On the interception of the optimal imaging plane for pleural line scanning with automatic robot assisted lung ultrasound: an experimental study

Abstract

Background:

Lung ultrasound (LUS) is nowadays an important tool to evaluate the state of lung surface. However, it is strongly operator-dependent, leading to reduced reproducibility of LUS analysis. Even though LUS acquisition protocols can improve LUS reproducibility and help standardizing LUS exams, human operators can guarantee only a limited precision in intercepting the optimal imaging plane. Hence, in this study, we assess the possibility to automatically intercept the optimal imaging plane in LUS examinations, i.e., the imaging plane perpendicular to the pleural plane (PP), by extracting three features, then utilized to guide a UR5e robotic arm handling an ultrasound probe.

Methods:

The main focus of this study consists on evaluating the potential of these three features in estimating the PP position with respect to the probe. To do so, we designed a simplified but highly controllable environment, where PP was mimicked with a steel plate (to simulate a highly reflective acoustic interface), while intercostal tissues were mimicked with a 2-cm-thick beef meat. The environment was imaged with a linear probe connected to an ULA-OP platform, which was held by an UR5e, programmed to explore 8 different paths of acquisitions with a rotational angle (RA) ranging from −20° to 20° (1° step size). This resulted in 328 positions that could be explored; each position with RA=0° corresponds to the optimal imaging plane. Radiofrequency data were acquired and post-processed to form normalized log-scale B-Mode images. A rectangular region of interest, defined to include PP, was considered to compute mean intensity at each depth of the region of interest, along lateral dimension. Mean intensity as a function of depth was then utilized to extract three different features, then fed to genetic algorithms to solve optimization problems to guide UR5e towards the optimal imaging plane.

Results and Conclusions:

Genetic algorithms converged towards an average error < 1° after exploring only 18 positions, showing strong potential in automatic probe placement for LUS.

Background

Lung ultrasound (LUS) is an important tool to assess the state of the lung surface, but it is strongly operator-dependent (1–3), thus leading to a reduced reproducibility of LUS analysis (4,5). This reproducibility can be improved by properly designing and adopting LUS acquisition protocols, which can also help standardizing LUS exams (4–6). Despite the use of standardized LUS acquisition protocols, human operators (HOs) can guarantee only a limited precision in intercepting the optimal imaging plane (O-ImP), i.e., “the imaging plane (ImP) perpendicular to the pleural plane (PP)”. Figure 1 clarifies how the intersection between the PP and the ImP is represented as the pleural line (PL) in the reconstructed B-Mode images.

Figure 1.

(A) An illustration of a LUS acquisition scenario is shown with (B) the corresponding reconstructed B-Mode image. It is important to observe how the intersection between PP and ImP (in this case, the O-ImP) is represented as the pleural line (PL) in the reconstructed B-Mode image.

Given the HOs’ limited precision in intercepting the O-ImP in LUS examinations, we here propose an experimental study to assess the possibility to automatically intercept the O-ImP in LUS exams. Specifically, in this study, we introduce three features extracted from radiofrequency (RF) ultrasound signals to be utilized to guide a UR5e robotic arm (Universal Robots, Odense, Denmark) handling an ultrasound probe towards the O-ImP. These specific features are chosen to exploit both the high acoustic reflectivity of PL and its geometric property to be approximated, at least locally, to a straight line. To reach this goal, we have designed a highly controllable environment where we can physically guarantee the probe aperture, which can be seen as a plane defining the elevation and lateral dimensions, to be parallel to the PP, and, thus, the ImP to be perpendicular to the PP. Then, the knowledge of the angle between ImP and PP can be utilized as ground truth to assess the potential of the three investigated features in automatically intercepting the O-ImP.

To the authors' knowledge, no studies on robot-assisted LUS focused on the use of highly controlled experimental models to evaluate the capability of specific ultrasound features in characterizing the O-ImP. In contrast, previous studies mainly focused on automatically placing the ultrasound probe parallel to the body surface to maximize acoustic matching (7,8). Only a recent study on robot-assisted LUS (Lei et al. (9)) presented a strategy to optimize the probe placement based on its position with respect to the PP. Specifically, Lei et al. utilized the PL in the observed B-Mode image as a feedback to adjust the position of the probe to maintain the alignment of the PL with the lateral dimension of the image (9). Even though this strategy can provide advantages when applied for a specific direction of rotation of the probe aperture with respect to the PP, i.e., the one along the lateral dimension, it does not guarantee the interception of the O-ImP. Indeed, besides the direction of rotation along the lateral dimension, other directions of rotation exist. In addition, contrary to what we propose in our study, Lei et al. did not rely on ultrasound features validated on an experimental model in which the orthogonality of the ImP with respect to the PP is physically guaranteed. Specifically, in our study, we propose three new ultrasound features that correlate with the orthogonality of the ImP with respect to the PP, and could thus be utilized to automatically intercept the O-ImP in LUS examinations.

The rest of the paper is organized as follows. In the “Materials and Methods” section, the experimental environment and the data acquisition process will be presented. Then, the features’ extraction procedure will be described and, finally, the genetic algorithms (GAs) used to solve the optimization problems aiming at guiding the UR5e robotic arm towards the O-ImP will be presented. The “Results” section will be dedicated to the quantitative results, whereas both discussion and conclusions will be provided in the last section (“Discussion and Conclusions”).

Materials and methods

Experimental environment

In this study, a highly controllable environment (called ENV_meat) was designed by mimicking the PP with a flat steel plate having dimensions of 17 by 5 cm along X and Y dimensions, respectively (Figure 2). The plate is composed of austenitic stainless steel AISI (American Iron and Steel Institute) 316L (Euronorm number = 1.4404), and its flat surface has an arithmetic mean roughness smaller than 5 µm. Intercostal tissues were mimicked including a 2-cm-thick beef meat, which was placed on top of the steel plate. The steel plate was utilized to simulate a highly reflective acoustic interface, which is an acoustic property shared with the tissue/air acoustic interface present in real cases scenarios with aerated lungs. Indeed, a tissue/steel acoustic interface has the absolute value of the reflection coefficient |R|≍ 0.93, and a tissue/air acoustic interface has |R|≍ 0.99 (10). These similar values of |R| are translated into a comparable percentage of energy reflected by these two acoustic interfaces. Moreover, we choose to utilize a flat steel plate rather than other models (as the sponge phantom presented by Blüthgen et al. (11)) as it guarantees a significantly high control in the experimental design, which cannot be guaranteed by the other models. Consistently, to validate the effectiveness of the proposed features, we required to have a flat surface. Moreover, even though the acoustic impedances of air and steel are significantly different (3.9 x 10^-4 and 46.69 MRayl, respectively), following the Snell law, the|R| values of tissue/air and tissue/steel acoustic interfaces remain comparable. As the high reflectivity was the property we were interested in, we opted to use a steel plate to mimic PP. Both steel plate and meat were then immersed in water to be imaged with a LA533 linear array probe (Esaote, Florence, Italy) [the probe’s pitch and element size along the lateral dimension are respectively equal to 245 and 220 µm (12)] connected to an ULA-OP platform (13). An UR5e manipulator was utilized to held the probe and move it within a 3D volume defined by the X, Y, and Z spatial dimensions (Figure 2). As shown in Figure 3, the UR5e was programmed to explore 8 different acquisition paths, which could intercept different ImPs with rotational angles (RAs) ranging from −20º to 20º (1º step size). These 8 acquisition paths were defined as follows:

Figure 2.

Experimental setup. (A) Picture of the UR5e robotic arm, handling the LA533 Esaote linear array probe. (B) Picture of the LA533 Esaote linear array probe immersed in water to image the meat and the steel plate (PP). The reference spatial coordinates X, Y, Z utilized to move the robot are also shown.

Figure 3.

An illustration of the 8 different acquisition paths is shown. Each acquisition path consists of 41 different positions, with RA ranging from -20º to 20º (with a 1º step size). To simplify the visualization, for each acquisition path, we only depicted the ImP with RA = [-20º, 0º, 20º]. The 8 ImPs perpendicular to PP (i.e., the ones with RA = 0º) are the O-ImPs. Acquisition paths going from 1 to 4 consists of a combination of rotation and translation movements, whereas acquisition paths going from 5 to 8 consists of only a rotation movement. For each path and RA, the yellow line represents the imaginary line lying inside the ImP that connects the center of the probe with the PP. The reference spatial coordinates X, Y, Z are also shown.

• Path 1. lateral dimension of the probe (i.e., the longer one) oriented along the X axis, and both rotation and translation movements along the X axis;

• Path 2. lateral dimension of the probe (i.e., the longer one) oriented along the X axis, and both rotation and translation movements along the Y axis;

• Path 3. lateral dimension of the probe (i.e., the longer one) oriented along the Y axis, and both rotation and translation movements along the Y axis;

• Path 4. lateral dimension of the probe (i.e., the longer one) oriented along the Y axis, and both rotation and translation movements along the X axis;

• Path 5. lateral dimension of the probe (i.e., the longer one) oriented along the X axis, and rotation movement along the X axis;

• Path 6. lateral dimension of the probe (i.e., the longer one) oriented along the X axis, and rotation movement along the Y axis;

• Path 7. lateral dimension of the probe (i.e., the longer one) oriented along the Y axis, and rotation movement along the Y axis;

• Path 8. lateral dimension of the probe (i.e., the longer one) oriented along the Y axis, and rotation movement along the X axis.

To further clarify, we here intend as “both rotation and translation movements” the application of a rotation (along a specific dimension) combined with a translation aiming at guaranteeing a specific property to be maintained. Specifically, this combination of rotation and translation movements guarantees that the intersection between the imaginary line lying inside the ImP and connecting the center of the probe with the PP remains the same (see the yellow lines drawn in Figure 3 for Paths 1, 2, 3, and 4). As clearly observable from Figure 3 (Paths 5, 6, 7, and 8), this property is not maintained when only a rotation movement is applied. The total number of positions to be possibly explored by the UR5e is determined by the number of positions explorable in each acquisition path (i.e., 41, as RA ranges from -20º to 20º with a 1º step size) multiplied by the total number of acquisition paths (i.e., 8). Therefore, a total of 328 positions (pos) could be possibly explored. As each pos with RA=0º corresponds to an O-ImP, the UR5e could intercept 8 O-ImPs, among the 328 pos that could be explored.

Data acquisition parameters

To acquire RF data, for each transmission/reception event, a modulated pulse having center frequency equal to 6 MHz and a -6-dB bandwidth ≍ 4 MHz was transmitted. These specific center frequency and bandwidth were chosen both to properly cover the transfer function of the probe (-6-dB bandwidth from 3.8 to 12 MHz (12,14)) and limit attenuation phenomena occurring inside meat; indeed, a higher center frequency would translate in higher attenuation. For each transmission/reception event, we utilized a sub-aperture of 64 elements, corresponding to the maximum number of elements that can be controlled simultaneously by the ULA-OP (13). To avoid saturation phenomena at the PL, the pressure output was kept low by properly setting the transmitted pulse’s amplitude. To reconstruct the images, dynamic focusing was applied in reception, whereas no focusing was utilized in transmission. No steering was applied in both transmission and reception phases. The post-beamformed images were reconstructed by linearly shifting the 64-elements sub-aperture over the entire array, composed of 192 elements. As a result, the reconstructed images consisted of 129 lines along the lateral dimension. The received signals were sampled with a 50-MHz sampling frequency, and a speed of sound of 1540 m/s was assumed for time to space conversion along depth dimension. Figure 4 shows examples of reconstructed log-scale B-Mode images for the 8 different acquisition paths as a function of RA (ranging from -20º to 20º with a 10º-step size). It is noticeable how at the shallowest depths of the images, i.e., up to approximately 20 mm, depending on the RA, the intensity values are significantly lower (depicted as black-colored pixels). Indeed, the shallowest part of the images is simply a reconstruction of the imaging area where only water is present. The post-processing operations applied to the RF data to form the normalized log-scale B-Mode images are described in the next section.

Figure 4.

Examples of reconstructed log-scale B-Mode images for the 8 different acquisition paths as a function of RA (ranging from −20º to 20º with a 10º-step size). To improve visualization, the images are zoomed and displayed with an imaging depth ranging from 15 to 45 mm.

Features’ extraction

Figure 5 shows how, after the acquisition, to form normalized log-scale B-Mode images, RF data were post-processed by sequentially applying

Figure 5.

Post-processing pipeline applied to the RF data to extract f₁, f₂, and f₃. Specifically, the green blocks indicate standard post-processing operations applied to the RF data to reconstruct log-scale B-Mode images, whereas the blue blocks indicate the processing operations (applied to the log-scale B-Mode images) utilized to extract f₁, f₂, and f₃. The feature extraction block is colored in light blue, and the specific operations performed inside that block are detailly described in Figure 6.

1. a 12th-order band-pass Butterworth filter (having a 6-MHz center frequency and a 4-MHz bandwidth),

2. a Hilbert transform (to extract the envelope),

3. log-scaling,

4. normalization with respect to the maximum value.

Then, after forming the normalized log-scale B-Mode images, we selected a rectangular region of interest (ROI), defined to entirely include the PL. Specifically, the ROI is always defined as the region covering depths from 3 to 6 cm and including the entire lateral dimension. Afterwards, the mean intensity (MeIn) was computed at each depth of the ROI (along the lateral dimension). Thus, we mathematically defined MeIn, at a specific depth d inside the ROI, as follows:

• - MeIn(d) =

where l is an index numbering the 129 lines of the normalized log-scale B-Mode image along the lateral dimension and intensity_dBScale(l,d) is the intensity value of the pixel at line l and depth d of the normalized log-scale B-Mode image.

MeIn as a function of depth was finally utilized to extract the three new ultrasound features, i.e.,

• - f₁ = maximum of cross-correlation of MeIn with the envelope of the transmitted pulse (computed in linear scale);

• - f₂ = variance of MeIn values;

• - f₃ = spatial -12-dB-width of MeIn.

The specific operations performed to extract f₁, f₂, and f₃ are visually described with an example in Figure 6. Specifically, to extract f₁ from an input signal (MeIn), the following operations were performed: (i) both the MeIn and the transmitted pulse envelope were converted in linear scale (conversion performed as intensity_LinearScale = 10^intensity_dBScale, where intensity_LinearScale and intensity_dBScale are the intensity values in linear scale and dB scale, respectively); (ii) the cross-correlation between the two signals obtained in step (i) was computed; (iii) the maximum of the cross-correlation corresponds to f₁. In this case, it is expected that f₁ increases as the ImP is closer to be perpendicular to the PP (as the MeIn signal is expected to be more similar to the envelope of the transmitted pulse). The extraction of f₂ is particularly straightforward as the distribution of values of the MeIn input signal was directly utilized to extract the MeIn variance, i.e., f₂. Also in this case, it is expected that f₂ increases as the ImP is closer to be perpendicular to the PP. Indeed, as the ImP is closer to be perpendicular to the PP, the distribution of MeIn values is expected to be broader due to the presence also of higher values of MeIn (see, as an example, the presence of values higher than -20 dB in Figure 6). Finally, to extract f₃, the MeIn input signal was normalized with respect to its maximum value, and f₃ computed as the spatial width of the normalized MeIn at -12 dB. Contrary to f₁ and f₂, it is expected that f₃ decreases as the ImP is closer to be perpendicular to the PP. Specifically, given the simplified experimental environment we designed (with a flat steel plate mimicking PP), when the ImP is perpendicular to the PP, it is expected that f₃ is closer to the axial resolution of the system at -12 dB, which should correspond to the width of the transmitted pulse envelope at -12 dB (i.e., ≈ 2.39×10^-1 mm).

Figure 6.

Operations performed inside the feature extraction block are depicted. The example shows how f₁, f₂, and f₃ are obtained from the reconstructed log-scale B-Mode image acquired from Path 1 with RA=0º.

Optimization problems’ design

The potential of the above-mentioned features in automatically intercepting the O-ImP was assessed by utilizing GAs. Specifically, f₁, f₂, f₃ were fed to GA₁, GA₂, GA₃, respectively, to solve the following optimization problems to guide UR5e towards the O-ImP:

• - GA₁ max_pos f₁(pos),

• - GA₂ max_pos f₂(pos),

• - GA₃ min_pos f₃(pos),

with pos being a position among the 328 explorable positions. Given that the velocity of convergence towards the O-ImP depends on the initialization pos, we made 328 runs for each GA. The performance was then evaluated in terms of “328-runs average angle error (AAE)”, i.e, the average among the 328 runs of the absolute difference (in degrees º) between the O-ImP and the intercepted ImP as a function of number of explored positions. The utilized GAs were implemented in MATLAB (MathWorks Inc., Natick, USA) with the “ga” function, and by setting as optimization options the “PopulationSize” and “EliteCount” parameters to 2 and 1, respectively. Therefore, for each run, the utilized GAs start by exploring two different positions. As a next step, the position showing the best value of f₁ (i.e., the maximum), f₂ (i.e., the maximum), and f₃ (i.e., the minimum) for GA₁, GA₂, and GA₃, respectively, will survive and be maintained in the next generation. This process is then repeated until exploring 26 positions. To clarify, following the GA’s terminology, each position here corresponds to an “individual”.

Additional analysis to test features’ combinations

Even though the use of a single feature at a time could be enough to precisely intercept the O-ImP, we also investigated whether a combination of f₁, f₂, and f₃ could improve the performance. However, before combining the features, a proper scaling should be applied to avoid features having a significantly higher absolute value (e.g., f₂) to have an excessively high impact on the maximization problem. To properly apply feature scaling, a further simplified experimental environment (ENV_NOmeat) was designed. Specifically, the 2-cm-thick beef meat was removed, and data were acquired and processed to extract the three features as done with ENV_meat. To differentiate f₁, f₂, and f₃ (extracted from ENV_meat) from the features extracted from ENV_NOmeat, we will name the latter as “f₁^NOmeat” ,”f₂^NOmeat”,and “f₃^NOmeat”. As f₁, f₂ needed to be maximized, whereas f₃ needed to be minimized, a pre-processing operation was applied to f₃ and f₃^NOmeat before scaling. Specifically, we defined

1. f₃^mod =- f₃ + offset,

2. f₃^NOmeat_mod =-f₃^NOmeat + offset,

where offset is an arbitrary offset of 1 meter. This operation was necessary to convert the convex shape of f₃ and f₃^NOmeat in a concave shape as f₁,f₁^NOmeat, f₂,f₂^NOmeat, and thus treating the optimization problem of the combined features as a maximization problem. After this preliminary operation applied to f₃ and f₃^NOmeat, scaling was applied as follows:

• -

• -

• -

with min(f₁^NOmeat), min(f₂^NOmeat), min(f₃^NOmeat_mod) [and max(f₁^NOmeat), max(f₂^NOmeat), max(f₃^NOmeat_mod)] being the global minima [and maxima] of f₁^NOmeat, f₂^NOmeat, and f₃^NOmeat_mod, respectively. Then all the possible combinations of f₁^scaled, f₂^scaled, and f₃^scaled were fed to GA₁₂, GA₁₃, GA₂₃, and GA₁₂₃ to solve the following optimization problems to guide UR5e towards the O-ImP:

• -

• -

• -

• -

with ||v¯|| being the Euclidean norm of a vector v¯ (having 2 components when considering GA₁₂, GA₁₃, GA₂₃ and 3 components when considering GA₁₂₃).

Results

Figure 7 shows the 328-runs AAE as a function of number of explored positions for GA₁, GA₂, and GA₃. After exploring 26 positions, the 328-runs AAE is about 0.009º, 1.406º, and 0.070º for GA₁, GA₂, and GA₃, respectively. The strong potential of f₁ and f₃ in automatically intercepting the O-ImP is confirmed when evaluating a 328-runs AAE < 1º. Indeed, in that case, while GA₂ never converges, GA₁ and GA₃ converge after exploring 19 and 18 positions, respectively. A further confirmation on the effectiveness of f₁ and f₃ in automatically intercepting the O-ImP is obtained when evaluating the combination of multiple features (Figure 8). Specifically, after exploring 26 positions, the 328-runs AAE is about 0.082º and 0.095º for GA₁₃ and GA₁₂₃, respectively (i.e., when both f₁^scaled and f₃^scaled are utilized). In contrast, the 328-runs AAE is higher when only one of those two features is utilized (after exploring 26 positions, the AAE is about 1.168º and 0.131º for GA₁₂ and GA₂₃, respectively). Moreover, while GA₁₂ is never converging to a 328-runs AAE < 1º, GA₁₃, GA₂₃, and GA₁₂₃ are converging after exploring 18 positions. As a final observation, Figure 9 confirms how, after exploring 26 positions, the use of f₂ (when evaluating GA₂) and f₂^scaled (when evaluating GA₁₂) leads to a AAE greater than 12º in 17 and 14 runs over 328 (i.e., 5.2% and 4.3%), respectively. This means that the features based on the variance of MeIn (i.e., f₂ and f₂^scaled) present a higher probability in incurring on significantly high errors.

Figure 7.

328-runs AAE as a function of number of explored positions for GA₁, GA₂, and GA₃. The AAEs obtained after exploring 26 positions were also depicted.

Figure 8.

328-runs AAE as a function of number of explored positions for GA₁₂, GA₁₃, GA₂₃, and GA₁₂₃. Thus, the first row depicts the results when 2 scaled features are combined, while the second row depicts the results when 3 scaled features are combined. The AAEs obtained after exploring 26 positions were also depicted.

Figure 9.

Distribution of 328-runs AAE after exploring 26 positions for GA₁, GA₂, GA₃, GA₁₂, GA₁₃, GA₂₃, and GA₁₂₃. The values are expressed in terms of percentage of occurrence (%) with respect to the 328 runs.

Discussion and conclusions

LUS is an imaging tool widely adopted in the clinical practice. It is however limited by a strong operator dependence in the acquisition and interpretation/analysis processes (4,5). While the operator dependence of the analysis could be mitigated by utilizing automatic and/or quantitative approaches (15–24), the operator dependence of the acquisition could nowadays be reduced only by designing and adopting LUS acquisition protocols (6). However, despite the use of LUS acquisition protocols, HOs can guarantee only a limited precision in intercepting the O-ImP.

Therefore, in this article, we have introduced three features to be utilized to automatically guide a robotic arm (handling an ultrasound probe) towards the O-ImP. It is indeed important to intercept the O-ImP to maximize the intensity at the PP, which is the target of LUS examinations. To further clarify, the transmission of ultrasound pressure along an ImP that is perpendicular to the PP should maximize the received pressure and, thus, allowing a more precise characterization of the PL (thus, indirectly, of the lung surface).

The obtained results show how the evaluated features, especially f₁ and f₃, have a strong potential in automatically intercepting the O-ImP in LUS examinations. Moreover, the results show how the use of multiple features at the same time seems to reduce the capability of the utilized GAs to intercept the O-ImP. However, promising results have been obtained also when combining f₁ and f₃ (the 328-runs AAE is about 0.082º for GA₁₃, which converges to a 328-runs AAE < 1º after exploring 18 positions). Despite the relatively higher 328-runs AAE (after exploring 26 positions) of GA₁₃ compared to GA₁ (+0.073º) and GA₃(+0.012), the use of a combination of features could be motivated by the fact that it may increase the robustness of the approach in a more complex scenario, e.g., in a clinical LUS examination.

The proposed robotic LUS setting is aimed at supporting the automatic interception of the O-ImP. The proposed approach could be utilized in a semi-supervised LUS exam, in which a human operator (HO) manually places the probe around a specific scanning area and, then, the GAs guide a robotic arm towards the local O-ImP. This would also help limiting the search area of the robot. Even though the proposed robotic LUS setting is aimed at supporting the automatic interception of the O-ImP, potentially, the three proposed features could be utilized as “quality parameters” for a manual scanning performed by a HO. As an example, the HO could start the manual scanning from a point and, while moving towards different directions, check if, e.g., f₁ decreases or increases. This information would alert the HO whether he/she is far or close to the local O-ImP.

In conclusion, it is fundamental to highlight how the GAs here utilized could not represent the best choice for this application but they were chosen to show the potential of the proposed three features (in automatically intercepting the O-ImP), which are indeed the focus of this work.

Moreover, it is important to highlight how the experimental model we utilized is simplified and, thus, could not be able to reflect all the possible aspects present in a real case scenario. As an example, PL is not a “straight” line and it is not necessarily true that PL covers the entire field of view along the lateral dimension. An additional level of complexity in a clinical LUS examination is represented by the motion of the patient, which can introduce a difficulty in guaranteeing the return of the probe to a better position previously found. Furthermore, when considering a pathological lung, the presence of specific LUS imaging patterns as vertical artifacts, consolidations, and pleural effusion could reduce the efficacy of the three proposed features. To mitigate the influence of these imaging patterns to the proposed features, automatic algorithms could be used to detect and segment them (17,22,23,25) before estimating the three proposed features. In this way, these pathological patterns could be removed from the analysis when estimating the MeIn and, consequently, the features’ values. It is important to mention that the water/meat acoustic interface is also changing orientation when varying RA, and this can have an impact on the PL intensity. Specifically, the change in orientation of the water/meat acoustic interface causes a change in the direction of propagation of the ultrasound wave before reaching PP, and this could impact on the PL intensity. This scenario is different from a real case scenario, where the contact point with the skin of the patient must be guaranteed and, thus, the water/meat acoustic interface is not present.

As future work, we will explore how these features can be adapted to real case scenarios, where the contact point with the skin of the patient must be guaranteed, and pathological imaging patterns can be present as well as motion of the patient.

Author’s Contributions:

FM analyzed, and interpret the data, and was a major contributor in writing the manuscript. All the authors designed the work, read and approved the final manuscript.

Funding:

Part of this work was supported by the Hub Life Science - Advanced Diagnosis (HLS-AD), PNRR PNC-E3-2022-23683266 PNC-HLS-DA, INNOVA – CUP: E63C22003780001, funded by the Italian Ministry of Health under the National Complementary Plan Innovative Health Ecosystem - Unique Investment Code: PNC-E.3.

Availability of Data and Material:

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Ethics Approval and Consent to Participate:

N/A.

Consent for publication:

N/A.

Competing Interests:

The authors declare that they have no competing interests.