Multivariate Mean Parameter Estimation by Using a Partly Exponential Model

Analysis of cerebral microvascular architecture--application to cortical and subcortical vessels in rat brain

Cerebral vascular morphology, including vascular diameters, lengths and branch points, was measured using quantitative three-dimensional (3D) imaging software developed in our laboratory, where data were collected from cortical and subcortical regions of a rat brain. To compare multiple records of the vascular morphological differences between anatomical regions with unpaired data, a simple analysis of variance (ANOVA) model may not be applicable, or may not be valid without considering correlation and unpaired data. In this paper, we formulate a novel outcome to study vascular morphological differences, discuss proper paired test statistics on unpaired data and apply the proposed methods to study the cerebral vascular morphological differences between cortical and sub-cortical regions in rats (N=6). The total vessel surface was analyzed as a composite of diameter, length and branches of vessels. The extended Fisher permutation test provides the paired test on unpaired data, which is equivalent to a permutation test based on the average of multiple sections; however, the permutation test may not be exact. The repeated measure analysis of variance using Generalized Estimating Equations (GEE) can be used to conduct the paired test on unpaired data as an alternative, when the permutation test is not exact. These new approaches can be applied in the study of treatment effects on changes of vascular morphology under physiological and pathological conditions.