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TECHNICAL PAPERS: Soft Tissue

# Viscoelasticity of Esophageal Tissue and Application of a QLV Model

[+] Author and Article Information
W. Yang, T. C. Fung

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore

K. S. Chian

School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

C. K. Chong

School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore

J Biomech Eng 128(6), 909-916 (May 11, 2006) (8 pages) doi:10.1115/1.2372473 History: Received December 03, 2005; Revised May 11, 2006

## Abstract

The time-dependent mechanical properties of the porcine esophagus were investigated experimentally and theoretically. It was hypothesized that the viscoelasticity was quasilinear, i.e., the time and strain effects were independent. In order to verify the separability of time and strain effects, the stress-relaxation test was conducted at various strains and the data were fitted with the Fung’s quasilinear viscoelastic (QLV) model. By using the material parameters obtained from the stress relaxation test, the cyclic peak stress and hysteresis were predicted. Results showed that the stress relaxed by 20–30% of the peak stress within the first $10s$ and stabilized at $∼50%$ at the time of $300s$. The relative stress relaxation $R2$ (i.e., the difference of stress at a particular time to the final equilibrium stress normalized by the total difference of the peak and final stress) was not different significantly for various strains. It was also found that, by using the stress-time data during both the ramp and relaxation phases, the correlation between parameters was substantially reduced. The model could also predict the cyclic peak stress and hysteresis except for the underestimate of valley stress. We conclude that the QLV model could be used as the material characterization of the esophageal tissue.

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## Figures

Figure 3

Illustration of the test protocol for the stress relaxation with precondition

Figure 4

Illustration of test protocol with precondition, stress relaxation and cyclic test. Five minutes were given for the tissue to get equilibrium prior to each test.

Figure 5

Normalized stress (a)R1 and (b)R2 as functions of time (t−tpi) at the strains of 1, 1.2, and 1.4 (mucosa-upper-1231-cir.)

Figure 6

Plot of stress-time curve during the “before” stress relaxation, preconditioning, and “after” stress relaxation

Figure 7

A typical curve fit to experimental data at the strain of 0.4 with the fitting error of 2% (muscle-middle-0308-cir.)

Figure 8

Measured stress and QLV model prediction using parameters estimated from the stress relaxation test (muscle-middle-0308-cir.)

Figure 9

Normalized peak stress predicted by the QLV model

Figure 10

Normalized hysteresis predicted by the QLV model (dotted line) and calculated from the cyclic test data (solid line)

Figure 11

Sensitivity coefficient Civ defined in Eq. 16(a) for all parameters and (b) an enlarged view of Civ for τ1 and τ2

Figure 1

(a) Photograph of the entire esophagus (b) three parts cut from the upper, middle, and lower regions, and (c) muscle and mucosal layer after separation

Figure 2

Illustration of the test protocol for the incremental stress relaxation without precondition

## Errata

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