A method of modeling a radio frequency transfer function of an active implantable medical device

Abstract

This invention relates to the field of magnetic resonance imaging technology, specifically disclosing a method for modeling the radio frequency transfer function of active implantable medical devices. This method constructs a suitable neural network algorithm and, based on learning important features such as the geometric parameters of the active implantable medical device and the characteristics of the surrounding tissue, enables it to quickly and effectively predict the radio frequency transfer function of the active implantable medical device in homogeneous and heterogeneous tissue environments. This overcomes the limitations of traditional in vitro experimental methods, such as low efficiency, high experimental costs, and the inability to simulate homogeneous tissues, providing a new option for modeling the radio frequency transfer function of active implantable medical devices.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance imaging technology, and more specifically, to a method for modeling the radio frequency transfer function of an active implantable medical device. Background Technology

[0002] Magnetic resonance imaging (MRI) has become one of the most important and widely used medical imaging tools in the clinical diagnosis of many diseases, with approximately 60 million MRI scans performed worldwide each year. With the aging global population and the prevalence of various chronic diseases, patients wearing active implantable medical devices (AIMDs) are now ubiquitous. Furthermore, with the widespread clinical application of MRI and the dramatic increase in cardiac-based treatments, it is estimated that 50-75% of patients wearing cardiac assist devices will require an MRI during the duration of their device use. Similarly, it is estimated that 56-57% of patients wearing deep brain stimulators (DBS) will require an MRI within five years of implantation, and 66-75% within ten years.

[0003] However, during MRI scans, the radiofrequency (RF) field induces currents in both the body and the implant. These induced currents deposit locally in the tissue surrounding the implant, causing elevated tissue temperatures and potentially irreversible damage, especially to patients wearing AIMDs. These potential safety risks prevent AIMD patients from undergoing MRI scans for diagnosis. Extensive research has been dedicated to quantifying and mitigating the problems of radiofrequency heating. For example, ISO / TS 10974 proposes a four-tier method to assess the heating of tissues surrounding the implant, with the third (Tier-3) and fourth (Tier-4) tiers suitable for AIMDs with longer electrical lengths. Tier-4 heavily relies on electromagnetic (EM) simulations, requiring high-precision modeling of details of the human body, implant structure, and MRI coil characteristics. This consumes significant computational time and necessitates high-power computing clusters. On the other hand, Tier-3 is based on the radio frequency transfer function model of AIMD. This model can be used to separate the interaction between the implant and the radio frequency field (represented by the transfer function) and the interaction between the human body and the radio frequency field (represented by the tangential incident electric field E). tan (This indicates) decoupling. With a suitable RF transfer function, this is achieved by integrating the AIMD transfer function and E... tan It is easy to assess the radiofrequency induced deposition power (Po) in human tissue near AIMD electrodes. depCurrently, the main methods for modeling the transfer function of implants include piecewise excitation, injection networks, and methods combining radio frequency magnetic fields and transceiver phase distribution. These methods not only require complex and expensive measurement equipment, but the tissue environment near the AIMD is also greatly simplified (using homogeneous tissue simulation fluid as a substitute), which may lead to a significant increase in measurement uncertainty, especially for AIMDs embedded in complex tissue spaces with different dielectric properties, such as superficial or partially implanted medical devices.

[0004] Therefore, there is an urgent need to propose a method for modeling the radio frequency transfer function of active implantable medical devices in magnetic resonance imaging, which can simultaneously and reliably evaluate the radio frequency transfer function of AIMD in different tissue environments, and then evaluate the radio frequency induced heating of AIMD during MRI examinations. Summary of the Invention

[0005] The purpose of this invention is to propose a radio frequency transfer function modeling method for active implantable medical devices (AIMDs), which can simultaneously and reliably evaluate the radio frequency transfer function of AIMDs in different tissue environments, and then evaluate the radio frequency induced heating of AIMDs during MRI examinations in patients.

[0006] This invention provides a method for modeling the radio frequency transfer function of an active implantable medical device, comprising the following steps:

[0007] a. Modeling parameters of active implantable medical devices: Collect the range of the lead length L, electrode tip length l, lead radius r, and lead insulation thickness t of the active implantable medical device, and take the appropriate values ​​within this range.

[0008] Establish a parameter model for active implantable medical devices by adjusting the step size;

[0009] b. Modeling the surrounding tissue of the active implantable medical device: collecting electrical conductivity data from the surrounding tissue.

[0010] The rate σ and relative permittivity ∈ r a. Establish a model of the surrounding environment of the active implantable medical device; c. Use electromagnetic simulation to model and acquire the radio frequency transfer function of the active implantable medical device, and analyze the acquired data.

[0011] The obtained radio frequency transfer function is normalized, as shown in equation (1):

[0012]

[0013] d. Select appropriate parameters to fit the RF transfer function to obtain the RF transfer function dataset. The RF transfer function is represented by the equivalent wavenumber k and the equivalent impedance Z, and the specific expression is shown in equation (2):

[0014]

[0015] Where S(l) is the radio frequency transfer function, C is a constant, k is the equivalent wavenumber, Z is the equivalent impedance, and L is...

[0016] The wire length, l is the electrode head length, and k and Z are represented as shown in equation (3) and equation (4):

[0017] k = k r +j·k i (3);

[0018] Z = Z r +j·Z i (4);

[0019] e. Establish a neural network model. The inputs to the neural network model are the conductor length L, electrode tip length l, conductor radius r, conductor insulation thickness t, and the conductivity σ and relative permittivity ε of the surrounding environment. r The output is k r k i Z r Z i A neural network model was trained using a dataset of radio frequency transfer functions.

[0020] Optionally, in step b, the surrounding environment tissue is either homogeneous or heterogeneous. The heterogeneous tissue is divided into several segments along the length of the active implantable medical device, each segment representing the same or different tissues, and including at least two different tissues.

[0021] Optionally, in step c, the electromagnetic simulation uses the finite-difference time-domain algorithm to model the radio frequency transfer function of the active implantable medical device.

[0022] Optionally, in step e, the activation function of the neurons in the neural network model is the SeLU function, and the expression of the SeLU function is shown in equation (5):

[0023]

[0024] Where λ and α are constants.

[0025] Optionally, in step e, the loss function of the neural network model is the root mean square error (MSE), and the expression of the root mean square error function is shown in equation (6):

[0026]

[0027] Where n is the number of data samples, y i For k r k i Zr Z i The target value was obtained through electromagnetic simulation. For k r k i Z r Z i Predicted values ​​obtained through neural network algorithms.

[0028] Optionally, in step e, the output expression of each neuron in the neural network model is shown in equation (7):

[0029]

[0030] in, Here, A is the input to the neuron, B is the weight of the neuron, and A is the bias of the neuron. f(·) represents the neuron's output in the current layer, which also serves as the input to the next layer.

[0031] Optionally, in step e, the backpropagation algorithm is used to correct the weights of each node in the neuron in each iteration of the neural network until the error is within an acceptable range. The correction expression of the backpropagation algorithm is shown in equation (8):

[0032]

[0033] Among them, y n This represents the equivalent wavenumber k and equivalent impedance Z of the radio frequency transfer function obtained from electromagnetic simulation. δ represents the value predicted by each layer of the neural network. n A represents the error in the result obtained by the node. n Let A represent the weight of a node. ′ n η represents the new weights of the nodes obtained by the backpropagation algorithm, and η represents the learning rate.

[0034] Optionally, in step e, the stability and reliability of the neural network are verified by 5-fold cross-validation. The stability and reliability of the neural network are represented by the normalized root mean square error (NMSE), as shown in equation (9):

[0035]

[0036] Where n is the number of data samples, y i For k r k i Z r Z i The target value obtained through electromagnetic simulation. For k r ki Z r Z i Predicted values ​​obtained through neural network algorithms.

[0037] Optionally, in step e, for homogeneous tissue, the neural network consists of one input layer, five hidden layers, and one output layer.

[0038] Optionally, in step e, for non-homogeneous tissue, the neural network consists of one input layer, eight hidden layers, and one output layer.

[0039] In summary, the present invention has at least one of the following beneficial effects:

[0040] 1. This invention differs from traditional experimental methods for testing the radio frequency transfer function (RF transfer function) of active implantable medical devices. It innovatively introduces machine learning methods into the modeling of the RF transfer function of active implantable medical devices, designing a neural network model capable of rapidly and effectively predicting the RF transfer function. With a trained model, only the geometric parameters of the active implantable medical device (lead length L, electrode tip length l, lead radius r, lead insulation thickness t) and the electrical parameters of the surrounding tissue (conductivity σ and relative permittivity ε) are needed. r This method can predict and reconstruct the radio frequency transfer function, which is faster, more efficient, and more convenient than traditional methods.

[0041] 2. This invention uses two key parameters, equivalent wavenumber k and equivalent impedance Z, to represent the radio frequency transfer function of an active implantable medical device. For the same implant, different tissue distributions around it will change the radio frequency response. Therefore, how to enable the neural network to learn this feature of tissue distribution is a challenge. However, fitting the radio frequency transfer function of the implant with equivalent wavenumber k and equivalent impedance Z can cleverly solve this problem, because the change in the distribution of surrounding tissue will also be reflected in the equivalent wavenumber k and equivalent impedance Z of the whole system of implant and surrounding tissue.

[0042] 3. In traditional experimental testing methods for active implantable medical devices, the surrounding tissue is usually greatly simplified, using a homogeneous tissue material as a substitute. This often introduces high uncertainty for medical devices with relatively complex implantation environments, as the distribution of tissue around the implant is also an important factor affecting its radio frequency transfer function. This invention considers both homogeneous and complex non-homogeneous implantation environments, and performs segmented modeling of non-homogeneous tissue. By designing and training a neural network model, it can achieve good predictive performance for active implantable medical devices in non-homogeneous tissue environments, improving the accuracy of radio frequency transfer function modeling for active implantable medical devices in non-homogeneous tissue environments and better reflecting clinical practice. Attached Figure Description

[0043] Figure 1 These are modeling illustrations of the AIMD and its surrounding tissue according to the present invention, (a) in a homogeneous tissue environment of Example 1 and (b) in a non-homogeneous tissue environment of Example 2.

[0044] Figure 2 The structures of the feedback neural network designed in this invention are shown in (a) and (b) respectively. (a) shows the homogeneous structure of Example 1 and (b) shows the non-homogeneous structure of Example 2.

[0045] Figure 3 This is a comparison between the predicted k and Z and the simulation results under the homogeneous case (a) of Example 1 and the non-homogeneous case (b) of Example 2 of the present invention.

[0046] Figure 4 This is the training history of the homogeneous prediction model (a) of Embodiment 1 and the non-homogeneous prediction model (b) of Embodiment 2 of the present invention, represented by loss and duration.

[0047] Figure 5 This is a comparison of the radio frequency transfer functions predicted by electromagnetic simulation and neural network model under the homogeneous case (a) of Embodiment 1 and the non-homogeneous case (b) of Embodiment 2 of the present invention. Detailed Implementation

[0048] This invention provides a method for modeling the radio frequency transfer function of an active implantable medical device. To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention is further described in detail below. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention.

[0049] This invention provides a method for modeling the radio frequency transfer function of active implantable medical devices. This method constructs a suitable neural network (ANN) algorithm and learns important features such as the parameters of the active implantable medical device and the characteristics of the surrounding tissue. This enables the method to quickly and effectively predict the radio frequency transfer function of the active implantable medical device in homogeneous and heterogeneous tissue environments. This breaks through the limitations of traditional in vitro experimental methods, such as low efficiency, high experimental cost, and the inability to simulate homogeneous tissues, and provides a new option for modeling the radio frequency transfer function of active implantable medical devices.

[0050] Example 1

[0051] This invention provides a method for modeling the radio frequency transfer function of an active implantable medical device, comprising the following steps:

[0052] a. Modeling the parameters of the active implantable medical device. In Example 1, the active implantable medical device (implant) uses a cardiac pacemaker. The pacemaker's electrode head and leads are as follows... Figure 1 As shown in Table 1, the range of lead length L, electrode head length l, lead radius r, and lead insulation layer thickness t of the active implantable medical device were collected. Within this range, an appropriate step size was selected to establish the parameter model of the active implantable medical device.

[0053] Table 1: Parametric model of implants.

[0054]

[0055] b. Modeling the surrounding tissue of active implantable medical devices, such as... Figure 1 As shown in (a), the surrounding environment tissue in Example 1 is homogeneous tissue. Homogeneous tissue refers to a single tissue along the length of the implant. The surrounding environment tissue in Example 1 was modeled as a homogeneous tissue material with an electrical conductivity of σ = 0.4–1.2 S / m (step size of 0.2 S / m) and a relative permittivity ∈ r The range is 10 to 80 (step size is 10). c. Electromagnetic simulation is used to model and collect the radio frequency transfer function of the active implantable medical device. The finite-difference time-domain (FDTD) solver in Sim4Life v6.2 (ZMT Zurich MedTech, Zurich, Switzerland) is used to perform computational electromagnetic (CEM) simulation. Unlike the traditional method of segmented excitation to measure the transfer function, the injection method based on antenna reciprocity theory is used to capture the current distribution around the implant as its radio frequency transfer function. The slender implantable medical device under radio frequency exposure can be regarded as a typical linear antenna. Based on antenna reciprocity theory, an ideal signal source can be placed at one end of the electrode head of the active implantable medical device to avoid coupling with the implant electrode and changing the characteristic impedance and transfer function characteristics of the implant. A current sensor is placed around the active implantable medical device to collect its current distribution under radio frequency action as its corresponding radio frequency transfer function and normalize it as shown in Equation (1):

[0056]

[0057] d. Fit the RF transfer function using appropriate parameters to obtain the RF transfer function dataset. Based on the analytical solution of the current distribution along a typical transmission line, the transfer function of an active implantable medical device can be represented by its equivalent wavenumber k and equivalent impedance Z:

[0058]

[0059] Where S(l) is the radio frequency transfer function, C is a constant (5000 in Example 1), k is the equivalent wavenumber, Z is the equivalent impedance, L is the wire length, and l is the electrode tip length. Since the equivalent wavenumber k is a complex wavenumber and the equivalent impedance Z is a complex impedance, for ease of subsequent neural network algorithm design, they are represented as k r k i Z r Z i , which are the real and imaginary parts of k and Z, respectively. The specific representations of k and Z are shown in equation (3) and equation (4):

[0060] k = k r +j·k i (3)

[0061] Z = Z r +j·Z i (4)

[0062] In Example 1, the MRI operating frequency was 128MHz, corresponding to a magnetic field of 3T. Through electromagnetic simulation modeling, 532 sets of radio frequency transfer functions (RF functions) for homogeneous tissue were obtained. These RF transfer functions were normalized, and curve fitting was performed to obtain a dataset of 532 sets of RF transfer functions in the environment surrounding the homogeneous tissue. The dataset includes the equivalent wavenumber k (derived from k). r and k i (represented by) and equivalent impedance Z (by Z) r and Z i express).

[0063] e. A neural network model is established for the homogeneous structure of Example 1. The inputs to the neural network model are the wire length L, electrode tip length l, wire radius r, wire insulation layer thickness t, and the conductivity σ and relative permittivity ε of the surrounding environment. r The output is k r k i Z r Z i .like Figure 2 (a) shows the overall architecture of the machine learning algorithm designed for a homogeneous environment. Implemented using Python and TensorFlow, a fully connected network based on Keras sequences has been designed for the homogeneous environment, considering the implant length L, electrode length l, wire radius r, insulation thickness t, and the conductivity σ and dielectric constant ε of the surrounding tissue. r The input is used as the input to the neural network, and the output is the equivalent wavenumber k and the equivalent impedance Z. The neural network consists of one input layer, five hidden layers, and one output layer. The number of neurons in each hidden layer is 20-20-10-10-10. The neuron activation function is SeLU, and the expression of the SeLU function is shown in equation (5):

[0064]

[0065] Where, λ SeLU =1.0507, α SeLU =1.6733.

[0066] The loss function is MSE (root mean square error function), and the expression of the root mean square error function is shown in equation (6):

[0067]

[0068] Where n is the number of data samples, specifically 532, y i For k r k i Z r Z i The target value was obtained through electromagnetic simulation. For k r k i Z r Z i Predicted values ​​obtained through neural network algorithms.

[0069] The nonlinear relationship between input and output is accurately characterized by weights and biases that are iteratively adjusted based on the training data. For each iteration, the output expression of each neuron in each layer is shown in Equation (7):

[0070]

[0071] in, Here, A is the input to the neuron, B is the weight of the neuron, and A is the bias of the neuron. f(·) represents the neuron's output in the current layer, which also serves as the input to the next layer.

[0072] Based on the aforementioned neural network model, the radio frequency transfer function dataset obtained from electromagnetic simulation was used to train the neural network. In each iteration, the backpropagation algorithm was used to correct the weights of each node in the neurons until the error was within an acceptable range. The correction expression for the backpropagation algorithm is shown in equation (8):

[0073]

[0074] Among them, y n The equivalent wavenumber k and equivalent impedance Z are obtained by fitting the radio frequency transfer function obtained from electromagnetic simulation. r k i Z r Z i express, δ represents the value predicted by each layer of the neural network. n A represents the error in the result obtained by this node. n Let A represent the weight of a node. ′ n This represents the new weights of the node obtained by the backpropagation algorithm, and η represents the learning rate, which is adaptively adjusted based on the current gradient magnitude using the Adam optimizer. A BatchNormalization layer is added after each fully connected layer to address the covariance drift problem.

[0075] The 532 sets of homogeneous data were randomly divided into training set (60%), validation set (20%) and test set (20%). The designed homogeneous neural network model was trained, and the stability and reliability of the model were verified by 5-fold cross-validation. The optimal model was selected from the results. Its stability and reliability are represented by NMSE (normalized root mean square error), and the expression is shown in Equation (9).

[0076]

[0077] Where n is the number of data samples, specifically 105, y i For k r k i Z r Z i The target value obtained through electromagnetic simulation. For k r k i Z r Z i Predicted values ​​using neural networks.

[0078] like Figure 3 As shown in (a), the final model's prediction performance for k and Z on the test dataset is displayed under homogeneous conditions. The average Pearson correlation coefficient under homogeneous conditions is r≈0.99. The results indicate that the designed neural network models achieve very good prediction performance under homogeneous conditions. Figure 4 (a) represents the training loss of the neural network model in the homogeneous case. The homogeneous neural network algorithm model shows good performance because the homogeneous model has more advantages. Due to the lower nonlinearity, the training loss of the homogeneous neural network algorithm model is greatly reduced.

[0079] After training the neural network model, a prediction model for the radio frequency transfer function of active implantable medical devices under homogeneous conditions is obtained. The wavenumber k and impedance Z can be predicted based on the implant's structure and surrounding tissue environment. The radio frequency transfer function can then be reconstructed according to formula (2). The predicted transfer function is then compared and verified with the transfer function obtained from electromagnetic simulation. The equivalent wavenumber and impedance of four homogeneous cardiac pacemakers of different lengths (the distribution of their surrounding tissues is summarized in Table 2) are predicted using the homogeneous neural network algorithm model. The radio frequency transfer function is reconstructed based on the prediction results, as shown in Table 2. Figure 5 (a) As shown by the dashed line, and with the results of its electromagnetic simulation, as follows: Figure 5 (a) As shown by the solid line, the comparison results show that the RF transfer function modeled by the neural network algorithm model matches the target RF transfer function well.

[0080] Table 2: Homogeneous tissue distribution in four groups of pacemakers of different lengths:

[0081]

[0082] Example 2

[0083] This invention provides a method for modeling the radio frequency transfer function of an active implantable medical device, comprising the following steps:

[0084] a. Modeling the parameters of the active implantable medical device. In Example 2, the active implantable medical device (implant) uses a cardiac pacemaker. The pacemaker's electrode head and leads are as follows... Figure 1 As shown in Table 3, the range of lead length L, electrode head length l, lead radius r, and lead insulation layer thickness t of the active implantable medical device were collected. Within this range, an appropriate step size was selected to establish the parameter model of the active implantable medical device.

[0085] Table 3: Parametric model of implants.

[0086]

[0087] b. Modeling the surrounding tissue of active implantable medical devices, such as... Figure 1 As shown in (b), the surrounding environment tissue in Example 2 is heterogeneous tissue. Heterogeneous tissue refers to the surrounding environment tissue along the length of the implant consisting of two or more tissues. The heterogeneous tissue is divided into several segments along the length of the active implantable medical device. Each segment represents the same or different tissues and includes at least two different tissues. Each tissue segment is randomly generated as the tissue category in Table 4. The conductivity σ and relative permittivity ∈ of the surrounding environment tissue are determined. r Furthermore, the remainder of the phantom was set as a high dielectric constant medium (HPM, σ = 0.47 S / m, ∈r =78).

[0088] Table 4: Different tissues used under non-homogeneous conditions.

[0089]

[0090]

[0091] c. Electromagnetic simulation was used to model and collect the radio frequency transfer function of the active implantable medical device. The finite-difference time-domain (FDTD) solver in Sim4Life v6.2 (ZMT Zurich MedTech, Zurich, Switzerland) was used to perform computational electromagnetic (CEM) simulation. Unlike the traditional method of segmented excitation to measure the transfer function, the injection method based on antenna reciprocity theory was used to capture the current distribution around the implant as its radio frequency transfer function. The slender implantable medical device under radio frequency exposure can be regarded as a typical linear antenna. Based on antenna reciprocity theory, an ideal signal source can be placed at one end of the electrode head of the active implantable medical device to avoid coupling with the implant electrode and changing the characteristic impedance and transfer function characteristics of the implant. A current sensor is placed around the active implantable medical device to collect its current distribution under radio frequency action as its corresponding radio frequency transfer function, and normalization is performed as shown in Equation (1):

[0092]

[0093] d. Select appropriate parameters to fit the radio frequency transfer function. Based on the analytical solution of the current distribution along a typical transmission line, the transfer function of an active implantable medical device can be represented by its equivalent wavenumber k and equivalent impedance Z:

[0094]

[0095] Where S(l) is the radio frequency transfer function, C is a constant (5000 in Example 2), k is the equivalent wavenumber, Z is the equivalent impedance, L is the wire length, and l is the electrode tip length. Since the equivalent wavenumber k is a complex wavenumber and the equivalent impedance Z is a complex impedance, for ease of subsequent neural network algorithm design, they are expressed as k r k i Z r Z i , which are the real and imaginary parts of k and Z, respectively. The specific representations of k and Z are shown in equation (3) and equation (4):

[0096] k = k r +j·k i (3)

[0097] Z = Zr +j·Z i (4)

[0098] In Example 2, the MRI operating frequency was 128MHz, corresponding to a magnetic field of 3T. Through electromagnetic simulation modeling, 592 sets of non-homogeneous radio frequency transfer functions were obtained. These radio frequency transfer functions were normalized, and curve fitting was performed to obtain a dataset of 592 sets of radio frequency transfer functions in the environment surrounding non-homogeneous tissue. The dataset includes the equivalent wavenumber k (derived from k...). r and k i (represented by) and equivalent impedance Z (by Z) r and Z i express).

[0099] e. A neural network model is established for the non-homogeneous structure of Example 2. The inputs to the neural network model are the wire length L, electrode tip length l, wire radius r, wire insulation layer thickness t, and the conductivity σ and relative permittivity ε of the surrounding environment. r The input conductivity σ and relative permittivity ε r This includes the conductivity σ and relative permittivity ε corresponding to different tissues. r The output is k r k i Z r Z i .like Figure 2 (b) shows the overall architecture of the machine learning algorithm designed for a non-homogeneous environment. Implemented using Python and TensorFlow, a fully connected network based on Keras sequences has been designed for non-homogeneous environments, considering factors such as implant length L, electrode length l, wire radius r, insulation thickness t, and the conductivity σ and dielectric constant ε of the surrounding tissue. r The input is used as the input to the neural network, and the output is the equivalent wavenumber k and the equivalent impedance Z. The neural network consists of one input layer, eight hidden layers, and one output layer. The number of neurons in each hidden layer is 140-120-100-80-60-40-20-10. The activation function of the neurons is the SeLU function, and the expression of the SeLU function is shown in equation (5):

[0100]

[0101] Where, λ SeLU =1.0507, α SeLU =1.6733.

[0102] The loss function is MSE (root mean square error function), and the expression of the root mean square error function is shown in equation (6):

[0103]

[0104] Where n is the number of data samples, specifically 592, y i For k r k i Z r Z i The target value was obtained through electromagnetic simulation. For k r k i Z r Z i Predicted values ​​obtained through neural network algorithms.

[0105] The nonlinear relationship between input and output is accurately characterized by weights and biases that are iteratively adjusted based on the training data. For each iteration, the output expression of each neuron in each layer is shown in Equation (7):

[0106]

[0107] in, Here, A is the input to the neuron, B is the weight of the neuron, and A is the bias of the neuron. f(·) represents the neuron's output in the current layer, which also serves as the input to the next layer.

[0108] Based on the aforementioned neural network model, the radio frequency transfer function dataset obtained from electromagnetic simulation was used to train the neural network. In each iteration, the backpropagation algorithm was used to correct the weights of each node in the neurons until the error was within an acceptable range. The correction expression for the backpropagation algorithm is shown in equation (8):

[0109]

[0110] Among them, y n The equivalent wavenumber k and equivalent impedance Z are obtained by fitting the radio frequency transfer function obtained from electromagnetic simulation. r k i Z r Z i express, δ represents the value predicted by each layer of the neural network. n A represents the error in the result obtained by this node. n Let A represent the weight of a node. ′ n This represents the new weights of the node obtained by the backpropagation algorithm, and η represents the learning rate, which is adaptively adjusted based on the current gradient magnitude using the Adam optimizer. A BatchNormalization layer is added after each fully connected layer to address the covariance drift problem.

[0111] The 592 sets of non-homogeneous data were randomly divided into training set (60%), validation set (20%) and test set (20%). The designed homogeneous neural network model was trained, and the stability and reliability of the model were verified by 5-fold cross-validation. The optimal model was selected from the results. Its stability and reliability are represented by NMSE (normalized root mean square error), and the expression is shown in Equation (9).

[0112]

[0113] Where n is the number of data samples, specifically 115, y i For k r k i Z r Z i The target value obtained through electromagnetic simulation. For k r k i Z r Z i Predicted values ​​using neural networks.

[0114] like Figure 3 As shown in (b), the final model's prediction performance for k and Z on the test dataset is displayed under homogeneous conditions. The average Pearson correlation coefficient under non-homogeneous conditions is r≈0.98. The results indicate that the designed neural network models achieve very good prediction performance under non-homogeneous conditions, consistent with those in Example 1. Figure 3 (a) The homogeneous neural network algorithm model in Example 1 shows better performance than the non-homogeneous neural network algorithm model. This is because the homogeneous model has more advantages. Due to the more complex tissue distribution under non-homogeneous conditions, its nonlinearity is higher. This can also be seen from... Figure 4 It is easy to see from (a) and (b) that, due to the lower nonlinearity, the training loss of the homogeneous neural network algorithm model is significantly reduced compared to the training loss of the non-homogeneous neural network model.

[0115] After training the neural network model, a prediction model for the radio frequency transfer function of active implantable medical devices under non-homogeneous conditions is obtained. The wavenumber k and impedance Z can be predicted based on the implant's structure and surrounding tissue environment. The radio frequency transfer function can then be reconstructed according to formula (2). The predicted transfer function and the transfer function obtained from electromagnetic simulation are then compared and verified. The equivalent wavenumber and impedance of four groups of non-homogeneous cardiac pacemakers of different lengths (the distribution of their surrounding tissues is summarized in Table 5) are predicted using the non-homogeneous neural network algorithm model. The radio frequency transfer function is reconstructed based on the prediction results, such as... Figure 5 (b) As shown by the dashed line, and with the results of its electromagnetic simulation, as follows: Figure 5(b) As shown by the solid line, the comparison results show that the RF transfer function modeled by the neural network algorithm model matches the target RF transfer function well.

[0116] Table 5: Distribution of heterogeneous tissue environment in four groups of cardiac pacemakers of different lengths:

[0117]

[0118] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method of modeling a radio frequency transfer function of an active implantable medical device, the method comprising: Includes the following steps: a. Model the parameters of the active implantable medical device: Collect the ranges of the lead length , the electrode tip length , the lead radius , and the lead insulation thickness of the active implantable medical device, take appropriate steps within the ranges, and establish a parameter model of the active implantable medical device; b. Modeling the surrounding tissue of active implantable medical devices: collecting the conductivity of the surrounding tissue. Relative permittivity To establish a model of the surrounding environment of active implantable medical devices; c. Electromagnetic simulation is used to model and acquire the radio frequency transfer function of active implantable medical devices. The acquired radio frequency transfer function is then normalized, as shown in the equation. : d. Select appropriate parameters to fit the RF transfer function to obtain the RF transfer function dataset. The RF transfer function is composed of the equivalent wavenumber. and equivalent impedance The specific expression is as follows: : in It is the radio frequency transfer function. constant, Equivalent wavenumber, Equivalent impedance, Wire length, , Represented as follows : e. Establish a neural network model, with the wire length as the input. Electrode head length , conductor radius and wire insulation thickness electrical conductivity of surrounding environment and relative permittivity The output is , , , A neural network model was trained using a dataset of radio frequency transfer functions.

2. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1, characterized in that, In step b, the surrounding environment tissue is either homogeneous or heterogeneous. The heterogeneous tissue is divided into several segments along the length of the active implantable medical device. Each segment represents the same or different tissues and includes at least two different tissues.

3. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1 or 2, characterized in that, In step c, the electromagnetic simulation uses the finite-difference time-domain algorithm to model the radio frequency transfer function of the active implantable medical device.

4. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1 or 2, characterized in that, In step e, the activation function of the neurons in the neural network model is the SeLU function. in, 5. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1 or 2, characterized in that, In step e, the loss function of the neural network model adopts the root mean square error (RMSE) function. Where n is the number of data samples, , , , The target value was obtained through electromagnetic simulation. , , , Predicted values ​​obtained through neural network algorithms.

6. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1 or 2, characterized in that, In step e, the output expression of each neuron in the neural network model. in, For the input of neurons, These are the weights of the neurons. It's the bias of neurons. f(·) represents the neuron's output in the current layer, which also serves as the input to the next layer.

7. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 6, characterized in that, In step e, each iteration of the neural network uses the backpropagation algorithm to correct the weights of each node in the neuron until the error is within an acceptable range. The correction expression of the backpropagation algorithm is... in, The equivalent wavenumber of the radio frequency transfer function obtained from electromagnetic simulation. and equivalent impedance , This represents the value predicted by each layer of the neural network. This represents the error in the result obtained by the node. Represents the weight of a node. This represents the new weight of the node obtained by the backpropagation algorithm. .

8. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 1 or 2, characterized in that, In step e, 5-fold cross-validation is used to verify the stability and reliability of the neural network. The stability and reliability of the neural network are represented by the normalized root mean square error (NMSE), expressed as follows: Where n is the number of data samples, , , , The target value obtained through electromagnetic simulation. , , , Predicted values ​​obtained through neural network algorithms.

9. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 2, characterized in that, In step e, for homogeneous tissue, the neural network consists of one input layer, five hidden layers, and one output layer.

10. The method for modeling the radio frequency transfer function of an active implantable medical device according to claim 2, characterized in that, In step e, for heterogeneous tissue, the neural network consists of one input layer, eight hidden layers, and one output layer.

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