A Mechanical Model for CCK-Induced Acalculous Gallbladder Pain W. G. LI, 1 X. Y. LUO, 1 N. A. HILL, 1 R. W. OGDEN, 1 A. SMYTHE, 2 A. MAJEED, 2 and N. BIRD 2 1 School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK; and 2 Academic Surgical Unit, Royal Hallamshire Hospital, Sheffield S10 2JF, UK (Received 12 August 2010; accepted 8 November 2010) Associate Editor Peter E. McHugh oversaw the review of this article. Abstract—This study investigates the potential correlation between acalculous biliary pain and mechanical stress during the bile-emptying phase. This study is built on the previously developed mathematical model used to estimate stress in the gallbladder wall during emptying [Li, W. G., X. Y. Luo, et al. Comput. Math. Methods Med. 9(1):27–45, 2008]. Although the total stress was correctly predicted using the previous model, the contribution from patient-specific active stress induced by the cholecystokinin (CCK) test was overlooked. In this article, we evaluate both the active and passive components of pressure in a gallbladder, which undergoes isotonic refilling, isometric contraction and emptying during the infusion of CCK. The pressure is estimated from in vivo ultrasonographical scan measurements of gallbladder emp- tying during CCK tests, assuming that the gallbladder is a thin ellipsoidal membrane. The passive stress is caused by the volume and shape changes during refilling at the gallbladder basal pressure, whereas the active stress arises from the pressure rise during the isometric gallbladder contraction after the CCK infusion. The effect on the stress estimates of the gallbladder to the liver is evaluated to be small by comparing numerical simulations of a gallbladder model with and without a rigid ‘flat top’ boundary. The model was applied to 51 subjects, and the peak total stress was found to have a strong correlation with the pain stimulated by CCK, as measured by the patient pain score questionnaires. Consistent with our previous study for a smaller sample, it is found that the success rate in predicting of CCK-induced pain is over 75%. Keywords—Gallbladder, Active stress, Passive stress, Acal- culous biliary pain, Emptying, Refilling, Isometric contrac- tion, Isotonic refilling, CCK. INTRODUCTION The human gallbladder is a small pear-shaped organ on the underside of the liver that is used to store bile. Bile is made in the liver and is stored in the gallbladder until it is needed to help the digestion of fat. Gall- bladder disease is a common condition that affects both women and men. The symptoms vary widely from discomfort to severe pain which mainly begins after food intake. In severe cases, the patient can suffer from jaundice, nausea and fever. When this happens, gallbladder removal (cholestectomy) via keyhole sur- gery is usually recommended. The most common cause of gallbladder disease is the presence of gallstones. However, it is common to have stones in the gallbladder that cause no symptoms. On the other hand, a proportion of people do suffer from severe acalculous (i.e. without gallstones) biliary pain. The decision to surgically remove the gallbladder is made when patients have symptoms (pain), not if they have gallstones. The burden of gallbladder disease has become epi- demic worldwide in recent years. It is the most com- mon abdominal reason for admission to hospital in developed countries and accounts for an important part of healthcare expenditure. The disease in the U.S. afflicts some 6.3 million men and 14.2 million women aged 20–74 years, making it the most costly digestive disorder at an estimated $6.5 billion annually. The extent of gallbladder disease in Europe is similar to the U.S., with a median prevalence in large population surveys, ranging from 5.9 to 21.9%. 44 Around 5.5 million people have gallstones in the United Kingdom, and over 50,000 cholecystectomies are per- formed each year. 4 Gallbladder attacks are extremely painful and can cause life-threatening infections. Most people who have a cholecystectomy have no problems afterwards. Unfortunately, a small percentage of peo- ple (10–15%) have post-cholecystectomy complica- tions. About 20% who have had their gallbladder removed had diarrhoea afterwards. Of a major concern is that not all patients benefit from the cholestectomy, and the symptoms continue even though the gallbladder has been removed. It has Address correspondence to X. Y. Luo, School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK. Electronic mail: x.y.luo@maths.gla.ac.uk Annals of Biomedical Engineering (Ó 2010) DOI: 10.1007/s10439-010-0205-1 Ó 2010 Biomedical Engineering Society