Learning Interactions Between Cardiac Shape and Deformation: Application to Pulmonary Hypertension

Abstract

Cardiac shape and deformation are two relevant descriptors for the characterization of cardiovascular diseases. It is also known that strong interactions exist between them depending on the disease. In clinical routine, these high dimensional descriptors are reduced to scalar values (ventricular ejection fraction, volumes, global strains...), leading to a substantial loss of information. Methods exist to better integrate these high-dimensional data by reducing the dimension and mixing heterogeneous descriptors. Nevertheless, they usually do not consider the interactions between the descriptors. In this paper, we propose to apply dimensionality reduction on high dimensional cardiac shape and deformation descriptors and take into account their interactions. We investigated two unsupervised linear approaches, an individual analysis of each feature (Principal Component Analysis), and a joint analysis of both features (Partial Least Squares) and related their output to the main characteristics of the studied pathology. We experimented both methods on right ventricular meshes from a population of 254 cases tracked along the cycle (154 with pulmonary hypertension, 100 controls). Despite similarities in the output space obtained by the two methods, substantial di↵erences are observed in the reconstructed shape and deformation patterns along the principal modes of variation, in particular in regions of interest for the studied disease.

Characterizing interactions between cardiac shape and deformation by non-linear manifold learning

“…In our preliminary work (Di Folco et al, 2020), we related shape and deformation using PLS, a linear dimensionality reduction method that considers the crosscovariance between the two descriptors. This work re-vealed that considering the two descriptors jointly or independently leads to substantial differences in areas of critical importance for the studied diseases.…”

“…The Procrustes alignment used a similarity transform and therefore removed scaling differences between subjects, which differs from our previous work (Di Folco et al, 2020) where we used a rigid transform. This allows observing finer shape differences compared to global differences previously reported in the literature (Dragulescu et al, 2013).…”

“…In this case, the correlation between descriptors is high, as they correspond to two instances of the same objects seen with different modalities. In preliminary work, we tested these linear techniques on myocardial shape and deformation, but only limited our assessment to the observation of substantial differences in zones of high interest for the studied diseases (Di Folco et al, 2020). In the present paper, we investigate this link much more in detail, on both synthetic and (larger) real populations.…”

“…We evaluated the interest of this alignment strategy over fusion methods (MKL), and the embedding of each descriptor independently (Diffusion Maps (DM)). We also evaluated its relevance over linear alignment based on PLS, which we used previously in (Di Folco et al, 2020).…”

“…In this section, we compared the MML results to the ones obtained with PLS, a linear approach used in our previous work (Di Folco et al, 2020), which involves computing the cross-covariance between the two descriptors. A similarity transform was applied for shape normalization to remain consistent with what was used for MML (a Procrustes alignment was used in (Di Folco et al, 2020)). Figure 10a reveals that PLS provides slightly different average shape and deformation from those obtained with MML, with differences comparable to those noted for DM and MKL in Fig.…”