Relation between the structural asymmetry of coronary branch vessels and the angle at their origin

Journal of Biomechanics 31 (1998) 273 — 278

Relation between the structural asymmetry of coronary branch vessels and the angle at their origin Morton H. Friedman*, Zhaohua Ding Biomedical Engineering Center, The Ohio State University, Columbus, OH 43210, U.S.A. Received in final form 3 July 1997

Abstract The relationship between the geometry of branch points on the left anterior descending coronary artery, and the morphometry of the proximal portions of the daughter vessels, was examined. The geometry at 23 branch points on 15 human hearts was derived from multiplane contrast angiograms, and the morphometry at 29 sites along the daughter vessels was obtained from transverse sections using computerized techniques. The angle of the branch at which the daughter originated was positively correlated with the maximum thicknesses of the intima and media, and with their circumferential asymmetry. The results suggest that large branch angles may favor eccentric intimal thickening, a phenomenon which may predispose to lipid accumulation and atherosclerosis. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Coronary artery; Vascular geometry; Angiography; Morphometry; Intimal thickening

1. Introduction In earlier work (Friedman et al., 1996) we demonstrated a relationship between the morphometry of the left anterior descending coronary artery (LAD) and certain geometric features of the vessels. In particular, the angle at which daughter vessels departed the LAD was strongly and positively correlated with almost all morphometric quantities examined, including the thicknesses of the intima and media of the LAD closely distal to the branch. Some of these relationships are believed to reflect the influence of branch angle on the flow field in the continuing parent vessel. The design of the previous work also provided morphometric data for the daughter vessels, which were seen to constitute a different population from the sites on the LAD. Indeed, the geometry at a branch site on the LAD might reasonably be expected to affect the daughter and continuing parent quite differently, since both the geometry and the flow are highly asymmetric at such sites. The geometry is similar to that of a straight tube with

* Corresponding author. Tel.: (614)-292-7165; fax: (614)-292-7301; e-mail: friedman. [email protected]. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S0021-9290(98)00013-X

a side arm, and numerous fluid mechanical studies in this geometry have demonstrated substantial asymmetries in the flow field; for instance, the sites of separation in the parent and side branch are quite different (e.g., He and Ku, 1995). Furthermore, the flow partition at these branches will generally favor the continuing LAD because of its greater size. The different effects of branching on the LAD and its daughters suggested that new inferences regarding the effect of mechanical forces on vessel morphology might be gained by exploring the relationships between geometry and morphometry for the daughter vessels as well. As will be seen, the relationships for the branch sites are similar to those for the LAD and can be explained in a consistent fashion without invoking any new hemodynamic mechanisms.

2. Materials and methods The methods used to obtain the necessary geometric and morphometric variables were the same as those in Friedman et al. (1996), where they are described in greater detail. Fifteen pressure-fixed cadaver hearts free of intrusive coronary artery lesions, and from subjects

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who died from causes other than cardiovascular disease, constituted the material for study. Demographic data were available for 14 of the subjects: they ranged in age from 18 to 62 yr (mean"33 yr), and included nine females and five males; seven were black, five were white, one was Asian and one was Hispanic. The left coronary arteries of each heart were injected with a radiopaque gel and angiograms were obtained at several viewing angles. The angiograms were used to identify the first two major branches off the LAD; ‘major branches’ are those (Brinkman et al., 1994) whose diameter is at least 2 mm. If two such branches could not be found on a heart, the size requirement was relaxed to 1 mm. Twenty-three branches were used in this study: 11 first diagonal branches, six second diagonal branches, and six septal perforator arteries. Fewer than thirty branches were used because, for some of the hearts, one of the branches dissected off the epicardium was too short to permit a section to be cut. The angiographic images were processed to obtain the three-dimensional (3D) axial geometry of the LAD and major branch vessels; this 3D representation is used to characterize the geometry of the regions of interest. After angiography, transverse sections of the branch arteries were cut 2—3 mm (and, if possible, 5—6 mm) from their origin and processed histologically. A reticle was used to divide the images of each section into quadrants. The reticle was positioned such that the quadrants were of similar size, without regard to the variation in intimal or medial thickness around the perimeter; however, no orientation information was available for these sections, so the orientation of the quadrants with respect to the myocardium was arbitrary. The histomorphometry at 29 sites was characterized from elastic-stained (Weigert’s) sections using computerized image processing techniques. Although some of the sites exhibited intimal thickening, none were atherosclerotic. The initial morphometric procedure provided (Friedman et al., 1996), for each quadrant and for the entire section: lumen, internal elastic lamina (IEL) and external elastic lamina perimeters; and intimal and medial cross-sectional areas. Correlations were sought between a set of four geometric parameters associated with each site, and each of 18 normalized morphometric variables obtained from the foregoing perimeters and areas. The four geometric variables were: (1) angle: The angle between the LAD and the branch at its origin. (2) radius: The radius of the vessel at the most proximal site examined in the branch, estimated as (IEL perimeter)/2n. Perimeter was used to estimate the radius of the original vessel because it is less sensitive than other measurements (such as the minimum or ‘hydraulic’ radius of the cross-section) to the distortion that accompanies sectioning and histological preparation. The

radius estimate used here assumes transverse sectioning and that the original artery was circular in cross-section. The errors arising from the failure of these assumptions are believed to be small. (3) dis: The axial distance from the section to the origin of the branch; the origin was defined as the intersection of the branch vessel axis and the plane perpendicular to it passing through the flow divider. (4) ratio: The area ratio at the origin of the branch, defined as the luminal area of the LAD divided by that of the branch, both estimated from the respective IEL perimeters 2-3 mm distal to the branch point. The local curvature at the site and its distance from the origin of the LAD, which were used in the analysis of the sites on the LAD, were not included as regressors in the present work. The curvature at the daughter vessel sites was small, and it was expected that the morphology of a site on a branch vessel would be more dependent on its distance from the origin of the branch than on the location along the LAD at which the branch originated. The morphometric variables were the same as in the earlier work, with two additions. The full set of variables included: f Eight (unscaled) dimensioned variables: the area, mean thickness, and mean thicknesses of the thickest and thinnest quadrants, of the intima and media. f Two asymmetries, of the intima and media, asymmetry being defined as the ratio of the tunica thickness in the quadrant in which it is greatest to the thickness in the quadrant in which it is least. f Eight scaled dimensionless variables, obtained by dividing each of the unscaled variables by the vessel radius at the site, raised to the appropriate power; thicknesses are divided by the radius, and intimal and medial areas are divided by the square of the radius. Scaling is intended to compensate to some extent for case and site variations in the size of the vessel. The mean thicknesses of intima or media in each entire section or quadrant were obtained by dividing the crosssectional area of the layer by the average of the bounding lamina perimeters; for instance, the mean thickness of the entire intima " (intimal area)/((lumen perimeter # IEL perimeter)/2). The means, standard deviations, and distribution of the eight unscaled variables and the two asymmetries are summarized in Table 1. All morphometric variables except the asymmetries were normalized; normalization is performed by dividing each variable at each site by the average value of that variable at all sites examined in that case. In a slight modification of this approach, the mean thicknesses of the thickest and thinnest quadrants were normalized by dividing them by the average value of the mean thicknesses of the entire cross-section. Thus, for each case, all intimal thickness measures were normalized by the same

M.H. Friedman, Z. Ding / Journal of Biomechanics 31 (1998) 273—278 Table 1 Statistics of selected morphometric variables (N"29) Variable!

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Table 2 Correlations of branch vessel morphometry with branch angle and area ratio

Mean value

Standard deviation

Range

Intimal area (mm)2

0.545

0.390

0.080—1.445

Mean intimal thickness (mm)

0.075

0.047

0.014—0.169

Mean intimal thickness, thickest quarant (mm)

0.117

0.087

0.018—0.379

Mean intimal thickness, thinnest quadrant (mm)

0.045

0.031

0.010—0.124

Intimal asymmetry

3.158

2.279

1.310—13.300

Medial area (mm)2

0.592

0.322

0.170—1.299

Mean medial thickness (mm)

0.074

0.025

0.032—0.135

Men medial thickness, thickest quadrant (mm)

0.087

0.032

Mean medial thickness, thinnest quadrant (mm)

0.061

Medial asymmetry

1.443

Variable"

r2

p-values! Angle

Intimal area

0.1862

Mean intimal thickness, thickest quadrant

0.3286

0.0014 (n "0.492) 2

Intimal asymmetry

0.6055

* (n "0.322) 1

Scaled intimal area

0.2098

0.037—0.169

Scaled mean intimal thicknes

0.2011

0.020

0.030—0.109

0.3114

0.289

1.036—2.316

Scaled mean intimal thickness, tickest quadrant Medical area

0.3166

Mean medial thickness, thickest quadrant

0.2315

0.0095 (n "1.625) 1

Medial asymmetry

0.5580

* (n "1.309) 1

Scaled medial area

0.2715

Scaled mean medial thickness

0.2889

Scaled mean medial thickness, thickest quadrant

0.2028

Scaled mean medial thickness, thinnest quadrant

0.3857

!All the morphometric variables in this able are unscaled and unnormalized.

quantity, and similarly for the medial thicknesses. A site exhibiting an intimal thickness equal to the average of the thickness of all sites in that case will have a normalized thickness of unity. Normalized variables are expected to be less sensitive to case variations in the overall level of disease, and to be more likely to reflect the local variations in morphometry that geometry might be expected to influence. Pairwise correlation coefficients were calculated for all morphometric parameters included in the correlations, to assess their independence of one another.

3. Results The initial regression used was applied separately to each of the 16 (8 unscaled and 8 scaled) normalized morphometric variables and the two asymmetries. For a given variable, m, the regression was as follows: m"a #a ]angle]exp(!n ]dis/radius) 0 1 1 #a ]ratio]exp(!n ]dis/radius), (1) 2 2 where a , a , a , n and n are coefficients to be deter0 1 2 1 2 mined. The effects of angle and ratio on the morphometric variables are assumed to decay exponentially with distance, dis, from the origin of the branch, measured as a multiple of vessel radius. The constants n and n , 1 2 measure the rate of this decay for each variable. The regression analysis for each morphometric variable was carried out in two steps. First, a nonlinear

Ratio 0.0313 (n "0.000) 2

0.0213 (n "0.539) 2 0.0246 (n "0.0555) 2 0.0020 (n "0370) 1 0.0034 (n "1.136) 2

0.0076 (n "0350) 2 0.0056 (n "0.336) 2 0.0239 (n "0.452) 2 0.0009 (n "0.098) 2

*p(10~4. ! Boldface designates positive correlation; plain font designates negative correlaion. " The variable list includes unscaled and scaled variables; the scaled ones are explicitly specified. All morphometric variables are normalized, except for the intimal and medial asymmetry.

regression was used to find the best values of n and n , 1 2 subject to the constraint that 0)n )3. The values of i n and n were then fixed and the data were reanalyzed 1 2 by standard multivariate linear regression methods, using a backward elimination procedure with a p-value for retention of 0.05. The results are summarized in Table 2. Angle was positively correlated, at p-values between (10~4 and 0.01, with the asymmetries and maximum thicknesses of both the intima and media, as well as the scaled maximum thickness of the intima. The correlations of intimal

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scaled morphometric variables; the p-values ranged from 0.0009 to 0.03. Owing to correlations among the morphometric variables, these regressions against geometry are not independent. Among the correlates of angle, the three intimal variables form a mutually correlated ‘cluster’ (r2*0.78), and the two medial variables are correlated as well (r2"0.60). The intimal and medial areas are also correlated (r2"0.62).

4. Discussion

Fig. 1. Intimal asymmetry (mean intimal thickness of the quadrant in which the intima is thickest/mean intimal thickness of the quadrant in which the intima is thinnest) in the proximal branches of the left anterior descending coronary artery (LAD) vs. angle (in degrees) between the LAD and the branch at its origin. See text for the definition of the terms in the abscissa. For this correlation, n "0.322, p(10~4, 1 r2"0.61. The five sites exhibiting the greatest asymmetries represent four different cases.

Fig. 2. Medial asymmetry (mean medial thickness of the quadrant in which the media is thickest/mean medial thickness of the quadrant in which the media is thinnest) in the proximal branches of the left anterior descending coronary artery (LAD) vs angle (in degrees) between the LAD and the branch at its origin. See text for the definition of the terms in the abscissa. For this correlation, n "1.309, p(10~4, r2"0.56. 1

and medial asymmetry with the angle term in Eq. (1) are shown in Figs. 1 and 2. The minimum thicknesses were not significantly correlated with angle. Ratio, which was known for only 25 sites, correlated negatively with intimal and medial areas, and positively with most of the

The analysis shows that the intima and media are more asymmetric in daughter vessels that depart the LAD at greater angles, and that this increased asymmetry is a consequence of greater thickening in the quadrant where the layer is thickest (rather than less thickening in the quadrant where the layer is thinnest). This result is of particular relevance to atherogenesis, since sites of eccentric intimal thickening such as these may be predisposed to lipid accumulation and the eventual development of clinically significant coronary atherosclerosis (Stary et al., 1992). Thus large branch angles may prove to be ‘geometric risk factors’ (Friedman et al., 1983) for disease in the proximal daughter vessels. In earlier work (Friedman et al., 1996), branch angle was shown to have a similar, though weaker, effect on the intimal (p"0.04) and medial (p"0.008) asymmetry of the LAD distal to the branch. A stronger effect on the daughter vessel is to be expected, since the course of the LAD does not deviate much at branch sites, and the branch angle defines primarily the angle through which the flow must turn to enter the daughter vessel. There have been few studies focussed on the effect of branch angle on the flow field in the daughter vessel when the parent continues without a major change in direction. Yamamoto et al. (1992) surgically varied the angle between the aorta and renal artery from 30° to 90° in a dog and found that larger angles caused increased flow reversal at the cranial wall of the renal artery and higher peak velocities near the caudal wall. In studies employing human pathology specimens (Caro et al., 1971; Friedman et al., 1981; Ku et al., 1985), flow reversal and the accompanying reduction in shear stress have been shown to be associated with intimal thickening. The notion that the effect of geometry is mediated hemodynamically is supported by the values of n in 1 Table 2. These values are 0.492 for maximum intimal thickness and 0.322 for intimal asymmetry, and indicate that the effect of branch angle on intimal morphometry decays distally with a characteristic length, radius/n , of 1 up to about three vessel radii. This length is comparable to the extent of the separation region in a 90° side branch with Reynolds numbers characteristic of the coronary circulation (He and Ku, 1995). The values of n for medial asymmetry and maximum 1 medial thickness are larger than those for the intima,

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indicating that the effect of angle on medial morphometry decays more rapidly with distance from the origin of the vessel. The effect of branch angle on the media may be related to mechanical stresses associated with the branch point (Thubrikar et al., 1990) and therefore might be expected to be more localized to the ostial region. The area ratio at the branch was found to correlate negatively with intimal and medial area, and positively with most of the scaled variables. The correlation with the areas of the media and intima probably arises because smaller branch vessels (characterized by larger ratio values) have thinner walls. This explanation is supported by the low values of n , which indicate that the 2 apparent effect of area ratio extends far into the daughter vessel, well beyond the expected range of influence of ostial geometry on branch vessel hemodynamics. The correlation between area ratio and the scaled variables probably reflects the fact that the area ratio as defined here is inversely proportional to the cross-sectional area of the branch vessel, while the scaled morphometric variables are derived by dividing the measured morphometry by luminal radius or area. Thus, vessel size affects area ratio and scaled morphometry similarly, leading to an apparent positive correlation. The asymmetry used in these analyses is based on the morphometry of quadrants of the transverse arterial sections. The quadrants are defined arbitrarily by superimposing crosshairs from a reticle on the image; no orientation information is available for these cases. More detailed descriptions of the circumferential variation of layer thickness could have been obtained from the images, but it was felt that the averaging implicit in the use of quadrant data would provide results less susceptible to the occasional localized thinning or thickening that might lead to an asymmetry value less representative of the section as a whole. Clearly, the calculated asymmetry is dependent on the placement of the reticle, but it would seem that the arbitrary demarcation of the borders of each quadrant should underestimate rather than overestimate asymmetry. The observed relation between tunica asymmetry and branch angle could have been more instructive with respect to the role of hemodynamic factors if orientation data had been available for these sections. In a companion study (unpublished), the LADs of five of the hearts. used in Friedman et al. (1996) were sectioned in such a way [using small incisions (Stary, 1989) and heavy inking] that orientation data were retained in 28 sections. For these sections, the reticle was placed to divide the wall into four quadrants of similar size, defined with respect to the surface of the heart (epicardial, myocardial) and the orientation of the immediately proximal major branch (ipsilateral, contralateral). Regressions of intimal and medial thickness similar to those used here and in Friedman et al. (1996), showed that the only quadrant

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whose intimal thickness depended significantly on angle was the contralateral quadrant, and that the correlation was positive, with p-values of 0.006 for intimal thickness and 0.009 for scaled intimal thickness. This quadrant might be expected to experience a relatively low shear environment that could be exacerbated by larger branch angles. The data set on which this analysis is based also included 13 sections on the left circumflex artery (LCX), which could be regarded as a daughter of the combined left main-LAD segment. Statistical analysis showed that the geometric parameters at the left main coronary artery bifurcation, and the regressions of the morphometry of the 13 sites against that geometry, were both different from those for the more distal vessels. A power analysis showed that the number of sites on the LCX were too few to preclude Type II errors with respect to the response of all morphometric variables. Accordingly, the sites on the LCX were excluded from the present analysis. This research continues to demonstrate relations between the morphometry of vessels free of significant atherosclerosis, and their local geometry. The morphometric response seen here can be related to an early phase in the atherogenic process. Relationships have also been seen (Ding et al., 1997; Friedmanet et al., 1993) between the distribution of sudanophilia, another indicator of early lesions, in the LAD and LCX, and the geometry of the left main coronary artery (LM) bifurcation, at which the two vessels originate. The sudanophilia results are not completely consistent with the morphometry; in Ding et al. (1997), proximal sudanophilia in the LAD was enhanced when the bifurcation angle was larger (and the bifurcation was more planar), but in Friedman et al. (1993), a larger angle was associated with less proximal staining in the LCX. Although the sudanophilia results by themselves are not inconsistent and may reflect different effects of branch geometry on the flow field or mechanics in the two daughter vessels, one might expect the LCX to be analogous to the branch vessels in the present work and to have demonstrated an adverse effect of large angles. It may be that different hemodynamic or mechanical environments prompt different early responses in the vessel wall, or there may be too great a difference between the local geometries of the LM bifurcation and the branch points on the LAD to expect the responses of the LCX and LAD branches to variations in branch angle to be the same.

Acknowledgments This research was supported by NIH Grant HL42302. Hearts were generously provided by Dr. P.B. Baker, Dr. W.P. Newman at Louisiana State University and Mr. R. Vigorito at University of Maryland. Technical support was provided by B.D. Kuban.

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References Brinkman, A.M., Baker, P.B., Newman, W.P., Vigorito, R., Friedman, M.H., 1994. Variability of human coronary artery geometry: an angiographic study of the left anterior descending arteries of 30 autopsy hearts. Annuals of Biomedical Engineering 22, 34—44. Caro, C.G., Fitz-Gerald, J.M., Schroter, R.C. 1971. Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proceedings of the Royal Society of London B177, 109—159. Ding, Z., Biggs, T., Seed, W.A., Friedman, M.H., 1997. Influence of the geometry of the left main coronary artery bifurcation on the distribution of sudanophilia in the proximal portions of the daughter vessels. Arteriosclerosis, Thrombosis, and Vascular Biology, accepted. Friedman, M.H., Baker, P.B., Ding, Z., Kuban, B.D., 1996. Relationship between the geometry and quantitative morphology of the left anterior descending coronary artery. Atherosclerosis 125, 183—192. Friedman, M.H., Brinkman, A.M., Qin, J.J., Seed, W.A., 1993. Relation between coronary artery geometry and the distribution of early sudanophilic lesions. Atherosclerosis 98, 193—199.

Friedman, M.H., Deters, O.J., Mark, F.F., Bargeron, C.B., Hutchins, G.M., 1983. Arterial geometry affects hemodynamics. A potential risk factor for atherosclerosis. Atherosclerosis 46, 225—231. Friedman, M.H., Hutchins, G.M., Bargeron, C.B., Deters, O.J., Mark, F.F., 1981. Correlation between intimal thickness and fluid shear in human arteries. Atherosclerosis 39, 425—436. He, X., Ku D.N., 1995. Flow in T-bifurcations: effect of the sharpness of the flow divider. Biorheology 32, 447—458. Ku, D.N., Giddens, D.P., Zarins, C.K., Glagov, S., 1985. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Arteriosclerosis 5, 293—302. Stary, H.C., 1989. Evolution and progression of atherosclerotic lesions in coronary arteries of childern and young adults. Arteriosclerosis Supplement 9, I19—I32. Stary, H.C. et al., 1992. A definition of the intima of human arteries and of its atherosclerosis-prone regions. Arteriosclerosis Thrombosis 12, 120—134. Thubrikar, M.J., Roskelley, S.K., Eppink, R.T., 1990. Study of stress concentration in the walls of the bovine coronary arterial branch. Journal of Biomechanics 23, 15—26. Yamamoto, T. et al., 1992. Blood velocity profiles in the origin of the canine renal artery and their relevance in the localization and development of atherosclerosis. Arteriosclerosis. Thrombosis 12, 626—632.