Thermal Memory Based Photoacoustic Imaging of Temperature

Abstract

Temperature mapping is essential in many biomedical studies and interventions to precisely control the tissue’s thermal conditions for optimal treatment efficiency and minimal side effects. Based on the Grüneisen parameter’s temperature dependence, photoacoustic (PA) imaging can provide relative temperature measurement, but it has been traditionally challenging to measure absolute temperatures without knowing the baseline temperature, especially in deep tissues with unknown optical and acoustic properties. Here, we report a new thermal-energy-memory-based photoacoustic thermometry (TEMPT). By illuminating the tissue with a burst of nanosecond laser pulses, TEMPT exploits the temperature dependence of the thermal energy lingering, which is probed by the corresponding PA signals acquired within the thermal confinement. A self-normalized ratiometric measurement cancels out temperature-irrelevant quantities and estimates the Grüneisen parameter. The temperature can then be evaluated, given the tissue’s temperature-dependent Grüneisen parameter, mass density, and specific heat capacity. Unlike the conventional PA thermometry, TEMPT does not require the knowledge of tissue’s baseline temperature, nor the optical properties. We have developed a mathematical model to describe the temperature dependence in TEMPT. We have demonstrated the feasibility of the temperature evaluation on tissue phantoms at 1.5 cm depth within a clinically relevant temperature range. Finally, as proof-of-concept, we applied TEMPT for temperature mapping during focused ultrasound treatment in mice in vivo at 2 mm depth. As a generic temperature mapping method, TEMPT is expected to find applications in thermotherapy of cancers on small animal models.

1. INTRODUCTION

Thermotherapy (or hyperthermia therapy), including radiofrequency ablation, photothermal therapy and focused ultrasound, has been widely employed for cancer treatment [1, 2]. For example, high intensity focused ultrasound (HIFU) has been approved by the Food and Drug Administration (FDA) in the United States for the treatment of benign and malignant tumors [3–5]. Photothermal therapy, combined with near-infrared (NIR) photoabsorbers, has shown unique advantages in cancer therapy including high specificity, minimal invasiveness and precise spatial-temporal selectivity [6]. Monitoring the temperature in thermotherapy can help precisely control the heating process, efficiently kill the tumor cells, and minimize collateral damage to healthy tissues [7–10]. Various imaging techniques such as magnetic resonance imaging (MRI) [11–14] and ultrasound imaging [15–18] have been used for temperature mapping. However, MR thermometry, based on the temperature dependence of proton resonance frequency, is an expensive modality and suffers from the relatively low imaging speed [11, 12]. Ultrasound thermometry, based on the temperature dependence of speed of sound, can sense only relative temperature change, and still lacks high accuracy due to native tissue motion artifacts [15, 17].

Photoacoustic (PA) imaging is a promising technology for noninvasive temperature sensing, taking advantage of the linear temperature dependence of the tissue’s Grüneisen parameter [19–27]. However, taking ratiometric measurements at different temperatures, conventional PA thermometry can only measure the relative changes in tissue temperature, assuming that the optical properties of the tissue do not change when the temperature changes [28]. To determine the absolute temperature in tissue, ex vivo calibrations of tissues with known optical properties have to be performed by measuring the relative changes in PA signals at multiple reference temperatures [20–25]. The calibration-based PA thermometry has achieved a relatively high accuracy of ∼0.6°C on homogenous phantoms and have been applied in monitoring photothermal therapy [23, 24] and cryoablation of prostate tissue [25]. However, the calibration process using a thermal coupler in deep tissue is extremely challenging if possible at all in practical applications. Moreover, the assumption that the tissue can maintain its optical and acoustic properties over the temperature change is most likely invalid during intensive thermal treatment, in which the tissue typically undergoes drastic anatomical and functional changes, including elevated blood perfusion, protein coagulation, and tissue narcosis. Therefore, the calibration-based PA thermometry has not yet achieved successful translation to in vivo thermal therapy applications. Without the calibration process and without knowing the baseline temperature, most of the PA thermometry methods are limited to superficial tissues within the optical diffusion limit (~1 mm) [20, 29]. We previously reported another temperature measurement method using the dual-temperature dependences of Grüneisen parameter and the speed of sound in tissue [30]. Although this method has achieved the absolute temperature measurement in deep tissue, it assumes a homogeneous temperature distribution, which is invalid for thermotherapy with a highly confined heating region. We recently also reported a theoretical work on an optical-diffusion-model based method that can potentially measure the absolute temperature in deep tissue, which, however, requires a multi-illumination strategy that is challenging to implement in thermotherapy [31]. So far, there still lacks a reliable photoacoustic thermometry that can measure the absolute temperatures in deep tissues.

Here we report a new thermal-energy-memory-based PA thermometry (TEMPT) to quantify the absolute temperature distribution in deep tissues. In TEMPT, instead of using a single laser pulse, a burst of high-speed laser pulses are sequentially delivered to the target tissue within the thermal relaxation time (typically less than 1 second), and the corresponding PA signals are recorded to probe the target’s local temperatures right at each laser pulse excitation. While the very first PA signal carries the information of the tissue’s baseline temperature, the following PA signals reflect the slightly elevated local temperature induced by the consecutive laser pulses due to the lingering thermal energy within the target. In other words, the PA signal acquired with each laser pulse is related to the cumulative thermal effect of the earlier laser pulses. The same burst of laser pulses not only generate the thermal effect but also provide the PA signals to probe the heating process. Using the acquired PA signals, we have developed a mathematical model that correlates the PA signal’s time course with the tissue’s Grüneisen parameter. A ratiometric measurement can then be constructed to estimate the absolute temperature, by canceling out the remaining temperature-irrelevant quantities that are challenging to calibrate. Given the tissue’s temperature-dependent Grüneisen parameter, mass density, and specific heat capacity, which are typically similar across different tissue types, a tomographic map of absolute temperature can then be reconstructed. We have validated TEMPT in tissue phantoms and demonstrated its feasibility for temperature mapping during proof-of-concept HIFU treatment in vivo.

2. METHODS

A nanosecond laser pulse generates a PA signal with the initial pressure rise $p_1$ (Pa) (Fig. 1a), within the stress and thermal confinements. $p_1$ can be expressed as [20]

$$p_1={\mathrm{\Gamma }}_0\left(T_0\right)\eta {\mu }_a\varphi \delta t,$$ (1)

where ${\mathrm{\Gamma }}_{\text{0}}\left(T_{\text{0}}\right)$ is the Grüneisen parameter at the baseline temperature T₀ at an arbitrary time point t₀ during the thermotherapy process (Fig. 1b), $\eta$ is the conversion efficiency of non-radiative relaxation, ${\mu }_a$ is the optical absorption coefficient (cm⁻¹), $\varphi$ is the optical intensity (Watt/cm²) and $\delta t$ is the laser pulsewidth (sec). For simplicity, we will use ‘PA signal amplitude’ and ‘initial pressure rise’ interchangeably.

Fig. 1. The thermal energy memory effect in TEMPT.

(a) PA signal generation by a single laser pulse. (b) TEMPT measurement performed at time t₀ during the thermotherapy. The local temperature is T₀. (c) The temporal pattern of a burst of laser pulses used in TEMPT. (d) The thermal energy accumulation during the laser pulse burst leads to a local temperature rise. (e) The pattern of PA signals generated by the laser pulse burst. Note that PA signal amplitude depends on the local temperature when the laser pulse strikes. The accumulated thermal energy from earlier laser pulses leads to increased PA signal amplitudes by later pulses.

When a burst of laser pulses are used to excite the same object within the thermal confinement (or thermal relaxation time) ${\tau }_{th}$ (Fig. 1c), the lingered thermal energy from earlier pulses leads to the rise of the object’s temperature (Fig. 1d). The PA signal amplitude generated by each laser pulse thus becomes increasingly stronger due to the elevated local temperature (Fig. 1e). Assuming the number of laser pulses is N and the pulse-to-pulse time interval is t_p, and ${\tau }_{th}$ is much longer than the total burst duration $N\cdot t_p$, the PA signal amplitude $p_N$ induced by the Nth laser pulse can be expressed as below [32]:

$$\begin{gathered} p_N=\left({\mathrm{\Gamma }}_0\left(T_{\text{0}}\right)+\mathrm{\Delta }\mathrm{\Gamma }\right)\eta {\mu }_a\varphi \delta t \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\left[{\mathrm{\Gamma }}_0\left(T_{\text{0}}\right)+b\eta {\mu }_a\varphi \delta t(N-1)\right]\eta {\mu }_a\varphi \delta t,N\ge \text{2,} \\ where\hspace{0.17em}b=\frac{k_T}{\rho C_V}, \end{gathered}$$ (2)

where b is the first-order derivative of the Grüneisen parameter with respect to the absorbed photon energy, with a unit of cm³/J or Pa⁻¹. $k_T$ is the linear dependence of the Grüneisen parameter on the temperature (0.0086 for muscle). $\rho$ is the mass density of the tissue (1 g/cm³ for muscle). $C_V$ is the specific heat capacity at constant volume (3.8 J/g/K for muscle). The detailed derivation of Eq. (2) is included in the Supplementary materials. Because ${\tau }_{th}$ is much longer than t_p, we can neglect the diffusion of residual thermal energy by the previous laser pulse into surrounding tissues before the arrival of the next laser pulse. Moreover, because the total duration of the laser pulse burst is on the level of milliseconds and the thermotherapy heating time is typically on the level of seconds, thermotherapy-induced temperature change during the laser burst is negligible.

A ratiometric measurement can be obtained using the first and the $Nth$ PA signal amplitude $p_1$ and $p_N$:

$$\frac{p_N-p_1}{p_1^2}=\frac{b{\eta }^2{\mu }_a^2{\varphi }^2\delta t^2}{{\mathrm{\Gamma }}_0^2{\eta }^2{\mu }_a^2{\varphi }^2\delta t^2}\cdot (N-1)=\frac{b}{{\mathrm{\Gamma }}_0^2}\cdot (N-1),\hspace{0.17em}\hspace{0.17em}N\ge \text{2}$$ (3)

From Eqs. (1–3), the Grüneisen parameter ${\mathrm{\Gamma }}_{\text{0}}$ at baseline temperature T₀ (at the first laser pulse excitation) can be expressed as

$${\mathrm{\Gamma }}_{\text{0}}\left(T_{\text{0}}\right)=\sqrt{\frac{p_1^{2}b(N-1)}{p_N-p_1}},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}N\ge \text{2}.$$ (4)

Because b is close to that of water (2.3×10⁻³ cm³/J), Eq. (4) has provided a quantification of the Grüneisen parameter, because the other temperature-irrelevant quantifies are cancelled out, including the optical fluence and optical absorption coefficient. This is the major difference between the TEMPT method over the conventional PA thermometry. Finally, the baseline temperature T₀ can be computed based on the temperature-dependence of the Grüneisen parameter in soft tissues [33]:

$$T_0=115.89{\mathrm{\Gamma }}_0-\mathrm{13.14.}$$ (5)

Figure 2 summaries the key steps to implement TEMPT on a typical PAT system with a linear ultrasonic transducer array [34]. Step 1: With a burst of laser pulses, the PA signals by each laser pulse are acquired by the transducer array, and a series of 2D initial pressure rise maps are reconstructed by traditional PAT reconstruction algorithms [35–38]. Step 2: Ratiometric measurement is performed over the initial pressure rise maps and a 2D map of the Grüneisen parameter is reconstructed. Step 3: Based on the reconstructed Grüneisen parameter map, a 2D absolute temperature map at time point t₀ can be obtained based on Eq. (5). Again, the major innovation of TEMPT over conventional PA thermometry technologies is that the absolute temperature can be computed from the ratiometric measurement, provided the temperature-dependent Grüneisen parameter, mass density, and specific heat capacity of the tissue are known.

Fig. 2. Three key steps of TEMPT.

Step 1: PA signal excitation, acquisition, and reconstruction with a burst of laser pulses. Step 2: Ratiometric measurement and reconstruction of the Grüneisen parameter. Step 3: Absolute temperature mapping at a single time point and during the thermotherapy treatment.

In TEMPT, as indicated in Eq. (1), we need to convert the measured PA signals from voltages into pressures at the signal origin, which is a routine practice to calibrate the ultrasound detection system, as we have previously published [39]. In the calibration, we first used a calibrated wideband needle hydrophone to map the acoustic field of a point photoacoustic source in water generated by a focused laser beam, and then we used our ultrasound probe to detect the same acoustic field. Considering the geometry and detection sensitivity of each transducer element, we were able to build a voltage-to-pressure mapping table. Using the calibration table, we were able to convert the received PA signals back to pressures at the transducer surface, and then through image reconstruction back to the pressures at the signal origin. Since we are using low-frequency transducer and mainly focusing on small animal applications, the acoustic attenuation in the tissue is not considered.

3. RESULTS

To validate the feasibility of TEMPT, phantom experiments were performed by using a PAT system based on a Verasonics ultrasound scanner (Fig. 3a). An optical fiber with two branches guided the light from an Nd:YAG laser (InnoSlab, Edgewave, Germany; Wavelength: 532 nm) for PA excitation. The phantom was made of two slices of chicken tissues, each with a thickness of 1.5 cm. Two transparent plastic tubes (0.5 mm diameter) filled with black ink solution were sandwiched between the chick tissues. The ink solution was driven through a water bath by a syringe pump to achieve different steady temperatures. The temperature of the ink solution in the tube was measured by a needle thermocouple placed outside the imaging field of view. Another water tank was used for acoustic coupling between the tissue surface and the ultrasonic transducer probe (L7–4, Verasonics, USA; Central frequency: 5 MHz; −6 dB bandwidth: 3 MHz). PA signal detection was synchronized with the laser firing. Traditional B-mode ultrasound images were also acquired.

Fig. 3. TEMPT of temperatures on tissue phantoms.

(a) Schematic of the PAT system. UT, ultrasonic transducer. Two ink-filled tubes with different temperatures were sandwiched between two slices of chicken tissue (each 1.5-cm thick). (b) Reconstructed PAT image of the tissue phantom, showing the positions of the two tubes. (c) Increase in PA signal amplitudes of the two tubes as a function of the laser pulse number, reflecting the elevated local temperatures. (d) TEMPT temperature map of the two tubes (shown in color) overlaid onto the ultrasound image (shown in gray). The temperatures measured by the thermocouple in Tube 1 and Tube 2 were 32 °C and 40 °C, respectively. (e) TEMPT temperatures of the two tubes as a function of the reference temperatures measured by the needle thermometer.

The spatial resolution of the PAT system is ~400 µm along the axial and lateral dimensions, and ~1 mm along the elevational dimension [40]. The thermal relaxation time, determined by the resolution voxel size, is ~680 ms. In the phantom experiment, we used a pulse energy of 1 mJ at 532 nm. The average fluence was 0.5 mJ/cm² at the tissue surface. The black ink solution has an optical absorption coefficient of ~300 cm⁻¹ at 532 nm. The effective attenuation coefficient of chicken breast is about 1.5 cm⁻¹ at 532 nm, so the 1.5-cm chicken tissue should attenuate the light by roughly 10 times.

The ink temperatures in the tubes were adjusted by the water bath to mimic highly confined HIFU treatment. A burst of 600 laser pulses with a repetition rate of 10 kHz were delivered to the tissue phantom within 60 ms. Correspondingly, the Verasonics system acquired 600 frames of PA signals. A delay-and-sum method was used to reconstruct the PA images [35]. Repeated TEMPT measurements were performed with the ink temperature adjusted within the range of 20–55 °C. Figure 3b is a representative PA image showing the positions of the two tubes inside the tissue phantom. The PA signals were clearly elevated during the burst of 600 laser pulses (Fig. 3c), reflecting the increased local temperature. From the signal amplitude increase (~10%), we derived that the laser burst caused a ~2° C transient temperature rise that lasted for about 0.7 seconds before it started to return to the baseline. The entire cooling time may take up to several seconds, depending on the size of the absorbing target. Figure 3d shows the recovered TEMPT temperature map of the two tubes overlaid on the concurrent ultrasound image. For Tube 1, the recovered TEMPT temperature is 32.6 °C with the thermocouple measurement of 32.6 °C. For Tube 2, the recovered TEMPT temperature is 39.3 °C with the thermocouple measurement of 40 °C. Within the range of 20–55 °C, a highly linear correlation (R²=0.98) is obtained between the TEMPT temperatures and the preset temperatures measured by the thermocouple (Fig. 3e), with an average measurement error of ~0.9 °C.

Proof-of-concept in vivo experiments were conducted to validate TEMPT. The in vivo experiment protocol was approved by the Institutional Animal Care and Use Committee (IACUC) of Duke University [41]. All the procedures on mice were performed in accordance with the relevant guidelines and regulations. In order to quickly change the temperature distribution inside the mouse, a proof-of-concept HIFU system was coupled with the PAT system, as shown in Fig. 4. A 3D printed two-level animal mount was used to precisely align the PAT system with the HIFU system. The HIFU transducer (H-102, Sonic Concepts, USA; Focal length: 63 mm) was fixed at the bottom level of the 3D mount. The HIFU transducer was operated at 1.1 MHz (1st harmonic) with a duty cycle of 10%, driven by a function generator and a 55-dB power amplifier (A150, Electronic Navigation Industries, USA). The mouse was anesthetized with 1.5% (v/v) isoflurane and fixed at the top level of the 3D mount, which was slightly below the focus of the HIFU transducer. The mount was immersed in degassed water up to the bottom skin surface of the mouse for HIFU wave coupling. The HIFU focus was about 2 mm beneath the top skin surface of the mouse’s left hindlimb. Above the top surface of the mouse was another water tank filled with degassed water for PA signal coupling. Here, myoglobin in the mouse muscles and hemoglobin in the small blood vessels provided the major PA signal contrast [42]. Hemoglobin in the blood and myoglobin in the type I and II muscle have an optical absorption coefficient of ~230 cm⁻¹ and 80 cm⁻¹, respectively. For in vivo experiment, we used optical fluence of 1.5 mJ/cm² at 532 nm on the skin surface. Before we applied the HIFU treatment in vivo, we performed the traditional HIFU heating on a piece of fresh chicken tissue and measured the temperature rise using a 0.1 mm bare-wire thermocouple (Custom designed IT-23, Physitemp Inc, Clifton, NJ) inserted close to the HIFU focus. The HIFU heating dynamics were shown in Supplementary Fig. S1, which were consistent with our previous published results [43].

Fig. 4. Schematic of in vivo TEMPT during HIFU heating.

Note that the HIFU focus was located at about 2 mm beneath the skin surface of the mouse left limb.

A 5-second HIFU treatment with an average power of 900 Watt/cm² was applied to elevate the temperature in the HIFU focus inside the mouse limb muscle, during which the TEMPT measurements were repeatedly performed. Each TEMPT measurement took 60 ms, with a time interval of 2 seconds. The relatively long time internal was to avoid the confounding of laser burst heating and HIFU heating. Each TEMPT measurement induced a transient temperature rise of ~1 °C. The TEMPT results in vivo are shown in Fig. 5. Temperature maps at three HIFU heating time points (1 s, 3 s and 5 s) were recovered (Fig. 5b, Visualization 1). The results show that the temperature within the HIFU focus was quickly raised up to 67 °C, while the background temperature was largely maintained around the baseline (Figs. 5c–d).

Fig. 5. TEMPT of absolute temperatures in vivo during HIFU treatment.

(a) Reconstructed PAT image of the mouse left hindlimb. (b) TEMPT temperature maps at different HIFU heating times. Note that the temperature maps are thresholded at 37 °C. The dashed lines indicate the approximate the HIFU focus. (c) TEMPT temperatures (shown in color) overlaid on the corresponding ultrasound images (shown in gray). (d) TEMPT temperatures in the HIFU focus (red box in (a)) and in a representative surrounding tissue area (blue box in (a)) as a function of the heating time. (e) Conventional PA thermometry of relative temperature changes at different HIFU heating times. (f) Conventional PA thermometry of relative temperature changes in the HIFU focus (red box in (a)) and in the surrounding tissue (blue box in (a)) as a function of the heating time.

For comparison, using only the Grüneisen parameter’s temperature dependence, relative temperature changes were reconstructed by the conventional PA thermometry (Figs. 5e–f) [22], with the assumption of unchanged optical and acoustic properties of the tissue. As expected, the relative PA temperature map is less accurate than TEMPT, with reconstruction artifacts over the entire field of view, especially in the regions outside the HIFU focus (Visualization 2). This relatively low accuracy is resulted from the unknown tissue property changes during HIFU heating.

4. DISCUSSION

Without knowing the baseline temperature, conventional PA thermometry has long been limited to ratiometric measurement of relative temperature changes in superficial tissues. Such limitation is not due to the ratiometric measurement itself, but the optical and acoustic properties are incorrectly assumed time-invariant during thermal treatment. TEMPT has addressed this issue by applying ratiometric measurement within tens of milliseconds before any significant changes in optical or acoustic properties can actually happen. Moreover, TEMPT does not need the knowledge of baseline temperature. However, it is important to note that TEMPT needs the calibration of the ultrasound detection system for the initial pressure rise, which is not needed in the conventional PA thermometry. The acoustic pressure calibration is nevertheless much less challenging than calibrating the tissue’s optical properties in the conventional PA thermometry.

TEMPT is promising for noninvasive, calibration-free and absolute temperature mapping, based on the thermal energy memory effect. TEMPT includes three key steps (Fig. 2). In the first step, a burst of short laser pulses are used to slightly heat up the target, and the corresponding PA signals are acquired and the initial pressure rise is reconstructed at each laser strike. In the second step, the reconstructed time course of the initial pressure rise is fed into a ratiometric model that cancels out the temperature-irrelevant quantities and quantifies the Grüneisen parameter of the target. In the third step, the distribution of Grüneisen parameter is converted into the absolute temperature map, provided the temperature-dependent Grüneisen parameter, mass density, and specific heat capacity of the tissue are known.

The phantom experiment results have confirmed the feasibility and accuracy of TEMPT (Fig. 3). An average measurement error of 0.9 °C has been achieved within the range of 20–55 °C at a 1.5 cm depth in tissue. The temperature accuracy is comparable to that of the reported MR thermometry [44] and ultrasound thermometry [45]. The in vivo experiments have demonstrated the performance of TEMPT in clinically relevant conditions, in which poof-of-concept HIFU heating was applied during the temperature mapping. Temperature elevation in the HIFU focus in the mouse hindlimb was clearly observed while the surrounding tissues were largely spared, consistent with literatures [46, 47] (Fig. 5). These results have collectively demonstrated the temperature mapping capability of TEMPT.

The burst duration (or the number of laser pulses) used for each TEMPT measurement eventually determines the speed, accuracy, and spatial resolution of the temperature mapping, and should be jointly considered with the available laser pulse energy and repetition rate. Generally speaking, a long burst improves the temperature measurement accuracy but reduces the measurement speed. A short burst may not induce sufficient thermal accumulation and thus PA signal increase, leading to reduced temperature measurement accuracy. Nevertheless, from Eq. (3), the duration of the laser burst should be much shorter than the thermal relaxation time of the target, which is a fundamental requirement to maintain the spatial resolution of the temperature mapping. Accordingly, the upper limit of the number of laser pulses is ${\tau }_{th}/t_p$. In our phantom and in vivo experiments, the number of laser pulses was 600 (or a total duration of 60 ms), which is much lower than the theoretical limit of 6800, and thus a good balance between the measurement accuracy and speed was achieved.

The time consumption of TEMPT measurement is another important metric, since real-time temperature monitoring is highly desired during thermotherapy treatment. In general, TEMPT can provide a sub-second temperature mapping. In our phantom and in vivo experiments, for each TEMPT measurement, the data acquisition took only 60 ms and the temperature map reconstruction took 500 ms. For more time-sensitive applications, the reconstruction speed can be improved by reducing the field of view of the temperature map and incorporating large-scale parallel computation [48].

Another important factor in TEMPT is the temperature elevation induced by thermotherapy heating during each laser burst, which may cause an underestimation of the temperature. To this end, the laser burst should be as short as possible so that the thermotherapy heating during each TEMPT measurement is negligible. In our proof-of-concept in vivo experiments, the temperature increase induced by HIFU heating during the laser burst was estimated to be ~0.3 °C, which was less than the thermal accumulation caused by the 600 laser pulses (~1 °C). However, it is clear that the thermotherapy heating during the TEMPT measurement is an error source, and thus should be minimized by shortening the laser burst. Moreover, TEMPT induced heating should also be minimized to avoid interruption to the thermotherapy treatment.

TEMPT eventually turns to the temperature dependence of the tissue’s Grüneisen parameter. Based on the literature, a linear temperature dependence in soft tissues (including muscles, blood and skin) is valid within the temperature range of approximately 4–75 °C, which covers typical thermotherapy procedures [19, 49]. We previously also reported PA temperature sensing on blood-rich soft tissue, in which we experimentally validated the linear dependence of the Grüneisen parameter in the temperature range of 10–55 °C [30]. Several studies have reported nonlinear or dual-linear temperature dependence of the Grüneisen parameter especially when the temperature exceeds the tissue’s coagulation threshold or the tissue has a high percentage of fat [49–51]. We believe that such non-linear dependence may be largely due to measurement errors caused by the changes in tissue’s optical/acoustic properties. In TEMPT, the absolute temperature is recovered from the estimated Grüneisen parameter only in the last step, so a nonlinear temperature dependence can be readily incorporated into our model. Previous work also shows that the optical fluence may affect the Grüneisen parameter’s temperature dependence [33]. We suspect that it is because the optical excitation actually changed the tissue’s optical and acoustic properties (e.g., coagulation). This has indeed highlighted the major merit of the TEMPT method, which is less sensitive to the change in tissue’s optical and acoustic properties during the HIFU treatment.

Variation of b and the thermal relaxation time among different tissue types will also contribute to the final temperature measurement accuracy. Based on the literature, the specific heat and thermal diffusion coefficient of the most common types of tissues (except fat, lung and bone) actually do not have significant variations, mainly because of the large water content (>70%) in these soft tissues [52, 53]. For example, the specific heat is 3.8 J/g/K for muscle and 3.68 J/g/K for brain. The thermal diffusion coefficient is 0.1289 mm²/s for muscle and 0.1283 mm²/s for brain. Therefore, we don’t expect significant errors induced to the temperature measurement by the variations in specific heat and thermal diffusion coefficient. Nevertheless, for tissues that have substantial amount of fat (such as abdominal tissue) or air (such as lung) [49], it is necessary to use different values of tissue properties to improve the measurement accuracy.

The temperature rise will change the speed of sound in the tissue and thus induce PA reconstruction errors. In our study, the transient temperature rise due to PA heating was at most 2 degrees, which would induce a 0.2% increase in the speed of sound. Such a small change in speed of sound is insignificant due to the relatively low spatial resolution of our PA system. However, for HIFU treatment, the temperature rise can be as high as 30 to 40 degrees, which will induce significant change in speed of sound in the HIFU focus. In this proof-of-concept work, we did not consider the impact of the HIFU heating on the speed of sound in the in vivo experiment, because the HIFU focus was highly confined within a few millimeters. The speed of sound change in the HIFU focus was unlikely to induce significant reconstruction errors. Nevertheless, our model can be further improved by incorporating the speed of sound in the image reconstruction.

Given the limited penetration depth of light, we expect TEMPT will find more applications in biomedical studies on small animal models including immunotherapy, tissue ablation, and drug delivery, while the clinical applications will be limited to superficial disease such as skin cancers [54, 55]. In practice, the biological tissue undergoing thermal treatment are unlikely to have strong optical absorption. Therefore, the transient temperature rise in TEMPT should be lower than that demonstrated in the phantom study. We propose three potential solutions to this critical issue. (1) We can increase the incidence light energy within the ANSI safety limit. By using NIR light, we will be able to use even stronger energy. (2) By further increasing the time interval between bursts, we will be able to use stronger light pulse without breaking the ANSI limit on the average optical power on the skin surface. (3) When longer optical wavelengths in the NIR region are used, the endogenous biomolecules will not provide strong absorption and thus sufficient transient temperature rise for TEMPT. In this case, we can use exogenous contrast agents, such as highly-absorbing NIR photosensitizers hat have been widely used in photothermal therapy [56–60]. These exogenous contrast can also be functionalized to specifically target the tumors to improve the heating efficiency of TEMPT.

Finally, heat convection due to blood flow is another channel of thermal dissipation for in vivo applications. However, the impact of convection may not be that significant. First, TEMPT is intended for thermal therapy studies in small animal models. The average blood flow speed in mouse muscle and skin is typically less than 2 mm/s [61]. The TEMPT measurement time is within 60 ms in our demonstration or less in the future. Therefore, the displacement of blood within TEMPT measurement is less than 120 µm, which is less than the spatial resolution (or voxel size). Reducing the spatial resolution by low-pass filtering will further minimize the convection impact. Nevertheless, our current model will be less accurate if we use hemoglobin as the imaging contrast in large blood vessels. In the future work, we will combine TEMPT with tumor-targeting exogenous NIR probes, which can provide larger penetration depth and less dependence on hemoglobin.