Model based deep learning method for focused ultrasound pathway scanning | Scientific Reports

Scientific Reports volume 14, Article number: 20042 (2024) Cite this article

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The primary purpose of high-intensity focused ultrasound (HIFU), a non-invasive medical therapy, is to precisely target and ablate tumors by focusing high-frequency ultrasound from an external power source. A series of ablations must be performed in order to treat a big volume of tumors, as a single ablation can only remove a small amount of tissue. To maximize therapeutic efficacy while minimizing adverse side effects such as skin burns, preoperative treatment planning is essential in determining the focal site and sonication duration for each ablation. Here, we introduce a machine learning-based approach for designing HIFU treatment plans, which makes use of a map of the material characteristics unique to a patient alongside an accurate thermal simulation. A numerical model was employed to solve the governing equations of HIFU process and to simulate the HIFU absorption mechanism, including ensuing heat transfer process and the temperature rise during the sonication period. To validate the accuracy of this numerical model, a series of tests was conducted using ex vivo bovine liver. The findings indicate that the developed models properly represent the considerable variances observed in tumor geometrical shapes and proficiently generate well-defined closed treated regions based on imaging data. The proposed strategy facilitated the formulation of high-quality treatment plans, with an average tissue over- or under-treatment rate of less than 0.06%. The efficacy of the numerical model in accurately predicting the heating process of HIFU, when combined with machine learning techniques, was validated through quantitative comparison with experimental data. The proposed approach in cooperation with HIFU simulation holds the potential to enhance presurgical HIFU plan.

High-intensity focused ultrasound (HIFU) is a non-invasive therapeutic method for cancer treatment using ultrasound energy1,2,3. Currently, HIFU has been applied to treat various solid tumors, including those of pancreas, liver, prostate, breast, uterine fibroids, and soft-tissue sarcomas4,5,6,7,8,9,10. Compared to traditional tumor/cancer therapeutic approaches such as open surgery, radiation, and chemotherapy, HIFU is truly a non-invasive method and has a lower rate of post-treatment complications11.

The main effect of HIFU treatment is tissue heating which is induced through the absorption of acoustic energy and its conversion to heat. It can cause necrosis in the form of almost instant protein coagulation, which irreversibly damages key cytosolic and mitochondrial enzymes12. Because the HIFU beam is concentrated at a specific location and elevates the temperature above cytotoxic levels only inside a limited volume, thermal damage to tissue is relatively small. The dimensions of tissue damage caused by HIFU can vary significantly depending on the frequency of the transducer. Higher frequency transducers (typically 3 to 10 MHz) with focal spot size of approximately 3 to 10 mm in diameter, usually create smaller lesions, with diameters ranging from 1 to 3 mm and depths of 3 to 10 mm. While lower frequency transducers (typically 0.5 to 3 MHz) with a focal spot size of approximately 3 to 10 mm in diameter, produce larger lesions, with diameters ranging from 3 to 10 mm and depths of 10 to 30 mm 13. Due to the small focal region, a scanning pathway is required to cover the entire tumor; otherwise, the risk of metastasis is raised following HIFU therapy, according to the data in recent studies14,15,16.

HIFU remains a treatment modality in development, despite its distinctiveness and promising first clinical findings11,15,17. Several technical issues are preventing it from becoming a generally used therapy for both patients and clinicians. Treatment of large tumors embedded in critical normal tissues may result in very long treatment times, where many heating pulses need to be precisely placed and applied to cover the entire volume5,18,19. Moreover, due to the small size of the focal region, there can be gaps between the treated areas, with distances between treated and untreated regions often being less than 50 \(\upmu \)m20. This proximity increases the probability that some cancer cells may survive in the untreated spaces between the focal regions.

Because of recent advances in numerical methods and information technology, detailed models that accurately describe the underlying physical behavior of focused ultrasonic waves and temperature distribution in heterogeneous tissue are now accessible21. As a result, the tool can be used for a variety of purposes, including patient selection (determining whether a patient is a good candidate for surgery based on anatomy) and treatment verification (analyzing the cause of adverse events or treatment failures). Moreover, the scanning pathway (determining the optimal transducer location and sonication parameters to deliver ultrasonic energy to the stated target volume) plays an important role in reducing the treatment time and avoiding metastasis by leaving cancerous cells between focal regions.

There are two ways to deliver energy to the target region in HIFU treatment: sequential discrete mode and continuous scanning mode 22,23. In sequential discrete mode, localized treatments are delivered sequentially by moving the HIFU transducer in a discrete manner. In continuous scanning mode, the HIFU transducer moves at a constant speed along a pre-designed trajectory. Thermal diffusion and heat accumulation from the nearby treated area cause the size of the lesion to gradually increase as the sequential discrete HIFU therapy progresses, potentially resulting in insufficient treatment of the initial spots and overtreatment of the later ones24,25,26. Giannakou et al.27 evaluated six alternative navigation algorithms to determine the amount of transducer generated heating in the pre-focal area, and Fennessy and Tempany 5 recommend 20–40 s of heating followed by 80–90 s of cooling. It would take 2.5 h to provide the appropriate dosage if every pulse consisted of 30 s of heating and 60 s of cooling. Clinical practitioners can shorten treatment times using a phased array by forming multiple focus patterns and regulating the electrical power given to the transducer, the sequence of focal zones, the length of heating pulses, and the cooling intervals between heating pulses28. Historically, researchers have altered a fixed treatment path by changing one of the other treatment variables5,6,29,30,31,32, such as the applied power magnitude29, ultrasound frequency29, or the inter-sonication delay period30, due to the computational complexity involved with optimizing multiple parameters simultaneously. Most researchers utilize defined heating pulses and inter-pulse cooling times to prevent scorching normal tissue5,6,30. Such regimens employed cautious heating and cooling intervals because of effectiveness and safety concerns, resulting in extremely extended treatment times31.

Payne et al.33 presented the findings of a new optimization approach that minimizes HIFU treatment periods by minimizing individual heating and interpulse cooling times while staying within normal tissue constraint limits at each sonication site. Fan and Hynynen34 mimicked noninvasive tumor surgery using focused transducers or phased arrays with several sonications. Liu et al.35 investigated two heuristic routes numerically: the shortest distance and the greatest distance between sequential small rapid scanning volumes. Based on the approach taken, researchers were able to achieve cumulative heating time differences of several minutes (cooling times were fixed at 1 min between sonications). A volumetric sonication approach is suggested, in which the focus point is guided along a preset trajectory consisting of numerous concentric outward-moving circles to create volume ablations by Kohler et al.36, which was extended by Enholm et al.37 and was based on that group’s previous work with nested spirals38,39.

Based on the minimal time formulation from optimal control theory40, a scanning path optimization algorithm was designed to treat the tumor volume as quickly as possible while keeping the temperature in the healthy tissue below the safe threshold (42 °C). In the theoretical simulation, achieving the optimal treatment required using many phased array elements (530) and a high number of focal points (300 for a sphere with a radius of 1.9 cm). While phased array transducers are used in some advanced HIFU systems, such as those in Israel and China, the specific configuration and number of elements and focal points simulated here are not typically available in most commercially available HIFU systems. This limitation is due to the high cost and complexity associated with manufacturing and operating such advanced systems. Therefore, while the theoretical approach demonstrates what is possible with ideal equipment, practical implementations may require adjustments to accommodate the capabilities of currently available technology. Luo et al.41 suggested an optimal sequential discrete mode, which alternated between long and short exposure durations of the treatment locations, reducing the accumulated impact of nearby treated spots, and generating uniformly sized lesions. In the experiments with gel phantoms and ex vivo bovine liver samples, Zhou et al.42 compared two new scanning pathways, spiral scanning from the center to the outside and spiral scanning from the outside to the center, with traditional raster scanning. The notion that adjusting the course of a HIFU therapy’s N focus zone heating pulse can greatly shorten treatment duration was tested by Coon et al.43. A theoretical and experimental study conducted by Qian et al.44 investigated the lesion development generated by HIFU operating in continuous scanning mode along a spiral channel. Lari et al.45 proposed a method enabling the generation of high-quality treatment plans with less than 0.08% mistreated and under-treated tissue. Other optimization methods have been attempted to boost the sequential discrete mode treatment impact like combining it with HIFU-induced biological effects in tissue46,47. However, more investigation is required to concentrate simultaneously on the scan path, treatment time, and minimum invasion in the normal tissue.

An ML-based approach to solving the treatment planning problem is presented for the first time in this paper. The aim is to propose a novel scanning path method to compute the best presurgical plan based on the target volume. The planned goal volume and organs at risk are the ML’s inputs, and the ML approach generates a viable treatment plan. An iterative artificial neural network (ANN) is implemented to consider several solutions and choose the optimal plan based on the predefined constraints. This approach is conducted both numerically and experimentally to investigate the performance and validation of the numerical method. As a result, HIFU treatment time can be significantly reduced, and the risk of metastasis from mistreated cancerous cells is minimized. Moreover, the proposed study can avoid possible overheating and necrosis of normal tissue. Despite its ease of use, the approach is used to increase HIFU patient targeting and reduce treatment times, leading to better clinical results.

The tumor overlaying skin is readily in touch with degassed water during HIFU therapy, which is administered under spinal or general anesthesia with the patient resting in a prone or supine posture. Many image processing approaches are used to select the tumor mass in the target region of US/MR images. The tumor lesion is made up of multiple two-dimensional (2-D) cross-slices, and the shapes and sizes of the slices are seldom the same. In fact, depending on the therapy approach, the tumor volume might be split into numerous cross-slices with 5- to 10-mm interval distances using directed movement 29. The target locations are determined based on the pictures of each slice and must then be destroyed utilizing concentrated scanning beams. A therapeutic plan is required to cover the whole tumor volume completely, be fast enough, and have the slightest invasion of normal tissue. Figure 1 shows the schematic of the HIFU surgery processes.

Schematics of the problem description.

The goals of this study were to propose a novel ML-based approach to significantly reduce the treatment time and ensure that the build-up of normal tissue overheating must be considered when the successive focal points are very close. To accomplish so, FEM was used to simulate a variety of treatment scenarios, and the resultant lesion forms were compared. In this study, the concentration is on the breast tumors which are located near vital organs such as the heart, lungs, rib cage, and major blood vessels, but the results can be extended to other types of tumors. Breast tumors were selected as a model to test the AI-based HIFU optimization approach due to their clinical importance, anatomical considerations, the need for non-invasive treatment options, the complexity of treatment planning, advancements in breast cancer research, and the feasibility of experimental validation.

In the preoperative treatment process, detection of the exact tumor geometry is required to set the most beneficial therapeutic plan and avoid any invasion of normal tissue. In order to obtain precise information on the breast and tumor geometries, 2D MRI images of breast cancer from four patients were used in this study (Fig. 2). Initially, comprehensive 3D MRI scans of the breast were obtained for each patient. These scans provided a detailed volumetric representation of the breast tissue, including the tumor regions. Using advanced image processing algorithms, such as semantic segmentation techniques employing a convolutional neural network (CNN), the tumor was segmented from the 3D MRI data. These algorithms identify the boundaries of the tumor within the 3D volume based on trained models and specific features in the MRI images48. After segmentation, the 3D tumor volume was systematically sliced into multiple 2D images. The slicing was done at regular intervals, every 5 mm, based on the resolution and the specific anatomy of the tumor. These intervals were chosen to ensure that the 2D slices accurately represented the spatial characteristics of the tumor without significant loss of information. The rationale for extracting 2D images from the 3D volume lies in the computational efficiency and ease of analysis. Working with 2D slices allows for the application of various image processing techniques and machine learning models that are well-established for 2D data. Additionally, 2D images facilitate the visualization and manual verification of tumor boundaries, which is crucial for accurate treatment planning. According to the Helsinki Agreement, the whole study was thoroughly explained to the patients. MRIs with and without contrast were performed on the Iran Breast Cancer Society patients in Tehran, Iran. As mentioned earlier, the aim was to propose an optimal therapeutic plan based on the unique geometry features of each patient’s tumor.

The CNN used for segmentation was trained on a comprehensive dataset of annotated MRI images, which included high-contrast and non-high-contrast regions of breast cancer. The training dataset was sourced from multiple medical institutions and included images with varied contrast and anatomical variations to ensure robustness. The performance of the CNN was rigorously validated using a separate validation set, which also included diverse MRI images. Metrics such as accuracy, sensitivity, specificity, and the Dice coefficient were used to evaluate the CNN’s performance. The model achieved high accuracy across these metrics, indicating its reliability in segmenting breast tumors. To guarantee that the enclosed areas are medically appropriate, the segmented regions produced by the CNN were reviewed by experienced radiologists. This review process ensured that the segmentation accurately represented the tumor boundaries, including non-high-contrast regions.

Segmented breast MRI of four patients.

The focusing of an ultrasonic signal is typically achieved either by using a phase delay or a focusing lens on the transducer side. In this model, a spherically focused ultrasound transducer with a concave lens emits the signal. The transducer housing and the lens are assumed to be rigid. The FDA-approved MATLAB code was modified and implemented to run HIFU simulation49. The two main parts of the code are the propagation (ultrasound field) and heating (temperature elevation) modules. The spherical bowl transducer with inner radius \(a_1=0\), outer radius \(a_2=3.2\) cm, and radius of curvature \(d=5.174\) cm radiating 50 W acoustic power at 1 MHz into water. The breast tissue is located at \(z=1\) cm, and the simulation terminates at the end of the tissue medium. The model setup is shown in Fig. 3.

Visualization of computational boundaries.

Many important properties of continuous-wave ultrasound beams and their heating effects are predicted by the HIFU simulation. From a frequency-domain perspective, this is accomplished by integrating a high-order parabolic approximation of the Westervelt equation, the wide-angle Khokhlov–Zabolotkaya–Kuznetsov (WAKZK) equation. This yields the spatial distribution of pressure for each harmonic, taking into account beam diffraction, interference effects, power-law frequency-dependence of attenuation and the corresponding phase velocity dispersion, the fraction of energy loss converted to heat, nonlinear effects of higher harmonic generation/wavefront steepening, and the augmented heat generation due to shocked waveforms. The average temporal intensity and power density are computed from these pressure fields. The power density is then fed into the bioheat transfer (BHT) equation, which is subsequently used to calculate the temperature and thermal dose fields.

The propagation equation approximates the generalized one-way Westervelt equation with a high-order (wide-angle) parabolic approximation:

where p (Pa) represents pressure, t (s) represents time, c (m/s) represents small-signal sound speed, \(\nabla ^2\) (cm\(^{-2}\)) represents the Laplacian in cylindrical coordinates, \(\alpha \) (cm\(^{-1}\)) represents the attenuation/dispersion function, \(\omega \) is angular frequency (rad/s), \(\beta \) (dimensionless) represents the nonlinear parameter, and \(\rho \) (kg/m3) represents mass density. The wide-angle parabolic approximation results in a one-way wave equation, so scattering and reflection are not taken into account. It results in a more tractable model which accurately represents off-axis propagation to about 45°, compared to about 20\(^{\circ }\) for the standard parabolic approximation used to obtain the KZK equation. For layered media, the transmission coefficient is calculated at interfaces to account for reflection loss, and c, \(\alpha \), \(\beta \), and \(\rho \) are piecewise constant functions of the axial coordinate z. The attenuation assumes the power law form \(Re[\alpha (f)]=\alpha _0(f/f_0)^\eta \) and requires \(\alpha _0\) value at \(f_0=\)1MHz and the exponent \(\eta \in [0,2]\) for each layer. From this, the corresponding phase velocity dispersion (imaginary part of \(\alpha \)) is calculated exactly using the differential form of the Kramers–Kronig relations. After p has been calculated, it is used to obtain the power density and intensity using the following relationships:

where \(p=\sum _k[A_k e^{i\omega k(z/c-t)} +A_k^* e^{-i\omega k(z/c-t)}]\), \(\phi \) (dimensionless) is the fraction of attenuation due to absorption, and k is the harmonic number. The summed terms result from viscous heating, while the derivative of the time average of the squared pressure accounts for nonlinear loss. With the power density known, the temperature dynamics are calculated using the bioheat transfer equation50,

Here \(C_p\) (J/kg \(^{\circ }\hbox {C}\)) is heat capacity, T (\(^{\circ }\hbox {C}\)) is temperature rise above equilibrium, \(\kappa \) (W/m \(^{\circ }\hbox {C}\)) is thermal conductivity, and w (kg/m3s) is the blood perfusion rate. From the temperature dynamics, thermal damage is estimated using the dose metric51

where t has units of cumulative equivalent seconds of exposure at 43 \(^{\circ }\hbox {C}\). This is divided by 60 to obtain the familiar unit CEM (cumulative equivalent minutes). Detailed information about the properties of all the materials utilized in the study can be found in Table 1.

It was recognized that the breast is not a perfectly homogeneous medium, and the amount of fat can vary significantly, especially in dense breasts. The MRI data indicated different densities among the four patients. To address this, for each patient, the MRI data was analyzed using a combination of intensity thresholding and region-based segmentation techniques to determine the proportion of fatty and glandular tissue. Intensity thresholding allowed us to differentiate between fat and glandular tissues based on their characteristic signal intensities in the MRI images. Region-based segmentation was then applied to accurately delineate and quantify the respective tissue types within the breast volume61. Based on this analysis, the acoustic and thermal parameters were adjusted to reflect the specific composition of each breast. The simulations used a weighted average of the parameters based on the proportions of fat and glandular tissue. For example, if a breast had 60% fatty tissue and 40% glandular tissue, the thermal and acoustic parameters were adjusted accordingly to reflect these proportions. As a result, breasts with higher fat content had adjusted parameters closer to those of fatty tissue, while denser breasts had parameters adjusted towards glandular tissue properties. Specific examples of training data include parameter sets such as a breast with 70% fatty tissue having a thermal conductivity of 0.29 W/m \(^{\circ }\)C and a specific heat capacity of 3070 J/kg \(^{\circ }\)C, whereas a breast with 70% glandular tissue had a thermal conductivity of 0.40 W/m \(^{\circ }\)C and a specific heat capacity of 3470 J/kg \(^{\circ }\)C.

It is not easy to train a deep learning system to recognize a nonlinear map from high-dimensional data pairs of inputs and outputs. Researchers have discovered that experimentally established rules may be used to regulate the time-dependent dynamics of a predefined system62,63,64. This underlying data may be used as a regularization factor to limit the space of potential solutions to a field domain that is allowable in the desired calculations. Incorporating this sort of structured data into a learning algorithm may improve performance by boosting the data’s functional content, allowing it to find the best possible answer with little training data and generalize effectively65,66.

Given the recent development in model-based deep learning techniques, a neural network that consists of an input/output layer, hidden layers with neurons, weights, and biases may be annotated as illustrated in Fig. 4. This neural network design has been shown to be capable of dealing with the simulation model and predicting solutions by embedding the provided nonlinear or linear partial differential equations (PDEs) into the solution procedure and considering the surgical HIFU constraints as a loss function. The supplied model, which is regulated by certain PDEs, makes it feasible to teach this neural network to anticipate the optimal HIFU presurgical plan.

Diagram of NN architecture for finding optimal HIFU pathway. The input layer of the NN includes tumor’s spatial inputs. The output layer computes the solution of the given model and embeds it into the loss function. By minimizing the loss function, NN can generate the surgical plan with respect to the previous conditions.

To properly cover a vast target zone with HIFU, many sonications are required. A possible solution I during treatment, the HIFU transducer follows a certain path through the tissue. The treatment is just transitory, and it takes place at points inside the tissue where the HIFU focus is placed. Its total number of sonications is limited to N, which is often inside the tens. The sonication length determines the amount much energy delivered during a single sonication (\(t_h\)) and the length of the subsequent cooling interval (\(t_c\)). This cooling interval refers to the time period during which the HIFU device is paused to allow the treated tissue to cool down. This interval is crucial to prevent overheating and potential damage to the surrounding healthy tissue. One sonication is therefore described as a 4-tuple \(S_i\) consisting of two spatial coordinates of the beam focus, as well as sonication and cooling intervals \(t_h\) and \(t_c\):

As a result, the patient management problem is described as determining the best location and sonication periods for a specific number of ablations to destroy the target volume while sparing the surrounding region.

The NN thermal damage model generates a spatial map of \(CEM_{43}\) that covers the whole treatment I. To create a binary mask of damaged tissue, this map is thresholded at 240. However, while assessing the HIFU therapy’s quality, every tissue in the target zone is destroyed, but these tissue outside the tumor (prohibited region) is left intact.

The fitness functions for presurgical treatment planning problems can be written as

D seems to be the binary mask that represents the treated area, \(\overline{D}\) seems to be the complementary mask that represents the non-treated zone, and C seems to be the target map that defines the area to be treated, where Z, R are the domain sizes in the z and r dimensions. Because C is stated as a space function, the user may specify the amount of urgency with which a certain location in the space should be addressed or safeguarded. This allows the fitness function to incorporate two key concepts: (1) good tuning of the shapes of the target and prohibited areas, and (2) the introduction of gradient into the fitness function space, which directs the prediction and optimization process away from prohibited and toward desired areas. The goal is to remove as much fitness capability as feasible.

In order to find an optimal presurgical plan, the target area must be defined for the algorithm. The boundary points on each 2D slice of the tumor have two coordinates (z, r) that reflect the geometric features of that area. These dimensions, along with the total number of sonications, are given to NN as input. The NN during the training process offers the best thermal dose parameters, including location, heating, and cooling times. Then go to the next area and do the same process. After finding the treatment parameters for each area, the fitness function (\(f_1\)) is checked. If the treated area is outside the tumor, this function takes on a positive value. In this case, the location of the proposed treatment area will change so that the value of this function is zero. This will prevent it from entering and damaging the prohibited area. Once the treatment parameters have been calculated for all areas, it is time to see if the entire target area has been effectively treated. For this purpose, the second fitness function (\(f_2\)) is examined to determine the effectiveness of the treatment. If an untreated area remains, this function will have a positive value, and if the entire target area is treated uniformly, the value will be zero. If the value is positive, it is clear that the areas are not small enough for one sonication to cover it all. As a result, all of the above steps are repeated for the same tumor with different sonication pathways. This loop continues until the entire target area is adequately covered. Each treatment plan will be evaluated by using the HIFU simulation and estimating the final loss function. This algorithm is shown in Fig. 5.

Diagram of NN architecture for solving the 2D optimal pathway scanning to predict the HIFU surgical plan. The first section is the NN with two spatial inputs z,r and the total number of sonication N, and the HIFU pathway parameters as the output value. The next two sections are acoustic and thermal analyses. The last section represents the HIFU loss function embedded with the deep learning algorithm, with the training sonication output. By minimizing the loss function, NN can generate the optimal HIFU pathway with respect to the predefined constraints.

The proposed deep learning method integrated the fundamental principles of physics with neural networks to solve complex HIFU presurgical plan problems. In clinical practice, when a region requires treatment, the user would input the spatial coordinates of the tumor boundaries (z, r), and the desired number of sonications (N). The AI model would then output the sonication points and parameters, including the specific coordinates (Z, R) for each sonication, and the corresponding \(t_h\) and \(t_c\) values. These values are the input parameters for the HIFU numerical analyses including acoustic and thermal simulations. Based on the numerical analyses, the loss functions can be calculated, thereby facilitating the learning process through their minimization over multiple iterations. This process ensures that the entire tumor volume is treated effectively while minimizing damage to surrounding healthy tissue. The spatial and temporal domain for the NN model is selected as 0.1 mm in each direction. The model is trained to ensure that given an input (z, r, N), the network outputs, \((Z,R,t_h,t_c)\) are fed to the wave and heat equations, and the loss functions are minimized. By obtaining numerical solutions of the governing physical laws, directly into the neural network’s loss function, this approach enabled the model to learn from the inherent physics of the problem. This approach leverages the NN’s capacity to approximate complex functions while ensuring that the solutions adhere to the known physical laws, thereby reducing the reliance on large datasets and enhancing the model’s generalizability.

The NN architecture used in this study consists of 9 layers and 20 neurons in each layer. This architecture was chosen to balance computational efficiency and the ability to capture complex nonlinear relationships within the data. The ReLU activation function was selected for the hidden layers due to its ability to mitigate the vanishing gradient problem and accelerate convergence during training. The neural network was trained using the Adam optimizer, with a learning rate of 0.001. The loss function used was Mean Squared Error (MSE), which is suitable for regression tasks involving continuous output variables. The model is trained for 100 epochs to ensure convergence and a batch size of 32 is used to balance computational efficiency and training stability. The total loss is computed as a sum of \(f_1\) and \(f_2\) which led to simultaneous optimization of both parameters, and the gradients of the total loss with respect to the NN parameters are obtained using backpropagation. These gradients indicate how much each NN parameter needs to change to reduce the total loss. As a result, the NN can adapt its parameters to minimize both \(f_1\) and \(f_2\), ensuring effective and safe treatment plans. Moreover, using NN allows for rapid optimization and real-time adjustments in the treatment planning process.

To validate the accuracy of the employed simulation and the proposed AI algorithm, nine HIFU treatment plans were developed for bovine liver tissue for the simulation, and five treatment plans were generated for the AI algorithm, respectively. As the acoustic and thermal parameters will differ from those used for breast cancer, empirical values for the ex vivo sample were measured through various tests and listed in Table 2. In order to have consistency between simulation and experiment, these parameters were implemented in the simulation to generate several scenarios with various parameters. In the ex vivo experiments, maintaining actual blood flow is not feasible. Therefore, the blood perfusion effect is neglected in both simulation and experiment. Before HIFU irradiation, the bovine liver tissue was degassed to remove dissolved gases that could lead to cavitation and boiling. This process involved placing the tissue in a vacuum chamber to reduce the gas content, thus minimizing the risk of cavitation. Then, the samples were placed in a degassed water bath maintained at a physiological temperature (37 \(^{\circ }\)C) to mimic in vivo conditions and HIFU transducer was calibrated and positioned to deliver focused ultrasound to the target areas within the liver samples. Temperature rise and lesion formation were monitored using thermocouples placed within the tissue and the experimental results were compared with simulation predictions to validate the accuracy of the model.

The experiments given in this study have three primary goals: (1) to confirm the notion that AI can create appropriate HIFU treatment plans, (2) to develop appropriate fitness functions for the algorithm, and (3) to assess the AI’s computational complexity. The study was done in actual settings during the assessment of the suggested method. Material qualities, transducer parameters, and simulation parameters have all been generated using real-world patient data, a real-world HIFU transducer, and numerical analysis.

This section assesses the AI’s ability to discover a viable treatment plan for a specific patient. The AI’s ability to come up with an effective treatment plan is the most important component. The optimal solution covers the whole treated region while leaving normal tissue unaffected when the fitness value is equal to 0. Using the proposed algorithm, the treatment plan for each epoch of the AI-based algorithm in the simulation is shown in Fig. 6. The boundary of the target area imported from MR image processing is shown with a red line. The treated area in which the CEM is greater than 240 and the affected area in which CEM is between 80 and 240 are shown in blue and yellow, respectively. The treatment plan gradually becomes larger to cover the entire tumor completely. In all, the algorithm recommends 13 consecutive sonications, which results in a more uniform thermal field than those who use the same HIFU energy for each treatment location42. As expected, at each iteration, the algorithm tried to cover the tumor uniformly. The shapes of the lesion were changing in order to satisfy the two fitness functions: (1) being harmless in a prohibited area (outside the tumor) and (2) covering the entire tumor with minimum treatment time. When the treatment sites were close enough, the heat source impact from surrounding lesions towards the current target caused the lesion size to alter swiftly for the final two places. As a result, lesion coalescence occurred, and the final solution had no gaps. Furthermore, by employing the iterative approach, severe lesion coalescence may be avoided, while uniform lesion generation is achieved with the least amount of sonication. The approach also has the advantage of having low computational overhead and being able to be used prior to HIFU treatment. As a result, the best presurgical strategy proposed here will be tested in vitro later.

The process that AI finds the best presurgical plan for a desired tumor.

The first finding reveals that the bigger the number of sonications the AI can employ, the higher the treatment plan’s average quality. The coverage control becomes more exact as the number of sonications increases (possibly shorter/smaller). On the other hand, as the length of therapy lengthens, it will become hard for both the patient and the computer to evaluate the treatment plan (more runs of the ANN).

In the majority of its runs, the AI can develop appropriate treatment plans if the minimal number of sonications is not too severe. As the sonication number (N) was continuously increased, the algorithm computed the investment idea between treatment plan quality and the number of sonications, and the operation was completed once the entire tumor was covered.

The heat source was sized using the nominal parameters of the H101 Sonic transducer and a single element transducer. With a such radius of curvature of 51.74 mm, an aperture diameter of 64 mm, and such frequency of 1 MHz, the concentrated beam elliptical size is around 10 × 1.4 mm. The spatial peak of the heat deposition rate (spatial peak intensity) was chosen at 1000 W/cm2, which is close to the values used in clinical treatments (Eq. 3).

According to numerical convergence tests, the parameters of the numerical thermal model were set as follows:

Discretized simulation domain size 810 \(\times \) 668 grid points, periodic boundary condition.

Spatial resolution 0.05 mm.

Temporal resolution 0.01 s.

The total length of the simulation \(\sum _{i=0}^N(t_{h,i}+t_{c,i})\).

Allowed positions of the ultrasound focus center limited to the bounding box at grid positions.

Maximum sonication and cooling periods \(t_h=[1,3 s]\), \(t_c=[0,2 s]\).

Number of sonications considered \(N\in \{1,2,...,\infty \}\).

The chosen sonication and cooling periods for the HIFU treatment were based on a combination of experimental setup, simulation results, and clinical considerations to ensure effective and safe treatment while minimizing the total treatment time. In HIFU treatments, cooling is an essential aspect of managing the temperature of both the targeted tissue and surrounding healthy tissues. The cooling conditions can differ between simulations and actual clinical practice, particularly in how the cooling is applied and managed. In this simulation, a uniform cooling condition is assumed across the entire tissue area. This simplification allows for consistent and controlled cooling, ensuring that heat is dissipated evenly and preventing hot spots. However, in actual clinical practice, cooling is typically applied to the propagation path of the HIFU using methods such as water bags, cooling pads, or other localized cooling devices. To address that, the boundary conditions in the simulations can be set to maintain a constant temperature at the edges of the tissue, mimicking the effect of a water bath or other cooling medium. While the initial settings for \(t_h\) and \(t_c\) are within the specified ranges, the NN-based optimization process allows for flexibility. Depending on the shape and size of the planned treatment area, and the physician’s recommendation, the heating and cooling time ranges can be adjusted to higher upper bounds to optimize the overall treatment efficacy and duration.

The four treatment plans are visualized in this section (Figs. 7, 8, 9, 10). Each plot in those images illustrates a single sonication layer in the treatment plan’s sequence of appearance. The yellow spot on the lesion map reveals exactly where \(CEM_{43}\) has surpassed a value of 240 min. The blue area represents a location that has not yet been properly treated and where the temperature rise is minimal (\(80<CEM_{43}<240\)). The first figure for each tumor indicates the target area in which the algorithm tried to find the treatment plan. The actual treatment area following the first layer of sonication is shown in the second picture of each tumor (including the cooling period). The portion of the energy from earlier layers has not yet dissipated, therefore the next layer of sonications is using it to elevate the treated region. For each patient, the whole target area is covered, eventually and shown in the final figure. At each step, the overheating of the normal tissue was calculated, and if the cumulative temperature in the prohibited area was rising rapidly, the solution procedure would be substituted with a less harmful one. It can be deduced that the non-treated area gradually decreased, and eventually, no mistreated area was left. The non-treated region denotes areas where the treatment failed (due to insufficient energy deposition), whereas the mistreated area denotes areas where the banned area was harmed.

Presurgical plan for patient 1.

Presurgical plan for patient 2.

Presurgical plan for patient 3.

Presurgical plan for patient 4.

The fitness value analyzes the plan quality since it is an aggregate of two metrics (see Eqs. 7, 8). Table 3 presents the treatment parameters at each sonication for all four patients. The first two columns for each patient determine the location of the focal point, and thus the location of the transducer will be specified. The last two columns show the suggested heating and cooling times, respectively. This table can be submitted to the HIFU therapists for the clinical decision and to evaluate their presurgical plan.

The number of sonications and the total treatment time can vary significantly between patients due to several factors. In this study, Table 3 shows that Patient 3 required fewer sonications, while Patient 4 required more. Patient 3 had a smaller and more regularly shaped tumor, which required fewer sonications to achieve complete ablation. A regularly shaped tumor typically has a symmetrical and simple geometric form, such as a sphere or ellipsoid, which allows for more efficient coverage with each sonication. In contrast, an irregularly shaped tumor has an asymmetrical and complex geometry, often with protrusions and indentations, which necessitates more sonications to ensure thorough coverage and complete treatment. The irregular shapes require additional sonications to target all regions effectively due to the increased complexity in covering the entire tumor volume uniformly. To illustrate the accuracy and reduction in treatment time, a comparative analysis between our previous method45, which purely implemented an optimization algorithm, and our AI-based approach was conducted. The results demonstrated a reduction (10%) in Mean Absolute Errors (MAE) and a significant decrease in total treatment time (30%) when using the AI-based optimization (Table 4). MAE is a measure of the difference between the predicted values and the actual values, calculated as the average absolute difference between the predicted and actual values. It provides an indication of the accuracy of the model. The Dice Score, also known as the Dice Similarity Coefficient, is a measure of the overlap between two sets, calculated as twice the size of the intersection divided by the sum of the sizes of the two sets. It is used to evaluate the accuracy of segmentation tasks.

Table 4 calculates the MAE and total time for the planned area and thermal dose range. It compares the predicted treatment parameters and coverage with the previous optimization method and the AI-based approach. Table 5 calculates the MAE and Dice Score for the actual coagulation area and thermal dose range. The actual coagulation area was extracted using thermal imaging and histological analysis of the treated tissue to determine the regions where effective coagulation occurred. The reduction in MAE and total treatment time in this study compared to the previous study is attributed to the AI-based approach’s ability to optimize the treatment parameters more effectively. The AI model can analyze complex patterns and relationships within the model, leading to more accurate predictions and efficient treatment plans. As a result, the AI-based approach achieves better coverage of the tumor with fewer sonications and shorter treatment times, improving overall treatment efficiency and effectiveness.

Subsequently, the effectiveness of the numerical HIFU treatment was assessed through nine separate trials conducted on bovine liver tissue. After HIFU irradiation, the tissue samples were fixed and sectioned to obtain thin slices for analysis. These slices were oriented to match the planes used in the simulation. The outcomes from these nine experiments are presented in Fig. 11. In the first and third columns, you can observe the lesion patterns as predicted by the numerical simulation, while the second and fourth columns illustrate the actual treated areas following HIFU exposure. Each trial encompassed three sonications with a 1-s cooling interval. The spacings between sonications were varied in the range of 0–5 mm in r and z directions and the heating durations were 3 s. In this figure, the labels “\(r=0\), \(z=0\), etc.” in the top left of each graph denote the specific coordinates in the radial (r) and axial (z) directions at which the data is being shown. The vertical axis (r in cm) represents the radial distance from the HIFU focus, while the horizontal axis (z in cm) represents the axial distance along the beam. For example, a graph labeled “\(r=0\)” presents data along the central axis (\(r=0\)) of the HIFU beam, with temperature or thermal dose varying along the z-axis. In contrast, a label such as “\(r=3\) mm” indicates that the data is shown at a radial distance of 3 mm from the center, with variations along the z-axis. Additionally, the quantitative evaluation of the proposed surgical plan is presented in Table 5, where MAE and Dice Scores are reported for nine distinct surgical plans. Despite the presence of minor areas where the intended 240 \(CEM_{43}\) dosage was not fully delivered, a comparison between the planned and actual treated regions reveals a notably high level of agreement. Variations in thermal diffusion within the tissue, slight differences in acoustic properties between the ex vivo tissue and the assumptions used in simulations, and potential errors in imaging could contribute to discrepancies.

Comparison of the numerical simulation with experimental treatment plan composed of 3 sonications.

During the experiments, the temperature rise was continuously monitored using thermal imaging and thermocouples. Thermocouples were carefully inserted into the bovine liver tissue at specific depths and locations to measure temperature directly within the target area, including at the HIFU focus. The thermocouples were placed using a stereotactic frame to ensure precise positioning, with one thermocouple positioned at the HIFU focal point and additional thermocouples placed in surrounding regions to monitor temperature gradients. The temperature distributions predicted in the central region of the tumor (focal point) during the progression of the ablation process including 10 s heating following bo 90 s cooling, are depicted in Fig. 12, alongside the results obtained by experiments. It is evident that our present study aligns well with the experimental findings, indicating a good agreement between the two studies.

Comparison of simulation and experimental results for the temperature distribution in the focal point during HIFU sonications including 10 s heating and 90 s cooling.

To confirm the accuracy of the proposed AI method, five preset HIFU treatment plans were developed for bovine liver tissue and also implemented to experiment with the conventional clinical procedure29. The treatment planning region, marked by green lines in Fig. 13, was precisely outlined to align with the targeted tumor area in the bovine liver samples. In addition to the location of each sonication (z, r), Optimal heating \((t_h)\) and cooling \((t_c)\) times were identified through iterative testing and comparison with the simulation predictions. The findings revealed that the effectiveness of the treatment with AI-optimized parameters was notably higher than the conventional method. The acoustic and thermal simulation outcomes combined with the deep learning approach were validated by comparing the predicted and actual treatment results, affirming the reliability of the AI method employed for ex vivo experiments. Table 6 provides the calculation of the MAE and Dice Score for the actual coagulation area and the thermal dose range, comparing both the proposed method and the conventional approach.

Comparison of the AI proposed method with conventional treatment plan.

In Asia and Europe, HIFU has been employed in clinics with encouraging results. However, it is still in its early stages, and technological and clinical concerns have yet to be resolved 11. The concentrated ultrasound beam is now scanned across the tumor in discrete regions (for example, the FEP-BY02 system) or along pre-determined scanning courses (for example, Chongqing Haifu Technology Ltd., Chongqing, China)29. HIFU settings are typically maintained throughout treatment until the patient’s intolerance requires modification. As the HIFU therapy advances, the lesion size will grow due to heat buildup and diffusion effects. As a result, computational modeling and in vitro studies have revealed that lesions formed at the outset of focused ultrasound therapy may be insufficient for coagulation while developing as the treatment advances, thus increasing the risk of undesirable thermal collateral damage. Predictable and consistent lesion development is required from the physician’s perspective. This work developed an AI-based algorithm for optimum lesion development, studied treatment time and quality, and validated lesion generation in bovine liver. The concentrated ultrasound energy given to the target may be varied by changing the input energy, the number of pulses, or the exposure length37. The acoustic output power, not the energy, was the most important component in the subjective pain response to HIFU pulses, according to clinical experience67. As a result, constant acoustic power and frequency and variable location and heating/cooling time were used in this research.

The focus zone of some kind of single HIFU beam is often the first tiny cigar-shaped volume (1–2 mm wide and 10 mm long), inadequate for complete tumor ablation. The production of linear vibrations, either continuously or discretely68 and electrical transducer steering69,70,71 has come from the development of different techniques for scanning a confined focus zone. Mechanical steering has the following advantages: cheap cost, great dependability, high resolution, and ease of control. It is possible that the movement speed (a few millimeters per second) is not rapid enough to compensate for the rate of breathing (i.e., 10–40 mm and 30–80 mm in the superior–inferior direction of the liver in shallow and deep breathing modes, respectively72). The precision for HIFU focus is influenced by the number of laser phased arrays utilized and the phase resolution provided to each element. Even when sparse random components (i.e., 5–10 mm) are used, the growth of the diffraction lobe will affect the safety of HIFU ablation if the divergence from the geometrical focal point is significant73. As a result, some mechanical motion is required by the phased array system, which is expected to boost HIFU coagulation efficiency. In this study, the time interval required to move the HIFU transducer from one treatment location to the next, known as the gap motion time, was found to affect the treatment outcome in breast tissue. Specifically, experimental observations and previous studies have shown that if the gap motion time was less than 3 s, it significantly influenced the thermal dose distribution and the resulting treatment efficacy. For instance, in our experiments with bovine liver tissue, we observed that shorter gap motion times led to overlapping thermal doses, resulting in excessive heating in certain regions and insufficient treatment in others. This observation is consistent with previous findings26, which also demonstrated that gap motion times below 3 s can lead to suboptimal thermal dose distribution. B-mode ultrasound images74,75 and acoustic radiation force imaging (ARFI)76 might be able to identify HIFU-induced lesions without being impeded by HIFU pulses77 if the interval period was increased.

In a powerful acoustic environment, bubble cavitation is a common occurrence. Bubbles are major acoustic wave scatterers that form when a fluid heats or when the negative pressure of an acoustic wave causes the formation of small gaseous nuclei. As a result, the pre-focal region absorbs more energy, the lesion changes from cigar to tadpole, and the transducer moves closer to the patient78. Boiling can cause localized hot spots and rapid temperature fluctuations, which are challenging to model accurately in simulations. The presence of vapor bubbles can scatter and absorb ultrasound energy, affecting the predicted thermal dose distribution. Simulating cavitation accurately requires complex models that account for bubble dynamics, which are often simplified in standard thermal simulations. In this simulation, the temperature rise profiles were carefully monitored to identify regions where temperatures might exceed 100 \(^{\circ }\)C. While the simulations aimed to avoid such high temperatures, certain conditions and high-intensity settings could lead to localized boiling predictions. During the experiments, the temperature rise was continuously monitored using thermocouples. Special attention was given to ensure that the temperature did not exceed 100 \(^{\circ }\)C, thereby preventing boiling and its associated complications. To address the potential influence of viscous heating at the HIFU focus, the measurements were corrected by calibrating the thermocouples against a known temperature standard before and after the experiment. Additionally, we used a numerical model to estimate the contribution of viscous heating and subtract this from the measured temperatures at the focus, ensuring that the reported values reflected the actual thermal effects of HIFU. The results of thermocouple measurements were closely aligned with the numerical simulation providing a comprehensive view of the temperature distribution across the entire tissue area and offering precise point measurements. The effects of burst kinetics and wave scattering on lesion progression have been investigated theoretically in the HIFU area, and they may be predicted and incorporated with BHTE79. Even though the in vivo experiment uses output power to replicate the pattern of lesion development, the particle diameter and concentration used in the simulation are difficult to detect with current technology. Using an array of passive receivers, passive cavitation mapping may be utilized to discover cavitation dispersion during HIFU exposure80. Due to a lack of data on 2D cavitation and subsequent tumor progression in the present model, HIFU treatment planning can be utilized to correct a tiny tumor in the post-focal area while avoiding overtreatment in the pre-focal.

The complex process of thermal energy transmission in living tissue includes transmission, convection, radiation, metabolism, evaporation, and phase change67. The degree of ischemia and vascular structure, which differ substantially between tumors and malignancies, influence convective heat transmission. As a result, reliable heat transfer forecasting in biomaterials demands a full understanding of tissue thermal and perfusion parameters. Thermal conductivity and diffusivity of biomaterials are commonly studied using thermal probe methods81,82. The temperature response for power deposition determines blood perfusion, albeit low perfusions are difficult to evaluate due to the dominance of conduction. It is, however, impossible to identify the temperature features of vascularity precisely and noninvasively in a deep-seated malignancy or solid tumor on the spot.

Furthermore, after HIFU therapy, color Doppler ultrasonography images indicated an abrupt pause accompanied by the cessation of blood flow inside the tumor arteries83,84,85. The progressive degradation of elastic fibers in the tunica media of the artery lowered vascular diameter and finally led to blood flow restriction owing to both the heat and mechanical impacts of HIFU. As a result of the lower “heat sink” impact of blood circulation, lesion development would consume less energy.

With an open-loop delivery strategy, temperature variables, plasma perfusion, geographic and temporal variability of tissue characteristics, and bubble concentration are difficult to measure (i.e., treatment planning). As a result, a significant difference between simulation and in vivo outcomes is predicted. In a number of methods, MRI thermometry has been used as feedback for closed-loop ultrasonic heating in the development of algorithms39,86,87. Because it only takes a few seconds for an MRI to identify lesion growth and quantify temperature rise during HIFU therapy with great precision and resolution, the temperature may be underestimated88. Averaging the temperature distribution throughout the volume of the MRI voxel (0.3 \(\times \) 0.5 \(\times \) 2 mm3) indicated a peak of 73 \(^{\circ }\)C after 7s of sustained HIFU exposure when boiling (100 \(^{\circ }\)C) commenced. The advantage of simulation can be combined with MRI thermometry to strengthen the control strategy. The lesion can be precisely calculated from the thermal dose using MRI thermometry following correction for the spatial and temporal averaging effect through the simulation. With the advancement of HIFU ablation, it is now possible to employ AI or a smart system to forecast how a new lesion will change form and location based on past lesion data.

However, there are several limitations associated with the proposed method. First, the accuracy of the simulation depends significantly on how well the acoustic, thermal, and structural parameters of the anatomical maps are set. Differences between simulated and actual parameters can affect the precision and reliability of the treatment outcomes. Second, simulating heat conduction in two dimensions simplifies the computational model but may neglect important spatial variations in temperature distribution. This simplification can lead to inaccuracies, particularly in complex anatomical regions. Finally, even when we conducted 2D thermal simulations without employing an acoustic model, the process required a significant amount of time, ranging from 36 to 48 h, to generate an effective treatment plan. To mitigate this, our next research phase will involve a complete algorithm overhaul, transitioning to high-performance programming languages like parallel C/C++, with the goal of reducing computation time by at least fivefold.

HIFU represents an advanced and less invasive approach to treating cancer. Nevertheless, achieving precise targeting of the ultrasound beam to selectively destroy the tumor while safeguarding healthy tissue requires extensive preoperative planning. The conventional methods of manual and semi-automated planning are not only time-consuming but also computationally demanding. Consequently, there is a growing interest in the development of fully automated treatment planning techniques to streamline this process.

This paper introduces an optimization deep learning technique for the HIFU tumor ablation procedure. The implementation of deep learning in HIFU planning yielded highly favorable results, with mismanaged and inadequately treated regions accounting for just 0.06%. These findings underscore the capability of deep learning to generate treatment plans that come remarkably close to the ideal. The key advantage of this method lies in its simplicity, as it only requires a patient’s anatomical map along with information about target and restricted areas. The neural network-based optimization process handles the remainder of the planning.

This study demonstrates the potential of an AI-based algorithm to optimize HIFU treatment parameters for effective and safe ablation of breast tumors. By leveraging ML techniques, the proposed method dynamically adjusts sonication points and parameters, significantly reducing treatment time and improving precision. The experimental validation in bovine liver tissue showed a high level of agreement between the planned and actual treated regions, highlighting the method’s accuracy and robustness.

All data used for this study are available from the author upon request. For requesting data produced in this study, please contact the corresponding author.

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This research was supported by Changwon-city, Republic of Korea through Korea-Canada Joint AI Research Program.

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Salman Lari & Hyock Ju Kwon

Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Mohammad Kohandel

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Conceptualization, S.L. and H.J.K.; methodology, M.K.; software, S.L.; validation, S.L. and M.K; formal analysis, H.J.K.; investigation, S.L.; resources, M.K.; writing—original draft preparation, S.L.; writing—review and editing, M.K. and H.J.K.; visualization, S.L. and M.K.; supervision, H.J.K. and M.K.; project administration, M.K.; funding acquisition, H.J.K. and M.K. All authors have read and agreed to the published version of the manuscript.

Correspondence to Hyock Ju Kwon.

The authors declare no competing interests.

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Lari, S., Kohandel, M. & Kwon, H.J. Model based deep learning method for focused ultrasound pathway scanning. Sci Rep 14, 20042 (2024). https://doi.org/10.1038/s41598-024-70689-9

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Received: 12 April 2024

Accepted: 20 August 2024

Published: 29 August 2024

DOI: https://doi.org/10.1038/s41598-024-70689-9

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