Background information

The Field program system uses the concept of spatial impulse responses as developed by Tupholme and Stepanishen in a series of papers [1, 2, 3]. The approach relies on linear systems theory to find the ultrasound field for both the pulsed and continuous wave case. This is done through the spatial impulse response. This response gives the emitted ultrasound field at a specific point in space as function of time, when the transducer is excitated by a Dirac delta function. The field for any kind of excitation can then be found by just convolving the spatial impulse response with the excitation function. The impulse response will vary as a function of position relative to the transducer, hence the name spatial impulse response.

The received response from a small oscillating sphere can be found by acoustic reciprocity. The spatial impulse response equals the received response for a spherical wave emitted by a point. The total received response in pulse-echo can, thus, be found by convolving the transducer excitation function with the spatial impulse response of the emitting aperture, with the spatial impulse response of the receiving aperture, and then taking into account the electro-mechanical transfer function of the transducer to yield the received voltage trace. An explanation and rigorous proof of this can be found in [4] and [5].

Any excitation can be used, since linear systems theory is used. The result for the continuous wave case is found by Fourier transforming the spatial impulse response for the given frequency. The approach taken here can, thus, yield all the diffent commenly found ultrasound fields for linear propagation.

Simulation

A number of different authors have calculated the spatial impulse response for different transducer geometries. But in general it is difficult to calculate a solution, and especially if apodization of the transducer is taken into account. Here the transducer surface does not vibrate as a piston, e.g. the edges might vibarte less then the center. The simulation program circumvents this problem by dividing the transducer surface into squares and the sum the response of these squares to yield the response. Thereby any tranducer geometry and any apodization can be simulated. The approach is described in [6].

The time for one simulation is also of major concern. As the squares making up the tranducer apertue are small, it is appropriate to use a far-field approximation, making simulation simple. Another issue in keeping the simulation time down is to use a low sampling frequency. Often spatial impulse responses are calculated using sampling frequencies in the GHz range due to the sharp discontinuities of the responses. These discontinuities are handled in the Field programs by accurately keeping track of the time position of the responses and uses the integrated spatial impulse response as an intermediate step in the calculations. Thereby no energy is lost in the response, which is far more important than having an exact shape of the spatial impulse response. Hereby the Field program ususally does better using 100 MHz sampling and approximate calculations, than using the exact analytic expression and GHz sampling.

More information

You can find more information about the background for the program in the references below. Especially [7] gives a through introduction to the background.

References

[1] G.E. Tupholme: Generation of acoustic pulses by baffled plane pistons, Mathematika 16, pp. 209-224, 1969.

[2] P.R. Stepanishen: The time-dependent force and radiation impedance on a piston in a rigid infinite planar baffle, J.Acoust.Soc.Am. 49 (3), pp. 841-849, 1971A.

[3] P.R. Stepanishen: Transient radiation from pistons in a infinite planar baffle, J.Acoust.Soc.Am. 49, pp. 1627-1638, 1971B.

[4] P.R. Stepanishen: Pulsed transmit/receive response of ultrasonic piezoelectric transducers, J.Acoust.Soc.Am. 69, pp. 1815-1827, 1981.

[5] J.A. Jensen: A Model for the Propagation and Scattering of Ultrasound in Tissue, J.Acoust.Soc.Am. 89, pp. 182-191, 1991.

[6] J.A. Jensen and N. B. Svendsen: Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers, IEEE Trans. Ultrason., Ferroelec., Freq. Contr., 39, pp. 262-267, 1992.

[7] J.A. Jensen: Linear description of ultrasound imaging systems, Notes for the International Summer School on Advanced Ultrasound Imaging, Technical University of Denmark July 5 to July 9, 1999, Technical University of Denmark, June, 1999.

[8] J.A. Jensen: Field: A Program for Simulating Ultrasound Systems, Paper presented at the 10th Nordic-Baltic Conference on Biomedical Imaging Published in Medical & Biological Engineering & Computing, pp. 351-353, Volume 34, Supplement 1, Part 1, 1996.

[9] J. A. Jensen, Darshan Gandhi, and William D. O'Brien: Ultrasound fields in an attenuating medium, Proceedings of the IEEE 1993 Ultrasonics Symposium, pp. 943-946, Vol. 2, 1993.

[10] J. A. Jensen: Ultrasound fields from triangular apertures, Journal of the Acoustical Society of America, Vol. 100(4), pp. 2049-2056, October, 1996.

[11] J. A. Jensen: Simulating arbitrary-geometry ultrasound transducers using triangles, Proceedings of IEEE International Ultrasonics Symposium, Vol. 2, pp. 885-888, 1996.

[12] J. A. Jensen and Peter Munk: Computer phantoms for simulating ultrasound B-mode and cfm images, 23rd Acoustical Imaging Symposium, Boston, Massachusetts, USA, April 13-16, 1997.

[13] J. A. Jensen: A new approach to calculating spatial impulse responses, Proceedings of IEEE Ultrasonics Symposium Proceedings, pp. 1755-1759, 1997

[14] J. A. Jensen: A new Calculation Procedure for Spatial Impulse Responses in Ultrasound, Journal of the Acoustical Society of America, Vol. 105, pp. 3266-3274, 1999.

[15] J. A. Jensen: Ultrasound Imaging and its modeling, in "Imaging of Complex Media with Acoustic and Seismic Waves", Editors: Fink, M.; Kuperman, W.A.; Montagner, J-P; Tourin, A., Topics in Applied Physics, Springer Verlag, pp. 135-165, 2002.

[16] J. A. Jensen: Speed-accuracy trade-offs in computing spatial impulse responses for simulation medical ultrasound imaging, Journal of Computational Acoustics, Vol.9, no..3, pp.731-744, 2001

[17] M. Schlaikjer, S. Torp-Pedersen and J. A. Jensen: Simulation of RF data with tissue motion for optimizing stationary echo canceling filters, Ultrasonics, Vol. 41 (6) , pp. 415-419. 2003.

[18] J. A. Jensen and S. Nikolov: Fast simulation of ultrasound images, Proceedings the IEEE Ultrasonics Symposium, vol. 2, pp. 1721-1724, 2000.