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Sir,—We read with interest the article by von Birgelen and colleagues in which they found both vessel and plaque volume in lesions with inadequate compensatory enlargement to be smaller than in lesions with adequate compensatory enlargement.1 They also found that the eccentricity index (EI)—calculated as minimum wall thickness divided by maximum wall thickness—was higher in lesions with inadequate remodelling than in those with adequate remodelling. Because endothelium dependent arterial dilatation, which has been proposed as a possible mechanism for arterial compensatory remodelling,2 requires a normally functioning endothelium, the higher eccentricity produced by a thick wall with plaque and a thin plaque free wall in lesions with adequate remodelling may support that hypothesis as mentioned by Varnava.3 The EI, however, would decrease in relation to the plaque enlargement with an increase in the maximum thickness even if the amount of plaque free endothelium is unchanged. The assumptions that both arterial contour and luminal contour are true circles lead to the following equations.
(1) P + L = π × [(Dmin + Dmax + Dlum)/2]2
where P is plaque area, L is luminal area, Dmin is minimum wall thickness, Dmax is maximum wall thickness, and Dlum is luminal diameter.
(2) L = π × [Dlum/2]2
(3) EI = Dmin/Dmax.
Finally, the equation, Dmin = 2 × EI × [(P+L)1/2 − L1/2]/[π1/2 × (EI + 1)], can be obtained from equations (1), (2) and (3).
For example, lesion A with L = 2.4 mm2, P = 10.9 mm2, and EI = 0.28 has a Dmin of 0.518 mm; lesion B with L = 2.3 mm2, P = 15.2 mm2, and EI = 0.21 has a Dmin of 0.522 mm. Although the EI of lesion B is smaller than that of lesion A, the calculated values of Dmin are comparable. Therefore, a smaller value of EI does not warrant the larger amount of preserved, normally functioning endothelium. These values used for lesions A and B are the mean values in lesions with adequate and inadequate remodelling, respectively, in the study of von Birgelen et al.
We proposed another hypothesis of mechanical deformation to explain arterial remodelling.4 This suggests that a larger length of plaque along the cross sectional wall may make a larger luminal enlargement. Although precise methods to determine the ratio of plaque to plaque free endothelium have not been established, Blank and Yeung, who proposed new indices for the ratio of the length of plaque to that of the cross sectional wall, found that a larger plaque produces a higher degree of arterial remodelling when the cross sectional plaque area is less than 55% of the total vessel area.5 Because adequate arterial remodelling occurs in the early stage of atherosclerosis,2 this observation supports the mechanical deformation hypothesis. We believe more sophisticated methods than calculating the EI for determination of eccentricity are required to assess the mechanism causing arterial remodelling.
This letter was shown to the authors, who reply as follows:
We thank Dr Oniki for his thoughtful and interesting comments on his work. We agree that the EI may decrease in relation to plaque enlargement (that is, an increase in maximum plaque thickness) even if the extent of plaque free, cross sectional area, and possibly normal functioning overlying endothelium is unchanged.
Indeed the EI is not a suitable parameter to characterise the presence and extent of plaque free endothelium. However, that was not the idea underlying the use of the EI in our paper. Rather we used the EI to define the eccentricity of plaque distribution. There appeared to be a significant difference between lesions with adequate compensatory enlargement and those with inadequate adaptive remodelling, suggesting that more concentric lesions in that phase of the disease had less compensatory enlargement.
We appreciate the suggestions that the disease free endothelial wall may play a role in the ability of the arterial wall to enlarge and to attract our attention to the hypothesis of mechanical deformation.
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