Reproducibility of Laplacian Wall Thickness Measurements of the Gallbladder with Varying CT Slice Thickness M. N. Prasad & M. S. Brown & C. Ni & D. Margolis & M. Douek & S. Raman & D. Lu & J. G. Goldin & S. K. Warfield Received: 12 January 2008 / Revised: 27 February 2008 / Accepted: 4 April 2008 # 2008 Springer Science + Business Media, LLC. Manufactured in The United States Abstract In measuring changes of gallbladder wall thick- ness using CT, robustness to differences in acquisition protocols including slice thickness can be important. We have developed an automated technique based on Laplace’ s equation to measure the gallbladder wall thickness using computer tomography (CT). The purpose of this work is to investigate the usefulness of the Laplacian technique in obtaining gallbladder wall thickness measurements that are reproducible with variations in CT slice thickness. This study included 2D (2D) and 3D (3D) wall thickness measurements using Laplace’ s equation. Ten subjects who had 5 mm (thick) and 2.5 mm (thin) reconstruction (from a single set of raw data) through the abdomen were randomly selected from a research database. Their volumetric CT images were acquired using a multidetector GE MEDICAL SYSTEMS– LightSpeed 16 scanner at 120 KVP, ~250 mAs, with standard filter reconstruction algorithm and manually segmented on all CT cross sections by a radiologist. The inner and outer boundaries of the gallbladder wall were obtained from the segmentation. The thickness of the wall was quantified by computing the distance between the boundaries for each scan and 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. The vector fields represent tangent vectors along field lines connecting both boundaries. The Laplacian technique was compared with the conventional Euclidean distance transformation (EDT) technique using coefficient of varia- tion. EDT results in an Euclidean distance mapping between the two extracted surfaces. Both techniques were compared in 2D and 3D. For the 2D and 3D wall thickness measure- ments, a mean difference of 0.35 and 0.25 mm between thin and thick reconstruction was found respectively using Laplace’ s equation. EDT resulted in a higher mean difference for both 2D and 3D. In addition, a significant difference in thickness between the Laplacian technique and EDT tech- niques (p <0.001) were obtained. The Laplacian measure- ment of gallbladder wall showed significantly lower variation compared to EDT on different CT slice thickness for both 2D and 3D techniques. Hence, proving to be an important technique for obtaining reproducible wall thickness mea- surements of the gallbladder using CT. Keywords CT . Ultrasound . Laplace’ s equation . Thickness . Reproducibility J Sign Process Syst DOI 10.1007/s11265-008-0199-1 M. N. Prasad (*) : M. S. Brown : C. Ni : D. Margolis : M. Douek : S. Raman : D. Lu : J. G. Goldin Department of Radiological Sciences, David Geffen School of Medicine, University of California, Los Angeles, CA, USA e-mail: mithunp@cse.unsw.edu.au M. S. Brown e-mail: MBrown@mednet.ucla.edu C. Ni e-mail: CNi@mednet.ucla.edu D. Margolis e-mail: DMargolis@mednet.ucla.edu M. Douek e-mail: MDouek@mednet.ucla.edu S. Raman e-mail: SRaman@mednet.ucla.edu D. Lu e-mail: DLu@mednet.ucla.edu J. G. Goldin e-mail: JGoldin@mednet.ucla.edu S. K. Warfield Department of Radiology, Children’ s Hospital Boston, 300 Longwood Avenue, Boston, MA, USA e-mail: simon.warfield@childrens.harvard.edu