A method and related device for inverting the concentration distribution of magnetic nanoparticles

Abstract

The present application discloses a method for inverting the concentration distribution of magnetic nanoparticles and related devices, which relate to the field of biomedical engineering technology. The method first uses an external magnetic field to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements, then uses ultrasonic equipment to collect ultrasonic ultrafast plane wave imaging data and detect axial vibration displacement. The measured axial vibration displacement data and the corresponding discrete space and time coordinates are input into the inversion model for iterative inversion to obtain the inversion result of the magnetic nanoparticle concentration distribution. The loss function of the inversion model includes a data-driven loss term and a physical information-driven loss term (based on the Navier equation). Compared with traditional technologies, this method introduces a physical information neural network and encodes the control equations such as the Navier equation into a fully connected neural network. There is no need to oversimplify the physical equations, nor is there a need for complex and time-consuming modeling of the experimental environment to obtain simulation data, and it has higher accuracy and stability.

Description

Technical Field

[0001] The present application relates to the field of biomedical engineering technology, and in particular to a method for inverting the concentration distribution of magnetic nanoparticles and related devices. Background Art

[0002] Magnetic nanoparticles (MNPs) are nanoscale particles with a core composed of a magnetic material and a surface-coated or functionalized shell. Due to their combined nanoscale effect and magnetic responsiveness, they have broad applications and significant significance in the biomedical field. Their basic components consist of a magnetic core and a functionalized shell. Due to their unique dual advantages—nanoscale effect and magnetic responsiveness—MNPs not only significantly improve diagnostic accuracy and therapeutic specificity, but also open new avenues for personalized medicine and precision drug delivery, making them a hot topic in nanomedicine research. Visualizing magnetic nanoparticles in regions of interest (ROIs) and quantifying their concentration not only helps reveal local molecular or cellular activity but is also crucial for the design and optimization of various magnetically controlled diagnostic and therapeutic strategies. Furthermore, for responsive therapies such as magnetic hyperthermia or acousto-magnetic synergistic therapy, particle concentration directly influences local energy deposition and therapeutic efficacy, making accurate characterization a prerequisite for personalized treatment.

[0003] Estimating the concentration of magnetic nanoparticles (MNPs) is a classic inverse problem. Existing approaches construct a mapping relationship from "displacement" to "concentration," incorporating physical excitation to induce a measurable displacement response from the magnetic nanoparticles. Based on inversion algorithms and mathematical models, the spatial concentration distribution of the particles is indirectly inferred from the observed displacement signal. However, existing approaches suffer from two problems. First, they oversimplify the physical equations and ignore divergent terms, resulting in halo-like artifacts in the concentration reconstruction results. Second, simulations using finite element software are time-consuming and difficult to guarantee accuracy and stability.

[0004] Therefore, how to overcome the defects of existing solutions and achieve rapid and accurate estimation of the concentration of magnetic nanoparticles is a technical problem that needs to be solved urgently in this field. Summary of the Invention

[0005] The purpose of this application is to provide a method and related device for inverting the concentration distribution of magnetic nanoparticles, which can ensure the accuracy and stability of the inversion of the concentration distribution of magnetic nanoparticles.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for inverting the concentration distribution of magnetic nanoparticles, comprising the following steps:

[0008] An external magnetic field is used to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles. Vibration detection is performed on the ultrasonic ultrafast plane wave imaging data to obtain the measured data of the axial vibration displacement of the magnetic nanoparticles.

[0009] The Navier equations are encoded into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a spatiotemporal neural network and a spatial neural network; the spatiotemporal neural network is used to use discrete spatial coordinates and discrete time coordinates as model inputs to output axial vibration displacement prediction results and lateral vibration displacement prediction results; the spatial neural network is used to use discrete spatial coordinates as model inputs to output magnetic nanoparticle concentration prediction results; the loss function calculates the total loss using the axial vibration displacement prediction results, lateral vibration displacement prediction results, axial vibration displacement measured data and magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles through an external magnetic field.

[0010] The discrete spatial coordinates and discrete time coordinates corresponding to the measured axial vibration displacement data are used as the first input data, and the discrete spatial coordinates corresponding to the measured axial vibration displacement data are used as the second input data, which are jointly input into the magnetic nanoparticle concentration inversion model, and the measured axial vibration displacement data are used as the label of the spatiotemporal neural network for iterative inversion to obtain the magnetic nanoparticle concentration distribution inversion result; the loss function includes data-driven loss terms and physical information-driven loss terms; the data-driven loss term is determined according to the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined according to the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result and the Navier equation; the magnetic nanoparticle concentration inversion result is the magnetic nanoparticle concentration prediction result output when the model meets the iteration exit condition after several iterations; for any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration of the corresponding position, and the magnetic nanoparticle concentration distribution inversion result can be determined according to the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data.

[0011] Optionally, the physical process of the external magnetic field inducing vibration of the magnetic nanoparticles is controlled by the Navier equation, which is shown as follows:

[0012] .

[0013] in, is the density of biological tissue, is the shear modulus, is the gradient operator, is the Lamé constant, is the displacement field, is the magnetic force per unit volume. x Direction and z The component form in the direction is used to calculate the physical information driven loss term; the physical information driven loss term is shown as follows:

[0014] .

[0015] in, LossPDE 1 and LossPDE 2 are x Direction and z The physical information of the direction drives the loss sub-item, and the sum of the two is LossPDE = LossPDE 1+ LossPDE 2 is the total physical information driven loss term, u x for x The inversion results of the vibration displacement in the direction, that is, the prediction results of the lateral vibration displacement, u z for z The inversion results of the vibration displacement in the direction, that is, the prediction results of the axial vibration displacement; x and z is the discrete space coordinate, t is the discrete time coordinate, f z is the axial magnetic force.

[0016] The magnetic force in the axial direction is calculated according to the following formula:

[0017] .

[0018] in, dV is the inversion result of magnetic nanoparticle concentration, is the magnetic susceptibility, is the volume fraction of the core, is the magnetic induction intensity, is the magnetic permeability of biological tissue, is the volume of a single magnetic nanoparticle.

[0019] Optionally, the data-driven loss term is calculated as follows:

[0020] .

[0021] in, LossData is the data-driven loss term, is the predicted result of the axial vibration displacement at the discrete spatial coordinates input into the magnetic nanoparticle concentration inversion model, is the measured value of the axial vibration displacement corresponding to the discrete spatial coordinate.

[0022] Optionally, an external magnetic field is used to excite the magnetic nanoparticles in the biological tissue to generate a small displacement, and an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles. The ultrasonic ultrafast plane wave imaging data is then subjected to vibration detection to obtain measured axial vibration displacement data of the magnetic nanoparticles, specifically including:

[0023] An external magnetic field is used to stimulate magnetic nanoparticles in biological tissues to produce tiny displacements, and multi-angle composite ultrafast plane wave imaging technology is used to collect ultrasonic ultrafast plane wave imaging data.

[0024] The autocorrelation algorithm is used to estimate the tiny displacements of each point in the biological tissue using ultrasonic ultrafast plane wave imaging data, and the measured data of the axial vibration displacement of the magnetic nanoparticles are obtained; the measured data of the axial vibration displacement are used to calculate the data-driven loss term.

[0025] Alternatively, the measured value of the axial vibration displacement of each point in the biological tissue is estimated according to the following formula:

[0026] .

[0027] in, is the measured value of axial vibration displacement, c is the speed of sound in the tissue, f c is the center frequency of the ultrasonic ultrafast plane wave imaging data before demodulation, Q ( m , i -1) is the i −1 frame time, position index is m at Q Component value, I ( m , i ) is the i Frame time and position index are m at I Component value, M is the axial sample range.

[0028] Optionally, an external magnetic field is used to excite the magnetic nanoparticles in the biological tissue to generate a small displacement, specifically comprising the following steps:

[0029] A signal generator is used to generate different excitation waveforms, which are applied to a coil with an iron core through a power amplifier to generate a time-varying magnetic field.

[0030] The time-varying magnetic field of the iron core coil is controlled to act on the magnetic nanoparticles in the biological tissue, so that the magnetic nanoparticles produce tiny displacement or vibration under the excitation of the magnetic field.

[0031] In a second aspect, the present application provides a magnetic nanoparticle concentration distribution inversion system, comprising the following functional modules:

[0032] The magnetic field excitation and displacement detection module is used to use an external magnetic field to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles, and vibration detection is performed on the ultrasonic ultrafast plane wave imaging data to obtain the measured axial vibration displacement data of the magnetic nanoparticles.

[0033] A concentration inversion model construction module is used to encode the Navier equations into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a space-time neural network and a spatial neural network; the space-time neural network is used to use discrete spatial coordinates and discrete time coordinates as model inputs to output axial vibration displacement prediction results and lateral vibration displacement prediction results; the spatial neural network is used to use discrete spatial coordinates as model inputs to output magnetic nanoparticle concentration prediction results; the loss function calculates the total loss using the axial vibration displacement prediction results, lateral vibration displacement prediction results, axial vibration displacement measured data and magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles through an external magnetic field.

[0034] The magnetic nanoparticle concentration distribution inversion module is used to input the discrete spatial coordinates and discrete time coordinates corresponding to the axial vibration displacement measured data as the first input data, and the discrete spatial coordinates corresponding to the axial vibration displacement measured data as the second input data, and input them together into the magnetic nanoparticle concentration inversion model, and use the axial vibration displacement measured data as the label of the spatiotemporal neural network for iterative inversion to obtain the magnetic nanoparticle concentration distribution inversion result; the loss function includes a data-driven loss term and a physical information-driven loss term; the data-driven loss term is determined based on the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined based on the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result and the Navier equation; the magnetic nanoparticle concentration inversion result is the magnetic nanoparticle concentration prediction result output when the model meets the iteration exit condition after several iterations; for any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration of the corresponding position, and the magnetic nanoparticle concentration distribution inversion result can be determined based on the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data.

[0035] In a third aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the magnetic nanoparticle concentration distribution inversion method described above.

[0036] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the magnetic nanoparticle concentration distribution inversion method described above.

[0037] In a fifth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the magnetic nanoparticle concentration distribution inversion method described above.

[0038] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0039] The present application provides a method for inverting the concentration distribution of magnetic nanoparticles and a related device. In this method, first, an external magnetic field is used to stimulate the magnetic nanoparticles in biological tissue to produce a small displacement, and then an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles and detect the axial vibration displacement; the measured axial vibration displacement data and the corresponding discrete spatial coordinates and discrete time coordinates are input into the magnetic nanoparticle concentration inversion model for iterative inversion to obtain the magnetic nanoparticle concentration distribution inversion result; the magnetic nanoparticle concentration inversion model constructed here includes a spatiotemporal neural network and a spatial neural network, both of which are models constructed based on deep neural networks, which are used to predict the output lateral vibration displacement and axial vibration displacement and predict the output magnetic nanoparticles respectively. Particle concentration, when performing iterative inversion in the magnetic nanoparticle concentration inversion model, the loss function of the model includes a data-driven loss term determined according to the error between the axial vibration displacement prediction result and the actual axial vibration displacement data, and a physical information-driven loss term determined according to the Navier equation; compared with the traditional MNPs concentration inversion technology, the present application introduces a physical information neural network (PINN) to invert the concentration distribution of magnetic nanoparticles, and encodes the control equations of the physical problem (such as the partial differential form of the Navier equation) into a fully connected neural network, without over-simplifying the physical equations; and there is no need to use computer software to perform detailed, complex and time-consuming modeling of the experimental environment (such as magnetic field equipment, various tissue parameters, etc.) to obtain software simulation data, which has higher accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1A flow chart of a method for inverting the concentration distribution of magnetic nanoparticles provided in one embodiment of the present application.

[0042] Figure 2 This is a flowchart of step B1 in a method for inverting the concentration distribution of magnetic nanoparticles provided in one embodiment of the present application.

[0043] Figure 3 A schematic diagram of the network structure of a magnetic nanoparticle concentration inversion model in a magnetic nanoparticle concentration distribution inversion method provided in one embodiment of the present application.

[0044] Figure 4 A schematic diagram of the main parameter values ​​of two deep neural networks in a magnetic nanoparticle concentration inversion model in a magnetic nanoparticle concentration distribution inversion method provided in one embodiment of the present application.

[0045] Figure 5 A two-dimensional MNPs concentration distribution map generated by a magnetic nanoparticle concentration distribution inversion method provided in one embodiment of the present application.

[0046] Figure 6 A schematic diagram of the functional modules of a magnetic nanoparticle concentration distribution inversion system provided in one embodiment of the present application.

[0047] Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0049] Due to the unique dual advantages of magnetic nanoparticles: nanoscale effect and magnetic response properties, MNPs can not only significantly improve diagnostic accuracy and therapeutic specificity, but also open up new avenues for personalized medicine and precision drug delivery, thus becoming a hot topic in nanomedicine research today.

[0050] The visualization of magnetic nanoparticles and the quantification of their concentration in regions of interest (ROIs) not only help reveal local molecular or cellular activity, but are also crucial for the design and optimization of various magnetically controlled diagnostic and therapeutic strategies. This is not only applicable to the evaluation of nanoparticle enrichment efficiency in drug-targeted therapy, but also plays a key role in tumor microenvironment monitoring, inflammation localization, and blood-brain barrier penetration analysis. For example, when targeting tumor tissue, quantitative imaging can help determine whether the particles have successfully crossed the vascular barrier and enriched in the core of the lesion; in the process of stem cell tracking or gene delivery, real-time imaging of particle concentration can reveal cell migration paths and transport efficiency. In addition, for responsive therapies such as magnetic hyperthermia or acoustomagnetic synergistic therapy, particle concentration directly affects local energy deposition and therapeutic effects, so its accurate characterization is a prerequisite for achieving personalized treatment.

[0051] Estimating the concentration of magnetic nanoparticles (MNPs) is a typical inverse problem, and its basic process can be summarized into the following three steps:

[0052] A1. Induce magnetic nanoparticles to vibrate through external magnetic field excitation and other means, thereby generating tiny mechanical disturbances or displacement responses in local tissues.

[0053] A2. Use ultrasound or other highly sensitive detection devices to collect and process the data to obtain the corresponding displacement signal.

[0054] A3. Based on the constructed physical mathematical model or software simulation, a direct expression, model-predicted displacement, or software-simulated displacement is obtained; the measured displacement data is used as the solution input; the concentration of the nanoparticles at the corresponding spatial position is reversely inferred through direct expression calculation or by minimizing the difference between the collected displacement and the model-predicted displacement / software-simulated displacement.

[0055] Essentially, this process establishes a mapping relationship from "displacement" to "concentration." Physical excitation induces a measurable displacement response in magnetic nanoparticles, and then, based on inversion algorithms and mathematical models, indirectly infers the spatial concentration distribution of the particles from the observed displacement signal. Because magnetic nanoparticles themselves cannot be directly observed, this method indirectly obtains quantitative information about the concentration distribution of magnetic nanoparticles by introducing displacement as an intermediary variable.

[0056] Based on this inversion principle, an existing scheme uses the Navier equation as a physical mathematical model, then ignores the divergent terms, approximates the second-order derivative of the axial displacement to the body force distribution through Laplace transform, and establishes a linear mapping relationship of "displacement-density"; then, the measured axial displacement is used to u z (Ultrasonic acquisition system can only obtain axial displacement) Calculate the axial magnetic force F z, thus obtaining the concentration distribution of MNPs. However, this method oversimplifies the physical equations and ignores the divergence term, resulting in halo artifacts in the reconstruction results. In addition, the calculation requires a coil current of up to 104A to induce measurable displacement, which is difficult to experiment in reality. Based on the constructed physical mathematical model, this article obtains a direct expression, starting from u z Calculate F z ,and F z It has a corresponding relationship with the number of MNPs, and the concentration of MNPs is then obtained.

[0057] Another approach, inverse magnetodynamic ultrasound (IMMUS), aims to quantitatively determine the local concentration of magnetic nanoparticles in biological tissue. IMMUS utilizes additional information not otherwise available in conventional MMUS, namely the material properties of the nanoparticles and surrounding tissue, as well as the characteristics of the electromagnet generating the time-varying magnetic field. Its fundamental concept is to use computer software to model and iteratively adjust the software simulation data to the acquired data. Specifically, the simulated tissue displacement field must be iteratively adjusted to the acquired displacement field. The hypothetical local concentration of magnetic nanoparticles calculated at this point is then the desired local concentration of magnetic nanoparticles in the biological tissue. The core of this approach involves modeling various parameters using finite element software simulation to obtain software-simulated displacements. The measured displacement data is then used as the solution input. By minimizing the difference between the acquired and software-simulated displacements, the nanoparticle concentration at the corresponding spatial location is inferred. However, this approach requires detailed, complex, and time-consuming computer software modeling of the experimental environment (e.g., magnetic field equipment, various tissue parameters, etc.) to generate the software simulation data. This software modeling is not always accurate and is prone to errors.

[0058] Therefore, the present application aims to propose a new magnetic nanoparticle concentration distribution inversion scheme to overcome the defects of existing schemes and achieve rapid and accurate estimation of magnetic nanoparticle concentration.

[0059] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0060] The present application provides a method for inverting the concentration distribution of magnetic nanoparticles. In an exemplary embodiment, as Figure 1 As shown, the following steps are included:

[0061] B1. An external magnetic field is used to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles. The ultrasonic ultrafast plane wave imaging data is then subjected to vibration detection to obtain the measured axial vibration displacement data of the magnetic nanoparticles.

[0062] In a specific embodiment, the external magnetic field is used to stimulate the magnetic nanoparticles in the biological tissue to produce a small displacement as follows:

[0063] A signal generator generates different excitation waveforms, which are applied to a coil with an iron core through a power amplifier to produce a time-varying magnetic field. The excitation waveform generated by the signal generator can be a sinusoidal signal, a pulse signal, or other signals. The time-varying magnetic field of the iron core coil is controlled to act on magnetic nanoparticles in biological tissue, causing the magnetic nanoparticles to produce tiny displacements or vibrations under the magnetic field excitation.

[0064] In a specific embodiment, Figure 2 As shown, step B1 specifically includes the following steps:

[0065] B11. An external magnetic field is used to stimulate magnetic nanoparticles in biological tissues to produce tiny displacements, and multi-angle composite ultrafast plane wave imaging technology is used to collect ultrasonic ultrafast plane wave imaging data.

[0066] In step B11, multi-angle composite ultrafast plane wave imaging is used to capture the tiny displacements of magnetic nanoparticles within biological tissues caused by external magnetic field excitation. This technique emits plane waves at different incident angles within a short period of time and performs time-delayed superposition processing on the echo signals. This enhances the spatial resolution and signal-to-noise ratio of the image while maintaining the ultrafast imaging frame rate, effectively improving the sensitivity of detecting tiny displacements. This acquisition yields ultrasonic IQ data: the in-phase component (I) and the orthogonal component (Q).

[0067] B12. An autocorrelation algorithm is used to estimate the minute displacements of various points in biological tissue using ultrasonic ultrafast plane wave imaging data, obtaining the measured axial vibration displacement data of the magnetic nanoparticles. This axial vibration displacement data is then used to calculate the data-driven loss term. Specifically, the autocorrelation algorithm estimates the differential mean displacement of the signal by calculating the average phase offset of the signal with respect to the center frequency, as shown in the following equation:

[0068] .

[0069] in, is the axial differential mean displacement, i.e. the measured value of the axial vibration displacement ; c is the speed of sound in the tissue, f c is the center frequency of the ultrasonic ultrafast plane wave imaging data before demodulation, Q ( m , i -1) is the i −1 frame time, position index is m atQ Component value, I ( m , i ) is the i Frame time and position index are m at I Component value, M is the axial sample range.

[0070] The measured value of the axial vibration displacement obtained at this time There are corresponding ( x , z , t ), x , z represents discrete space coordinates, t Represents discrete time coordinates. Discrete space coordinates and discrete time coordinates serve as input data for subsequent neural networks.

[0071] B2. Encode the Navier equations into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a space-time neural network and a spatial neural network; the space-time neural network is used to use discrete space coordinates and discrete time coordinates as model inputs to output axial vibration displacement prediction results and lateral vibration displacement prediction results; the spatial neural network is used to use discrete space coordinates as model inputs to output magnetic nanoparticle concentration prediction results; the loss function calculates the total loss based on the axial vibration displacement prediction results, lateral vibration displacement prediction results, axial vibration displacement measured data and magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles through an external magnetic field.

[0072] B3. The discrete spatial coordinates and discrete time coordinates corresponding to the measured data of axial vibration displacement are used as the first input data, and the discrete spatial coordinates corresponding to the measured data of axial vibration displacement are used as the second input data. They are input into the magnetic nanoparticle concentration inversion model together, and the measured data of axial vibration displacement is used as the label of the spatiotemporal neural network for iterative inversion to obtain the inversion result of the magnetic nanoparticle concentration distribution.

[0073] The loss function of the magnetic nanoparticle concentration inversion model includes a data-driven loss term and a physical information-driven loss term; the data-driven loss term is determined based on the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined based on the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result and the Navier equation; the magnetic nanoparticle concentration inversion result is the magnetic nanoparticle concentration prediction result output when the model meets the iteration exit condition after several iterations.

[0074] For any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration at the corresponding position. The magnetic nanoparticle concentration distribution inversion results can be determined based on the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data.

[0075] Specifically, the data-driven loss term is calculated as follows:

[0076] .

[0077] in, LossData is the data-driven loss term, is the predicted result of the axial vibration displacement at the discrete spatial coordinates input into the magnetic nanoparticle concentration inversion model, is the measured value of the axial vibration displacement corresponding to the discrete spatial coordinate.

[0078] Physically-Informed Neural Networks (PINNs) are an innovative computational approach that directly incorporates physical laws into the neural network's iterative inversion process by encoding the governing equations of a physical problem (such as partial differential equations) into a fully connected neural network. This approach not only leverages the powerful data learning and pattern recognition capabilities of deep learning models but also effectively incorporates the laws of physics, making the model more robust in handling complex problems and offering better physical interpretability. With increasing research, PINNs have become a powerful tool for solving both direct and inverse problems, demonstrating significant application potential and promising prospects, particularly for complex problems involving the coupling of multiple physical fields.

[0079] Because the magnetic force needs to be determined based on its magnetic behavior, this example uses superparamagnetic iron oxide (SPIO) as an example. Therefore, the MNPs mentioned in the magnetic force formula below refer to SPIO. However, the inversion method described above is not only applicable to SPIO; by simply changing the magnetic force expression, this reaction method can be applied to ferromagnetic nanoparticles or other types of magnetic nanoparticles.

[0080] In the case of magnetic permeability In a non-magnetic medium, the total volume is The magnetic gradient force on MNPs (representing superparamagnetic iron oxide SPIO) can be expressed as:

[0081] .

[0082] in, is the magnetic susceptibility, is the volume fraction of the core, is the magnetic induction intensity, is the gradient operator.

[0083] Therefore, the physical process of the external magnetic field inducing the vibration of magnetic nanoparticles is controlled by the Navier equation. Under the excitation of the external magnetic field, the physical process of the surrounding tissue moving along with the MNPs under the action of the magnetic force can be expressed by the Navier equation as follows:

[0084] .

[0085] in, is the density of biological tissue, is the shear modulus, is the gradient operator, is the Lamé constant, is the displacement field, It is the magnetic force per unit volume.

[0086] The physical information neural network (PINN) is used to solve the above Navier equation, that is, the above Navier equation is encoded into the PDE loss term of PINN, thereby inverting the concentration of MNPs.

[0087] As mentioned above, Navier's equations are x Direction and z The component form in the direction is converted into a physical information driven loss term. Here, the physical information driven loss term is shown as follows:

[0088] .

[0089] in, LossPDE 1 and LossPDE 2 are x Direction and z The physical information of the direction drives the loss sub-item, and the sum of the two LossPDE = LossPDE 1+ LossPDE 2 is the total physical information driven loss term, u x for x The inversion results of the vibration displacement in the direction, that is, the prediction results of the lateral vibration displacement, u z for z The inversion results of the vibration displacement in the direction, that is, the prediction results of the axial vibration displacement; x and z is the discrete space coordinate, t is the discrete time coordinate, f z is the axial magnetic force. Since MNPs are almost only subjected to the axial (z-direction) magnetic force in the experiment, only Quantity,

[0090] The magnetic force in the axial direction is calculated according to the following formula:

[0091] .

[0092] in, dV is the concentration of magnetic nanoparticles, is the magnetic susceptibility, is the volume fraction of the core, is the magnetic induction intensity, is the magnetic permeability of biological tissue, is the volume of a single magnetic nanoparticle.

[0093] like Figure 3 As shown in the figure, the magnetic nanoparticle concentration inversion model constructed in this step includes two deep neural networks: the first main network is a spatiotemporal neural network, which is used to predict the vibration displacement, and its input is , representing discrete space coordinates and discrete time coordinates respectively, the model output is and , which represent the network's prediction results for lateral vibration displacement (x direction) and axial vibration displacement (z direction). The second auxiliary network is a spatial neural network, which is used to predict the concentration of magnetic nanoparticles. Its input is , represents the discrete space coordinates, there is no This is because the concentration of MNPs does not change with time. The predicted output is , represents the concentration of MNPs. The main parameters of the two deep neural networks are as follows Figure 4 shown.

[0094] Combined with the above data-driven loss term LossData and physical information driven loss terms LossPDE , the total loss function value is Loss = LossData + LossPDE Then the loss of the neural network is returned, using Adam (learning rate lr =1e -3 ) optimizer performs iterative optimization of network parameters.

[0095] The iteration exit condition can be the maximum number of iterations or Figure 3 As shown in Loss Less than the preset threshold e When , the iterative inversion stops. According to the dual constraints of measured data and physical equations, the output of the concentration inversion model , from the chaotic and meaningless values ​​in the initial stage, it will gradually converge to the real MNPs concentration distribution that meets the conditions.

[0096] Since for each discrete space coordinate The concentration inversion model will output a corresponding concentration The numerical value is obtained to obtain the inversion results of the magnetic nanoparticle concentration at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data, thereby realizing the inversion of the MNPs concentration distribution, and the following can be obtained: Figure 5 The two-dimensional MNPs concentration distribution is shown.

[0097] The method provided in the above embodiment of the present application uses a physical information neural network (PINN) to invert the concentration distribution of magnetic nanoparticles, and encodes the control equation of the physical problem, that is, the Navier equation in partial differential form, into a fully connected neural network. There is no need to over-simplify the physical equation, and the halo artifact effect is weak. Compared with existing solutions, there is no need to use computer software to perform detailed and complex modeling of the experimental environment (such as magnetic field equipment, various tissue parameters, etc.) to obtain software simulation data, and software simulation is not necessarily accurate and prone to errors. Therefore, this method has higher accuracy and stability. In addition, it also has stronger generalization ability and expansion potential. It only needs to modify the specific physical control equations in the network (such as changing the magnetic force expression caused by different types of magnetic nanoparticles) and the network structure (such as adjusting the number of neurons in the deep neural network, etc.) to apply it to the inversion of the concentration distribution of other magnetic nanoparticles.

[0098] Based on the same inventive concept, the present application also provides a system for implementing the above-mentioned method for inverting the concentration distribution of magnetic nanoparticles. The solution provided by the system is similar to the solution described in the above-mentioned method. In an exemplary embodiment, Figure 6 As shown, a magnetic nanoparticle concentration distribution inversion system is provided, including the following functional modules:

[0099] The magnetic field excitation and displacement detection module is used to use an external magnetic field to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles, and vibration detection is performed on the ultrasonic ultrafast plane wave imaging data to obtain the measured axial vibration displacement data of the magnetic nanoparticles.

[0100] A concentration inversion model construction module is used to encode the Navier equations into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a space-time neural network and a spatial neural network; the space-time neural network is used to use discrete spatial coordinates and discrete time coordinates as model inputs to output axial vibration displacement prediction results and lateral vibration displacement prediction results; the spatial neural network is used to use discrete spatial coordinates as model inputs to output magnetic nanoparticle concentration prediction results; the loss function calculates the total loss using the axial vibration displacement prediction results, lateral vibration displacement prediction results, axial vibration displacement measured data and magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles through an external magnetic field.

[0101] The magnetic nanoparticle concentration distribution inversion module is used to input the discrete spatial coordinates and discrete time coordinates corresponding to the axial vibration displacement measured data as the first input data, and the discrete spatial coordinates corresponding to the axial vibration displacement measured data as the second input data, and input them together into the magnetic nanoparticle concentration inversion model, and use the axial vibration displacement measured data as the label of the spatiotemporal neural network for iterative inversion to obtain the magnetic nanoparticle concentration distribution inversion result; the loss function includes a data-driven loss term and a physical information-driven loss term; the data-driven loss term is determined according to the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined according to the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result and the Navier equation in x direction, z The component form in the direction is determined; the magnetic nanoparticle concentration inversion result is the magnetic nanoparticle concentration prediction result output when the model meets the iteration exit condition after several iterations; for any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration at the corresponding position, and the magnetic nanoparticle concentration distribution inversion result can be determined based on the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data.

[0102] certainly, Figure 6 The architecture shown is only exemplary and can be omitted according to actual needs when implementing different functions. Figure 6 One or at least two components of the system shown.

[0103] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 7 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a magnetic nanoparticle concentration distribution inversion method provided in the previous embodiment can be implemented.

[0104] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0105] In an exemplary embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0106] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0107] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0108] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0109] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0110] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0111] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0112] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for inverting the concentration distribution of magnetic nanoparticles, characterized in that: include: An external magnetic field is used to stimulate the magnetic nanoparticles in the biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles. The ultrasonic ultrafast plane wave imaging data is then subjected to vibration detection to obtain measured axial vibration displacement data of the magnetic nanoparticles. The Navier equations are encoded into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a spatiotemporal neural network and a spatial neural network; the spatiotemporal neural network is used to output axial vibration displacement prediction results and lateral vibration displacement prediction results using discrete spatial coordinates and discrete time coordinates as model inputs; the spatial neural network is used to output magnetic nanoparticle concentration prediction results using discrete spatial coordinates as model inputs; the loss function calculates the total loss using the axial vibration displacement prediction results, the lateral vibration displacement prediction results, the axial vibration displacement measured data, and the magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles by an external magnetic field; The discrete spatial coordinates and discrete time coordinates corresponding to the axial vibration displacement measured data are used as the first input data, and the discrete spatial coordinates corresponding to the axial vibration displacement measured data are used as the second input data, which are inputted into the magnetic nanoparticle concentration inversion model together, and the axial vibration displacement measured data are used as the label of the spatiotemporal neural network for iterative inversion to obtain the magnetic nanoparticle concentration distribution inversion result; the loss function includes a data-driven loss term and a physical information-driven loss term; the data-driven loss term is determined according to the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined according to the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result and the Navier equation; the magnetic nanoparticle concentration inversion result is the magnetic nanoparticle concentration prediction result output when the model satisfies the iteration exit condition after several iterations; for any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration of the corresponding position, and the magnetic nanoparticle concentration distribution inversion result can be determined according to the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data; The physical process of the external magnetic field inducing the vibration of magnetic nanoparticles is controlled by the Navier equation, which is shown as follows: ； in, is the density of biological tissue, is the shear modulus, is the gradient operator, is the Lamé constant, is the displacement field, is the magnetic force per unit volume; the Navier equation is x Direction and z The component form in the direction is used to calculate the physical information driven loss term; the physical information driven loss term is shown as follows: ； in, LossPDE 1 and LossPDE 2 are x Direction and z The physical information of the direction drives the loss sub-item, and the sum of the two is LossPDE = LossPDE 1+ LossPDE 2 is the total physical information driven loss term, u x for x The inversion results of the vibration displacement in the direction, that is, the prediction results of the lateral vibration displacement, u z for z The inversion results of the vibration displacement in the direction, that is, the prediction results of the axial vibration displacement; x and z is the discrete space coordinate, t is the discrete time coordinate, f z is the axial magnetic force; The magnetic force in the axial direction is calculated according to the following formula: ； in, dV is the inversion result of magnetic nanoparticle concentration, is the magnetic susceptibility, is the volume fraction of the core, is the magnetic induction intensity, is the magnetic permeability of biological tissue, is the volume of a single magnetic nanoparticle.

2. The method for inverting the concentration distribution of magnetic nanoparticles according to claim 1, characterized in that: The data-driven loss term is calculated according to the following formula: ； in, LossData is the data-driven loss term, is the predicted result of axial vibration displacement at the discrete spatial coordinates input into the magnetic nanoparticle concentration inversion model, is the measured value of the axial vibration displacement corresponding to the discrete spatial coordinate.

3. The method for inverting the concentration distribution of magnetic nanoparticles according to claim 1, characterized in that: An external magnetic field is used to stimulate the magnetic nanoparticles in biological tissue to produce tiny displacements. At the same time, an ultrasonic device is used to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles. The ultrasonic ultrafast plane wave imaging data is then subjected to vibration detection to obtain measured axial vibration displacement data of the magnetic nanoparticles, specifically including: An external magnetic field is used to stimulate magnetic nanoparticles in biological tissue to produce tiny displacements, and multi-angle composite ultrafast plane wave imaging technology is used to collect ultrasonic ultrafast plane wave imaging data; An autocorrelation algorithm is used to estimate the minute displacements of various points in biological tissue using the ultrasonic ultrafast plane wave imaging data to obtain measured data of the axial vibration displacements of the magnetic nanoparticles; the measured data of the axial vibration displacements are used to calculate the data-driven loss term.

4. The method for inverting the concentration distribution of magnetic nanoparticles according to claim 3, characterized in that: Estimate the measured value of the axial vibration displacement of each point in the biological tissue according to the following formula: ； in, is the measured value of axial vibration displacement, c is the speed of sound in the tissue, f c is the center frequency of the ultrasonic ultrafast plane wave imaging data before demodulation, Q ( m , i -1) is the i −1 frame time, position index is m at Q Component value, I ( m , i ) is the i Frame time and position index are m at I Component value, M is the axial sample range.

5. The method for inverting the concentration distribution of magnetic nanoparticles according to claim 1, characterized in that: An external magnetic field is used to stimulate magnetic nanoparticles in biological tissue to produce tiny displacements, including: A signal generator is used to generate different excitation waveforms, which are applied to a coil with an iron core through a power amplifier to generate a time-varying magnetic field. The time-varying magnetic field of the iron core coil is controlled to act on the magnetic nanoparticles in the biological tissue, so that the magnetic nanoparticles generate a small displacement or vibration under the excitation of the magnetic field.

6. A magnetic nanoparticle concentration distribution inversion system, characterized in that: include: A magnetic field excitation and displacement detection module is used to use an external magnetic field to excite magnetic nanoparticles in biological tissue to produce tiny displacements, while simultaneously using an ultrasonic device to collect ultrasonic ultrafast plane wave imaging data of the magnetic nanoparticles, and to perform vibration detection on the ultrasonic ultrafast plane wave imaging data to obtain measured axial vibration displacement data of the magnetic nanoparticles; A concentration inversion model construction module is used to encode the Navier equations into the loss function of the physical information neural network to construct a magnetic nanoparticle concentration inversion model; the magnetic nanoparticle concentration inversion model includes a spatiotemporal neural network and a spatial neural network; the spatiotemporal neural network is used to use discrete spatial coordinates and discrete time coordinates as model inputs to output axial vibration displacement prediction results and lateral vibration displacement prediction results; the spatial neural network is used to use discrete spatial coordinates as model inputs to output magnetic nanoparticle concentration prediction results; the loss function calculates the total loss using the axial vibration displacement prediction results, the lateral vibration displacement prediction results, the axial vibration displacement measured data, and the magnetic nanoparticle concentration prediction results; the Navier equations are used to control the physical process of inducing vibration of magnetic nanoparticles through an external magnetic field; A magnetic nanoparticle concentration distribution inversion module is configured to input the discrete spatial coordinates and discrete time coordinates corresponding to the axial vibration displacement measured data as first input data, and the discrete spatial coordinates corresponding to the axial vibration displacement measured data as second input data, and input both of them into the magnetic nanoparticle concentration inversion model, and perform iterative inversion using the axial vibration displacement measured data as labels of a spatiotemporal neural network to obtain a magnetic nanoparticle concentration distribution inversion result; the loss function comprises a data-driven loss term and a physical information-driven loss term; the data-driven loss term is determined based on the error between the axial vibration displacement prediction result and the axial vibration displacement measured data; the physical information-driven loss term is determined based on the magnetic nanoparticle concentration prediction result, the lateral vibration displacement prediction result, the axial vibration displacement prediction result, and the Navier equation; the magnetic nanoparticle concentration inversion result is a magnetic nanoparticle concentration prediction result output when the model satisfies an iteration exit condition after several iterations; for any discrete spatial coordinate, the magnetic nanoparticle concentration inversion model outputs the concentration at the corresponding position, and the magnetic nanoparticle concentration distribution inversion result can be determined based on the magnetic nanoparticle concentration inversion results at all discrete spatial coordinates in the ultrasonic ultrafast plane wave imaging data; The physical process of the external magnetic field inducing the vibration of magnetic nanoparticles is controlled by the Navier equation, which is shown as follows: ； in, is the density of biological tissue, is the shear modulus, is the gradient operator, is the Lamé constant, is the displacement field, is the magnetic force per unit volume; the Navier equation is x Direction and z The component form in the direction is used to calculate the physical information driven loss term; the physical information driven loss term is shown as follows: ； in, LossPDE 1 and LossPDE 2 are x Direction and z The physical information of the direction drives the loss sub-item, and the sum of the two is LossPDE = LossPDE 1+ LossPDE 2 is the total physical information driven loss term, u x for x The inversion results of the vibration displacement in the direction, that is, the prediction results of the lateral vibration displacement, u z for z The inversion results of the vibration displacement in the direction, that is, the prediction results of the axial vibration displacement; x and z is the discrete space coordinate, t is the discrete time coordinate, f z is the axial magnetic force; The magnetic force in the axial direction is calculated according to the following formula: ； in, dV is the inversion result of magnetic nanoparticle concentration, is the magnetic susceptibility, is the volume fraction of the core, is the magnetic induction intensity, is the magnetic permeability of biological tissue, is the volume of a single magnetic nanoparticle.

7. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the magnetic nanoparticle concentration distribution inversion method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for inverting the concentration distribution of magnetic nanoparticles according to any one of claims 1 to 5 is implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for inverting the concentration distribution of magnetic nanoparticles according to any one of claims 1 to 5 is implemented.

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