TY - JOUR

T1 - Evaluation of the spectral fit algorithm as functions of frequency range and Δka eff

AU - Bigelow, Timothy A.

AU - O'Brien, William D.

N1 - Funding Information:
This work was supported by the University of Illinois Research Board, by a NDSEG Fellowship awarded to T. A. Bigelow, and by a Beckman Institute Graduate Fellowship awarded to T. A. Bigelow.

PY - 2005/11

Y1 - 2005/11

N2 - Considerable effort has been directed at quantifying the properties of the tissue microstructure (i.e., scatterer correlation length) to diagnose disease and monitor treatment. In vivo assessments have had limited success due to frequency-dependent attenuation along the propagation path (i.e., total attenuation) masking the frequency dependence of the scattering from the tissue microstructure. Previously, both total attenuation and scatterer correlation length, given by the effective radius, were solved simultaneously by a two-parameter minimization of the mean squared error between a reference spectrum, modified by the attenuation and scatterer effective radius, and the backscattered waveforms using an algorithm termed the spectral fit algorithm. Herein, the impact of frequency range (largest frequency minus smallest frequency) and δka eff (largest ka eff value minus smallest ka eff value; k is wave number and a eff is scatterer effective radius) used by the spectral fit algorithm on estimating the scatterer effective radius, and total attenuation was assessed by computer simulations while excluding frequencies of the backscattered power spectrum dominated by electronic noise. The simulations varied the effective radius of the scatterers (5 μm to 150 μm), the attenuation of the region (0 to 1 dB/cm-MHz), the bandwidth of the source, and the amount of electronic noise added to the radio frequency (rf) waveforms. The center frequency of the source was maintained at 8 MHz. Comparable accuracy and precision of the scatterer effective radius were obtained for all the simulations whenever the same Δka eff was used to obtain the estimates. A Δka eff of 1 gave an accuracy and precision of ∼15% ± 35%, and a width of 1.5 gave an accuracy and precision of ∼5% ± 15% consistently for all of the simulations. Similarly, the accuracy and precision of the total attenuation estimate were improved by increasing the frequency range used by the spectral fit algorithm.

AB - Considerable effort has been directed at quantifying the properties of the tissue microstructure (i.e., scatterer correlation length) to diagnose disease and monitor treatment. In vivo assessments have had limited success due to frequency-dependent attenuation along the propagation path (i.e., total attenuation) masking the frequency dependence of the scattering from the tissue microstructure. Previously, both total attenuation and scatterer correlation length, given by the effective radius, were solved simultaneously by a two-parameter minimization of the mean squared error between a reference spectrum, modified by the attenuation and scatterer effective radius, and the backscattered waveforms using an algorithm termed the spectral fit algorithm. Herein, the impact of frequency range (largest frequency minus smallest frequency) and δka eff (largest ka eff value minus smallest ka eff value; k is wave number and a eff is scatterer effective radius) used by the spectral fit algorithm on estimating the scatterer effective radius, and total attenuation was assessed by computer simulations while excluding frequencies of the backscattered power spectrum dominated by electronic noise. The simulations varied the effective radius of the scatterers (5 μm to 150 μm), the attenuation of the region (0 to 1 dB/cm-MHz), the bandwidth of the source, and the amount of electronic noise added to the radio frequency (rf) waveforms. The center frequency of the source was maintained at 8 MHz. Comparable accuracy and precision of the scatterer effective radius were obtained for all the simulations whenever the same Δka eff was used to obtain the estimates. A Δka eff of 1 gave an accuracy and precision of ∼15% ± 35%, and a width of 1.5 gave an accuracy and precision of ∼5% ± 15% consistently for all of the simulations. Similarly, the accuracy and precision of the total attenuation estimate were improved by increasing the frequency range used by the spectral fit algorithm.

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U2 - 10.1109/TUFFC.2005.1561669

DO - 10.1109/TUFFC.2005.1561669

M3 - Article

C2 - 16422412

AN - SCOPUS:23744444533

VL - 52

SP - 2003

EP - 2010

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

SN - 0885-3010

IS - 11

ER -