Piet Claus

Maarten Volkaerts, Marie Cloet, Hans Dierckx et al.

We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell contraction in the heart wall and can support cardiac arrhythmia treatment. We consider an illustrative case motivated by a cardiac arrhythmia, namely, by intra-atrial reentrant tachycardia. We estimate a low-dimensional geometrical parameter that describes the boundary of an electrically non-conducting region in the heart tissue from synthetic electrical measurements outside of the tissue. Instead of relying on a deterministic fit for this region, we estimate a posterior distribution on the geometrical parameter using Bayesian inference that captures the uncertainty due to measurement errors. We propose a likelihood based on a set of quantities that characterize the data for improved accuracy. To efficiently approximate the posterior distribution, we propose a compressed likelihood function and an adapted Metropolis-Hastings (MH) algorithm. We obtain an algorithm that strongly decreases the number of samples by using an adaptive proposal strategy. Our algorithm also gives attention to the impact of discretization errors on inference outcomes, as these introduce artificial discontinuities in the posterior if not properly addressed. We account for discretization errors in the likelihood and in the accept-reject step of our adapted MH algorithm to improve the robustness of our estimates and to further increase the sampling efficiency. All of these elements combined give us a method that efficiently estimates the non-conducting parameters with uncertainty. We perform several experiments with different amounts of measurement noise and illustrate how this translates into the posterior distributions.

Sofie Tilborghs, Tom Dresselaers, Piet Claus et al.

Semantic segmentation using convolutional neural networks (CNNs) is the state-of-the-art for many medical segmentation tasks including left ventricle (LV) segmentation in cardiac MR images. However, a drawback is that these CNNs lack explicit shape constraints, occasionally resulting in unrealistic segmentations. In this paper, we perform LV and myocardial segmentation by regression of pose and shape parameters derived from a statistical shape model. The integrated shape model regularizes predicted segmentations and guarantees realistic shapes. Furthermore, in contrast to semantic segmentation, it allows direct calculation of regional measures such as myocardial thickness. We enforce robustness of shape and pose prediction by simultaneously constructing a segmentation distance map during training. We evaluated the proposed method in a fivefold cross validation on a in-house clinical dataset with 75 subjects containing a total of 1539 delineated short-axis slices covering LV from apex to base, and achieved a correlation of 99% for LV area, 94% for myocardial area, 98% for LV dimensions and 88% for regional wall thicknesses. The method was additionally validated on the LVQuan18 and LVQuan19 public datasets and achieved state-of-the-art results.