A KLM-circuit model of a multi-layer transducer for acoustic bladder volume measurements

In a preceding study a new technique to non-invasively measure the bladder volume on the basis of non-linear wave propagation was validated. It was shown that the harmonic level generated at the posterior bladder wall increases for larger bladder volumes. A dedicated transducer is needed to further verify and implement this approach. This transducer must be capable of both transmission of high-pressure waves at fundamental frequency and reception of up to the third harmonic. For this purpose, a multi-layer transducer was constructed using a single element PZT transducer for transmission and a PVDF top-layer for reception. To determine feasibility of the multi-layer concept for bladder volume measurements, and to ensure optimal performance, an equivalent mathematical model on the basis of KLM-circuit modeling was generated. This model was obtained in two subsequent steps. Firstly, the PZT transducer was modeled without PVDF-layer attached by means of matching the model with the measured electrical input impedance. It was validated using pulse-echo measurements. Secondly, the model was extended with the PVDF-layer. The total model was validated by considering the PVDF-layer as a hydrophone on the PZT transducer surface and comparing the measured and simulated PVDF responses on a wave transmitted by the PZT transducer. The obtained results indicated that a valid model for the multi-layer transducer was constructed. The model showed feasibility of the multi-layer concept for bladder volume measurements. It also allowed for further optimization with respect to electrical matching and transmit waveform. Additionally, the model demonstrated the effect of mechanical loading of the PVDF-layer on the PZT transducer.