Electronic device for tracking cell trajectory in Positron Emission Tomography images and tracking method thereof

Abstract

A method for tracking the movement path of a cell in a positron emission tomography (PET) image performed by an electronic device according to an embodiment of the present invention may include: (a) receiving PET information including the coordinates and timestamp of a PET detector when gamma rays are detected; (b) setting a loss function for a path determination matrix based on the coordinates and the estimated positions of the cell; (c) calculating a gradient of the loss function using backpropagation; (d) updating the path determination matrix using the calculated gradient; (e) repeating steps (c) and (d) to identify a first path determination matrix that minimizes the loss function; and (f) identifying the movement path of the cell using the first path determination matrix.

Description

Technology Field

[0001] The present invention relates to an electronic device for tracking the movement path of cells in positron emission tomography images and a tracking method thereof. Background Technology

[0002] Advancements in molecular imaging algorithms and tools have deepened insights into molecular dynamics within complex biological systems. One such innovation is Cell GPS, an algorithm designed to track the trajectory of a single cell in vivo using Positron Emission Tomography (PET).

[0003] Cell GPS is an algorithm that reconstructs cell migration paths with high accuracy by utilizing data from radiolabeled cells captured via PET scans. Importantly, Cell GPS has undergone in vivo testing and demonstrated sufficient capability for path tracking under low radiation conditions without damaging cellular activity. Tracking radiolabeled cancer cells in vivo using Cell GPS can deepen our understanding of cancer metastasis. Furthermore, by tracking immune cells and stem cells injected into patients, medical professionals can predict treatment efficacy with greater accuracy.

[0004] Despite its significant potential, the computational speed of the Cell GPS algorithm remains a critical bottleneck. To improve the accuracy of Cell GPS, it is necessary to optimize hyperparameters for each condition, such as various radiation levels, cell migration, and PET environments. Since finding optimal hyperparameters enhances algorithm accuracy, hyperparameter tuning is a critical process in model setup.

[0005] However, the hyperparameter tuning process often requires analyzing hundreds of data points, which is time-consuming and acts as a limitation. Therefore, there is a need for measures to accelerate the computational speed of the Cell GPS algorithm. (Prior Art 1) PET Trajectory Reconstruction Technique for Single-Cell Tracking, IEEE Transactions on Medical Imaging, 2015, 34(4), pp.994-1003 (Nov. 21, 2014) The problem to be solved

[0006] The objective of the present invention is to provide an electronic device and a tracking method for tracking the movement path of cells in positron emission tomography images at a faster computational speed.

[0007] The object of the present invention is to provide an electronic device and a tracking method that more accurately track the movement path of cells in positron emission tomography images. means of solving the problem

[0008] A method for tracking the movement path of a cell in a positron emission tomography (PET) image performed by an electronic device according to an embodiment of the present invention may include: (a) receiving PET information including the coordinates and timestamp of a PET detector when gamma rays are detected; (b) setting a loss function for a path determination matrix based on the coordinates and the estimated positions of the cell; (c) calculating a gradient of the loss function using backpropagation; (d) updating the path determination matrix using the calculated gradient; (e) repeating steps (c) and (d) to identify a first path determination matrix that minimizes the loss function; and (f) identifying the movement path of the cell using the first path determination matrix.

[0009] The above step (b) may include the step of representing the estimated position of the cell at the timestamp using the path determination matrix and the three-dimensional cubic spline function.

[0010] The above step (b) may include the step of converting the three-dimensional cubic spline function into a matrix.

[0011] The above matrix (B nj )silver, Represented as, and b n-1,3 (τ j ) is a 3D cubic spline function, τ j It is characterized in that is the timestamp of the event (j), K is the number of occurrences of the event (j), and N is the average number of detections in one spline interval.

[0012] The above step (b) may include setting an upper limit for the mean squared distance between the straight lines connecting the coordinates and the estimated positions of the cells.

[0013] The above loss function (J(A)) is, And, K of the above loss function (J(A)) is the number of occurrences of event (j), D j is the distance between the straight lines connecting the above coordinates and the estimated locations of the cell, d max It is characterized by the fact that is the upper limit of the mean squared distance, λ is a hyperparameter, N is the average number of detections in one spline interval, and A is the path decision matrix.

[0014] An electronic device for tracking the movement path of a cell in a positron emission tomography (PET) image according to an embodiment of the present invention may include a processor that (a) receives PET information including the coordinates and timestamp of a PET detector when gamma rays are detected, (b) sets a loss function for a path determination matrix based on the coordinates and the estimated positions of the cell, (c) calculates the gradient of the loss function using backpropagation, (d) updates the path determination matrix using the calculated gradient, (e) repeats steps (c) and (d) to identify a first path determination matrix that minimizes the loss function, and (f) identifies the movement path of the cell using the first path determination matrix.

[0015] The processor can represent the estimated position of the cell at the timestamp using the path determination matrix and a three-dimensional cubic spline function.

[0016] The processor can convert the three-dimensional cubic spline function into a matrix.

[0017] The processor can set an upper limit for the mean squared distance between the straight lines connecting the coordinates and the estimated locations of the cells. Effects of the invention

[0018] According to one embodiment of the present invention, as the speed of tracking the movement path of a cell becomes very fast, the time required for hyperparameter adjustment can be reduced and the algorithm can be finely adjusted.

[0019] According to one embodiment of the present invention, the calculation speed can be significantly improved without losing the accuracy of path tracking.

[0020] According to one embodiment of the present invention, a large amount of data can be easily analyzed using a faster algorithm. Brief explanation of the drawing

[0021] FIG. 1 is a block diagram illustrating the configuration of an electronic device according to one embodiment of the present invention. FIG. 2 is a diagram illustrating a method for tracking the movement path of a cell in a positron emission tomography image according to one embodiment of the present invention. FIG. 3 is a diagram illustrating a method for tracking the movement path of a cell in a positron emission tomography image according to one embodiment of the present invention. FIG. 4 is a diagram illustrating a cell movement path using conventional actual data, a conventional algorithm, and a cell movement path according to an embodiment of the present invention. FIGS. 5a to 5d are drawings comparing the reconstruction time and accuracy when using a conventional algorithm and the algorithm of the present invention. FIGS. 6a to 6d illustrate graphs comparing the difference in reconstruction time, the reconstruction time ratio, and the number of iterations for convergence when using a conventional algorithm and the algorithm of the present invention according to changes in hyperparameters. Specific details for implementing the invention

[0022] Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings. The detailed description disclosed below, together with the accompanying drawings, is intended to describe exemplary embodiments of the present invention and is not intended to represent the only embodiment in which the present invention can be practiced. In order to clearly explain the present invention in the drawings, parts unrelated to the description may be omitted, and the same reference numerals may be used for identical or similar components throughout the specification.

[0023] A method for tracking the movement path of cells in positron emission tomography (hereinafter also referred to as PET) images according to one embodiment of the present invention aims to increase the computational speed. When the computational speed of the Cell GPS algorithm is increased, the time required for hyperparameter adjustment may be reduced, and potentially, the possibility of more precise adjustment of the algorithm may be opened. Furthermore, medical professionals can analyze large amounts of data more easily through a faster algorithm.

[0024] The present invention introduces a new approach using backpropagation to optimize the gradient calculation of Cell GPS.

[0025] Backpropagation is an algorithm commonly used in the field of deep learning that allows for the effective training of neural networks by efficiently calculating the error gradient and updating parameters within it to reduce the loss between model predictions and actual measurements. Based on this function, backpropagation is applied to Cell GPS to optimize the gradient calculation step, thereby optimizing the computation speed.

[0026] A method for tracking the movement path of cells in a PET image according to one embodiment of the present invention can be performed by an electronic device (100). The electronic device (100) can be implemented as a computer, server, smartphone, tablet PC, smart pad, laptop, etc.

[0027] Hereinafter, the configuration and operation of an electronic device according to an embodiment of the present invention will be described in detail with reference to the drawings.

[0028] FIG. 1 is a block diagram illustrating the configuration of an electronic device according to one embodiment of the present invention.

[0029] An electronic device (100) according to one embodiment of the present invention includes an input unit (110), a communication unit (120), a display unit (130), a storage unit (140), and a processor (150).

[0030] The input unit (110) generates input data in response to user input of the electronic device (100). For example, user input may be a user input that starts the operation of the electronic device (100), a user input that sets a loss function, a user input that adjusts hyperparameters of the Cell GPS algorithm, a user input that sets an upper limit of the mean squared distance between the lines connecting PET detector coordinates and the estimated locations of the cells, and other user inputs that are necessary for tracking the movement path of the cells may be applied without limitation.

[0031] The input unit (110) includes at least one input means. The input unit (110) may include a keyboard, a key pad, a dome switch, a touch panel, a touch key, a mouse, a menu button, etc.

[0032] The communication unit (120) performs communication with external devices such as PET equipment and servers to transmit and receive PET information, cell movement paths, etc.

[0033] To this end, the communication unit (120) can perform wireless communication such as 5G (5th generation communication), LTE-A (long term evolution-advanced), LTE (long term evolution), Wi-Fi (wireless fidelity), Bluetooth, or wired communication such as LAN (local area network), WAN (Wide Area Network), and power line communication.

[0034] The display unit (130) displays display data according to the operation of the electronic device (100). The display unit (130) can display a screen displaying a PET image, a screen displaying a tracking process or tracking result (such as the tracked movement path of a cell), a screen receiving user input, etc.

[0035] The display unit (130) includes a liquid crystal display (LCD), a light emitting diode (LED) display, an organic light emitting diode (OLED) display, a micro electro mechanical systems (MEMS) display, and an electronic paper display. The display unit (130) can be combined with the input unit (110) to be implemented as a touch screen.

[0036] The storage unit (140) stores operation programs of the electronic device (100). The storage unit (140) includes storage with non-volatile properties that can preserve data (information) regardless of whether power is provided, and memory with volatile properties in which data to be processed by the processor (150) is loaded and data cannot be preserved if power is not provided. Storage includes flash memory, hard-disc drive (HDD), solid-state drive (SSD), and ROM (Read Only Memory), and memory includes buffer and RAM (Random Access Memory).

[0037] The storage unit (140) can store PET information, algorithms required during the tracking process, source code, etc. The storage unit (140) can store computation programs required during the process of setting loss functions, calculating gradients, updating path decision matrices, identifying path decision matrices, identifying cell movement paths, etc.

[0038] The processor (150) can control at least one other component (e.g., hardware or software component) of the electronic device (100) by executing software such as a program, and can perform various data processing or operations.

[0039] A processor (150) according to one embodiment of the present invention can (a) receive PET information including the coordinates and timestamp of a PET detector when gamma rays are detected, (b) set a loss function for a path determination matrix based on the coordinates and the estimated positions of the cells, (c) calculate the gradient of the loss function using backpropagation, (d) update the path determination matrix using the calculated gradient, (e) repeat the operation (c) and the operation (d) to identify a first path determination matrix that minimizes the loss function, and (f) identify the movement path of the cells using the first path determination matrix.

[0040] Meanwhile, the processor (150) may perform at least some of the data analysis, processing, and result information generation for performing the above operations using at least one of machine learning, neural network, or deep learning algorithms as a rule-based or artificial intelligence algorithm. Examples of neural networks may include models such as CNN (Convolutional Neural Network), DNN (Deep Neural Network), RNN (Recurrent Neural Network), and Vision Transformer.

[0041] FIG. 2 is a diagram illustrating a method for tracking the movement path of a cell in a positron emission tomography image according to one embodiment of the present invention.

[0042] The tracking method may include the step (S10) of receiving PET information including the coordinates and timestamp of the PET detector when gamma rays are detected.

[0043] Positron emission tomography (PET) is a method of determining the distribution within the body by injecting a drug combined with a positron-emitting radioisotope into the body and tracking it using a positron emission tomography scanner. The isotope administered into the body decays while emitting a single positron. The emitted positron undergoes annihilation with a nearby electron, generating two gamma rays traveling in opposite directions. A PET device can be composed of multiple gamma ray detectors (PET detectors) arranged to surround the human body and a circuit that determines the simultaneity of two photon signals. If two PET detectors simultaneously detect gamma rays, it indicates that annihilation occurred along the straight line connecting those two detectors.

[0044] In other words, each chance event of a photon pair, known as a Line of Response (LoR), is stored individually, and for each of these LoRs, the coordinates of the two detectors involved in the photon pair detection and the time at which the gamma ray was detected are recorded as a timestamp.

[0045] The processor (150) can receive PET information including the coordinates and timestamps of the PET detector. The processor (150) can receive PET information from the PET equipment. The PET information can be collected using the PET list mode data format. The processor (150) can simulate the movement path of the cell using particle simulation software and generate list mode data through the actual movement path. The particle simulation software may be, for example, TOPAS.

[0046] The tracking method may include the step (S20) of setting a loss function for a path decision matrix based on coordinates and the estimated positions of the cells.

[0047] The purpose of the Cell GPS algorithm is to estimate the trajectory of a single radiolabeled cell of a living organism from PET information, and to find the path with the smallest sum of squared distances between the lines connecting the PET detector coordinates and the estimated locations of the cell, which is the LoR.

[0048] The movement path of a cell (point source) can be represented by a 3D cubic spline. Specifically, the movement path (r(t)) is spline b n-1,3 (t) and coefficient A ·n = (a n x , a n y , a n z ) T It consists of a linear combination of. The movement path (r(t)) can be expressed as shown in the following mathematical equation 1.

[0049]

[0050] In this case, just as a straight line in linear regression is determined by its slope and intercept, the migration path of a cell reconstructed by a 3D cubic spline is determined by A, which is a matrix of variables that determine the path. A is also called the path determination matrix, and Finding the optimal movement path is equivalent to finding the optimal matrix A.

[0051] The following mathematical equation 2 is the coordinates (P j ) and estimated locations of cells (M j =r(τ j Euclidean distance (D) between )) j It represents ).

[0052]

[0053] Coordinates (P j ) is defined as the position of one of the detectors at event j, and the unit length direction of the line is v j It is indicated as. The timestamp of event j is τ j It is displayed as. Timestamp τ j Estimated location of the cell M at j (=r(τ j )) can be represented as a path determination matrix and a three-dimensional cubic spline function as shown in Equation 1 above.

[0054] Equation 3 represents the loss function I(A) for the limited mean squared distance.

[0055]

[0056] As previously described, while it is possible to calculate using the normal equation by minimizing only the sum of squared distances between the lines connecting the PET detector coordinates and the estimated cell locations, the accuracy of the reconstructed path may be reduced due to noise generated during PET measurements. Therefore, while minimizing the sum of squared distances, the upper bound (d) of the mean squared distance between the lines connecting the PET detector coordinates and the estimated cell locationsmax You can set ). Through this, you can exclude noise and reconstruct the path using the data actually needed.

[0057] In addition, since the function can have local minima in multiple places, the path cannot be determined using the normal equation. Therefore, the algorithm can be guided to the desired solution by adding a term multiplied by the hyperparameter λ and R(A) to the loss function. This can be expressed by the following mathematical equations 4 and 5.

[0058]

[0059] R(A) is the mean square difference between consecutive columns of A.

[0060]

[0061] Finally, the loss function (also called the objective function) according to one embodiment of the present invention is J(A) according to Equation 5. The processor (150) can estimate the position of the cell at the timestamp using a path determination matrix and a three-dimensional cubic spline function. The processor (150) can set a loss function for the path determination matrix based on the coordinates of the PET detector and the estimated positions of the cell. At this time, if the optimal path determination matrix (A) that minimizes J(A) is found, the optimal cell movement path can be found.

[0062] The tracking method may include a step (S30) of calculating the gradient of the loss function using backpropagation.

[0063] Conventional Cell GPS algorithms calculate gradients used to optimize the loss function by numerically differentiating it, but this method is relatively slow. Since conventional algorithms evaluate the function at two slightly different points and calculate an approximation by determining the slope of the line connecting those points, the amount of computation can become very large when there are many elements for which the slope is calculated at A. For example, if there are 3N elements at A, at least 3N+1 evaluations of the loss function are required to calculate the gradient.

[0064] In this invention, the speed of gradient calculation can be improved by applying backpropagation. Backpropagation can rapidly calculate gradients by using the chain rule to differentiate the loss function. To do so, the loss function must be expressed as a composition of simple, differentiable operations.

[0065] Specifically, the loss function can be modified to allow backpropagation by calculating the estimated position of the cell at each timestamp, which is necessary when calculating the sum of squared distances, through matrix multiplication.

[0066] As described above, the estimated position of a cell at a timestamp can be represented by a path determination matrix and a 3D cubic spline function. Therefore, if the 3D cubic spline function can be converted into a matrix, the estimated position of a cell at each timestamp can be calculated through matrix multiplication.

[0067] The expression representing a 3D cubic spline function as an NxK matrix is ​​given by the following mathematical equation 6.

[0068]

[0069] Therefore, by expressing the cell's movement path as the product of matrices A and B, the gradient of the loss function can be calculated by applying the backpropagation algorithm. This reduces the number of loss function evaluations from the existing 3N + 1 times to just 1 time, thereby significantly improving computational efficiency.

[0070] The tracking method may include a step (S40) of updating the path decision matrix using the calculated gradient.

[0071] The processor (150) can update the path decision matrix using the current path decision matrix and the calculated gradient. This means that the cell's movement path can be updated. At this time, the update can use gradient descent, but is not limited to either method.

[0072] The tracking method may include a step (S50) of identifying a first path decision matrix that minimizes the loss function by repeating S30 and S40. The processor (150) may continue to calculate gradients and update the path decision matrix until the Cell GPS algorithm converges, and may identify the first path decision matrix when the algorithm converges.

[0073] The tracking method may include a step (S60) of identifying the movement path of a cell using a first path determination matrix. Since the movement path of a cell is determined by a path determination matrix, the processor (150) can identify the movement path of a cell using the first path determination matrix.

[0074] In the present invention, a Jacobian matrix option can be used to utilize backpropagation, enabling more efficient gradient calculation for optimization. Additionally, in the present invention, to improve the precision of the Cell GPS algorithm, two or more different upper bounds (d max The result can be derived through a two-step convergence process using ).

[0075] According to one embodiment of the present invention, the calculation speed can be significantly improved without losing the accuracy of path tracking.

[0076] FIG. 3 is a diagram illustrating a method for tracking the movement path of a cell in a positron emission tomography image according to an embodiment of the present invention. Any content in FIG. 3 that overlaps with FIG. 2 is borrowed from the content described in relation to FIG. 2.

[0077] A Cell GPS algorithm according to one embodiment of the present invention first inputs PET information (PET list mode data) and initializes a three-dimensional cubic spline function regarding the movement path of a cell.

[0078] The function regarding the movement path is optimized by calculating the gradient on the loss function regarding the cell's movement path (Calculate Gradient and Optimize Spline).

[0079] Check if the Cell GPS algorithm converges; if it does not converge, repeat the gradient calculation and function optimization process (Converged). If it converges, output the optimized cell movement path (Output: Cell Trajactory).

[0080] FIG. 4 is a diagram illustrating a cell movement path using conventional actual data, a conventional algorithm, and a cell movement path according to an embodiment of the present invention.

[0081] The accuracy of the conventional algorithm and the algorithm according to one embodiment of the present invention is the measured trajectory (gt(θ) for time points at equal intervals (e.g., 0.05 seconds) within the detected time range. i )) and reconstructed trajectory(r(θ i It can be evaluated by calculating the RMS (Root Mean Square) distance of )). This is as shown in the following mathematical formula 7.

[0082]

[0083] Q is the number of time points, and θ i is the i-th time point of equal intervals, and the measured trajectory (gt(θ i )) and reconstructed trajectory(r(θ i It corresponds to ))

[0084] FIG. 4 is an example of a cell migration path reconstructed using PET information using two algorithms: a conventional algorithm and an algorithm according to an embodiment of the present invention. The cell migration path is shown as a function of time in (a) and in three dimensions in (b).

[0085] Referring to Figure 4, it can be seen that there is no noticeable difference in accuracy between the two algorithms.

[0086] In terms of reconstruction time, it can be seen that the backpropagation approach according to the present invention has significantly improved the computation speed. While the conventional algorithm achieved trajectory reconstruction in 8.44 seconds, the current algorithm takes only 0.139 seconds, reducing the reconstruction time by 60.7 times.

[0087] Below, we examine how various hyperparameter settings affect calculation speed.

[0088] FIGS. 5a to 5d are drawings comparing the reconstruction time and accuracy when using a conventional algorithm and the algorithm of the present invention.

[0089] Figures 5a and 5c are graphs measuring reconstruction time and accuracy by adjusting hyperparameters. In Figures 5a and 5c, the y-axis is displayed on a logarithmic scale.

[0090] The left graph in Fig. 5a shows the reconstruction time measured by increasing the average number of detections by 10 for a single spline interval (d) from 10 to 100. The hyperparameters are λ = 0.0044, d max1 = 2.8cm, d max2It was set to = 0.6cm.

[0091] From the left graph of Fig. 5a, it can be seen that as one spline interval decreases, the reconstruction time of the two algorithms increases.

[0092] The graph on the right in Fig. 5a shows the reconstruction time measured by adjusting λ in increments of 0.001 from 0.001 to 0.01. The hyperparameters are set to an average number of detections per spline interval of 36, and d max1 = 2.8cm, d max2 = Set to 0.6cm.

[0093] From the graph on the right in Fig. 5a, it can be seen that the reconstruction time of the two algorithms decreases as λ increases. However, the reconstruction time did not change by the same amount as the hyperparameters were adjusted. As λ increased, the average reconstruction time for the conventional algorithm changed from 9.96 seconds to 6.35 seconds, and for the current algorithm, it changed from 0.12 seconds to 0.07 seconds.

[0094] The left graph in Fig. 5c shows the accuracy measured by increasing the average number of detections by 10 at a single spline interval from 10 to 100. The hyperparameters are λ = 0.0044, d max1 = 2.8cm, d max2 It was set to = 0.6cm.

[0095] The graph on the right in Fig. 5c shows the accuracy measured by adjusting λ in increments of 0.001 from 0.001 to 0.01. The hyperparameters are set to set the average number of detections per spline interval to 36, and d max1 = 2.8cm, d max2 = Set to 0.6cm.

[0096] Figures 5b and 5d are graphs showing the reconstruction time and accuracy measured by adjusting experimental conditions.

[0097] The hyperparameters of Figs. 5b and 5d represent the average number of detections in a single spline interval as 36, λ = 0.0044, d max1 = 2.8cm, d max2 = Set to 0.6cm.

[0098] The left graph of Fig. 5b is a graph of reconstruction time measured by adjusting the detection time in 2-minute increments from 6 minutes to 14 minutes, and the right graph of Fig. 5b is a graph of reconstruction time measured by increasing the radioactivity in 25-Bq increments from 50 Bq to 200 Bq.

[0099] The left graph of Fig. 5d is a graph showing the accuracy measured by adjusting the detection time in 2-minute increments from 6 minutes to 14 minutes, and the right graph of Fig. 5d is a graph showing the accuracy measured by increasing the radioactivity in 25-Bq increments from 50 Bq to 200 Bq.

[0100] FIGS. 6a to 6d illustrate graphs comparing the difference in reconstruction time, the reconstruction time ratio, and the number of iterations for convergence when using a conventional algorithm and the algorithm of the present invention according to changes in hyperparameters.

[0101] Figure 6a shows that the average number of detections for a single spline interval increases from 10 to 100 in increments of 10, and the hyperparameters are λ = 0.0044, d max1 = 2.8cm, d max2 It was set to = 0.6cm.

[0102] In Fig. 6b, λ was changed from 0.001 to 0.01 in increments of 0.001, and the hyperparameter was set to an average number of detections per spline interval of 36, and d max1 = 2.8cm, d max2 = Set to 0.6cm.

[0103] A dataset containing 100 simulated trajectories of cells with a radioactivity level of 100 Bq for 10 minutes was used for both Figure 6a and Figure 6b.

[0104] Figure 6c shows that the detection time of the simulation was changed in 2-minute increments from 6 minutes to 14 minutes, and the radioactivity of the simulated cell was 100 Bq.

[0105] In Fig. 6d, the radioactivity of the cell in the simulation varied from 25 Bq to 200 Bq. The detection time in the simulation was 10 minutes.

[0106] For both Fig. 6c and Fig. 6d, the hyperparameters are set to an average number of detections per spline interval of 36, λ = 0.0044, d max1 = 2.8cm, d max2 = Set to 0.6cm. Explanation of the symbols

[0107] 100: Electronic device 110: Input section 120: Communications Department 130: Display unit 140: Storage section 150: Processor

Claims

Claim 1 A method for tracking the movement path of a cell in a Positron Emission Tomography (PET) image performed by an electronic device, comprising: (a) receiving PET information including the coordinates of a PET detector and a timestamp when gamma rays are detected; (b) representing the estimated position of the cell at the timestamp as a path determination matrix and a 3D cubic spline function, and setting a loss function through matrix multiplication of the matrix obtained by converting the path determination matrix and the 3D cubic spline function into a matrix; (c) calculating the gradient of the loss function using backpropagation; (d) updating the path determination matrix using the calculated gradient; (e) repeating steps (c) and (d) to identify a first path determination matrix that minimizes the loss function; and (f) identifying the movement path of the cell using the first path determination matrix. Claim 2 delete Claim 3 delete Claim 4 In claim 1, the matrix (B) obtained by converting the three-dimensional cubic spline function into a matrix nj )silver, Represented as, and b n-1,3 (τ j ) is a 3D cubic spline function, τ j A method characterized in that is the timestamp of event (j), K is the number of occurrences of event (j), and N is the average number of detections in one spline interval. Claim 5 A method according to claim 1, wherein step (b) comprises setting an upper limit of the mean squared distance between the straight lines connecting the coordinates and the estimated positions of the cells. Claim 6 In paragraph 5, the loss function (J(A)) of step (e) above is, And, K of the above loss function (J(A)) is the number of occurrences of event (j), D j is the distance between the straight lines connecting the above coordinates and the estimated locations of the cell, d max A method characterized in that is an upper limit of mean squared distance, λ is a hyperparameter, N is the average number of detections in one spline interval, and A is a path decision matrix. Claim 7 An electronic device for tracking the movement path of a cell in a Positron Emission Tomography (PET) image, comprising: (a) receiving PET information including the coordinates and timestamp of a PET detector when gamma rays are detected; (b) representing the estimated position of the cell at the timestamp as a path determination matrix and a 3D cubic spline function, and setting a loss function through matrix multiplication of the matrix obtained by converting the path determination matrix and the 3D cubic spline function into a matrix; (c) calculating the gradient of the loss function using backpropagation; (d) updating the path determination matrix using the calculated gradient; (e) repeating the operation in (c) and the operation in (d) to identify a first path determination matrix that minimizes the loss function; and (f) identifying the movement path of the cell using the first path determination matrix. Claim 8 delete Claim 9 delete Claim 10 In claim 7, the matrix (B) obtained by converting the above three-dimensional cubic spline function into a matrix nj )silver, Represented as, and b n-1,3 (τ j ) is a 3D cubic spline function, τ j An electronic device characterized in that is a timestamp of event (j), K is the number of occurrences of event (j), and N is the average number of detections in one spline interval. Claim 11 In claim 7, the processor is an electronic device that sets an upper limit of the mean squared distance between the straight lines connecting the coordinates and the estimated positions of the cells. Claim 12 In paragraph 11, the loss function (J(A)) of the above (e) operation is, And, K of the above loss function (J(A)) is the number of occurrences of event (j), D j is the distance between the straight lines connecting the above coordinates and the estimated locations of the cell, d max An electronic device characterized in that is an upper limit of mean squared distance, λ is a hyperparameter, N is the average number of detections in one spline interval, and A is a path decision matrix.

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