**3. Results**

The ability of the ONELAB software platform to simulate both PACT (optical source) and RACT (radio frequency source) with the same tool and on the same mesh, is demonstrated using the phantoms described in the methods section. Below we first present PACT and RACT results for the homogeneous phantom embedded with two absorbers and then the results for the breast phantom with tumor.

#### *3.1. Photoacoustic Computed Tomography (PACT) of the Homogeneous Phantom*

The optical excitation for the first phantom uses a wavelength of 800 nm. This specific wavelength was chosen as it is often used in photoacoustics, due to the absorption spectrum of the absorbers of interest, such as hemoglobin. With the homogeneous phantom parameters, the simulated optical fluence is given in Figure 2.

The position of the absorbers is easily approximated by the nulls in the fluence distribution. The approximate shapes can be identified, which can be used for more stable reconstruction of the material parameters. The 8 mm spacing is large enough to identify two distinct absorbers, with the ultimate resolution governed by the reconstruction of the fluence that would be done in practice. The initial pressure induced by this fluence distribution, as well as the original and reconstructed absorption coefficient images are provided in Figure 3.

The fluence is not constant across the domain, and so the two absorbers induce slightly different initial pressures. The larger object is reconstructed with less error, since it is approximately constant over a larger area. Non-idealities in the reconstructed background pressure are suppressed by using the fluence, and so the reconstructed objects are clearly separated from the background.

#### *3.2. RF-Acoustic Computed Tomography (RACT) of the Homogeneous Phantom*

The RACT simulation used the same finite element mesh that was used for the photoacoustic simulation, utilizing a typically used radio frequency source of 434 MHz. For the parameters given in the methods section, the electric field magnitude is provided in Figure 4.

**Figure 2.** Total optical fluence distribution inside the homogeneous phantom with two absorbers using an 800 nm source. The circular and elliptical absorbers, simulating hemoglobin with absorption coefficient *μa* = 0.425 mm<sup>−</sup><sup>1</sup> at 800 nm, are located 4 mm to the left and right of the center. The background has a *μa* = 0.001 mm<sup>−</sup>1, and a reduced scattering coefficient *μs* = 1 mm<sup>−</sup>1. *μs* = 0 for the absorbers.

**Figure 3.** Photoacoustic computed tomography (PACT) simulations using an 800 nm source on the homogeneous phantom with two light absorbing inclusions; (**a**) the true optical absorption distribution; (**b**) the initial pressure rise induced by the photoacoustic effect; (**d**) the reconstructed pressure, calculated using the time-reversal algorithm; and (**c**) the reconstructed absorption, obtained by dividing the reconstructed pressure with the fluence.

Unlike the PACT case, the electric field alone does not provide any information on the location of the absorbers. Since the wavelength is much larger than the simulation domain, and there is small difference in conductivity between the absorbers and background, the electric field intensity is approximately constant. The results of the RF acoustic simulation of this homogeneous phantom are shown in Figure 5.

**Figure 4.** Total electric field intensity distribution inside the homogeneous phantom containing two absorbers, using a 434 MHz radio frequency (RF) source. The circular and elliptical absorbers, with conductivity *σ* = 10 S/m, are located 4 mm to the left and right of the center, and have a dielectric constant *εr* = 25. The background has *σ* = 0.1 S/m, and *εr* = 5.

**Figure 5.** Radio frequency (RF)-induced acoustic computed tomography (RACT) simulations using a 434 MHz RF source on the homogeneous phantom with two absorbers. (**a**) The true RF conductivity distribution; (**b**) the initial pressure rise induced by the thermoacoustic effect; (**d**) the reconstructed pressure, calculated using the time-reversal algorithm; and (**c**) the reconstructed conductivity, obtained by dividing the reconstructed pressure by the electric field intensity.

#### *3.3. Photoacoustic Computed Tomography (PACT) of the Breast Phantom*

Figure 6 shows the fluence distribution generated by ONELAB for the breast phantom described in the methods section. A rough estimate of the tumor location can be predicted from the fluence map, but no shape information can be obtained from the fluence distribution alone. The photoacoustic simulation is able to identify the shape of the tumor, as well as the difference between cancerous and glandular tissue. Results in Figure 7 show the initial pressure rise and the resulting reconstructed absorption distribution.

**Figure 6.** Total optical fluence distribution using an 800 nm wavelength source on the breast phantom. The background absorption coefficient is *μa* = 0.0005 mm<sup>−</sup>1, with a reduced scattering coefficient *μs* = 1.5742. Glandular tissue (*μa* = 0.0059 mm<sup>−</sup>1, *μs* = 1.12 mm<sup>−</sup>1) surrounds a tumor (*μa* = 0.0021, *μs* = 0.625 mm<sup>−</sup>1) located 32.5 mm deep from the right side of the phantom.

**Figure 7.** Photoacoustic computed tomography (PACT) simulations of the breast phantom at 800 nm wavelength; (**a**) the true optical absorption; (**b**) the initial pressure rise induced by the photoacoustic effect; (**d**) the reconstructed pressure, calculated using the time reversal algorithm; and (**c**) the reconstructed absorption, obtained by dividing the reconstructed pressure with the fluence. The elliptical region similar to the background is the tumor, surrounded by the glandular tissue.

#### *3.4. RF-Induced Acoustic Computed Tomography (RACT) of the Breast Phantom*

The radio frequency source for the breast phantom, similar to the homogeneous phantom, operates at 434 MHz. The field distribution is provided in Figure 8.

The forward simulation of the electric field is able to directly detect the tumor and an estimation of its location. The conductivity has a much more significant effect on the wave, since the wavelength is larger than the region of interest. In the large wavelength regime, scattering due to dielectric contrast does not distort the electromagnetic wave as much as the substantial conductivity. While the approximate location of the tumor can be inferred from the electric field intensity, the specific shape and glandular tissue identification requires further processing, such as the RF acoustic simulation. Figure 9 shows the initial pressure and the resulting reconstructed pressure and conductivity maps of the breast phantom.

**Figure 8.** Total electric field intensity distribution of a 434 MHz radio frequency source inside the breast phantom. The background has a conductivity *σ* = 0.0353 S/m and dielectric constant *εr* = 5.51. Glandular tissue (*σ* = 8.86 S/m, *εr* = 61.3) surrounds a tumor (*σ* = 13.03 S/m, *εr* = 25.25) located 32.5 mm deep from the right side of the phantom.

**Figure 9.** RF-induced acoustic computed tomography (RACT) simulations of the breast phantom using a 434 MHz RF source; (**a**) the true RF conductivity; (**b**) the initial pressure rise induced by the thermoacoustic effect; (**d**) the reconstructed pressure, calculated using the time-reversal algorithm; and (**c**) the reconstructed absorption, found by dividing the reconstructed pressure by the electric field intensity. The elliptical region with significantly larger conductivity is the tumor, surrounded by the glandular tissue.
