A Statistical Model for Quantification and Prediction of Cardiac Remodelling: Application to Tetralogy of Fallot

Abstract

Cardiac remodelling plays a crucial role in heart diseases. Analyzing how the heart grows and remodels over time can provide precious insights into pathological mechanisms, eventually resulting in quantitative metrics for disease evaluation and therapy planning. This study aims to quantify the regional impacts of valve regurgitation and heart growth upon the end-diastolic right ventricle (RV) in patients with tetralogy of Fallot, a severe congenital heart defect. The ultimate goal is to determine, among clinical variables, predictors for the RV shape from which a statistical model that predicts RV remodelling is built. Our approach relies on a forward model based on currents and a diffeomorphic surface registration algorithm to estimate an unbiased template. Local effects of RV regurgitation upon the RV shape were assessed with Principal Component Analysis (PCA) and cross-sectional multivariate design. A generative 3-D model of RV growth was then estimated using partial least squares (PLS) and canonical correlation analysis (CCA). Applied on a retrospective population of 49 patients, cross-effects between growth and pathology could be identified. Qualitatively, the statistical findings were found realistic by cardiologists. 10-fold cross-validation demonstrated a promising generalization and stability of the growth model. Compared to PCA regression, PLS was more compact, more precise and provided better predictions.

A Non-parametric Statistical Shape Model for Assessment of the Surgically Repaired Aortic Arch in Coarctation of the Aorta: How Normal is Abnormal?

“…mean shape) of the Control group was computed with the exoshape code framework as proposed by Durrleman [6] and introduced to cardiac research by Mansi [5], using mathematical currents [4] as non-parametric shape descriptors. Based on a forward approach [6], the template T and its transformations ϕ i towards each subject shape T i are computed simultaneously using an alternate two-step algorithm, minimising the distance between the deformed template ϕ i (T ) and T i in the vector space of currents.…”

“…The latter is generated by two Gaussian kernels: K W for the shape representations and K V for the transformations ϕ. The associated kernel widths λ W and λ V are defined as the resolution of the currents representation and the stiffness of the deformations, respectively [5]. In order to find an adequate set of λ parameters, an initial template of the Control group T Control,initial was computed using starting values of λ W,initial =15mm and λ V,initial =47mm.…”

“…T Control,f inal was validated using 10-fold cross-validation [5]. Further, gross geometric parameters of T Control,f inal (volume V, surface area A surf , centreline length L CL and median diameter along the centreline D med ) were compared to the respective mean values of the Control population.…”

“…The transformations ϕ, encoding all shape features present in the population, are parametrised by moment vectors β, which deform T Control,f inal towards each subject shape in the space of currents [5]. The moment vectors β, obtained from transforming T Control,f inal towards all Control and CoA shapes, constituted the input (predictors) for a Partial Least Squares regression (PLS).…”

“…The method is based on the forward approach, whereby transformations of an ideal unbiased template shape towards each subject shape within the population encode all global and regional 3D shape information [5], [6]. We hypothesised that by analysing how a template shape of a healthy (not surgically altered) arch transforms towards each CoA arch shape, a shape vector as a subject-specific measure of abnormality can be derived.…”