Simulating arbitrary-geometry ultrasound transducers using triangles

Calculation of ultrasound fields from medical transducers is often done by applying linear acoustics and using the Tupholme-Stepanishen method of calculation. Here the spatial impulse response is found and, together with the basic one-dimensional pulse, it is used to find both the emitted and pulse-echo field. The spatial impulse response has only been determined analytically for a few geometries and using apodization over the transducer surface generally makes it impossible to find the response analytically. A popular approach to find the general field is thus to split the aperture into small rectangles, and then sum the weighted response from each of these. The problem with rectangles is their poor fit to apertures which do not have straight edges, such as circular and oval shapes. The simulation thus introduces artifacts in the response, that necessitates the use of a large number of rectangles for a precise simulation. A triangle better fits these aperture shapes, and the field from a triangle has recently been derived. A new field simulation program has been made based on the triangular shape. It is written in C and interfaced to the Matlab environment through a set of M-files. A large number of transducers can be defined and their properties manipulated. The program can calculate all types of ultrasound fields, and can also be used for simulating B-mode and color flow images. Both the focusing and apodization can be set to be dynamic with respect to time, and it is thus possible to simulate images focused at different zones. The time-integrated spatial impulse response is used in the program to minimize the effect of the sharp edges of the spatial impulse response in a sampled signal. Since the integrated response from a triangular element cannot be analytically evaluated, a simple numerical integration is used. Using this program, the geometrical artifacts from fitting the aperture with a basic element are significantly reduced and is in most instances negligible. The time for running the program is, however, increased by a factor of 3.3 to 1000 compared to using the simple far-field response of a rectangle, as the triangle equations are far more complicated. This approach is therefore best suited for accurate modeling of fields, whereas the rectangle program is better suited to make fast simulated images, since contributions from many scatterers are summed here and the error is thereby reduced.