2.1.

Experimental Setup

Figure 1 shows the schematic of the experiment in top and side view. A 532-nm Q-switched Nd:YAG laser, delivering 6-ns pulses with a 10-Hz repetition rate, was used for PA excitation to generate laser-induced US from the passive elements and PA signals in the test object. The pulse energy was 40 mJ with a beam diameter of 16 mm in a Gaussian beam profile. As passive elements, we used eight horsetail hairs with a diameter of 200 to 250 μm positioned in such a way that the object lies completely within the fanbeam traced by the line of sight from the passive element to the edge detector elements for all projections, as discussed in Ref. 15. The signal detected from the passive element of 200 to 250 μm is typically dominated by the detector center frequency and bandwidth. The test object, whose details are provided further, is mounted in a rotary stage and immersed in water in the imaging tank. The PA signals and US transmission signals are detected using a curvilinear array (Imasonic, Besançon, France) composed of 32 piezoelements ($10\times 0.25{\mathrm{mm}}^2$), with a central frequency of 6.25 MHz and 80% bandwidth. A 32-channel pulse-receiver system (Lecoeur Electronique, Chuelles, France) was used for data acquisition at a sampling rate of 80 MHz and 60 dB gain. With this system, 2-D PA tomograms can be developed with an in-plane resolution of 0.125 mm and an elevation resolution of 1.5 mm; SOS tomograms can be developed with an in-plane resolution of roughly 1 mm and elevation resolution of 5 mm.¹⁷ A 532-nm CW laser (Verdi V6) was used for photothermal excitation in the test object by illumination from beneath along the $z$ axis.

Fig. 1

A schematic of the setup using the passive-element approach. Pulsed laser light at 532 nm illuminates the fixed passive elements and a test object mounted on a rotary stage. Laser-induced ultrasound from the passive elements (horsetail hairs) and photoacoustic signals from the object are detected using a curvilinear array. A continuous wave (CW) laser (Verdi, 532 nm) photothermally heats the object from the bottom side ($z$ direction).

2.2.

Sample Preparation

The test object consisted of a cylinder with a diameter of 26 mm made out of 2% ($\mathrm{w}/\mathrm{v}$) agar and 3% ($\mathrm{w}/\mathrm{v}$) (dilution) of 20% stock Intralipid® with a tissue-mimicking reduced scattering coefficient (${\mu }_s^{\prime }$) of $6{\mathrm{cm}}^{-1}$ and carrying three spherical sodium-alginate beads. The 4-mm-diameter beads were embedded in the imaging plane, positioned 5 mm away from the radial surface [Fig. 2(a)] and 10 mm distant from the CW illuminating at the bottom surface. Two of the alginate beads had different concentrations of 50-nm diameter gold nanospheres (AuNS)¹⁸ dispersed in them, while the third bead was a control with undiluted 20% stock Intralipid®. We used AuNS for this first study in preference to the more popular gold nanorods (AuNR) since spheres are simpler to synthesize, are not susceptible to pulsed laser-induced optical property changes, and do not require special treatments.¹⁸ Figure 2(a) shows the photograph of the object with the beads still visible during the fabrication of the test object. Figure 2(b) shows the optical absorption spectrum obtained from suspensions of AuNS at concentrations $c_1\sim {10}^{11}$ and $c_2\sim {10}^{10}$ (particles/ml) leading, respectively, to absorption coefficients (${\mu }_a$) of 2.5 and $0.26{\mathrm{mm}}^{-1}$ at 532 nm.

Fig. 2

(a) Photograph of top-view of the agar test object during fabrication showing the three alginate beads. Two of these beads contain different concentrations ($c1$ and $c2$) of gold nanospheres (AuNS) and the third bead was made from 20% stock Intralipid. (b) Absorption spectra of the used AuNS concentrations, (c) photoacoustic slice image shows the two absorbing beads with different contrasts, (d) the speed-of-sound (SOS) image shows the bead with Intralipid having a lower sound velocity than agar. The alginate beads with AuNS are not visualized.

2.3.

Measurement and Reconstruction Procedures

The experiments were performed at a room temperature of 25°C. A reference measurement is first made of the time-of-flight (TOF) of the passive element signals through water without the object. When the object is introduced, 10 projections around 360 deg are acquired, with 10 averages per projection: data for one 2-D image is acquired every 30 s. The object is imaged before CW illumination, and the PA and SOS maps are reconstructed off-line. The PA map is reconstructed using filtered backprojection. For the SOS images, the integrated TOF measurements are estimated when the sample is present for every passive element, at every detector element and every view. This is obtained by first calculating a reference template signal by averaging the received passive element signals of the reference measurement in water from all detection elements. Using a matched filter, the passive element signals of the object at each element for every view are correlated with the reference template. This results in TOF values, accurate up to the sampling period of the time signal, which gives an initial guess of TOF. Subsequently, we obtain subsample accuracy using a maximum likelihood estimator discussed in Ref. 19. From the TOF data, the SOS map is reconstructed using a ray-driven discretized measurement model. This is discussed in detail in Refs. 17 and 19.

We then performed photothermal heating of the AuNS-embedded beads by irradiating the object from below using the CW beam expanded to a diameter of 1 cm. The sequence is as follows: the injected power is increased from 1 to 3.3 W in steps of 0.5 W at intervals of 6 min except for the last increase, which was around 0.8 W; the power is then lowered to 1.5 W for 11 min, after which the illumination is switched off. The heating and cooling down sequence is completed within 40 min. Meanwhile, we continuously performed hybrid imaging of PA and SOS. The SOS tomogram images are converted to temperature maps using the relationship between SOS in water and temperature,²⁰ which is a valid first approximation since the objects and beads are composed of 98% water.

2.4.

Modeling

To support the experimental results, we modeled the experimental situation to verify the observed temperature evolution. Monte Carlo simulation²¹ was first used to estimate the absorbed energy at each bead position. The known optical properties of the object were used in the model, with the beads having a 4-mm diameter, positioned 10-mm deep from the illuminating surface. To reproduce the illumination conditions of the experiment, we have modified the illumination profile from the point source to a Gaussian profile by using inverse cumulative distribution function, which provides a photon injection position with a Gaussian probability distribution. The increase of irradiating power over time was described using a piecewise polynomial. The obtained absorbed energy density over time is then included as source in the heat-diffusion equation:

3.1.

PA and SOS Imaging

The US and PA images of the phantom are presented in Fig. 2. In the PA map of the object [Fig. 2(c)], we see the presence of two spheres with different contrasts, due to the difference in AuNS concentrations. The third sphere is not visible since it does not contain any absorbers. The SOS map [Fig. 2(d)], however, clearly shows the third bead with lower SOS than the surrounding area; the contrast arises due to the higher concentration of lipids in the bead than in agar. The other inclusions are not visible, suggesting that the used AuNS concentrations have few effects on the SOS. The differences in SOS between agar and water are also clearly visible.

3.2.

Temperature Monitoring

Figures 3(a) and 3(b) represent the SOS maps covering $40\times 40{\mathrm{mm}}^2$ at two different power levels. The images show the presence of confined SOS increase at the locations of the AuNS-embedded beads, whereas the SOS of the control bead and the surrounding agar remains unchanged. The SOS changes are due to the temperature rise in the beads and their immediate vicinity due to the photothermal heating and heat diffusion. The SOS maps are converted into temperature maps after subtracting the reference image before irradiation. Figure 3(c) shows a graph of the temperature increase sampled at three different locations in the temperature maps: the center of the ${\mu }_a=2.5{\mathrm{mm}}^{-1}$ bead, the center of the ${\mu }_a=0.26{\mathrm{mm}}^{-1}$ bead, and the center of the test object. A progressively step-wise increase in temperature is observed at the beads that follows the sequence of increasing optical power delivered. Within each step, a sharp rise in temperature is observed before a slow down to saturation after a few minutes of irradiation. This saturation is a consequence of the competition between the accumulated absorbed energy in the bead and heat diffusion to the surrounding medium. During the temperature increase sequence, the center of the object shows a 3°C increase due to heat diffusion from beads. When the optical power is reduced to 1.5 W, the temperatures at all locations drop to the same level observed during the rising sequence. When the laser is switched off, the temperatures return toward the initial baseline values.

Fig. 3

(a) and (b) SOS maps at two different levels of irradiation, (c) temperature evolution at three locations in the temperature maps estimated from the SOS tomograms: at center of bead with AuNS concentration $c_1$ (${\mu }_a=2.5{\mathrm{mm}}^{-1}$), at center of bead with concentration $c_2$ (${\mu }_a=0.26{\mathrm{mm}}^{-1}$), and at center of test object. The continuous (red) lines are obtained from simulation combining Monte Carlo and the heat diffusion equation.

Modeling was done based on a combination of Monte Carlo simulations for light propagation and absorption and solving of the heat diffusion equation for thermal propagation from the sites of optical absorption. The results are shown in Fig. 3(c) (red curves): we observe that the simulated temperature evolution corresponds well with the experiment for the bead with lower concentration. The experimentally derived temperatures for the bead with higher concentration are slightly lower than in the simulation, especially at higher powers. The deviations may be due to the inaccuracies in defining parameters related to illumination conditions, optical and thermal properties of the object and beads, and the exact depth. A faster temperature increase is also observed in the simulation compared to experiment. This is likely due to the experimentally slow acquisition time compared to the simulation.