# Multivariate Normal Distribution Method for a Virtual Cerebral Arterial Population

## TL;DR

This paper introduces a new method using multivariate normal distribution to generate realistic virtual cerebral arteries that mimic real ones in shape and diversity.

## Contribution

A novel MVND-based approach for generating virtual cerebral arterial populations with preserved geometric diversity and anatomical continuity.

## Key findings

- Virtual arteries generated using MVND show similar geometric features to real arteries.
- The distribution of geometric features in virtual arteries matches that of real arteries.
- MVND captures correlations between vascular parameters to reproduce anatomical characteristics.

## Abstract

Recently, the concept of a virtual population (Vpop) has attracted attention to provide large‐scale, diverse datasets without compromising individual privacy. The development of the Vpop modelling method for the cerebrovasculature shape is necessary to be established with simple parameter tuning and post‐processing. This study introduces a multivariate normal distribution (MVND) method to generate a Vpop for the cerebrovasculature shape. We defined an MVND by using the position and inner radius, which represent the vascular shape (centerline), as variables. Patient‐specific arteries (basilar artery and internal carotid artery) obtained from MR images were used as a real population (Rpop) to generate an MVND. Then, virtual arteries were sampled from this MVND to generate a Vpop. To evaluate the validity of this method for reproducing shape diversity, we calculated the geometrical features of the centerline in each population. The centerline shows qualitatively similar characteristics between Vpop and Rpop. Geometrical features such as average length calculated from Vpop are in the same range as those of Rpop. Moreover, the distribution of geometrical features exhibits a good degree of fit between Vpop and Rpop. Since MVND considers the correlation among all position and inner radius variables, centerline continuity and anatomical characteristics of cerebrovasculature can be automatically included. Hence, geometric features and their distribution can be reproduced without any parameter tuning. The consistency in geometric parameters between the two populations supports the validity of the MVND method and indicates the potential for generating a Vpop for the cerebrovasculature in a more straightforward and simplified manner.

A simple multivariate normal distribution (MVND) method for generating a population of distributed virtual arteries with multiple geometric features was developed. The distribution of geometric features in virtual arteries represents the distribution in real arteries.