CN109919916B - Wall shear stress optimization method and device and storage medium - Google Patents

Abstract

The embodiment of the invention discloses a wall shear stress optimization method and device and a storage medium, wherein the method comprises the following steps: when the blood vessel nuclear magnetic resonance data are acquired, constructing a blood vessel three-dimensional model according to the blood vessel nuclear magnetic resonance data; obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model; optimizing the initial blood vessel velocity field based on a mass conservation condition to obtain an optimized blood vessel velocity field; and calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain the distribution information of the wall shear stress of the blood vessel.

Description

Wall shear stress optimization method and device and storage medium

Technical Field

The invention relates to a shear stress calculation technology in the technical field of biomedical engineering, in particular to a wall shear stress optimization method and device and a storage medium.

Background

In clinical medical diagnosis, color ultrasound Imaging, Magnetic Resonance Imaging (MRI), digital subtraction angiography and the like are common medical Imaging technologies for measuring blood flow velocity, and the medical Imaging technologies perform perspective Imaging on a human body through different principles to obtain gray image information representing tissues and organs in the human body and can capture blood flow information of the human body to measure blood flow velocity. The doctor gives a diagnosis opinion by analyzing the case of the patient through the gray image information and the blood flow information. Therefore, accurate acquisition of quantitative indicators of blood flow by medical imaging techniques is very important for medical diagnosis. Among the numerous quantitative indicators of blood flow, Wall Shear Stress (WSS) plays an important role in the development and development of vascular disease.

In the prior art, the wall shear stress is usually obtained by first obtaining the blood flow information by using the medical imaging technology and then analyzing the blood flow information to obtain the wall shear stress. However, in the above process of acquiring the wall shear stress, due to the constraints of various aspects such as the imaging principle, the radiography technology, and the hardware device performance, the acquired blood flow information has the problems of high noise, more bad points of the velocity field, low spatial and temporal resolution, and the like, so that the wall shear stress acquired by analyzing the blood flow information is not accurate.

Disclosure of Invention

In order to solve the above technical problems, embodiments of the present invention provide a method and an apparatus for optimizing wall shear stress, and a storage medium, which can improve the accuracy of the wall shear stress.

The technical scheme of the invention is realized as follows:

in a first aspect, an embodiment of the present invention provides a wall shear stress optimization method, where the method includes:

when blood vessel nuclear magnetic resonance data are acquired, constructing a blood vessel three-dimensional model according to the blood vessel nuclear magnetic resonance data;

obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model;

optimizing the initial blood vessel velocity field based on a mass conservation condition to obtain an optimized blood vessel velocity field;

and calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain blood vessel wall shear stress distribution information.

In the above scheme, the constructing a three-dimensional model of a blood vessel according to the blood vessel nuclear magnetic resonance data includes:

acquiring an initial blood vessel three-dimensional image in the blood vessel nuclear magnetic resonance data;

denoising the initial blood vessel three-dimensional image to obtain a denoised initial blood vessel three-dimensional image;

extracting blood vessel information from the denoised initial blood vessel three-dimensional image by adopting a preset segmentation algorithm to obtain a point cloud blood vessel three-dimensional image;

and reconstructing the point cloud blood vessel three-dimensional image by adopting a preset reconstruction algorithm to obtain the blood vessel three-dimensional model.

In the above scheme, the obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model includes:

acquiring a blood vessel velocity field in the blood vessel nuclear magnetic resonance data;

interpolating the blood vessel velocity field according to a preset interval to obtain an interpolated blood vessel velocity field;

and marking the velocity nodes in the interpolated blood vessel velocity field on the blood vessel three-dimensional model according to the blood vessel boundary to obtain the initial blood vessel velocity field.

In the above scheme, the optimizing the initial blood vessel velocity field based on the mass conservation condition to obtain an optimized blood vessel velocity field includes:

determining derivative information corresponding to the initial blood vessel velocity field according to the condition that the wall surface has no slippage;

constructing a blood vessel velocity field optimization equation corresponding to the initial blood vessel velocity field based on the mass conservation condition and the derivative information;

determining optimized smooth parameters based on the blood vessel velocity field optimization equation, a preset cross validation algorithm and a preset optimization algorithm;

and inputting the optimized smoothing parameters into the blood vessel velocity field optimization equation to obtain the optimized blood vessel velocity field.

In the foregoing solution, the determining derivative information corresponding to the initial blood vessel velocity field according to the wall surface no-slip condition includes:

calculating the wall surface distance of a velocity node in the initial blood vessel velocity field;

dividing the velocity nodes in the initial blood vessel velocity field into near wall surface points and far wall surface points according to a preset distance and the wall surface distance;

calculating a derivative of the near wall point based on the wall distance, the wall non-slip condition and a first preset derivative algorithm to obtain corresponding first derivative information;

calculating a derivative of the far wall point based on the wall distance, the wall non-slip condition and a second preset derivative algorithm to obtain corresponding second derivative information;

taking the first derivative information and the second derivative information as the derivative information.

In the foregoing solution, the calculating a derivative of the near-wall point based on the wall distance, the wall no-slip condition, and a first preset derivative algorithm to obtain corresponding first derivative information includes:

determining a vessel wall point and a nearest speed node of the near-wall surface point according to the wall surface distance;

according to the wall surface distance, the blood vessel wall point, the nearest speed node, the wall surface no-slip condition and the first preset derivative algorithm, obtaining a first derivative and a second derivative corresponding to the near wall surface point, wherein the first preset derivative algorithm is used for determining derivative information of the near wall surface point;

taking the first derivative and the second derivative as the first derivative information.

In the above scheme, the constructing a vessel velocity field optimization equation corresponding to the initial vessel velocity field based on the mass conservation condition and the derivative information includes:

determining the corresponding smoothness and dispersion degree of the initial blood vessel velocity field according to the derivative information;

constructing an initial blood vessel velocity field optimization objective function corresponding to the initial blood vessel velocity field according to the smoothness, the dispersion divergence and the mass conservation condition;

converting the initial blood vessel velocity field optimization objective function according to a Lagrange multiplier algorithm to obtain a converted initial blood vessel velocity field optimization objective function;

and carrying out minimization processing on the converted initial blood vessel velocity field optimization objective function to obtain the blood vessel velocity field optimization equation.

In the above scheme, the determining an optimized smoothing parameter based on the blood vessel velocity field optimization equation, a preset cross validation algorithm, and a preset optimization algorithm includes:

constructing smooth verification information according to the preset cross verification algorithm;

determining at least one initial smoothing parameter based on the preset optimization algorithm;

respectively inputting the at least one initial smoothing parameter into the blood vessel velocity field optimization equation to obtain at least one corresponding initial optimized blood vessel velocity field;

determining at least one smoothing verification value corresponding to the smoothing verification information according to the at least one initial optimized blood vessel velocity field;

and taking the initial smoothing parameter corresponding to the minimum smoothing verification value in the at least one smoothing verification value as the optimized smoothing parameter.

In the foregoing solution, the determining, according to the at least one initial optimized velocity field of the blood vessel, at least one smoothing verification value corresponding to the smoothing verification information includes:

determining coefficient information in the smoothing verification information according to the derivative information;

determining a characteristic value corresponding to the coefficient information according to a preset fitting algorithm;

inputting the characteristic value into the smooth verification information to obtain corresponding simplified smooth verification information;

and respectively inputting the at least one initial optimized blood vessel velocity field into the simplified smooth verification information to obtain the at least one smooth verification value.

In the above scheme, the calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain blood vessel wall shear stress distribution information includes:

performing interpolation in the wall surface normal direction of the blood vessel three-dimensional model according to the optimized blood vessel velocity field and the preset interval to obtain an interpolation velocity;

determining the blood flow direction according to the interpolation speed and the wall surface normal direction;

obtaining a corresponding fitting curve according to the interpolation speed and the blood flow direction;

and obtaining the wall shear stress distribution information according to the blood flow direction, the fitting curve and a preset hemodynamic viscosity coefficient.

In the above scheme, obtaining a corresponding fitted curve according to the interpolation speed and the blood flow direction includes:

calculating the projection information of the interpolation speed on the blood flow direction to obtain corresponding speed distribution information;

and fitting the speed distribution information to obtain the fitting curve.

In the above scheme, the fitting the speed distribution information to obtain the fitted curve includes:

obtaining blood attribute information;

fitting the speed distribution information according to the blood attribute information, at least one preset blood vessel wall surface friction speed, a preset fitting coefficient and a preset fitting algorithm to obtain at least one corresponding initial fitting curve, wherein the preset fitting algorithm is used for fitting the speed distribution information;

determining at least one piece of distinguishing information of the at least one initial fitting curve respectively corresponding to the speed distribution information;

and taking an initial fitting curve corresponding to the distinguishing information with the minimum difference in the at least one distinguishing information as the fitting curve.

In the above scheme, the preset fitting algorithm is as follows:

wherein V' is a continuous dependent variable value u corresponding to the initial fitting curve_τAnd setting the preset blood vessel wall friction speed as W', the wall normal height corresponding to each speed in the speed distribution information as K and s, the preset fitting coefficient as P, the density of blood in the blood attribute information as rho, and the dynamic viscosity coefficient of blood in the blood attribute information as mu.

In a second aspect, an embodiment of the present invention provides a wall shear stress optimization apparatus, where the apparatus includes: a processor, a memory and a communication bus, the memory communicating with the processor through the communication bus, the memory storing a program executable by the processor, the program, when executed, executing the wall shear stress optimization method as described above through the processor.

In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a program is stored, and when the program is executed by a processor, the program implements the wall shear stress optimization method as described above.

The embodiment of the invention provides a wall shear stress optimization method, a wall shear stress optimization device and a storage medium, and the method comprises the following steps of firstly, when blood vessel nuclear magnetic resonance data are obtained, constructing a blood vessel three-dimensional model according to the blood vessel nuclear magnetic resonance data: secondly, obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model; then, optimizing the initial blood vessel velocity field based on a mass conservation condition to obtain an optimized blood vessel velocity field; and finally, calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain the distribution information of the wall shear stress of the blood vessel. By adopting the technical scheme, the optimized blood vessel velocity field is obtained by optimizing the initial blood vessel velocity field by the wall shear stress optimizing device through the mass conservation condition, and the smoothness and the non-dispersity of the optimized blood vessel velocity field can be ensured by the mass conservation condition, so that the optimized blood vessel velocity field and other blood flow information have low noise, few dead points of the velocity field and high space-time resolution, and the accuracy of the wall shear stress is improved when the wall shear stress optimizing device calculates the wall shear stress according to the optimized blood vessel velocity field.

Drawings

Fig. 1 is a flowchart illustrating an implementation of a method for optimizing wall shear stress according to an embodiment of the present invention;

FIG. 2 is an exemplary vessel wall shear stress distribution information provided by an embodiment of the present invention;

FIG. 3 is a schematic diagram of an exemplary velocity grid provided by embodiments of the present invention;

FIG. 4 is a schematic diagram of an exemplary deterministic fit curve provided by an embodiment of the present invention;

fig. 5 is an exemplary calculated vascular wall shear stress distribution information based on equation (9) according to an embodiment of the present invention;

FIG. 6 is a diagram illustrating exemplary wall shear stress distribution information of a blood vessel calculated based on a wall second-order polynomial according to an embodiment of the present invention;

fig. 7 is a first schematic structural diagram of a wall shear stress optimization apparatus according to an embodiment of the present invention;

fig. 8 is a schematic structural diagram of a wall shear stress optimization apparatus according to an embodiment of the present invention.

Detailed Description

The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

Example one

An embodiment of the present invention provides a wall shear stress optimization method, and fig. 1 is a flow chart of an implementation of the wall shear stress optimization method provided in the embodiment of the present invention, as shown in fig. 1, the wall shear stress optimization method includes:

s101, when the blood vessel nuclear magnetic resonance data are obtained, a blood vessel three-dimensional model is constructed according to the blood vessel nuclear magnetic resonance data.

In the embodiment of the invention, when the blood flow velocity of the blood vessel is measured, the nuclear magnetic resonance equipment is used for carrying out nuclear magnetic resonance on the part where the blood vessel is located to obtain corresponding blood vessel nuclear magnetic resonance data; when the blood vessel nuclear magnetic resonance data is input into the wall shear stress optimization device, the wall shear stress device obtains the blood vessel nuclear magnetic resonance data; at this time, since the blood vessel nuclear magnetic resonance data includes the initial blood vessel three-dimensional image, the wall shear stress apparatus separates the initial blood vessel three-dimensional image from the blood vessel nuclear magnetic resonance data, and performs image processing on the initial blood vessel three-dimensional image, thereby constructing a blood vessel three-dimensional model including only blood vessels.

It should be noted that the blood vessel nmr data represents initial data obtained after nmr of the blood vessel, such as: the time resolution of the nmr image was 49.2ms, the pixel size of the initial three-dimensional image of the vessels was 256 × 25 × 80 and the individual voxel size was 0.8 × 1.5mm³The nuclear magnetic resonance technique is a 4D (Dimensional) flow MRI technique, a three-Dimensional velocity field (blood vessel velocity field), or the like. Further, here, the three-dimensional model of the blood vessel represents a three-dimensional geometric model of the blood vessel, for example, a three-dimensional geometric model of the aorta.

And S102, obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model.

In the embodiment of the invention, because the blood vessel nuclear magnetic resonance data comprises the blood vessel velocity field, the wall shear stress device separates the blood vessel velocity field from the blood vessel nuclear magnetic resonance data and preprocesses the blood vessel velocity field on the blood vessel three-dimensional model, thereby obtaining the initial blood vessel velocity field.

It is noted that the initial vessel velocity field characterizes the velocity field of the vessel that has been preprocessed and can be used to optimize the velocity field of the vessel.

S103, optimizing the initial blood vessel velocity field based on the mass conservation condition to obtain an optimized blood vessel velocity field.

In the embodiment of the invention, the wall shear stress is used for measuring the flow of blood in the blood vessel by the nuclear magnetic resonance technology, and belongs to the category of non-compressible flow, so that the velocity field in the blood vessel meets the mass conservation condition (non-dispersion condition); therefore, after the initial blood vessel velocity field is obtained by the wall shear stress, the initial blood vessel velocity field is optimized based on the mass conservation condition from the aspects of non-dispersion property and smoothness, and the optimized blood vessel velocity field corresponding to the initial blood vessel velocity field, namely the optimized blood vessel velocity field, is obtained.

It should be noted that the difference between the optimized blood vessel velocity field and the initial blood vessel velocity field satisfies a preset condition, where the representation difference of the preset condition is as small as possible, and meanwhile, the optimized blood vessel velocity field has no divergence, that is, the divergence is zero. Thus, compared with the initial blood vessel velocity field or the blood vessel velocity field in the blood vessel nuclear magnetic resonance data, the optimized blood vessel velocity field has low noise, less flow dead points and high space-time ratio.

In addition, the optimized vessel velocity field corresponds to a three-dimensional model of the vessel. That is, the optimized vessel velocity field refers to the velocity field of the vessel in the three-dimensional model of the vessel.

And S104, calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain the distribution information of the wall shear stress of the blood vessel.

In the embodiment of the invention, the device for optimizing the wall shear stress of the blood vessel represents the shear stress obtained by calculating the wall shear stress on the three-dimensional model of the blood vessel according to the velocity field of the blood vessel, so that after the device for optimizing the wall shear stress obtains the three-dimensional model of the blood vessel and the velocity field of the optimized blood vessel (the velocity field of the blood vessel), the device for optimizing the wall shear stress of the blood vessel can calculate the wall shear stress of the blood vessel according to the three-dimensional model of the blood vessel and the velocity field of the optimized blood vessel, and thus the wall shear stress of each area on the three-dimensional model of the blood vessel.

The blood vessel wall shear stress distribution information represents information on the distribution of the wall shear stress of the blood vessel on the blood vessel.

Fig. 2 is exemplary blood vessel wall shear stress distribution information provided by an embodiment of the present invention, and as shown in fig. 2, a unit of a blood vessel wall shear stress WSS is Pa, a corresponding value range is 0.0 to 1.0, and a region indicated by a marked line is a high wall shear stress region when a wall shear stress represented by a larger value is larger.

It can be understood that the wall shear stress optimization device optimizes the initial blood vessel velocity field obtained through nuclear magnetic resonance data by using a mass conservation condition, so that the optimized blood vessel velocity field has the effects of low noise, less flow dead points and high space-time ratio rate while ensuring the non-dispersity and the smoothness of the blood vessel velocity field, and the post-processing effect of the blood vessel velocity field is improved. In addition, when the wall shear stress optimization device calculates the wall shear stress according to the optimized velocity field of the blood vessel, the accuracy of the obtained wall shear stress can be high, and therefore the accuracy of the distribution information of the wall shear stress in the three-dimensional model of the blood vessel is improved.

Further, in the embodiment of the present invention, the wall shear stress optimization device in S101 constructs a three-dimensional model of a blood vessel according to the blood vessel nuclear magnetic resonance data, specifically including S101a-S101d, where:

s101a, obtaining an initial blood vessel three-dimensional image in the blood vessel nuclear magnetic resonance data.

In the embodiment of the invention, after nuclear magnetic resonance is performed on the blood vessel by the nuclear magnetic resonance equipment, the obtained blood vessel nuclear magnetic resonance data comprises the initial three-dimensional image of the blood vessel, namely the initial three-dimensional image of the blood vessel, and the wall shear stress optimization device extracts the initial three-dimensional image of the blood vessel in the blood vessel nuclear magnetic resonance data, namely the initial three-dimensional image of the blood vessel in the blood vessel nuclear magnetic resonance data is obtained.

S101b, denoising the initial blood vessel three-dimensional image to obtain a denoised initial blood vessel three-dimensional image.

In the embodiment of the invention, because the initial blood vessel three-dimensional image comprises noise, the wall shear stress optimization device performs denoising processing on the initial blood vessel three-dimensional image after acquiring the initial blood vessel three-dimensional image, and then the denoised initial blood vessel three-dimensional image with less noise or without noise is obtained.

It should be noted that the denoised initial blood vessel three-dimensional image represents a three-dimensional image of a blood vessel satisfying a preset noise condition, where the preset noise condition is, for example: less than a preset noise threshold.

Exemplarily, when the initial blood vessel three-dimensional image is an aorta three-dimensional image, the wall shear stress optimization device performs denoising processing on the aorta three-dimensional image by adopting a neighborhood variance method and a neighborhood plus-minus method to obtain an approximate outline of the aorta; and performing median filtering in the approximate outline of the aorta, thereby removing all residual noise and obtaining a noiseless aorta three-dimensional image (the denoised initial blood vessel three-dimensional image).

The wall shear stress optimization device can be used for denoising the initial blood vessel three-dimensional image to obtain the denoised initial blood vessel three-dimensional image, so that convenience and accuracy are provided for subsequent processing of the denoised initial blood vessel three-dimensional image.

S101c, extracting blood vessel information of the denoised initial blood vessel three-dimensional image by adopting a preset segmentation algorithm to obtain a point cloud blood vessel three-dimensional image.

In the embodiment of the invention, after the wall shear stress optimization device obtains the denoised initial blood vessel three-dimensional image, the blood vessel information is extracted on the denoised initial blood vessel three-dimensional image by using a preset segmentation algorithm, and the extracted blood vessel information is the point cloud blood vessel three-dimensional image.

The point cloud blood vessel three-dimensional image represents a three-dimensional image of a blood vessel represented by a point cloud, and the point cloud blood vessel three-dimensional image includes only blood vessel information and does not include information other than the blood vessel information. And the preset segmentation algorithm is used for extracting the blood vessel information, such as a maximum inter-class variance method.

Illustratively, the wall shear stress optimization device performs automatic threshold segmentation on a noiseless aorta three-dimensional image (a denoised initial blood vessel three-dimensional image) by adopting a maximum inter-class variance method, completes extraction of the aorta, and obtains an aorta lattice cloud form image (a point cloud blood vessel three-dimensional image).

S101d, reconstructing the point cloud blood vessel three-dimensional image by adopting a preset reconstruction algorithm to obtain a blood vessel three-dimensional model.

In the embodiment of the invention, after the point cloud blood vessel three-dimensional image is obtained by the wall shear stress optimization device, the point cloud blood vessel three-dimensional image can be subjected to surface reconstruction by using a preset reconstruction algorithm, so that a blood vessel three-dimensional model is obtained.

It should be noted that the preset reconstruction algorithm is used for surface reconstruction of the blood vessel image, such as poisson surface reconstruction.

Illustratively, the wall shear stress optimization device adopts Poisson surface reconstruction to process an image (point cloud blood vessel three-dimensional image) in an aorta lattice cloud form, so as to obtain an aorta geometric model (blood vessel three-dimensional model).

It can be understood that the wall shear stress optimization device reconstructs a three-dimensional blood vessel model by processing the three-dimensional initial blood vessel image in the nuclear magnetic resonance data, and the three-dimensional blood vessel model can more accurately describe the geometric information of the blood vessel relative to the three-dimensional initial blood vessel image.

Further, in the embodiment of the present invention, the wall shear stress optimization device in S102 obtains an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model, and specifically includes S102a-S102b, where:

s102a, obtaining a blood vessel velocity field in the blood vessel nuclear magnetic resonance data.

In the embodiment of the invention, after nuclear magnetic resonance is performed on the blood vessel by the nuclear magnetic resonance equipment, the obtained blood vessel nuclear magnetic resonance data comprises a blood vessel velocity field, and the wall shear stress optimization device extracts the blood vessel velocity field in the blood vessel nuclear magnetic resonance data, namely the blood vessel velocity field in the blood vessel nuclear magnetic resonance data is obtained.

S102b, the blood vessel velocity field is interpolated according to the preset distance to obtain the blood vessel velocity field after interpolation.

In the embodiment of the invention, the vessel velocity field is a physical field formed by velocity vectors corresponding to a large number of velocity nodes, and meanwhile, the intervals between the velocity nodes are unequal, so that the calculation of wall shear stress according to the vessel velocity field cannot be completed; here, the wall shear stress optimization device interpolates the blood vessel velocity field according to a preset pitch (for example, the preset pitch h is 1.57mm) (for example, an equidistant spline difference), and selects all velocity nodes having a pitch between the velocity nodes as the preset pitch, thereby forming the interpolated blood vessel velocity field.

It should be noted that, when the blood vessel velocity field is a three-dimensional velocity field, the distances of each velocity node in the interpolated blood vessel velocity field in the three-dimensional direction are all preset distances. The interpolated vascular velocity field is three-dimensional, for example, 186 × 122 × 57.

S102c, marking the velocity nodes in the interpolated blood vessel velocity field according to the blood vessel boundary on the blood vessel three-dimensional model to obtain an initial blood vessel velocity field.

In the embodiment of the invention, after the wall shear stress optimization device obtains the interpolated blood vessel velocity field and the blood vessel three-dimensional model, the blood vessel boundary is determined on the blood vessel three-dimensional model, and the velocity nodes in the interpolated blood vessel velocity field are marked according to the blood vessel boundary, specifically, the velocity nodes inside the blood vessel and the velocity nodes outside the blood vessel are respectively marked according to the blood vessel boundary, and the marked velocity nodes inside the blood vessel form the initial blood vessel velocity field.

Illustratively, after the blood vessel is an aorta and the wall shear stress optimization device determines the blood vessel boundary on the three-dimensional model of the blood vessel, the marking variable corresponding to the velocity node in the aorta is set to 1, and the marking variable corresponding to the velocity node outside the blood vessel is set to 0. A total of 86379 velocity nodes with a tag variable of 1 constitute the initial vessel velocity field.

It can be understood that the wall shear stress optimization device further improves the accuracy of measurement by taking an initial blood vessel velocity field formed by velocity nodes in the blood vessel as data for measuring the blood flow velocity.

Further, in the embodiment of the present invention, the wall shear stress optimization device in S103 optimizes the initial blood vessel velocity field based on a mass conservation condition and a wall non-slip condition to obtain an optimized blood vessel velocity field, which specifically includes S103a-S103d, where:

s103a, determining derivative information corresponding to the initial blood vessel velocity field according to the wall surface non-slip condition.

In the embodiment of the invention, after the wall shear stress optimization device obtains the initial blood vessel velocity field, the initial blood vessel velocity field can be optimized, and the wall shear stress optimization device respectively determines the derivative information corresponding to the velocity nodes in the initial blood vessel velocity field according to the condition that the velocity of blood on the blood vessel wall is zero, namely the wall has no slippage.

It should be noted that the derivative information represents derivative difference information corresponding to a velocity node in the initial blood vessel velocity field, for example, the derivative information represents a difference equation corresponding to a first derivative and a difference equation corresponding to a second derivative of the velocity node in the initial blood vessel velocity field.

Further, in the embodiment of the present invention, the wall shear stress optimization device determines derivative information corresponding to the initial blood vessel velocity field according to the wall non-slip condition, and specifically includes S103a1-S103a5, where:

and S103a1, calculating the wall surface distance of the velocity node in the initial blood vessel velocity field.

In the embodiment of the invention, the speed nodes in the initial blood vessel speed field are equal in distance in all directions and are preset distances, so that a speed grid corresponding to the initial blood vessel speed field is formed, and each grid node in the speed grid corresponds to one speed node. In the velocity mesh, a three-dimensional model of the blood vessel is marked, and at the moment, the wall shear stress optimization device acquires the wall distance from the velocity node in the initial velocity field of the blood vessel to the wall of the blood vessel wall of the three-dimensional model of the blood vessel.

The wall surface distance is the shortest distance from the velocity node to the blood vessel wall.

And S103a2, dividing the velocity nodes in the initial blood vessel velocity field into near wall points and far wall points according to the preset distance and the wall distance.

In the embodiment of the invention, after the wall surface shear stress optimization device obtains the wall surface distance, the wall surface distance is compared with the preset distance, the speed node of which the wall surface distance is greater than or equal to the preset distance is taken as a far wall surface point, and the speed node of which the wall surface distance is smaller than the preset distance is taken as a near wall surface point.

S103a3, calculating a derivative for the near wall point based on the wall distance, the wall no-slip condition and a first preset derivative algorithm to obtain corresponding first derivative information.

In the embodiment of the invention, the wall shear stress optimization device adopts different algorithms to determine the derivative information for the near wall surface point and the far wall surface point in the initial blood vessel velocity field, wherein the wall shear stress optimization device calculates the derivative information of the near wall surface point, namely the first derivative information according to the wall surface distance, the wall surface no-slip condition and the first preset derivative algorithm.

It should be noted that, the first preset derivative algorithm is to determine, in the velocity mesh, a derivative information calculation direction of a velocity node (i.e., a direction corresponding to the shortest distance from the velocity node to the wall surface) according to the wall surface distance, determine, by using a specified number of velocity nodes that are closest to the velocity node in the derivative information calculation direction of the velocity node, and a point on the blood vessel wall that is closest to the velocity node in the derivative information calculation direction, that is, a blood vessel wall point, the derivative information corresponding to the velocity node.

Specifically, the wall shear stress optimization device determines a vessel wall point close to a wall surface point and a nearest speed node according to a wall surface distance; according to the wall surface distance, the blood vessel wall point, the nearest speed node, the wall surface non-slip condition and a first preset derivative algorithm, obtaining a first derivative and a second derivative corresponding to the near wall surface point, wherein the first preset derivative algorithm is used for determining derivative information of the near wall surface point; and the first derivative and the second derivative are taken as first derivative information.

Illustratively, fig. 3 is a schematic diagram of an exemplary velocity grid provided by an embodiment of the present invention, as shown in fig. 3, the initial velocity field of the blood vessel is a two-dimensional velocity field, the corresponding coordinate system includes an x-axis and a y-axis, the exemplary velocity grid further includes a blood vessel wall (velocity on the blood vessel wall is zero), and exemplary two near-wall surface points a and B; wherein, the wall distance from A to the vessel wall is a horizontal distance dx (dx)>0，dx<A preset distance h), and the distance from the B to the wall surface of the vessel wall is a vertical distance dy (dy)>0，dy<h) (ii) a For A, selecting a point A on the vessel wall in the horizontal direction¹(vessel wall points), and A is the 1 closest velocity node A in the horizontal direction²And with u₀、u₁And u₂Respectively represent A¹A and A²Corresponding velocity values (where u is based on the wall no-slip condition₀0), then the Taylor expansion is carried out on the speed at the point A and the corresponding first can be obtained according to the arrangement of the condition that the wall surface has no slipDerivative information: differential equation corresponding to first derivative

Differential equation corresponding to second derivative

Respectively shown in formula (1) and formula (2):

where θ represents a ratio of the wall surface distance of a to a preset pitch, that is, θ ═ dx/h.

Similarly, the first derivative information of B: differential equation corresponding to first derivative

Differential equation corresponding to second derivative

Here, by v₀、v₁、v₂And dy/h, solving a difference equation corresponding to the first derivative of B and a difference equation corresponding to the second derivative, wherein v₀、v₁And v₂Respectively represent B¹B and B²Corresponding velocity values (where v is based on the wall no-slip condition, v)₀Is 0), and B¹Is a point on the vessel wall in the vertical direction B, i.e. a vessel wall point, B²B is the 1 closest velocity node in the vertical direction.

S103a4, calculating a derivative of the far wall point based on the wall distance, the wall no-slip condition and a second preset derivative algorithm to obtain corresponding second derivative information.

In the embodiment of the invention, the wall shear stress optimization device calculates the derivative information of the far wall point, namely second derivative information, according to the wall distance, the wall non-slip condition and a second preset derivative algorithm; here, the second preset derivative algorithm is an algorithm different from the first preset derivative algorithm, for example, when the first preset derivative algorithm is the formula (1) and the formula (2), the second preset derivative algorithm is in the central difference format.

S103a5, using the first derivative information and the second derivative information as derivative information.

Here, the wall shear stress optimization device uses the first derivative information corresponding to the near wall surface point and the second derivative information corresponding to the far wall surface point together as the derivative information of the velocity node in the initial blood vessel velocity field.

S103b, constructing a blood vessel velocity field optimization equation corresponding to the initial blood vessel velocity field based on the mass conservation condition and the derivative information.

In the embodiment of the invention, after the wall shear stress optimization device obtains the derivative information of the velocity node in the initial vessel velocity field, the initial vessel velocity field is optimized based on the mass conservation condition and the derivative information, and the optimization is realized by constructing a corresponding vessel velocity field optimization equation. Here, the vessel velocity field optimization equation characterizes the optimization objective of the initial vessel velocity field.

Further, in the embodiment of the present invention, the wall shear stress optimization apparatus constructs a blood vessel velocity field optimization equation corresponding to the initial blood vessel velocity field based on the mass conservation condition and the derivative information, specifically including S103b1-S103b4, where:

s103b1, according to the derivative information, determining the corresponding smoothness and discrete divergence of the initial blood vessel velocity field.

In the embodiment of the invention, after the wall shear stress optimization device obtains the derivative information of the velocity node in the initial blood vessel velocity field, the smoothness and the dispersion degree of the velocity node in the initial blood vessel velocity field can be determined according to the derivative information.

Specifically, when the derivative information characterizes a difference equation corresponding to the first derivative and a difference equation corresponding to the second derivative, the degree of smoothing is determined based on the difference equation corresponding to the second derivative, and the degree of dispersion is determined based on the difference equation corresponding to the first derivative.

Illustratively, the difference equation corresponding to the second derivative of the velocity node in the initial vessel velocity field constitutes a discrete second derivative operator D (without taking into account the cross terms), where D is in the form of a matrix and the values of the matrix are the difference equations corresponding to the second derivative of the corresponding velocity node (three-dimensional velocity node), i.e.:

in this case, the degree of smoothness R (U) is represented by formula (3):

R(U)＝‖DU‖²＝U^TD^TDU (3)

wherein U is the optimized vessel velocity field to be determined, also called initial optimized vessel velocity field.

In addition, the difference equation corresponding to the first derivative of the velocity node in the initial vessel velocity field constitutes the dispersion:

or a CU.

S103b2, constructing an initial blood vessel velocity field optimization objective function corresponding to the initial blood vessel velocity field according to the smoothness, the dispersion and the mass conservation condition.

In the embodiment of the invention, after the wall shear stress optimization device obtains the smoothness and the dispersion, an initial blood vessel velocity field optimization objective function corresponding to the initial blood vessel velocity field is constructed according to the smoothness, the dispersion and the mass conservation condition, and the optimal blood vessel velocity field corresponding to the initial blood vessel velocity field is determined by the initial blood vessel velocity field optimization objective function.

Illustratively, when the degree of smoothness is as shown in equation (3), the dispersion is

Then, the initial vessel velocity field optimization objective function j (u) is shown as formula (4):

wherein s characterizes the initial smoothing parameter, and s>The larger 0, s represents a smoother velocity field of the vessel. J (U) is characterized by a divergence

0, and the initial vessel velocity field U_mThe determination of the initial optimal vessel velocity field U is made when the difference is minimal.

S103b3, converting the initial blood vessel velocity field optimization objective function according to the Lagrange multiplier algorithm to obtain the converted initial blood vessel velocity field optimization objective function.

In the embodiment of the invention, after the wall shear stress optimization device obtains the initial vessel velocity field optimization objective function, in order to determine the optimized vessel velocity field according to the initial vessel velocity field optimization objective function, the initial vessel velocity field optimization objective function needs to be converted according to a lagrange multiplier algorithm, and the converted initial vessel velocity field optimization objective function is converted into a converted initial vessel velocity field optimization objective function convenient to calculate.

Illustratively, when the lagrange multiplier is the undetermined coefficient λ and the initial vessel velocity field optimization objective function j (U) is equation (5), then the converted initial vessel velocity field optimization objective function L (U, λ) is as shown in equation (5):

s103b4, carrying out minimization processing on the converted initial blood vessel velocity field optimization objective function to obtain a blood vessel velocity field optimization equation.

In the embodiment of the invention, after the wall shear stress optimization device obtains the converted initial blood vessel velocity field optimization objective function, the converted initial blood vessel velocity field optimization objective function is subjected to minimization processing, so that a solvable blood vessel velocity field optimization equation can be obtained.

Illustratively, the wall shear stress optimization device performs minimization processing on the transformed initial vessel velocity field optimization objective function shown in equation (5), specifically by setting the first derivative of L (U, λ) with respect to U and λ to 0, so as to obtain a vessel velocity field optimization equation shown in equation (6):

here, the first and second liquid crystal display panels are,

and optimizing a coefficient matrix of the equation for the blood vessel velocity field, wherein the related matrixes are all sparse matrixes, specifically I is an identity matrix, and C is a sparse matrix associated with the difference equation corresponding to the first derivative in the smoothing information.

S103c, determining optimized smoothing parameters based on the blood vessel velocity field optimization equation, the preset cross validation algorithm and the preset optimization algorithm.

In the embodiment of the invention, after the wall shear stress optimization device obtains the blood vessel velocity field optimization equation, because the blood vessel velocity field optimization equation has the initial smooth parameter to be determined, the wall shear stress optimization device adopts a preset cross validation algorithm and a preset optimization algorithm and determines the optimal smooth parameter, namely the optimized smooth parameter according to the blood vessel velocity field optimization equation.

It will be appreciated that since the noise level of the velocity field of the blood vessel cannot be determined, and therefore the initial smoothing parameters cannot be determined, the wall shear stress optimisation means provides an implementable solution for the determination of the optimised smoothing parameters by optimising the initial smoothing parameters.

Further, in the embodiment of the present invention, the wall shear stress optimization device determines the optimized smoothing parameters based on the blood vessel velocity field optimization equation, the preset cross validation algorithm and the preset optimization algorithm, and specifically includes S103c1-S103c5, where:

s103c1, constructing smooth verification information according to a preset cross-verification algorithm.

In the embodiment of the invention, when determining the optimized smooth parameters, the wall shear stress optimization device firstly constructs smooth verification information according to a preset cross verification algorithm; here, the smoothing verification information characterizes optimization information of the smoothing parameter to be determined.

It should be noted that the preset cross validation algorithm is a generalized cross validation function (GCV), and the optimized smoothing parameter can be determined by minimizing the GCV function. The preset cross validation algorithm may also be other algorithms for determining an optimized smoothing parameter, which is not specifically limited in this embodiment of the present invention.

Illustratively, the smoothing verification information gcv(s) is represented by equation (7):

wherein n is the number of unknowns in formula (7), Tr represents the trace of the matrix, s represents the initial smoothing parameter, U represents the initial smoothing parameter_mRepresenting the initial optimized vessel velocity field to which s corresponds.

S103c2, determining at least one initial smoothing parameter based on a preset optimization algorithm.

In the embodiment of the present invention, when determining the optimized smoothing parameter, the wall shear stress optimization apparatus further needs to determine at least one initial smoothing parameter based on a preset optimization algorithm, so that the optimized smoothing parameter is determined from the at least one initial smoothing parameter. Here, the at least one initial smoothing parameter characterizes a plurality of values corresponding to the smoothing parameter to be determined.

S103c3, respectively inputting at least one initial smoothing parameter into the blood vessel velocity field optimization equation to obtain at least one corresponding initial optimized blood vessel velocity field.

In the embodiment of the invention, after the wall shear stress optimization device obtains at least one initial smoothing parameter, the vessel velocity field optimization equation represents the corresponding relationship among the smoothing parameter, the lagrange multiplier and the initial optimized vessel velocity field, and the wall shear stress optimization device respectively inputs the at least one initial smoothing parameter into the vessel velocity field optimization equation to obtain the corresponding at least one initial optimized vessel velocity field.

Here, the wall shear stress optimization means determines an optimized vessel velocity field from at least one initial optimized vessel velocity field.

S103c4, determining at least one smooth verification value corresponding to the smooth verification information according to the at least one initial optimized blood vessel velocity field.

In the embodiment of the invention, after the wall shear stress optimization device obtains at least one initial optimized blood vessel velocity field, the at least one initial optimized blood vessel velocity field is respectively input into the smoothing verification information, and at least one corresponding smoothing verification value can be obtained through calculation.

Specifically, in the embodiment of the present invention, the determining, by the wall shear stress optimization device, at least one smoothing verification value corresponding to the smoothing verification information according to at least one initial optimized blood vessel velocity field includes: determining coefficient information in the smoothness verification information by the wall shear stress optimization device according to the smoothness information; determining a characteristic value corresponding to the coefficient information according to a preset fitting algorithm; inputting the characteristic value into the smooth verification information to obtain corresponding simplified smooth verification information; and respectively inputting the at least one initial optimized blood vessel velocity field into the simplified smooth verification information to obtain at least one smooth verification value.

That is, since the smoothing verification information contains a feature value corresponding to the coefficient information, here, the coefficient information represents information determined from the smoothing information (e.g., D in equation (7))^TD) And the coefficient information is in the form of a sparse matrix; the wall shear stress optimization device accurately solves the feature values of the preset number (for example, the first m) of the coefficient information, and fits the feature values according to the feature values of the preset number (for example, an exponential function fitting algorithm) by adopting a preset fitting algorithm to obtain feature value distribution, so that all the feature values are approximately calculated; here, the number of eigenvalues is N and the eigenvalue is λ_iAnd i is an integer of 1 to N.

It should be noted that the number of feature values corresponding to the coefficient information is consistent with the number of velocity nodes in the initial velocity field of the blood vessel, for example, when the velocity nodes in the initial velocity field of the blood vessel are 86379, in this case, the coefficient information D is used to calculate the coefficient information D^TD is 86379 × 259137, D is approximately solved by fitting algorithm^TD corresponds to all the characteristic values.

At this time, when the smoothing verification information is represented by equation (7), the simplified smoothing verification information is represented by equation (8):

since the simplified smoothing verification information represents the corresponding relationship between the initial blood vessel velocity field, the initial optimized blood vessel velocity field and the initial smoothing parameters, at least one smoothing verification value can be determined after the wall shear stress optimization device obtains the initial blood vessel velocity field, at least one initial optimized blood vessel velocity field and at least one initial smoothing parameter.

S103c5, using the initial smoothing parameter corresponding to the minimum smoothing verification value in the at least one smoothing verification value as the optimized smoothing parameter.

In the embodiment of the present invention, after the wall shear stress optimization device obtains at least one smoothing verification value, since the smoothing verification value represents the optimization performance of the initial smoothing parameter, specifically, when the smoothing verification value is smaller, the optimization performance of the corresponding initial smoothing parameter is higher, so that the wall shear stress optimization device takes the initial smoothing parameter corresponding to the minimum smoothing verification value in the at least one smoothing verification value as the optimized smoothing parameter, and the optimal smoothing parameter is obtained.

S103d, inputting the optimized smoothing parameters into the blood vessel velocity field optimization equation to obtain the optimized blood vessel velocity field.

In the embodiment of the invention, after the optimized smoothing parameters are obtained by the wall shear stress optimizing device, the optimized smoothing parameters and the optimized blood vessel velocity field are represented by the blood vessel velocity field optimizing equation, so that the optimized blood vessel velocity field can be obtained by inputting the optimized smoothing parameters into the blood vessel velocity field optimizing equation by the wall shear stress optimizing device.

It can be understood that the wall shear stress optimization device determines a blood vessel velocity field optimization equation according to the derivative information and the initial blood vessel velocity field, the blood vessel velocity field optimization equation represents the corresponding relation between the optimized smoothing parameter and the optimized blood vessel velocity field, after the optimized smoothing parameter is determined, the velocity field which simultaneously meets the non-dispersive constraint and the smoothness can be determined, and the problem of inaccurate wall shear stress caused by large error of the velocity field is avoided.

Further, in the embodiment of the present invention, the wall shear stress processing device in S104 calculates wall shear stress according to the three-dimensional model of the blood vessel and the optimized velocity field of the blood vessel, and obtains distribution information of wall shear stress of the blood vessel, which specifically includes S104a-S104d, where:

s104a, carrying out interpolation in the wall surface normal direction of the blood vessel three-dimensional model according to the optimized blood vessel velocity field and the preset distance to obtain an interpolation velocity.

In the embodiment of the invention, after the optimized blood vessel velocity field is obtained by the wall shear stress optimization device, the wall normal direction of the blood vessel three-dimensional model is determined, and a preset number (for example, 7) of velocity vectors are selected from the velocity vectors of the optimized blood vessel velocity field in the wall normal direction, so that the interpolation velocity is obtained. Here, the first velocity vector in the interpolated velocities is the velocity vector on the blood vessel wall, and the corresponding velocity is zero.

And S104b, determining the blood flow direction according to the interpolation speed and the wall surface normal direction.

In the embodiment of the invention, after the wall shear stress optimization device obtains the interpolation speed and the wall normal direction, the blood flow direction can be determined according to the direction corresponding to the interpolation speed and the wall normal direction. Here, the blood flow direction represents a flow direction of blood in a blood vessel.

Specifically, an intermediate direction is set, which is a direction corresponding to the interpolation velocity, and the wall surface normal direction are in a perpendicular relationship, so that the wall surface shear stress optimization device takes the cross product of the intermediate direction and the wall surface normal direction as the blood flow direction.

And S104c, obtaining a corresponding fitting curve according to the interpolation speed and the blood flow direction.

In the embodiment of the invention, after the wall shear stress optimization device obtains the interpolation speed and the blood flow direction, a speed curve corresponding to the interpolation speed, namely a fitting curve, can be obtained.

Specifically, in the embodiment of the present invention, the wall shear stress optimization device obtains a corresponding fitting curve according to the interpolation speed and the blood flow direction, and includes: the wall shear stress optimization device calculates the projection information of the interpolation speed in the blood flow direction to obtain corresponding speed distribution information; and fitting the speed distribution information to obtain a fitting curve.

Preferably, the wall shear stress optimization device performs fitting on the speed distribution information to obtain a fitting curve, and specifically performs fitting by using the following steps: firstly, obtaining blood attribute information; here, the blood property information represents the self property of blood flowing in the blood vessel, such as the density of blood and the kinetic viscosity coefficient of blood. Then, fitting the speed distribution information according to the blood attribute information, at least one preset blood vessel wall surface friction speed, a preset fitting coefficient and a preset fitting algorithm to obtain at least one corresponding initial fitting curve, wherein the preset fitting algorithm is used for fitting the speed distribution information; here, at least one initially fitted curve is fitted by at least one preset blood vessel wall friction speed. Finally, determining at least one piece of distinguishing information of the at least one initial fitting curve corresponding to the speed distribution information respectively; taking an initial fitting curve corresponding to the distinguishing information with the minimum difference in the at least one distinguishing information as a fitting curve; here, at least one initial fitting curve corresponding to the velocity distribution information is determined by a preset fitting algorithm according to at least one preset blood vessel wall friction velocity, and an initial fitting curve having the smallest difference with the velocity distribution information is selected from the at least one initial fitting curve as a fitting curve corresponding to the velocity distribution information.

That is to say, in the embodiment of the present invention, when the wall shear stress optimization device performs fitting on the speed distribution information, an implicit wall function (preset fitting algorithm) with higher precision is adopted, specifically as shown in formula (9):

wherein, W' is the height of the wall surface normal direction corresponding to each speed in the speed distribution information; parameter u_τρ and μ are the blood vessel wall friction velocity, the density of blood, and the kinetic viscosity coefficient of blood, respectively (for example, ρ is 1060 and μ is 0.0035, where ρ and μ are the density of blood and the kinetic viscosity coefficient of blood, respectively, in the blood attribute information); κ and s are preset fitting coefficients, both constant (e.g., 0.41 and 0.001093 for κ and s, respectively, determined empirically). Here, the only unknown in equation (9) is the blood vessel wall friction velocity u_τU is obtained by curve fitting_τThe best value of (2); and for u_τThe initial value of (b) is a preset blood vessel wall friction speed, an initial fitting curve of the speed distribution information is determined by the preset blood vessel wall friction speed (where V 'is a continuous dependent variable value corresponding to the initial fitting curve), and the initial fitting curve that most matches the speed distribution curve is used as the fitting curve U' of the speed distribution information.

It should be noted that the formula (9) is only one fitting method, and the velocity distribution information of the wall surface may also be fitted in the form of a polynomial, an logarithmic rate, other wall functions, and the like. By contrast, the error of the wall shear stress obtained by the formula (9) is the smallest.

Fig. 4 is a schematic diagram of an exemplary determined fitting curve provided by an embodiment of the present invention, as shown in fig. 4, which is a cross-sectional view of a velocity field, the coordinate system is a local coordinate system established at each vertex position of a three-dimensional model of a blood vessel, where a preset number of interpolation is 7, distances between interpolation velocities are the same as a preset interval, X ' is a blood flow direction, Y ' is a wall surface normal direction, an arrow mark line indicates velocity distribution information corresponding to the interpolation velocities (a velocity on a wall surface of a blood vessel wall is 0), and U ' is the fitting curve.

And S104d, obtaining wall shear stress distribution information according to the blood flow direction, the fitted curve and the preset hemodynamic viscosity coefficient.

In the embodiment of the invention, the wall shear stress represents the corresponding relation between the blood flow direction, the fitting curve and the preset hemodynamic viscosity coefficient, so that the wall shear stress can be determined after the wall shear stress optimizing device obtains the blood flow direction, the fitting curve and the preset hemodynamic viscosity coefficient, and the determined wall shear stress constitutes wall shear stress distribution information.

Illustratively, when a fitted curve characterizes the functional relationship of U 'and Y', the wall shear stress τ is as shown in equation (10) or equation (11):

wherein, the results calculated by the formula (10) or the formula (11) are the same and are completely equivalent; the direction of the wall shear stress coincides with the direction of blood flow.

In addition, in equation (11), the preset blood vessel wall surface friction speed corresponding to the fitting curve is determined in S104c, and the wall surface shear stress is calculated from the density of blood in the blood attribute information and the preset blood vessel wall surface friction speed.

Illustratively, fig. 5 illustrates an exemplary vessel wall shear stress distribution information calculated based on equation (9), as shown in fig. 5, identifying regions of high wall shear stress; FIG. 6 illustrates an exemplary vessel wall shear stress distribution information based on wall second-order polynomial calculations, such as shown in FIG. 6, identifying regions of high wall shear stress; compared with the actual result corresponding to the blood vessel, the wall shear stress distribution information obtained by the method is closer to an accurate value, and the accuracy is higher.

It should be noted that, after the wall shear stress optimizing device obtains the wall shear stress distribution information, the blood flow rate measurement is completed based on the wall shear stress distribution information as data on which the diagnosis of the vascular disease is based. For example, intracranial arterial blood flow and abdominal vascular blood flow are measured using the wall shear stress distribution information.

It can be understood that, because the optimized blood vessel velocity field is obtained by optimizing the initial blood vessel velocity field by the wall shear stress optimizing device through the mass conservation condition, and because the mass conservation condition can ensure the smoothness and the non-dispersion property of the optimized blood vessel velocity field, the optimized blood vessel velocity field and other blood flow information has low noise, few dead points of the velocity field and high space-time resolution, and the accuracy of the wall shear stress is improved when the wall shear stress optimizing device calculates the wall shear stress according to the optimized blood vessel velocity field.

Example two

Based on the same inventive concept of the embodiments, the embodiments of the present invention provide a wall shear stress optimization device 1, which corresponds to a wall shear stress optimization method; fig. 7 is a schematic structural diagram of a wall shear stress optimization apparatus according to an embodiment of the present invention, as shown in fig. 7, the wall shear stress optimization apparatus 1 includes:

the constructing unit 10 is configured to construct a blood vessel three-dimensional model according to blood vessel nuclear magnetic resonance data when the blood vessel nuclear magnetic resonance data is acquired;

the obtaining unit 11 is configured to obtain an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model;

the optimization unit 12 is configured to optimize the initial blood vessel velocity field based on a mass conservation condition to obtain an optimized blood vessel velocity field;

and the calculating unit 13 is used for calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain the distribution information of the wall shear stress of the blood vessel.

Further, the constructing unit 10 is specifically configured to acquire an initial blood vessel three-dimensional image in the blood vessel nuclear magnetic resonance data; denoising the initial blood vessel three-dimensional image to obtain a denoised initial blood vessel three-dimensional image; extracting blood vessel information from the denoised initial blood vessel three-dimensional image by adopting a preset segmentation algorithm to obtain a point cloud blood vessel three-dimensional image; and reconstructing the point cloud blood vessel three-dimensional image by adopting a preset reconstruction algorithm to obtain the blood vessel three-dimensional model.

Further, the acquiring unit 11 is specifically configured to acquire a blood vessel velocity field in the blood vessel nuclear magnetic resonance data; interpolating the blood vessel velocity field according to a preset interval to obtain an interpolated blood vessel velocity field; and marking the velocity nodes in the interpolated blood vessel velocity field on the blood vessel three-dimensional model according to the blood vessel boundary to obtain the initial blood vessel velocity field.

Further, the optimization unit 12 includes a first determination unit 120, a target construction unit 121, a second determination unit 122, and an input unit 123;

the first determining unit 120 is configured to determine derivative information corresponding to the initial blood vessel velocity field according to a wall surface non-slip condition;

the target construction unit 121 is configured to construct a blood vessel velocity field optimization equation corresponding to the initial blood vessel velocity field based on the mass conservation condition and the derivative information;

the second determining unit 122 is configured to determine an optimized smoothing parameter based on the blood vessel velocity field optimization equation, a preset cross validation algorithm, and a preset optimization algorithm;

the input unit 123 is configured to input the optimized smoothing parameter to the blood vessel velocity field optimization equation, so as to obtain the optimized blood vessel velocity field.

Further, the first determining unit 120 is specifically configured to calculate a wall distance of a velocity node in the initial blood vessel velocity field; dividing the velocity nodes in the initial blood vessel velocity field into near wall surface points and far wall surface points according to a preset distance and the wall surface distance; calculating a derivative of the near wall point based on the wall distance, the wall non-slip condition and a first preset derivative algorithm to obtain corresponding first derivative information; calculating a derivative of the far wall point based on the wall distance, the wall non-slip condition and a second preset derivative algorithm to obtain corresponding second derivative information; taking the first derivative information and the second derivative information as the derivative information.

Further, the first determining unit 120 is specifically configured to determine, according to the wall distance, a blood vessel wall point and a nearest velocity node of the near-wall surface point; according to the wall surface distance, the blood vessel wall point, the nearest speed node, the wall surface no-slip condition and the first preset derivative algorithm, obtaining a first derivative and a second derivative corresponding to the near wall surface point, wherein the first preset derivative algorithm is used for determining derivative information of the near wall surface point; and using the first and second derivatives as the first derivative information.

Further, the target constructing unit 121 is specifically configured to determine a smoothing degree and a divergence degree corresponding to the initial blood vessel velocity field according to the derivative information; constructing an initial blood vessel velocity field optimization objective function corresponding to the initial blood vessel velocity field according to the smoothness, the dispersion divergence and the mass conservation condition; converting the initial blood vessel velocity field optimization objective function according to a Lagrange multiplier algorithm to obtain a converted initial blood vessel velocity field optimization objective function; and carrying out minimization processing on the converted initial blood vessel velocity field optimization objective function to obtain the blood vessel velocity field optimization equation.

Further, the second determining unit 122 is specifically configured to construct smooth verification information according to the preset cross-validation algorithm; determining at least one initial smoothing parameter based on the preset optimization algorithm; respectively inputting the at least one initial smoothing parameter into the blood vessel velocity field optimization equation to obtain at least one corresponding initial optimized blood vessel velocity field; determining at least one smoothing verification value corresponding to the smoothing verification information according to the at least one initial optimized blood vessel velocity field; and taking the initial smoothing parameter corresponding to the minimum smoothing verification value in the at least one smoothing verification value as the optimized smoothing parameter.

Further, the second determining unit 122 is further specifically configured to determine, according to the derivative information, coefficient information in the smoothing verification information; determining a characteristic value corresponding to the coefficient information according to a preset fitting algorithm; inputting the characteristic value into the smooth verification information to obtain corresponding simplified smooth verification information; and respectively inputting the at least one initial optimized blood vessel velocity field into the simplified smooth verification information to obtain the at least one smooth verification value.

Further, the calculating unit 13 is specifically configured to perform interpolation in the wall surface normal direction of the blood vessel three-dimensional model according to the optimized blood vessel velocity field and a preset interval to obtain an interpolation velocity; determining the blood flow direction according to the interpolation speed and the wall surface normal direction; obtaining a corresponding fitting curve according to the interpolation speed and the blood flow direction; and obtaining the wall shear stress distribution information according to the blood flow direction, the fitting curve and a preset hemodynamic viscosity coefficient.

Further, the calculating unit 13 is further specifically configured to calculate projection information of the interpolation speed in the blood flow direction, so as to obtain corresponding speed distribution information; and fitting the speed distribution information to obtain the fitting curve.

Further, the calculating unit 13 is specifically configured to obtain blood attribute information; fitting the speed distribution information according to the blood attribute information, at least one preset blood vessel wall surface friction speed, a preset fitting coefficient and a preset fitting algorithm to obtain at least one corresponding initial fitting curve, wherein the preset fitting algorithm is used for fitting the speed distribution information; determining at least one piece of distinguishing information of the at least one initial fitting curve corresponding to the speed distribution information respectively; and taking an initial fitting curve corresponding to the distinguishing information with the minimum difference in the at least one distinguishing information as the fitting curve.

Further, the preset fitting algorithm is as follows:

wherein V' is a continuous dependent variable value u corresponding to the initial fitting curve_τFor the preset blood vessel wall friction speed, W' is each of the speed distribution informationThe height of the wall surface normal direction corresponding to the speed, kappa and s are the preset fitting coefficients, rho is the density of blood in the blood attribute information, and mu is the dynamic viscosity coefficient of the blood in the blood attribute information.

In practical applications, the constructing Unit 10, the obtaining Unit 11, the optimizing Unit 12, the calculating Unit 13, the first determining Unit 120, the target constructing Unit 121, the second determining Unit 122 and the input Unit 123 may be implemented by a processor 14 located on the wall shear stress optimizing apparatus 1, and specifically implemented by a Central Processing Unit (CPU), an MPU (Microprocessor Unit), a Digital Signal Processor (DSP), a Field Programmable Gate Array (FPGA), or the like.

An embodiment of the present invention further provides a wall shear stress optimization device 1, as shown in fig. 8, where the wall shear stress optimization device 1 includes: a processor 14, a memory 15 and a communication bus 16, wherein the memory 15 is in communication with the processor 14 through the communication bus 16, and the memory 15 stores a program executable by the processor 14, and when the program is executed, the wall shear stress optimization method according to the first embodiment is executed by the processor 14.

In practical applications, the Memory 15 may be a volatile Memory (volatile Memory), such as a Random-Access Memory (RAM); or a non-volatile Memory (non-volatile Memory), such as a Read-Only Memory (ROM), a flash Memory (flash Memory), a Hard Disk (Hard Disk Drive, HDD) or a Solid-State Drive (SSD); or a combination of the above types of memories and provides instructions and data to processor 14.

The embodiment of the present invention provides a computer-readable storage medium, on which a program is stored, and the program, when executed by the processor 14, implements the wall shear stress optimization method according to the first embodiment.

It can be understood that, because the optimized blood vessel velocity field is obtained by optimizing the initial blood vessel velocity field by the wall shear stress optimizing device through the mass conservation condition, and because the mass conservation condition can ensure the smoothness and the non-dispersion property of the optimized blood vessel velocity field, the optimized blood vessel velocity field and other blood flow information has low noise, few dead points of the velocity field and high space-time resolution, and the accuracy of the wall shear stress is improved when the wall shear stress optimizing device calculates the wall shear stress according to the optimized blood vessel velocity field.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (14)

1. A method of optimizing wall shear stress, the method comprising:

when blood vessel nuclear magnetic resonance data are acquired, constructing a blood vessel three-dimensional model according to the blood vessel nuclear magnetic resonance data;

obtaining an initial blood vessel velocity field according to the blood vessel nuclear magnetic resonance data and the blood vessel three-dimensional model;

optimizing the initial blood vessel velocity field based on a mass conservation condition to obtain an optimized blood vessel velocity field;

calculating wall shear stress according to the blood vessel three-dimensional model and the optimized blood vessel velocity field to obtain blood vessel wall shear stress distribution information;

wherein, the optimizing the initial blood vessel velocity field based on the mass conservation condition to obtain an optimized blood vessel velocity field comprises:

determining derivative information corresponding to the initial blood vessel velocity field according to the condition that the wall surface has no slippage;

constructing a blood vessel velocity field optimization equation corresponding to the initial blood vessel velocity field based on the mass conservation condition and the derivative information;

determining optimized smooth parameters based on the blood vessel velocity field optimization equation, a preset cross validation algorithm and a preset optimization algorithm;

and inputting the optimized smoothing parameters into the blood vessel velocity field optimization equation to obtain the optimized blood vessel velocity field.

2. The method of claim 1, wherein constructing a three-dimensional model of the vessel from the vessel NMR data comprises:

acquiring an initial blood vessel three-dimensional image in the blood vessel nuclear magnetic resonance data;

denoising the initial blood vessel three-dimensional image to obtain a denoised initial blood vessel three-dimensional image;

extracting blood vessel information from the denoised initial blood vessel three-dimensional image by adopting a preset segmentation algorithm to obtain a point cloud blood vessel three-dimensional image;

and reconstructing the point cloud blood vessel three-dimensional image by adopting a preset reconstruction algorithm to obtain the blood vessel three-dimensional model.

3. The method of claim 1, wherein obtaining an initial vessel velocity field from the vessel nmr data and the vessel three-dimensional model comprises:

acquiring a blood vessel velocity field in the blood vessel nuclear magnetic resonance data;

interpolating the blood vessel velocity field according to a preset interval to obtain an interpolated blood vessel velocity field;

and marking the velocity nodes in the interpolated blood vessel velocity field on the blood vessel three-dimensional model according to the blood vessel boundary to obtain the initial blood vessel velocity field.

4. The method of claim 1, wherein determining derivative information corresponding to the initial vessel velocity field according to the wall no-slip condition comprises:

calculating the wall surface distance of a velocity node in the initial blood vessel velocity field;

dividing the velocity nodes in the initial blood vessel velocity field into near wall surface points and far wall surface points according to a preset distance and the wall surface distance;

calculating a derivative of the near wall point based on the wall distance, the wall non-slip condition and a first preset derivative algorithm to obtain corresponding first derivative information;

calculating a derivative of the far wall point based on the wall distance, the wall non-slip condition and a second preset derivative algorithm to obtain corresponding second derivative information;

taking the first derivative information and the second derivative information as the derivative information.

5. The method of claim 4, wherein the calculating a derivative of the near-wall point based on the wall distance, the wall no-slip condition, and a first preset derivative algorithm to obtain corresponding first derivative information comprises:

determining a vessel wall point and a nearest speed node of the near-wall surface point according to the wall surface distance;

according to the wall surface distance, the blood vessel wall point, the nearest speed node, the wall surface no-slip condition and the first preset derivative algorithm, obtaining a first derivative and a second derivative corresponding to the near wall surface point, wherein the first preset derivative algorithm is used for determining derivative information of the near wall surface point;

taking the first derivative and the second derivative as the first derivative information.

6. The method according to claim 1, wherein the constructing a vessel velocity field optimization equation corresponding to the initial vessel velocity field based on the mass conservation condition and the derivative information comprises:

determining the corresponding smoothness and dispersion degree of the initial blood vessel velocity field according to the derivative information;

constructing an initial blood vessel velocity field optimization objective function corresponding to the initial blood vessel velocity field according to the smoothness, the dispersion divergence and the mass conservation condition;

converting the initial blood vessel velocity field optimization objective function according to a Lagrange multiplier algorithm to obtain a converted initial blood vessel velocity field optimization objective function;

and carrying out minimization processing on the converted initial blood vessel velocity field optimization objective function to obtain the blood vessel velocity field optimization equation.

7. The method of claim 1, wherein determining optimized smoothing parameters based on the vessel velocity field optimization equation, a preset cross-validation algorithm, and a preset optimization algorithm comprises:

constructing smooth verification information according to the preset cross verification algorithm;

determining at least one initial smoothing parameter based on the preset optimization algorithm;

respectively inputting the at least one initial smoothing parameter into the blood vessel velocity field optimization equation to obtain at least one corresponding initial optimized blood vessel velocity field;

determining at least one smoothing verification value corresponding to the smoothing verification information according to the at least one initial optimized blood vessel velocity field;

and taking the initial smoothing parameter corresponding to the minimum smoothing verification value in the at least one smoothing verification value as the optimized smoothing parameter.

8. The method according to claim 7, wherein the determining at least one smoothing verification value corresponding to the smoothing verification information according to the at least one initial optimized vessel velocity field comprises:

determining coefficient information in the smoothing verification information according to the derivative information;

determining a characteristic value corresponding to the coefficient information according to a preset fitting algorithm;

inputting the characteristic value into the smooth verification information to obtain corresponding simplified smooth verification information;

and respectively inputting the at least one initial optimized blood vessel velocity field into the simplified smooth verification information to obtain the at least one smooth verification value.

9. The method according to claim 1, wherein the calculating wall shear stress according to the three-dimensional model of the blood vessel and the optimized velocity field of the blood vessel to obtain information of distribution of wall shear stress of the blood vessel comprises:

performing interpolation in the wall surface normal direction of the blood vessel three-dimensional model according to the optimized blood vessel velocity field and the preset interval to obtain an interpolation velocity;

determining the blood flow direction according to the interpolation speed and the wall surface normal direction;

obtaining a corresponding fitting curve according to the interpolation speed and the blood flow direction;

and obtaining the wall shear stress distribution information according to the blood flow direction, the fitting curve and a preset hemodynamic viscosity coefficient.

10. The method of claim 9, wherein said deriving a corresponding fitted curve based on said interpolated velocity and said blood flow direction comprises:

calculating the projection information of the interpolation speed on the blood flow direction to obtain corresponding speed distribution information;

and fitting the speed distribution information to obtain the fitting curve.

11. The method of claim 10, wherein said fitting the velocity profile information to obtain the fitted curve comprises:

obtaining blood attribute information;

fitting the speed distribution information according to the blood attribute information, at least one preset blood vessel wall surface friction speed, a preset fitting coefficient and a preset fitting algorithm to obtain at least one corresponding initial fitting curve, wherein the preset fitting algorithm is used for fitting the speed distribution information;

determining at least one piece of distinguishing information of the at least one initial fitting curve respectively corresponding to the speed distribution information;

and taking an initial fitting curve corresponding to the distinguishing information with the minimum difference in the at least one distinguishing information as the fitting curve.

12. The method of claim 11, wherein the predetermined fitting algorithm is:

wherein V' is a continuous dependent variable value u corresponding to the initial fitting curve_τAnd setting the preset blood vessel wall friction speed as M', the wall normal height corresponding to each speed in the speed distribution information as K and s, the preset fitting coefficient as P, the density of blood in the blood attribute information as rho, and the dynamic viscosity coefficient of blood in the blood attribute information as mu.

13. A wall shear stress optimization device, comprising: a processor, a memory and a communication bus, the memory in communication with the processor through the communication bus, the memory storing a program executable by the processor, the program, when executed, causing the processor to perform the method of any of claims 1-12.

14. A computer-readable storage medium, on which a program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1-12.

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