Photoacoustic Imaging Group

Mathematical models of the physical mechanisms underlying photoacoustic signal generation, propagation and detection provide important simulation tools for optimising the design of photoacoustic imaging instrumentation, for example identifying the optimum acoustic detection aperture and spatial sampling parameters. Such models also have an important role in generating data for evaluating image reconstruction algorithms and, more generally, as a tool for helping to understand and interpret the anatomical and physiological significance of photoacoustic signals and images. An essential requirement is an accurate and computationally efficient model for describing the propagation of the acoustic wave from the initial source distribution produced by the absorption of the laser energy. For this purpose, a range of k-space models, which though their use of the FFT, offer significant gains in computational efficiency. k-space methods also have the advantage that they can incorporate an arbitrary, complex, frequency-dependent, directional response and so model the characteristics of a practical receiver, unlike, for example, the commonly used Poisson time-domain model. 2 models have been implemented. One uses an exact time propagator to calculate the acoustic field at all points on a grid for a single time following the absorption of the laser pulse. Unlike finite difference methods, in which the time step must be small to avoid instability, the acoustic field at any time may be predicted in one step without the need to calculate the field at intermediate times. With this model, the evolution of 3D fields through time can be visualized, an example of this is shown in figure 1.

Figure 1 Output of k-space time stepping model showing the evolution of the acoustic field at times t=0, 0.5, 1, and 1.5 µs following the absorption of a laser pulse incident on a pure absorber at a pressure release boundary.

A second model calculates the pressure on a chosen line or plane for many times in a single step by mapping the pressure as a function of vertical spatial wavenumber to the pressure as function of temporal frequency. The power of this approach is that it can be used to rapidly simulate the output of a linear or 2D array of detectors. This can then be used as simulated data that is input to an image reconstruction algorithm, either to test the algorithm or as tool for identifying the optimum field mapping parameters in order to refine the design of the detection instrumentation.

References

Cox, BT, Arridge, SR, and Beard, PC (2007): K-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics, Journal of the Acoustical Society of America 121, 3453-3464 Download PDF file
Cox BT and Beard PC, Fast calculation of pulsed photoacoustic fields in fluids using k-space methods, Journal of the Acoustical Society of America, 117 (6), pp3616-3627, 2005 Download PDF File
Cox BT, Laufer J, Köstli K, Beard PC, Experimental Validation of Photoacoustic k-Space Propagation Models, Proc. SPIE 5320, pp238-248, 2004 Download PDF File