Mild hyperthermia by MR-guided focused ultrasound in an ex vivo model of osteolytic bone tumour: optimization of the spatio-temporal control of the delivered temperature

The procedure was performed using an MR-compatible phased array HIFU transducer (Imasonic, Besançon, France). The transducer was a spherical cap of radius 130 mm working at a frequency of 1.031 MHz and powered by a 256-channel beam-former (Image Guided Therapy, Pessac, France). The most central 172 elements of the transducer were active yielding an aperture of 120 mm (f-number = 1.08). The applied acoustic power was 60 W, which corresponds to 432 W/cm² at the focal point according to a study by Saletes and al. [64]. The duty cycle was adapted on-the-fly to the measured tissue temperature, as detailed below. In these conditions, the wave propagated essentially in linear regime with a focal negative peak pressure of -3.6 MPa and a focal positive peak pressure of 4 MPa. Hynynen K. [65] demonstrated this pressure range does not produce inertial cavitation.

Experiments were carried out on a 3T MRI scanner (Prisma Fit, Siemens) with an 11 cm diameter receive loop coil. Geometry of the tissue sample and HIFU transducer were verified on a high resolution T1-weighted 3D MR sequence with spatial resolution and a T1 contrast optimized for visualization of cortical bone, bone marrow, muscle and tissue mimicking gel (gradient echo, TE = 2.46 ms, TR = 5.36 ms, flip angle = 10°, bandwidth [BW] = 390 Hz/pixel, slice thickness = 0.8 mm, isotropic voxel).

Temperature elevation in tissue mimicking gel and muscles was measured using the PRFS method. As already reported, PRFS method does not apply to the cortical bone nor the bone marrow [66, 67]. Here a single slice, segmented gradient echo EPI GRE-EPI sequence was acquired, either perpendicular or parallel to the bone axis, with a spatial resolution of 1 mm × 1 mm × 4 mm and a temporal resolution of 1.6 s. The imaging parameters were: a 1-2-1 binomial spectrally selective pulse train to exclude the fat signal, TE = 8.46 ms, TR = 70 ms, EPI factor = 7, flip angle = 15°, BW = 698 Hz/pixel, acquisition matrix 128 × 128, FOV = 128 × 128 mm, number of averages = 1 and phase encoding direction parallel to the B₀ field. The current TE value appeared to be the best compromise between magnitude SNR, phase CNR and partial volume mitigation at bone interface.

B₀ drift correction is mandatory over a long period of MR acquisition. Therefore, PRFS thermometry data was corrected for background phase drift using a small unheated ROI positioned in the muscular tissue unheated by the HIFU beam.

An anatomic model mimicking osteolytic bone tumors was used, consisting of drilled and mechanically excavated lamb tibia in situ. The procedures were performed in a bath of 0.9% NaCl physiologic serum, to avoid the penetration of air.

We started with a thin incision on the superficial aponeurosis and muscles in front of the desired target. A deeper incision was made over the intermuscular septus to expose the tibial shaft. A marking point on the surface of the bone was made with a scalpel. This marking point was further used as the starting point for bone drilling with an initial cylindrical bit of 6 mm diameter. In a second step, a larger cylindrical bit (10 mm diameter) or a conical bit (Fig. 2a) were used to reproduce an osteolytic lesion. The effect of the drilling was controlled interleaved with conventional radiography (Fig. 2b). Curettage was performed in order to create a bone medullar cavity by removing the fat. After drilling the cortical bone, an orthopedic surgical 10 mm curette was used to excavate the medullary fat, to remove it and thereby to produce lacuna mimicking a lytic bone tumor. Cavity size was dependent on the bone diameter, the latter was measured retrospectively to be between 7.6 and 15.5 mm (Fig. 3a, b). Medullar cavities were filled with tissue-mimicking gel [68, 69], exhibiting thermo-acoustic properties similar to soft tissue. The gel was composed of water (80.1%), glycerol (11.2%) added to adjust the acoustic velocity, agar (3%) added to adjust the stiffness and SiO₂ (5.59%) added to adjust the acoustic attenuation [68]. Ramnarine et al. [69], reported the gel properties to be very similar to human tissue, namely: speed of sound = 1541 ± 3 cm s⁻¹, attenuation = 0.5 ± 0.03 dB cm⁻¹ MHz⁻¹ over a frequency range of approximately 3–10 MHz, and density = 1054 ± 1 kg m⁻¹. The mixture was liquid above 50 °C and set as a gel in a less than one minute after intra-cavitary injection via a 16G needle. Standard ultrasonic gel was applied at the interface between the cavity and muscles. The procedure was finished by sewing the different teguments with a surgical knot using non-absorbable 2–0 suture (PolysorbTM, Covidien, Dublin, Ireland).

The prepared lamb shank was degassed for 30 min under vacuum to prevent exogenous cavitation nuclei and near field scattering. Then, the shank was placed in the aperture of the MR loop coil and acoustically coupled with the HIFU transducer, see Fig. 3c. The tibia was lying approximately horizontal and the sample was rotated to approximately align the cortical breakthrough with the main direction of the HIFU beam (vertical). Fourteen experiments were conducted on six bone specimens (Table 1). A single focal point was positioned (1) in front of the medullar cavity, (2) in the plane of the cortical breakthrough or (3) inside the medullar cavity. Each scenario was tested with preset power sonication and controlled hyperthermia at + 6 °C above baseline, maintained within the tissue-mimicking gel for 12 min.

MR thermometry in the cortical bone is limited, mainly due to the lack of signal as the T2* is very short. Thus, in order to assess the method’s safety with respect to bone heating, the temperature in the cortical bone was monitored using a gold standard method, namely a fluoroptic temperature sensor (0.9 mm diameter, STF-5, Luxtron, Santa Clara, CA, USA) ensuring a precision of 0.1 °C for relative temperature measurement. To this purpose, the cortical bone was drilled nearly parallel to its long axis with a thin bit (1 mm diameter), at a 10° angle relative to the tangential direction, until approximately 2/3 of the cortical thickness. Standard ultrasonic gel was injected in the resulting “tunnel” for optimal thermal coupling and finally the sensor was inserted into (Figs. 2c, 3a). PRFS thermometry measurements in soft tissue adjacent to the periosteum were cross-correlated with the fluoroptic measurements inside the cortical bone. Since fluoroptic sensors will not be available during clinical application, these correlations will allow the extrapolation of PRFS measurements to the cortical bone region for safety assessment.

Extensive work has been reported for temperature control of ultrasound based thermal therapy [23, 24, 70, 71]. Some commercial products including Sonalleve^® and TUSLA^® devices from Profound Medical (2400 Skymark Avenue, Unit, Mississauga, ON L4 W 5K5, Canada), have standard capabilities for automatic feedback. These systems are insufficient for the current application due to the prolonged temperature elevation delay inside the cavity after HIFU sonication. The feedback control should predict temperature elevation for several minutes in advance.

A predictive temperature controller was designed, which automatically adjusted the acoustic energy deposition. A temperature elevation inside the medullar cavity is obtained via two mechanisms. The first mechanism is the direct absorption of focused ultrasound beam around the focal point, located in the tissue-mimicking gel or in the skeletal muscle in front of the cortical breakthrough. The second mechanism consists of the so-called “acoustic oven effect”, namely a high absorption of the post-focal acoustic energy on the internal facet of the cortical wall, followed by passive heat flow centripetally inside the cavity. The second mechanism, simulated quantitatively in the next section, yields a temporal lag between the acoustic power command and the temperature response at the location of the focal point, on the order of 1 min and increasing with the size of the cavity.

Practically, heat conduction requires a time interval to propagate the temperature elevation from the internal cortical facet to the actual location of the focal point. The designed temperature controller aims to stabilize the temperature elevation at the location of the focal point according to a prescribed level. The propagation delay between the input signal and the output function of a regulated system is a well-known problem impacting the process stability. This problem can be alleviated either using a long dwell time of the regulation loop (defined as the time interval after which the controlled parameter is modified), or a predictive physical model to anticipate the system response. Since increasing the dwell time would impact the precision, which is incompatible with the rather narrow range of acceptable temperature elevation for mild hyperthermia, we opted for a predictive approach.

In order to keep the acoustic intensity invariant during active periods of HIFU energy delivery, the controlled parameter was chosen to be the sonication duty cycle δ, varying in the interval [0, 1]. The amount of energy, E, delivered to the tissue during the acquisition of one MR thermometry map with temporal resolution \(\Delta t\) is expressed as:where P is the measured acoustic power, calibrated in the free field using the radiation force balance. The hyperthermia treatment starts with the initial condition \(\delta = \delta_{0}\). The temperature controller is activated when the temperature elevation in a small ROI around the focus reaches an out-of-noise threshold defined here at 1.5 °C, which was 5 to 10 times the noise standard deviation of the input function.

The temperature elevation above the physiological baseline at the focal point location, using a sonication duty cycle \(\delta\), is denoted as \(T\left( {\delta , t} \right).\) The physical principle is to estimate the asymptotic level of temperature elevation that would be reached if the parameter \(\delta\) was kept constant, \(T\left( {\delta , t \to \infty } \right)\), see Fig. 4a. Ideally, this estimation should match the prescribed level of temperature elevation, denoted as \(T_{target}\). Otherwise, the parameter \(\delta\) should be increased or decreased, depending on the position of the asymptote below or above the prescribed level. Thus, the update of the parameter \(\delta\) after \(n\) intervals of dwell time is calculated using the following master equation:

The asymptotic level of temperature elevation \(T\left( {\delta , t \to \infty } \right)\) is estimated from the measured temperature values within a temporal sliding window of observation. The length of the observation window \(t_{obs}\) was empirically chosen (here, 32 s) to be half of the dwell time of controller (here, 64 s), in order to achieve a compromise between robustness against measurement noise when computing the numerical derivative, and reaction speed of the temperature controller. The estimation of \(T\left( {\delta , t \to \infty } \right)\) at any time point \(t_{0}\) during hyperthermia is based on approximating the further evolution of the temperature elevation at the focal point as a mono-exponential function (Fig. 4a). The details of the estimation are presented in Appendix 1.

Theoretically, the sonication duty cycle can vary between 0 and 1. However, the effective range of 0.1 to 0.9 to accommodate the time request for hardware communication, switching delays, and feedback power meters. Since the master equation of the temperature controller [2] is multiplicative, we have chosen as starting value for this parameter the geometric mean between the two extremes, namely \(\delta_{0} = 0.3\). Practically, every half second the beam former emits a pulse length of \(0.5 \cdot \delta\) (s), followed by an off period of \(0.5 \cdot \left( {1 - \delta } \right)\) (s).

A Matlab^® (MATLAB 9.2, MathWorks, Inc., Natick, Massachusetts, USA) numerical simulation estimated the time lag between the application of sonication and focal point peak temperature elevation. The simulation also suggested the optimal focal point position relative to the bone cavity. The bone was modelled as a cylinder of radius Rc. The radius of the cortical bone (Rc) in the axial plane was varied in the range of 6 to 10 mm, and the focal point position was prescribed at various loci relative to the center of the breakthrough in the range (− R_c, R_c). To mimic an osteolytic tumour, the cavity in the bone diaphysis was simulated as the intersection between the bone cylinder and a cone of aperture 72°, whose axis was normal to the cylinder axis, and whose apex was on the cylinder axis. A single element transducer of focused ultrasound was considered, with diameter 120 mm, radius 130 mm, and operating frequency 1 MHz.

The physical interaction HIFU beam/bone is a complex phenomenon [72, 73]. The analytical description of the underlying physics is considered beyond the scope of this report. Instead, we shall further employ a semi-empirical model that is consistent with the observed thermal effects. The following aspects were considered: (1) the acoustic properties are significantly different in cortical bone as compared to the adjacent soft tissue, by a factor of 2 in term of celerity and a factor of 3.6 in term of mechanical impedance; these differences are generating strong boundary conditions (reflection, refraction and, above the critical incidence angle, evanescent waves); (2) due to its solid structure, the bone supports the generation and propagation of shear waves in addition to the longitudinal compressional wave; (3) the thickness of the studied cortical bone (i.e. a few millimeters) is comparable with the wavelength of compressional and shear waves, and also comparable to the penetration depth of evanescent waves.

An evanescent wave can be described as a near-field wave, which is traveling along a boundary, so that the pressure and particle motion amplitudes decay exponentially as a function of the actual depth into the surrounding media. Multiple boundary reflections can occur as a wave travels forth and back inside the cortical bone, e.g. “wave guide” effect. Petrusca et al. [41] described near isotropic isotherms around near field sonicated ribs, that is, thermal patterns rotationally invariant with respect to the direction of the incident HIFU beam. In our numerical computation, we modelled these phenomena as a global averaging operator applied to the acoustic energy distribution within the segment of the cortical bone crossing the conical HIFU beam.

The thermal effect of the absorbed acoustic waves was computed as a three-step process. The technique is similar to the approach described by Salomir [71]. First the complex pressure field and the acoustic intensity generated by the transducer was calculated. Then the effect of the cortical bone was taken into account by extracting the acoustic intensity along the 3D cortical bone internal facet exposed to the HIFU beam, and applying an averaging operation on the respective surface (mean intensity). This step models the mechanical energy redistribution mentioned above and observed by [41], also called herein “acoustic oven effect”. Finally, heat diffusion during HIFU sonication was simulated by iterative convolution with a Gaussian kernel [71], considering both the cortical and tumoral absorption. The details of the computation are provided in Appendix 2.

The results of the simulations are presented in Figs. 5 and 6. The cortical source of thermal energy is illustrated in Fig. 5a, and the cumulated source of cortical and tumoral thermal energy is illustrated in Fig. 5d. Post-sonication tissue cooling was simulated similarly to Eq. (A9) by nulling the \(\alpha\) and \(\beta\) coefficient. The relaxation process following a short sonication (i.e. impulse response function) is illustrated in Fig. 5b, c for the cortical source, and in Fig. 5e, f for the cumulated source.

The analysis of the impulse response, shown in Fig. 5, indicated that the main contribution to the intra-cavitary heating is the “acoustic oven effect” on the cortical border. However, because of the cortical breakthrough, the isotherms would remain asymmetric. The other source of energy, namely the direct heat deposition around the focal point, positioned at the site of the breakthrough, had the role to bridge the circumferential isotherms. The symmetry of the resulting isotherms was influenced by several factors, namely the size of the breakthrough, the actual position of the focus and the ratio of ultrasound absorption between the cortical bone and tumoral tissue. In general, the balance of these factors under the typical conditions of an osteolytic tumour yielded approximately circumferential isotherms. The heat diffusion tended to attenuate the residual inhomogeneities, if any, as seen in Fig. 5f.

The analysis of long duration sonication confirmed the generation of circumferential isotherms under the effect of the double source of heating and the heat diffusion (Fig. 6). When the focal point was shifted inside the cavity, a “hot spot” was detected at the proximal internal facet of the cortex, as the two heating sources were locally cumulated (Fig. 6g). This configuration may yield a thermal risk. Reciprocally, when the focal point was set at the center of the breakthrough, the temperature map evolved more rapidly towards a uniform spatial profile (Fig. 6e). Finally, shifting the focal point opposite to the cavity (Fig. 6b) had less influence of the local cortical heating. However, when the size of the breakthrough was small, this condition yielded hot spots at the edges of the breakthrough. Overall, we confirmed hereby the optimal positioning of the focal point at the center of the breakthrough, using an ideal single element applicator or a phased array with equivalent F-number (frames g–l).

The described numerical model permitted the estimation of the time lag (\(\varepsilon\), expressed in s) between the end point of HIFU sonication and the time point where the temperature elevation reaches a maximum at the focal point location as a function of two parameters: the bone section radius \(R\) (expressed in mm) and the focal point offset with respect to the breakthrough plane, denoted as \(H\) (expressed in mm). Because the time lag is due to the “acoustic oven effect”, only the heat generation on the internal surface of the cortical bone was considered in the calculations. The time lag was described with very good accuracy by a quadratic function (average error 10 s):where \(c_{00} = 236\;{\text{s}},\;c_{10} = 7.83 \;{\text{s/m}}, c_{01} = 65\;{\text{s/m}},\;c_{20} \; = \;1.54 \;{\text{s/m}}^{2} ,\;c_{11} \; = \; - \;4\;{\text{s/m}}^{2} ,\) and \(c_{02} = 7.94 \;{\text{s/m}}^{2} .\) A graphical illustration is provided in Additional file 1. The time lag rapidly increased with the radius of the bone section. Therefore, the dwell time of the automatic temperature controller needs to be increased for larger lesions.

When the focal point offset \(H\) was set to zero, which is the optimal condition according to the previous observations, Eq. [3] simplifies to a second order polynomial of R. Given that the average radius of our samples was 6 mm, the time lag was calculated to be 126 s. Further details on the numerical results are provided in Additional file 1.

Geometrically, the ex vivo model was very similar to the clinical conformation, see for comparison Figs. 1a and 2d. The described experimental model was systematically free of air bubble contamination at tissue interfaces, as demonstrated by high resolution 3D MR imaging (Fig. 3). The most challenging step appeared to be the uniform curettage of the medullar cavity, since this step was lacking imaging guidance. Subsequently, the medullar cavity might contain residual fatty tissue, further impacting the PRFS MR thermometry near the internal facet of the cortical bone.

HIFU targeting of bone pseudo-tumor was feasible in all specimens. Low energy pilot sonications permitted visualization of the focal spot on MR thermometry axial or parallel to the bone, and consequent application of electronic steering until the main beam axis was centered on the cortical breakthrough. No acoustic obstacle or beam distortion by tissue interfaces was noted to occur from the injection of tissue mimicking gel, the local dissection of the muscle, the mitigation of the tissue dissection using ultrasonic gel, or the sewing of the different teguments with surgical wire.

The pixel-wise temporal standard deviation of MR thermometry in the tissue mimicking gel was on average 0.2 °C. Figure 4b illustrates an example of the experimental temperature elevation at the focus versus time, using the automatic temperature control, together with the actual parameter \(\delta\) applied per dwell time interval. The duty cycle gradually converged to a value of approximately 0.18 (60% of the initial one), corresponding to 11 W average acoustic power, which is 79 W/cm² focal acoustic intensity, and corresponds to 1.5 MPa positive peak pressure and 1.3 MPa negative peak pressure. A steady-state regimen, defined by an absolute offset of less than 0.2 °C between the actual temperature elevation and the predefined target, was obtained in 260 s in average (min: 160 s, max: 370 s). The steady-state temperature elevation calculated as the spatio-temporal average inside a 13 pixel ROI during the steady-state was 6.16 ± 0.23 °C in 14 procedures, compared to the pre-defined temperature elevation of 6 °C. The average relative error was therefore inferior to 4%. Given the consensual hyperthermia range between 41 and 43 °C, corresponding to a 95% confidence interval of ± 1 °C, the average precision of temperature control should be at least as low as 0.5 °C.

The measured temperature maps demonstrated that the thermal build-up inside the medullar cavity can be approximated by concentric isotherms originating on the cortical bone (Fig. 7b–d), as a joint effect of superficial averaging of acoustic energy on the internal facet of the cortical bone and of heat diffusion, the so-called “acoustic oven effect”. In frame (d) it is clearly visible that the local energy deposition by the focal point at the breakthrough site is bridging the circumferential isotherm. Figure 8 provides further insights into the spatio-temporal distribution of the temperature. The plots indicate that the temperature elevation at representative locations in soft tissue (adjacent to the periosteum lateral and posterior to the acoustic axis, adjacent to the breakthrough edge) was confined in the range 50% to 100% of the + 6 °C target. Figure 9 illustrates the comparative results for a variable depth (− 5, 0 and 5 mm) of the focus with respect to the plane of cortical breakthrough, on the same sample, all other parameters remaining unchanged. Positioning the focus in the plane of the cortical breakthrough (Fig. 9e) yields nearly perfect thermal patterns. Deeper positioning (inside the medullar cavity) yielded preferential heating of the opposite cortex wall where was inserted the fluoroptical sensor. For each focal depth (− 5, 0 and 5 mm), the sensor read the following highest values of temperature elevation 4.5 °C, 5.4 °C and 5.7 °C. More proximal positioning (in front of the breakthrough) yielded enhanced heating at the lateral edges (see black arrows in frame 9h). Plots of the cross correlation between PRFS thermometry data and sensor data are provided in Fig. 9c, f, g. PRFS thermometry data obtained in a voxel adjacent to the periosteum immediately behind the focal point and preserving sufficient MR signal, was found to be in very good agreement with the sensor data (mean offset 0.75 °C, min − 0.5 °C, max 1.7 °C), for each geometry of the HIFU beam.

In terms of temperature controllability and absence of thermal risk for the exposed cortical bone, the optimal positioning of the focal point was therefore found to be the geometrical center of the cortical breakthrough. These findings are consistent with numerical simulations (section C). The temperature controller performance was stable for each focal depth. Only one global maximum was observed on the time temperature curves and no oscillations were depicted. When the focal point was in the optimum position, the observed overshoot was minor, if any, and lower than 1 °C.