  The generation of virtual populations (VPs) of anatomy is essential for
conducting in silico trials of medical devices. Typically, the generated VP
should capture sufficient variability while remaining plausible and should
reflect the specific characteristics and demographics of the patients observed
in real populations. In several applications, it is desirable to synthesise
virtual populations in a \textit{controlled} manner, where relevant covariates
are used to conditionally synthesise virtual populations that fit a specific
target population/characteristics. We propose to equip a conditional
variational autoencoder (cVAE) with normalising flows to boost the flexibility
and complexity of the approximate posterior learnt, leading to enhanced
flexibility for controllable synthesis of VPs of anatomical structures. We
demonstrate the performance of our conditional flow VAE using a data set of
cardiac left ventricles acquired from 2360 patients, with associated
demographic information and clinical measurements (used as
covariates/conditional information). The results obtained indicate the
superiority of the proposed method for conditional synthesis of virtual
populations of cardiac left ventricles relative to a cVAE. Conditional
synthesis performance was evaluated in terms of generalisation and specificity
errors and in terms of the ability to preserve clinically relevant biomarkers
in synthesised VPs, that is, the left ventricular blood pool and myocardial
volume, relative to the real observed population.
