From the Graduate School of Biomedical Engineering, University of New
South Wales, Sydney, Australia.
Correspondence to A/Prof A. Avolio, Graduate School of Biomedical Engineering, University of New South Wales, Sydney NSW 2052, Australia. E-mail a.avolio{at}unsw.edu.au
Abstract
Abstract—The structure of medial
elastin determines arterial function and affects wall
mechanical properties. The aim of this study was to (1) characterize
the structure of elastin in terms of textural features, (2) relate
structural parameters to total number of cardiac cycles
(TC), and (3) determine the contribution of medial elastin to lumen
mechanical stress. Images of pressure-fixed aortic sections stained for
elastin were obtained from specimens collected postmortem from 35
animals of different species with a wide range of age, heart rate, and
TC and divided into 2 groups:
TClow=3.69±0.38x108 (n=17) and
TChigh=15.8±2.38x108 (n=18)
(P<0.001). A directional fractal curve was generated
for each image, and image texture was characterized by directional
fractal curve parameters. Elastin volume fraction and
interlamellar distance were obtained by image analysis. Wall
stress distribution was determined from a finite element model of the
arterial wall with multiple layers simulating elastin
lamellae. DFC amplitude was related to elastin volume fraction.
Increased TC (TClow versus TChigh) was
associated with lower directional fractal curve amplitude (0.23±0.02
versus 0.14±0.02; P<0.001), reduced elastin volume
fraction (36.5±2.6% versus 25.7±2.1%; P<0.01), and
increased interlamellar distance (8.5±0.5 versus 11.5±1.0 µm;
P<0.05). Loss of medial elastic function increased
pressure-dependent maximal circumferential stress. Structural
alterations of medial elastin, quantified by fractal
parameters, are associated with cumulative effects of
repeated pulsations due to the combined contribution of age and heart
rate. Loss of medial functional elasticity increases luminal wall
stress, increasing the possibility of endothelial
damage and predisposition to atherosclerosis.
The
phylogenetic distribution of the presence of the elastin protein
suggests that arterial elastin evolved as an adaptive
response to mechanical stresses imposed on arteries by the
high-pressure circulatory system achieved early in vertebrate
evolution.1 Because of the inherent stability of
the elastin protein,2 the unceasing application
of these same pulsatile mechanical stresses due to oscillatory
arterial pressure throughout the animal's lifetime makes
arterial elastin susceptible to the degenerative effects of
mechanical fatigue.3 Medial elastin is a major
determinant of arterial distensibility and capacitive
effects of large arteries. Alteration of arterial
elasticity due to structural modifications of the elastin matrix
results in functional changes of arterial properties,
affecting arterial pressure through altered vessel
compliance, wave transmission properties, and secondary effects of wave
reflection.3 Arterial elasticity also
affects the mechanical load-bearing function of the
arterial wall, and the structural orientation of the
elastin fibers affects the stress distribution throughout the
wall.4 In addition to and separate from the
relative content of elastin, alteration in structure therefore is an
important factor determining the functional properties of arteries.
Arterial elastin is usually characterized by concentric
lamellar structures, and the lamellar unit, consisting of an elastin
lamella associated with the two adjacent interlamellar zones, is
considered a functional and structural unit of the arterial
wall.5 Although lamellar elastin is what is
essentially seen with conventional elastic stains using light
microscopy, contrast stains and electron microscopy reveal that a
substantial area of the interlamellar zones is occupied by elastin
fibers.6 7 The interlamellar connections to the
main lamellae could also determine functional properties, as has been
shown in recent studies implicating changes in interlamellar elastin in
the pathogenesis of aortic dissecting
aneurysms.8 9
The elastin structure can be quantified in terms of simple geometric
lamellar parameters (eg, lamella thickness, interlamellar
distance)3 7 or texture-based
parameters (eg, fractal dimensions).6
The self-similarity property, which is the basis for fractal
analysis, has been shown to be present from the low-level
supramolecular structure10 to the macro-level
structure of the lamellar and interlamellar
fibers11 obtained from scanning electron
microscope images. This investigation applies similar fractal
analysis techniques to light microscopy images of aortic
sections stained for elastin. In this study, structural
parameters were obtained from images of the aortic wall
acquired from a range of animal species with a wide range of heart rate
and lifespans to provide quantitative comparisons of the effect of
accumulated total number of cardiac cycles on the changes in elastin
structure.
The effects of altered medial elastic structure on arterial
stiffness were modeled by finite element techniques to obtain the
contribution of medial elasticity on wall stress distribution. This
technique enabled calculation of stress contours in the presence of an
intraluminal pressure, with different values of medial stiffness
modeled by altered elasticity of concentric elastin layers and
nonelastin layers. Change in luminal stress concentration at the
intimal surface due to material property of the media indicates a
possible causative effect of arterial stiffness and
atherogenesis, independent of other intimal processes such as material
transport.
Methods
Arterial Specimens
Histology
Light Microscopy and Image Acquisition
Statistics
Elastin Content
Fractal Analysis
A power-law relation is defined in terms of the rate at which the
Fourier power spectrum of an image falls off with increasing spatial
frequency13 :
Directional Fractal Dimensions
For real natural surfaces, a single fractal dimension cannot be applied
at all possible scales but rather only over a range of
scales.14 That is, there is a particular range of
f where the linear log-log relation of Equation 2
Directional Fractal Curve
The best-fit sinusoidal wave was determined by Levenberg-Marguardt
algorithm,15 with which the curve
parameters were sought by an iterative process to minimize
the sum of the squared difference between the values of the observed
and predicted values of F(
Finite Element Modeling
Elastin lamellae were assumed to be uniform circumferential structures
with a single Young's modulus of elasticity. Functional change of
arterial wall results in change of elastic moduli of
layers. For example, functional loss of elastin may result in
stiffening of the nonlamellar layers, which are composed of collagen
and elastin. This may result in an increase in difference between
elastic moduli of lamellar (E1) and nonlamellar
(E2) layers. A nondimensional
parameter (Q) was defined as the ratio
E1/E2, so a change in Q
simulates change of elastic function of arterial wall.
Because interlamellar layers have a nonlinear stress-strain
relationship with incremental Young's modulus of elasticity, the slope
of the initial part of the stress-strain curve was considered in the
ratio. In addition to variation in Q, stepwise increases in luminal
pressure (P) were applied. Resultant stress values were obtained for
different Q values (changing in the range of 1/10 to 1/100) and luminal
pressures [0.005 MPa (37.5 mm Hg), 0.01 MPa (75 mm Hg),
0.0133 MPa (100 mm Hg), 0.016 MPa (120 mm Hg), and 0.02 MPa
(150 mm Hg)]. Calculations were performed for a model consisting
of 31 layers using a mesh of 1500 elements.
Results
Fractal Parameters
Figure 3
Finite Element Model
Discussion
Structural Quantification
In this study, results in the 2 groups of animals show that increased
number of TC are associated with decreased amplitude of DFC, an index
of structural organization of elastin. This was obtained from the aorta
of a whole range of animal species with a 5-fold range of heart rate
(40 to 203 bpm) and a 15-fold range of age (3 to 45 years), resulting
in a 28-fold range of TC (1.38x108 to
38.08x108). In relating the structural
modifications to the fatiguing effects of the accumulated pulsations,
the inherent assumption is that the elastin in all the animals studied
undergoes similar fatiguing effects and, by implication, that the
elastin is similar in all species. Any species difference that may
exist regarding elastin isoforms has not been evaluated in this study.
Although it has been shown that species differences in amino acid
composition do exist,19 amino acid content also
seems to be subject to effects of age,20 similar
to the macrostructure of elastic fibers. Furthermore, since all
arterial sections from all animals took up similar elastic
stain, it is reasonable to assume that essentially similar elastic
structures have been analyzed.
Functional Quantification of Wall Stress
Calculations from the finite element model do not include residual
stress. It is known that residual circumferential stress does exist in
arteries, with a suggestion that it contributes to vascular
remodeling.21 It exhibits compression at the
lumen and tension at the adventitial side22 and
to some extent seems to be species dependent (comparison between pig
and rat23 ). Residual stress cannot be readily
determined and is estimated indirectly by measurement of residual
strain using the opening angle of cut arterial
rings.21 Using nominal values for
arterial Young's modulus in porcine and bovine aortas,
Vaishnav and Vassoughi22 estimated residual
compressive stress at the lumen of the order of 14% of the mean
circumferential stress. Thus, luminal stress calculated from the finite
element model would be reduced by this amount. However, since increased
medial stiffness or loss of elastic function would have the effect of
decreasing the compressive residual stress, the calculated
circumferential stress would be reduced by a smaller amount. In
essence, this would increase the slopes of the curves in Figure 4
Effects of Elastin Structure on Wall Function
The LEF can also be related to the parameter Q describing
the relative stiffness of elastic (lamellar) (E1)
and stiffer nonelastic (interlamellar) (E2)
components in the finite element model; ie, LEF
These results reinforce the association between wall medial properties
and intimal stress. If intimal stress is a factor for atherogenesis, it
links the structural elements of the load-bearing properties of the
media with intimal processes such as atherosclerosis.
Thus, in addition to high blood pressure being a risk factor for
atherosclerosis through direct effect on intimal wall
stress, arterial stiffness per se can also be considered a
possible risk factor through its structural effects on maximum luminal
stress. If the modification of wall elasticity is then related to the
accumulated effects of cyclic fatigue, the deleterious effects of these
processes could be minimized by reduction of heart rate. Because of the
current possibilities of modification of heart rate through continued
pharmacotherapy or physical exercise over long periods of time, this
topic is receiving considerable interest with respect to heart rate and
life expectancy, as is manifested by a recent
editorial.24
Selected Abbreviations and Acronyms
Received January 24, 1998;
first decision February 10, 1998;
accepted April 8, 1998.
References
© 1998 American Heart Association, Inc.
Third Workshop on Structure and Function of Large
Arteries: Part I
Quantification of Alterations in Structure and Function of Elastin in the Arterial Media
Key Words: fractals • stress, mechanical • fatigue • aging
Aortic specimens were collected from a range of animal species
from the Sydney Taronga Park Zoo within 24 hours after autopsy and
fixed under pressure (100 mm Hg) in a buffered formalin solution.
A fixation pressure of 100 mm Hg was chosen because this is the
approximate average in vivo pressure for all animals in this study, and
it has been previously shown12 that at this
pressure, elastic lamellae are sufficiently distended and that higher
pressures cause minimal distension to alter the lamellar pattern.
Histology sections for analysis were taken from the
upper descending thoracic aorta. Blocks were processed overnight on an
automatic tissue processor (Tissue-Tek VIP) and embedded in paraffin
wax. Sections were cut at 5 µm on a rotary microtome and stained
with Verhoeff's iron hematoxylin for elastic fibers.
Aortic sections were examined by light microscopy (Olympus
BX-50), and digital images were obtained by a commercial imaging system
(PulnicX TM-6CN miniature high-resolution monochrome CCD camera; Data
Translation DT3155 PCI monochrome frame grabber board; Data Translation
DT3155 WiT hardware server [WiT-H-DT3155]; Logical Vision WiT
(version 5.01) image analysis software) at x200
magnification.
Mean and standard errors were calculated for each
parameter, and 2-tailed Student's t tests were
performed for comparisons between the groups. The level of significance
was taken as P=0.05. Analysis was performed on 2
groups of approximately equal numbers (n1=17,
n2=18) of high and low cardiac cycles, high and
low heart rate, and old and young age. Groups were determined by
ranking in terms of cardiac cycles, heart rate, and age.
EVF (percentage) and interlamellar distance ILD
(micrometers) were obtained by image analysis. EVF
was determined using WiT image analysis software (Logical
Vision). A threshold operation was performed on each image to select
the elastic tissue and produce a binary image. Pixels corresponding to
elastic tissue were counted and expressed as a percentage of the total
image area. ILD was determined by geometric procedures as previously
described.7
Light microscope images were analyzed using
custom-written software.6 7 11 The fractal
dimensions were determined from the Fourier power spectrum of the
image.
therefore
(1)
where A is the amplitude of the Fourier
spectrum, f is spatial frequency, and H is
defined as the Hurst coefficient. The fractal dimension F is
a function of H:
(2)
The fractal dimension of the image can be obtained from the
slope of the log-log plot of the amplitude A as a
function of spatial frequency, f.
(3)
A 128x128-pixel mask was placed randomly on the 512x512 pixel
image to select 10 locations for fast-Fourier transformation. The
corresponding Fourier spectrum of each mask was obtained by Equation 4
below:
where R(f,
(4) 
) and
I(f,) are the real and imaginary components of
F(f,), respectively, and is the
angle defining the direction on the plane of the image where the
Fourier spectrum was calculated. 
is
satisfied (Figure 1). For the images
obtained at the particular magnification, the range of the spatial
frequency was found to be between 12 and 60 bins (corresponding to
0.252 and 1.262 cycles/µm, respectively). A single regression line
was fitted to the spectrum data at a specific angle , and the
fractal dimension was derived from the slope of the line (using
Equations 2, and 3) and denoted as Fi(),
with i indicating the sequence of the masks and
equal to 1,2, ... 10. Because of the symmetry of the power spectrum,
Fi() needs to be calculated only in the
range 0° to 178°. Calculation was done at intervals of 2°. The
mean value of 10 Fi(), denoted as
F(), was calculated to generate the DFC for each
image.
View larger version (15K):
[in a new window]
Figure 1. Logarithmic relation between amplitude of
Fourier spectrum (|A|) and spatial frequency
(f) (see text for description). The fractal
dimension is determined from the slope of the linear regression line in
the section between the vertical lines [log(f)
range, 2.54 to 4.1]. Regression equation:
log(|A|)=-2.4log(f)+11.96;
r=0.79; P<0.01.
The DFC (F) composed of 90 F() was then fitted
with a 2-term sinusoid of the form: F=A1 sin
(B1+C1)+A2
sin (B2+C2)+D, where
Ai is amplitude, Bi is
period, Ci is phase (i=1,2), D is offset, and
is angle. ). Based on this method, a good
fit was obtained by a 2-term sinusoid. Figure 2 shows an example of the
histological image and associated curve for 2 animals
of similar age but different heart rate (hence markedly different
TC).
View larger version (80K):
[in a new window]
Figure 2. Verhoeff's elastic stains of aortic sections of a
tiger and jaguarundi of similar age but different heart rate (top) with
respective DFCs (bottom, see text for description). Left panels show
low cardiac cycles (505 million cycles) from a 15-year-old tiger (heart
rate, 64 bpm). Right panels show high cardiac cycles (1025 million
cycles) from a 15-year-old jaguarundi (heart rate, 130 bpm). The higher
number of TC is associated with a more disorganized textural image of
elastin fibers and a corresponding lower DFC amplitude. Magnification
for both images x400.
Effects of change in luminal pressure and elastic function of
wall components were studied by means of a finite element stress
analysis using MSC-Nastran software. Calculations were
performed for an arterial geometry of 10 mm inner
radius and 1 mm thickness. Medial structure was modeled by
creation of lamellar and interlamellar layers. Interlamellar layers
were assumed to be a network of collagen and elastin fibers with a
nonlinear stress-strain relationship. The stress-strain curve for these
layers was based on experimental data for the human
aorta.16
The Table shows results for 2
separate groups for TC, heart rate, and age. The significant
parameters were DFC amplitude of the first sinusoid
component, EVF, and ILD. Other DFC parameters were not
significant. The most significant difference was found for TC. Heart
rate also showed a significant but smaller difference with a reduced
P value. Age did not produce any significant difference for
the 3 parameters. The 2 groups had a 4-fold difference in
mean TC
(TClow=3.69±0.38x108
[n=17],
TChigh=15.8±2.38x108
[n=18]; P<0.001). Increased number of cardiac cycles was
associated with a 40.4% decrease in the amplitude (A) of the first
sinusoid component of the DFC (Alow=0.23±0.02;
Ahigh=0.137±0.162; P<0.001), a
29.6% decrease in lamellar EVF
(EVFlow=36.5±2.55%,
EVFhigh=25.7±2.14%; P<0.003), and a
34.6% increase in interlamellar distance
(ILDlow=8.75±0.46 µm,
ILDhigh=11.54±1.0 µm;
P<0.02).
View this table:
[in a new window]
Table 1. Results for Low (Group 1) and High (Group 2) TC, Heart Rate,
and Age shows scatterplots for DFC
amplitude as the dependent variable as a function of TC, EVF, and
ILD. There is a trend for DFC amplitude to decrease with cardiac
cycles, indicating an association between elastin structure and
accumulated pulsations. This becomes significant when data are divided
into 2 groups (Table). There is also a trend for DFC amplitude to
decrease with ILD and increase significantly (r=0.4,
P<0.05) with EVF, suggesting a structural association with
elastin content in the arterial wall.
View larger version (16K):
[in a new window]
Figure 3. Scatterplots of DFC amplitude for TC (top), ILD
(middle), and EVF (bottom). The regression lines with 95% confidence
limits show trends for each parameter. Correlation is
significant for EVF (r=0.4,
P<0.05).
Figure 4 shows maximum
circumferential stresses on the luminal surface for different Q and
luminal pressures. Loss of functional elastin causes higher relative
stiffness in nonlamellar layers and an increase in difference between
elastic moduli of layers (ie, an increase in Q), and this elevates
maximum circumferential stress. An increase in luminal pressure results
in an increase in maximum circumferential stress on the luminal
surface. Occurrence of both effects, ie, an increase in luminal
pressure and functional loss of elastin, accelerates increase of
maximum circumferential stress.
View larger version (25K):
[in a new window]
Figure 4. Maximal circumferential stress (MPa) at lumen
calculated by the finite element model for pressures corresponding to
37.5, 75, 100, 120, and 150 mm Hg. The upper panel shows stress
as a function of the inverse ratio 1/Q, where
Q=E1/E2 (E1 is elastin modulus of
lamellar layer, E2 is elastin modulus of nonlamellar layer;
E2>E1). An increase in 1/Q indicates an
increase in relative stiffness or a loss of functional elasticity. Note
that luminal circumferential stress is between 35 and 80 times the
level of mean blood pressure.
Texture analysis of images of elastin allows
quantification of structure of the elastin network by means of fractal
parameters that facilitate comparison of
arterial structure and function. Previous studies have
shown that like other physiological textural images
such as lung scans or mammographic parenchymal
patterns,17 18 micrographs of
arterial elastin exhibit properties of self-similarity and
thus can be characterized in terms of fractal
dimensions.10 11 It was also shown that because
of the directional preference of elastin fibers, a single global
fractal dimension is not sufficient to describe the image, but rather a
DFC was developed to account for the anisotropic
features.11 The components of the DFC were also
shown to be associated with degree of "disorganization" of the
image, due to disorientation and fragmentation of elastin fibers as
seen with age or disease.11
Finite element modeling of the aortic wall has been used to
calculate change in stress distribution due to change in functional
elasticity of the wall material. This was done by modeling concentric
layers composed of pure elastin with elastic modulus
E1 and interlammelar zones composed of a stiffer
material with elastic modulus E2
(E1<E2). The change in
functional elasticity was simulated by altering the ratio
E1/E2. The caveat is that
E1 is essentially linear and that
E2 is nonlinear, hence the stress dependency due
to increase in luminal pressure is not similar. This was resolved by
obtaining values for the linear part of the stress-strain
curve16 and interpolating values for each
iteration of the model. The results indicate that structural changes in
wall elastic components affect maximal stress at the lumen for a given
blood pressure. That is, change in medial elastic properties can
influence intimal stress concentration without change in luminal
pressure. .
From the fractal analysis, a conceptual framework could be
developed where the effects of mechanical fatigue could be related to
loss of elastic function. Because the amplitude of the DFC was shown to
be related to structural disorganization associated with loss of
elasticity with age,11 a relationship could be
estimated between LEF and TC by assuming that DFC amplitude is
inversely proportional to LEF. From the Table, a 327% increase in TC
is related to a 64% increase in LEF (calculated from the reciprocal of
DFC amplitude), that is, a doubling (100% increase) of TC is related
to a 20% loss of elastic function. This assumption is supported by the
fact that a 40.4% reduction in DFC amplitude is associated with a drop
of 29.6% in EVF. 
1/Q or
LEFE2/E1. That is,
elastic function is decreased (increase in LEF) either by mechanisms
that increase the relative stiffness of the nonlamellar components, as
can happen when interlamellar connections are broken so that the load
is taken up by the stiffer collagenous components. From finite element
model results and these associations between LEF, total cardiac
pulsations and relative stiffness (1/Q), the combined effect of blood
pressure and total cardiac pulsations could be estimated. From Figure 2, the effect of luminal pressure on maximum luminal stress is
therefore a function of LEF. For a 20% change in LEF (corresponding to
the estimated effect of doubling TC and calculated from the values for
1/Q=40 and 1/Q=50), maximum luminal stress changes at a rate of
0.023%/mm Hg. For a 43% change in LEF (corresponding to
approximately 200% increase in TC and calculated from the values of
1/Q=40 and 1/Q=70), the maximum luminal stress increases at a rate of
0.062%/mm Hg. That is, for a doubling of TC, the effect of a similar
rise in blood pressure is 2.7 times greater. In fact, this would be an
underestimation if residual stresses were take into account. In other
words, if blood pressure rises over a given period, the deleterious
effects on intimal mechanical stress can be compensated for by a
reduction of the total number of pulsations, ie, by reduction of heart
rate.
DFC
=
directional fractal curve
EVF
=
elastin volume fraction
ILD
=
interlamellar distance
LEF
=
loss of elastic function
Q
=
relative stiffness parameter defined as ratio of elastic
modulus (E1) of elastic (lamellar) component of the wall to
the modulus (E2) of the nonelastic (interlamellar)
component (Q=E1/E2)
TC
=
total cardiac cycles ([heart rate]x[age])
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A. M. Dart and B. A. Kingwell Pulse pressure--a review of mechanisms and clinical relevance J. Am. Coll. Cardiol., March 15, 2001; 37(4): 975 - 984. [Abstract] [Full Text] [PDF]
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 W. W. Nichols and D. G. Edwards Arterial Elastance and Wave Reflection Augmentation of Systolic Blood Pressure: Deleterious Effects and Implications for Therapy Journal of Cardiovascular Pharmacology and Therapeutics, March 1, 2001; 6(1): 5 - 21. [Abstract] [PDF]
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 W. Wojakowski, J. Gminski, K. Siemianowicz, M. Goss, and M. Machalski The influence of angiotensin-converting enzyme inhibitors on the aorta elastin metabolism in diet-induced hypercholesterolaemia in rabbits Journal of Renin-Angiotensin-Aldosterone System, March 1, 2001; 2(1): 37 - 42. [Abstract] [PDF]
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 Y Aggoun, D Sidi, B I Levy, S Lyonnet, J Kachaner, and D Bonnet Mechanical properties of the common carotid artery in Williams syndrome Heart, September 1, 2000; 84(3): 290 - 293. [Abstract] [Full Text] [PDF]
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