due to the particular anatomical structure of the vessel Goldsmith, 1985) to natural vesselsin order to confirm wall at each branching site, i.e. the sharp curvature of our findings on the formation of recirculation zones, the wall at the Row divider, the gentle round curvature and to compare the differences in various anatomical at the bend opposite to it, and the sudden step-wise decrease in the aortic diameter distal to each branch, and flow characteristics between the model and natuno recirculation zone was formed in the side branches ral vessels.
T. KARINO er al.
546
1.400~
1.200
-
1.000
-
fb 800.
600.
400.
200.
0 -,-
0.2
*--!l--1-
A-O.6 0.4
08
-I
1.0
ii:
Fig. 8. Plot of the inflow Reynolds number for the aorlo-left renal artery junction showing the measured critical Reynolds numhcrs for the formation of spiral secondary flows (open circles) and lully develoPed disturhcd flows (closed circles) as a function of the flow catc ratio Q,/Q,,. fhc vertical dashed line indicates the geometrical flow rate ratio for this Tjunction.
at the geometrical flow rate ratios. At a given flow rate ratio, Q,/Qo, the measured critical Reynolds numbers, Res. for the formation of fully developed disturbed flows were much higher in aortic T-junctions than those obtained in glass model T-junctions having equivalent branching angles and diameter ratios, d/D, (side/parent vessel). For example, in the aorto-celiac and aorto-superior mesenteric artery junctions, Re, at their geometrical
flow rate ratios was approximately
whereas Re, in the corresponding glass model T-junctions was approximately 400 and 300 respectively. These data indicate that, in the circulation, conditions at arterial T-junctions appear to be optimal for minimizing the formation of disturbed flows. However, even in such well designed natural arteries, there were some regions where flow was locally disturbed and both the fluid elements and suspended particles behaved in a manner different from that in the mainstream. As previously observed in glass model T-junctions, a standing recirculation 900 and 1400 respectively,
zone consisting of a pair of thin-layered spiral secondary flows was formed at the flow divider of each branching site in the dog descendingaorta over a wide range of flow conditions including the time-averaged estimated mean values of the physiological flow rates and flow rate ratios (Attinger. 1964; Lutz er al., 1975). Thus, at each major branching site of the dog descending aorta, the behavior of plasma and cells located in the vicinity of the vessel wall was completely different from those in the core ROW. Due to the particular flow patterns described above, vascular endothelial cells at aortic T-junctions will experience shear stresses in different directions depending on their locations. Since it is known that these endothelial cells are susceptible to flow and exhibit certain morphological changes corresponding to the direction and magnitude of fluid shear stress( Flaherty et al., 1972; Reidy and Bowyer. 1971; Dewey et al.. 1981; Levesqueet al.. 1986). it is likely that, at aorticTjunctions. endothelial cells located within the regions ofspiral secondary flows are elongated in the direction of the local flows which, in some regions, are completely different from those in the mainstream. In the present paper, we have shown that velocity distributions in the common median plane arc skewed toward the inner walls at each tlow divider. It is possible to calculate the local wall shear stresses from these velocity distributions, although WCdid not do this for the following reason. The common median plane is a very special plant bccausc it is not only a plane of symmetry of the vcssclwall, but also of the flow field. Thus, the intcrscction between the common median plane and the inner walls downstream of the flow divider in both the aorta and side branch acts as a line of stagnation on either side of which flow is deflected and spiral secondary flows are formed. It is likely that the wall shear stresses calculated along the lines of stagnation do not provide the maximum or representative values prevailing around the flow divider. In fact, the results from a model mass transfer experiment by Adamson and Roach (1981) indicate that, at T-junctions, the regions of high wall shear stressare located not on the common median plane (line of stagnation) but in a paired arrangement, symmetrically on both sides of it in a pattern similar to the spiral secondary flows shown earlier in Figs 3 and 4 in the present paper. Due to the large variation in the magnitude of wall shear stressin the recirculation zone, as well as in the mainstream proximal to the leading edge of the side branches and distal to each flow divider, the degree ofelongation of individual endothelial cells will also be diRerent from region to region, the highest being around the flow divider and the lowest along the outer orbits of the spiral secondary flows in the backflow region and at the leading edge of the side branch opposite to the flow divider. Such large variations in wall shear stress and the morphology of endothelial cells, as well as the particular flow pattern itself, may atTecttransport phenomena at the bloodvessel wall boundary although no visible atheroscler-
Flow patterns in the dog descending aorta
otic lesion was found at such sites in dog aortas prepared in the present study. Presumably, this was due to the relatively shorter life span of dogs compared to that of humans. Recently, we have looked at some human aortas and found that the anatomical structure of the vesselwall at major junctions is very much similar to that observed in dog aortas, i.e. the curvature of the vesselwall is very sharp at the flow divider and gently rounded opposite it. Thus, it is possible that similar flow patterns exist at the major junctions of human descending aorta where atherosclerotic lesions were found in most autopsy specimens. Although no direct correlation has been established so far between flow patterns, spatial distribution of wall shear stressand the sites of atheromatous plaques and atherosclerotic wall thickenings along the wall of the human aorta, the existing data indicate that preferential areas for the formation ofatherosclerotic lesionsin man lie around the proximal leading edge and lateral sides of the orifices of side branches (Murphy et al.. 1962; Caro et al., 1971; Zarins. 1986). In light of our present findings, these correspond to the regions of slow flow, hence low wall shear stress.where endothelial cells are likely to be minimally elongated. In such regions, it is possible that because of the much lower translational velocity and shear stressprevailing there, platelets and lipids have more opportunity to interact for longer periods with the vesselwall than anywhere else. This, in turn, may enhance the deposition of platelets. if activated, on the vessel wall and increase the uptake of lipids by the endothelial cells existing in such regions. What is not clear at present is how much the uptake of atherogenic lipoproteins by endothelial cells is aflected by the magnitude of the local wall shear stressand the nature of the individual ceils located in different regions of the vesselwall at arterial branching sites. In this regard, there have been several interesting reports which indicate that cell turnover is enhanced in regions of round-shaped endothclial cells (Caplan and Schwartz, 1973), that exposure ofendothelial cells to moderate to high shear stress prevents atherosclerosis in monkeys (Zarins et 01.. 1981). enhances the production of prostacyclin by the cells ( Frangos et al., 1985). and that vesicular pinocytosis in endothelial cells is enhanced by a change in the level of shear stress (Davies et al., 1984). However, it is still not clear how these individual effects are incorporated in the long process of localized genesis and development of atherosclerotic lesions in the circulation. To find a full explanation for the localization of atherosclerosis in the human arterial tree, it is necessary to further investigate the erect of disturbed flows on the transport and uptake of atherogenic lipoproteins by endothelial cells, and the effects of high and low shear stresseson the morphology and functions of endothelial cells under various flow conditions. AcknowledgemenfrThis work was supported by Grant HL29502 from the National Heart, Lung and Blood Institute. N.I.H., U.S.A.. Grant MT-7084 and MT-1835 from the
s4-l
Medical ResearchCouncil of Canada.and a grant from the Quebec Heart Foundation. The authors thank C. Artigas and M. Sgro for their technical assistance and D. Bessofor typing the manuscript.
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