**4. Discussion**

#### *4.1. Merits of ONELAB for Thermoacoustic Imaging*

Using an open source platform, ONELAB, allowed a single interface to simulate hybrid thermoacoustic imaging, with the choice of optical, radio-frequency, or other sources to induce a pressure wave response. The components of ONELAB Gmsh (mesh) and GetDP (FEM solver) were applied for this purpose. Since GetDP only solves the user defined finite element equations, fine control over every aspect of the thermoacoustic simulation was possible. This is especially important when performing reconstruction, since, for instance, time-reversal can have drastically different performance depending on the amount of time steps and the duration per time step. The benefits of Gmsh include its standard mesh creation, with the ability to automatically interface with other standard mesh formats. This allows the user to write a wrapper around any given finite element mesh. Besides simulating expected results, this platform is also ideal for post-processing the results. All of the data from the simulated PACT and RACT experiments was in the same format, used the same finite element mesh, without the need for interpolation or data transformation. Using the data in such a complementary fashion demonstrated the benefits of ONELAB over more established simulation tools used for a single imaging modality.

#### *4.2. Simulation Workflow for both PACT and RACT*

We first tested our algorithms on a simple phantom that consisted of two absorbing regions of different shapes inside a homogeneous background. The second phantom simulated a human breast with a tumor. The same phantom mesh was used to define both optical and RF-acoustic properties of the tissue. The optical diffusion equation was solved to obtain the optical fluence maps of the phantoms (Figures 2 and 6), while the solution to Maxwell's equations mapped the electric field distribution for these phantoms (Figures 4 and 8). Subsequently, maps of the initial pressure rises, due to electromagnetic absorption and the thermoacoustic effect, were generated using the optical fluence maps in PACT and electric field intensity in RACT. The initial pressure distributions of both PACT and RACT were then propagated using the same time-domain equations. Respective maps of the reconstructed pressure were generated using a time-reversal algorithm. Optical absorption and conductivity of the tissue phantoms were recovered by dividing the related reconstruction pressures by the optical fluence and electric field intensity distributions, respectively (Figures 3, 5, 7 and 9).

#### *4.3. Analysis of PACT and RACT Results*

Overall, our simulation results on two different tissue phantoms have shown that ONELAB can effectively simulate photoacoustic computed tomography (PACT) as well as RF-induced acoustic computed tomography (RACT). The optical fluence distribution (Figure 2) and electric field intensity (Figure 4) for the homogeneous phantom were significantly different, though the PACT/RACT reconstruction (Figures 3 and 5) is of similar accuracy. The relative error of the maximum absorption coefficient was 1.25% for the PACT case, and 8.70% in the RACT case. PACT for this phantom had a much lower relative error, since the contrast between absorber was much larger than the same difference in the RACT case. Imperfect reconstruction of the absorbers is due to error in reconstructing the initial pressure, instead of differences in the field intensity distribution. The relative shape of the absorbers, using either PACT or RACT, is easily identified from the reconstruction, with further processing only necessary for very precise characterizations. The successfully simulated results on a generic phantom gave us confidence to further validate our algorithms on a real tissue phantom mimicking the optical and RF properties of a human breast.

When the approximate optical and RF parameters corresponding to breast tissue are used (Figures 6 and 8), the optical and electric field intensities resemble each other, and have similar accuracy to the homogeneous phantom. The relative error of the maximum absorption coefficient was 23.2% for PACT and 6.92% for RACT. In the realistic tissue, RACT had more contrast, leading to less error in the reconstruction. The difference in field intensity between the homogeneous and breast phantom did not have a significant effect on the reconstruction accuracy. Both PACT and RACT are able to approximately reconstruct the tumor and the surrounding glandular tissue with no further processing. Even though the tumor had properties similar to the background, the PACT reconstruction was still able to identify the tumor surrounded by the glandular tissue. In RACT, the tumor is readily identified as being significantly different from the background.

In summary, our work demonstrated that ONELAB is a viable simulation platform for use in PACT and RACT, and is well suited for experiments that exploit both modalities. Reconstructed images of the phantoms provided both qualitative and quantitative information about the tissue optical and conductivity properties, including the size, shape, and location of the target regions. This work laid a foundation for future studies to develop and validate more robust multimodality reconstruction algorithms that will help improve quantitative accuracy.
