Peterson D.R., Bronzino J.D. (Eds.) Biomechanics: Principles and Applications
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9-8 Biomechanics
laser Doppler anemometry experiments have shown that these flow patterns are dependent on the valve
geometry and thus can be used to evaluate function and fitness of the heart valve [Sung and Yoganathan,
1990].
9.2 Mitral and Tricuspid Valves
The mitral (Figure 9.5) and tricuspid valves are similar in structure with both valves composed of four
primary elements: (1) the valve annulus, (2) the valve leaflets, (3) the papillary muscles, and (4) the
chordae tendineae. The base of the mitral leaflets form the mitral annulus, which attaches to the atrial and
ventricular walls, and aortic root. At the free edge of the leaflets, the chordae tendinae insert at multiple
locations and extend to the tips of the papillary muscles. This arrangement provides continuity between
the valve and ventricular wall to enhance valvular function. The valvular apparatus, or complex, requires
an intricate interplay between all components throughout the cardiac cycle.
The mitral annulus is an elliptical ring composed of dense collagenous tissue surrounded by muscle. It
goes through dynamic changes during the cardiac cycle by not only changing in size, but also by moving
three-dimensionally. The circumference of the mitral annulus ranges from 8 to 12 cm during diastole.
Recent studies involving the measurement of annular shape have also shown that the mitral annulus is not
planar, but instead has a three-dimensional form. The annulus actually forms a saddle, or ski-slope shape
[Levine et al., 1987; Komoda et al., 1994; Pai et al., 1995; Glasson et al., 1996]. This three-dimensional
shape must be taken into account when non-invasively evaluating valvular function.
The mitral valve is a bileaflet valve comprised of an anterior and posterior leaflet. The leaflet tissue is
primarily collagen-reinforced endothelium, but also contains striated muscle cells, non-myelinated nerve
fibers, and blood vessels. The anterior and posterior leaflets of the valve are actually one continuous piece
of tissue, as shown in Figure 9.6. The free edge of this tissue shows several indentations of which two
are regularly placed, called the commisures. The commisures separate the tissue into the anterior and
posterior leaflets. The location of the commisures can be identified by the fan-like distribution of chordae
tendinae and the relative positioning of the papillary muscles. The combined surface area of both leaflets is
approximately twice the area of the mitral orifice; this extra surface area permits a large line of coaptation
and ample coverage of the mitral orifice during normal function and provides compensation in cases of
disease [He, 1997, 1999]. The posterior leaflet encircles roughly two-thirds of the mitral annulus and is
essentially an extension of the mural endocardium from the free walls of the left atrium. The anterior
leaflet portion of the annulus is a line of connection, for the leaflet, the wall of the ascending aorta,
Posteromedial
papillary
muscle
Chordae
tendineae
Annulus
Anterior
leaflet
Posterior
leaflet
Anterolateral
papillary
muscle
FIGURE 9.5 Schematic of the mitral valve showing the valve leaflets, papillary muscles, and chordae tendineae.
Heart Valve Dynamics 9-9
Anterior leaflet Posterior leaflet
Anterolateral
commisure
Anterolateral
papillary
muscle
Posteromedial
papillary
muscle
Chordae
tendineae
Chordae
tendineae
Medial
scallop
Posteromedial
commisure
Central
scallop
Lateral
scallop
FIGURE 9.6 Diagram of the mitral valve as a continuous piece of tissue. The posterior and anterior leaflets are
indicated, as are the scallops, chordae tendineae, and papillary muscles.
the aortic valve, and the atrial septum. The anterior leaflet is slightly larger than the posterior leaflet,
and is roughly semi-lunar in shape as opposed to the quadrangular shaped posterior leaflet. The normal
width and height of the anterior leaflet is approximately 3.3 and 2.3 cm, respectively. The height of the
posterior leaflet is 1.3 cm, while the commisure height is less than 1.0 cm. The posterior leaflet typically
has indentations, called scallop, that divide the leaflet into three regions: (1) the medial, (2) central, and
(3) lateral scallop [Silverman and Hurst, 1968; Raganathan et al., 1970; Roberts, 1983; Barlow, 1987;
Kunzelmar et al., 1994].
The mitral leaflet tissue can be divided into both a rough and clear zone. The rough zone is the thicker
part of the leaflet and is defined from the free edge of the valve to the valve’s line of closure. The term
“rough” is used to denote the texture of the leaflet due to the insertion of the chordae tendineae in this
area. The clear zone is thinner and translucent and extends from the line of closure to the annulus in the
anterior leaflet and to the basal zone in the posterior leaflet. Unlike the mitral valve, the tricuspid valve has
three leaflets: (1) an anterior leaflet, (2) a posterior leaflet with a variable number of scallops, and (3) a
septal leaflet. The tricuspid valve is larger and structurally more complicated than the mitral valve and
the separation of the valve tissue into distinct leaflets is less pronounced than with the mitral valve. The
surface of the leaflets is similar to that of the mitral valve; however, the basal zone is present in all of the
leaflets [Silver et al., 1971].
Chordae tendineae from both leaflets attach to each of the papillary muscles. The chordae tendineae
consist of an inner core of collagen surrounded by loosely meshed elastin and collagen fibers with an
outer layer of endothelial cells. In the mitral complex structure, there are marginal and basal chordae
that insert into the mitral leaflets. From each papillary muscle, several chordae originate and branch into
the marginal and basal chordae. The thinner marginal chordae insert into the leaflet free edge at multiple
insertion points, while the thicker basal chordae insert into the leaflets at a higher level towards the annulus.
The marginal chordae function to keep the leaflets stationary while the basal chordae seem to act more as
supports [Kunzelman, 1994].
The left side of the heart has two papillary muscles, called anterolateral and posteromedial, that attach
to the ventricular free wall and tether the mitral valve in place via the chordae tendinae. This tethering
prevents the mitral valve from prolapsing into the atrium during ventricular ejection. On the right side of
the heart, the tricuspid valve has three papillary muscles. The largest one, the anterior papillary muscle,
attaches to the valve at the commissure between the anterior and posterior leaflets. The posterior papillary
muscle is located between the posterior and septal leaflets. The smallest papillary muscle, called the septal
muscle, is sometimes not even present. Improper tethering of the leaflets will result in valve prolapse
during ventricular contraction, permitting the valve leaflets to extend into the atrium. This incomplete
10
Arterial
Macrocirculatory
Hemodynamics
Baruch B. Lieber
State University of New York-Buffalo
10.1 Blood Vessel Walls ....................................
10-1
10.2 Flow Characteristics ...................................10-2
10.3 Wave Propagation .....................................10-4
10.4 Velocity Profiles .......................................10-5
10.5 Pathology .............................................10-8
Defining Terms ..............................................10-9
References ...................................................10-10
Further Information .........................................10-10
The arterial circulation is a multiply branched network of compliant tubes. The geometry of the network
is complex, and the vessels exhibit nonlinear viscoelastic behavior. Flow is pulsatile, and the blood flowing
through the network is a suspension of red blood cells and other particles in plasma that exhibits complex
non-Newtonian properties. Whereas the development of an exact biomechanical description of arterial
hemodynamics is a formidable task, surprisingly useful results can be obtained with greatly simplified
models.
The geometrical parameters of the canine systemic and pulmonary circulations are summarized in
Table 10.1. Vessel diameters vary from a maximum of 19 mm in the proximal aorta to 0.008 mm (8 μm)
in the capillaries. Because of the multiple branching, the total cross-sectional area increases from 2.8 cm
2
in the proximal aorta to 1357 cm
2
in the capillaries. Of the total blood volume, approximately 83% is in
the systemic circulation, 12% is in the pulmonary circulation, and the remaining 5% is in the heart. Most
of the systemic blood is in the venous circulation, where changes in compliance are used to control mean
circulatory blood pressure. This chapter will be concerned with flow in the larger arteries, classes 1 to 5 in
the systemic circulation and 1 to 3 in the pulmonary circulation in Table 10.1. Flow in the microcirculation
is discussed in Chapter 13, and venous hemodynamics is covered in Chapter 14.
10.1 Blood Vessel Walls
The detailed properties of blood vessels weredescribed earlier in this section, but a few general observations
are made here to facilitate the following discussion. Blood vessels are composed of three layers: the intima,
media, and adventitia. The inner layer, or intima, is composed primarily of endothelial cells, which line the
10-1
10-2 Biomechanics
TABLE 10.1 Model of Vascular Dimensions in 20-kg Dog
Total Percentage
Mean Diameter Number Mean Length Cross-Section Total Blood of Total
Class Vessels (mm) of Vessels (mm) (cm
2
) Volume (ml) Volume
Systemic
1 Aorta (19–4.5) 1 (2.8–0.2) 60
2 Arteries 4.000 40 150.0 5.0 75
3 Arteries 1.300 500 45.0 6.6 30
4 Arteries 0.450 6000 13.5 9.5 13 11
5 Arteries 0.150 110,000 4.0 19.4 8
6 Arterioles 0.050 2.8 × 10
6
1.2 55.0 7
7 Capillaries 0.008 2.7 × 10
9
0.65 1357.0 88 5
8 Venules 0.100 1.0 × 10
7
1.6 785.4 126
9 Veins 0.280 660,000 4.8 406.4 196
10 Veins 0.700 40,000 13.5 154.0 208
11 Veins 1.800 2100 45.0 53.4 240
12 Veins 4.500 110 150.0 17.5 263 67
13 Venae cavae (5–14) 2 (0.2–1.5) 92
Total 1406
Pulmonary
1 Main artery 1.600 1 28.0 2.0 6
2 Arteries 4.000 20 10.0 2.5 25 3
3 Arteries 1.000 1550 14.0 12.2 17
4 Arterioles 0.100 1.5 × 10
6
0.7 120.0 8
5 Capillaries 0.008 2.7 ×10
9
0.5 1357.0 68 4
6 Venules 0.110 2.0 × 10
6
0.7 190.0 13
7 Veins 1.100 1650 14.0 15.7 22
8 Veins 4.200 25 100.0 35 5
9 Main veins 8.000 4 30.0 6
Total 200
Heart
Atria 2 30
Ventricles 2 54 5
Total 84
Total
circulation 1690 100
Source: Milnor, W.R. 1989. Hemodynamics, 2nd ed., p. 45. Baltimore, Williams and Wilkins. With permission.
vessel and are involved in control of vessel diameter. The media, composedof elastin,collagen, and smooth
muscle, largely determines the elastic properties of the vessel. The outer layer, or adventitia, is composed
mainly of connective tissue. Unlike in structures composed of passive elastic materials, vessel diameter and
elastic modulus vary with smooth-muscle tone. Dilation in response to increases in flow and myogenic
constriction in response to increases in pressure have been observed in some arteries. Smooth-muscle
tone is also affected by circulating vasoconstrictors such as norepinephrine and vasodilators such as
nitroprusside. Blood vessels, like other soft biological tissues, generally do not obey Hooke’s law, becoming
stiffer as pressure is increased. They also exhibit viscoelastic characteristics such as hysteresis and creep.
Fortunately, for many purposes a linear elastic model of blood vessel behavior provides adequate results.
10.2 Flow Characteristics
Blood is a complex substance containing water, inorganic ions, proteins, and cells. Approximately 50% is
plasma, a nearly Newtonian fluid consisting of water, ions, and proteins. The balance contains erythrocytes
Arterial Macrocirculatory Hemodynamics 10-3
(red blood cells), leukocytes (white blood cells), and platelets. Whereas the behavior of blood in vessels
smaller than approximately 100 μm exhibits significant non-Newtonian effects, flow in larger vessels can
be described reasonably accurately using the Newtonian assumption. There is some evidence suggesting
that in blood analog fluids wall shear stress distributions may differ somewhat from Newtonian values
[Liepsch et al., 1991].
Flow in the arterial circulation is predominantly laminar with the possible exception of the proximal
aorta and main pulmonary artery. In steady flow, transition to turbulence occurs at Reynolds numbers
(N
R
) above approximately 2300
N
R
=
2rV
ν
(10.1)
where r = vessel radius, V = velocity, v = kinematic viscosity = viscosity/density.
Flow in the major systemic and pulmonary arteries is highly pulsatile. Peak-to-mean flow amplitudes
as high as 6 to 1 have been reported in both human and dog [Milnor, 1989, p. 149]. Womersley’s [1957]
analysis of incompressible flow in rigid and elastic tubes showed that the importance of pulsatility in the
velocity distributions depended on the parameter
N
w
= r
ω
v
(10.2)
where ω = frequency.
This is usually referred to as the Womersley number (N
w
)orα-parameter. Womersley’s original report is
notreadilyavailable;however, Milnorprovides a reasonablycomplete account[Milnor, 1989, pp. 106–121].
Mean and peak Reynolds numbers in human and dog are given in Table 10.2, which also includes mean,
peak, and minimum velocities as well as the Womersley number. Mean Reynolds numbers in the entire
systemic and pulmonary circulations are below 2300. Peak systolic Reynolds numbers exceed 2300 in
the aorta and pulmonary artery, and some evidence of transition to turbulence has been reported. In
dogs, distributed flow occurs at Reynolds numbers as low as 1000, with higher Womersley numbers
increasing the transition Reynolds number [Nerem and Seed, 1972]. The values in Table 10.2 are typical for
individuals at rest. During exercise, cardiac output and hence Reynolds numbers can increase severalfold.
The Womersley number also affects the shape of the instantaneous velocity profiles as discussed below.
TABLE 10.2 Normal Average Hemodynamics Values in Man and Dog
Dog (20 kg) Man (70 kg, 1.8 m
2
)
N
w
Velocity (cm/sec) N
R
N
w
Velocity (cm/sec) N
R
Systemic Vessels
Ascending aorta 16 15.8 (89/0)
a
870 (4900)
b
21 18 (112/0)
a
1500 (9400)
a
Abdominal aorta 9 12 (60.0) 370 (1870) 12 14 (75/0) 640 (3600)
Renal artery 3 41 (74/26) 440 (800) 4 40 (73/26) 700 (1300)
Femoral artery 4 10 (42/1) 130 (580) 4 12 (52/2) 200 (860)
Femoral vein 5 5 92 7 4 104
Superior vena cava 10 8 (20/0) 320 (790) 15 9 (23/0) 550 (1400)
Inferior vena cava 11 19 (40/0) 800 (1800) 17 21 (46/0) 1400 (3000)
Pulmonary vessels
Main artery 14 18 (72/0) 900 (3700) 20 19 (96/0) 1600 (7800)
Main vein
c
7 18 (30/9) 270 (800) 10 19 (38/10) 800 (2200)
a
Mean (systolic/diastolic).
b
Mean (peak).
c
One of the usually four terminal pulmonary veins.
Source: Milnor, W.R. 1989. Hemodynamics, 2nd ed., p. 148, Baltimore, Williams and Wilkins. With permission.
10-4 Biomechanics
TABLE 10.3 Pressure Wave Velocities in Arteries
a,b
Wave
Artery Species Velocity (cm/sec)
Ascending Aorta Man 440–520
Dog 350–472
Thoracic aorta Man 400–650
Dog 400–700
Abdominal aorta Man 500–620
Dog 550–960
Iliac Man 700–880
Dog 700–800
Femoral Man 800–1800
Dog 800–1300
Popliteal Dog 1220–1310
Tibial Dog 1040–1430
Carotid Man 680–830
Dog 610–1240
Pulmonary Man 168–182
Dog 255–275
Rabbit 100
Pig 190
a
All data are apparent pressure wave velocities (although
the average of higher frequency harmonics approximates
the true velocity in many cases), from relatively youngsub-
jects with normal cardiovascularsystems, at approximately
normal distending pressures.
b
Ranges for each vessel and species taken from Table 9.1
of source.
Source: Milnor, W.R. 1989. Hemodynamics, 2nd ed.,
p. 235, Baltimore, Williams and Wilkins. Withpermission.
10.3 Wave Propagation
The viscoelasticity of blood vessels affects the hemodynamics of arterial flow. The primary function of
arterial elasticity is to store blood during systole so that forward flow continues when the aortic valve
is closed. Elasticity also causes a finite wave propagation velocity, which is given approximately by the
Moens–Korteweg relationship
c =
Eh
2ρr
(10.3)
where E = wall elastic modulus, h = wall thickness, ρ = blood density, r = vessel radius.
Although Moens [1878] and Korteweg [1878] are credited with this formulation, Fung [1984, p. 107]
has pointed out that the formula was first derived much earlier [Young, 1808]. Wave speeds in arterial
blood vessels from several species are given in Table 10.3. In general, wave speeds increase toward the
periphery as vessel radius decreases and are considerably lower in the main pulmonary artery than in the
aorta owing primarily to the lower pressure and consequently lower elastic modulus.
Wave reflections occur at branches where there is not perfect impedance matching of parent and
daughter vessels. The input impedance of a network of vessels is the ratio of pressure to flow. For rigid
vessels with laminar flow and negligible inertial effects, the input impedance is simply the resistance and is
independent of pressure and flow rate. For elastic vessels, the impedance is dependent on the frequency of
Arterial Macrocirculatory Hemodynamics 10-5
the fluctuations in pressure and flow. The impedance can be described by a complex function expressing
the amplitude ratio of pressure to flow oscillations and the phase difference between the peaks.
¯
Z
i
(ω) =
¯
P (ω)
¯
Q(ω)
|
¯
Z
i
(ω)|=
¯
P (ω)
¯
Q(ω)
(10.4)
θ
i
(ω) = θ[(
¯
P (ω))] − θ[(
¯
Q(ω))]
where
¯
Z
i
is the complex impedance, |
¯
Z
i
| is the amplitude, and θ
i
is the phase.
For an infinitely long straight tube with constant properties, input impedance will be independent of
position in the tube and dependent only on vessel and fluid properties. The corresponding value of input
impedance is called the characteristic impedance Z
0
given by
Z
0
=
ρc
A
(10.5)
where A = vessel cross-sectional area.
In general, the input impedance will vary from point to point in the network because of variations
in vessel sizes and properties. If the network has the same impedance at each point (perfect impedance
matching), there will be no wave reflections. Such a network will transmit energy most efficiently. The re-
flection coefficient R, defined as the ratio of reflected to incident wave amplitude, is related to the relative
characteristic impedance of the vessels at a junction. For a parent tube with characteristic impedance Z
0
branching into two daughter tubes with characteristic impedances Z
1
and Z
2
, the reflection coefficient is
given by
R =
Z
−1
0
−
Z
−1
1
+ Z
−1
2
Z
−1
0
+
Z
−1
1
+ Z
−1
2
(10.6)
and perfect impedance matching requires
1
Z
0
=
1
Z
1
+
1
Z
2
(10.7)
The arterial circulation exhibits partial impedance matching; however, wave reflections do occur. At
each branch point, local reflection coefficients typically are less than 0.2. Nonetheless, global reflection
coefficients, which account for all reflections distal to a given site, can be considerably higher [Milnor,
1989, p. 217].
In the absence of wave reflections, the input impedance is equal to the characteristic impedance. Wom-
ersley’s analysis predicts that impedance modulus will decrease monotonically with increasing frequency,
whereas the phase angle is negative at low frequency and becomes progressively more positive with in-
creasing frequency. Typical values calculated from Womersley’s analysis are shown in Figure 10.1. In the
actual circulation, wave reflections cause oscillations in the modulus and phase. Figure 10.2 shows input
impedance measured in the ascending aorta of a human. Measurements of input resistance, characteristic
impedance, and the frequency of the first minimum in the input impedance are summarized in Table 10.4.
10.4 Velocity Profiles
Typical pressure and velocity fluctuations throughout the cardiac cycle in man are shown in Figure 10.3.
Although mean pressure decreases slightly toward the periphery due to viscous effects, peak pressure
shows small increases in the distal aorta due to wave reflection and vessel taper. A rough estimate of
mean pressure can be obtained as 1/3 of the sum of systolic pressure and twice the diastolic pressure.
10-6 Biomechanics
–0.3
0
2 4 6 8 10
–0.2
–0.1
0
0.1
Womersley number
Phase angle (radians)
0
0
2 4 6 8 10
2
1
3
4
5
Womersley number
Normalized impedance modulus
FIGURE 10.1 Characteristic impedance calculated from Womersley’s analysis. The top panel contains the phase of
the impedance and the bottom panel the modulus, both plotted as a function of the Womersley number N
w
,whichis
proportional to frequency. The curves shown are for an unconstrained tube and include the effects of wall viscosity.
The original figure has an error in the scale of the ordinate, which has been corrected. (From Milnor, W.R. 1989.
Hemodynamics, 2nd ed., p. 172, Baltimore, Williams and Wilkins. With permission.)
Velocity peaks during systole, with some backflow observed in the aorta early in diastole. Flow in the
aorta is nearly zero through most of the diastole; however, more peripheral arteries such as the iliac and
renal show forward flow throughout the cardiac cycle. This is a result of capacitive discharge of the central
arteries as arterial pressure decreases.
Velocity varies across the vessel due to viscous and inertial effects as mentioned earlier. The velocities
in Figure 10.3 were measured at one point in the artery. Velocity profiles are complex because the flow is
pulsatile and vessels are elastic, curved, and tapered. Profiles measured in the thoracic aorta of a dog at
normal arterial pressure and cardiac output are shown in Figure 10.4. Backflow occurs during diastole,
and profiles are flattened even during peak systolic flow. The shape of the profiles varies considerably with
mean aortic pressure and cardiac output [Ling et al., 1973].
Arterial Macrocirculatory Hemodynamics 10-7
120
60
0
–60
–120
0
2 4 6 8 10
Frequency (Hz)
Phase angle (degrees)
4000.0
3500.0
3000.0
2500.0
2000.0
1500.0
1000.0
500.0
0.0
0
2 3 5 7 91 4 6 8 10
Frequency (Hz)
Modulus of impedance (dynes cm
–5
)
FIGURE 10.2 Input impedance derived from the pressure and velocity data in the ascending aorta of Figure 10.3. The
top panel contains the modulus and the bottom panel the phase, both plotted as functions of frequency. The peripheral
resistance (DC impedance) for this plot was 16,470 dyne sec/cm
5
. (From Mills C.J., Gabe I.T., Gault J.N. et al. 1970.
Pressure–flow relationships and vascular impedance in man. Cardiovasc. Res. 4: 405. With permission.)
TABLE 10.4 Characteristic Arterial Impedances in Some Mammals: Average (±SE)
a,b
Species Artery R
in
Z
0
f
min
Dog Aorta 2809–6830 125–288 6–8
Dog Pulmonary 536–807 132–295 2–3.5
Dog Femoral 110–162
c
4.5–15.8
c
8–13
Dog Carotid 69
c
7.0–9.4
c
8–11
Rabbit Aorta 20–50
c
1.8–2.1
c
4.5–9.8
Rabbit Pulmonary 1.1
c
3.0
Rat Aorta 153
c
11.2
c
12
Abbreviations: R
in
, input resistance (mean arterial pressure/flow) in dyn sec/cm
5
; Z
0
, characteris-
tic impedance, in dyn sec/cm
5
, estimated by averaging high-frequency input impedances in aorta
and pulmonary artery; value at 5Hz for other arteries, f
min
, frequency of first minimum of Z
i
.
a
Values estimated from published figures if averages were not reported.
b
Ranges for each species and vessel taken from values in Table 7.2 of source.
c
10
3
dyn sec/cm
5
.
Source: Milnor, W.R. 1989. Hemodynamics, 2nd ed., p. 183, Baltimore, Williams and Wilkins.
With permission.
10-8 Biomechanics
Right subclavian
artery
Ascending
aorta
Right renal artery
P
120
80
P
120
80
60
V
0
60
V
0
50
V
0
60
V
0
100
P
60
90
P
45
Right common
Iliac artery
0.2 sec
110
70
80
V
0
80
V
0
P
110
70
P
60
V
0
110
70
P
80
V
0
110
70
P
Abdominal
aorta L1
Descending
aorta T10
Descending
aorta T7
Innominate artery
FIGURE 10.3 Simultaneous pressure and blood velocity patterns recorded at points in the systemic circulation of a
human. Velocities were recorded with a catheter-tip electromagnetic flowmeter probe. The catheter included a lumen
for simultaneous pressure measurement; V is the velocity (cm/sec), P is the pressure (mmHg). (From Mills, C.J.,
Gabe, I.T., Gault, J.N. et al., 1970. Cardiovasc. Res. 40: 405. With permission.)
In more peripheral arteries the profiles are resembling parabolic ones as in fully developed laminar flow.
The general features of these fully developed flow profiles can be modeled using Womersley’s approach,
although nonlinear effects may be important in some cases. The qualitative features of the profile depend
on the Womersley number N
w
. Unsteady effects become more important as N
w
increases. Below a value
of about 2 the instantaneous profiles are close to the steady parabolic shape. Profiles in the aortic arch are
skewed due to curvature of the arch.
10.5 Pathology
Atherosclerosis is a disease of the arterial wall that appears to be strongly influenced by hemodynamics.
The disease begins with a thickening of the intimal layer in locations that correlate with the shear stress
distribution on the endothelial surface [Friedman et al., 1993]. Over time the lesion continues to grow until
a significant portion of the vessel lumen is occluded. The peripheral circulation will dilate to compensate