INTRODUCTION

Today, noninvasive HIFU (high-intensity focused ultrasound) surgery is used in clinics around the world for a number of medical applications. These include the destruction of tumor tissue (uterine fibroids, prostate, and thyroid tumors), treating essential tremor, palliative care for patients with bone tissue metastases, and tightening of subcutaneous structures in aesthetic medicine [1–7]. Preclinical studies have demonstrated the potential of using HIFU to solve medical issues such as stopping internal bleeding, targeted drug delivery, etc. [1, 3, 8, 9]. The idea underlying HIFU is to focus ultrasound waves on the targeted region, causing tissue heating due to acoustic energy absorption, followed by thermal necrosis [1, 2, 9].

At present, despite the advances in HIFU technology, its widespread use has limitations, mainly associated with the effects of heat diffusion around the targeted region, overheating of skin and bones in the near field of the HIFU transducer, and the need for expensive MRI imaging to monitor the treatment process [10, 11]. A significant manifestation of the thermal diffusion effect around the treatment region can lead to unwanted overheating and damage to intact nearby tissues, making it difficult to obtain localized destruction and irradiation near critical structures (vessels, nerves, intestines, skin). This also makes it challenging to irradiate highly perfused organs (liver, kidney). In addition, low thermal ablation rates are achieved in clinical protocols (about 2 cm3/min) [12].

This study aims at developing a recently proposed approach to thermal HIFU technology, in which, instead of the quasi-linear continuous modes traditional for clinical practice, nonlinear shock-wave pulse-periodic modes are used in irradiation protocols [13–15]. The main advantage of using such irradiation modes is ultrafast heating of biological tissue at the focus due to the absorption of ultrasound beam energy at the shock fronts [14–16]. When shock fronts of 80−100 MPa amplitude are present in the focal waveform, tissue heating to the boiling point and, consequently, formation of a single lesion, occurs within milliseconds, which is several orders of magnitude faster than heating and thermal ablation by a harmonic wave of the same intensity [16, 17]. At the same time, the region of effective energy absorption under shock-wave action is small, on the order of several millimeters in the direction of ultrasound beam propagation and a fraction of a millimeter in the transverse direction [16, 18].

To create a volumetric lesion in clinical HIFU systems, a single focus of a transducer is sequentially moved along a specified trajectory [19–21]. In the clinical Sonalleve V1 3.0T MR-HIFU system (Profound Medical Corp., Canada), the focus of the therapeutic array, due to electronic phasing, moves in a discrete manner along points located on concentric circles with radii of 2, 4, 6, and 8 mm [19, 22]. Irradiation begins from points of the inner circle, which is repeatedly irradiated until the threshold of thermal dose corresponding to complete tissue necrosis is reached [19, 20]. Then, the points of the next circle are repeatedly irradiated, etc. In this case, the order of sonicating single foci on each circle is selected so that the sequentially irradiated points are located as far as possible from each other. Homogeneous volumetric thermal ablation is formed through the merging of multiple single lesions by thermal diffusion, which results in two- to three-fold elongation of the destruction shape in the axial direction compared to the transverse size of the total trajectory [12, 19].

In [23], for the Sonalleve V1 MR-HIFU system, the heating efficiency of a clinically significant volume of biological tissue in quasi-linear continuous and shock-wave pulse-periodic irradiation modes with the same time-average power (105 W) was compared. In this case, the maximum high-amplitude mode achievable in a clinical system with a peak power of 1.3 kW, corresponding to the mode of saturation of the shock front amplitude at the array focus, was chosen as the sonication protocol for shock-wave exposure. The irradiation trajectory and thermal dose control were consistent with those used in clinical practice in the conventional quasi-linear HIFU protocol described above. It was shown that when the shock-wave mode is used, the tissue ablation rate increases approximately twofold compared to the quasi-harmonic mode, and the obtained lesion corresponds in shape to the irradiated region which is due to the suppression of heat diffusion along the beam axis. However, in order to achieve more uniform heating of the tissue by the shock-wave beam, the need for optimizing the focus trajectory became apparent.

In [24], which was a development of [23], it was proposed, when using the shock-wave mode in the protocol, to scale clinical trajectories by two times, reducing the spatial steps between the foci, as well as to change the method of controlling the thermal dose in forming volumetric destruction. The new control method consisted of sequential irradiation of all points of the scaled clinical trajectory and subsequent switching off of the inner circles as they reached the thermal dose threshold. In addition, the sequence of irradiation of discrete foci on each circle remained consistent with the clinical protocol. Furthermore, in [25] it was demonstrated that in shock-wave pulse-periodic irradiation modes implemented in the Sonalleve V2 system, the temperature field “remembers” the sequence of the last six irradiated foci, while the heated spots from previous single exposures spreads out due to thermal diffusion. The influence of the order of irradiation of discrete foci in the shock-wave mode on the final volume and shape of the created lesion, as well as on the thermal ablation rate and spatial distributions of the temperature field, was studied in [26] for three different sequences (“spiral”, “clinical”, and “snake”).

This study, which is a logical continuation of a series of previous works [23–26], develops the most advantageous trajectories for shock-wave pulse-periodic thermal effects of HIFU. Based on the formation of single small-sized lesion resulting from a single shock-wave burst, this study proposes using trajectories uniformly filled with discrete foci within a given shape and sonicating each focus once. A critical advantage of such protocols is that there is no need to control the thermal dose when generating thermal ablation. In addition, experimentally, the presence of vapor-gas boiling cavities that form in the focal region during shock-wave treatment can be clearly observed as areas of increased echogenicity with standard ultrasound imaging using a diagnostic probe in B-mode, which would eliminate the need for MRI monitoring and significantly reduce the cost of HIFU systems. To obtain clinically significant thermal ablation volumes on the order of cubic centimeters, this study proposes layer-by-layer shock-wave irradiation of tissue along single-exposure trajectories.

Thus, the aim of this study was to develop trajectories of single action of ultrasound bursts containing shocks to create homogeneous, well-localized volumetric thermal ablation of biological tissue using the Sonalleve V1 clinical MR-HIFU system. The study determined the optimal distances between foci sufficient to merge isolated single lesions and suppress thermal diffusion effects along the beam axis. The influence of the initial peak power of the array and the geometry of the outer contour of the trajectory (circle, square) on the choice of the step between discrete foci, the shape and volume of the resulting tissue lesion, and the volumetric thermal ablation rate was analyzed. The authors considered single- and three-layer trajectory configurations, and foci were sonicated starting from the center of each lesion layer in a spiral-shaped sequence.

FORMULATION OF THE PROBLEM

Using numerical methods, an experiment with irradiation of a bovine liver tissue sample in situ was simulated using the model of a high-power therapeutic phased array of the Sonalleve V1 MR-HIFU clinical system. The spherical surface of the array with an aperture of 128 mm and a focal length of 120 mm consisted of randomly arranged 256 circular elements with a diameter of 6.6 mm and an operating frequency of 1.2 MHz (Fig. 1a) [27]. The ultrasound beam, after passing through the coupling medium (water), was focused to a depth of 2.5 cm into a sample of bovine liver tissue.

Fig. 1.
figure 1

(a) Scheme of numerical experiment. The ultrasound beam is generating by a randomized HIFU array (256 round elements with a diameter of 6.6 mm): aperture 128 mm, operating frequency 1.2 MHz, focal length F = 120 mm. Focusing occurs in a sample of bovine liver tissue at a depth of h = 2.5 cm, the transducer and tissue sample are both placed in water. (b) Pressure waveforms (two cycles) at the focus of the array in the tissue for the saturation mode (I0 = 15 W/cm2, red line) and the fully developed shock-formation mode (I0 = 8 W/cm2, blue dash-dotted line). (c, d) Discrete trajectories of single irradiation on each focus, bounded by an external contour in the form of equal areas (c) a circle with a radius of 4 mm and (d) a square with a side of 7 mm; foci are located on a uniform grid with a step s. The spiral sequence of electronic movement of the array focus is shown by an arrow in the highlighted circle (from the center outward).

Full size image

Two exposure modes were considered with a constant time-average acoustic power of the array (105 W) and a pulse repetition period of 20 ms, which is the minimum possible time interval of electronic refocusing in the Sonalleve V1 clinical system:

(1) the mode with the maximum achievable peak power at which the shock amplitude at the focus is saturated (for brevity, we will call it the saturation mode) [28]. In the Sonalleve V1 system, this mode corresponded to a peak acoustic power of 1.3 kW and peak intensity at the array elements of I0 = 15 W/cm2. The duration of a single focus sonication was theat = 1.6 ms.

(2) the most effective focusing mode is when the ratio of the pressure jump Ash at the shock front in the focal waveform of the wave to the initial pressure amplitude of the wave on the array elements reaches its maximum (for brevity, the fully developed shock-formation mode) [29]. This mode corresponded to a peak acoustic power of 700 W and peak intensity at the array elements of I0 = 8 W/cm2. The duration of irradiation of a single focus was theat = 3 ms.

A detailed study of the acoustic field parameters in a wide range of peak powers of the Sonalleve V1 array transducer was carried out previously for focusing in water [27, 30] and for the considered water–biological tissue medium configuration [23]. The shock amplitudes in the pressure waveform at the focus in bovine liver tissue for the considered modes are Ash = 90 MPa and Ash = 120 MPa for I0 = 8 W/cm2 and I0 = 15 W/cm2, respectively (Fig. 1b). Calculations carried out in [24] showed that times-to-boiling of tissue in the studied modes are several tenths of a millisecond shorter than the selected heating times. Thus, the formation of a single lesion occurs as a result of a single impact in both considered shock-wave modes. For the fully developed shock-formation mode (I0 = 8 W/cm2), the dimensions of the ablation volume created during heating theat, determined by the threshold thermal dose, is 0.25 × 0.25 × 2.3 mm [24]. In saturation mode (I0 = 15 W/cm2), the single lesion has a larger size of 0.4 × 0.4 × 3.5 mm [24].

The dimensions of the created single lesions were taken into account when developing the motion trajectories of the focus of the ultrasound beam in its focal plane. The present study considered trajectories of a single sonication, which were geometric contours with the same area uniformly filled with discrete foci in the form of a circle with a radius of 4 mm (Fig. 1c) and a square with sides of 7 mm (Fig. 1d). Discrete focal points of the trajectories were irradiated in a sequence from the center outward in a spiral (shown by the arrow in the circle in Fig. 1c). This sequence was chosen after analyzing three different ways of bypassing the foci along “snake”-type trajectories, which is an analogue of the clinical and spiral sequences [26]. Since in the last two cases the results were similar and more advantageous in terms of the uniformity of destruction and thermal ablation rate compared to the snake-type sequence, the authors present here only the results for the spiral sequence as the simplest to implement. To find the optimal distance s between the foci for each of trajectory, its value varied from the transverse size of a single lesion (s = 0.25 mm for I0 = 8 W/cm2 and s = 0.4 mm for I0 = 15 W/cm2) up to s = 0.8 mm in increments of 0.05 mm. Based on the modeling results, optimal single-layer trajectories were developed to obtain fine (3–5 mm) volumetric thermal ablation well localized along the ultrasound beam axis.

To create clinically significant volumetric lesions, the study proposes irradiating the tissue layer by layer, starting from the one farthest from the array and moving towards it. When constructing layer-by-layer irradiation trajectories, the accompanying heating from the previous layer was taken into account by increasing the interfocal distance in the current trajectory layer. Three-layer trajectory configurations were considered, and the distance between layers (5 mm) was selected based on an assessment of the thickness of the effective heat release layer [23, 24].

Based on the simulation results, the volume of destruction V and thermal ablation rate was calculated for each sonication protocol. The ablation volume was determined after cooling of the sample using the threshold value of the thermal dose; the ablation rate was calculated as the ratio of the lesion volume to the irradiation time. The cooling time in each irradiation mode was determined by the time the lesion volume stopped increasing due to heat diffusion that continued after the end of the exposure.

NUMERICAL MODEL

Acoustic Field

The theoretical and numerical models used in this study are described in detail in [23, 24]. They are briefly presented below.

Ultrasound beam focusing in water and then in bovine liver specimen, was governed by the modified Westervelt equation, which takes into account nonlinear and diffraction effects, as well as absorption in tissue [15, 31]:

$$\frac{{{{\partial }^{2}}p}}{{\partial \tau \partial z}} = \frac{{{{c}_{0}}}}{2}\Delta p + \frac{\beta }{{2{{\rho }_{0}}c_{0}^{3}}}\frac{{{{\partial }^{2}}{{p}^{2}}}}{{\partial {{\tau }^{2}}}} + \frac{\delta }{{2c_{0}^{3}}}\frac{{{{\partial }^{3}}p}}{{\partial {{\tau }^{3}}}} + L\left( p \right),$$
(1)

where \(p~\,\, = p\left( {x,y,z,\tau } \right)\) is pressure, \(\Delta = {{{{\partial }^{2}}} \mathord{\left/ {\vphantom {{{{\partial }^{2}}} {\partial {{x}^{2}}}}} \right. \kern-0em} {\partial {{x}^{2}}}} + \) \({{{{\partial }^{2}}} \mathord{\left/ {\vphantom {{{{\partial }^{2}}} {\partial {{y}^{2}}}}} \right. \kern-0em} {\partial {{y}^{2}}}} + {{{{\partial }^{2}}} \mathord{\left/ {\vphantom {{{{\partial }^{2}}} {\partial {{z}^{2}}}}} \right. \kern-0em} {\partial {{z}^{2}}}}\) is the Laplace operator, \(z~\) is the coordinate along which the beam is focused, \(\tau ~\,\, = \,\,~t~ - {{~z} \mathord{\left/ {\vphantom {{~z} {{{c}_{0}}}}} \right. \kern-0em} {{{c}_{0}}}}\) is time in the accompanying coordinate system, and parameters \({{c}_{0}},~\beta ,~{{\rho }_{0}}~\) and δ are the sound speed, nonlinearity coefficient, density of the medium, and coefficient of thermoviscous absorption in the medium, respectively. The values of the indicated physical parameters for water were \({{\rho }_{0}}\) = 998 kg/m3, \({{c}_{0}}\) = 1485 m/s, β = 3.5, and for bovine liver tissue \({{\rho }_{0}}\) = 1050 kg/m3, \({{c}_{0}}\) = 1580 m/s, β = 4.0 [24, 32, 33]. The thermoviscous absorption coefficient in both media was chosen the same: δ = 4.33 × 10–6 m2/s.

In addition to thermoviscous absorption, the operator L(p) was used to simulate absorption in liver tissue, which corresponded to a linear dependence of the absorption coefficient on frequency, absorption value \({{{{\alpha }}}_{0}}\) equal to 8.43 m–1 at a frequency of \({{f}_{0}}\) = 1.2 MHz, and to a logarithmic dispersion law \({{\left( {c\left( f \right) - {{c}_{0}}} \right)} \mathord{\left/ {\vphantom {{\left( {c\left( f \right) - {{c}_{0}}} \right)} {{{c}_{0}}~}}} \right. \kern-0em} {{{c}_{0}}~}} = {{\left( {{{c}_{0}}{{\alpha }_{0}}} \right)} \mathord{\left/ {\vphantom {{\left( {{{c}_{0}}{{\alpha }_{0}}} \right)} {({{\pi }^{2}}{{f}_{0}})~}}} \right. \kern-0em} {({{\pi }^{2}}{{f}_{0}})~}}\ln \left( {{f \mathord{\left/ {\vphantom {f {{{f}_{0}}}}} \right. \kern-0em} {{{f}_{0}}}}} \right)\) [15, 16].

To set the boundary condition, we used the Sonalleve V1 idealized array model [27], which assumed a uniform distribution of the vibrational velocity on the surface of the elements.

The result of simulating Eq. (1) was the spatial distribution of the power density of the heat sources Q(x, y, z) in liver tissue, calculated as the rate of decrease in wave intensity at each axial grid step when calculating the nonlinear and absorption operators [15, 23].

Temperature Field

The spatial distributions of the power density of heat sources Q in tissue obtained as a result of simulating the Westervelt equation (1) were used to calculate the temperature field by numerically solving the inhomogeneous heat equation:

$$\frac{{\partial T}}{{\partial t}} = \chi \Delta T + \frac{Q}{{{{C}_{v}}}},$$
(2)

where T is temperature, t is time, χ is the thermal diffusivity coefficient, \({{C}_{v}}\) is the heat capacity of the sample, and Q is the power density of the heat sources in the tissue, calculated based on the Westervelt equation (1). The values of the physical parameters in Eq. (2) corresponded to liver tissue: \({{\chi }} = 1.93 \times {{10}^{{ - 7}}}\,\,{{{{{\text{m}}}^{{\text{2}}}}} \mathord{\left/ {\vphantom {{{{{\text{m}}}^{{\text{2}}}}} {\text{s}}}} \right. \kern-0em} {\text{s}}}\), \({{C}_{v}} = 3.06 \times {{10}^{6}}\,\,{{{{\;J}}} \mathord{\left/ {\vphantom {{{{\;J}}} {({{{\text{m}}}^{3}}~\,\,^\circ {\text{C}})}}} \right. \kern-0em} {({{{\text{m}}}^{3}}~\,\,^\circ {\text{C}})}}\) [23, 32, 33]. The initial temperature of the sample before irradiation was 20°C. After irradiation ended, cooling of the sample was simulated for 10 s for I0 = 8 W/cm2 and 7 s for I0 = 15 W/cm2 to take into account the increase in the destruction volume due to continuing heat diffusion.

Thermal Dose

The integral value of the thermal dose was used as a criterion for thermal tissue necrosis:

$${{t}_{{56.0}}} = \mathop \smallint \limits_0^{{{t}_{{{\text{heat}}}}}} R_{0}^{{56.0 - T\left( {{\mathbf{r}},t} \right)}}dt \geqslant 1.76,$$
(3)

where the coefficient \({{R}_{0}}\) takes a value of \(0.5\,\,{\text{ for}}~\,\,T\left( {{\mathbf{r}},t} \right) \geqslant 43^\circ {\text{C}}\) and \(0.25~\,\,{\text{for}}\,\,~T\left( {{\mathbf{r}},t} \right) < 43^\circ {\text{C}}\) [34], \({{t}_{{56.0}}}\) is the time equivalent of the threshold destructive thermal dose commonly used in HIFU modes, which is 240 min at a temperature of 43°C and 1.76 s if it is determined for a temperature of 56°C [1, 21, 35].

RESULTS

1 Single-Layer Trajectories for a Single Exposure of Shock-Wave Bursts

When developing trajectories for a single exposures of millisecond-long shock-wave bursts, an important parameter is the spatial step between the nodes of a uniform grid in which discrete foci are located. The optimal interfocal step s should, on the one hand, lead to the merging of single lesions due to thermal diffusion effects, and on the other hand, the thermal diffusion effects should not be so pronounced as to cause elongation of an even layer of volumetric ablation with the required shape along the beam axis. The most advantageous case would be when the volumetric lesion has sharp, clear, predictable boundaries, while the thermal ablation rate is not inferior to the values achieved in quasi-linear modes typical of clinical practice (about 2 cm3/min [12]).

Figure 2 shows how the shape of thermal volumetric lesion changes in the focal and axial planes during irradiation in the saturation mode (Fig. 2, left column) and in the fully developed shock-formation mode (Fig. 2, right column) with increasing interfocal step s of a discrete trajectory bounded by an external contour in the shape of a circle. For both shock-wave modes, the nature of the change in the shape of the lesion with increasing s is characterized by the following stages:

Fig. 2.
figure 2

Spatial temperature distributions at the end of heating t with shock-wave irradiation in saturation mode (I0 = 15 W/cm2, left column) and fully developed shock-formation mode (I0 = 8 W/cm2, right column) along a discrete trajectory bounded by an external contour in the shape of a circle, with different interfocal distances s: (a) 0.40, (b) 0.55, (c) 0.60, (d) 0.65, (e) 0.75 mm for 15 W/cm2 and (f) 0.25, (g) 0.45, (h) 0.50, (i) 0.52, (j) 0.55 mm for 8 W/cm2, respectively. The black outline indicates the area within which the thermal dose exceeded its threshold value after the sample cooled. Each spatial temperature distribution shows the end time of heating, the achieved thermal ablation rate, and the value of the ablated volume.

Full size image

(1) tendency of the axial shape of the lesion to become cigar-shaped as a result of significant manifestation of the thermal diffusion effect (Figs. 2a, 2f) and pronounced overheating of the target region;

(2) gradual straightening of the ablation boundaries due to suppression of the thermal diffusion effect (Fig. 2b, 2g) and a decrease in the average temperature over the volume of the irradiated region at the end of ultrasound exposure;

(3) formation of ablation in the form of a thin even layer (Fig. 2c, 2h);

(4) the appearance of “teeth” on the walls of the lesion in the axial plane (Figs. 2d, 2i);

(5) cessation of merging single foci into a volumetric lesion (Figs. 2e, 2j).

Let us look at each stage in more detail. With steps that correspond to the dimensions of single lesions (s = 0.4 mm for 15 W/cm2 and s = 0.25 mm for 8 W/cm2 [24]), significant overheating of the target region leads to strong elongation of the destruction shape in the axial direction; however, the highest rates of thermal ablation are achieved (Figs. 2a, 2f). The use of overheating of the center of the irradiated region to increase the thermal ablation rate of tissue was discussed in [19, 22, 24]. In this case (Figs. 2a, 2e), the volumes and axially elongated shapes of lesions are similar to those obtained in clinical practice during in situ irradiation in quasi-linear mode for the Sonalleve system along the conventional trajectory of the same transverse size [24], but the thermal ablation rate in shock-wave modes are approximately two-fold higher. It is noteworthy that, based on the values presented in Figs. 2a and 2e, it is incorrect to conclude that the fully developed shock mode is superior to the saturation mode for achieving the highest thermal ablation rate, since the protocols correspond to different exposure times. At the same exposure times, the thermal ablation rate in saturation mode (3.5 cm3/min, Fig. 2b) is higher than in the fully developed shock mode (1.1 cm3/min, Fig. 2j).

With increasing trajectory step s, the exposure time is reduced and, as a consequence, the average temperature of volumetric ablation at the end of sonication decreases. The thermal diffusion effect in this case becomes less pronounced, as a result of which the front and rear boundaries of the shape of lesion in the axial plane are aligned (Figs. 2b, 2g). In this case, the necrosis tissue volume V and thermal ablation rate decrease (Figs. 2b, 2g vs. Figs. 2a, 2f).

A further increase in interfocal steps to s = 0.6 mm for 15 W/cm2 and s = 0.5 mm for 8 W/cm2 (Fig. 2c, 2h) makes it possible to suppress the extension of thermal damage along the array axis by weakening the manifestation of thermal diffusion in the axial direction. The longitudinal dimensions of the ablation are 4.2 mm for the saturation mode (Fig. 2c) and 2.4 mm for the fully developed shock-formation mode (Figs. 2c, 2h), which is comparable to the corresponding axial sizes of single lesions (3.5 and 2.3 mm, respectively). Volumetric lesions have a shape of a thin layer with smooth walls without pronounced “teeth” and a uniform distribution of the temperature field within the lesion (Figs. 2c, 2h). From the viewpoint of formation of even, sharp, predictable lesion boundaries, the considered case of interfocal steps (s = 0.6 mm for 15 W/cm2 and s = 0.5 mm for 8 W/cm2) is the most advantageous, while in the saturation mode, the interfocal step s was about 1.5 times greater than the transverse size of a single lesion, and in the fully developed shock-formation mode, 2 times. It is noteworthy that shock-wave irradiation along single-exposure trajectories with the above steps gives an advantage over shock-wave irradiation considered earlier in [24] using scaled clinical trajectories: in both modes of 8 and 15 W/cm2, the corresponding exposure times are reduced (3.26 and 4.82 s (Figs. 2c, 2h) vs. 3.88 and 6.62 s [24]); the thermal ablation rates reach higher values (3.4 and 1.6 cm3/min (Figs. 2c, 2h) vs. 3.0 and 1.5 cm3/min [24]), and the lesion has similar shape.

With a subsequent increase in step s between single foci in both shock-wave modes, the formation of “teeth” at the lesion boundaries is observed as a result of the amount of absorbed acoustic energy being insufficient for the merging of single foci in the axial plane (Figs. 2d, 2i). At the same time, the thermal ablation rates are reduced.

At interfocal steps s exceeding 0.75 mm for 15 W/cm2 and 0.55 mm for 8 W/cm2 (Figs. 2e, 2j), undestroyed areas appear in the target zone, since the energy absorbed by the tissue is insufficient to merge single foci into a homogeneous volumetric lesion.

Selecting the optimal interfocal step s, ensuring the formation of smooth walls of the volumetric lesions in the form of a thin layer, turned out to be independent of the external contour limiting the impact trajectory in the focal plane. Thus, for a trajectory with an external contour in the form of a square (Fig. 1d) with the same cross-sectional area of the target region as the circular trajectory considered above (Fig. 1c), similar results were obtained to those presented in Fig. 2. Figure 3 shows the shape and parameters of volumetric thermal ablation for the case of irradiation along a square trajectory with an optimal interfocal step s = 0.6 mm for 15 W/cm2 and s = 0.5 mm for 8 W/cm2. The resulting thermal ablation rates (3.3 cm3/min for 15 W/cm2 and 1.6 cm3/min for 8 W/cm2), axial dimensions of the volumetric lesion (4.1 mm for 15 W/cm2 and 2.4 mm for 8 W/cm2), as well as the shape of the lesion in the axial plane yz are in exact agreement with similar results for the case of a circular trajectory (Figs. 3, 2c, 2h). In this case, the transverse shape of the ablated volume in each sonication protocol replicates the initial external contour of the trajectory.

Fig. 3.
figure 3

Spatial temperature distributions at the end of heating t (a) with shock-wave irradiation in saturation mode (I0 = 15 W/cm2) and (b) in the fully developed shock-formation mode (I0 = 8 W/cm2) along a discrete trajectory bounded by an external contour in the form of a square with a side of 7 mm, with an optimal interfocal step s (0.6 mm for 15 W/cm2 and 0.5 mm for 8 W/cm2). The black outline indicates the area within which the thermal dose exceeded its threshold value after the sample cooled. Each spatial temperature distribution shows the end time of heating, the achieved thermal ablation rate, and the value of the destroyed volume.

Full size image

Thus, using a single-layer configuration of single foci on a uniform grid and irradiating them in a spiral sequence, it is possible to obtain predictable thin volumetric thermal damage with an arbitrary shape within the outer contour of the trajectory. An increase in initial peak intensity I0 on the array elements makes it possible to achieve higher thermal ablation rates, use larger interfocal distances s, and, as a result, obtain thermal necrosis of the target region with a shorter exposure time. The highest thermal ablation rate is observed in the saturation mode (3.4 cm3/min), which is twofold higher than in the fully developed shock-formation mode (1.6 cm3/min) and 1.6 times higher than the value corresponding to the clinical protocol in situ (2.2 cm3/min [24]). Thus, in the Sonalleve V1 clinical HIFU system, the maximum achievable peak power saturation shock-wave mode is the most advantageous for producing predictable, localized, sharp-edged thermal lesions. In the fully developed shock-formation mode, the lowest volumetric thermal ablation rate is observed. However, this mode may be preferable for destroying thin (2–3 mm) tissue layers. It is worth noting that the volumes obtained in shock-wave modes and single-layer ablation (0.2 cm3) are small compared to those observed in clinical practice (on the order of a cubic centimeter) when using trajectories of the same transverse size. To increase the thermal ablation volume while maintaining the predictability of its shape, this study proposes sequential irradiation of several layers of tissue.

2 Three-Layer Volumetric Ablation Configuration

To increase the volume of thermal ablation of tissue using shock-wave irradiation modes, multilayer configurations of the trajectory of the array focus should be used. The number of required layers is predicted based on knowledge of the volume of the targeted region, the thickness and volume of one ablation layer, and the transverse shape of the outer contour of the trajectory along which irradiation will occur. In this case, it is necessary to begin irradiation from the farthest layer from the transducer, gradually moving the axial coordinate of each subsequent layer towards the array. This order of irradiation is justified by several factors. First, simultaneously with the sonication of distant tissue layers, the ultrasound beam gradually heats the layers of the target region closer to the array. This can be used to subsequently accelerate volumetric thermal ablation by increasing the interfocal step s in these layers. Second, when irradiated in shock-wave modes, vapor-gas boiling cavities are formed, which are strong ultrasound scatterers, and the irradiation of layers in reverse order would be inefficient.

This study demonstrates the feasibility of layer-by-layer tissue irradiation in both considered shock-wave modes for the case of a three-layer trajectory configuration, the outer contour of which is bounded by a circle in the transverse plane. The choice of layer thickness (5 mm) was made based on the analysis of power losses in tissue along the axial coordinate carried out previously in [23]. The coordinates z of the location of the layers were z = 123 mm (far layer from the array), 118 mm (central layer) and 113 mm (near layer). For saturation mode (I0 = 15 W/cm2), the planned volume of the target region (700 mm3) is the volume of a cyl-inder with a circular base of 4 mm radius and 14 mm height, obtained by adding the distance between the outer layers equal to 10 mm and two half-thicknesses of single-layer ablation from the base of the cylinder (4 mm). In the case of a fully developed shock-formation regime (I0 = 8 W/cm2), the target region has a smaller resulting cylinder height (12.4 mm) due to a narrower single-layer destruction (2.4 mm) and, as a result, a smaller volume (620 mm3).

To use the additional thermal effect from the irradiation of deeper layers of tissue, the interfocal step s should be increased for each subsequent irradiated layer. Our analysis showed that for the problem under consideration, it is optimal to increase the interfocal step s by 0.05 mm in every next layer towards the array compared to the previous one. In this case, it is optimal to start irradiating the most distant layer with a step s exceeding by 0.05 mm the optimal step for a single-layer configuration (s = 0.6 mm for 15 W/cm2 and s = 0.5 mm for 8 W/cm2), which will compensate for the further manifestation of thermal diffusion from the central part of this layer. Thus, the value of the spatial step s between the nodes of a uniform grid of discrete focus locations for the saturation mode (15 W/cm2) was s = 0.65, 0.7, and 0.75 mm in the distant, central, and near layers, respectively (Fig. 4a), and for the fully developed shock-formation mode, s = 0.55, 0.6, and 0.65 mm (Fig. 4b).

Fig. 4.
figure 4

Spatial temperature distributions at the end of heating t (a) with shock-wave irradiation of a liver sample in saturation mode (I0 = 15 W/cm2) and (b) in the fully developed shock-formation mode (I0 = 8 W/cm2) along a three-layer trajectory. The distance between adjacent layers was 5 mm; irradiation began from the layer farthest from the array. The black outline indicates the area within which the thermal dose exceeded its threshold value after the sample cooled. The top row shows the distribution in the focal plane for each layer, and the bottom row shows the distribution in the axial plane. The distributions indicate interfocal steps s in each layer, irradiation duration t, the achieved thermal ablation rates, and the resulting destruction volumes.

Full size image

The shape of thermal volumetric lesions obtained with irradiation of three layers was close to cylindrical both in the saturation mode (Fig. 4a) and in the fully developed shock-formation mode (Fig. 4b). In this case, the main differences between the shapes of the thermal ablation and cylindrical areas are near the boundaries of the lesion and do not exceed deviations of 1 mm for the saturation mode and 2 mm for the fully developed shock-formation mode. The resulting ablation volumes were 670 and 600 mm3, which agrees with the above estimates within 5% (700 and 620 mm3) obtained for cylindrical volumes in modes of 15 and 8 W/cm2, respectively.

Three-layer irradiation of tissue in saturation mode made it possible to achieve the highest volumetric thermal ablation rate of 5.4 cm3/min, which is 1.5 times higher than the corresponding rate for the fully developed shock-formation mode (3.6 cm3/min) and 2.5 times higher than the typical value (2.2 cm3/min [24]) for the conventional quasi-linear clinical treatment. An increase in the interfocal steps s, taking into account previous heating of the nearby tissue layers, made it possible to reduce the time of irradiation of the target region in the saturation and fully developed shock-formation modes to 7.38 and 10.02 s, respectively, which is 12 and 16% faster than in the case of sonication with the same steps s. In this case, the most advantageous, both from the viewpoint of the formation of a given shape lesion with sharp boundaries, and the achievement of the highest volumetric thermal ablation rate, is shock-wave irradiation in the maximum achievable mode in the Sonalleve clinical HIFU system (saturation mode with I0 = 15 W/cm2).

It is worth mentioning the dynamics of changes in the shape of thermal ablation depending on the distance between the layers and discrete focal points of the trajectory located at the nodes of a uniform grid. When layers were spread to a distance of more than 5 mm, instead of the required shape of a flat side surface of the cylinder, an isthmus began to form in the regions between the layers, which became thinner as the layers were moved apart, which demonstrated insufficient heat accumulation in this region. Conversely, when the layers were located closer than 5 mm apart, thermal diffusion caused overheating of the target region and elongation of the shape of volumetric thermal ablation along the beam axis. In this case, the thermal lesion volume decreased and it`s shape tended to become more elliptical, similar to that observed during irradiation in quasi-linear clinical modes. Changing interfocal steps s in the sonicated layers caused similar changes in the thermal destruction parameters: either elongation of its shape along the beam axis with decreasing steps or the formation of isthmuses between layers with increasing s, accompanied by a decrease in the thermal ablation rate.

Thus, the use of shock-wave pulse-periodic modes in irradiation protocols with a three-layer configuration of the motion trajectory of the HIFU array focus made it possible to obtain predictable volumetric thermal lesion with a given shape, comparable in volume to that obtained with a clinical protocol in quasi-linear irradiation mode along a single-layer circular path with the same transverse size (radius 4 mm). At the same time, the use of shock-wave irradiation in the saturation mode with maximum achievable peak power for research purposes in the Sonalleve V1 system, made it possible to accelerate volumetric thermal ablation by 2.5 times compared to the quasi-linear irradiation mode. In addition, the use of the shock-wave irradiation modes makes it possible to significantly suppress thermal diffusion along the ultrasound beam axis and obtain, for a given transverse size of the trajectory, an arbitrary shape of the target ablation region, in contrast to the ellipsoidal one in the quasi-linear case.

CONCLUSIONS

The study demonstrates the potential of using HIFU protocols using shock-wave pulse-periodic irradiation of biological tissue to quickly obtain predictable and localized volumetric thermal lesions with a suppressed thermal diffusion effect along the ultrasound beam axis.

Based on the findings, the following practical rec-ommendations can be made:

(1) For the Sonalleve V1 clinical HIFU system, the most advantageous in terms of the volumetric thermal ablation rate and the shape of the resulting thermal lesion is the use of shock-wave pulse-periodic irradiation in the maximum achievable peak power mode (I0 = 15 W/cm2, peak power 1300 W, pulse duration 1.6 ms, duty cycle 8%) using trajectories of the focus movement of the HIFU array in its focal plane along the nodes of a uniform grid, bounded by a contour with a given shape and using single irradiation per focus.

(2) Single-layer configurations of single shock-wave exposures (I0 = 15 W/cm2) and trajectories uniformly filled with discrete foci with a spatial step 1.5 times greater than the transverse size of a single lesion, make it possible to increase the thermal ablation rate by 1.6 times compared to the clinical quasi-linear mode and obtain volumetric thermal localized lesion in the form of an even layer, which is fundamentally important during irradiation near critical structures of various organs. When constructing single-exposure trajectories uniformly filled with foci, the choice of interfocal distance is essential, while the geometry of the outer contour of the trajectory and sequence of irradiation of discrete foci are less significant.

(3) To obtain clinically significant volumetric lesions in biological tissue, it is recommended to use layer-by-layer shock-wave pulse-periodic exposure, in which irradiation begins from the layer farthest from the array, and the spatial step between discrete foci of a uniform grid gradually increases as the layers approach the transducer. The distance between layers should be selected based on analysis of the width of the region of effective power losses in tissue along the beam axis, and the initial interfocal step in the layer farthest from the array should be slightly larger than the optimal interfocal step of the single-layer trajectory configuration. The three-layer irradiation of tissue considered in this study made it possible to accelerate volumetric thermal ablation by 2.5 times in the shock-wave mode of the maximum peak power achievable for the Sonalleve V1 system (saturation mode with I0 = 15 W/cm2) compared to the clinical quasi-linear mode and to obtain a volumetric ablation close in shape to a cylindrical one with sharp boundaries.

(4) When choosing the peak power, it is important to take into account that at powers exceeding the level required to form a fully developed shock in the focal pressure waveform, the size of single lesions increases with increasing peak power. This will affect the choice of the optimal interfocal step of the discrete irradiation trajectory and the achieved thermal ablation rate. In this study, the optimal protocol for thermal ablation of tissue in the mode of a fully developed shock (peak power 700 W) included the use of an interfocal step of a single-layer trajectory two times greater than the transverse size of a single thermal lesion. The thermal ablation rate in this protocol was slightly lower than the characteristic value for the conventional clinical protocol. However, it was possible to obtain thin (2–3 mm) evenly ablated single layers of tissue. The three-layer irradiation path configuration allowed a 1.6-fold acceleration of volumetric thermal ablation compared with quasi-linear exposure, but it was inferior in shape and rate of destruction to shock-wave irradiation using a higher peak power (1300 W).

The findings and practical recommendations of this study can be generalized to other clinical HIFU systems similar to Sonalleve. Using the motion trajectory of the HIFU array focus in its focal plane along the nodes of a uniform grid, bounded by a given external geometric contour, with a single shock-wave pulse irradiation of each focus can allow treatments without accompanying MRI control of the thermal dose in real time. In addition, the generation of vapor-gas boiling cavities during irradiation in shock-wave modes makes it possible to visualize and control the process of tissue ablation using B-mode ultrasound.

As a further development of the study, the authors plan to implement the developed shock-wave protocols for tissue irradiation ex vivo in a physical laboratory experiment.