The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.

In Part 1 of this paper, the sampling grid points for the differential quadrature method to give unconditionally stable higher‐order accurate time step integration algorithms are proposed to solve first‐order initial value problems. In this paper, the differential quadrature method is extended to solve second‐order initial value problems. The conventional approaches to impose the given initial conditions are discussed. A new approach to impose the given initial conditions is then presented. It is found that the proposed approach could generate unconditionally stable higher‐order accurate time step integration algorithms for second‐order equations directly. Furthermore, the procedure can be generalized to construct unconditionally stable higher‐order accurate time step integration algorithms for third‐ and higher‐order initial value problems without any difficulties. The computational procedures for multi‐degree‐of‐freedom systems and non‐linear problems are also discussed. As demonstrated by the numerical examples, the differential quadrature method using the proposed sampling grid points and the proposed method to impose the given initial conditions is found to be more efficient than the conventional differential quadrature method in solving initial value problems. Copyright © 2001 John Wiley & Sons, Ltd.

The esophagus, like other soft tissues, exhibits nonlinear and anisotropic mechanical properties. As a composite structure, the properties of the outer muscle and inner mucosal layer are different. It is expected that the complex mechanical properties will induce nonhomogeneous stress distributions in the wall and nonuniform tissue remodeling. Both are important factors which influence the function of mechanosensitive receptor located in various layers of the wall. Hence, the characterization of the mechanical properties is essential to understand the neuromuscular motion of the esophagus. In this study, the uniaxial tensile tests were conducted along two mutually orthogonal directions of porcine esophageal tissue to identify the directional (circumferential and axial), regional (abdominal, thoracic, and cervical), and layer (muscle and mucosa) variations of the mechanical properties. A structure-based constitutive model, which took the architectures of the tissue's microstructures into account, was applied to describe the mechanical behavior of the esophagus. Results showed that the constitutive model successfully described the mechanical behavior and provided robust estimates of the material parameters. In conclusion, the model was demonstrated to be a good descriptor of the mechanical properties of the esophagus and it was able to facilitate the directional, layer, and regional comparisons of the mechanical properties in terms of the associated material parameters.

In this paper, unconditionally stable higher-order accurate time-step integration algorithms with controllable numerical dissipation are presented. The algorithms are based on the Newmark method with complex time steps. The ultimate spectral radius ( ), the sub-step locations ( H ) and the weighting factors ( H ) are the algorithmic parameters. For an algorithm that is (2n!1)th order accurate, the sub-step locations which may be complex, are shown to be the roots of an nth degree polynomial. The polynomial is given explicitly in terms of n and . The weighting factors are then obtained by solving a system of n simultaneous equations. It is further shown that the order of accuracy is increased by one for the non-dissipative algorithms with "1. The stability properties of the present algorithms are studied. It is shown that if the ultimate spectral radius is set between !1 and 1, the eigenvalues of the numerical amplification matrix are complex with magnitude less than or equal to unity. The algorithms are therefore unconditionally C-stable. When the ultimate spectral radius is set to 0 or 1, the algorithms are found to be equivalent to the first sub-diagonal and diagonal Pade´approximations, respectively. The present algorithms are more general as the numerical dissipation is controllable and are very suitable for parallel computers. The accuracy of the excitation responses is found to be enhanced by the present complex-time-step procedure. To maintain high-order accuracy, the excitation may need some modifications.

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