Comparison of deconvoluted-convoluted reconstituted ultrasound signals with their experimental original in a porous composite, cancellous bone

Abstract

Langton previously suggested that the transmission of ultrasound through cancellous bone, a complex structured porous composite, may be considered as an array of parallel sonic-rays. The transit time of each sonic-ray is determined by the proportion of bone tissue and bone marrow, with minimum (tmin) and maximum (tmax) values corresponding to entire bone tissue and bone marrow, respectively. Moreover, a transit time spectrum (TTS) describes the proportion of sonic-rays as a function of transit time, P(ti), detected within the aperture of the receive transducer. The TTS effectively serves as the time-integrated impulse response (IR) of a test sample, and may be derived by deconvolution of experimentally derived output oe(t) and input ie(t) ultrasound signals. Conversely, a reconstituted output signal, or(t), may be obtained by convolution of oe(t) and the test sample's TTS. This study aimed to test these deconvolution and convolution relationships utilizing natural tissue cancellous bone samples. 1 MHz broadband experimental output transmission ultrasound signals, oe(t), through 16 natural tissue samples of human femoral cancellous bone samples were recorded. Corresponding reconstituted output signals, or(t), were derived through a two-stage deconvolution-convolution process. A linear regression fit yielded a high degree of agreement between experimental and reconstituted ultrasound output signals, with an average coefficient of determination (R2) of 0.96 ± 0.03. This study therefore provides further evidence for the reliability and validity of ultrasound transit time spectroscopy (UTTS) as an assessment technique that provides quantitative information on both the quantity and quality of cancellous bone.