Detecting Inclusions in a Silicone Rubber Phantom Using Standing Lamb Waves and Multiple Frequency Footprints

Abstract: The thesis deals with one major question: is it possible, using one piezoelectric sensor/vibrator, to detect a hard inclusion in a silicone rubber phantom? The question was approached with an open mind and the task was subdivided into three clearly identifiable parts: characterization of the piezoelectric sensor/vibrator (paper I), creating a model of the visco-elastic properties of a tissue-like material (phantom) in contact with the sensor/vibrator (paper II), and to detect the presence of a hard inclusion in the phantom (paper III). All vibrations of the sensor/vibrator and phantom was modeled using a finite element method (FEM). To minimize the computational time and to maximize the FEM model's ability to correctly reproduce the vibrations, a two-dimensional model system consisting of a cylindrical piezoelectric sensor/vibrator, emitting radial elastic waves in to a cylindrical disk-shaped phantom, was chosen. The piezoelectric sensor/vibrator was characterized using a parameter tuning procedure using harmonic overtones. The procedure enables tuning of the electro-elastic parameters of the sensor/vibrator so that the measured and calculated impedance frequency responses match. Silicone rubber was chosen as a phantom to mimic soft tissue. The properties of the phantom was modeled using a fractional derivative visco-elastic model. The hyperelastic effect at the first radial resonance of the sensor vibrator was corrected for by a compensating function. The high frequency complex visco-elastic modulus of the silicone rubber was determined using the transitions of standing Lamb waves in the phantom. The presence of a ring-shaped inclusion in the phantom, of polyamide, was detected using the change of the transitional Lamb wave patterns in the phantom. The tuning of the PZT5A1 sensor/vibrator parameters yielded a match between the calculated and the measured impedance spectra better than 0.54%. The average, complex, elastic modulus of three silicone rubber, Silgel 612, samples were: (0.97 + 0.009i) GPa  at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz. The presence of a polyamide inclusion, PA6GPE, was detected in the phantom using multiple frequency footprints.