Modeling Acoustic Field Propagation for Medical Devices

Computational algorithms for the accurate and efficient modeling of acoustic beam propagations are presented. The algorithms are used to describe the propagations of biomedical ultrasonic imaging devices and lithotripters. The models as implemented are limited to axially symmetric sources. Linear algorithms or methods are presented which appear to form a uniquely efficient framework for describing beam propagations. The convolutionally-correct use of spatial domain sampling of the point source function (h) and the alternative of ray theory-directed sampling of the propagation function (H) are considered. The discrete Hankel transform is also presented as a means of greatly simplifying the propagation of axially symmetric sources. Nonlinear beam propagation models are presented which appear to offer significant advantages over the established nonlinear parabolic equation models. In particular, the models presented appear to offer near-field and off-axis accuracy, as well as the ability to represent beam propagations involving shockwaves. The nonlinear beam model framework should also be applicable to other forms of beam propagation involving progressive nonlinear effects. Transform-based dispersion relations are presented which appear to be a useful alternative to the traditional Kramers-Kronig relations. The new relations are used to derive a relation for the computation of discrete harmonic velocity values. Similarly, an analogous relation for computing discrete harmonic absorption values can be obtained. Problems associated with local dispersion relations are also considered. The new computational models are used to consider the in vivo or tissue path performance of biomedical ultrasonic devices. The significance of nonlinearity to tissue path beam propagations are predicted to lag well behind the corresponding water path significance. At high source intensities, though, the models predict that nonlinearity can become important to focal wave shape and focal tissue heating. For example, in the case of a high intensity, first trimester fetal examination, the inclusion of nonlinearity is predicted to account for an order of magnitude increase in the predicted focal heating rate. An extension of the nonlinear beam propagation model appropriate for modeling extracorporeal shockwave lithotripters is presented. The model is shown to agree well with water path measurements of the Dornier HM3 lithotripter. The performance of the HM3 is predicted to be strongly effected by nonlinearity in both water and tissue paths. The model predicts that the HM3's in vivo performance is quite similar to its water path performance. The model, together with measurements, suggest that the HM3's focal performance is strongly affected by the tensile strength of the fluid medium. The models presented appear to be well suited to the task of modelling axially symmetric acoustic beam propagations. Both continuous wave and pulsed sources can be considered. One of the nonlinear beam propagation models is currently available as a supported software package. Generalizing the models by dropping the constraint of axial symmetry is straightforward.