Abstract
In measuring changes of gallbladder wall thickness 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 variation. 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 measurements, 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 techniques (p < 0.001) were obtained. The Laplacian measurement 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 measurements of the gallbladder using CT.
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References
Alterman, D. D., & Hochsztein, J. G. (1996). Computed tomography in acute cholecystitis. Emergency Radiology, 3, 25–29.
Bennett, G. L., & Rusinek, H. (2002). CT Findings in acute gangrenous cholecystitis. AJR, American Journal of Roentgenology, 178, 275–281.
Bland, J. M., & Altman, D. G. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, 1(8476), 307–310 (Feb 8).
Cheng, S. M., Ng, S. P., & Shih, S. L. (2004). Hyperdense gallbladder wall. Sign: An overlooked sign of acute cholecystitis on unenhanced CT. Clinical Imaging, 28(2), 128–131.
Colbert, J. A., Gordon, A., Roxelin, R., Silva, S., Silva, J., Rocha, C., et al. (2007). Ultrasound measurement of gallbladder wall thickening as a diagnostic test and prognostic indicator for severe dengue in pediatric patients. Pediatric Infectious Disease Journal, 26(9), 850–852.
Danielson, P. E. (1980). Euclidean distance mapping. Computer Graphics and Image Processing, 14, 227–248.
DuChateau, P., & Zachmann, D. (1989). Applied partial differential equations. New York: Harper and Row.
Engel, J. M., Deitch, E. A., & Sikkema, W. (1980). Gallbladder wall thickness: Sonographic accuracy and relation to disease. AJR American Journal of Roentgenology, 134(5), 907–909 (May).
Fidler, J., Paulson, E. K., & Layfield, L. (1996). CT evaluation of acute cholecystitis: Findings and usefulness in diagnosis. AJR American Journal of Roentgenology, 166(55), 1085–1088.
Finberg, H. J., & Birnholz, J. C. (1979). Ultrasound evaluation of the gallbladder wall. Radiology, 133, 695–699.
Gore, R. M., Yaghmai, V., Newmark, G. M., Berlin, J. W., & Miller, F. H. (2002). Imaging of benign and malignant disease of the gallbladder. Radiologic Clinics of North America, 40, 1307–1323.
Haidar, H., Egorova, S., & Soul, J. (2005). New numerical solution of the Laplace equation for tissue thickness measurement in 3D MRI. Journal of Mathematical Modelling and Algorithms, 4(1), 83–97 (15 March).
Handler, S. J. (1979). Ultrasound of gallbladder wall thickening and its relation to cholecystitis. AJR American Journal of Roentgenology, 132(4), 581–585 (Apr).
Jaume, S., Ferrant, M., Macq, B., Hoyte, L., Fielding, J. R., Schreyer, A., et al. (2003). Tumor detection in the bladder wall with a measurement of abnormal thickness in CT scans. IEEE Transaction on Biomedical Engineering, 50(3), 383–390.
Jones, S. E., Buchbinder, B. R., & Aharon, I. (2000). 3D mapping of cortical thickness using Laplace’s equation. Human Brain Mapping, 11, 12–32.
Laird, N. M., & Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963–974.
Marchel, G., Crolla, D., Baert, A. L., Fevery, J., & Kerremans, A. (1978). Gallbladder wall thickening: a new sign of gallbladder disease visualized by gray scale cholecystosonography. JCU, 6, 117–179.
Paulson, E. K. (2000). Acute cholecystitis: CT findings. Seminars in Ultrasound, CT, and MR, 21, 56–63.
Prasad, M., Brown, M. S., Ni, C., Margolis, D., Douek, M., Raman, S., et al. (2008) Three-dimensional mapping of gallbladder wall thickness on CT using Laplace’s equation. Academic Radiology (in press).
Pu, Y., Yamamoto, F., Igimi, H., Shilpakar, S. K., Kojima, T., Yamamoto, S., et al. (1994). comparative study usefulness of magnetic resonance imaging in the diagnosis of acute cholecystitis. Journal of Gastroenterology, 29(2), 192–198.
Rumack, C. M., Wilson, S. R., & Charboneau, J. W. (1998). Diagnostic ultrasound (pp. 175–2002nd ed.). St. Louis: Mosby.
Saverymuttu, S. H., Grammatopoulos, A., Meanock, C. I., Maxwell, J. D., & Joseph, A. E. (1990). Gallbladder wall thickening (congestive cholecystopathy) in chronic liver disease: A sign of portal hypertension. British Journal of Radiology, 63(756), 922–925 (Dec).
Wilbur, A. C., Gyi, B., & Renigres, S. A. (1988). High-field MRI of primary gallbladder carcinoma. Gastrointestinal Radiology, 170, 1491–1495.
William, S. A., Press, H., Flannery, B. P., & Vetterling, W. T. (1993). Numerical recipes in C: The art of scientific computing. Cambridge: Cambridge University Press.
Wu, K. L., Changchien, C. S., Kuo, C. H., et al. (2004). Early abdominal sonographic findings in patients with dengue fever. Journal of Clinical Ultrasound, 32(8), 386–388 (Oct).
Zeman, R. K., & Garra, B. S. (1991). Gallbladder imaging: The state of the art. Gastroenterology Clinics of North America, 20, 127–156.
Zissin, R., Osadchy, A., Shapiro-Feinberg, M., & Gayer, G. (2003). CT of a thickened-wall gall bladder. British Journal of Radiology, 76(902), 137–143 (February 1).
Acknowledgement
This investigation was supported in part by NIH grants R03 CA126466, R01 RR021885, R01 GM074068 and R01 EB008015.
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Prasad, M.N., Brown, M.S., Ni, C. et al. Reproducibility of Laplacian Wall Thickness Measurements of the Gallbladder with Varying CT Slice Thickness. J Sign Process Syst Sign Image Video Technol 55, 67–75 (2009). https://doi.org/10.1007/s11265-008-0199-1
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DOI: https://doi.org/10.1007/s11265-008-0199-1