# Automatic volumetric temperature regulation during in vivo MRI-guided laser-induced thermotherapy (MRg-LITT) with multiple laser probes

Manon Desclides, Valéry Ozenne, Pierre Bour, Thibaut Faller, Guillaume Machinet, Christophe Pierre, Julie Carcreff, Stéphane Chemouny, Bruno Quesson

► To cite this version:

Manon Desclides, Valéry Ozenne, Pierre Bour, Thibaut Faller, Guillaume Machinet, et al. Automatic volumetric temperature regulation during in vivo MRI-guided laser-induced thermotherapy (MRg-LITT) with multiple laser probes. Computers in Biology and Medicine, 2024, 184, pp.109445. 10.1016/j.compbiomed.2024.109445. hal-05369559

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# Automatic volumetric temperature regulation during in vivo MRI-guided laser-induced thermotherapy (MRg-LITT) with multiple laser probes

Manon Desclides<sup>a,b,*</sup>, Valéry Ozenne<sup>a</sup>, Pierre Bour<sup>b</sup>, Thibaut Faller<sup>b</sup>, Guillaume Machinet<sup>c</sup>, Christophe Pierre<sup>c</sup>, Julie Carcreff<sup>c</sup>, Stéphane Chemouny<sup>b</sup>, Bruno Quesson<sup>a</sup>

## ARTICLE INFO

**Keywords:**

MR-thermometry

LITT

PID

Regulation

Thermotherapy

Multiple laser probes

## ABSTRACT

**Background:** Clinical Laser-Induced Thermotherapy (LITT) currently lacks precise control of tissue temperature increase during the procedure. This study presents a new method to automatically regulate the maximum temperature increase in vivo at different positions by adjusting LITT power delivered by multiple laser probes using real-time volumetric MR-thermometry.

**Methods:** The regulation algorithm was evaluated in vivo on a pig leg muscle. Temperature regulation was performed in volumes surrounding each laser probe tip. The power delivered to each laser probe was automatically adjusted every second using a feedback control algorithm by processing on-the-fly MR-thermometry images (10 slices/second) on a 1.5 T clinical scanner (1.56 mm × 1.56 mm × 3 mm resolution), using the proton-resonance frequency (PRF) shift technique. Several experimental conditions were tested with predefined temperature-time profiles corresponding to conditions of thermal ablation (+30 °C above body temperature) or moderate hyperthermia (+10 and +15 °C). Control images were acquired after injection of Gadolinium at the end of experiment and were compared with the thermal dose images calculated from the thermometry images.

**Results:** The mean difference and root mean squared error between target temperatures and measured ones remained below 0.5 °C and 2 °C respectively, for 5 min duration. Lesion sizes observed on thermal dose and on images acquired after gadolinium injection were in good agreement.

**Conclusion:** Automatic regulation of in vivo temperature increase during LITT procedures with multiple laser emitters control is feasible. The method provides an adaptative solution to improve the safety and efficacy of such clinical procedures.

## 1. Introduction

Laser Induced Thermal Therapies (LITT) are established minimally invasive surgical procedures to treat tumors [1] in various organs (e.g. prostate [2,3], liver [4–6], brain [7,8]) or epilepsy [9]. Whatever the application, laser light energy is applied to the targeted tissue through an optical fiber to induce temperature elevation leading to cell death in the treated region.

In this context, MR-thermometry can map temperature elevation during thermal ablative procedures in various organs (e.g. in the brain [10,11], in the liver [5,12] and in the prostate [13,14]) using the proton resonance frequency shift (PRFS) technique [15]. The resulting temperature images and associated cumulative thermal dose maps were

used to assess treated and untreated tissues in real time, and to avoid damaging healthy or sensitive areas.

In current clinical procedures, the laser power and emission duration are arbitrarily set based on predefined operating modes provided by the manufacturer, often resulting from experiments performed on ex vivo tissue. However, tissue perfusion can play a major role in heat evacuation, thus laser power must be increased in vivo. It has been reported that excessive power deposition often leads to tissue charring and bubble creation near the laser probe tip [16], preventing precise control of the therapy. The generation of bubbles near the probe tip can also create significant susceptibility artifacts on MR-thermometry sequences [17, 18] that result in temperature maps of poor quality, leading to therapeutic failure in a significant number of cases, as reported for the brain

<footnote><sup>a</sup> University of Bordeaux, CNRS, CRMSB, UMR 5536, IHU Liryc, Bordeaux, France</footnote>

<footnote><sup>b</sup> Certis Therapeutics, Pessac, France</footnote>

<footnote><sup>c</sup> ALPhANOV, Talence, France</footnote>

<footnote>* Corresponding author. IHU Liryc, Avenue du Haut Lévéque – Site Xavier Arnosan, 33600, Pessac, France.</footnote>

<footnote>E-mail address: manon.desclides@u-bordeaux.fr (M. Desclides).</footnote>
[19].

On a more sophisticated approach than basic temperature monitoring, MR-thermometry could be used to interactively adapt local energy deposition by modulating the emitted laser power in real time to force tissue temperature to follow a predefined temperature-time profile. Such an approach avoids reaching excessive temperature increase, therefore reducing risks of tissue boiling or carbonization. A recent study [20] reported the possibility of automatically regulating temperature during LITT in pig muscle in vivo using a single optical laser probe. Multiple laser probes can be inserted into the tissue with individual adjustable power with objective of creating larger ablation sizes [21–23] by compensating heat sink effects of perfusion, and generating conformal thermal ablation [24]. To fully exploit such possibilities, MR-thermometry should ideally cover the complete ablation zone (several centimeters) in 3D, be precise (around 1–2 °C) to compute relevant thermal dose images, be spatially resolved (around millimetric spatial resolution) and rapid (around 1 s update time).

We present in this study a method to automatically control tissue temperature at multiple positions simultaneously during LITT using several laser probes connected to a programmable multichannel laser generator. An automatic regulation algorithm integrating the Bio Heat Transfer Equation (BHTE) is combined with fast volumetric MR-thermometry to force tissue temperature in predefined regions to follow predefined target profiles. The tissue thermal parameters of the BHTE and the heating pattern of each laser probe in the targeted tissue, which are input parameters for the controller, are experimentally estimated in a calibration step. The method was successfully evaluated in vivo on a large animal model using a clinical MRI scanner.

## 2. Material and methods

### 2.1. Animal preparation

Experimental validation of the temperature regulation was performed in vivo in the leg of a pig. The protocol was approved by the ethics committee Comité d'Ethique en Expérimentation Animale of Bordeaux n°50 (CEEA50, France) and was performed following European rules for animal experimentation. After sedation of the animal by intramuscular injection of Ketamine (10–20 mg/kg), acepromazine (0.1 mg/kg), and Buprénorphine (9 µg/kg), the animal was anesthetized with an intravenous injection of Propofol (1–2 mg/kg). Then, it was intubated and ventilated at 15 breaths per minute using an MR-compatible ventilator (Aestivia, General Electric, Fairfield, CT, U.S.A.) and placed in the MRI scanner in the supine position. Continuous breathing of isofluorane (1.5–3%) in a mixture of air/oxygen 50/50 helped maintain anesthesia during the whole experiment. Intra-arterial pressure and cardiac rhythm were monitored during the entire experiment (Carescape, General Electric, Fairfield, CT, U.S.A.).

### 2.2. Laser device

The laser generator was a customized prototype (ALPhANOV, France) which consisted of a module comprising six fiber-coupled laser diodes (976 nm wavelength, core diameter of 200 µm and numerical aperture of 0.22). In our experiments, three laser probes prototypes (CeramOptec GmbH/Biolitec, Germany) terminated with a 2 cm-long diffuser inserted in a 1.8 mm-diameter glass bundle were used. Each probe was connected to one laser diode which could emit at a maximum power of 18 W. The output power of each diode was independently controllable through TCP-IP communication. Spatial characterization of the heating produced by the probes used in this study was done with MR-thermometry. To do so, one laser probe with a 2 cm diffusing tip was inserted in the leg of an anesthetized pig. Then, 6 W were applied for 30 s under MR-thermometry. This experiment was repeated twice, positioning the stacks of MR images in 2 different orthogonal directions to characterize the heating pattern of the probe in 3D.

### 2.3. MR-imaging protocol

MRI data were acquired on a 1.5 T clinical scanner (Avanto, Siemens Healthineers, Germany). A 4-channel array coil was positioned above the leg, and two elements of the coil integrated into the MRI bed (12 channels in total) were combined to acquire the MR signal. For each experiment, the following imaging pipeline was used.

#### 2.3.1. Probes placement and localization

First, a 3D MPRAGE (Magnetization Prepared RApid Gradient Echo) sequence was acquired (TI = 1100 ms, TE = 3.3 ms, TR = 2000 ms, FA = 15°, 1.17 mm × 1.17 mm × 1 mm voxel resolution, Field Of View (FOV) = 300 mm × 253 mm × 120 mm) and analyzed on the manufacturer console to define the entry points of the MR-compatible introducers (KIM13/14T, Innovative Tomography Products GmbH, Germany) and the targeted location within the thigh muscle. Small skin incisions were performed to facilitate the insertion of each introducer at the predefined depth. Particular attention was paid to inserting the introducers parallel to each other and the three laser probes were approximately distant from each other by 2 cm. The 3D MPRAGE sequence was repeated to verify the resulting position and a slight correction in position was performed if necessary. Then, the laser probes were introduced in place of the trocar of the introducer. Each introducer was then carefully withdrawn by 2.5 cm to expose tissue to the diffusing tips of the probes. The 3D MPRAGE sequence was repeated to confirm the positions of the probes.

#### 2.3.2. MR-thermometry acquisition

Three orthogonal slices centered on the positions of the diffusing tips were generated from the reformatted MPRAGE volume and served to position a stack of 10 contiguous MR-thermometry slices oriented perpendicular to the laser probes to cover a volume of 3 cm depth centered on this region. The sequence was a multi-slice single-shot gradient echo planar imaging sequence (EPI) [25,26] with the following parameters: TE = 21 ms, TR = 1000 ms, FA = 50°, 1.56 mm × 1.56 mm × 3 mm voxel resolution, GRAPPA acceleration = 2, partial Fourier = 6/8, EPI factor = 48, bandwidth/pixel = 1150 Hz, and FOV = 200 mm × 200 mm. The number of repetitions was adjusted to cover the duration of the laser emission followed by a cooling period and the thermometry volume (10 slices) was updated every second (100 ms/slice).

#### 2.3.3. Real-time implementation

Thermometry images were reconstructed in real-time from streamed raw data within the Gadgetron framework [27] using the PRF technique (PRF constant of -0.0094 ppm/°C) and a reference phase image corresponding to the average of the 10 first repetitions. For each slice and at every repetition, the phase drift was estimated and compensated with a spatio-temporal first-order polynomial function on voxels with high SNR, as already proposed [26]. Thermal dose images were computed by applying the Cumulative Equivalent Minutes at 43 °C model [28] with a lethal threshold set at 240 min.

In addition, a dedicated Gadgetron module implementing the regulation algorithm was added to the pipeline immediately after thermometry reconstruction to calculate the power to be applied for the temperature to follow target profiles and to transmit the command directly to the laser generator at each new stack of thermometry slices (update rate 1 Hz).

Both thermometry and thermal dose images were displayed in real-time (Certis Solution, Certis Therapeutics, France), and a homemade Python GUI was used in parallel to show temperature regulation curves.

#### 2.3.4. Post-ablation acquisition

At the end of the experimentation, gadoteric acid (0.5 mmol/kg, Clariscan Gé®, GE Healthcare) was injected intravenously, and 3D T1-weighted images were acquired 1 min later to visualize the non-perfused volumes, using the following parameters: TE = 2.16 ms, TR = 4.49 ms, FA = 10°, 1.19 mm × 1.19 mm × 1.2 mm voxel resolution,
FOV = 308 mm × 380 mm × 120 mm. Images were visualized in the manufacturer's console and reformatted with the imaging orientation of the thermometry images.

by each laser probe is not possible. Indeed, the temperature evolution in a ROI can be induced by the contribution of several heating sources. However, it is possible to calculate the temperature evolution $x_m$ required to follow the target temperature in each ROI:

$$x_m(t \to t + \Delta t) = \frac{\partial T_{t,m}(t)}{\partial t} - D \cdot \nabla^2 T(r_{max,m}, t) + \omega_b T(r_{max,m}, t) + q \xi_m(t) + \frac{q^2}{4} \int_0^\tau \xi_m(t) \, d\tau \quad (4)$$

## 2.4. Automatic multipoint temperature regulation algorithm

A way to link a power $p(t)$ applied by a heating source of spatial distribution $S(\vec{r})$ on a tissue to its temperature evolution $\frac{\partial T(\vec{r}, t)}{\partial t}$ at a time $t$ and location $\vec{r}$, is to use the Bio Heat Transfer Equation (BHTE) given in Eq. (1):

$$\frac{\partial T(\vec{r}, t)}{\partial t} = D \cdot \nabla^2 T(\vec{r}, t) - \omega_b \cdot T(\vec{r}, t) + \alpha \cdot S(\vec{r}) \cdot p(t), \quad (1)$$

where $D$ (mm²·s⁻¹), $\omega_b$ (mL·mL⁻¹·s⁻¹) and $\alpha$ (°C·s⁻¹·W⁻¹) are the thermal diffusivity, perfusion, and absorption of the sample, respectively.

Using this equation to directly compute the power to apply could be considered but may lead to unstable regulation because of temperature measurement noise and estimation uncertainties on $D$, $\omega_b$, and $\alpha$ values. To improve the stability of the regulation process, a proportional, integral, and derivative (PID) controller can be introduced (Eq. (2)):

$$q \xi(\vec{r}, t) + \frac{q^2}{4} \int_0^\tau \xi(\vec{r}, t) d\tau + \frac{\partial \xi(\vec{r}, t)}{\partial t} = 0, \quad (2)$$

Since the equation Eq. (4) needs to be computed for each ROI (thus $M$ times), a direct consequence of increasing the number of regulated regions is a longer computation time, which can be detrimental to the stability of the algorithm. Moreover, calculating the Laplacian of temperature values with the finite element method in each ROI is intrinsically prone to noise due to the computation of the second derivative over the space of temperature images. Alternatively, we computed the temperature spatial derivative $\nabla^2 T(\vec{r}, t)$ term once for the entire image, corresponding to the temperature decrease by thermal diffusivity between two consecutive measurements, in the Fourier space over the spatial coordinates:

$$\nabla^2 T(\vec{r}, t) = FT^{-1}[-k^2 T^*(\vec{k}, t)], \quad (5)$$

with $T^*(\vec{k}, t)$ the Fourier transform of $T(\vec{r}, t)$ over spatial coordinates.

Temperature increase terms $x_m$ associated with each controlled ROI $m$ can then be computed and grouped in the matrix $X$ of size $(M, 1)$, so that $X = (x_m)_{1 \le m \le M}$ with:

$$x_m(t) = \frac{\partial T_{t,m}(t)}{\partial t} + D \cdot FT^{-1}[k^2 T^*(\vec{k}, t)](r_{max,m}, t) + \omega_b T(r_{max,m}, t) + q \xi_m(t) + \frac{q^2}{4} \int_0^\tau \xi_m(t) \, d\tau \quad (6)$$

where $\xi(\vec{r}, t)$ is the error at a time $t$ between the target temperature $T_t(\vec{r}, t)$ and the measured one $T(\vec{r}, t)$.

The controller equation (Eq. (2)) allows to compensate for the current error (proportional term), while taking into account past errors to reduce the static error (integral term), and to predict future errors (derivative term). The combination of PID controller equation and Bio Heat Transfer Equation leads to the expression (Eq. (3)) of power $p$ to be applied from time $t$ to time $t + \Delta t$ to force the temperature $T(r_{max}, t+\Delta t)$ to follow the target temperature $T_t(t+\Delta t)$ at position $\vec{r} = r_{max}$ (position of the voxel with maximal measured temperature rise in the controlled Region Of Interest):

$$p(t \to t + \Delta t) = \frac{1}{\alpha \cdot S(\vec{r})} \left[ \frac{\partial T_t(t)}{\partial t} - D \cdot \nabla^2 T(r_{max}, t) + \omega_b \cdot T(r_{max}, t) \right. \\ \left. + q[T_t(t) - T(r_{max}, t)] + \frac{q^2}{4} \int_0^\tau [T_t(t) - T(r_{max}, t)] d\tau \right] \quad (3)$$

A similar expression was initially proposed for single-point regulation using HIFU [29] or LITT [20].

For a multiple-point regulation using multiple laser probes (and thus multiple heating sources), direct computation of the power to be applied

and with $\xi_m(t)$ the error at time $t$ between the target temperature $T_{t,m}(t)$ and the maximum temperature $T(r_{max,m}, t)$ in the associated ROI $m$.

Once we know the temperature evolution $X(t)$ required to reach the desired temperature in each controlled ROI, we need to translate them into actual power $p_n$ to be emitted from each of the $N$ probes taking into account the relative contribution of their heating distribution $S_n$ to a given ROI (see paragraph 2.5 for determination of $q_{m,n}$). This is expressed by the following equation (Eq. (7)):

$$x_m(t) = \sum_{n=1}^{N} q_{m,n} \cdot p_n(t) \quad (7)$$

Unknown powers $P(t) = (p_n)_{1 \le n \le N}$ to apply to each probe $n$ at time $t$ can then be found by solving the equation Eq. (8):

$$Q \cdot P(t) = X(t) \quad (8)$$

At every new dynamic, the position $\vec{r} = r_{max}$ of the maximum temperature point measured was updated for each ROI used for regulation, after eliminating noisy voxels (i.e. voxels with SNR < 5 % of the maximum of the average magnitude over 8 consecutive frames or with a temperature standard deviation before heating superior to 2 °C) to avoid estimating power to apply from noisy temperature data. The voxels in
the ROIs satisfying this condition were labelled “valid” voxels.

The regulation algorithm was implemented in a dedicated gadget in C++ in the Gadgetron thermometry pipeline. Eq. (8) was solved by linear regression using the LAPACK library with imposed limits on solutions such as $0 \le p_n < 14$, 14 W being considered as the maximum power needed to achieve the temperature rises required for this work. All experiments were performed with an Intel Xeon® W-2275 CPU @ 3.30 GHz × 28 cores.

## 2.5. Calibration step

Before automatic temperature regulation, a calibration step was performed for each probe to obtained information needed by the regulation algorithm i.e. 1) the location of the hottest voxel associated to each probe in the thermometry imaging stack, 2) the tissue thermal parameters, and 3) the heating distribution of each laser probe.

To do this, a laser emission at low energy (6 W for 30 s) was applied successively on each probe under continuous MR-thermometry (see paragraph 2.3 for details on acquisition parameters and temperature processing), observing a cooling period of 50 s between each emission. These low-power shots (one per probe, three in total) were then analyzed.

Firstly, the hottest voxel was selected for each probe emission and a 3x3 voxels region of interest was automatically selected around its position. Each ROI was propagated along all slices, resulting in 3 × 3 × 10 voxels-sized ROIs surrounding each laser probe. All the ROIs defined at this step were injected into the regulation algorithm, determining regions where to control temperature.

Secondly, thermal diffusivity $D$ (mm²·s⁻¹) and perfusion $\omega_b$ (mL·mL⁻¹·s⁻¹) of the tissue were estimated from the same dataset using fits to the bio-heat-transfer equation (BHTE) for each individual laser probe and results were averaged, assuming those parameters to be constant over the ablation zone, as previously proposed by Dragonu et al. [30].

Thirdly, the heating distributions $S_n(\vec{r})_{n \in [1,...,N]}$ ($N$ being the number of probes used for temperature regulation) were characterized by injecting the previously determined $D$ and $\omega_b$ parameters into the so-

lution of the Fourier-transformed expression of the BHTE [31] according to the following equation (Eq. (9)) (detailed calculations are provided in the appendix):

$$ \alpha S_n(\vec{r}) = TF^{-1} \left[ \frac{k^2 D + \omega_b T^*(\vec{k}, t + \Delta t) - e^{-(k^2 D + \omega_b) \Delta t} T^*(\vec{k}, t)}{p_n \left( 1 - e^{-(k^2 D + \omega_b) \Delta t} \right)} \right], \quad (9) $$

where $p_n$ is the power set to the laser diode connected to the $n$th probe during the fixed period $\Delta t$, $T^*(\vec{k}, t)$ is the Fourier transform of the temperature map at time $t$ and $D$ (mm²·s⁻¹), $\alpha$ (°C·s⁻¹·W⁻¹) and $\omega_b$ (mL·mL⁻¹·s⁻¹) are the thermal diffusivity, absorption, and perfusion of the sample, respectively.

To reduce the impact of measurement noise on the estimation of $\alpha S_n(\vec{r})$, this calculation was iterated over each temperature map acquired during the heating period of the $n$th probe showing a maximum temperature increase higher than 3 °C. The results were averaged together and each slice of the resulting 3D matrix $\alpha S_n(\vec{r})$ was then fitted to a 2D Gaussian function.

To consider the case where a ROI has its voxels heated by several probes, it is necessary to know the contribution of each heating source to the temperature rise in each region. To do this, a matrix $Q = (q_{m,n})$ is created once the $M$ ROIs have been selected and the $N$ heating distributions calculated, where $q_{m,n}$ is equal to the maximum contribution of the heating distribution of the $n$th probe in the $m$th ROI i.e. $q_{m,n} = \max(\alpha S_n(\vec{r})_{\vec{r} \in ROI_m})$. This matrix is then used in the temperature regulation algorithm.

Implementation of thermodynamic parameters computation and heating distributions estimation was done in Python language and took approximately 10 s to be executed for each probe.

## 2.6. Analysis of the efficiency of temperature regulation

The efficiency of the temperature regulation algorithm was analyzed by computing mean and root mean squared errors (RMSE) between target and maximum temperature in their associated ROIs as a function

<figure><img src="image_3.png" /><figcaption>Fig. 1. Spatial characterization of laser probe energy deposit. Isotherms images corresponding to two MR-thermometry acquisitions performed in orthogonal views, with the left image (transversal view) placed parallel to the tip of the laser probe, and the right image (coronal view) placed perpendicular to the probe tip, at the position indicated by the green dashed line in the left image. The heating pattern visible in the images was produced by applying 6 W for 30 s in a pig leg muscle. Isotherms are drawn above the magnitude of MR-thermometry acquisitions and their X and Y spatial profiles (white lines) are plotted. An indication of the fiber position is given by the red dashed line.</figcaption></figure>
of time during the different plateaus of regulation. The mean error during heating indicates if the measured temperature is close to the target while the RMSE value assess the stability of the regulation.

The temporal mean and standard deviation of each voxel of each ROI over the 20 repetitions before starting temperature regulation were also computed. The maximum mean in the ROIs before heating is an indicator of the temporal stability of MR-thermometry and the standard deviation is a measure of the uncertainty of the MR-thermometry.

# 3. Results

## 3.1. Laser probe

Spatial characterization of the heating produced by the diffusing probe is presented in Fig. 1. Resulting temperature isotherms superposed to magnitude images of the MR-thermometry sequence are displayed in the corresponding transversal (left image) and coronal (right image) views. Spatial profiles of temperature increase along white lines are plotted next and below corresponding images (Y and X directions respectively). Temperature increase along the probe is homogeneous over the entire length of the 2 cm diffuser tip (left image, probe represented by the red dashed line) and displays a full width at half maximum in the orthogonal directions (image right) around 8 mm.

## 3.2. Probes placement and calibration step

A calibration step performed in vivo before automatic temperature regulation is presented in Fig. 2. The first part of Fig. 2 (part A) shows a coronal (left image) and two transversal (images on the right) views. The resulting temperature slices acquired at the end of the shot with the first probe (t = 60 s) are shown as an illustrative example in Fig. 2B as well as the 3 × 3 × 10 voxels ROI created to control the region around this probe (black rectangles). The heating distribution of this probe is shown in Fig. 2C. The thermal diffusivity and perfusion estimated from temperature data of the three low-power shots were averaged together, with resulting values of $D = 0.17 \pm 0.04 \text{ mm}^2 \cdot \text{s}^{-1}$ and $\omega_b = 5 \pm 2 \times 10^{-3} \text{ s}^{-1}$.

## 3.3. Temperature regulation

Four experiments of automatic temperature regulation performed with several diffusing laser probes inserted into the leg muscle of a pig are presented in Fig. 3. Tissue thermal parameters ($D = 0.17 \text{ mm}^2 \cdot \text{s}^{-1}$, $\omega_b = 5 \times 10^{-3} \text{ s}^{-1}$) determined from data of the first experiment (corresponding to data shown in Fig. 2) were kept identical in each experiment and $q$ was empirically chosen equal to $q = 0.3 \text{ s}^{-1}$.

Experiments A and B were performed using three probes with identical target temperature-time profiles in their respective ROIs, targeting a unique plateau of 20 °C temperature increase for experiment A during 300 s and of 30 °C for experiment B during 275 s. Experiments C and D were performed using two probes with different target temperature-time profiles. In experiment C, two successive plateaus – of 10 °C and 15 °C temperature increase during 90 s and 110 s respectively – were planned in the first ROI while a single plateau of 15 °C increase during 215 s was planned in the second ROI. In experiment D, target profiles were composed of two successive plateaus of 15 °C and 25 °C, lasting 65 s and 120 s respectively for the first ROI, and a unique plateau of 25 °C during 180 s for the second ROI.

Experiments A and B aim at demonstrating that temperature control with identical targets could be performed on three probes simultaneously. Since temperature increase may influence precision of MR-thermometry, two different final target temperatures were chosen (+20 °C and +30 °C, respectively). Experiments C and D were designed to demonstrate the possibility to regulate tissue temperature simultaneously around two probes with different targets. The method was tested for two different final temperature increases (+15 °C and +25 °C). These experiments were designed to assess the performance of

the regulation algorithm under different configurations.

For each experiment, we observe that the temperature in each ROI follows the predefined target profile. Temperature maps obtained in the middle of each plateau are shown above curves (t = 250 s for exp. A and B, t = [150, 250] s for exp. C and D), showing the spatial extent of the temperature distribution for each experimental condition.

Corresponding power curves for each experimental condition and associated comments are provided in Supplementary Fig. 2.

## 3.4. Regulation algorithm performance

Both mean errors and root mean square errors between target profiles and maximum temperature measured in their associated ROIs were computed to quantify the precision of the algorithm. Resulting values are reported in Table 1, as well as the mean and standard deviation of voxels inside ROIs before heating, for comparison. Overall, the results show a maximum below ($0.29 \pm 1.67$ °C (mean error $\pm$ RMSE) with a maximum mean value of $0.14 \pm 1.05$ °C (mean $\pm$ STD) inside ROIs before heating. Thermometry was stable with a minimum number of valid voxels of 88 out of 90 initially included in each ROI.

We observed a constant latency (about 2 s) between the completion of the MR stack or slice acquisition and the effective update of the laser power on each source. This latency included ~1 s for MR-thermometry reconstruction (for 10 slices) in the Gadgetron pipeline and between 300 ms and 900 ms for power computation (depending on the convergence speed of the regression). The latency between sending a power order and its actual update in the laser generator was measured at around 500 ms.

## 3.5. Thermal dose images and non-perfused volumes

Temperature maps and associated thermal doses of all slices at the end of temperature regulation for each example are shown in Fig. 4. It can be seen that every ROI – represented by black rectangles – includes the hottest point and that for the same type of probe used, the positioning, the degree, and the duration of tissue heating produce different ablation shapes and sizes.

In addition, Fig. 5 shows (i) two slices of computed thermal doses from thermometry data at the end of experiments A and B and (ii) two reformatted slices (in position and orientation to the thermometry sequence) from the 3D volume acquired after gadolinium injection at the end of the session to visualize the non-perfused volume (NPV). The measured ablation sizes (width, length) on thermal dose maps and NPV images are (2 cm, 3.4 cm) vs (1.8 cm, 3 cm) for experiment A, and (3.2 cm, 3.3 cm) vs (3.4 cm, 3.8 cm) for experiment B, respectively.

# 4. Discussion

This work shows the possibility of automatically regulating tissue temperature at different positions and in real-time during the LITT procedure by using multiple and independent laser sources under real-time multi-slice MR-thermometry guidance (10 slices/sec).

The proposed multi-point regulation algorithm has been evaluated in vivo in a pig leg muscle using a clinical scanner (1.5 T) and prototype laser probes. It is based on our method previously proposed in Ref. [20] for the regulation of a single laser probe (PID, low power initial shot) and on the resolution of the BHTE by Fourier transform used to control HIFUs in Ref. [31].

In our approach, no assumption is made regarding the tissue thermal properties. In practice, these parameters (absorption, diffusivity and perfusion) are estimated at the beginning of each procedure by performing the initial low-power calibration shot previously proposed [20]. The method was tested in vivo in a leg muscle tissue in this study, and could be applicable to other organs such as the liver or brain, for example. The only requirement for this calibration is to achieve a sufficient accuracy (~1 °C standard deviation) of the MR-thermometry in
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Calibration step example. (A) Thermometry stack of slices (blue rectangle) placement shown on a 3D MPRAGE coronal view (left image) and two transversal views (green and red slices). Transversal views correspond to slices highlighted with red and green lines on the coronal view. Laser probes were spaced by approximately 2 cm and are represented by white, yellow, and pink arrows. (B) MR-temperature maps at the end (t = 60 s) of the first laser probe initialization shot (6 W for 30 s), ROI placement around the maximum heating point covering all slices (black rectangle) and probe tip indicated by the red arrow. (C) 2D fitted heating distribution of the first probe used for temperature regulation.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 3.** Multipoint automatic temperature regulation in a pig leg muscle for experiments A, B, C, and D. Target temperature profiles are displayed in solid and dashed black lines. Maximum temperature increase measured in the 3 × 3 × 10 voxels of ROIs #1, #2, and #3 are represented with red, blue, and yellow markers respectively. ROIs positions are represented by colored squares on schematic views, top left of each graph. Black crossed data are temperature values in non-heated voxels to verify the stability of thermometry during experiments. Image insets: temperature maps obtained in the middle of each temperature plateau.</figcaption></figure>

**Table 1**

**Regulation algorithm evaluation.** A table containing 1) spatio-temporal mean and mean of temporal standard deviation of temperature voxels of each ROI before heating (during the 20 s preceding the start of regulation), and 2) the temperature mean error and root mean squared error (RMSE) between the target temperature profile and maximum temperature measured in its associated ROI, for each ROI and each plateau, as well as the minimum number of valid voxels (regarding the conditions defined in 2.4) observed during the entire experiment.

<table><thead><tr><th rowspan="2">Experiment</th><th colspan="3">Before heating</th><th colspan="4">Regulation</th></tr><tr><th>ROI (#)</th><th>&lt;T&gt;</th><th>&lt;σ<sub>T</sub>&gt;</th><th>Target T (°C)</th><th>Mean error (°C)</th><th>RMSE (°C)</th><th>Minimum # of valid voxels(/90)</th></tr></thead><tbody><tr><td rowspan="3">A</td><td>1</td><td>0.14</td><td>1.04</td><td>20</td><td>0.03</td><td>0.91</td><td>90</td></tr><tr><td>2</td><td>0.09</td><td>0.99</td><td>20</td><td>0.28</td><td>1.13</td><td>90</td></tr><tr><td>3</td><td>-0.02</td><td>0.89</td><td>20</td><td>0.17</td><td>1.63</td><td>90</td></tr><tr><td rowspan="3">B</td><td>1</td><td>0.03</td><td>1.04</td><td>30</td><td>-0.01</td><td>1.67</td><td>89</td></tr><tr><td>2</td><td>0.1</td><td>1.03</td><td>30</td><td>0.19</td><td>1.38</td><td>89</td></tr><tr><td>3</td><td>-0.02</td><td>1.05</td><td>30</td><td>0.09</td><td>1.23</td><td>90</td></tr><tr><td rowspan="3">C</td><td>1</td><td>0.14</td><td>0.92</td><td>10</td><td>0.28</td><td>1.28</td><td>88</td></tr><tr><td></td><td></td><td></td><td>15</td><td>0.19</td><td>1.08</td><td></td></tr><tr><td>2</td><td>-0.05</td><td>0.99</td><td>15</td><td>-0.02</td><td>1.22</td><td>90</td></tr><tr><td rowspan="3">D</td><td>1</td><td>-0.09</td><td>0.97</td><td>15</td><td>0.19</td><td>1.01</td><td>90</td></tr><tr><td></td><td></td><td></td><td>30</td><td>0.29</td><td>1.41</td><td></td></tr><tr><td>2</td><td>-0.05</td><td>0.91</td><td>30</td><td>0.14</td><td>1.02</td><td>88</td></tr></tbody></table>

the targeted organ, which was already established for various organs such as brain [32–34], prostate [35,36] and liver for example [37–40].

The calibration dataset used for thermal tissue properties estimation also served to experimentally characterize the heating distribution

function of each probe and to automatically determine their position within the image stack. Thus, the method may easily be applied to any LITT device, such as straight laser probes with/without a diffuser at their tip [41], probes with different diffuser lengths [42], probes with lateral
<figure><img src="image_9.png" /><figcaption>**Fig. 4.** Comparison of ablation sizes and shapes between thermal dose images and non-perfused volumes. Thermal doses computed from thermometry data at the last repetition of experiments A and B (t = 500 s) over their respective magnitude (i) and non-perfused volumes zoomed on ablation resulting in experiments A and B (ii) at approximately the same position than in (i), with length (red lines) and width (green lines) measurements.</figcaption></figure>

illumination [11], or a combination of them.

Consequently, the duration of the initial low-power calibration increases with the number of probes. In this study, this calibration step took around 5 min for 3 probes due to successive illumination of each probe interleaved with cooling periods. From the perspective of a clinical application, this calibration step may be shortened and used only for probes localization. Indeed, tissue thermodynamic parameters could be extracted from the literature for most of the organs to be treated [43]. Even in case of slight differences between experimental and literature values, the PID controller should be able to accommodate such variations and provide efficient temperature regulation as shown in previous work [44,45]. The heating distribution of the probes might also be characterized once in a phantom to create a model to integrate directly into the regulation algorithm, requiring only defining the position of each probe in a 3D volume. However, in presence of a large vessel in the vicinity of one or several heat sources, calibration may still be required since the heat sink effect in such a configuration may substantially modify the temperature distribution in the tissue surrounding the probe (s) compared to the model(s) and result in suboptimal temperature regulation. Such a situation could not be investigated here since the central objective of the study was to propose and evaluate the feasibility of multipoint temperature regulation during LITT in the muscle.

Multi-slice MR-thermometry allows visualization and control of temperature distribution in 3D. In our implementation, a 3x3 voxels ROI was positioned on the hottest point around each probe during the calibration step and duplicated on each slice, leading to a 3 × 3 × 10 voxels-sized ROI associated with each probe. The benefit of these volumetric ROIs is to take into account all voxels that can potentially be heated by all probes and ensure that the maximum temperature increase around each probe follows the target temperature. However, this requires that the probe diffusing tip is strictly perpendicular to the imaging stack, which is unlikely to be always feasible in clinical practice, and impossible if the probes are oriented differently. Defining each probe

trajectory in the imaging stack by manual or automatic segmentation or enlarging the ROI dimension to encompass the heating voxels in each slice would circumvent such a limitation.

The temperature regulation algorithm showed good performances for up to three diffusing probes spaced by approximately 2 cm. Only few small oscillations of the controlled temperature were observed which may result from potential errors in the PID terms [45] and from the assumption that the thermodynamic coefficients of the tissue were temporally and spatially constant. Since the regulation is performed over a volume covering 10 slices (i.e. 3 cm) and considering that each thermodynamic coefficients may vary with temperature [43], such an assumption may remain questionable. Irreversible damage reduces tissue perfusion (see Fig. 4) and protein denaturation associated with temperature increase may also modify the absorption and thermal diffusion coefficients during the procedure. However, combining the BHTE model with a PID controller allowed to achieve good temperature regulation for each tested configuration. Another simpler implementation of the PID may consist of not including the BHTE into the controller, as proposed in Ref. [46]. However, this requires fine tuning of each coefficient of the PID for each practical configuration, which increases the risk of creating additional temperature oscillations and larger differences between target and measured temperatures. For these reasons, we preferred to incorporate the BHTE into the PID controller, including estimation of tissue thermal parameters and characterization of each source from the calibration step. The residual oscillations in the controlled temperature may also result from suboptimal adjustment of the system response time that was chosen empirically and kept constant throughout the experiments. Despite this, the root mean squared error remained below 2 °C (maximum was 1.67 °C for the +30 °C regulation plateau), which was considered acceptable given the reduction of thermometry accuracy at high temperature increase due to T1 lengthening and T2* shortening. Moreover, the average error remained close to 0, with a maximum mean offset value of 0.3 °C. Two examples of
<figure><img src="image_10.png" /><figcaption>Fig. 5. Observation of ablation sizes and shapes with thermal doses. Temperature (i) and thermal dose (ii) images of experiments A, B, C, and D at the end of the regulation (t = [430, 430, 305, 335] seconds respectively. Black rectangles represent ROIs used for automatic regulation.</figcaption></figure>

temperature regulation at +20 °C and +30 °C above body temperature for 5 min are presented, leading to sufficient thermal energy deposition to reach a lethal thermal dose, as confirmed by post-ablation (NPV visualization) 3D images. We also show two other examples of temperature regulation, at different temperature targets, with two laser probes. Such a feature opens interesting perspectives for exploiting non-lethal temperature increase (e.g. delivery of encapsulated drugs into thermally sensitive nanoscale containers [47,48]) – as in experiment C, where only a few voxels reached the lethal thermal dose – or creating different ablation shapes with several probes arranged in different spatial configurations.

In order to remain reliable, the proposed regulation algorithm requires a precise thermometry. This is related to 1) the spatial resolution and volume coverage of the acquisition sequence with respect to the heated region by the laser probe, 2) the update time of the MR-thermometry with respect to the target temperature curve, and 3) the uncertainty of MR-thermometry relative to the maximal target temperature. In our configuration, we measured temperature over a volume of 3 cm positioned around a laser diffuser of 2 cm length. The update time of 1 s was sufficient to control temperature during several minutes of heating and the standard deviation of thermometry remained around 1 °C. Such conditions appear relevant in the context of LITT for oncology applications in static organs (e.g. brain, prostate). Robustness of the method should however be investigated under different situations, for example in the liver, where thermometry standard deviation may be higher and update time of the temperature measurements will be increased to compensate for respiratory motion. Stable respiratory

triggered MR-thermometry on the liver has already been reported, at the cost of an update time of several seconds. The combination of a PID controller and a physically realistic model of temperature evolution in tissue proposed here is however expected to compensate for the need of frequent update of MR-thermometry.

## 5. Conclusion

In conclusion, our approach shows that conformal LITT ablation can be achieved. The proposed regulation algorithm is fast enough to ensure an online update of laser power on multiple laser probes although 10 temperature slices are acquired continuously with 1 s update time. Therapeutic systems with several laser outputs are commercially available but still operate as standalone devices or in combination with basic MR-thermometry monitoring, including only a few slices acquired at a slower frame rate. The present study shows the potential improvement offered by real-time multi-slice temperature monitoring to favor synergistic heating from several sources when combined with automatic control of thermal energy deposition on multiple laser probes simultaneously. The proposed algorithm may thus be used to optimize existing therapies, avoiding inducing excessive temperature increases in structures to be preserved (e.g. brain structures surrounding the tumors or erectile nerves and rectum wall for the prostate), while ensuring reaching the lethal thermal dose in targeted pathologic tissue.
### CRediT authorship contribution statement

**Manon Desclides:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Conceptualization.
**Valéry Ozenne:** Writing – review & editing, Software, Methodology.
**Pierre Bour:** Writing – review & editing, Software, Resources.
**Thibaut Faller:** Software, Resources.
**Guillaume Machinet:** Resources.
**Christophe Pierre:** Resources.
**Julie Carcreff:** Resources.
**Stéphane Chemouny:** Software, Resources, Funding acquisition.
**Bruno Quesson:** Writing – review & editing, Writing – original draft, Validation, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Manon Desclides reports a relationship with Certis Therapeutics that includes: employment. Bruno Quesson reports a relationship with Certis Therapeutics that includes: consulting or advisory and equity or stocks. Valéry Ozenne reports a relationship with Certis Therapeutics that includes: consulting or advisory and equity or stocks. Pierre Bour reports a

relationship with Certis Therapeutics that includes: employment. Thibaut Faller reports a relationship with Certis Therapeutics that includes: employment. Stephane Chemouny reports a relationship with Certis Therapeutics that includes: employment and equity or stocks. Guillaume Machinet reports a relationship with ALPhANOV Optical and Laser Technological Centre that includes: employment. Christophe Pierre reports a relationship with ALPhANOV Optical and Laser Technological Centre that includes: employment. Julie Carcreff reports a relationship with ALPhANOV Optical and Laser Technological Centre that includes: employment. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

Stéphane Bloquet and Virgine Loyer are gratefully acknowledged for their assistance during the animal experiment. This study was conducted in the framework of the University of Bordeaux's IdEx "Investments for the Future" program RRI "IMPACT" that received financial support from the French government. This work was partly funded by research grants from Agence Nationale de la Recherche (projects CARCOI (ANR-19-CE19-0008-02) and IHU-LIRYC (ANR-10-IAHU04-LIRYC)).

## Appendix

The BHTE is given by Eq. (A.1):

$$ \frac{\partial T(\vec{r}, t)}{\partial t} = D \nabla^2 T(\vec{r}, t) - \omega_b T(\vec{r}, t) + \alpha S(\vec{r}) p(t), \quad (A.1) $$

A way to solve this equation is to apply the Fourier transform on spatial coordinates so that the equation becomes the following 1st-order differential equation:

$$ \frac{\partial T^*(\vec{k}, t)}{\partial t} + (k^2 D + \omega_b) T^*(\vec{k}, t) = \alpha S^*(\vec{k}) p(t) \quad (A.2) $$

Leading to the solution:

$$ T^*(\vec{k}, t + \Delta t) = e^{-(k^2 D + \omega_b) \Delta t} T^*(\vec{k}, t) + \frac{1 - e^{-(k^2 D + \omega_b) \Delta t}}{k^2 D + \omega_b} \alpha S^*(\vec{k}) p(t) \quad (A.3) $$

By applying the inverse Fourier transform on spatial coordinates, one can get the expression of the spatial distribution of the heating distribution $\alpha S_n(\vec{r})$:

$$ \alpha S_n(\vec{r}) = TF^{-1} \left[ \frac{k^2 D + \omega_b}{p_n} \frac{T^*(\vec{k}, t + \Delta t) - e^{-(k^2 D + \omega_b) \Delta t} T^*(\vec{k}, t)}{1 - e^{-(k^2 D + \omega_b) \Delta t}} \right] \quad (A.4) $$

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.compbiomed.2024.109445.

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