Three-Dimensional Atrial Wall Thickness Measurement Algorithm From a Segmented Atrial Wall Using a Partial Differential Equation

Despite advancements in high-precision segmentation technology for computed tomographic angiography (CTA)-based cardiac wall segmentation, the accurate detection of the endocardial (Endo) and epicardial (Epi) boundaries remains a prerequisite for automated measurements of the cardiac wall thickness (WT). We proposed a novel algorithm for automated three-dimensional (3D) atrial WT (AWT) measurements, including an automatic Endo-Epi boundary detection. We detected the boundaries that were topologically indistinguishable due to an open geometry at the anatomical boundaries using the combined Convex hull and Poisson solver methods. The Laplace equation for the WT measurement was solved by a partial differential equation combining the two detected boundaries of the myocardial wall. We verified the robustness of our algorithm in mask images of the atrial wall that were separated from the CTA images of 20 patients and a phantom model. The accuracy of the automatically detected Endo-Epi boundaries was acceptable as compared to that manually extracted from the phantom model (Dice coefficient = 0.979). The 3D AWTs calculated by the novel automated method from the CTA images obtained from 20 patients with atrial fibrillation had <10% error as compared to the conventional manual AWT measurement method for comparing the regional WT in all locations except the left antral area. The proposed algorithm's AWT detection time was 27.15 +/- 6.99 s per patient, which was 1/40 that of the conventional method. Consequently, our results showed that the proposed automatic 3D AWT measurement algorithm had the potential to significantly improve the efficiency of calculating the AWT while maintaining the existing level of accuracy.

Automated summary

This study proposes a novel algorithm for automated three-dimensional cardiac wall thickness measurement, including automated boundary detection and solving geometric problems. The results of the verification experiments demonstrate the potential of the algorithm in terms of measurement accuracy and efficiency.