# Do Plaques Grow Upstream or Downstream?

## An Angiographic Study in the Femoral Artery

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## Abstract

*Abstract* Although the distribution of atherosclerosis has been described, little is known about the direction of growth of plaques. In this study, 237 patients with slight or moderate atherosclerosis underwent femoral angiography twice at a 3-year interval, and the films were studied with computerized image analysis. First, atherosclerosis was measured as edge roughness, and the change in roughness of each 1-cm segment over the 3-year period was related to the edge roughness of the segments immediately upstream and downstream. On the medial side of the artery, the change in edge roughness was found to be more strongly related to the roughness values upstream than to those downstream of the segment studied. This suggests that growth in the downstream direction is more common than growth in the upstream direction. On the lateral side, more equivocal results were obtained. Atherosclerosis was also assessed by study of the cross-sectional area of the artery as a function of distance along the vessel. A mathematical model of plaque growth was formulated as a nonlinear filtering of this curve. Growth in the downstream direction was significantly (*P*<.001) more frequent than growth in the upstream direction. The findings are compatible with an atherogenic effect of fluid mechanical disturbances, such as flow separation, that may occur downstream of a stenosis.

- Received February 16, 1996.
- Accepted September 17, 1996.

The topographical distribution of atherosclerosis within the arterial system has been fairly well described.^{1} ^{2} ^{3} An increased frequency of lesions is seen around bifurcations and in curved parts of the arterial tree. This has been attributed to the potentially atherogenic effect of low shear stress or separated flow.^{4} ^{5} Most studies have been based on autopsy materials, and hence, little is known of the longitudinal development of lesions within the same individual. More specifically, the direction of growth of plaques seems never to have been examined in a longitudinal study in vivo.

However, if the theories associating atherogenesis with low shear and separated flow are true, this would have implications for the direction of growth of an atherosclerotic plaque. Model studies and numerical simulation have indicated that separation zones and low-shear regions tend to occur immediately downstream of a stenosis.^{6} ^{7} ^{8} ^{9} Upstream of the stenosis, no such phenomena have been reported. On the contrary, moderately elevated shear rates have been found in the upstream region.^{10} In those cases in which the stenosis is due to a raised atherosclerotic plaque, the area immediately downstream of the plaque would seem to be at greater risk for further progression of atherosclerosis. Thus, plaques would be more prone to grow in the downstream than in the upstream direction.

The intention of this study was to test this hypothesis by digital analysis of consecutive angiography films of identical segments of the femoral artery in a well-defined population. To this end, we have developed mathematical models of plaque growth that can be applied to longitudinal angiography data in digitized form.

## Methods

In 237 hypercholesterolemic patients of either sex and 35 to 70 years old at the beginning of the study, femoral angiography was performed on two occasions at a 3-year interval as part of the Probucol Quantitative Regression Swedish Trial (PQRST).^{11} For inclusion in the study, total serum cholesterol values >6.88 mmol/L, LDL cholesterol values >4.53 mmol/L, and total triglyceride values ≤4 mmol/L were required. All patients had slight or moderate femoral atherosclerosis confirmed by angiography (visible wall irregularity but no occlusion, segmental vasospasm, or ectasia in the femoral artery nor any major aneurysm proximally). At the time of the first examination, they had been put on a diet and lipid-lowering drug treatment with cholestyramine and probucol, limited to two 8-week test periods. In the interval between the two examinations, they received lipid-lowering treatment consisting of cholestyramine alone or cholestyramine and probucol. The entire PQRST was approved by the Stockholm Committee on Research Ethics.

The angiography and digitization procedures have been described in detail earlier.^{12} In brief, standard angiographic technique was used with the same equipment on both occasions. During the angiography, the patient's foot was fixed in a device that ensured consistent positioning between investigations. The films were then digitized with a pixel size of 114 μm and analyzed on an image processing workstation (Imtec Epsilon; Imtec AB). On each occasion, two femoral angiography series were obtained 10 minutes apart. Four consecutive segments, each 5 cm long, were digitized, so that the superficial femoral artery was available for study within a 20-cm portion of the thigh.

When the location and extent of lesions is to be correlated between investigations, it is crucial that identical portions of the vessel be studied on both occasions. To this end, we used as reference points arterial bifurcations, which were considered reliable anatomic landmarks.

The edges and midline of the vessel were detected as described earlier.^{12} From the detected edges, the degree of stenosis in percent of the maximum diameter (percent stenosis) is easily calculated. In the PQRST, however, two different approaches have been used to assess the amount of atherosclerosis. One of the measures was the edge roughness, first proposed by Crawford et al.^{13} To compute this, two versions of the edge are compared, one slightly filtered (11-pixel average) and one strongly filtered (113-pixel average).^{14} The 11-pixel filter eliminates noise by ignoring deviations of the vessel edge that are <11 pixels, ie, <1.3 mm long, whereas the 113-pixel filter eliminates everything <113 pixels, or <12.9 mm. Thus, the difference between them will reflect irregularity between 1.3 mm and 12.9 mm in length, which is assumed to be the scale corresponding to atherosclerotic lesions. The edge roughness is defined as the root mean square distance between the two filtered edges. More specifically, if the transverse coordinates of the two filtered curves are denoted by f_{11}(x) and f_{113}(x), then the edge roughness is expressed by the formula (Equation 1) where n is the number of pixels. This calculation, which is usually carried out over an entire 20-cm segment, was also performed here for each 1-cm segment separately. Since neighborhood information is required for the filtering, no values were obtained for the first and last segments, such that 18 edge roughness values were available for each of the two edges (medial and lateral) in every patient.

To study segments upstream and downstream of a plaque, a 1-cm segment of either edge was defined as pathological if its roughness value exceeded 1 mm. The change in edge roughness over the 3-year period was then studied with general linear models (unbalanced ANOVA). Segments downstream of pathological segments were compared with segments that were not downstream of such segments, while the variation explained by interindividual differences and systematic differences between levels was controlled for, and likewise for segments upstream. This analysis was performed separately for the medial and lateral edges. With the change in edge roughness at level *l* in patient p denoted as ΔRo_{pl}, the model is described by the following equation: (Equation 2).

Here B_{d} and B_{u} are binary variables (with values of 0 or 1) indicating whether the segment studied is downstream of a pathological segment or upstream of such a segment (possibly both). The linear model computation yields least-square estimates of the coefficients a, b, and c, whereas C_{p} and D_{l} are constant terms particular for each patient and each level in the vessel, respectively.

Another analysis of the same data, not dependent on the somewhat arbitrary definition of pathological segments, was also carried out. In this case, a general linear model was used that predicted the change in roughness of each segment from the baseline levels of the segment itself and the segments immediately upstream and downstream while controlling for the variation explained by interindividual differences and systematic differences between levels. This model is expressed by the regression equation (Equation 3) where Ro^{0}_{p,l} denotes the baseline edge roughness at level l in patient p and level l−1 is the segment immediately upstream of level l. All general linear model calculations were carried out in JMP (SAS Institute Inc).

The second method to quantify atherosclerosis in the PQRST has combined geometric and densitometric information in the angiogram to measure the lumen volume segmentwise.^{12} This calculation is based on curves representing the cross-sectional area as a function of distance along the vessel (Fig 1⇓). In such a curve, a plaque will appear as a local depression surrounded by segments with higher values. A mathematical model of plaque growth can be formulated as a nonlinear filtering of the curve with a minimum filter of varying length. For growth in the downstream direction, each depression of the curve (corresponding to a plaque) is extended in the positive direction (downstream) by a certain length q according to the equation (Equation 4). Here, the unfiltered curve is denoted by f(x) and the filtered curve by g(x). Growth upstream is described by extending all depressions in the opposite direction: (Equation 5) where q is negative. The algorithm applied this theoretical model to curves that were obtained at the first examination, tested all values of q in the interval (−10 mm, +10 mm), and compared the predicted curves with the curves recorded 3 years later by use of a least-squares criterion. If no local minimum was found, the corresponding case was excluded from the analysis. The frequency of downstream growth was then statistically compared with that of upstream growth (one-sample sign test).

## Results

An example of the appearance of a lesion at the beginning and end of the study period is given in Fig 2⇓. On the first occasion, a single moderate stenosis is seen; 3 years later, an additional plaque has developed downstream.

The mean edge roughness value for the entire 20-cm segment at the first examination was 0.90 mm (SD, 0.34 mm); for comparison, the mean percent stenosis was 35% (SD, 11%). At the second examination, the mean edge roughness was 0.87 mm (SD, 0.37 mm). The distribution of the change in overall edge roughness is shown in Fig 3⇓. In 153 cases, the roughness value decreased, and in 82 cases it increased.

The mean change in edge roughness for segments downstream of a pathological segment is compared with that of other segments in Table 1⇓. For both the medial and the lateral edges, higher values were found in the downstream segments, compatible with progression of the disease. This finding was somewhat more constant at the lateral edge, as reflected by a smaller SD. However, similar differences were also present between segments that were upstream of pathological segments and those that were not (Table 2⇓). In this case, the least variable result (smallest SD) was found on the medial side.

The significance of these findings was tested with the linear model simultaneously including locations downstream and upstream of pathological segments (Table 3⇓). It was found that location downstream of a pathological segment had a highly significant effect on the change in edge roughness on both the lateral and the medial sides, whereas the effect of upstream location was only moderately significant (on the medial side) or not significant at all (lateral side).

Results of the regression model not using the concept of pathological segments (Equation 3) are presented in Table 4⇓. In addition to the highly significant dependence on the baseline edge roughness of the segment itself (which is an immediate consequence of the fact that this value is used to compute the roughness change), there was, for the medial side, a clearly significant dependence on baseline roughness in the segment above the one studied but not for the segment below. On the lateral side, no significant dependence was found for baseline edge roughness of either the upstream or the downstream segment. The actual regression equation obtained for the medial edge was (Equation 6) and for the lateral edge (Equation 7).

Comparisons of upstream versus downstream growth according to the nonlinear filtering model (Equations 4 and 5) are presented in Table 5⇓. For the whole population, growth in the downstream direction was significantly more common than growth upstream. When the analysis was restricted to men, to patients <55 years old, and to the subpopulation in which the mean edge roughness values for the entire 20-cm segment indicated an overall progression of the disease, this predominance was more pronounced, so that downstream growth was more than twice as common as upstream growth. A weaker trend in the same direction was present, but not significant, in the subpopulations defined by women and individuals >55 years old. It can be noted that the predominance for downstream growth was significant both for patients with a more severe and for those with a less severe maximum stenosis, as judged from the percent stenosis measure, although it was more pronounced in the less diseased cases. Conversely, it was not significant for the smaller subpopulations defined by more marked hypercholesterolemia, hypertension, or symptoms of vascular disease.

## Discussion

The detailed study of patterns for the development of atherosclerotic plaques over time, like that for the direction of growth, is inevitably associated with certain difficulties. First, the method used must be applicable on several occasions in the same individual and the same vessel. Hence, one must use in vivo techniques rather than postmortem methods. This practically restricts the choice to the radiological arsenal: angiography, ultrasound, and magnetic resonance imaging (MRI) are all used in clinical practice to diagnose atherosclerosis. Quantitative methods to assess atherosclerosis have also been proposed using angiography,^{13} ^{14} ultrasound,^{15} ^{16} ^{17} and MRI.^{18} ^{19} ^{20} However, the MRI methods are relatively new and as yet not satisfactorily documented.

A second requirement is the ability to accurately identify corresponding locations within the vessel, even after a long time interval. In our study, this could be accomplished with standardized positioning and well-defined reference points at arterial bifurcations. The corresponding problem appears to be harder to solve for ultrasound measurements.

The two most important visual observations indicating atherosclerosis in an angiogram are narrowing of the artery and irregularity of the vessel edge. These features are closely related to the two quantitative measures of atherosclerosis used in the PQRST: lumen volume and edge roughness. In this study, we have applied both these principles to the problem of growth direction. For the edge roughness, two methods were used to analyze the data: one involving a classification of segments as normal or pathological (Equation 2) and one avoiding these concepts (Equation 3).

Thus, essentially the same data were analyzed three times with various methodologies. The analysis yielded, rather consistently, results that have not been reported previously. In all three cases, the results indicate that growth in the downstream direction is more typical than growth upstream, at least on the medial side of the artery. For the lateral side, this was also suggested by one of the two models distinguishing between medial and lateral edges (Table 3⇑), whereas the regression model (Table 4⇑) did not give any clear indication of the direction of growth.

The subpopulation analyses (Table 5⇑) suggest that the predominance for downstream growth may be less pronounced or even absent in women and in elderly patients. The insignificant results obtained in the four subgroups defined by clinical or biochemical criteria may be related to the smaller sizes of these subpopulations and cannot be considered to be a proof of a weaker effect of downstream position in these conditions.

It should be realized that the patients used in this study were rather narrowly selected. The subjects all had moderate or severe hypercholesterolemia combined with moderately pathological findings at the time of the first angiographic examination.^{11} It remains to be shown that the same holds true in nonhypercholesterolemic patients or at more advanced stages of atherosclerosis. Likewise, it is not known whether the conclusion may be generalized to other arteries than the femoral.

As pointed out in the introduction, an increased frequency of plaque growth downstream would be an expected consequence if one accepts the theories linking atherogenesis to fluid mechanical phenomena, such as flow separation, that are likely to occur downstream of stenoses. The fact that the predominance for downstream growth was more pronounced in cases with overall atherosclerosis progression (Table 5⇑) tallies well with that explanation. It cannot be excluded, however, that other mechanisms, such as the gravitational force in the erect human body, may exert some influence. To resolve that dilemma, studies in other arterial domains would seem necessary. One should also bear in mind that the methods used do not allow us to distinguish with certainty between elongation of an existing plaque and the initiation of a new lesion. In both cases, however, the progression may be related to local blood flow patterns. The more unequivocal findings in younger patients and in those with a less severe maximum stenosis suggest that the proposed mechanisms may have the greatest effect at the earliest stages of the disease.

A limitation of the present study is the fact that a two-dimensional projection is used to study the three-dimensional geometry of the artery. Hence, plaques on the ventral and dorsal aspects of the vessel, which may certainly influence the fluid dynamics of the vessel, are ignored in the roughness calculation. For the filtering model of growth, however, the situation is different. Since the calculation includes densitometric information from the entire cross section, it should, in principle, be sensitive for such plaques as well. On the other hand, it should be realized that atherosclerotic plaques, in particular in the early stages of the disease, can grow predominantly in the outward direction, with only minor restriction of the lumen.^{21} ^{22} This fact can be a problem with methods relying on the lumen volume and may be one reason to prefer edge roughness as an angiographic measure of atherosclerosis.

The difference between the medial and the lateral sides was a rather unexpected finding. This might be related to the curvature of the femoral artery, which is normally directed away from the midline of the body and which may influence the blood flow pattern. In an earlier article, we demonstrated a greater degree of atherosclerotic involvement in the inner curves than in the outer curves of the femoral artery.^{23} We have also found that tortuosity of the femoral artery is accompanied by an accelerated rate of atherosclerosis progression.^{24} From the first study, it was clear that curvature and medial versus lateral localization were closely correlated, so that the inner curve tended to coincide with the lateral wall. In fact, when both factors were studied simultaneously, it turned out that the strongest effects on atherosclerosis were seen with inner versus outer curves. In the present study, however, it was impractical to take this factor into account, in view of the definition problems that will arise around inflection points: what was the inner curve will be the outer curve in the next 1-cm segment, etc. Hence, it seemed safer to use the unequivocal concepts of medial and lateral.

A factor obscuring our analysis is the variability between subjects in body size and hence arterial anatomy with regard to the localization of curves and bifurcations. However, distal to the origin of the profunda femoris (which lies above our area of interest), the variations in bifurcation geometry seem to be greater than can be explained by variations in height. Thus, it did not seem meaningful to make any kind of standardization for body size. Instead, the effect of bifurcations will be the subject of a forthcoming study.

To further complicate the situation, the fluid mechanics at a stenosis may be more complex than has been sketched above. Model experiments have indicated that areas of low and high shear can both emerge downstream of even a minimal geometric disturbance.^{10} ^{25} ^{26} Even so, the flow profile at the upstream border of the stenosis would be expected to be more regular, because the contraction causes acceleration and hence stabilization of the flow, whereas expansion downstream is accompanied by deceleration and destabilization of the flow.^{27} In other words, there are several types of flow disturbances that may occur at a stenosis, but all are more likely to develop downstream than upstream. Thus, the increased tendency toward growth in the downstream direction is consistent with several fluid mechanical theories of atherogenesis. Both high and low shear rates have, indeed, been implicated as contributing factors in atherogenesis.^{4} ^{28}

A central parameter describing flow is the Reynolds number (Re),^{29} which can be defined, for a cylindrical vessel, as (Equation 8) with d denoting the tube diameter, v the kinematic viscosity, and Q the volume flow rate. In the absence of pulsatility, Re >2500 usually implies turbulent flow. Nilsson et al^{30} found that the mean value of the average diameter of the femoral artery was 5.9 mm, and Demolis et al^{31} reported a mean flow rate in the femoral artery of 6.5 mL/s. Assuming a high shear value for whole-blood kinematic viscosity of ≈4×10^{−6} m^{2}/s,^{32} this would give an Re of ≈350.

To characterize pulsatile flow in a cylindrical vessel, one often uses the frequency parameter (Womersley's α),^{33} defined from the frequency f by (Equation 9). The greater α is, the farther the velocity profile will deviate from the parabolic shape.^{34} If the above approximations are used, a cardiac frequency of 70 bpm would correspond to a frequency parameter value of ≈4.

A paradoxical and somewhat related concept that has been the subject of earlier study is the poststenotic dilatation.^{35} ^{36} According to Roach,^{35} this phenomenon occurs only at stenoses severe enough to cause turbulence downstream, as indicated by the presence of a thrill and bruit. This situation is hardly representative for the slight or moderate lesions visualized by angiography in our patients. However, recent findings of Ojha and Langille^{37} suggest that the phenomenon may be related to high shear rates rather than turbulence. If this is true, then poststenotic dilatation may have influenced our results, making them less clear-cut than would have been the case otherwise.

In conclusion, the present study has indicated that, in the femoral artery of hypercholesterolemic patients with slight or moderate atherosclerosis, the region immediately downstream of a plaque is more likely to develop the disease than the region immediately upstream, at least on the medial side in male patients <55 years old. For other subpopulations, the same tendency was present but not significant. A conceivable explanation is that fluid mechanical phenomena, such as flow separation, that can occur downstream of a stenosis may contribute to the further development of the plaque or to the inception of new lesions.

## Acknowledgments

Financial support for this study was received from the Swedish Medical Research Council (grant 10884) and the Swedish Society for Medical Research (SSMF).

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- Do Plaques Grow Upstream or Downstream?Örjan SmedbyArteriosclerosis, Thrombosis, and Vascular Biology. 1997;17:912-918, originally published May 1, 1997http://dx.doi.org/10.1161/01.ATV.17.5.912
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- Do Plaques Grow Upstream or Downstream?Örjan SmedbyArteriosclerosis, Thrombosis, and Vascular Biology. 1997;17:912-918, originally published May 1, 1997http://dx.doi.org/10.1161/01.ATV.17.5.912

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