Fibrous intimal thickening and atheronecrosis of the thoracic aorta. Some background for mathematical theory.

: Paraffin sections from the lateral walls of the thoracic aorta, stained with a nigrosin-Gomori trichrome combination, were used to separate subjects into those having (Yes-A) and not having (No-A) atheronecrosis, as operationally defined. In 174 of the 211 No-A subjects, the dispersal of fibrous intimal thickening (FIT) over a carefully selected set of loci was fitted well (goodness of fit p greater than 0.05) by the negative binomial distribution. In 99 of the 125 Yes-A subjects, negative binomial forms were fitted well to the data. The Poisson and positive binomial forms also fitted well in most aortas. In some aortas, departures from the negative binomial, positive binomial, or Poisson forms could be attributed to the presence (among a total of 40 points) of a set of one to five points having accelerated fibroplasia. Atheronecrosis and accelerated fibroplasia tended to coexist in the same subjects and also to be found together in the same loci within aortas. Both features of advanced plaques were characteristic of older subjects. These results taken together affirm that several decades of progression of FIT precede an abrupt emergence of the two features of late phase atherogenesis. The findings suggest that atherosclerosis progresses by a two-phase stochastic process. In phase one, FIT evolves such that a form resembling the negative binomial is generated with approximations of the mean as a linear function of time and the standard deviation as a quadratic function of the mean. In phase two the set of points with greatest FIT acquires either atheronecrosis, or accelerated fibroplasia, or both.