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Research Papers

# Determination of Homeostatic Elastic Moduli in Two Layers of the Esophagus

[+] Author and Article Information
Hans Gregersen

Centre of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital,  Aarhus University HospitalThe Science and Innovation Center, Søndre Skovvej 15, DK-9000 Aalborg, Denmark; Institute of Health Technology, Aalborg University, DK-9100 Aalborg, Denmark

Donghua Liao1

Centre of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital,  Aarhus University HospitalThe Science and Innovation Center, Søndre Skovvej 15, DK-9000 Aalborg, Denmark; Institute of Health Technology, Aalborg University, DK-9100 Aalborg, Denmarkdliao@miba.auc.dk

Yuan Cheng Fung

Biomechanics Lab, Institute of Biomedical Engineering, UC San Diego, 9500 Gilman Drive, La Jolla, CA 92093

1

Corresponding author.

J Biomech Eng 130(1), 011005 (Feb 05, 2008) (8 pages) doi:10.1115/1.2838031 History: Received August 15, 2006; Revised June 11, 2007; Published February 05, 2008

## Abstract

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of $59.4±13.2deg$). The neutral axis was located $27%±1.9%$away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.

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## Figures

Figure 1

Schematic diagram of a cross section of an esophageal ring at the no-load state

Figure 2

Schematic of the experimental design: (a) inflation test with internal pressure Pi, (b) uniaxial stretch test with longitudinal stretching (c) circumferential bending test. A thin metal plate (length of 8mm and height of 0.2mm) was used to impose small forces on the midportion of the sample. A similar plate placed on the other side of the sample was used for measuring the force and (d) axial bending test. The esophageal sample was mounted between two connectors and stretched to the in vivo length. Internal pressure was not applied. A thin nylon surgical suture was wound around the sample. These four types of in vitro experiments can be used to determine the six incremental elastic moduli of the two layers of esophagus at a homeostatic state. Counting an experiment of Type A with variable longitudinal stretch and another experiment of Type B with variable internal pressure as two additional experiments, we have a total of six experiments for the six unknowns.

Figure 3

Details of the circumferential bending experiment. The local rectangular Cartesian coordinates θ, x, z with origin on the neutral surface. The forces, pressures, moments, and deformations were involved in a circumferential bending test of the esophagus at homeostatic conditions: (a) esophagus with thin metal plates, (b) cross section of the esophagus, and (c) half of a cross section on the centerline of the metal plate with moments and forces indicated.

Figure 4

Experimental data illustrated from (a) the inflation, (b) axial stretch, (c) circumferential bending, and (d) the axial bending test. For the inflation test, the outer diameter and longitudinal force as functions of pressure are given at the homeostatic state axial stretch ratio (175%). For the axial stretch test, the longitudinal force and the outer diameter as functions of the longitudinal stretch ratio are given at zero transmural pressure: the stretch ratios were referenced to the length at the in vitro state. For the circumferential bending test, the relationship between the segment outer diameter at the θ=π∕2 location and the forces acting on the metal plates are given. For the axial bending test, the suture force and the outer diameter relationship were obtained.

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