Explanatory models for a tactile resonance sensor system-elastic and density-related variations of prostate tissue in vitro

Abstract

Tactile sensors based on piezoelectric resonance have been adopted for medical applications. The sensor consists of an oscillating piezoelectric sensor-circuit system, and a change in resonance frequency is observed when the sensor tip contacts a measured object such as tissue. The frequency change at a constant applied force or mass load is used as a stiffness-sensitive parameter in many applications. Differential relations between force and frequency have also been used for monitoring intraocular pressure and stiffness variations in prostate tissue in vitro. The aim of this study was to relate the frequency change (Deltaf), measured force (F) and the material properties, density and elasticity to an explanatory model for the resonance sensor measurement principle and thereby to give explanatory models for the stiffness parameters used previously. Simulations of theoretical equations were performed to investigate the relation between frequency change and contact impedance. Measurements with a resonance sensor system on prostate tissue in vitro were used for experimental validation of the theory. Tissue content was quantified with a microscopic-based morphometrical method. Simulation results showed that the frequency change was dependent upon density (rho) and contact area (S) according to Deltaf proportional, variant rhoS(3/2). The experiments followed the simulated theory at small impression depths. The measured contact force followed a theoretical model with the dependence of the elastic modulus (E) and contact area, F proportional, variant ES(3/2). Measured density variations related to histological variations were statistically weak or non-significant. Elastic variations were statistically significant with contributions from stroma and cancer relative to normal glandular tissue. The theoretical models of frequency change and force were related through the contact area, and a material-dependent explanatory model was found as Deltaf proportional, variant rhoE(-1)F. It explains the measurement principle and the previously established stiffness parameters from the material properties point of view.