Method and system for multi-parameter ultrasonic imaging of bones by acoustic velocity guided depth prior full waveform inversion

Abstract

The application discloses a multi-parameter ultrasonic imaging method and system for muscle-bone by using sound velocity guided depth prior full waveform inversion, and belongs to the technical field of medical ultrasonic quantitative imaging. In view of the problems that wave field propagation in muscle-bone tissue is complex, sound velocity and density joint inversion is ill-posed, and density reconstruction is easily affected by parameter crosstalk, the application takes adjustable latent variables as input, and uses a U-Net network with a shared encoding-decoding backbone and a sound velocity and density double-output channel to jointly re-parameterize a sound velocity distribution map and a density distribution map. Unlike directly updating acoustic parameters on each spatial grid point, the application maps network output to a preset physical range, and substitutes into a variable-density acoustic wave equation to generate simulated received waveforms. Network parameters and adjustable latent variables are alternately optimized through a physical waveform matching objective function, without the need for external training samples.

Description

Technical Field

[0001] This invention relates to the fields of medical ultrasound imaging, ultrasound computed tomography, and medical image inversion, specifically to a multi-parameter ultrasound imaging method and system for sound velocity-guided depth prior full waveform inversion of musculoskeletal structures, which is particularly suitable for the joint quantitative reconstruction of acoustic parameters such as sound velocity and density. Background Technology

[0002] Quantitative acoustic parametric imaging of musculoskeletal tissues can reflect the acoustic properties of structures such as soft tissues, bones, blood vessels, and tendons, which is of great significance for tissue composition assessment, structural abnormality identification, and disease-related change analysis. Ultrasound imaging has advantages such as no ionizing radiation, low cost, portability, and real-time detection. However, traditional B-mode ultrasound imaging is usually based on simplified beamforming models, which makes it difficult to accurately describe the refraction, scattering, and multipath propagation of ultrasound waves at the high-contrast interface of bone and soft tissue, resulting in limited image resolution and quantitative reliability.

[0003] Full waveform inversion, by solving the wave equation and matching the observed waveform with the simulated waveform, can retrieve the spatial distribution of sound velocity, density, and other parameters from ultrasound transmission data, providing a physically interpretable quantitative ultrasound imaging solution. However, multi-parameter full waveform inversion is a highly nonlinear and ill-posed inverse problem. The objective function is prone to local minima and periodic jumps, and the effects of sound velocity and density on the same waveform data are coupled, easily leading to parameter crosstalk. Sound velocity perturbations mainly affect phase and travel time information and are usually recovered earlier and more stably; density perturbations are more reflected in amplitude and impedance information and are more susceptible to noise, source uncertainty, attenuation, and modeling errors, thus making density reconstruction more difficult.

[0004] To improve convergence, researchers have proposed various approaches in existing technologies, including multi-scale inversion, improved mismatch functions, empirical density constraints, staged inversion, and decoupling strategies based on the Hessian approximation. These methods alleviate periodic skipping and crosstalk problems to some extent, but often rely on reliable low-frequency components, precise initial models, empirical parameter relationships, or complex parameter selection. In actual musculoskeletal ultrasound experiments, low-frequency signals are limited by transducer bandwidth, accurate initial models are difficult to obtain, and empirical sound velocity-density relationships may also limit the expression of real tissue differences.

[0005] In recent years, deep learning methods have been used in ultrasound tomography and full waveform inversion to improve reconstruction quality and sound velocity. However, many supervised learning methods rely on large-scale simulation training data, and the domain differences between simulation data and in vivo experimental data limit their generalization ability. Deep image prior full waveform inversion does not require external training data; instead, it utilizes the convolutional network structure itself as implicit regularization, representing the parameter graph as the neural network output and optimizing the network parameters. However, traditional deep image prior full waveform inversion typically uses fixed random inputs, failing to absorb reliable structural information that gradually emerges during the iteration process.

[0006] Therefore, there is an urgent need for a multi-parameter ultrasound imaging method for musculoskeletal tissue that does not require external training data, can utilize reliable early structural information from the sound velocity channel, reduce sound velocity-density parameter crosstalk, and improve density reconstruction stability.

[0007] In view of this, the present invention is proposed. Summary of the Invention

[0008] To solve the above-mentioned technical problems, the basic concept of the technical solution adopted by the present invention is as follows:

[0009] The purpose of this invention is to overcome the difficulties of existing multi-parameter full-waveform inversion methods for musculoskeletal tissue, such as strong dependence on the initial model, significant crosstalk between sound velocity and density parameters, and insufficient stability of density reconstruction. This invention provides a sound velocity-guided depth prior full-waveform inversion method and system for multi-parameter ultrasound imaging of musculoskeletal tissue, named VSDIP-FWI (Velocity-steeredDeep Image Prior Full-waveform Inversion). This method does not directly update the sound velocity and density values ​​at each spatial grid point. Instead, it generates sound velocity and density distribution maps by optimizing shared neural network parameters. Furthermore, it uses the sound velocity structure to guide the update of adjustable latent variables, in addition to updating the network parameters, thereby achieving joint reconstruction of sound velocity and density without establishing a fixed empirical relationship between sound velocity and density.

[0010] To achieve the above objectives, the technical solution of the present invention is as follows:

[0011] Step S1: Data acquisition, preprocessing and initial model setup.

[0012] Acquire the ultrasonic transmission waveform data of the musculoskeletal tissue to be imaged using a ring array. The transmission waveform data includes full matrix waveform signals corresponding to multiple transmitting array elements and multiple receiving array elements. Perform various processing on the full matrix waveform signals, such as bad channel removal, baseline correction, time window truncation, and bandpass filtering, to obtain the observed waveform data. Establish acoustic forward modeling calculation conditions based on the array element positions, sampling time, reconstruction region, sound source waveform, and boundary conditions of the ring array transducer, and set the initial sound velocity model and initial density model corresponding to the uniform coupling medium.

[0013] Step S2: Construct the shared U-Net network and the full waveform inversion objective function.

[0014] A U-Net network is constructed with adjustable latent variables as input, featuring a shared encoder-decoder backbone and dual output channels for sound velocity and density. The adjustable latent variables are input into the U-Net network, and the dual output channels generate raw sound velocity and density outputs. Sound velocity and density distribution maps within a preset physical range are obtained through bounded mapping functions. These sound velocity and density distribution maps are then substituted into the variable-density acoustic wave equation as acoustic medium parameters. The ultrasonic field is solved for each transmitting element, and simulated received waveforms are extracted at the receiving element locations. Based on the differences between the simulated received waveforms and observed waveforms, as well as the spatial regularization constraints of the sound velocity and density distribution maps, a full waveform inversion objective function is constructed.

[0015]

[0016] Where P(x,t) is the sound pressure field, v(x) is the sound velocity distribution, ρ(x) is the density distribution, and S(x,z,t) is the sound source term.

[0017] Step S3: Fix the adjustable latent variables and update the shared U-Net network parameters.

[0018] In each inversion iteration, the current adjustable latent variables are kept constant. Based on the full waveform inversion objective function constructed in step S2, the gradient of the objective function with respect to the network parameters is calculated using automatic differentiation. The Adam optimizer is then used to update the network parameters, so that the simulated received waveform corresponding to the network output gradually approximates the observed waveform data. After the network parameters are updated, the updated network parameters are kept unchanged in subsequent latent variable update steps, thus forming an alternating optimization of network parameters and adjustable latent variables.

[0019] Step S4: Generate the sound velocity structure guidance signal and calculate the dynamic activation weights.

[0020] After updating the network parameters in step S3, the current sound velocity distribution map is extracted and normalized to the same numerical range as the adjustable latent variable to obtain the sound velocity structure guidance signal. Gradient propagation relative to the network parameters is stopped when generating the sound velocity structure guidance signal. Dynamic activation weights are calculated based on the current iteration number, ensuring that the sound velocity structure guidance remains weak in the early iteration stages and smoothly strengthens as the sound velocity structure gradually stabilizes in the later stages.

[0021] Step S5: Update the adjustable latent variables based on the sound velocity structure-guided signal.

[0022] A latent variable guidance loss is constructed based on the difference between the adjustable latent variable and the sound velocity structure guidance signal after gradient cessation. Dynamic activation weights are used to adjust the influence of this latent variable guidance loss on the update of the adjustable latent variable, causing the adjustable latent variable to evolve towards the sound velocity structure guidance signal, and the updated latent variable is constrained within a preset numerical range. This update is used to inject the earlier recovered geometry in the sound velocity channel into the shared input representation of the U-Net network, rather than directly copying the sound velocity distribution map to the density distribution map, nor imposing a fixed sound velocity-density function constraint on the density distribution map.

[0023] Step S6: Iterative convergence judgment and result output.

[0024] Repeat steps S2 to S5, alternately updating network parameters and adjustable latent variables until a preset stopping condition is met. The preset stopping condition includes one or more of the following: reaching a preset number of iterations, the relative change of the full waveform inversion objective function being less than a preset threshold, and the relative change of the sound velocity distribution map and density distribution map of adjacent iterations being less than a preset threshold. After the stopping condition is met, output the sound velocity distribution map and density distribution map of the musculoskeletal tissue to be imaged.

[0025] Further, in step S1, the annular array ultrasonic transmission waveform data is acquired by an annular ultrasonic transducer, which includes 128 array elements, an inner diameter of 10 cm, a center frequency of 1 MHz, and a sampling frequency of 25 MHz. During acquisition, each array element is used as a transmitting element in sequence, and all array elements synchronously receive the transmitted ultrasonic signal. The initial sound velocity model can be set to a uniform water model of 1500 m / s, and the initial density model can be set to a uniform density model of 1000 kg / m³.

[0026] Furthermore, the encoder of the U-Net network includes a four-level downsampling module with 64, 128, 256, and 512 feature channels respectively, and the bottleneck layer has 1024 feature channels. The decoder adopts an upsampling structure corresponding to the encoder and forms a sound velocity output channel and a density output channel through 1×1 convolution. The sound velocity distribution can be mapped to 1400–2300 m / s, and the density distribution can be mapped to 900–1500 kg / m³. The U-Net network structure and the sound velocity-guided latent variable update relationship are as follows: Figure 2 As shown.

[0027] Furthermore, this invention does not employ the traditional time-sampling point L2 waveform residual, but instead uses the Sinkhorn-regularized Wasserstein divergence as the data fidelity term for each transmit-receive channel. For the s-th transmit element and the r-th receive element, the channel-by-channel mismatch between the observed waveform and the simulated waveform obtained by forward modeling from the current model parameters is defined as... ,in Let p represent the Sinkhorn-regularized Wasserstein divergence with transmission index p, and ε be the entropy regularization strength, preferably p=1. Summing the squared mismatches of all effective transmit-receive channels and adding total variation regularization for sound velocity and density, we obtain... , and These are the regularization weights for the total variation of sound speed and the total variation of density, respectively.

[0028] Furthermore, in step S4, the sound velocity structure guiding signal Based on the current sound speed distribution map We obtain the result using the normalization operator N(·). The dynamic activation weight The Sigmoid form is adopted, and its value gradually increases with the number of iterations. ,in s is the activation center and s is the smoothing parameter.

[0029] Furthermore, in step S5, the adjustable latent variable is based on Update, among which Let be the adjustable latent variable for the i-th iteration. Update the step size for latent variables. To dynamically activate weights, The signal is a guide for the sound velocity structure.

[0030] This invention also provides a multi-parameter ultrasound imaging system for musculoskeletal tissue based on sound velocity-guided depth image prior full waveform inversion. The system includes a ring array ultrasound transducer, an ultrasound excitation and data acquisition device, a memory, and a processor. The ring array ultrasound transducer is used to transmit ultrasound signals and receive transmitted waveform data; the ultrasound excitation and data acquisition device is used to drive the transducer and acquire transmitted waveform data; the memory is used to store waveform data, network parameters, latent variables, and a computer program; when the processor executes the computer program, it performs data preprocessing, acoustic forward modeling, network parameter updating, sound velocity-guided structure generation, latent variable updating, and reconstruction result output.

[0031] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-described method for multi-parameter ultrasound imaging of musculoskeletal tissue by prior full waveform inversion of sound speed-guided depth images.

[0032] The beneficial effects of this invention include:

[0033] (1) This invention utilizes a U-Net network with a shared encoder-decoder backbone and dual output channels for sound velocity and density to represent the sound velocity distribution map and density distribution map as dual-channel outputs under the same implicit prior structure. This reparameterization method utilizes the low-frequency bias and implicit regularization of the convolutional network, which helps to reduce the risk of the inversion getting trapped in local minima; the inversion process does not require paired training samples or external supervision labels, which can reduce the influence of domain differences between simulation data and in vivo data.

[0034] (2) In addition to the network parameter update, the present invention introduces an adjustable latent variable update mechanism, which enables the tissue boundaries and geometric structures recovered earlier in the sound velocity channel to be passed to the subsequent decoding process through shared input representation, which helps to improve the boundary continuity and numerical stability of the density distribution map.

[0035] (3) The present invention adopts dynamic activation weight control of sound velocity structure guidance intensity, which can suppress the misleading effect of erroneous structure on latent variables when the early sound velocity estimation is not reliable, and gradually enhance the auxiliary role of reliable sound velocity structure in density recovery in the middle and late stages.

[0036] (4) This invention employs Sinkhorn regularized Wasserstein divergence to measure the channel-by-channel difference between the observed and simulated waveforms of each effective transmit-receive channel, and combines the sum of squared mismatches for each channel with the total variation regularization of sound velocity and density. This mismatch measure compares waveforms from the perspective of optimal transmission and has better robustness to local amplitude and phase distortions compared to the point-by-point residual norm based on amplitude; the total variation regularization can suppress high-frequency oscillation artifacts in the reconstructed image and preserve tissue boundaries. This invention can achieve joint quantitative reconstruction of sound velocity and density starting from the initial sound velocity model and initial density model corresponding to a homogeneous water medium.

[0037] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the process of the present invention;

[0039] Figure 2 This is a schematic diagram of the shared U-Net network structure and sound speed-guided latent variable update of the present invention;

[0040] Figure 3 A schematic diagram of the experimental setup for a circular array forearm ultrasound and a two-dimensional numerical model of the forearm.

[0041] Figure 4 A comparison of sound velocity and density reconstruction results from different methods in numerical simulation of the human forearm;

[0042] Figure 5 This is a comparison of the reconstruction results of different methods in an in vivo experiment on the human forearm. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention.

[0044] Example 1: VSDIP-FWI Network Structure and Overall Implementation Process

[0045] This embodiment illustrates a multi-parameter ultrasound imaging method for sound velocity-guided depth-prior full-waveform inversion of musculoskeletal structures. The method is performed according to steps S1 to S6 as shown in the accompanying drawings. Figure 2 This represents the shared U-Net network, dual-channel output of sound velocity and density, acoustic forward modeling data stream, and the relationship between sound velocity-guided latent variable updates. Overall, this method uses the transmitted waveform of the ring array as the observation data, provides physical constraints with the variable-density acoustic wave equation, provides depth image priors with the shared U-Net network, and improves density channel recovery by guiding the evolution of latent variables through sound velocity structure.

[0046] Step S1 involves setting up the data and initial conditions. Transmission waveform data of the musculoskeletal tissue to be imaged is acquired using a ring array ultrasound system. Each array element sequentially transmits ultrasound pulses, and multiple array elements receive the transmitted signals, forming complete waveform data with multiple transmit and receive channels. Bad channels are removed and baseline correction is performed on the acquired data. A time window is selected based on the transmission time, direct wave arrival time, and effective scattered wave duration. Bandpass filtering is performed based on the effective bandwidth of the transducer. Subsequently, acoustic forward modeling conditions are established based on the transducer element positions, sampling time, reconstructed region size, sound source waveform calibrated by a water tank experiment, and perfectly matched layer boundary conditions. Initial models for uniform water sound velocity and uniform water density are also set.

[0047] Step S2 involves constructing the shared network, the acoustic forward model, and the objective function. For example... Figure 2 As shown, a single-channel adjustable latent variable is set. As a shared U-Net network The input, the adjustable latent variable, has the same spatial size as the reconstruction domain, and its initial value can be generated by a uniform or Gaussian distribution. The U-Net network includes a four-level encoder, a 1024-channel bottleneck layer, a symmetric decoder, and skip connections. The ends are processed by 1×1 convolutions to form the raw sound velocity and raw density outputs, which are then obtained through bounded mappings. The sound speed distribution map and density distribution map Input variable density acoustic wave equation The acoustic pressure field corresponding to each transmitting element is solved using finite difference calculus, and the simulated received waveform is extracted at the location of the receiving element according to the sampling time. The data mismatch gradient between the observed waveform and the simulated received waveform is transferred to the sound velocity and density outputs and network parameters through automatic differentiation.

[0048] Step S3 updates the network parameters. This is done while maintaining the current latent variables. Without changing the objective function J, the parameters of the shared U-Net network are adjusted. Perform backpropagation and gradient update. To obtain the updated network parameters And the corresponding sound velocity distribution map and density distribution map. This step mainly utilizes the physical consistency between the observed waveform and the simulated waveform to simultaneously correct the sound velocity and density output.

[0049] Step S4 involves guiding the generation of the sound velocity structure. The current sound velocity distribution map is obtained based on the network output updated in step S3. The sound speed structure guidance signal is obtained through the normalization operator N(·). This yields a sound velocity structure guidance signal g(i) that matches the numerical range of the latent variables; a stopping gradient operation is applied to g(i) to prevent the latent variable updates from negatively altering the current network parameters. Simultaneously, based on... Calculate dynamic activation weights This results in weaker sound velocity guidance in the early iteration stages, which gradually strengthens in the middle and later stages after the sound velocity structure has stabilized.

[0050] Step S5 is for latent variable update. Construct the latent variable guided loss and follow... The adjustable latent variables are updated to incorporate the tissue boundaries and geometries recovered earlier in the sound velocity channel into the shared input representation. This step does not directly constrain the density distribution map, nor does it establish a fixed sound velocity-density empirical function relationship. Instead, it transmits structural information in the shared latent space, thereby reducing multi-parameter crosstalk and assisting density recovery.

[0051] Step S6 involves iterative convergence and result output. Steps S2 to S5 are repeated, alternately updating network parameters and adjustable latent variables, until the preset number of iterations is reached. The final output is the sound velocity distribution map and density distribution map of the musculoskeletal tissue to be imaged, which can be further used for two-dimensional slice display, tissue acoustic parameter analysis, and subsequent medical evaluation.

[0052] Example 2: Objective Function for Full Waveform Inversion

[0053] This embodiment provides a specific method for constructing the objective function. Unlike traditional pointwise L2 waveform residuals, this invention uses Sinkhorn-regularized Wasserstein divergence as a waveform mismatch metric for the transmit-receive channel. For the s-th transmit element and the r-th receive element, the observed waveform is denoted as... The simulated waveform obtained by forward modeling the current sound speed and density model is: Then channel mismatch can be expressed as , where ε is the entropy regularization strength.

[0054] This embodiment presents a specific method for constructing the variable-density acoustic forward model and objective function. For sound velocity v(x) and density ρ(x), the sound pressure field P(x,t) satisfies A perfectly matched layer or other absorbing boundary is set around the computational region to reduce artificial boundary reflections; the sound pressure field is time-sampled at each receiving element location to obtain the simulated received waveform. .

[0055] Unlike traditional time-series sampling point L2 waveform residuals, this invention uses Sinkhorn-regularized Wasserstein divergence as the channel-by-channel data fidelity term. For the s-th transmitting element and the r-th receiving element, the observed waveform is denoted as... The simulated waveform obtained by forward modeling from the current model parameters {v, ρ} is d. s ,ᵣˢ 1 If ᵐ(m), then the waveform mismatch of the transmit-receive channel is defined as... ,in Let p represent the Sinkhorn-regularized Wasserstein divergence with a transmission index of p, and ε be the entropy regularization strength; in one specific implementation, p = 1.

[0056] Summing the mismatches of all effective transmit-receive channels and adding total variation regularization for sound velocity and density, we obtain the following objective function:

[0057]

[0058] in, and The intensity of sound velocity and density regularization are controlled separately. Sinkhorn regularization and Wasserstein divergence compare the observed and simulated waveforms from the optimal transmission perspective, and have better robustness to local amplitude and phase distortions compared to the pointwise residual norm based on amplitude. Total variation regularization is used to suppress high-frequency oscillation artifacts in the reconstructed image while maintaining the boundary between bone and soft tissue.

[0059] Example 3: Shared U-Net Network and Latent Variable Settings

[0060] This embodiment illustrates the specific structure of the shared U-Net network. The shared U-Net network receives a single-channel latent variable tensor as input, and the latent variable tensor has the same spatial size as the reconstruction domain. The network output is a dual-channel image, where the first channel is a sound velocity distribution map and the second channel is a density distribution map.

[0061] Specifically, the encoder employs a four-stage downsampling structure with 64, 128, 256, and 512 feature channels respectively, and a 1024-channel bottleneck layer is set at the end of the encoder. The decoder adopts a symmetrical structure, recovering spatial resolution step by step through bilinear upsampling and skip connections. Finally, the decoder features are projected onto the sound velocity and density channels through 1×1 convolution. To ensure that the inversion starts from a uniform water model, the bias of the sound velocity output channel is initialized to 1500 m / s, and the bias of the density output channel is initialized to 1000 kg / m³.

[0062] Since sound velocity and density are represented by the same latent variable and the same shared network, the two parameters can share implicit representations related to geometry and boundaries; at the same time, the two output channels still have their own numerical distributions, without needing to set density directly as a function of sound velocity, and without forcing the density map to copy the sound velocity map.

[0063] Example 4: Sound Speed-Guided Latent Variable Evolution and Dynamic Activation

[0064] This embodiment illustrates the core sound speed guidance mechanism of the present invention. In the i-th iteration, the latent variable is first fixed. Based on the objective function J, the network parameters Update: ,in The learning rate is used for the network parameters. After the network parameters are updated, the updated sound velocity distribution map is obtained. .

[0065] Then Input the normalization operator N(·) to obtain the sound speed structure guidance signal. The normalization operator maps the sound speed structure to a numerical range that matches the latent variables. The latent variable-guided loss can be expressed as... The latent variable is updated to ,in Update the step size for latent variables. To dynamically activate weights, The signal is a guide for the sound velocity structure.

[0066] To avoid misleading latent variables when early sound speed estimates are unreliable, this invention employs dynamic activation weights in the form of sigmoid: ,in Let 's' be the activation center and 's' be the smoothing parameter. In the early iteration stages, The network is relatively small, primarily relying on depth image priors to form stable implicit representations; in the mid-to-late iteration stages, as the sound velocity structure gradually stabilizes, As the acoustic structure guide signal is gradually injected into the latent variable, the density channel benefits from the boundary and geometric information that has been recovered in the acoustic channel.

[0067] This latent variable update does not impose direct constraints on the density map, nor does it establish an empirical sound velocity-density relationship. Instead, it transmits structural information at the shared input representation level. Through dynamic activation, it can reduce the propagation of early erroneous sound velocity structures while assisting in density reconstruction and maintaining the differences in the distributions of the two parameters, sound velocity and density.

[0068] Example 5: Data Setup and Experimental Parameters

[0069] This embodiment illustrates the data settings that can be used when applying the present invention to musculoskeletal tissues. The first type of data is a numerical simulation model of the human forearm, with a computational domain of 510×510 and a spatial interval of 0.02 cm. The model is constructed based on the anatomical structure of the human forearm, including tissue regions such as water, fat, muscle, blood vessels, skin, and bone, and the sound velocity and density of each tissue are set according to empirical acoustic parameters. To match the geometry of real experimental acquisitions, a 128-element ring transducer is used in the simulation, and the sound source signal is calibrated using uniform water experimental measurement data. A perfectly matched layer is set around the computational domain.

[0070] The second type of data consists of in vivo experimental data from the human forearm, acquired using a Verasonics Vantage 256 ultrasound system and a 128-element ring transducer. The ring transducer has an inner diameter of 10 cm, the center frequency of each element is 1 MHz, and the sampling frequency is 25 MHz. During the experiment, the human forearm was placed near the center of the ring array and immersed in homogeneous water at room temperature. Each element served as a transmitter sequentially, and all 128 elements simultaneously received the transmitted signals. For qualitative comparison, high-resolution MRI images of the same subject's forearm were acquired as anatomical references.

[0071] In this embodiment, both network parameters and latent variables are optimized end-to-end using an automatic differentiation framework. The shared U-Net network parameters can be optimized using the Adam optimizer with a learning rate of 0.001; the latent variable update step size can be set to 0.5; the dynamic activation center can be set to 100 iterations; and the total number of iterations can be set to 400. To ensure fair comparison, different inversion methods can use the same forward model, sound source waveform, receiver geometry, initial physical model, and data fidelity term.

[0072] In each iteration, sound velocity and density distribution maps are first generated from the current latent variables. Then, forward modeling is used to generate simulated waveforms and calculate the objective function. Next, the network parameters are updated. Finally, a sound velocity structure guidance signal is generated based on the updated sound velocity distribution map, and the latent variables are updated again. When the preset number of iterations is met, the final sound velocity and density distribution maps are output.

[0073] Example 6: Numerical Simulation and In Vivo Experiment Results of the Forearm

[0074] To verify the effectiveness of the velocity-guided depth image prior full waveform inversion method described in this invention for the joint reconstruction of sound velocity and density in musculoskeletal tissue, this embodiment verifies the method on a human forearm numerical model and in vivo experimental data of the human forearm, and compares the method of this invention with traditional full waveform inversion methods and depth image prior full waveform inversion methods. Specifically, the full waveform inversion method that directly updates the sound velocity and density parameters on a discrete grid is denoted as traditional FWI; the method that uses fixed random latent variables as input to the U-Net network and updates the network parameters only through a waveform mismatch objective function is denoted as DIP-FWI, i.e., depth image prior full waveform inversion; and the method that uses a shared U-Net network to jointly represent sound velocity and density and dynamically guides the update of adjustable latent variables according to the current sound velocity distribution is denoted as VSDIP-FWI, i.e., the velocity-guided depth image prior full waveform inversion method described in this invention.

[0075] like Figure 4As shown, the first row displays the true sound velocity distribution of the human forearm numerical model and the sound velocity reconstruction results obtained by traditional FWI, DIP-FWI, and VSDIP-FWI. The second row displays the corresponding true density distribution and density reconstruction results. Traditional FWI can recover the approximate location of the forearm's outer contour and two bone tissues, but it exhibits significant oscillation artifacts and structural distortions near the high-contrast bone-soft tissue interface. The density results are particularly affected by parameter crosstalk, resulting in poor continuity of internal tissue boundaries. Both DIP-FWI and VSDIP-FWI utilize implicit image priors provided by the U-Net network structure, effectively suppressing large-scale oscillation artifacts in traditional FWI. The sound velocity reconstruction results obtained by the two methods are generally similar, both clearly recovering the forearm's outer contour, major soft tissue structures, and bone tissue locations, indicating that network reparameterization can improve the stability of sound velocity inversion. The differences between the different methods are mainly reflected in the density reconstruction results. While DIP-FWI can recover the overall forearm contour, bone location, and some internal tissue structures, its reconstructed density values ​​are significantly higher than the real model, especially in the internal soft tissue regions where density overestimation is quite pronounced. Furthermore, some tissue boundaries are blurred, and localized ring artifacts remain near the bone. In contrast, VSDIP-FWI guides the update of adjustable latent variables through the current sound velocity distribution, allowing the tissue contours and geometries recovered earlier in the sound velocity channel to enter the shared implicit representation, thus assisting in density channel reconstruction. Its density results not only show a more continuous forearm outer boundary, subcutaneous tissue, and bone-soft tissue interface, but also significantly reduce density overestimation in soft tissue regions, resulting in reconstructed values ​​closer to the real model. It should be noted that VSDIP-FWI does not directly copy the sound velocity distribution to the density channel, nor does it impose a fixed sound velocity-density empirical relationship. Sound velocity information only provides structural guidance through shared latent variables; the specific values ​​of the density parameters are still determined by the mismatch constraints between the observed and simulated waveforms. Therefore, even if sound velocity and density have different spatial distributions in some tissue regions, the method is still able to maintain the reconstruction characteristics of each of the two parameter channels.

[0076] like Figure 5As shown, in the in vivo experiment on the human forearm, since it is impossible to obtain the true sound velocity and density distribution that completely corresponds to the ultrasound reconstruction section, this embodiment uses MRI images of similar sections from the same subject as anatomical references, mainly comparing the outer contour of the forearm, the location of bone tissue, and the morphology of major soft tissues. Traditional FWI results show obvious ring artifacts and background contamination, with significant interference to internal tissue structures. Both DIP-FWI and VSDIP-FWI can suppress some oscillation artifacts and restore the outer contour of the forearm and two bone tissue regions corresponding to the MRI reference image. The sound velocity results obtained by the two methods show little overall difference, both displaying relatively clear tissue contours and relatively stable bone tissue locations. Regarding density reconstruction, although DIP-FWI can recover some internal tissue structures of the forearm, its reconstructed density values ​​are generally too high, especially in large soft tissue areas where significant density overestimation occurs, weakening the density contrast between different soft tissues and blurring some tissue boundaries. In contrast, the density map obtained by VSDIP-FWI shows good consistency between the forearm outer contour and bone tissue location and the MRI reference image. The overall density level of the soft tissue region is significantly reduced, effectively alleviating density overestimation. More reasonable density differences are observed between different tissue regions, and the boundary between bone tissue and surrounding soft tissue is clearer. However, due to factors such as in vivo measurement noise, source and array element response errors, sound attenuation, three-dimensional propagation effects, and approximation of the forward model, local artifacts and numerical biases still exist in the in vivo sound velocity and density results, and the internal parameters of bone tissue cannot be completely and accurately recovered. Nevertheless, compared to traditional FWI and DIP-FWI with fixed latent variables, VSDIP-FWI can further improve the continuity of tissue boundaries and the rationality of parameter distribution in the density map while maintaining the stability of sound velocity reconstruction.

[0077] The numerical simulations and in vivo experiments described above demonstrate that this invention, through joint reparameterization of sound velocity and density using a shared U-Net network, can suppress oscillation artifacts generated during traditional grid-by-grid updates by leveraging depth image priors. Simultaneously, by employing a dynamically activated sound velocity structure guidance mechanism, earlier recovered tissue boundaries and geometric structures in the sound velocity channel are injected into shared latent variables, assisting density reconstruction without imposing a fixed empirical sound velocity-density relationship. Therefore, this invention improves the structural continuity and stability of density reconstruction in multi-parameter ultrasound imaging of musculoskeletal tissues and reduces parameter crosstalk in joint sound velocity and density inversion, making it suitable for joint quantitative imaging of sound velocity and density in musculoskeletal tissues such as the human forearm.

Claims

1. A multi-parameter ultrasound imaging method for musculoskeletal musculoskeletal fusion based on sound velocity-guided depth prior full waveform inversion, characterized in that... Includes the following steps: Step S1: Collect the ultrasonic transmission waveform data of the musculoskeletal tissue to be imaged using a ring array, and preprocess the transmission waveform data; establish acoustic forward modeling calculation conditions based on the array element position, reconstruction area, sampling time, sound source waveform and boundary conditions of the ring array transducer, and set the initial sound velocity model and initial density model. Step S2: Construct a neural network with an adjustable latent variable as input, a shared encoder-decoder backbone, and dual output channels for sound velocity and density. Map the outputs of the dual output channels to sound velocity distribution maps and density distribution maps within a preset physical range, respectively. Substitute the sound velocity distribution maps and density distribution maps as acoustic medium parameters into the variable density acoustic wave equation, solve the ultrasonic field for each transmitting array element, and extract the simulated received waveform at the receiving array element position. Construct a full waveform inversion objective function based on the observed waveform and the simulated received waveform; Step S3: In each round of inversion iteration, keep the current adjustable latent variable unchanged, and perform gradient update on the network parameters of the neural network according to the full waveform inversion objective function to obtain the updated sound velocity distribution map and density distribution map; Step S4: While keeping the updated network parameters unchanged, normalize the updated sound velocity distribution map to generate a sound velocity structure guidance signal with the same spatial size and numerical range as the adjustable latent variable, and calculate the dynamic activation weight based on the current iteration number. Step S5: Construct a latent variable guidance loss based on the difference between the adjustable latent variable and the sound speed structure guidance signal after stopping the gradient. Use the dynamic activation weight to control the update intensity of the adjustable latent variable by the latent variable guidance loss, so that the adjustable latent variable is updated toward the sound speed structure guidance signal, thereby injecting the recovered structural information in the sound speed channel into the shared input representation. Step S6: Repeat steps S2 to S5 to alternately update the network parameters and the adjustable latent variables until a preset number of iterations is reached, and output the sound velocity distribution map and density distribution map of the musculoskeletal tissue.

2. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, The ultrasonic transmission waveform data of the ring array is acquired by a ring array ultrasonic transducer containing multiple transmitting and receiving array elements; each array element transmits ultrasonic signals in sequence, and multiple array elements receive ultrasonic signals synchronously; the initial sound velocity model and the initial density model are the uniform sound velocity model and the uniform density model corresponding to the uniform coupling medium, respectively.

3. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 2, characterized in that, The ring array ultrasonic transducer comprises 128 array elements with an inner diameter of 10 cm, an array element center frequency of 1 MHz, and a sampling frequency of 25 MHz. Each array element serves as a transmitting element in sequence and receives ultrasonic signals from all array elements. The initial sound velocity model is a uniform water sound velocity model of 1500 m / s, and the initial density model is a uniform water density model of 1000 kg / m³.

4. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, The neural network is a U-Net network, which includes an encoder, a bottleneck layer, a decoder, and skip connections. The encoder includes at least two downsampling modules, and the decoder includes an upsampling module corresponding to the encoder. The decoder ends form a sound speed output channel and a density output channel through an output layer. The sound speed output channel and the density output channel are respectively mapped to a preset sound speed range and a preset density range through bounded mapping functions.

5. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, The full-wave inversion objective function includes a data fidelity term, a total sound velocity variation regularization term, and a total density variation regularization term for each transmit-receive channel; for the s-th transmit element and the r-th receive element, the channel mismatch is defined as... The overall objective function is ,in, The observed waveforms are for the s-th transmitting element and the r-th receiving element. The simulated received waveform is obtained by forward modeling the sound velocity distribution map v and the density distribution map ρ. Let p represent the Sinkhorn-regularized Wasserstein divergence with a transmission index of p, and ε be the entropy regularization strength, preferably p=1. and These are the regularization weights for the total variation of sound speed and the total variation of density, respectively.

6. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, The variable-density acoustic wave equation is: Where P(x,t) is the sound pressure field and S(x,t) is the sound source term; the acoustic forward model adopts absorbing boundary conditions or fully matched layer boundary conditions, and obtains the gradient of the full waveform inversion objective function with respect to the network parameters through automatic differentiation.

7. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, In step S3, during the i-th iteration, the current adjustable latent variable is... Input shared U-Net network The sound speed distribution map was obtained. and density distribution map ; Fix the current adjustable latent variable Unchanged, and in accordance with Update network parameters, among which, Let be the network parameters for the i-th iteration. The learning rate is the network parameter.

8. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, In step S4, the sound speed structure guide signal Based on the current sound speed distribution map The result is obtained using the normalization operator N(·). The dynamic activation weight The Sigmoid form is adopted, and its value gradually increases with the number of iterations. ,in, s is the activation center and s is the smoothing parameter.

9. The multi-parameter ultrasound imaging method for sound velocity-guided depth prior full waveform inversion of musculoskeletal structure according to claim 1, characterized in that, In step S5, the adjustable latent variable is based on To be updated, among which, Let be the adjustable latent variable for the i-th iteration. Update the step size for latent variables. To dynamically activate weights, The signal guides the sound velocity structure; in the early iteration stage Smaller, in the mid-to-late iteration stage Gradually increase.

10. A multi-parameter ultrasound imaging system for musculoskeletal tissue based on sound velocity-guided depth image prior full waveform inversion, characterized in that, The method includes a ring array ultrasonic transducer, an ultrasonic excitation and data acquisition device, a memory, and a processor; the ring array ultrasonic transducer is used to transmit ultrasonic signals to the musculoskeletal tissue to be imaged and to receive transmitted waveform data; the ultrasonic excitation and data acquisition device is used to drive the ring array ultrasonic transducer and acquire the transmitted waveform data; the memory stores a computer program; and the processor executes the computer program to implement the method according to any one of claims 1 to 9.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the multi-parameter ultrasound imaging method for musculoskeletal tissue based on sound speed-guided depth image prior full waveform inversion as described in any one of claims 1 to 9.

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