Three-dimensional Mapping of Gallbladder Wall Thickness on Computed Tomography Using Laplace's Equation

Traditionally, maximum gallbladder wall thickness is measured at a single point on ultrasonography. The purpose of this work was to develop an automated technique to measure the thickness of the gallbladder wall over the entire gallbladder surface using computer tomography (CT).Subjects who had (5-mm) thick and thin (2.5-mm) reconstruction through the abdomen were selected from a research database. Their volumetric computed tomographic images were acquired using a multidetector GE Medical Systems LightSpeed 16 scanner at 120 kVp, approximately 250 mAs, with standard filter reconstruction algorithm and segmented in three dimensions. Two segmentation boundaries were obtained, an inner and an outer boundary of the gallbladder wall. The thickness of the wall was quantified by computing the distance between the boundaries over the entire volume using Laplace's equation from mathematical physics. The distance between the surfaces is found by computing normalized gradients that form a vector field, representing tangent vectors along field lines connecting both boundaries. The Laplacian technique was compared with the well-known Euclidean distance transformation (EDT) technique that provides a three-dimensional Euclidean distance mapping between the two extracted surfaces.The technique was tested on 10 subjects who had thin- and thick-section computed tomographic datasets reconstructed from a single scan. The mean thickness for the thick- and thin-section CT using Laplace was 3.18 and 2.93 mm, respectively. The smooth transition between surfaces resulting from the Laplace technique resulted in a coefficient of variation that was less than 1% compared to EDT.EDT technique is very sensitive to imperfect segmentations, resulting in higher variation compared to the Laplacian technique. The smooth transition between surfaces makes the Laplacian technique more robust compared to EDT for the measurement of CT gallbladder thickness.