Research Papers

A Quasi-Nonlinear Analysis of the Anisotropic Behaviour of Human Gallbladder Wall

[+] Author and Article Information
W. G. Li, N. A. Hill

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

X. Y. Luo1

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

R. W. Ogden

 School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK; School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, UK

A. Smythe, A. W. Majeed, N. Bird

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


Corresponding author.

J Biomech Eng 134(10), 101009 (Oct 05, 2012) (9 pages) doi:10.1115/1.4007633 History: Received May 01, 2012; Revised September 14, 2012; Posted September 25, 2012; Published October 05, 2012; Online October 05, 2012

Estimation of biomechanical parameters of soft tissues from noninvasive measurements has clinical significance in patient-specific modeling and disease diagnosis. In this work, we present a quasi-nonlinear method that is used to estimate the elastic moduli of the human gallbladder wall. A forward approach based on a transversely isotropic membrane material model is used, and an inverse iteration is carried out to determine the elastic moduli in the circumferential and longitudinal directions between two successive ultrasound images of gallbladder. The results demonstrate that the human gallbladder behaves in an anisotropic manner, and constitutive models need to incorporate this. The estimated moduli are also nonlinear and patient dependent. Importantly, the peak stress predicted here differs from the earlier estimate from linear membrane theory. As the peak stress inside the gallbladder wall has been found to strongly correlate with acalculous gallbladder pain, reliable mechanical modeling for gallbladder tissue is crucial if this information is to be used in clinical diagnosis.

Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 2

A typical GB mesh and a 4-node membrane element showing the material local Cartesian system (a), (b), (c). ϕ, θ, and n are the spherical coordinates of GB model with the origin O (see Fig. 1). In the simulations, we choose these two coordinate systems to be the same. The boundary conditions are applied at the two apexes A1 and A2, see text for details.

Grahic Jump Location
Figure 1

(a) The pressure-volume (p–V) diagram, and (b) the ellipsoid model of GB

Grahic Jump Location
Figure 8

Comparison of the peak displacements along the three axes of the 6 GB models between the images and computed results. The solid lines are the computed values, and the symbols are from images. Note the computed ΔDi (i = 1,2) agree automatically with ΔDiexp for all samples except GB-D.

Grahic Jump Location
Figure 10

In vitro measurement of GB compliance for four different samples, during and post CCK applications, with a mean value of C = 2.73 mL/mmHg (dotted line)

Grahic Jump Location
Figure 3

Illustration of the incremental approach, with the computations starting from the initial configuration B at the end of emptying, and proceeding to the beginning of the emptying. (a) Incremental pressure loading and volume, (b) incremental stress and strain, and (c) sketch of the computational procedure. V and Vexp are the estimated and measured GB volumes, respectively.

Grahic Jump Location
Figure 4

Flow chart for the inverse estimation of the elastic moduli, where ΔDi and ΔDiexp(i = 1,2,3), are the estimated and measured maximal displacements along the three axes of ellipsoid, respectively. Note only V and ΔD3 are used in the error control.

Grahic Jump Location
Figure 5

The ultrasound image of GB-E (see Table 2) at the beginning of the emptying, in which the three axes D1 , D2 , and D3 are shown. These are used to provide the comparison for the inverse approach, and the computed ellipsoid has the same axes within 0.1% error tolerance in D3 and the volume.

Grahic Jump Location
Figure 6

Values of elastic moduli in the circumferential and longitudinal directions and their ratios for the six GB samples: (a) Eϕ, (b) Eθ, and (c) Eϕ/Eθ

Grahic Jump Location
Figure 7

Values of the peak principal stresses σ1, σ2 versus corresponding cumulative principal strains ɛ1, ɛ2 of the six GB models: (a) σ1 – ɛ1, (b) σ2 – ɛ2. Note that GB-C, GB-D, and GB-E have higher stress curves than the others, especially in the first principal direction.

Grahic Jump Location
Figure 9

Comparison of the stress component distributions between the linear membrane solution of the linear membrane model (Li [7]) and the present approach for GB-F at the beginning of emptying, (a)–(c) linear membrane, (d )–(f ) present results



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In