A method and system for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution

Abstract

This invention discloses a method and system for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution, belonging to the field of ultrasound medical image processing technology. The method extracts geometric features of the vascular boundary and a set of temporal spatial coordinate points within the blood vessel from the ultrasound super-resolution vascular structure map and blood flow velocity map of the target object to form a coordinate dataset. It then assimilates high-resolution instantaneous velocity vectors with hemodynamic simulation values ​​to construct an auxiliary dataset. A physical information neural network is constructed, using the coordinate dataset and auxiliary dataset as training datasets. The physical information neural network is iteratively trained and optimized to obtain the optimal model for estimating the super-resolution blood flow velocity and pressure fields. The instantaneous super-resolution blood flow velocity and pressure fields are predicted based on this optimal model without other constraints. This method solves the problem of low temporal and spatial resolution in estimating the velocity field during ultrasound super-resolution imaging, enabling rapid calculation of blood flow velocity and pressure fields with super-spatiotemporal resolution.

Description

Technical Field

[0001] This invention belongs to the field of ultrasound medical image processing technology, specifically a method and system for analyzing blood flow velocity and pressure fields with ultra-high spatiotemporal resolution. Background Technology

[0002] Malignant tumors have become one of the leading causes of death worldwide, seriously threatening human health and life. Currently, tumor diagnosis and treatment face multiple challenges, from early screening and diagnosis to various treatment methods, efficacy evaluation, and recurrence monitoring. Therefore, tumor diagnosis and treatment have become a core area of ​​research in clinical medicine. Imaging is currently an important means of early tumor detection. Clinical CT, MRI, and conventional ultrasound imaging methods mainly rely on morphology and routine perfusion information for tumor diagnosis, lacking the ability to capture microvascular dynamics information sensitive to changes in early tumor microvessels. Furthermore, one of the essential characteristics of tumor malignancy is the induction of angiogenesis. Tumor angiogenesis involves the growth of new capillaries within existing blood vessels; this process of microvascular formation and blood circulation establishment within the tumor is crucial for tumor development, growth, and metastasis. For example, in liver tumors, the intratumoral vascular network typically transforms from large vessels to abnormal microvessels. Therefore, studying the hemodynamic parameters of tumor microvessels and peripheral blood vessels is of great significance for the early detection of tumor-related diseases.

[0003] Ultrasound imaging, as a non-invasive diagnostic tool, enables real-time imaging without damage. It is simple to operate and inexpensive. However, due to the diffraction limit of ultrasound waves, its imaging resolution is relatively low, limiting its application in early tumor diagnosis. Ultrasound super-resolution imaging (UMI) overcomes the diffraction limit by detecting, locating, and tracking microbubbles in ultrasound blood flow signal data. After time accumulation, these microbubbles are superimposed to form a super-resolution image of blood vessels, enabling the reconstruction of micron-level vascular structures. Simultaneously, UMI tracking algorithms can obtain the displacement of microbubbles, further revealing the velocity of blood flow within the vessel. However, the number of instantaneous microbubbles that can be located within the vessel during UMI is limited. Thousands of single-frame velocity maps need to be superimposed to form the final super-resolution velocity map. Furthermore, the velocity obtained from the super-resolution velocity map tends to the average velocity of the blood vessel. Therefore, obtaining the super-resolution velocity distribution within the blood vessel while maintaining temporal resolution remains a significant challenge. Moreover, UMI only provides blood flow velocity values ​​and cannot provide calculations for other hemodynamic parameters, such as pressure distribution. In summary, at present, there is no method to quickly calculate the spatiotemporal resolution of blood flow velocity and pressure fields of target blood vessels and vascular networks based on the geometric features of super-resolution imaging and the sparse spatial coordinates within blood vessels. The difficulty lies in the low resolution of ultrasound imaging leading to unclear morphology of blood vessels and vascular networks, the limited number of microbubbles distributed within the target blood vessel, and the limitations of existing motion tracking algorithms. Summary of the Invention

[0004] To address the problem of rapidly calculating intravascular hyperspatiotemporal resolution blood flow velocity and pressure fields using contrast-enhanced ultrasound blood flow data, particularly for microvessels and vascular networks, this invention provides a method and system for analyzing hyperspatiotemporal resolution blood flow velocity and pressure fields. Based on ultrasound super-resolution imaging, and taking a hemodynamic perspective, combined with deep learning concepts, this invention solves the problems of low resolution, poor real-time performance, and lack of physical accuracy in current calculations of intravascular blood flow velocity fields. Furthermore, the pressure field can be calculated based on the spatial coordinates of any sampled location within the blood vessel, significantly improving both computational efficiency and spatiotemporal resolution.

[0005] This invention is achieved through the following technical solution:

[0006] A method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution includes the following steps:

[0007] Step 1: Based on the ultrasound super-resolution vascular structure map and blood flow velocity map of the target object, extract the geometric features of the vascular boundary and the set of temporal spatial coordinate points in the vascular area to form a coordinate dataset;

[0008] High-resolution instantaneous velocity vectors are obtained from blood flow velocity maps. These high-resolution instantaneous velocity vectors are then assimilated with hemodynamic simulation values ​​to construct an auxiliary dataset.

[0009] Step 2: Construct a physical information neural network. Based on the mean square error of the physical residual network, the mean square error of the velocity vector in the blood vessel and its predicted value, construct the physical residual network and the corresponding loss function term driven by the data. Based on the geometric features of the blood vessel boundary, extract the given velocity at the boundary position point and the mean square error of its predicted value to construct the boundary condition term of the loss function.

[0010] Step 3: Use the coordinate dataset and auxiliary dataset as training datasets to iteratively train the physical information neural network. After iterative optimization, obtain the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity field and pressure field. Predict the instantaneous super-resolution blood flow velocity field and pressure field based on the optimal model of the physical information neural network.

[0011] Preferably, in step 1, contrast-enhanced ultrasound blood flow data of blood vessels or vascular networks in the target area are extracted, and super-resolution imaging is performed on the ultrasound blood flow data to obtain a super-resolution vascular structure map and blood flow velocity map.

[0012] Preferably, the method for obtaining the ultrasound super-resolution vascular structure map and blood flow velocity map is as follows:

[0013] The tissue signals in the contrast-enhanced ultrasound blood flow data of the target object are filtered to obtain the blood flow signal. The super-resolution vascular structure map and blood flow velocity map are obtained by using a multi-scale statistical feature localization algorithm and a tracking algorithm that minimizes the total matching distance between adjacent frames.

[0014] Preferably, the method for constructing the auxiliary dataset in step 1 is as follows:

[0015] The high-resolution instantaneous velocity vector is constructed by stacking super-resolution blood flow velocity vectors within a set time frame based on blood flow velocity maps, and then fused with hemodynamic simulations through data assimilation to obtain an auxiliary dataset.

[0016] Preferably, the velocity vectors obtained by ultrasound super-resolution tracking are preprocessed using the standardized median filtering method and the boundary value solver smooth interpolation method. The preprocessed super-resolution velocity vectors within the set time are stacked and constructed into an auxiliary dataset through data assimilation with hemodynamic simulation.

[0017] Preferably, in step 3, the Navier-Stokes equations are encoded as a physical residual network in the physical information neural network, as follows:

[0018]

[0019] e3 = e1 + e2

[0020] Where e1, e2, and e3 represent the residual networks of the physical information network, Let be the dynamic viscosity of blood flow; u and v be dimensionless velocity vectors; p be dimensionless pressure; and t be dimensionless time. It is the gradient operator. U is the Laplace operator representing a two-dimensional velocity vector.

[0021] Preferably, the training method for the physical information neural network is as follows:

[0022] The training dataset is input into the physical information neural network model to obtain the error function between the output value and the input value. An optimization algorithm is used to minimize the loss function and update the network model parameters. After multiple iterations of optimization, the optimal model is obtained.

[0023] In physical information neural networks, chain rules are applied to solve differential functions using automatic differentiation, allowing physical control equations to participate in the updating and optimization of the network model.

[0024] Preferably, during the training process of the physical information neural network, an optimizer is used to minimize the loss function. The optimizers are the Adam optimizer and the L-BFGS optimizer.

[0025] Preferably, the loss function of the physical information neural network is as follows:

[0026] L = L D +L E +L B

[0027]

[0028] Among them, L D L E and L B These are the loss function terms corresponding to data-driven, physical residual networks, and super-resolution blood vessel boundary features, respectively. β and β represent the weights of the corresponding terms, N represents the total number of data points, i represents the number of residual networks, and p represents the prediction result. This represents the velocity value corresponding to the data point on the nth boundary.

[0029] A system for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution includes:

[0030] The feature extraction module is used to extract the geometric features of the blood vessel boundary and the set of temporal spatial coordinate points within the blood vessel to form a coordinate dataset based on the ultrasound super-resolution vascular structure map and blood flow velocity map of the target object.

[0031] High-resolution instantaneous velocity vectors are obtained from blood flow velocity maps. These high-resolution instantaneous velocity vectors are then assimilated with hemodynamic simulation values ​​to construct an auxiliary dataset.

[0032] The network module is used to construct a physical information neural network. It constructs the physical residual network and the corresponding loss function terms based on the mean square error, velocity vector and its predicted value of the physical residual network. It also extracts the mean square error of the given velocity and its predicted value of the boundary position point based on the geometric features of the blood vessel boundary to construct the boundary condition terms of the loss function.

[0033] The prediction module is used to use the coordinate dataset and auxiliary dataset as training datasets to iteratively train the physical information neural network. After iterative optimization, the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity field and pressure field is obtained. Based on the optimal model, the instantaneous super-resolution blood flow velocity field and pressure field are predicted according to the set of spatial coordinate points in the intravascular time series.

[0034] Compared with the prior art, the present invention has the following beneficial technical effects:

[0035] This invention provides a rapid method for calculating and analyzing blood flow velocity and pressure fields with ultra-high spatiotemporal resolution. First, a coordinate dataset is constructed by extracting the geometric features of the blood vessel boundary and the set of temporal spatial coordinate points within the blood vessel based on ultrasound super-resolution results. Simultaneously, an auxiliary dataset is constructed by assimilating the preprocessed velocity vectors obtained from ultrasound super-resolution tracking with hemodynamic simulation data. Using the training dataset comprised of the auxiliary dataset and the coordinate dataset, a physical information neural network is optimized and trained to obtain the optimal model for calculating the ultra-high spatiotemporal resolution blood flow velocity and pressure fields. This optimal model is then input into the set of temporal spatial coordinate points within the blood vessel, allowing for the rapid acquisition of the ultra-high spatiotemporal resolution blood flow velocity and pressure fields without requiring additional constraints.

[0036] This method, based on a physical information neural network model, utilizes sparse super-resolution blood flow velocity vectors within stacked short-time sets and the geometric features of super-resolution vessel boundaries to calculate blood flow velocity and pressure fields at super-spatiotemporal resolution. It overcomes the limitations of existing super-resolution imaging methods, which are constrained by microbubble concentration and tracking algorithms, hindering rapid and high-precision estimation of blood flow velocity fields. Furthermore, it predicts the corresponding pressure field simultaneously with the velocity field calculation, ensuring the physical correctness of the hemodynamic parameter calculations. In addition, the boundary condition term of the loss function constructed in the physical information neural network not only calculates hemodynamic parameters for single vessels in the target region but also enables the calculation and analysis of hemodynamic parameters for complex vascular networks within the target region, providing a powerful tool for monitoring tumor microvascular and surrounding vascular development.

[0037] Furthermore, the preprocessed velocity vectors obtained from ultrasound super-resolution tracking are assimilated with hemodynamic simulations to obtain an auxiliary dataset, which effectively reduces the gap between the training dataset and the real blood flow conditions. This helps to improve the generalization ability of the physical information neural network model and its friendliness to real experimental data, and accelerates the convergence of the network. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to the present invention;

[0039] Figure 2 This is a framework diagram of the method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to the present invention;

[0040] Figure 3 This is a diagram showing the assimilation results of super-resolution velocity vector and hemodynamic simulation data in this invention.

[0041] Figure 4 This is a result diagram of the super-resolution blood flow velocity field of the target blood vessel in this invention.

[0042] Figure 5This is a result diagram of the super-resolution blood flow pressure field of the target blood vessel in this invention. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings. These descriptions are intended to explain the invention and not to limit it.

[0044] See Figure 1 A fast, high-resolution method for analyzing blood flow velocity and pressure fields includes several parts: acquiring blood flow data and performing super-resolution imaging, generating a training dataset, preprocessing the data, constructing a physical information neural network, and iteratively optimizing the network model. Specific steps include:

[0045] Step 1: Obtain contrast-enhanced ultrasound blood flow data of the target object.

[0046] Specifically, an ultrasound contrast agent is injected into the target object (the target object includes: bionic blood vessels, animal blood vessels, and human blood vessels), so that the microbubbles follow the blood flow and circulate to the target location. A transducer of appropriate frequency is used to emit plane waves or divergent waves and focused waves at an angle equal to or greater than a certain angle. The ultrasound echo signals of the contrast microbubbles in the target area of ​​the blood vessels are collected to reflect the blood flow movement. Contrast-enhanced ultrasound blood flow image data are obtained through beamforming.

[0047] Step 2: The contrast-enhanced ultrasound blood flow image data generated in Step 1 is processed using the Singular Value Decomposition (SVD) algorithm to filter out tissue signals in the target region while retaining blood flow signals. Then, a multi-scale statistical feature localization algorithm and a tracking algorithm that minimizes the total matching distance between adjacent frames are used to process the SVD-processed ultrasound blood flow data to obtain ultrasound super-resolution vascular structure maps and blood flow velocity maps.

[0048] The SVD method is an important matrix factorization method in linear algebra, particularly in dealing with matrix rank, eigenspace, and least squares problems in numerical linear algebra. In the field of ultrasound medical image processing, SVD is used to process contrast-enhanced ultrasound imaging data, decomposing the ultrasound signal of the target region into several matrix multiplications to represent the feature information in the ultrasound image. In ultrasound echo data, it is assumed that tissue is stationary and blood flow is flowing; therefore, tissue has high spatiotemporal coherence, which manifests in the ultrasound image as the consistency of a large number of spatial pixels on a temporal scale, represented by larger eigenvalues ​​and corresponding eigenvectors in the matrix. Blood flow echo signals, on the other hand, have lower spatiotemporal coherence, representing blood flow as smaller eigenvalues ​​and their corresponding eigenvectors in the matrix. In addition, some noise in the ultrasound echo signal needs to be filtered out; therefore, in practice, a bidirectional threshold method is used to filter out tissue signals while simultaneously achieving noise reduction. Specifically, the SVD method can be described as follows:

[0049] S f =SVI f V * =UΔ f V *

[0050] Among them, S f This is the data after SVD filtering; I f It is a matrix filter, where the first few diagonal elements of the diagonal identity matrix are set to 0 to remove the eigenvalues ​​corresponding to tissue motion. Therefore, it is a truncated diagonal matrix, corresponding to the threshold diagonal matrix for removing singular values ​​of tissue motion; S is the input contrast-enhanced ultrasound data after wave combination, U and V are orthogonal matrices, * denotes conjugate transpose, Δ f It is a diagonal matrix. Similarly, since noise signals also have low spatiotemporal correlation and are mixed with blood flow information in small eigenvalues, a bidirectional threshold is set to simultaneously filter out tissue signals and noise signals.

[0051] The multi-scale statistical feature localization algorithm uses a multi-scale Hessian matrix to perform convolution to calculate feature values, constructs regional energy and microbubble spot features to determine microbubble candidate groups and separates overlapping microbubbles, and then models the multi-scale kernel and orientation kernel. Based on the set threshold, regions with statistical feature confidence scores higher than the threshold are retained as accurate microbubble signal locations.

[0052] Specifically, first, the eigenvalues ​​and vectors of the Hessian matrix are determined, and based on these, the region energy and speckle features are calculated to separate overlapping microbubbles, which can be expressed as:

[0053]

[0054] Where, λ n,j It is the j-th normalized eigenvector in the Hessian matrix. The corresponding eigenvalues, where n is the computational scale. Based on the Hessian matrix, we can calculate the region energy to distinguish between background and noise, while the calculation of microbubble spot features can be used to separate overlapping microbubbles. The combination of these two methods constitutes a microbubble separation filter. Finally, the maximum response value of the microbubble separation filter within a specified range is obtained, which represents the separated microbubble. Specifically, it can be expressed as:

[0055]

[0056] Among them, Fr e and Fr b These are region energy filtering and microbubble spot feature filtering, γ e and γ bIt is used to control the sensitivity of the above filtering. The filter is a microbubble separation filter, which achieves the separation of overlapping microbubbles by calculating the maximum value of the microbubble separation filter at each pixel.

[0057] Next, multi-scale kernels and orientation kernels are used to model the microbubble morphology. The ultrasound images are convolved, and regions with statistical feature confidence scores higher than a custom threshold are retained as accurate microbubble signal locations. The statistical feature confidence scores include amplitude and gradient feature confidence scores. Finally, a weighted average method is used to achieve sub-pixel localization of the microbubbles by applying weighted averages to all maximum values ​​within the same cluster.

[0058] The tracking algorithm that minimizes the total matching distance between adjacent frames transforms the data association problem in multi-target (localization microbubble) tracking into solving a bipartite graph maximum matching problem. The bipartite graph consists of search boxes in adjacent frames, and we assume the set of all search boxes in the current frame is (X... n ,Y n The set of all search boxes in the previous or next frame (X) n-1 ,Y n-1 In this method, different search boxes within the same frame are not interconnected, while search boxes in adjacent frames are connected. This allows for near-perfect matching of microbubble localization points within the search boxes of adjacent frames, and microbubble motion tracking is achieved by minimizing the total matching distance. This process includes the appearance of new targets (microbubbles), the disappearance of old targets (microbubbles), and the matching of microbubble identifiers between neighboring frames and the current frame.

[0059] Step 3: Based on the super-resolution vascular structure map and blood flow velocity map, extract the geometric features of the vessel boundaries from the super-resolution structure map, including morphological information such as vessel location and diameter. Generate a time-series spatial coordinate set of the vessel based on the vascular morphological information; the above two constitute the coordinate dataset.

[0060] Simultaneously, the instantaneous velocity vector of the target blood vessel or vascular network is obtained based on the super-resolution blood flow velocity, including the two-dimensional velocity value and its corresponding spatial location. Furthermore, the velocity vector undergoes data preprocessing. Since the distribution of super-resolution velocity vectors within the target region's blood vessels is relatively small, high-resolution instantaneous velocity vectors are constructed by stacking super-resolution blood flow velocity vectors within short time intervals. The obtained high-resolution instantaneous velocity vector is then assimilated with hemodynamic simulation values ​​to obtain a complete, uniformly distributed instantaneous blood flow velocity vector. These operations constitute an auxiliary dataset, used as a data-driven component to accelerate convergence during the training of the physical information neural network.

[0061] Data preprocessing involves standardized median filtering and boundary value solver smooth interpolation.

[0062] The standardized median filtering method is an outlier detection method that adapts to local flow conditions. This filtering method evaluates the fluctuations in velocity relative to the median in a 3*3, 5*5, or 7*7 neighborhood around the center vector, and then processes the median of the fluctuations using the median test normalization.

[0063] The boundary value solver smooth interpolation method is used to replace missing data at locations where outliers have been removed. Similarly, in 3*3, 5*5, or 7*7 neighborhoods, the boundary value solver smooth interpolation method calculates the mean value tending towards the boundary velocity and fills the missing data with this mean value in areas with a large number of missing data.

[0064] See Figure 3 The high-resolution instantaneous velocity vectors are assimilated with hemodynamic simulation values. Specifically, the positions and number of velocity vectors are identified within a defined search area. Weighted averages are then applied based on the distance of each velocity vector within the search area from the search center, yielding the velocity vector at the center. For locations within the search area where velocity vectors cannot be identified, hemodynamic simulation values ​​are used to fill in the missing data, creating an auxiliary dataset. It is noteworthy that the auxiliary dataset has the same data dimension as the coordinate dataset.

[0065] Step 4: Based on the coordinate dataset and auxiliary dataset obtained in Step 3, a training dataset was constructed. Furthermore, a physical information neural network for rapidly calculating the blood flow velocity field and pressure field with ultra-high spatiotemporal resolution was constructed using the two-dimensional Navier-Stokes equations (NS equations).

[0066] The physical information neural network mainly includes the following components: a data mapping network and a physical residual network that encodes the Navier-Stokes equations.

[0067] The data mapping network consists of an input layer, hidden layers, and an output layer. The input layer is used to input training data, mainly a set of temporal spatial coordinates. The hidden layers map blood flow velocity and pressure, which is the output layer of the data mapping network. Each hidden layer contains at least two network channels. The physical residual network encoded by the Navier-Stokes equation is primarily built upon the Navier-Stokes equation, which is expressed as:

[0068]

[0069] In the above formula, u represents fluid velocity, p represents pressure, t represents time, and ρ represents fluid density. This is expressed as dynamic viscosity. The left side of the equation represents inertial force, while the right side corresponds to pressure, viscous force, and external force acting on the fluid, respectively.

[0070] A physical information neural network for optimizing hemodynamic parameters is constructed using two-dimensional Navier-Stokes equations, where the physical residual network is shown below:

[0071]

[0072] e3 = e1 + e2

[0073] In the above formula, e1, e2, and e3 represent the residual networks corresponding to the basic parameters, assuming that the blood flow is an incompressible fluid. It is the gradient operator, representing the sum of the first derivatives with respect to all directions in space. It is the Laplace operator, representing the sum of the second derivatives with respect to all directions in space, where U represents the two-dimensional velocity vector. It is expressed as dynamic viscosity.

[0074] Step 5: Construct the loss function of the physical information neural network structure, iteratively optimize the physical information neural network structure to obtain the optimal network model, which is used to calculate the blood flow velocity field and pressure field with ultra-spatial resolution.

[0075] Specifically, the loss function of the physical information neural network was constructed by summing the mean squared error between the high-resolution instantaneous velocity vector, the hemodynamic simulation assimilated data, and the predicted output value; the mean squared error of the physical residual network; and the mean squared error of the given velocity and its predicted value at the super-resolution blood vessel boundary location. During iterative training, the Adam optimizer and L-BFGS were selected to train the neural network, and sin(x) was chosen as the activation function to initialize the network parameters, satisfying the convergence requirements of the network model. Furthermore, the convergence speed of the neural network was further accelerated by adjusting the fixed learning rate or setting an adaptive learning rate, the number of iterations, and the size of the training dataset selected for each training iteration. Finally, the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity and pressure fields was obtained.

[0076] In physical information neural networks, the boundary condition term of the loss function is constructed by extracting the given velocity and the mean square error of the predicted value of the boundary position point based on the geometric features of the blood vessel boundary. This can limit the blood flow range of the target area, especially the range of complex blood flow in the entire blood vessel network, and further obtain the corresponding blood flow velocity vector and its spatial position point.

[0077] The loss function for constructing the physical information neural network can be specifically expressed as:

[0078] L = L D +L E +L B

[0079]

[0080] Among them, LD L E and L B These are the loss function terms corresponding to data-driven, physical residual networks, and super-resolution blood vessel boundary features, respectively. β and β represent the weights of the corresponding terms, N represents the total number of data points, i represents the number of residual networks, and p represents the prediction result. This represents the velocity value corresponding to the data point on the nth boundary.

[0081] Step 6: Train the physical information neural network using the training dataset. During iterative training, the training dataset is input into the data mapping network, which outputs blood flow velocity and pressure after passing through the hidden layer. The output velocity and pressure values ​​are then input into the physical residual network for partial differential equation calculation. Further, the results from both the data mapping network and the physical residual network are passed to the Adam optimizer and the L-BFGS optimizer for gradient optimization. The optimization results are fed back into the aforementioned networks, thus iteratively updating the network parameters to obtain the optimal model for calculating the hyperspatial-temporal resolution blood flow velocity and pressure fields. Finally, the time-series intravascular spatial coordinate set is input into the aforementioned optimal model, enabling non-invasive and rapid calculation of hyperspatial-temporal resolution blood flow velocity and pressure fields without any constraints.

[0082] Figure 4 This is a hyperspatiotemporal resolution blood flow velocity field map calculated based on the trained optimal model; Figure 5 This is a hyperspatiotemporal resolution blood flow pressure field map calculated based on the trained optimal model.

[0083] In another aspect, the present invention provides a super-spatiotemporal resolution blood flow velocity field and pressure field analysis system, comprising: an ultrasound super-resolution imaging and feature extraction module, a data preprocessing module, a network model construction and optimization module, and a super-spatiotemporal resolution blood flow velocity field and pressure field calculation module.

[0084] The ultrasound super-resolution imaging and feature extraction module is used to acquire contrast-enhanced ultrasound blood flow data and obtain super-resolution vascular structure maps and blood flow velocity maps by using singular value filtering, scale statistical feature localization algorithm and tracking algorithm that minimizes the total matching distance between adjacent frames. Furthermore, the geometric features of the vascular boundary in the target area, the set of temporal spatial coordinate points in the blood vessel, and the blood flow velocity vector obtained by super-resolution tracking are extracted from the super-resolution imaging data.

[0085] The data preprocessing module is used to preprocess the velocity vectors obtained by ultrasound super-resolution tracking using the normalized median filtering method and the boundary value solver smooth interpolation method. The preprocessed super-resolution velocity vectors in the short time set are stacked and finally constructed into an auxiliary dataset by data assimilation with hemodynamic simulation, which is used as part of the training dataset.

[0086] The network model construction and optimization module is used to construct a physical information neural network and construct the geometric features of the blood vessel boundary in the target region as the boundary condition term of the loss function of the physical information neural network. After iterative optimization, an optimal model of the physical information neural network for rapidly estimating the hyperspatial resolution blood flow velocity field and pressure field is obtained.

[0087] The super-spatiotemporal resolution blood flow velocity field and pressure field calculation module is used to calculate the super-spatiotemporal resolution blood flow velocity field and pressure field by taking into account the optimal model of the physical information neural network of the super-resolution blood flow velocity field and pressure field obtained through training, without requiring the geometric features of the blood vessel boundary.

[0088] The boundary condition term in the loss function of the physical information neural network is obtained by calculating the mean square error between the position coordinates of the blood vessel boundary and the corresponding velocity values ​​obtained from the super-resolution blood vessel structure and the output value of the physical information network. The boundary condition term in the above loss function allows the constructed physical information neural network to not only calculate the blood flow velocity field and pressure field of a single blood vessel in the target region at super-spatiotemporal resolution, but also to calculate and analyze the hemodynamic parameters (velocity and pressure) of complex blood vessel networks in the target region at super-spatiotemporal resolution.

[0089] This method uses the geometric features of the blood vessel boundary and the set of temporal spatial coordinates within the blood vessel obtained from ultrasound super-resolution images as the coordinate dataset for a physical information neural network. Furthermore, it constructs an auxiliary dataset by assimilating the velocity vectors obtained from ultrasound super-resolution tracking with hemodynamic simulations. After data preprocessing, the auxiliary dataset is combined with the coordinate dataset to train the physical information neural network. Through multiple iterations, the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity and pressure fields is obtained. Based on this optimal model, any set of spatial coordinates within the blood vessel is used as input to predict the corresponding blood flow velocity and pressure fields without providing other constraints. This invention solves the problem of low temporal and spatial resolution in estimating the velocity field during ultrasound super-resolution imaging by stacking velocity vectors from short time sets and assimilating them with hemodynamic simulations. Further optimization using the physical information neural network establishes a prediction model, enabling rapid calculation of blood flow velocity and pressure fields with high temporal and spatial resolution.

[0090] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution, characterized in that, Includes the following steps: Step 1: Based on the ultrasound super-resolution vascular structure map and blood flow velocity map of the target object, extract the geometric features of the vascular boundary and the set of temporal spatial coordinate points in the vascular area to form a coordinate dataset; High-resolution instantaneous velocity vectors are obtained from blood flow velocity maps. These high-resolution instantaneous velocity vectors are then assimilated with hemodynamic simulation values ​​to construct an auxiliary dataset. Step 2: Construct a physical information neural network. Based on the mean square error of the physical residual network, the mean square error of the velocity vector in the blood vessel and its predicted value, construct the physical residual network and the corresponding loss function term driven by the data. Based on the geometric features of the blood vessel boundary, extract the given velocity at the boundary position point and the mean square error of its predicted value to construct the boundary condition term of the loss function. Step 3: Use the coordinate dataset and auxiliary dataset as training datasets to iteratively train the physical information neural network. After iterative optimization, obtain the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity field and pressure field. Predict the instantaneous super-resolution blood flow velocity field and pressure field based on the optimal model of the physical information neural network.

2. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, Step 1 involves extracting contrast-enhanced ultrasound blood flow data of blood vessels or vascular networks in the target area, performing super-resolution imaging on the ultrasound blood flow data, and obtaining super-resolution vascular structure maps and blood flow velocity maps.

3. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, The method for obtaining the ultrasound super-resolution vascular structure map and blood flow velocity map is as follows: The tissue signals in the contrast-enhanced ultrasound blood flow data of the target object are filtered to obtain the blood flow signal. The super-resolution vascular structure map and blood flow velocity map are obtained by using a multi-scale statistical feature localization algorithm and a tracking algorithm that minimizes the total matching distance between adjacent frames.

4. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, The method for constructing the auxiliary dataset mentioned in step 1 is as follows: The high-resolution instantaneous velocity vector is constructed by stacking super-resolution blood flow velocity vectors within a set time frame based on blood flow velocity maps, and then fused with hemodynamic simulations through data assimilation to obtain an auxiliary dataset.

5. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 4, characterized in that, The velocity vectors obtained from ultrasound super-resolution tracking were preprocessed using the standardized median filtering method and the boundary value solver smooth interpolation method. The preprocessed super-resolution velocity vectors within a set time period were stacked and an auxiliary dataset was constructed by assimilating the data with hemodynamic simulation.

6. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, In step 3, the Navier-Stokes equations are encoded as a physical residual network in the physical information neural network, as follows: e3 = e1 + e2 Where e1, e2, and e3 represent the residual networks of the physical information network, θ is the dynamic viscosity of blood flow; u and v are dimensionless velocity vectors, p is dimensionless pressure, and t is dimensionless time. It is the gradient operator. U is the Laplace operator representing a two-dimensional velocity vector.

7. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, The training method for the physical information neural network is as follows: The training dataset is input into the physical information neural network model to obtain the error function between the output value and the input value. An optimization algorithm is used to minimize the loss function and update the network model parameters. After multiple iterations of optimization, the optimal model is obtained. In physical information neural networks, chain rules are applied to solve differential functions using automatic differentiation, allowing physical control equations to participate in the updating and optimization of the network model.

8. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 7, characterized in that, During the training process of the physical information neural network, optimizers are used to minimize the loss function. The optimizers are Adam optimizer and L-BFGS optimizer.

9. The method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution according to claim 1, characterized in that, The loss function of the physical information neural network is as follows: L=L D +L E +L B Among them, L D L E and L B These are the loss function terms corresponding to data-driven, physical residual networks, and super-resolution blood vessel boundary features, respectively. β and β represent the weights of the corresponding terms, N represents the total number of data points, i represents the number of residual networks, and p represents the prediction result. This represents the velocity value corresponding to the data point on the nth boundary.

10. A system for performing the method for analyzing blood flow velocity and pressure fields with super-spatiotemporal resolution as described in any one of claims 1-9, characterized in that, include: The feature extraction module is used to extract the geometric features of the blood vessel boundary and the set of temporal spatial coordinate points within the blood vessel to form a coordinate dataset based on the ultrasound super-resolution vascular structure map and blood flow velocity map of the target object. High-resolution instantaneous velocity vectors are obtained from blood flow velocity maps. These high-resolution instantaneous velocity vectors are then assimilated with hemodynamic simulation values ​​to construct an auxiliary dataset. The network module is used to construct a physical information neural network. It constructs the physical residual network and the corresponding loss function terms based on the mean square error, velocity vector and its predicted value of the physical residual network. It also extracts the mean square error of the given velocity and its predicted value of the boundary position point based on the geometric features of the blood vessel boundary to construct the boundary condition terms of the loss function. The prediction module is used to use the coordinate dataset and auxiliary dataset as training datasets to iteratively train the physical information neural network. After iterative optimization, the optimal model of the physical information neural network for estimating the super-resolution blood flow velocity field and pressure field is obtained. Based on the optimal model, the instantaneous super-resolution blood flow velocity field and pressure field are predicted according to the set of spatial coordinate points in the intravascular time series.

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