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A Mechanical Model for CCK-Induced Acalculous Gallbladder Pain

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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 emptying 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%.

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Acknowledgment

The project was supported by EPSRC through grant EP/G015651.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

    W. G. Li, X. Y. Luo, N. A. Hill & R. W. Ogden

  2. Academic Surgical Unit, Royal Hallamshire Hospital, Sheffield, S10 2JF, UK

    A. Smythe, A. Majeed & N. Bird

Authors
  1. W. G. Li
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  2. X. Y. Luo
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  4. R. W. Ogden
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Correspondence to X. Y. Luo.

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Associate Editor Peter E. McHugh oversaw the review of this article.

Appendix: Grid Independence Test for the Adina Numerical Model

Appendix: Grid Independence Test for the Adina Numerical Model

Element

Mesh size (mm) (length of an edge)

Peak σ xx (Pa)

Peak σ yy (Pa)

Peak σ zz (Pa)

4-node quad

0.75

9607

13,179

13,178

1.0 (the chosen grid)

9607

13,175

13,172

1.25

9602

13,168

13,166

8-node quad

1.0

9612

13,192

13,189

Triangle

1.0

9609

13,186

13,185

Note that the effect of choosing different types of element is equivalent to choosing one type of element and different grid points. The test shows that the peak stress components do not change significantly when using different grids, therefore the 4-node quadrilateral element with 1-mm mesh size was chosen for the final results.

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Li, W.G., Luo, X.Y., Hill, N.A. et al. A Mechanical Model for CCK-Induced Acalculous Gallbladder Pain. Ann Biomed Eng 39, 786–800 (2011). https://doi.org/10.1007/s10439-010-0205-1

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  • DOI: https://doi.org/10.1007/s10439-010-0205-1

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