TY - JOUR

T1 - Use of Taylor Series Expansions for Time Savings in Computation of Accurate Transducer Pressure Fields

AU - Madsen, Ernest L.

AU - Hall, Timothy J.

AU - Zagzebski, James A.

AU - Insana, Michael F.

N1 - Funding Information:
Manuscript received April 24, 1986; revised August 24, 1986. Thisw ork was supported inp art by the National Institutes of Health under Grants R01 CA25634 and R01 CA39224. E. L. Madsen, T. 1. Hall, and J. A. Zagzebski are with the Department of Medical Physics, 1530 Medical Science Center. Universily of Wiscon- sin, Madison, W1 53706, USA. M. F. Insana is with the Center for Devices and Radiological Health, Food and Drug Administration, Rockville, MD 20857, USA. IEEE Log Number 8612684.

PY - 1987/5

Y1 - 1987/5

N2 - In the method of data reduction used in our laboratory to determine acoustic backscatter coefficients in tissues and tissuelike media, computation of the complex acoustic pressure in an attenuating medium due to a nonfocused disk radiator is required at a large number of field points and over a frequency band of about 1 MHz. Computer CPU time and input/output time can be considerable because of the need to evaluate an integral corresponding to each field point P and frequency, ω. The fact that the frequency dependence of this integral is restricted to a factor in the integrand of the form exp (ikr’ ), where r’ is the dummy variable and k = k( ω ) is the complex wave number, makes the integral part of the expansion in a Taylor series straightfor-ward. The first five terms of the Taylor series have been derived, and tests of the accuracy of the expansion are presented. While maintaining adequate accuracy, the CPU time savings accrued through use of the series corresponds to a factor of 1/7 and an input/output time savings factor of at least 1 /6. (The factor 1 /7 means, e.g., that a CPU time of 35 min without using the Taylor series becomes 5 min using the Taylor series).

AB - In the method of data reduction used in our laboratory to determine acoustic backscatter coefficients in tissues and tissuelike media, computation of the complex acoustic pressure in an attenuating medium due to a nonfocused disk radiator is required at a large number of field points and over a frequency band of about 1 MHz. Computer CPU time and input/output time can be considerable because of the need to evaluate an integral corresponding to each field point P and frequency, ω. The fact that the frequency dependence of this integral is restricted to a factor in the integrand of the form exp (ikr’ ), where r’ is the dummy variable and k = k( ω ) is the complex wave number, makes the integral part of the expansion in a Taylor series straightfor-ward. The first five terms of the Taylor series have been derived, and tests of the accuracy of the expansion are presented. While maintaining adequate accuracy, the CPU time savings accrued through use of the series corresponds to a factor of 1/7 and an input/output time savings factor of at least 1 /6. (The factor 1 /7 means, e.g., that a CPU time of 35 min without using the Taylor series becomes 5 min using the Taylor series).

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U2 - 10.1109/T-UFFC.1987.26948

DO - 10.1109/T-UFFC.1987.26948

M3 - Article

AN - SCOPUS:84944020244

SN - 0885-3010

VL - 34

SP - 300

EP - 308

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

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

IS - 3

ER -