Dynamic measurement of soft tissue viscoelastic properties with a torsional resonator device

Abstract

A new method for measuring the mechanical properties of soft biological tissues is presented. Dynamic testing is performed using a torsional resonator, whose free extremity is in contact with a tissue sample. An analytical model of a semi-infinite, homogenous, isotropic medium is used to model the shear wave propagation in the material sample and allows determining the complex shear modulus of the soft tissue. By controlling the vibration amplitude, shear strains of less than 0.2% are induced in the tissue so that the material response can be considered as linear viscoelastic. Experiments are performed at different eigenfrequencies of the torsional oscillator and the complex shear modulus is characterized in the range 1–10 kHz. In vitro experiments on bovine and porcine liver are presented in order to demonstrate the sensitivity of the proposed technique, and the reliability of the measurements is confirmed with comparative tests on synthetic material. The experiment does not damage the soft tissue and allows a fast and local measurement, these being prerequisites for future applications in vivo during open surgery.

Introduction

Measurement of the mechanical properties of biological tissues is required for medical applications, such as diagnostics, surgery simulation and planning (Greenleaf et al., 2003, Picinbono et al., 2002, Snedeker et al., 2005, Szekely, 2003). The realism of the mechanical response of the soft tissues contributes to a great extent to the quality of the simulation of organ deformations.

Mechanical testing of biosolids is accomplished by destructive and non-destructive techniques. Destructive testing utilizes material samples extracted from the organ and experiments are performed according to standard methods of material characterization such as tensile tests as reported by Fung (1967) or compression tests (e.g., Snedeker et al., 2005). Non-destructive techniques present the great advantage of a possible direct application in vivo, during open surgery, eliminating the uncertainties due to the alterations of the material when extracted from its biochemical environment. Techniques based on tissue indentation are used in vivo (Carter et al., 2001, Miller et al., 2000, Ottensmeyer and Salisbury, 2001, Ottensmeyer, 2002), being the control of the boundary conditions the major obstacle in data analysis for quantitative evaluations. The aspiration experiment originally developed by Vuskovic (2001) provides well defined kinematic and kinetic boundary conditions and allows accurate fitting of material parameters. The application of this quasi static test on soft human organs (Kauer et al., 2002, Mazza et al., 2004, Nava et al., 2004a, Nava et al., 2004b) has provided quantitative sets of material parameters for use in large deformation calculations with “slow” deformations.

Testing the materials at high deformation rates provides additional information on the constitutive behavior of the tissue, with applications in diagnostics and trauma research (Snedeker et al., 2002, Snedeker et al., 2005). Dynamic methods for testing soft biological materials range from standard rheometers operating at 0.01–10 Hz (Nasseri et al., 2002), to devices suitable for modelling the behavior at loading rates up to 350 Hz (Arbogast et al., 1997). Methods based on magnetic resonance elastography provide dynamic measurements of elastic moduli of soft tissues, reaching frequencies up to 400 Hz (Kruse et al., 2000, Manduca et al., 2001). Rotary shear tests have been proposed for in vivo tests by Kalanovic et al. (2003) for the low frequency range (up to 20 Hz).

A new non-destructive method for dynamic testing of soft tissue is presented in this paper and is used in our laboratory in order to complement the quasi-static tissue characterization obtained from the aspiration experiments (Nava et al., 2003). The mechanical properties are derived from the material response to harmonic shear excitation at discrete frequencies in the range (1–10 kHz). Mechanical characterization at high frequencies (outside the range of physiological loading conditions) provides relevant information for the determination of constitutive models of soft biological tissue, and for discriminating between healthy and unhealthy tissue conditions (diagnostics).

In the present experiment the material is in contact with the free end of a torsional resonator and influences the dynamic behavior of the resonator. The use of a phase locked loop technique provides a high sensitivity to the device. The measurement is fast and, due to the small contact area, a local characterization is achieved. Adherence of soft tissue and torsional oscillator is ensured by vacuum clamping. The soft tissue is modelled analytically as a semi-infinite, homogenous, isotropic medium; a suitable kinematic boundary condition is applied in correspondence of the contact with the resonator. The analytical model consists of a torsional radiating source on a semi infinite space (Dorn, 1980, Robertson, 1967, Sagoci, 1944) and is used to extract the material parameters. A mapping procedure and reference tables enable real-time parameter extraction. The reliability of the measurement procedure has been verified with comparative experiments on synthetic materials. The results obtained in vitro on bovine and porcine liver are reported and discussed, showing the sensitivity and the repeatability of the measurements.