An ultrasonic craniocerebral tomography method based on physical embedded neural network

Abstract

The application provides an ultrasonic craniocerebral tomography method based on a physically embedded neural network, and steps are as follows: firstly, according to the distribution characteristics of a craniocerebral biological tissue, a real physical CT brain model is converted into a craniocerebral acoustic velocity distribution map; secondly, according to the craniocerebral velocity distribution map and the physical characteristics of craniocerebral ultrasonic signal propagation, a sound field time domain signal is acquired; thirdly, the sound field time domain signal is subjected to data preprocessing to acquire a frequency domain data matrix, and a numerical simulation database is established; then, a neural network structure based on a full waveform inversion algorithm and embedding physics is built, and the network is trained by using the craniocerebral acoustic velocity distribution map and the frequency domain data matrix to obtain a combination of optimal network hyperparameters; finally, the frequency domain data matrix to be predicted is input into the network to realize high-precision and real-time ultrasonic craniocerebral tomography. The application realizes quantitative imaging and evaluation of brain structure, and has the advantages of fast imaging speed and high imaging precision.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of brain imaging, in particular to an ultrasonic brain tomography method based on a physically embedded neural network. BACKGROUND

[0002] Ultrasound imaging devices have pushed medical ultrasound technology to the forefront of non-invasive imaging due to its affordability, portability, safety, ease of operation, and the absence of the need for anesthesia. It is particularly worth mentioning that the widespread use of ultrasound in the examination of pregnant women fully demonstrates its versatility and reliability. Despite the recognized advantages of ultrasound imaging, there are still challenges in achieving high-resolution imaging of the adult human brain. One of the main challenges is that skull sutures close with age, affecting the effectiveness of high-frequency signals (5-12 MHz) used by traditional transcranial ultrasound. In addition, the speed difference between the skull, soft tissue, and cavities filled with gas or liquid causes scattering, refraction, and diffraction of ultrasound waves when they pass through the brain, which in turn leads to signal wavefront distortion and imaging complexity. Although some low-frequency ultrasound technologies (below 1 MHz) have been successfully developed to visualize specific brain structures using pulse-echo B-mode imaging, spatial resolution is usually sacrificed. In addition, the use of low frequency (2 MHz) through a relatively thin bone window has been shown to facilitate the Doppler imaging of intracerebral arteries. However, to achieve high-resolution ultrasound imaging of the adult human brain, further research and technological progress are still needed.

[0003] In addition to ultrasound, several other imaging modalities, such as MRI, CT, and photoacoustic imaging, are considered to have the potential to become competitive alternatives for brain imaging. However, compared to these modalities, ultrasound remains the most widely used and least invasive imaging method. In the field of medical ultrasound, full waveform inversion (FWI) provides a potential solution to the challenges related to tomographic imaging. However, traditional FWI faces challenges in clinical applications due to high computational requirements, resulting in prolonged imaging times (e.g., 32 hours for 3D imaging). In addition, FWI relies heavily on an appropriate initial model, and in brain imaging, prior knowledge of the skull is particularly important due to the speed difference between the skull and the tissue. Deep learning-based FWI is considered to have the potential to address these challenges. Despite this, deep learning-based FWI algorithms still face challenges in terms of training speed and imaging resolution, and a universally applicable, safe and stable brain imaging technology has not yet been established. Despite the challenges, ongoing research and development indicate that deep learning-based FWI has the potential to revolutionize medical imaging and significantly enhance our understanding of complex biological structures. SUMMARY

[0004] In view of the problems in the prior art, the present application provides an ultrasonic craniocerebral tomography method based on a physically embedded neural network, which solves the problems of period jump in the existing full waveform inversion method under unknown skull conditions and real-time imaging.

[0005] The technical scheme of the present application is implemented as follows:

[0006] An ultrasonic craniocerebral tomography method based on a physically embedded neural network, the steps of which are as follows:

[0007] Step 1: Convert the real physical CT brain model into a craniocerebral acoustic velocity distribution map according to the distribution characteristics of the craniocerebral biological tissue;

[0008] Step 2: Obtain the sound field time domain signal according to the craniocerebral acoustic velocity distribution map and the propagation physical characteristics of the craniocerebral ultrasonic signal in the biological tissue isotropic medium;

[0009] Step 3: Perform data preprocessing on the obtained sound field time domain signal to obtain a frequency domain data matrix and construct a numerical simulation database;

[0010] Step 4: Build a neural network model based on the full waveform inversion algorithm and embedded physics, including a forward convolution network and an inversion sub-convolution network; use the craniocerebral acoustic velocity distribution map and the frequency domain data matrix after data preprocessing to train the neural network model based on the full waveform inversion algorithm and embedded physics, and obtain the optimal network parameters;

[0011] Step 5: Use the frequency domain data matrix to be predicted as input to the trained neural network model based on the full waveform inversion algorithm and embedded physics to perform ultrasonic brain tomography.

[0012] The implementation method of Step 1 is as follows:

[0013] Considering the distribution characteristics of the craniocerebral biological tissue and the bone porosity of the real physical CT brain model, the coupled changes of the model density, acoustic velocity and absorption are described, as shown in formula (1):

[0014] φ=1-(HU / 1000) (1);

[0015] wherein HU represents "Hounsfield Unit", which is a unit for measuring the density of tissue in a CT image, and φ represents the porosity map; the acoustic velocity reference values (c water , c bone ) of water and bone are used as standards to perform linear interpolation on the porosity map, as shown in formula (2):

[0016] m t =φ×c water +(1-φ)×c bone (2).

[0017] According to the above, the real physical CT brain model can be converted into a craniocerebral acoustic velocity distribution map m t .

[0018] The implementation method of step two is:

[0019] According to the craniocerebral acoustic velocity distribution map and the propagation physical characteristics of the craniocerebral ultrasonic signal in the biological tissue isotropic medium, the boundary of the brain acoustic velocity distribution map is regarded as an absorption layer, and a damping term is added in the wave equation, and the isotropic medium wave equation is used to obtain the sound field time domain signal, and the acoustic wave equation is as shown in formula (3):

[0020]

[0021] Wherein, M(x) is a global mass matrix of n*n size, P(x) is a global damping matrix of n*n size, C(x) is a global stiffness matrix of n*n size, is a sound pressure wave field or an elastic displacement wave field of n*1 size, F(x,t) is a point source term of n*1 size, x and t represent the spatial coordinate system and the time coordinate system; When solving the ultrasonic wave field of the brain model, the initial condition is defined as:

[0022]

[0023] At the same time, the Green function is embedded into the acoustic wave equation (3) to obtain formula (5):

[0024]

[0025] Wherein the initial condition is transformed into

[0026]

[0027] As a substitute for high-order time, the wave equation in spatial frequency domain can be obtained by Fourier transform as formula (7):

[0028]

[0029] Wherein ω represents the angular frequency; The transformation relationship with the spatial time domain is as shown in formula (8):

[0030]

[0031] Through simplification, formula (9) can be obtained:

[0032]

[0033] Formula (9) is expressed as a linear equation and is solved using LU decomposition, which is applied to the coefficient matrix, and only one operation is required to divide it into a lower triangular matrix and an upper triangular matrix; meanwhile, in the craniocerebral acoustic velocity distribution map, the transmitters and receivers of the circular array are uniformly arranged around the brain medium; the brain medium is located inside the circular array, and the transmission mode is to apply a Ricker wavelet excitation signal to one transmitter, while all receivers record the time-domain signal of the acoustic field; and so on, until all transmitters are used as an excitation source; the time-domain signal of the acoustic field is solved according to formula (9), the craniocerebral acoustic velocity distribution map, the transmitter and receiver positions and the transmission mode.

[0034] The data preprocessing is a signal processing algorithm, which converts the time-domain signal of the acoustic field obtained in step two into a frequency-domain signal by Fourier transform, and extracts the spatial frequency-domain amplitude and phase of the center frequency of the transmission signal to form a frequency-domain data matrix.

[0035] The method for training the network using the craniocerebral acoustic velocity distribution map after data preprocessing and the frequency-domain data matrix to obtain the optimal network parameters is:

[0036] For the forward convolution network, the craniocerebral acoustic velocity distribution map after data preprocessing is taken as the input, and the frequency-domain data matrix is taken as the output to train the forward convolution network, so as to obtain the optimal network parameters of the forward convolution network; the trained forward convolution network and the untrained inversion sub-convolution network are iteratively embedded with each other, and the specific way is: taking the output of the forward convolution network as the input of the inversion sub-convolution network, and taking the output of the inversion sub-convolution network as the input of the forward convolution network, which is cycled to form a physically embedded neural network; the physically embedded neural network is trained to obtain the optimal parameters of the physically embedded neural network;

[0037] The training method of the forward convolution network is:

[0038] After Fourier transform of the time-domain signal of the acoustic field, the frequency-domain data matrix composed of the spatial frequency-domain amplitude and phase of the center frequency of the transmission signal is obtained, and the convolution network is used to realize feature extraction, as shown in formula (10):

[0039]

[0040] wherein, d k is the i-th channel in the output feature map of the convolution layer, N is the channel number of the input image, W kj is the weight of the convolution kernel, X j is the j-th channel of the input image, b k is the bias term, and f is the activation function; the training process is as follows: ① randomly initialize the weights W kj and the bias bk ; ② input X j , and forward propagation is performed by formula (10) to obtain the predicted value d k ; ③ the loss function is calculated using the predicted value d k and the true value dt; ④ the gradient of the loss function weight W kj and the bias b k is calculated using the back propagation algorithm; ⑤ the weight W kj and the bias b k are updated using the gradient descent method to reduce the predicted value d k of the loss function; ⑥ steps ②-⑤ are repeated until a predetermined stopping condition is reached, i.e., the maximum number of iterations is reached or the loss function predicted value d k converges to a set threshold.

[0041] The input of the forward convolution network is the brain acoustic velocity distribution map, and the output is the frequency domain data matrix, which is used to explore the nonlinear mapping relationship between the brain model and the wave field; the loss function of the forward convolution network is defined as the mean square error between the frequency domain data matrix calculated by the forward convolution network and the frequency domain data matrix calculated in step three, as shown in formula (11):

[0042]

[0043] Wherein, N F represents the loss function of the forward convolution network, N t represents the number of transmitting sources, N r represents the number of receiving sources, represents the real part or imaginary part of the i'th channel transmitting and j'th channel receiving frequency domain data calculated in step three, represents the real part or imaginary part of the i'th channel transmitting and j'th channel receiving frequency domain data calculated by the forward convolution network.

[0044] The inversion sub convolution network realizes the nonlinear mapping from the wave field to the model; in the whole neural network structure, the forward convolution network and the inversion sub convolution network are embedded and iterated with each other, wherein in the first iteration, the residual error between the frequency domain data matrix d t calculated in step three and the frequency domain data matrix d0 corresponding to the initial model is taken as the input of the inversion sub convolution network; in the subsequent iterations, the frequency domain data matrix d t calculated in step three and the frequency domain data matrix d k predicted by the forward convolution network are taken as the input of the inversion sub convolution network, k = 1, 2, …, N'; the inversion sub convolution network can map the residual error of the frequency domain data matrix to the corresponding brain acoustic velocity distribution residual velocity distribution map m f , and then map the residual velocity distribution map m fm = m0+ m k ; the iterative process is shown in formula (12):

[0045]

[0046] Wherein, m0 represents the initial model velocity distribution map obtained from finite difference, d0 represents the corresponding frequency domain data matrix of the initial model velocity distribution map obtained from finite difference, N' represents the number of iterations, m k represents the predicted craniocerebral acoustic velocity distribution map in the iteration process, d k represents the frequency domain data matrix in the iteration process, represents the forward convolution network of each iteration, represents the inversion subnetwork of each iteration, i"=1,2,…,N'.

[0047] The loss function of the full waveform inversion algorithm and the embedded physical neural network model is defined as the mean square error between the input craniocerebral acoustic velocity distribution map m t and the predicted craniocerebral acoustic velocity distribution map m N' , as shown in formula (13):

[0048]

[0049] Wherein, N S represents the loss function of the physical embedded network, G represents the length of the velocity distribution map, H represents the width of the velocity distribution map, represents the velocity value of the i0th row and j0th column in the craniocerebral acoustic velocity distribution map, represents the velocity value of the i0th row and j0th column in the predicted craniocerebral acoustic velocity distribution map.

[0050] Compared with the prior art, the present application has the following beneficial effects:

[0051] 1) Compared with the latest development of medical imaging using full waveform inversion (FWI), the present application can realize high-precision imaging without any prior information, and only uses single-frequency information to construct a simulation database to obtain the velocity distribution map of the brain, and the success is due to the unique design of the mutually embedded forward convolution network and the inversion subnetwork.

[0052] 2) The structure similarity of the two-dimensional brain tomography imaging result of the built physical embedded neural network to the real image is more than 0.94, which is sufficient to prove the significant accuracy of the method of the present application.

[0053] 3) The built physical embedded neural network can image various types of blood clots in the brain, including circular blood clots with fixed sound velocity distribution, irregularly shaped blood clots with Gaussian sound velocity distribution, and different slices of irregularly shaped clots with Gaussian sound velocity distribution. This beneficial effect demonstrates the effectiveness of the method of the present application in dealing with various imaging challenges.

[0054] 4) The loss function is divided into two parts, the loss function N F of the forward convolutional network and the loss function N S of the physical embedded network, wherein the successful N F is iterated with the inversion sub-network to form N S , which provides the necessary physical conditions for the success of the brain inversion.

[0055] 5) The ultrasonic brain tomography technology of the present application is easy to implement, solves the cycle jump problem of full waveform inversion, and has fast imaging speed. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0057] Figure 1 is the flowchart of the present application.

[0058] Figure 2 is the network structure diagram of the present application based on physical embedding.

[0059] Figure 3 is the training and verification loss comparison of the full convolutional network of the present application.

[0060] Figure 4 is the two-dimensional brain model imaging result and cross-sectional view of the known skull prior information of the present application.

[0061] Figure 5 is the two-dimensional brain model imaging result and cross-sectional view of the pure water as the initial model of the present application.

[0062] Figure 6 is the imaging result and cross-sectional view of different two-dimensional brain model slices with pure water as the initial model of the present application. DETAILED DESCRIPTION

[0063] With reference to the drawings and embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative effort belong to the scope of protection of the present application.

[0064] As shown in Figure 1 , the embodiment of the present application provides an ultrasonic craniocerebral tomography method based on a physically embedded neural network. First, according to the distribution characteristics of craniocerebral biological tissues, a craniocerebral physical model is converted into a craniocerebral acoustic velocity distribution map. Second, according to the craniocerebral acoustic velocity distribution map and the physical characteristics of craniocerebral ultrasonic signal propagation, a sound field time domain signal is obtained. Third, the obtained sound field time domain signal is preprocessed to obtain a frequency domain data matrix, that is, Fourier transform is performed to convert to a spatial frequency domain, a one-to-one correspondence between the sound velocity distribution model and the frequency domain data matrix is established, and a numerical simulation database is established. Fourth, a neural network structure based on full waveform inversion algorithm and embedded physics is built, and the preprocessed craniocerebral acoustic velocity distribution map and the frequency domain data matrix are used to train the physically embedded network, and the weights and structure of the network are optimized to obtain the combination of optimal network hyperparameters. Finally, the parameters and weights of the optimal network are read, and the test set frequency domain data matrix is taken as input to realize craniocerebral tomography. The specific steps are as follows:

[0065] Step one: according to the distribution characteristics of craniocerebral biological tissues, a real physical CT brain model is converted into a craniocerebral acoustic velocity distribution map.

[0066] Considering the distribution characteristics of craniocerebral biological tissues and the bone porosity of the original CT data, the coupling change of model sound velocity and absorption is described, as shown in formula (1):

[0067] φ = 1-(HU / 1000) (1);

[0068] Where HU represents "Hounsfield unit", which is a unit for measuring the density of tissues in a CT image, and φ represents the porosity map. The sound velocity reference values (c water , c bone ) of water and bone are taken as standards, and the porosity map is linearly interpolated, as shown in formula (2):

[0069] m t = φ × c water + (1-φ) × c bone (2);

[0070] Where c water = 1500 m / s, c bone = 3100 m / s.

[0071] According to formula (2), the real physical CT brain data is converted into a brain acoustic velocity distribution map m containing acoustic velocity t As a physical model for subsequent calculation of acoustic field time domain data.

[0072] Step two: according to the brain acoustic velocity distribution map and the propagation physical properties of the brain ultrasound signal in the biological tissue isotropic medium, the boundary of the brain acoustic velocity distribution map is regarded as an absorption layer, and a damping term is added to the wave equation, and the isotropic medium wave equation is used to obtain the acoustic field time domain signal, and the acoustic wave equation is shown as formula (3):

[0073]

[0074] Wherein, M(x) is a global mass matrix of n*n size, P(x) is a global damping matrix of n*n size, C(x) is a global stiffness matrix of n*n size, The acoustic pressure wave field or elastic displacement wave field is n*1 size, F(x,t) is a point source term of n*1 size, x and t represent the spatial coordinate system and the time coordinate system; When solving the brain model of the ultrasonic wave field, the initial condition is defined as:

[0075]

[0076] At the same time, the Green function is embedded into the acoustic wave equation (3) for solving, as shown in formula (5):

[0077]

[0078] Wherein the initial condition is transformed into

[0079]

[0080] As an alternative to high-order time, the wave equation in spatial frequency domain can be obtained by Fourier transform as formula (7):

[0081]

[0082] Wherein ω represents the angular frequency; The transformation relationship with the spatial time domain is shown as formula (8):

[0083]

[0084] By simplifying, formula (9) can be obtained:

[0085]

[0086] Formula (9) is represented as a linear equation and is solved using LU decomposition, which is applied to the coefficient matrix and only requires one operation to divide it into a lower triangular matrix and an upper triangular matrix; these stored LU factors can be substituted into the equation to be solved, thereby reducing the calculation time; meanwhile, in the craniocerebral acoustic velocity distribution map, the transmitters and receivers of the circular array are uniformly arranged around the brain medium; the brain medium is located inside the circular array; the transmission mode is to apply a Ricker wavelet excitation signal to one transmitter, and all receivers record the time-domain signal of the acoustic field; and so on until all transmitters are used as an excitation source once. The time-domain signal of the acoustic field is solved according to formula (9), the craniocerebral acoustic velocity distribution map, the transmitter and receiver positions and the transmission mode.

[0087] Step three: data preprocessing is performed on the acquired time-domain signal of the acoustic field to obtain a frequency domain data matrix, and a numerical simulation database is constructed; the data preprocessing is a signal processing algorithm, Fourier transform is performed on the time-domain signal of the acoustic field acquired in step two to convert the time-domain signal into a frequency domain signal, and the spatial frequency domain amplitude and phase of the center frequency of the transmission signal are extracted to form a frequency domain data matrix.

[0088] Step four: a neural network structure based on full waveform inversion algorithm and physical embedding is built, including a forward convolution network and an inversion sub-convolution network. For the forward convolution network: the craniocerebral acoustic velocity distribution map after data preprocessing is taken as input, and the frequency domain data matrix is taken as output to train the forward convolution network, so that the optimal combination of network parameters and weights is obtained; the trained forward convolution network and the untrained inversion sub-network are embedded and iterated with each other, and the specific way is: the output of the forward convolution network is taken as the input of the inversion sub-convolution network, and the output of the inversion sub-convolution network is taken as the input of the forward convolution network; this process is repeated to form a physically embedded neural network. The physically embedded neural network is trained to obtain the optimal parameters and weight combination of the final physically embedded network.

[0089] As shown in Figure 2 The physically embedded network structure in the application includes a forward convolution network and an inversion sub-convolution network. The forward convolution network is composed of an input layer, a convolution layer, a pooling layer, a full connection layer and an output layer. The craniocerebral acoustic velocity distribution map is taken as input, the convolution layer is used for feature extraction, the network depth is increased to retain more effective information, the pooling layer is used for down-sampling of the feature map, the network complexity is simplified, and the calculation amount is reduced, the full connection layer is used for matching the size of the feature map and the output layer, and the nonlinear mapping fitting degree of the feature map and the output layer is improved. The inversion sub-network is composed of an input layer, a full connection layer, a convolution layer, a deconvolution layer and an output layer. The deconvolution layer is used for up-sampling of the input feature map, and the low-resolution feature map is converted into a high-resolution feature map, so as to better restore the detail information of the input image.

[0090] The training method is:

[0091] After Fourier transform of the time-domain signal of the sound field, a frequency domain data matrix composed of the spatial frequency domain amplitude and phase of the center frequency of the transmitted signal is obtained, and a convolution network is used to realize feature extraction, as shown in formula (10):

[0092]

[0093] Wherein, d k is the i-th channel of the output feature map of the convolution layer, N is the number of channels of the input image, W kj is the weight of the convolution kernel, X j is the j-th channel of the input image, b k is the bias term, and f is the activation function. The training process is as follows: ① randomly initialize the weights W kj and the bias b k ; ② pass the input X j through formula (10) for forward propagation to obtain the predicted value d k ; ③ use the predicted value d k and the true value dt to calculate the loss function; ④ use the back propagation algorithm to calculate the gradient of the loss function weights W kj and the bias b k ; ⑤ use the gradient descent method to update the weights W kj and the bias b k to reduce the predicted value d k of the loss function; ⑥ repeat steps ②-⑤ until a predetermined stopping condition is reached (the maximum number of iterations is reached or the predicted value d k of the loss function converges to a set threshold).

[0094] The input of the forward convolution network is the acoustic velocity distribution map of the brain, and the output is the frequency domain data matrix, which is used to explore the nonlinear mapping relationship between the brain model and the wave field; the loss function of the forward convolution network is defined as the mean square error between the frequency domain data matrix calculated by the forward convolution network and the frequency domain data matrix calculated in step three, as shown in formula (11):

[0095]

[0096] Wherein, N F represents the loss function of the forward convolution network, N t represents the number of transmitting sources, N r represents the number of receiving sources, represents the real part or imaginary part of the i'-th channel transmitting and j'-th channel receiving frequency domain data calculated in step three, represents the real part or imaginary part of the i'-th channel transmitting and j'-th channel receiving frequency domain data calculated by the forward convolution network.

[0097] The inverse subconvolutional neural network realizes the nonlinear mapping from the wave field to the model. In the entire neural network structure, the forward modeling convolutional network and the inverse subconvolutional neural network are inter-embedded and iterated. In the first iteration, the frequency domain data matrix d calculated in step three is... t The residual between the frequency domain data matrix d0 and the initial model is used as the input to the inversion subnetwork; in subsequent iterations, the frequency domain data matrix d0 calculated in step three is used as the input to the inversion subnetwork. t The frequency domain data matrix d predicted by the forward-modeling feedforward convolutional network k As input to the inversion subnetwork, k = 1, 2, ..., N-1; the inversion subnetwork can map the residual of the frequency domain data matrix to the corresponding residual map of the cranial acoustic velocity distribution m. f Furthermore, the residual velocity distribution map m f The predicted intracranial acoustic velocity distribution map m is obtained by adding it to the initial model velocity distribution map m0. k The iterative process is shown in formula (12):

[0098]

[0099] Where m0 represents the initial model velocity distribution map obtained from the finite difference method, d0 represents the corresponding frequency domain data matrix of the initial model velocity distribution map obtained from the finite difference method, N represents the iteration number, and m k The image represents the distribution of acoustic velocity in the brain during the iterative process, d k This represents the frequency domain data matrix during the iteration process. This represents the forward-propagating convolutional network for each iteration. The inversion subnetwork represents each iteration, i” = 1, 2, ..., N-1; the loss function of the entire network structure is defined as the brain acoustic velocity distribution map m t And network-predicted acoustic velocity distribution map m N The mean square error between them is shown in formula (13):

[0100]

[0101] Where, N S The loss function of the physical embedded network is represented by G, where G represents the length of the velocity distribution map and H represents the width of the velocity distribution map. This represents the velocity value in the i0th row and j0th column of the intracranial acoustic velocity distribution map. This represents the velocity value in the i0th row and j0th column of the network-predicted acoustic velocity distribution map.

[0102] Step 5: Input the frequency domain data matrix to be predicted into the trained network for ultrasound brain tomography.

[0103] Figure 3 The training and validation loss comparison of the physically embedded network in the present application is shown. The training set contains 1024 samples, and the validation set contains 256 samples. The loss function changes of the forward convolution network and the physically embedded network after 500 iterations are shown in the figure. It is worth noting that in the early stage of training, the loss value decreases rapidly, and then gradually stabilizes, indicating that the training efficiency of the network is very high.

[0104] Figure 4 The two-dimensional brain model imaging results of the known skull prior information in the present application are shown. Figure 4 (a) and (b) show the real velocity map of the 4th training set sample and the inversion result of the embedded physical network, and the corresponding image structural similarity is 0.968411. Figure 4 (d) and (e) show the real velocity map of the 36th test set sample and the inversion result of the embedded physical network, and the corresponding image structural similarity is 0.964238. Figure 4 (c) and (f) are the full waveform inversion results of the 4th training set sample and the 36th test set sample, respectively, and the image structural similarity with the corresponding real model is 0.810728 and 0.808360, respectively. From Figure 4 It can be seen that the physically embedded network can well distinguish between blood clots and brain tissues, and its inversion result is significantly better than that of full waveform inversion. Figure 4 The cross-sectional view of the visualization imaging result of (g) and (h) further confirms the superiority of the inversion result of the physically embedded network.

[0105] Figure 5 The two-dimensional brain model imaging results and cross-sectional views of the present application using pure water as the initial model are shown. Figure 5 (a) is the real velocity distribution map of the 51st sample in the test set, Figure 5 (b) is the inversion result of the physically embedded network, Figure 5 (c) is the full waveform inversion result, Figure 5 (g) is the cross-sectional view of the visualization imaging result. The similarity of the inversion result and the real image is calculated, and the physically embedded network and the full waveform inversion result are 0.949014 and 0.616744, respectively. It can be seen that when the skull is missing as the initial model, the full waveform inversion will produce a period jump phenomenon, causing the inversion process to fall into a local minimum value, rather than a global minimum value. Figure 5 (d) to (h) are the real velocity distribution map, the physically embedded network inversion result, the full waveform inversion result, and the cross-sectional view of the visualization imaging result of the 88th sample, respectively. It can be seen that in the 88th sample, the physically embedded network inversion result is still better than the full waveform inversion result.

[0106] Figure 6 The imaging results and cross-sectional images of different two-dimensional brain model slices of the present application using pure water as the initial model are shown. Figure 6 (a), (b), (c) are the first slice velocity distribution model, the physical embedded network inversion result and the full waveform inversion result of the real brain sample, and the corresponding image structural similarities are 0.946463 and 0.536388 respectively. Similarly, Figure 6 (e), (f) show the physical embedded network inversion result and the full waveform inversion result of slice 3, and the derived image structural similarities are 0.937720 and 0.528342 respectively. It can be seen that even with the addition of the multi-slice training set, the inversion result of the physical embedded network is always superior to that of the full waveform inversion, effectively proving the strong generalization ability of the physical embedded network.

[0107] The above merely describes preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for ultrasonic craniocerebral tomography based on a physically embedded neural network, characterized in that, The steps are as follows: Step one: converting a real physical CT brain model into a craniocerebral acoustic velocity distribution map according to the distribution characteristics of the craniocerebral biological tissue; Step two: obtaining an acoustic field time domain signal according to the craniocerebral acoustic velocity distribution map and the propagation physical characteristics of the craniocerebral ultrasound signal in the biological tissue isotropic medium; Step three: obtaining a frequency domain data matrix by performing data preprocessing on the obtained acoustic field time domain signal to construct a numerical simulation database; Step four: building a neural network model based on the full waveform inversion algorithm and embedded physics, including a forward convolution network and an inversion sub-convolution network; using the data preprocessed craniocerebral acoustic velocity distribution map and the frequency domain data matrix to train the neural network model based on the full waveform inversion algorithm and embedded physics to obtain optimal network parameters; Step five: inputting the frequency domain data matrix to be predicted into the trained neural network model based on the full waveform inversion algorithm and embedded physics to perform ultrasonic brain tomography.

2. The physics-embedded neural network-based ultrasonic cranial tomography method of claim 1, wherein, The implementation method of step one is: Considering the distribution characteristics of the craniocerebral biological tissue and the bone porosity of the real physical CT brain model, the coupled changes of the model density, acoustic velocity and absorption are described, as shown in formula (1): φ = 1 - (HU / 1000) (1); where HU stands for "Hounsfield Unit", a unit used to measure tissue density in CT images, and φ stands for the porosity map; the sound speed reference values (c water , c bone ) of water and bone are used as standards to linearly interpolate the porosity map, as shown in equation (2): HU = c water φ + c bone (1 - φ) (2) m t = φ x c water + (1 - φ) x c bone (2); According to the above, the real physical CT brain model can be converted into a craniocerebral acoustic velocity distribution map m t .

3. The ultrasonic craniocerebral tomography method based on the physical embedded neural network according to claim 1, characterized in that, The implementation method of step two is: According to the craniocerebral acoustic velocity distribution map and the propagation physical characteristics of the craniocerebral ultrasound signal in the biological tissue isotropic medium, the boundary of the brain acoustic velocity distribution map is regarded as an absorption layer, and a damping term is added to the wave equation, and the isotropic medium wave equation is used to obtain the acoustic field time domain signal, and the acoustic wave equation is as shown in formula (3): where M(x) is a global mass matrix of n x n size, P(x) is a global damping matrix of n x n size, C(x) is a global stiffness matrix of n x n size, is the acoustic pressure wave field or elastic displacement wave field of n x 1 size, F(x, t) is a point source term of n x 1 size, and x and t represent the spatial coordinate system and the time coordinate system; the initial condition is defined as: At the same time, the Green function is embedded into the acoustic wave equation (3) to solve, and formula (5) is obtained: Where the initial condition is transformed into As a substitute for high-order time, the wave equation in the spatial frequency domain can be obtained by Fourier transform as formula (7): Where ω represents the angular frequency; the transformation relationship with the spatial time domain is as shown in formula (8): Through simplification, formula (9) can be obtained: Formula (9) is expressed as a linear equation and solved using LU decomposition; the LU decomposition is applied to the coefficient matrix, which can be divided into a lower triangular matrix and an upper triangular matrix only once; at the same time, in the craniocerebral acoustic velocity distribution map, the transmitters and receivers of the circular array are uniformly arranged around the brain medium; the brain medium is located inside the circular array, and the transmission mode is to apply a Ricker wavelet excitation signal to one transmitter, and all receivers record the acoustic field time domain signal; in this way, until all transmitters are used as an excitation source; the acoustic field time domain signal is solved according to formula (9), the craniocerebral acoustic velocity distribution map, the transmitter and receiver positions and the transmission mode.

4. The physics-embedded neural network-based ultrasonic cranial tomography method according to claim 1 or 3, characterized in that, The data preprocessing is a signal processing algorithm, which converts the acoustic field time domain signal obtained in step two into a frequency domain signal by Fourier transform, and extracts the spatial frequency domain amplitude and phase of the center frequency of the transmission signal to form a frequency domain data matrix.

5. The physics-embedded neural network-based ultrasonic cranial tomography method of claim 4, wherein, The method for obtaining optimal network parameters by using the preprocessed acoustic velocity distribution map and the frequency domain data matrix of the brain is: For the forward convolution network, the preprocessed acoustic velocity distribution map of the brain is taken as the input, and the frequency domain data matrix is taken as the output to train the forward convolution network, so as to obtain optimal network parameters of the forward convolution network; the trained forward convolution network and the untrained inversion sub-convolution network are iteratively embedded with each other, and the specific method is as follows: the output of the forward convolution network is taken as the input of the inversion sub-convolution network, and the output of the inversion sub-convolution network is taken as the input of the forward convolution network, and the process is repeated to form a physical embedded neural network; the physical embedded neural network is trained to obtain optimal parameters of the physical embedded neural network.

6. The physical embedded neural network-based ultrasonic brain tomography method according to claim 5, characterized in that, The training method of the forward convolution network is: After the Fourier transform of the time-domain signal of the sound field is performed, the frequency domain data matrix composed of the spatial frequency domain amplitude and phase of the center frequency of the transmission signal is obtained, and the convolution network is used to realize feature extraction, as shown in formula (10): where d k is the i-th channel of the output feature map of the convolutional layer, N is the number of channels of the input image, W kj is the weight of the convolutional kernel, X j is the j-th channel of the input image, b k is the bias term, and f is the activation function; the training process is as follows: ① randomly initializing the weights W kj and the bias b k ; ② performing forward propagation on the input X j through formula (10) to obtain the predicted value d k ; ③ using the predicted value d k and the true value dt to calculate the loss function; ④ using the backpropagation algorithm to calculate the gradient of the loss function weight W kj and the bias b k ; ⑤ using the gradient descent method to update the weight W kj and the bias b k to reduce the predicted value d k of the loss function; ⑥ repeat steps ②-⑤ until a predetermined stopping condition is reached, i.e. the maximum number of iterations is reached or the predicted value d k of the loss function converges to a set threshold value.

7. The physics-embedded neural network-based ultrasonic cranial tomography method of claim 6, wherein, The input of the forward convolution network is the acoustic velocity distribution map of the brain, and the output is the frequency domain data matrix, which is used to explore the nonlinear mapping relationship between the brain model and the wave field; and the loss function is defined as the mean square error between the frequency domain data matrix calculated by the forward convolution network and the frequency domain data matrix calculated in step three, as shown in formula (11): where N F represents the loss function of the forward convolutional network, N t represents the number of transmitting sources, N r represents the number of receiving sources, represents the real or imaginary part of the i'th channel transmitting, j'th channel receiving frequency domain data calculated in step three, represents the real or imaginary part of the i'th channel transmitting, j'th channel receiving frequency domain data calculated by the forward convolutional network.

8. The physics-embedded neural network-based ultrasonic cranial tomography method of claim 5, wherein, The anti-convolutional network realizes the nonlinear mapping from wave field to model; in the whole neural network structure, the forward convolutional network and the anti-convolutional network are embedded and iterated, wherein, in the first iteration, the frequency domain data matrix d calculated in step three is taken as the input of the anti-convolutional network t The residual error between the frequency domain data matrix d0 corresponding to the initial model is taken as the input of the anti-convolutional network; in the subsequent iteration, the frequency domain data matrix d calculated in step three is taken as the input of the anti-convolutional network t The residual error between the frequency domain data matrix d calculated in step three and the frequency domain data matrix d predicted by the forward convolutional network is taken as the input of the anti-convolutional network k = 1, 2, …, N' k The anti-convolutional network can map the residual error of the frequency domain data matrix to the corresponding residual velocity distribution of the brain acoustic velocity distribution m f , and then add the residual velocity distribution m f to the initial model velocity distribution m0 to obtain the predicted brain acoustic velocity distribution m k ; the iteration process is shown in formula (12): where m0represents the initial model velocity distribution map obtained from finite differences, d0represents the frequency domain data matrix corresponding to the initial model velocity distribution map obtained from finite differences, N' represents the number of iterations, m k represents the predicted brain acoustic velocity distribution map in the iteration process, d k represents the frequency domain data matrix in the iteration process, represents the forward convolutional network of each iteration, represents the inversion subnetwork of each iteration, i"=1,2,…,N'.

9. The physics-embedded neural network-based ultrasonic cranial tomography method of claim 8, wherein, The loss function of the full waveform inversion algorithm and the embedded physics-based neural network model is defined as the mean square error between the input brain acoustic velocity distribution map m t and the predicted brain acoustic velocity distribution map m N' as shown in equation (13): wherein N S represents a loss function of the physical embedded network, G represents the length of the velocity distribution map, H represents the width of the velocity distribution map, represents the velocity value of the i0th row and the j0th column in the craniocerebral acoustic velocity distribution map, represents the predicted velocity value of the i0th row and the j0th column in the craniocerebral acoustic velocity distribution map.

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