A Pointwise Method for Identifying Biomechanical Heterogeneity of the Human Gallbladder

Abstract

Identifying the heterogeneous biomechanical property of human gallbladder (GB) walls from non-invasive measurements can have clinical significance in patient-specific modeling and acalculous biliary pain diagnosis. In this article, a pointwise method was proposed to measure the heterogeneity of ten samples of human GB during refilling. Three different points, two on the equator of GB body 90° apart and one on the apex of GB fundus, were chosen to represent the typical regions of interest. The stretches at these points were estimated from ultrasound images of the GB during the bile emptying phase based on an analytical model. The model was validated against the experimental data of a lamb GB. The material parameters at the different points were determined inversely by making use of a structure-based anisotropic constitutive model. This anisotropic model yielded much better accuracy when compared to a number of phenomenologically-based constitutive laws, as demonstrated by its significantly reduced least-square errors in stress curve fitting. The results confirmed that the human GB wall material was heterogeneous, particularly toward the apex region. Our study also suggested that non-uniform wall thickness of the GB was important in determining the material parameters, in particular, on the parameters associated with the properties of the matrix and the longitudinal fibers-the difference could be as large as 20-30% compared to that of the uniform thickness model.

Keywords: anisotropic property; constitutive law; gallbladder; heterogeneity; inverse problem; optimization; strain energy function.

Figure 1

A typical ultrasonic image of human gallbladder during the emptying phase.

Figure 2

The imaged-based ellipsoid model for GB during the refilling phase, (A) ellipsoid model with three control points on the surface, (B) the stretch components estimated from the ellipsoid model for GB sample No.1 listed in Table 1.

Figure 3

The GB wall is composed of matrix and two families of fibers, the thirteen material parameters are location dependent, changing from points 1–3.

Figure 4

A GB wall thickness profile, showing the thickest wall at the GB apex and thinnest wall near the neck, adopted from Su (2005) with permission.

Figure 5

A comparison of errors in the least-squares stress curve fitting between the present constitutive law and existing laws proposed by Fung, Choi-Vito, and Zhou-Fung, respectively.

Figure 6

Comparison of the modeled (lines) and estimated (symbols) circumferential and longitudinal stresses with the image-based ellipsoid membrane mechanic model at points 1, 2, 3, for GB 3 (A–C), and GB 39 (D–F).

Figure 7

Effect of GB wall thickness at the apex on the error in stress, the thickness at the apex is varied to be 2.25, 2.5, 3.0, 5.0, and 7.0 mm, respectively, while the thickness at the other two points 1 and 2 is kept to be 2.5 mm.

Figure 8

Comparison of the peak tension from the ellipsoid model with the in vitro experimental tension of a lamb GB (Genovese et al., 2014) at the internal pressure of 20 and 50 mmHg, respectively, two plots in the top row are from Genovese et al. (2014), with permission.