Method for estimating a flow profile in a shadow region based on ultrasonic signal data

Abstract

The invention relates to a method, in particular a computer-implemented method for estimating a flow profile of a fluid flow in a pipe, comprising the steps of: - acquiring a series of ultrasonic signal data comprising information about a fluid flow in the pipe, - identifying a shadow region in the ultrasonic signal data which lacks information about the fluid flow in the pipe; - determining a flow profile of the fluid from the ultrasonic signal data about a flow region outside the shadow region of the pipe, - estimating a flow profile in the shadow region with a physics-informed machine learning method, wherein the physics-informed machine learning method is trained with flow data comprising information about flow profiles determined for flow regions located outside the shadow region and position data comprising a plurality of positions within and / or outside the shadow region and their associated time points.

Description

Technical Field

[0001] The present invention relates to a method, and more particularly to a computer-based method for estimating the flow profile of fluid flow in a pipe. Background Technology

[0002] Ultrasound flow imaging has become a leading tool for diagnosing a range of conditions, including vascular stenosis and congenital heart disease. Its high frame rate (> tens of hertz) offers a unique advantage in accurately capturing complex blood flow patterns that may have clinical significance but are difficult to achieve with other imaging modalities such as magnetic resonance imaging (MRI) and computed tomography (CT).

[0003] On the other hand, ultrasound blood flow imaging presents specific difficulties in challenging situations, such as acoustic shadowing obscuring the visualization of the flow field and related vascular morphology.

[0004] Stroke is one of the leading causes of death and disability worldwide, ranking alongside cancer and ischemic heart disease. Atherosclerosis, primarily manifested as plaque, is the cause of many stroke cases. In response to micro-damage to the arterial wall, endothelial-triggered biochemical signals induce a repair process. Inflammatory cells, cholesterol, fat, and other substances accumulate at the damaged site, forming fatty plaques that protrude into the blood vessel lumen. The inner diameter of the blood vessel subsequently decreases, eventually leading to narrowing.

[0005] Compared to other imaging modalities, ultrasound imaging has become the primary method for non-invasive diagnosis of vascular stenosis, offering advantages such as being radiation-free, bedside access, and cost-effective. Two commonly used methods for quantitatively analyzing the degree of stenosis using ultrasound are morphological analysis (ratio percentage method) and peak systolic velocity (PSV) measurement. Appropriate thresholds are then used to assess severity and provide a basis for subsequent diagnostic and treatment methods.

[0006] However, calcification exists in many plaques, and calcified plaques can cause acoustic shadowing, obscuring the vascular lumen and hindering the sonographer's ability to obtain ultrasound measurements. For example, in a study involving 400 consecutive carotid artery ultrasound scans, acoustic shadowing was found in 14.7% of the participants. Acoustic shadowing occurs when highly reflective plaques on the vessel wall are illuminated by an ultrasound beam. This artifact is projected onto areas with lower echo intensity below, leading to significant problems in the morphological and hemodynamic assessment of stenosis.

[0007] Since the flow profile within the shadowed area cannot be determined, there is an urgent need to address this sound and shadow problem. Summary of the Invention

[0008] The present invention is disclosed by claim 1. Advantageous embodiments are described in the dependent claims.

[0009] According to a first aspect of the present invention, a method for estimating the flow profile of fluid flow in a pipe, particularly a computer-implemented method, comprises the following steps: Acquire a series of ultrasonic signal data, including information about the fluid flow in the tube. Identify shadowed areas in the ultrasonic signal data that lack information about the fluid flow in the tube; The flow profile of the fluid is determined from ultrasonic signal data of the flow region outside the shaded area of ​​the tube. The flow profile in the shaded region is estimated using a physically based machine learning method, wherein the physically based machine learning method is trained using flow data and location data, the flow data including information about flow profiles determined for flow regions located outside the shaded region, and the location data including multiple locations within and / or outside the shaded region and their associated time points.

[0010] By using a physical information-based machine learning method, it is possible to improve the prediction of blood flow within a vascular shadow area based on the physical laws and properties considered by the physical information-based machine learning method.

[0011] Based on the results of the first approach, it is better able to reflect the more likely fluid flow in blood vessels than other machine learning methods trained to predict fluid flow in shaded areas, because these methods may not depend on physical laws, fluid properties, and tube geometry.

[0012] In particular, it is also possible to predict the time evolution of the fluid flow.

[0013] According to another embodiment of the invention, flow profiles are determined for at least two flow regions, wherein a first flow region in the at least two flow regions is located upstream of the shaded region, and a second flow region in the at least two flow regions is located downstream of the shaded region, and in particular, wherein the fluid flow is from the upstream region of the shaded region to the downstream region.

[0014] Therefore, the upstream and downstream regions are defined based on the net flow direction. The upstream and / or downstream regions may include one or more pipes.

[0015] According to another embodiment of the invention, the flowing region is located adjacent to the shaded region. According to another embodiment of the invention, the shaded region is automatically detected by the method.

[0016] According to another embodiment of the invention, the shaded area can extend along the net flow direction to 5 mm, 10 mm, 20 mm, 50 mm, 100 mm, 150 mm, or even 300 mm. In particular, the diameter of the shaded area or the container within the shaded area can range from 0.5 mm to 50 mm, and especially from 1 mm to 30 mm.

[0017] According to another embodiment of the present invention, a fully connected deep neural network is used to implement a machine learning method based on physical information. The fully connected deep neural network can take spatial and temporal coordinates, i.e., location and time point, as input and predict multidimensional velocity components and pressure. For a two-dimensional flow profile, the inputs are spatial coordinates x, y and the corresponding time coordinate t, and the outputs are velocity components u, v and pressure p. For a three-dimensional flow profile, an additional input z, i.e., a third spatial coordinate, is added, and an additional output w, i.e., a third velocity component, is added. The fully connected deep neural network can contain multiple hidden layers, each with multiple neurons. Each neuron can use a sinusoidal activation function. Note that other activation functions can also be used, especially as long as they have a meaningful second derivative for the determination of physical loss as described below.

[0018] According to another embodiment of the invention, a machine learning method based on physical information is trained using streaming data to reconstruct velocities at multiple locations and time points based on a streaming data loss function, so as to match the velocities contained in the flow profile, wherein the streaming data loss function indicates the deviation between the reconstructed velocities and the velocities contained in the flow profile.

[0019] According to another embodiment of the invention, location data can be sampled both inside and outside the shaded region, wherein the location data is used to train a physically based machine learning method to apply a physical loss function to reconstruct the velocity and pressure at multiple locations and time points within the shaded region. By integrating physical laws into the learning process in the form of a loss function, the machine learning method is constrained to produce solutions that follow the fundamental physical properties of the flow, even within the shaded region.

[0020] According to another embodiment of the invention, training of physically based machine learning methods is facilitated by minimizing a composite error function comprising a streaming data loss function and a physical loss function. Streaming data sampled outside the shaded region is used as boundary or initial conditions to guide the solution. Conventional machine learning methods may produce non-physical flow profiles in the shaded region due to a lack of training data. By enforcing physical laws in the form of a loss function as a regularization method, solutions deviating from these laws are penalized. Physically based machine learning methods can be trained to universally satisfy the governing equations throughout the domain. Therefore, they can generalize to shaded regions without direct measurements, providing a structured way to reconstruct coherent and physically reliable dense flow profiles throughout the domain of interest, including the shaded region.

[0021] According to another embodiment of the present invention, the composite loss function and its corresponding composite loss value are minimized by gradient descent.

[0022] According to another embodiment of the invention, flow data is generated, particularly sampled from a flow profile defined for a flow region, wherein the flow data includes information about the velocity of the fluid at multiple locations at multiple associated time points.

[0023] This flow data represents a spatially resolved fluid dynamics or flow profile in an unobstructed pipe section, such as a flow region.

[0024] Those skilled in the art know how to generate flow data from ultrasonic signal data. Various methods are available for determining flow based on signal data. For example, flow profiles can be determined using speckle tracing and vector Doppler methods.

[0025] According to another embodiment of the invention, the streaming data is limited to locations contained within the streaming region. The streaming data may contain velocity information about one or more points in time at one or more locations within the streaming region. According to another embodiment of the invention, training a physically based machine learning method includes: providing information about locations and points in time from the streaming data as input to the physically based machine learning method, wherein the physically based machine learning method determines an estimated velocity for each location and point in time, wherein a streaming data loss function determines a streaming data loss value, which indicates the deviation between the velocity included in the streaming data and the velocity estimated by the physically based machine learning method.

[0026] It is worth noting that, in the context of this specification, the terms "flow data loss" and "data loss" are used synonymously. Flow data that includes flow profile information is particularly well-suited for physically-based machine learning methods because fluid flow can be physically modeled based on the dynamic information of the fluid's flow profile.

[0027] This embodiment enables, for example, training a physically based machine learning method to reconstruct the velocity of regions outside the shadow area. This allows for matching the velocity, and thus, for example, as a constraint on a physical loss function based on the Navier-Stokes equations.

[0028] According to another embodiment of the present invention, training a physical information-based machine learning method includes: providing at least some locations and associated time points from location data as input to the physical information-based machine learning method, wherein the physical information-based machine learning method determines, for each location and time point, an estimated velocity and an estimated pressure of the fluid at that location and time point, wherein the estimated velocity and estimated pressure are provided to a physical loss function comprising the Navier-Stokes equations, wherein the physical loss function determines a physical loss value indicating the deviation of the velocity and pressure estimated by the physical information-based machine learning method from the velocity and pressure obtained by solving the Navier-Stokes equations.

[0029] Assigning the Navier-Stokes equations to a physical loss function provides a suitable, physically-based, and physically constrained loss function, thus limiting the estimation results of machine learning methods to physically meaningful flow profiles within the shaded region.

[0030] According to another embodiment of the invention, training includes a first stage, a second stage, and a third stage, wherein in the first stage, the data loss value is determined; in the second stage, the physical loss value is determined; and in the third stage, a composite loss value is determined from a composite loss function comprising the data loss function and the physical loss function, particularly wherein the composite loss function comprises the sum of the data loss function and the physical loss function, particularly a weighted sum, wherein the composite loss function is minimized during training epochs.

[0031] This three-stage process can model a robust training process where the streaming data loss function and the physical loss function are separable, and their contributions to the output estimation of the streaming profile can be adjusted by a composite loss function.

[0032] According to another embodiment of the invention, the Navier-Stokes equations correspond to the Navier-Stokes equations adjusted for incompressible fluids, momentum conservation, and mass conservation.

[0033] According to another embodiment of the invention, the flow profile is determined in three dimensions or two dimensions.

[0034] This makes it possible to apply the method to a variety of ultrasound recording systems that can be designed to record two-dimensional or three-dimensional streaming data.

[0035] According to another embodiment of the invention, when the flow profile is determined in three dimensions, the physical loss function includes a physical residual function based on terms of the Navier-Stokes equations. , , , : , , , , in, To represent a partial differential operator, Indicates time, This specifically refers to a constant fluid density. Indicates the viscosity of a fluid. , , The velocity is estimated along three dimensions by a machine learning method based on physical information. , , The velocity component, where, The stress is estimated by a machine learning method based on physical information, where the physical loss value... The physical loss function is determined according to the following formula: , in, This indicates that the location of the physical loss function and the number of associated time points have been evaluated.

[0036] According to another embodiment of the invention, when the flow profile is determined in a two-dimensional manner, the physical loss function includes a physical residual function based on terms of the Navier-Stokes equations. , , : , , , in, To represent a partial differential operator, Indicates time, This specifically refers to a constant fluid density. Indicates the viscosity of a fluid. , It is estimated along two dimensions by a machine learning method based on physical information. , The velocity component, where, The stress is estimated by a machine learning method based on physical information, where the physical loss value... The physical loss function is determined according to the following formula: , in, This indicates that the location of the physical loss function and, in particular, the number of associated time points have been evaluated.

[0037] According to another embodiment of the present invention, when the flow profile is determined in a three-dimensional manner, the data loss function and the data loss value are... Determined according to the following formula: , in , It refers to the time point of velocity estimated by a machine learning method based on physical information. Location The velocity component, and among which, , , It is the velocity component corresponding to the velocity of the provided streaming data, where, This indicates that the location of the data loss function and, in particular, the number of associated time points have been evaluated during the round.

[0038] According to another embodiment of the present invention, when the flow profile is determined in a two-dimensional manner, the data loss function and the data loss value are... Determined according to the following formula: , in , It refers to the time point of velocity estimated by a machine learning method based on physical information. Location The velocity component, and among which, , It is the velocity component corresponding to the velocity of the provided streaming data, where, This indicates that the location of the data loss function and, in particular, the number of associated time points have been evaluated during the round.

[0039] According to another embodiment of the present invention, the composite loss value according to Confirmed, among which and A positive number representing the contribution to the weighted physical loss value and the data loss value.

[0040] According to another embodiment of the invention, the tube is a blood vessel in a living organism.

[0041] The shaded area may be caused by calcified tubular wall segments.

[0042] According to another embodiment of the invention, the method is performed during an ultrasound imaging examination of a patient, wherein the training of the physical information-based machine learning method is performed at least once for each patient.

[0043] This makes it possible to predict patient-specific flow profiles within the shaded area.

[0044] It should be noted that sufficient training data can be obtained quickly because the region adjacent to the shaded area provides a time flow profile that repeats after each heartbeat, so training data can be easily obtained with just one or a few heartbeats.

[0045] The acquisition process can last from 0.5s to 10s.

[0046] According to another embodiment of the invention, a pipe boundary is determined at least for the flow region, wherein the velocity of the determined flow profile is set to zero at the boundary, outside the flow region, and outside the shaded region.

[0047] This allows for robust estimation of the flow profile within the shaded region.

[0048] According to another embodiment of the invention, by inputting corresponding spatial and temporal coordinates, such as location data and associated time points, the flow profile within the shaded area is determined using an estimated velocity estimated by a trained physical information-based machine learning method.

[0049] According to another embodiment of the invention, a trained machine learning method based on physical information is used to estimate the temporally resolved velocity and / or pressure distribution of at least a portion of the shadow region, particularly the entire shadow region.

[0050] According to another embodiment of the invention, it is possible to evaluate and determine important parameters characterizing the state of pipe flow without relying on more complex or invasive measurement systems.

[0051] According to another embodiment of the invention, velocity and / or pressure estimated by a trained physical information-based machine learning method are displayed, particularly wherein the estimated velocity and / or estimated pressure are displayed in conjunction with a flow region and a shaded region.

[0052] According to another embodiment of the invention, a sequence of velocities and / or pressures estimated by a machine learning method based on physical information is generated, particularly in the form of a video, thereby generating a temporal evolution of velocities and / or pressures, particularly the temporal evolution of velocity distributions and / or estimated pressure distributions, wherein the one or more sequences are displayed together with a flow profile, particularly with velocities in the flow region, so that the flow region and the shaded region exhibit a continuous flow profile that evolves over time, particularly in the form of a video.

[0053] This allows personnel to assess the dynamics within the pipe, even in shaded areas.

[0054] According to another embodiment of the invention, the flow profile in the flow region is determined by tracking a tracer included in the fluid.

[0055] Such tracers can include microbubbles.

[0056] According to another embodiment of the invention, the method includes the step of segmenting the tube to at least determine the boundaries of the tube, and more specifically, the lumen of the tube, wherein the step is performed together with, in particular, the step of estimating the flow profile.

[0057] According to a second aspect of the invention, a computer program comprising computer program code, when executed on a computer, causes the computer to perform the method according to any one of the preceding claims.

[0058] The computer program can be stored on a non-transitory storage medium.

[0059] According to a third aspect of the present invention, an ultrasonic measurement system includes at least the following components: An ultrasonic transducer head system configured to generate and record ultrasonic signal data; A computer, connected to the ultrasonic transducer head system and configured to receive ultrasonic signal data, The feature is that the computer is configured to execute the method according to the first aspect of the invention or the computer program according to the second aspect of the invention.

[0060] By utilizing flow data available in the upstream and downstream flow regions of the acoustic shadowing area, this method aims to reconstruct the missing flow profile and vessel boundary information under acoustic shadowing, and can be directly applied to the analysis of vascular stenosis.

[0061] General working principle / inventive concept The inventors have discovered a remarkable method for estimating flow profiles in shaded regions where flow data is unavailable.

[0062] The core of this invention lies in a machine learning method based on physical information, which generates solutions that conform to or at least substantially conform to physical principles through design.

[0063] Regarding this invention, the underlying physical principles include fluid dynamics principles or laws. By penalizing the machine learning method during training based on deviations from the underlying physical principles or laws, the machine learning method is biased towards physically meaningful estimates, i.e., estimates that highly conform to the physical principles behind the observed natural phenomenon (here, for example, fluid flow through a blood vessel).

[0064] This inventive concept extends in particular to the use of one or more equations that are specially constructed to act as error functions that penalize deviations from the equations (i.e., the expected physical solutions).

[0065] In this example, it is necessary to determine the fluid flow within a certain region. Therefore, machine learning methods based on physical information include an error function that at least partially contains the laws of fluid dynamics. In the context of this specification, this part is referred to as the physical loss function.

[0066] However, in addition to this understanding, the inventors also faced a problem: how to prevent machine learning methods from generating solutions in the shadow region that, while adhering to the physical loss function, produce unrealistic outputs (such as speed and pressure).

[0067] The inventors realized that in the flow region outside (especially adjacent shaded regions), there exists information that can be used to prevent the generation of unrealistic solutions that, although minimizing the physical loss function, are physically meaningless.

[0068] To bias physically-based machine learning methods toward physically meaningful solutions, the inventors realized that the machine learning method could be trained by also applying an error function to the flow region outside the shaded area to recover / reconstruct the velocities in these regions, i.e., the flow profile. This error function is called the data loss function. The data loss function does not necessarily have to be an equation simulating the physical process, but can be any function suitable for training a physically-based machine learning method to reconstruct a (known) flow profile. For example, the chi-square deviation between the estimated velocity at a certain location at a certain time point and the velocity at the same location at the same time point determined from flow data.

[0069] Therefore, this method may only need to take the location and time point as input to ultimately (after training) estimate the velocity at that location at that time point. Clearly, the trained method can then predict the velocity at almost any location in the flow region outside the shaded area at any time point.

[0070] This training can be performed on the collected data and does not require a specific training dataset.

[0071] Now, since a possibility has been created to generate boundary conditions for the velocity at the interface between the shaded and flowing regions, the aforementioned physical loss function can be constrained to a solution connected to these boundary conditions. Therefore, machine learning methods can also be trained on this physical loss function by submitting coordinate positions and time points within and outside the shaded region, where the velocity (and, as a “byproduct,” the pressure dominated by the physical loss function) will be determined in a way that smoothly connects the velocity to the flow profile within the flowing region.

[0072] For example, the physical loss function based on the Navier-Stokes equations has sufficient detail and requires no additional boundary or initial conditions other than those already present in the flow region (i.e., the velocity reconstructed by the data loss function).

[0073] As shown in the following figure description, indeed, the machine learning method trained with these two error functions is able to achieve surprisingly accurate estimates of the flow profile, velocity, and / or pressure in the shaded area of ​​the pipe.

[0074] Furthermore, the method is designed to reconstruct flow profiles, velocities, and pressures at time points before or after data acquisition.

[0075] To balance the impact of the data loss function and the physical loss function, it may be advantageous to combine these two functions into a weighted composite function.

[0076] For example, two functions can use the same weights, i.e., apply a 1:1 (50:50) weight ratio. Alternatively, different weights can be used. Those skilled in the art can select weights by experimenting with different weights or by referring to performance parameters that indicate the most suitable weights. Attached Figure Description

[0077] Specifically, exemplary embodiments are described below with reference to the accompanying drawings. The drawings are appended to the claims and accompanied by text explaining the various features of the illustrated embodiments and aspects of the invention. Each individual feature shown in the drawings and / or mentioned in the text of the drawings may be incorporated (or separated) into the claims relating to the method or apparatus according to the invention.

[0078] Figure 1 shows a phantom used for exemplary data acquisition; Figure 2 shows a representation of ultrasound signal data acquired in single-frame format; Figure 3 shows the pulsating flow profile of the liquid in the tube at three different time points; Figure 4 illustrates the ability of this method to estimate flow profiles in shaded regions; Figure 5This demonstrates the method's ability to determine the area occupied by the pipe; and Figure 6 illustrates different examples of reconstructing flow profiles in a narrow tube within a shaded area according to the method of the present invention. Detailed Implementation

[0079] Figure 1A A phantom of a polylactic acid (PLA) tube 1 core is shown, including a bifurcation structure for demonstration purposes. The tube 1 core is then embedded in a material that provides ultrasound signals similar to human tissue. In the embodiment described herein, the PLA tube core is subsequently dissolved using chloroform, and a wall-less carotid bifurcation phantom is constructed using a polyvinyl alcohol (PVA) cryogel. The diameters of the common carotid artery, internal carotid artery, and external carotid artery branches are 6 mm, 4.2 mm, and 3.5 mm, respectively, all dimensions within the normal range for adult carotid arteries. At the entrance of the internal carotid artery branch, a 50% eccentric stenosis (according to the North American Symptomatic Carotid Endarterectomy Trial (NASCET) criteria) is added to construct a pathological state with vascular stenosis.

[0080] Figure 1B An experimental setup for performing the method according to the invention is shown. After the core is removed with chloroform, the wallless flow channel is connected to pipe 3 via a hose connector to pump liquid through pump device 2.

[0081] Ultrasonic imaging is accomplished by repeatedly emitting short pulses from transducer head 4 and beamforming the returned echoes from each emission. Using an unfocused ultrasound beam (plane wave / divergent wave), images can be reconstructed from a single pulse transmission, achieving a high frame rate (approximately several kilohertz), which is highly useful for blood flow imaging. When using a focused beam, the region of interest needs to be scanned sequentially using a line-by-line scanning scheme, resulting in a lower frame rate (determined by the density of the imaging lines). It is important to note that the described flow and boundary reconstruction method is not limited to the type of ultrasound transducer and ultrasound beam used.

[0082] Experiments were conducted using a fabricated phantom and a pulsating flow of 60 beats / min and 3 mL / beat generated by a pulsating flow pump 2 (Model 1405, Harvard Instruments, MASS). This flow rate is within the range of human carotid artery blood flow. SonoVue microbubbles diluted 1:2000 were used as tracers for flow estimation (the proposed method is not limited to the use of microbubble contrast agents). The Ultrasonic Array Research Platform IIa (UARP IIa), developed by the Ultrasonics and Embedded Systems Research Group at the University of Leeds, was used for ultrasonic excitation generation and data acquisition. The UARP IIa system employed a five-element excitation scheme and harmonic suppression scheme. A Verasonics L11-4V linear array transducer (Verasonics, Inc., WA) was connected to the UARP IIa, and a two-cycle sinusoidal waveform with a center frequency of 7.55 MHz was used for excitation. The bifurcation flow phantom was scanned using zero-degree unfocused plane wave imaging with a pulse repetition frequency of 6 kHz (corresponding to a frame rate of 6 kHz) and a mechanical index of 0.1. Ultrasonic radio frequency (RF) data was acquired at a sampling frequency of 40 MHz. The acquired RF data was transmitted to a local PC 5 for beamforming and 2D motion estimation (at each pixel) by finding inter-frame displacement. Results and control information can be displayed. Figure 1B The system is shown on display 6. It should be noted that the system according to the invention typically does not include a flow pump, piping, or phantom.

[0083] Delayed stacked beamforming was employed to reconstruct ultrasound images. Singular value decomposition (SVD) filters were applied to the image sequences to remove tissue background signals. Subsequently, a correlation-based motion estimation method was used to perform 2D vector flow mapping on the RF frames after beamforming and SVD filtering. The generated flow field maps had a frame rate of 6 kHz.

[0084] exist Figure 2A The image depicts a wallless flow phantom, i.e., embedded tube 1, recorded in a single frame (number #01131) using an ultrasonic measurement system. In this example, the liquid includes a tracer to enhance liquid contrast. It should be noted that blood can be recorded without using a tracer while still providing sufficiently high contrast in the image to estimate the flow profile within the tube.

[0085] Figure 2B The image depicts a filtered image in which background signals from the tissue material (i.e., the embedded material of tube 1 around tube 1) have been removed by a software filter.

[0086] This, in turn, allows for the determination of pipe boundaries within the flow region.

[0087] The flow profiles obtained from single-frame ultrasonic signal data are depicted in Figure 3 at three different time points. Figure 3AThe middle point is time 814, in Figure 3B The middle is time point 1072, and in Figure 3C The value in the middle represents time point 1612. Specifically, velocity vectors are displayed at multiple locations within the blood vessel for each time point. Color coding indicates the magnitude of the velocity.

[0088] exist Figure 4A In this process, the data was processed to generate a shaded area by removing data that was included in the area between two flow areas, one of which was upstream of the shaded area and the second flow area was downstream of the shaded area.

[0089] This method determines flow data from two flow regions, including velocities at different time points and locations. Segments of the pipe boundary available outside the acoustic shadow can also be determined. For the tissue background outside the acoustic shadow region, the flow velocity value is assigned to zero (no flow there).

[0090] We construct a physical information-based neural network based on flow data to determine flow characteristics and fill in the missing flow and pipe boundary information.

[0091] In one implementation, the shaded region is artificially created by removing data (organizational background and flow) below the pipe boundary. This configuration allows for obtaining a realistic view to evaluate the performance of the method according to the invention. To implement the physical information machine learning method, the inventors utilize the ability of deep neural networks as general function approximators to identify nonlinear mappings between spatiotemporal coordinates and flow parameters. A deep neural network is defined and trained to match available velocity data over a time period, while constraining its solutions to satisfy prior computational fluid dynamics knowledge for interpreting the observed data. In this setting, the temporal correlation characteristics of the flow pattern are captured by the trained neural network, which is then used to infer the spatiotemporal flow field under acoustic shadowing. The physical information-based neural network takes spatial coordinates (x, y) and time coordinates (t) as input. In an exemplary embodiment, the physical information-based neural network has 10 hidden fully connected layers, each containing 120 neurons, and outputs two-dimensional velocity components (u, v) and pressure (p). That is, the physical information-based neural network maps the input (x, y, t) to the output (u, v, p). Hyperbolic tangent or sine functions are used as the nonlinear activation function for each neuron. To train the neural network, streaming data (pixel positions [x, y]) along with temporal information (t) corresponding to each training point are fed into the network as input. To penalize the neural network, a velocity mismatch is used between its output velocity components [u, v] and the measured reference value. The Navier-Stokes equations are effective as physical constraints within the flow region. During the training phase, it is also recommended to enforce physical constraints across the entire region of interest (including the observable flow region and the tissue background region). For the tissue background region, its velocity is assigned to zero. The visible zero-velocity tissue background region also participates in the calculation of the aforementioned velocity data mismatch and penalizes velocity predictions deviating from zero. With this setup, the trained neural network can be used for prediction by inputting arbitrary spatial coordinates, including those located within the acoustically shaded tissue background (whose predicted velocity values ​​approach zero). In this implementation, 200 ms of data covering the peak velocity period is used. The neural network parameters are optimized using the Adam optimization algorithm for 20,000 iterations. The learning rate starts at 1e-3 and decreases by 25% every 1000 iterations.

[0092] Once the neural network is trained, it can be used to reconstruct the flow field beneath the dark acoustic shadow region by inputting the corresponding spatial and temporal coordinates. Figure 4A An example of stream data 100 with acoustic shadow region 103 is shown (note that the two-dimensional velocity component is set to zero outside the dark acoustic shadow 103 and inside the background region 105). Figure 4B This demonstrates a real-world scenario where all ultrasound signals are available. Figure 4C This is the corresponding estimation result according to the method of the present invention.

[0093] Figure 4A The recorded flow data 200 represents a single point in time as fluid flows through the pipe. The pipe has branches, and shaded areas are arranged at the branches.

[0094] Shadow area 103 is generated in the realistic scenario (see...) Figure 4B It was added later by manually removing all stream information within the shaded area 103.

[0095] In this way, the true situation is known, which can be used to benchmark the method according to the invention.

[0096] exist Figure 4B The image shows stream data 200 excluding the shaded area.

[0097] Figure 4C The solution generated by the method according to the present invention is described. A deep neural network and the training parameters described in the previous section are used (10 hidden fully connected layers, each containing 120 neurons, using 200 ms of data covering the peak flow rate period; the neural network parameters are optimized through 20,000 iterations using the Adam optimization algorithm. The learning rate starts from 1e-3 and decreases by 25% after every 1,000 iterations).

[0098] It can be seen that, Figure 4A In the previously shaded area, the estimated flow profile 104 is compared with the recorded flow data ( Figure 4B The flow profiles in the data look very similar. Although Figure 4 only shows the flow profile at a single time point, it is clear that the method applies to all frames of the recorded flow data and produces comparable results.

[0099] The estimated velocity for shaded region 103 is very accurate. The average error for the lateral velocity component in the shaded region is 2.43 ± 0.26 cm / s. The average error for the axial velocity component in the shaded region is 2.14 ± 0.35 cm / s. These errors are approximately 4% relative to the peak velocity of approximately 55 cm / s.

[0100] The grayscale value represents the speed recorded or estimated in tube 1.

[0101] An additional benefit of this method is its ability to depict the pipe boundary under the acoustic shadowing region based on the generated flow velocity map, which will be of great value in anatomical analysis.

[0102] exist Figure 5 An embodiment of the invention is shown, which allows the boundary of pipe 1 to be determined from an estimated flow profile. Figure 5A shows the estimated boundary of tube 1, where the boundary was determined by experts.

[0103] exist Figure 5 Figure B shows the boundary of the same pipe estimated by mathematical methods (such as Otsu's method) using the predicted flow profile obtained through analysis. It can be seen that the results are very similar.

[0104] It should be noted that this method allows for the estimation of the pipe boundary in the shaded area.

[0105] The area containing pipe 1 is black, while the area not extended into by pipe 1 is white. The boundary is located at the transition point from black to white.

[0106] Figure 6 shows another example of reconstructing the flow profile within the shaded region of a pipe, similar to Figure 4. In this case, the pipe does not branch, but its inner diameter narrows in the shaded region, for example, due to the presence of a narrowing. The training of the machine learning method based on physical information is essentially the same as described in the sections related to Figure 4 and the training procedure. The neural network architecture used is the same, i.e., it has the same number of layers and neurons as the network used in Figure 4.

[0107] This example demonstrates that the method is indeed applicable to a wide range of situations without prior knowledge of the tube's geometry or other parameters. The high degree of consistency between the reconstructed flow profile and the actual (and hidden for the purpose of demonstrating the invention's capabilities) flow profile in the shaded region, as well as the accuracy of the predicted vessel shape within the shaded region, are both remarkable.

[0108] Figure 6A This shows an example of recorded stream data 100 with an acoustically shaded region 103, approximately 10 mm long along the net flow direction. This stream data originates from a narrow blood vessel present in the shaded region. The method of acquiring this dataset is similar to... Figure 4A Similar to the dataset, the streaming data obtained from the real-world dataset is modified, and shaded regions are artificially applied. Therefore, the upstream and downstream flow regions 101 and 102 of the shaded region 103 are the same as the corresponding regions in the real-world dataset, which corresponds to the real-world measurement scenario.

[0109] Figure 6B This shows the actual availability of all ultrasound signals.

[0110] Figure 6C This represents the velocity 104 within the shadow region 103 reconstructed using the method of the present invention.

[0111] Figure 6A The recorded flow data 200 is depicted, representing a single point in time as the recorded fluid flows through the pipe. Unlike Figure 4, this pipe does not branch, but shows a narrowing in the central region.

[0112] The shaded area 103 was created by artificially removing... Figure 6B It is obtained by removing all stream information from the recorded data.

[0113] In this way, the actual situation is known and can be used to benchmark the method of the present invention.

[0114] Figure 6C The solution generated by the method of the present invention is described.

[0115] It can be seen that, Figure 6A In the previously shaded area, the estimated flow profile 104 and the recorded flow data ( Figure 6B The flow profiles in the data look very similar. Although Figure 6 only shows the flow profile at one point in time, it is clear that the method can be applied to all frames recording the flow data and yield comparable results.

[0116] The specific experimental setup for the data shown in Figure 6 is described below.

[0117] The experiment in Figure 6 was conducted using a walled, narrow polyvinyl alcohol (PVA) straight tube phantom with an inner diameter of 6 mm. A pulsating flow of 60 beats / min and 2 mL / beat was employed. Coherent plane wave imaging was performed at three deflection angles of -3, 0, and 3 degrees, with a pulse repetition frequency of 6 kHz, resulting in an effective frame rate of 2 kHz. All other experimental setups, beamforming, and signal conditioning steps were identical to those used for the bifurcation flow experiment described in Figure 4. Motion estimation was performed prior to recombination using the corresponding low-resolution beamforming image pairs. For the 200 ms flow data, a fully connected deep neural network with the same architecture and training configuration as used for the bifurcation flow data in Figure 4 was processed, as detailed in the preceding paragraphs. In this experiment, the accuracy of the flow profile reconstruction within the shaded region was as follows: lateral mean velocity error (across time): 1.71 ± 0.16 cm / s, axial mean velocity error (across time): 0.54 ± 0.14 cm / s.

[0118] These results demonstrate the high accuracy and reliability of the method of the present invention.

Claims

1. A method, particularly a computer-based method for estimating a flow profile (100) of a fluid flow in a pipe (1), comprising the following steps: Acquire a series of ultrasonic signal data (200), including information about the fluid flow in the tube (1). The shadowed region (103) in the ultrasonic signal data was identified, which lacked information about the fluid flow in the tube (1); The flow profile (100) of the fluid is determined from ultrasonic signal data of the flow region (101, 102) outside the shaded region (103) of the tube (1). The flow profile (104) in the shaded region (103) is estimated using a physical information-based machine learning method, wherein the physical information-based machine learning method is trained using flow data and location data, the flow data including information about flow profiles (100) determined for flow regions (101, 102) located outside the shaded region (103), and the location data including multiple locations inside and / or outside the shaded region (103) and their associated time points.

2. The method according to any one of the preceding claims, wherein, The flow profile (100) is determined for at least two flow regions (101, 102), wherein a first flow region (101) of the at least two flow regions (101) is located upstream of the shaded region (103), and a second flow region (102) of the at least two flow regions (101, 102) is located downstream of the shaded region (103), and in particular, the fluid flow is from the upstream region (101) of the shaded region (103) to the downstream region (102).

3. The method according to any one of the preceding claims, wherein, Flow data (200) is generated from the flow profile determined for the flow region, wherein the flow data (200) includes information about the velocity of the fluid at multiple locations at multiple associated time points.

4. The method according to any one of the preceding claims, wherein, The training of the physical information-based machine learning method includes: providing information about location and time points from the streaming data (200) as input to the physical information-based machine learning method, wherein the physical information-based machine learning method determines an estimated velocity for each location and time point, wherein a streaming data loss function determines a streaming data loss value that indicates the deviation between the velocity included in the streaming data (200) and the velocity estimated by the physical information-based machine learning method.

5. The method according to any one of the preceding claims, wherein, The training of the physical information-based machine learning method includes: providing at least some locations and associated time points from the location data as input to the physical information-based machine learning method, wherein the physical information-based machine learning method determines, for each location and time point, an estimated velocity and an estimated pressure of the fluid at that location and time point, wherein the estimated velocity and the estimated pressure are provided to a physical loss function including the Navier-Stokes equations, wherein the physical loss function determines a physical loss value that indicates the deviation of the velocity and pressure estimated by the physical information-based machine learning method from the velocity and pressure obtained by solving the Navier-Stokes equations.

6. The method according to claims 4 and 5, wherein, The training includes a first phase, a second phase, and a third phase, wherein in the first phase, the data loss value is determined; in the second phase, the physical loss value is determined; and in the third phase, a composite loss value is determined from a composite loss function that includes the data loss function and the physical loss function, specifically, the composite loss function includes the sum of the data loss function and the physical loss function, particularly a weighted sum, wherein the composite loss function is minimized during training epochs.

7. The method according to any of the preceding claims, wherein the flow profile (100) is determined in a three-dimensional or two-dimensional manner.

8. The method according to claim 7, wherein, When the flow profile is defined in three dimensions, the physical loss function includes a physical residual function based on terms of the Navier-Stokes equations. , , , : , , , , in, To represent a partial differential operator, Indicates time, This specifically refers to a constant fluid density. Indicates the viscosity of a fluid. , , The velocity is estimated along three dimensions by a machine learning method based on physical information. , , The velocity component, where, The stress is estimated by a machine learning method based on physical information, where the physical loss value... The physical loss function is determined according to the following formula: ， in, This indicates the number of locations where the physical loss function has been evaluated, or the number of locations and associated time points.

9. The method according to claim 7, wherein, When the flow profile (100) is determined in a two-dimensional manner, the physical loss function includes a physical residual function based on terms of the Navier-Stokes equations. , , : , , , in, To represent a partial differential operator, Indicates time, This specifically refers to a constant fluid density. Indicates the viscosity of a fluid. , The velocity is estimated along two dimensions by a machine learning method based on physical information. , The velocity component, where, The stress is estimated by a machine learning method based on physical information, where the physical loss value... The physical loss function is determined according to the following formula: ， in, This indicates the number of locations where the physical loss function has been evaluated, or the number of locations and associated time points.

10. The method according to claim 7 or 8, wherein, When the flow profile (100) is determined in three dimensions, the data loss function and the data loss value, Determined according to the following formula: ， in , It refers to the time point of velocity estimated by a machine learning method based on physical information. Location The velocity component, and among which, , , It is the velocity component corresponding to the velocity of the provided streaming data, where, This indicates the location or number of time points for which the data loss function has been evaluated during the round.

11. The method according to claim 7 or 9, wherein, When the flow profile (100) is determined in a two-dimensional manner, the data loss function and the data loss value, Determined according to the following formula: ， in , It refers to the time point of velocity estimated by a machine learning method based on physical information. Location The velocity component, and among which, , It is the velocity component corresponding to the velocity of the provided streaming data, where, This indicates the location or number of time points for which the data loss function has been evaluated during the round.

12. The method according to any one of the preceding claims, wherein, The method is performed during an ultrasound imaging examination of a patient, wherein the training of the physical information-based machine learning method is performed at least once for each patient.

13. The method according to any one of the preceding claims, wherein, The temporally resolved velocity and / or pressure distribution of at least a portion of the shadow region (103), particularly the entire shadow region, is estimated using a trained physical information-based machine learning method.

14. A computer program comprising computer program code, which, when executed on a computer, causes the computer to perform the method according to any one of the preceding claims.

15. An ultrasonic measurement system, comprising at least the following components: An ultrasonic transducer head system configured to generate and record ultrasonic signal data; A computer, connected to the ultrasonic transducer head system and configured to receive ultrasonic signal data, Its features are, The computer is configured to execute the method according to any one of claims 1 to 13 or the computer program according to claim 14.

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