An Inverse Eikonal Method for Identifying Ventricular Activation Sequences from Epicardial Activation Maps

A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence - the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls - from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity - a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient- specific parameterization of activation models.

Semi-automatic 3D morphological reconstruction of neurons with densely branching morphology: Application to retinal AII amacrine cells imaged with multi-photon excitation microscopy

BACKGROUND

Accurate reconstruction of the morphology of single neurons is important for morphometric studies and for developing compartmental models. However, manual morphological reconstruction can be extremely time-consuming and error-prone and algorithms for automatic reconstruction can be challenged when applied to neurons with a high density of extensively branching processes.

NEW METHOD

We present a procedure for semi-automatic reconstruction specifically adapted for densely branching neurons such as the AII amacrine cell found in mammalian retinas. We used whole-cell recording to fill AII amacrine cells in rat retinal slices with fluorescent dyes and acquired digital image stacks with multi-photon excitation microscopy. Our reconstruction algorithm combines elements of existing procedures, with segmentation based on adaptive thresholding and reconstruction based on a minimal spanning tree. We improved this workflow with an algorithm that reconnects neuron segments that are disconnected after adaptive thresholding, using paths extracted from the image stacks with the Fast Marching method.

RESULTS

By reducing the likelihood that disconnected segments were incorrectly connected to neighboring segments, our procedure generated excellent morphological reconstructions of AII amacrine cells.

COMPARISON WITH EXISTING METHODS

Reconstructing an AII amacrine cell required about 2h computing time, compared to 2-4days for manual reconstruction. To evaluate the performance of our method relative to manual reconstruction, we performed detailed analysis using a measure of tree structure similarity (DIADEM score), the degree of projection area overlap (Dice coefficient), and branch statistics.

CONCLUSIONS

We expect our procedure to be generally useful for morphological reconstruction of neurons filled with fluorescent dyes.