Presented at NACOB 98: North American Congress on Biomechanics Canadian Society for Biomechanics - American Society of Biomechanics University of Waterloo Waterloo, Ontario, Canada August 14-18, 1998

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MATERIAL CHARACTERIZATION AND MATHEMATICAL MODELLING OF THE PIG KIDNEY IN RELATION WITH BIOMECHANICAL ANALYSIS OF RENAL TRAUMA

Mehdi Farshad ¹ , Michel Barbezat ¹ , Franz Schmidlin ² , Luc Bidaut ² , Peter Niederer ³ , Pierre Graber ^2
1 EMPA, Dübendorf, Switzerland
² University Hospital, Geneva, Switzerland
³ ETH Zürich, Switzerland

INTRODUCTION

The objective of this study, which is part of an on-going work, was an investigation of the material properties of the fresh pig kidney, the parametric characterisation of the elastic and inelastic material behaviour and the numerical Finite Element simulation of the entire kidney. Material testing included density measurements, uniaxial as well as three-dimensional compression tests, tensile tests, and shear tests on tissues taken from the fresh pig kidney.

REVIEW AND THEORY

Security devices such as air bags and lateral reinforcements in motor vehicles greatly reduce the number of severe injuries to the car occupants. Improvements in the sport equipment design also help to reduce the injuries due to the sporting activities. Nevertheless, injuries resulting from traffic or sport accidents are still considered as a major cause of death and disablement. A significant part of these injuries are related to the organs located in the abdominal region of the body including kidneys. A validated simulation model based on the measured material properties and verified mathematical models can be a tool for improving the safety measures. The motivation for this work was to construct a simulation model which simulates the kidney injuries under various loading conditions. To construct this model the kidney material was to be characterised and the real geometrical properties as well as the accident data were to be used. For material characterisation non linear and viscoelastic mathematical models were to be constructed. This information was then to be used in the numerical simulation of the kidney trauma by the Finite Elements Method.

PROCEDURES

Density of the tissue was measured by the immersion method. Compression tests of the cortex tissue were performed at various loading rates in the radial and the tangential directions. Three-axial compression tests were performed on the cortex tissues placed in a saline solution in a compression chamber. Shear tests were performed by punching a cylinder out of a slice extracted from the cortex. Tensile tests were carried out on the capsule which was tenderly peeled from the fresh kidney. For characterisation of the material behaviour, a non linear theoretical simulation based on a two parameter Blatz model was used. For characterisation of the time-dependent behaviour of the pig kidney cortex, a four parameter linear viscoelastic model composed of a Kelvin solid connected in series with a Maxwell fluid was employed.

RESULTS

The general behaviour of the pig kidney cortex samples under compression was found to be highly non-linear; showing the typical features of soft tissues. The stress strain diagram was composed of a very flat part at very low stress level to about 30% relative deformation which was followed by a steeply rising stiffening up to fracture. Uniaxially compressed specimens from the cortex failed by radial rupturing; the maximum nominal rupture strain reached to about 50%. The uniaxial compression tests on the cortex which were performed at various loading rates on the radial and the tangential directions of the kidney showed an increase of the rupture stress with the loading rate. They also showed that the difference between the rupture strains in the radial and in the tangential direction would become more pronounced increasing the loading rate. Long term uniaxial compression tests under sustained constant load performed on the cortex specimens showed an instantaneous deformation followed by a creep response which eventually approached an asymptote. The preliminary three axial tests on the cortex tissue and some soft synthetic materials including gels showed that the cortex tissue was slightly more compressible than the water, but was less compressible than synthetic gels. Through theoretical modelling, linear viscoelastic and non-linear parameters of the cortex tissue were obtained. Figure (1) shows a result of the curve fitting using the Blatz model for uniaxial compression test. Figure (2) shows the experimental compression creep curve and the corresponding viscoelastic model.

Figure (1) Experimental results from the uniaxial compression tests on the pig kidney cortex samples and the related non-linear Blatz model. The solid lines show the predictions according to the experimentally adapted Blatz model; the experimental results are shown by the squares (tangential) and triangles (radial).

Figure (2) Experimental results (data points) from the uniaxial compression creep tests (0.015 MPa) on the pig kidney cortex samples in the tangential direction and the experimentally adapted linear four parameter viscoelastic model (solid line). The four viscoelastic constants of the cortex were obtained by a curve fitting process.

Some other related results have been reported elsewhere (Farshad et al.). The information gained from the material characterisation was used in the Finite Element simulation of the kidney under lateral load. Figure 3 shows the result of the Finite Element simulation of the left human kidney.

Figure 3: Von Mises stress field in the kidney under lateral load.

DISCUSSION

Since investigations of the nature presented here were not found in the literature, comparison of the present results with other studies was not possible. Nevertheless, a qualitatively good agreement was found with some earlier classical data (Yamada 1970). The methodology used for the material characterisation of the pig kidney can be used for the material studies of other very soft tissues. This investigation offers some novel results which can be considered to be contribution to this field. The parametric characterisation of the kidney material with non linear Blatz model and linear viscoelastic model can also be used for further studies. The Finite Element simulation has resulted in stress fields corresponding to the clinically observed injury patterns (Schmidlin et al., 1997).

REFERENCES

Farshad M. et al. submitted to J. Biomechanics. Schmidlin F.R. et al. Ann Urol, 31, 246-252, 1997.

Yamada H. Strength of biological materials, Williams & Wilkins Comp. Baltimore, 1970.

ACKNOWLEDGMENTS

This work is funded by the "Swiss Foundation for Traffic Safety" and by the Research Council of EMPA. This support is thankfully acknowledged.