# Predilection of Atherosclerosis for the Inner Curvature in the Femoral Artery

## A Digitized Angiography Study

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## Abstract

*Abstract *The degree of atherosclerosis in the inner and outer curvature of the femoral artery was studied by using digitized angiography and edge-roughness calculations in 301 hyperlipidemic patients. When the two edges of the vessel were compared no significant difference was seen, but when the local curvature was taken into account, inner curves were found to be more atherosclerotic than outer curves, and both inner and outer curves were more affected than straight segments. The same pattern was encountered in subpopulations defined by clinical or blood lipid criteria. The suggested explanation is that flow disturbances such as low shear rates or separated flow, which tend to arise along the inner curvature, promote the development of atherosclerosis.

- Received September 15, 1994.
- Accepted March 28, 1995.

The distribution of atherosclerotic lesions within the arterial tree and its relation to vessel geometry have long attracted the attention of pathologists.^{1} Tjøtta^{2} found that curved portions of the coronary arteries had more lesions than straight portions, and Willis^{3} noted that lesions tended to be more advanced along the inner curvature of the femoral artery. Similar observations based on autopsy data have been made in the coronary^{4} and carotid^{5} arteries.

An explanation for these findings in fluid mechanical terms was offered by the hypothesis advanced by Caro et al.^{6} They postulated that low shear stress, which tends to occur along the inner curvature of a curved vessel, promotes the development of atheroma. Evidence in support of this theory has been provided by coronary angiography studies^{7} ^{8} and ultrasound experiments in canine coronary arteries.^{9} A related theory implicates zones with separated flow (local backflow adjacent to the vessel wall), which also tend to arise along the inner curvature of curved tubes.^{10} Flow experiments with laser Doppler velocimetry, when correlated with histopathology, have demonstrated a spatial covariation of atheromatous plaques with both low shear rates and reverse flow.^{11} ^{12} As explanations of these observations, the role of monocyte invasion into the intima and shear-dependent gene regulation have been discussed.^{13} ^{14} A possibly relevant related observation is the enhanced adhesion of monocytes that has been demonstrated in regions of low shear.^{15}

Back et al^{16} ^{17} have carried out visualization flow experiments in glass models with geometries derived from femoral arteriograms. Flow separation or helical secondary flow was found to occur along the inner curvature, where atherosclerotic lesions would be most prominent. This was true both for a vessel with almost constant curvature and in the presence of a reverse curvature that gave the vessel a slight S shape.

Numerical computation has also been used to evaluate the effect of curvature on arterial fluid mechanics.^{18} ^{19} These studies confirm the presence of lower wall shear and helical secondary flow adjacent to the inner curvature in the curved coronary arteries.

We have developed a technique for the detection of flow separation with digitized cineangiography.^{20} In a model study, good agreement was found with laser Doppler velocimetry–proven separated flow, and when applied to a clinical material the method revealed an increased frequency of similar flow disturbances along the inner curvature of the femoral artery.^{21}

Visual observations of individual angiography films can provide examples supporting the idea that inner curves are at higher risk for developing atherosclerotic lesions than are outer curves (Fig 1⇓). However, such observations will inevitably be quite subjective and can hardly be regarded as convincing evidence for a relation between flow phenomena and atherogenesis.

Computer-analyzed angiography is an alternative method that yields quantitative measurements of atherosclerosis in vivo and has been used both by our group and others. Edge roughness, a measure that has been used in several studies to quantify atherosclerosis from digitized angiograms,^{21} ^{22} ^{23} correlates with both clinical symptoms of vascular disease and arterial cholesterol content.^{22} ^{24}

The aim of our present study was to undertake, in a larger clinical sample than has been used hitherto, a quantitative angiographic analysis of early atherosclerosis in the femoral artery that would compare the extent of lesions in the inner and outer curvatures of the curved vessel. Such a comparison is likely to reveal whether a causal relation exists between the disturbed flow in a curved artery and the pathogenesis of atherosclerosis.

## Methods

Hypercholesterolemic patients of both sexes (27 to 71 years of age; n=301) underwent angiography as part of the Probucol Quantitative Regression Swedish Trial (PQRST).^{25} All had slight or moderate femoral atherosclerosis confirmed by angiography. At the time of this examination they had been placed on a lipid-lowering diet and received lipid-lowering drug treatment with cholestyramine and probucol that was limited to two 8-week test periods. Of the 301 patients, 47 had peripheral vascular disease, defined as intermittent claudication according to Rose’s questionnaire.^{26}

The details of the angiography and digitization procedures are available.^{23} In brief, standard angiographic technique was used, after which the films were digitized and analyzed in an image-processing workstation (Imtec Epsilon, Imtec AB). For each patient, two femoral angiography series 10 minutes apart were obtained. Four consecutive 5-cm-long segments were digitized so that the superficial femoral artery was available for study within a 20-cm portion of the thigh.

The edges and midline of the vessel were detected.^{23} From the midline coordinates, the curvature κ, which equals the inverse of the radius of the curvature but is endowed with a sign indicating the direction of curvature (Fig 2⇓), was computed for each pixel (every 114 μm).^{21} In this computation, smoothing of the midline was accomplished by applying a 15-element filter 80 times (the filtering scheme found most useful in our previous study), after which the value of κ was obtained from first- and second-order difference quotients.^{21}

The amount of atherosclerosis was assessed as edge roughness.^{22} ^{23} To compute this measure, two versions of the edge are compared, one slightly filtered and one strongly filtered (Fig 3⇓). Roughness is defined as the root mean square distance between these filtered edges. More specifically, if the coordinates of the two filtered curves are denoted by *f* and *g*, then the edge roughness (*Ro*) is given by the formula

where *n* is the number of pixels. Normally, this aggregation is extended over both edges of an arterial segment, but the same definition can be applied to each edge separately and to continuous or discontinuous subsegments.

When inner and outer curves were to be compared, the vessel was classified in each pixel as being straight or curved by comparing the local value of κ with a threshold value. In this study, we used a threshold value of 0.01 cm^{−1} (corresponding to a radius of 100 cm), but the calculations were repeated with thresholds of 0.02 cm^{−1} and 0.05 cm^{−1}. In pixels in which the vessel was curved, ie, |κ|>0.01 cm^{−1}, the sign of κ was used to determine the direction of curvature and to identify the inner and outer curvatures. To compute *Ro* for inner curves, Equation 1 was used with the sum extending over the inner curvature of all curved segments, and correspondingly for outer curves. For a roughness value for straight segments, both edges were included in the summation.

An alternative analysis was also made that compared the lateral and medial edges of the artery. This was achieved by simply applying Equation 1 to each edge separately.

Comparisons between inner curves, outer curves, and straight segments as well as between lateral and medial edges were made by using ANOVA, taking into account the two measurements available for each patient (a repeated-measures model with two within-subject factors). The relation with age was studied with simple linear regression for inner and outer curves separately. Appropriate linear models were used to relate the difference between inner and outer curves to clinical and other data. When roughness differences were related simultaneously to several clinical and chemical variables, each variable was tested separately while correcting for all remaining independent variables. All calculations were performed on superanova (Abacus Concepts). The criterion for significance was *P*<.01.

## Results

In 4 of the 301 patients, the algorithm failed to detect the edges and midline of the artery or else yielded clearly unreasonable roughness values (more than fivefold greater than previous calculations on the same patient). These 4 patients were excluded, and all subsequent calculations were based on the remaining 297 patients.

The lengths of curved and straight vessel segments are given in Table 1⇓. Using our definitions, the curved segments make up about five-sixths of the analyzed part of the femoral artery and have an average length of 24 mm each.

When inner curves, outer curves, and straight segments were compared (Table 2⇓), the inner curves had significantly higher edge roughness than the outer curves, and both inner and outer curves had significantly higher values than the straight segments. When roughness values were computed for each edge separately, there was no significant difference between the lateral and medial side of the artery (Table 3⇓). Although edge roughness increases with age for both inner and outer curves (Fig 4⇓), this age dependence is stronger for the inner curves, so that the difference between inner and outer curves also tends to increase with age.

The same analysis shown in Table 2⇑ was repeated for the subgroup of patients having, in both series, no more than one inflection point in the studied arterial segment (Table 4⇓). Significantly higher values were again found for inner curves, whereas the difference between outer curves and straight segments was no longer significant.

The same basic pattern as in the total population was encountered when subgroups with more severe hyperlipidemia, ie, with a total cholesterol exceeding 10 mmol/L or total triglycerides exceeding 2.5 mmol/L, were studied (Table 4⇑). Similar results were also obtained for the male and female subpopulations separately and for the subpopulations with previously diagnosed hypertension and angina pectoris. In the smaller group with segmental vasoconstriction^{27} the differences were less pronounced and no longer significant.

When the presence of intermittent claudication was taken into account (Fig 5⇓ and Table 4⇑), it was found, as expected, that patients with claudication had higher roughness values for both inner and outer curves than those without this symptom. In addition, there was a significant interaction, so that the difference between inner and outer curves was also greater in the group with intermittent claudication.

Finally, the difference between inner and outer curves was related simultaneously to blood lipid levels (total cholesterol, LDL cholesterol, and total triglycerides), sex, age, and the presence or absence of hypertension, claudication, and angina (not shown). The difference was found to be significantly higher with increased age, with high triglyceride levels, in men, and in the presence of claudication. After correction for the mean overall roughness value in each patient, the result was still significant for total triglycerides, sex, and claudication, indicating that variations in the degree of general atherosclerotic involvement could not account for the greater difference between inner and outer curves in the presence of these risk factors.

## Discussion

We have introduced a novel method to study arterial curvature and, indirectly, the relation between flow phenomena and atherogenesis. It is quantitative and allows longitudinal measurements in the same individuals. With this new method and a larger sample size, the present study confirms earlier observations of the distribution of atherosclerosis but also yields some new information. As expected, there was a distinct and strongly significant pattern with higher edge-roughness values, ie, more severe atherosclerosis, in inner than in outer curves. In addition, outer curves had higher roughness than straight segments. The inner curvature, according to fluid mechanical theory, is characterized by lower shear stresses and an increased frequency of flow separation.^{28}

In principle, a disparity between inner and outer curves could be explained by structural differences between the medial and lateral wall of the vessel rather than by flow phenomena in view of the fact that the curvature is normally directed away from the midline of the body in the greater part of the femoral artery, so that inner curves and lateral walls tend to coincide. However, such an explanation would inevitably lead to similar or more pronounced differences in roughness between the medial and lateral edges of the vessel (Table 3⇑). The absence of a significant difference here tells strongly against this hypothesis.

With our method, the angiographic midline is used to identify inner and outer curves. An undesired consequence of this is that curvature determined from the midline may, in certain cases, be the result of a plaque encroaching from one side of the artery (Fig 6⇓). In this case, the inner curve at the neck of the stenosis and possibly the outer curves immediately proximal and distal to it would represent severely diseased portions of the vessel. This means that the computed curvature value for a point on the vessel midline may be influenced by the degree of atherosclerosis in its surroundings. In other words, the atherosclerosis and curvature measures may, to a certain extent, measure the same features of the vessel, which would make the demonstrated correlations less informative. In some patients with numerous inflection points, such an explanation seems plausible when the angiogram is studied visually. In other patients, numerous inflection points are found even in a quite normal vessel segment. However, when a plaque gives rise to a curved vessel midline, this will normally result in two inflection points (Fig 6⇓). The fact that a significant difference between inner and outer curves was also found in the much smaller subgroup with no more than one inflection point (Table 4⇑) indicates that curvature secondary to intrusion of plaques, which may contribute to our findings, is not a sufficient explanation.

Thus we are left with fluid mechanical phenomena as the most plausible explanation for the differences in atherosclerosis severity between inner and outer curves. The results of the present study agree with theories linking atherogenesis to low shear stress and separated flow.^{6} ^{10} ^{15} Our study with digitized cineangiography demonstrated that flow disturbances such as flow separation are frequent in the femoral artery, especially in the inner curvature.^{21} It is more difficult, however, to distinguish the effects of separated flow from those of lower shear rates, as both these phenomena are expected to occur in the same locations. Indeed, any attempt to separate the effect of several related features of arterial flow will encounter great problems due to the high correlations between them.^{29}

An interesting and somewhat unexpected finding was the fact that outer walls proved more diseased than straight segments. The asymmetrical velocity profile in a curved tube should give rise to higher shear rates in the outer curvature than in a corresponding straight tube.^{28} On the other hand, helical secondary flow may result in greater variability in the direction of the velocity vector close to the outer wall than in a straight vessel. This could conceivably favor the development of atherosclerosis.^{12} An alternative and perhaps more likely explanation is that a plaque originating from the inner curve grows in a circumferential manner, eventually involving the outer curvature as well.^{30}

Both increasing age and triglyceride levels and presence of intermittent claudication increased the difference between inner and outer curves (Figs 4⇑ and 5⇑). This may reflect the comparatively healthy state of our population^{24} ; as long as there are only incipient changes, hardly any differences are expected to be found between the walls, but as the lesions evolve they will occur earlier on the side at greatest risk. However, the significant relations persisting after correction for overall roughness value indicate that this is not a sufficient explanation. At any rate, we do not know whether equal, larger, or smaller differences might be found at a later stage of the disease.

Some choices in the methodology of this study were inevitably, to a degree, arbitrary; eg, the definition of curved versus straight segments depends heavily on the curvature limit (in this case 0.01 cm^{−1}) as well as on the filtering algorithm. A curvature of 0.01 cm^{−1}, corresponding to a radius of 100 cm, is a quite gentle curve, and its fluid mechanical importance is questionable. The effects of curvature on the flow field in a curved tube are often characterized by using the Dean number^{17} :

where *Re* denotes the Reynolds number (nondimensional flow rate) and *r*_{t} is the tube radius. With a vessel diameter of 6 mm,^{23} a high-shear, whole-blood viscosity of about 4.5 mPa s,^{31} and a flow rate of 6.5 mL/s in the femoral artery,^{32} a curvature radius of 100 cm implies a Dean number of 17. However, Back et al^{17} studied secondary flow in a model of the femoral artery at Dean numbers of 10 through 100 and found unmistakable helical patterns even at the lowest Dean numbers. When our computations were repeated with higher curvature limits, the inner curves consistently had higher roughness values than the outer curves and straight segments. Thus, the outcome is independent of the definition of curvature limits.

As for the choice of filtering method, the 15-element filter applied 80 times yielded, in our earlier study,^{21} results most in agreement with our visual impression. If a weaker filtering scheme were to be used, the mean curve length would probably be shorter than the 24 mm used in the present study, and the results would probably be more closely related to minute irregularities of the vessel walls, with no substantial effect on the blood flow.

It should also be noted that atherosclerotic plaques, particularly in the early stages of the disease, can grow predominantly in the outward direction with only minor effects on the lumen.^{30} This fact may be a problem when estimation of the lumen volume is used to quantify atherosclerosis and is one reason to prefer edge roughness as an angiographic measure of atherosclerosis. Nevertheless, even with edge roughness we cannot exclude that the degree of atherosclerosis is in some cases underestimated due to such growth patterns or secondary remodeling and that this tendency may vary between inner and outer curves. This may, of course, bias our estimates of the difference in lesion severity between regions.

A limitation of the present study is the fact that a two-dimensional projection is used to study the three-dimensional course of the artery. Hence, curving in the sagittal direction, which may certainly influence the fluid dynamics of the vessel, is ignored. With access to two orthogonal angiographic projections it is theoretically possible to compute the three-dimensional curvature vector, but it is not immediately clear how a comparison of inner and outer curves should be performed in such a case.

We have considered the state of the artery on only one occasion. A possible extension of the present study would be to relate curvature to the development of atherosclerosis over time in a longitudinal study in which subpopulations differing in initial degree of atherosclerosis could be studied separately. This is one of our plans for future work with the PQRST material.

In conclusion, we have found that the inner curves of the femoral artery show a higher degree of atherosclerotic involvement than the outer curves and that both inner and outer curves are more affected than are straight segments. A plausible explanation is that low shear rates or separated flow promote the development of atherosclerosis along the inner curvature, from where the plaques grow circumferentially toward the outer curvature.

## Acknowledgments

Financial support was received from the Swedish Medical Research Council (grants B94-39X-10884-01A and 06962), the Swedish Society of Medical Research, and Marion Merrell Dow, Inc, Kansas City, Mo. The authors are indebted to Nils Högman for computational assistance.

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- Predilection of Atherosclerosis for the Inner Curvature in the Femoral ArteryÖ. Smedby, J. Johansson, J. Mölgaard, A. G. Olsson, G. Walldius and U. EriksonArteriosclerosis, Thrombosis, and Vascular Biology. 1995;15:912-917, originally published July 1, 1995http://dx.doi.org/10.1161/01.ATV.15.7.912
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- Predilection of Atherosclerosis for the Inner Curvature in the Femoral ArteryÖ. Smedby, J. Johansson, J. Mölgaard, A. G. Olsson, G. Walldius and U. EriksonArteriosclerosis, Thrombosis, and Vascular Biology. 1995;15:912-917, originally published July 1, 1995http://dx.doi.org/10.1161/01.ATV.15.7.912

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