Modeling wave propagation through the skull for ultrasonic transcranial Doppler

Abstract

One problem associated with transcranial Doppler ultrasound (TCD) is the relatively low energy penetrating inside the brain through the skull, seriously limiting the image quality. This may be due to the impedance mismatch at the bone interface and to the bone frequency dependent attenuation. The objective of this paper is to model ultrasonic wave propagation through the skull. To do so, an analytical model was developed based on the estimation of the transmission coefficients inside the brain, leading to frequency dependent overall transmission coefficient for a given skin and bone thickness. Moreover, a finite element model was developed taking into account absorption phenomena. Both methods were validated experimentally by comparing the numerical and analytical results with results obtained from a phantom mimicking the skull having an attenuation coefficient equal to 30 dB/cm at 2.25 MHz and a thickness of 4.4 mm. A 2 mm layer of water mimicked the skin. The difference between the maximum amplitude of normalized received US signals obtained analytically and experimentally was 1%. The average relative difference between them was 0.3%. Thus, a working model is designed which can predict the energy inside the brain. Furthermore, the results show that impedance mismatch plays a major role in transmission loss rather than frequency dependent attenuation