Female pelvic floor dysfunction disease risk model construction system

Abstract

The invention relates to the technical field of pelvic floor MRI (Magnetic Resonance Imaging) risk modeling, and discloses a female pelvic floor dysfunction disease risk model construction system which comprises the following steps: firstly, acquiring dynamic magnetic resonance data including resting, contraction, force application and emptying stages under a supine position, and recording time information of each stage; and determining a smegtail line in a median sagittal view, establishing a fixed reference coordinate, and mapping a functional region of the smegtail line in a resting stage to each frame. Then calculating a relative resting displacement field in the reference coordinate through registration, and extracting a normalized displacement curve along the tail side direction of the smegmatis tail line; and taking the starting point of the force stage as a reference, detecting a first slope change maximum point of a displacement curve in a logarithmic time domain as a critical moment, and performing weighted fitting in a rear window to obtain a second slope as a critical post-power-law softening index. And finally, a female pelvic floor dysfunction risk prediction model is constructed according to the index, individual risk probability output is realized, and the method has the advantages of high sensitivity and quantification.

Description

Technical Field

[0001] This invention relates to the field of pelvic floor MRI risk modeling technology, and more specifically, to a system for constructing a risk model of female pelvic floor dysfunction. Background Technology

[0002] The development of female pelvic floor dysfunction is influenced by various factors, including pregnancy, childbirth, age, and gravitational stress. Its pathological basis lies in the continuous deformation and mechanical degeneration of the pelvic floor support system. While traditional pelvic floor MRI provides high-resolution anatomical images, it typically only performs quantitative measurements during resting or single-stress phases, failing to capture the dynamic evolution of tissues from initial stress to instability. With the development of dynamic imaging techniques, CINE MRI can continuously record the temporal changes of organs and muscle groups during stress and emptying processes. However, clinical analysis often remains at the level of geometric parameters such as displacement amplitude, angle, or area. These parameters only reflect the results of structural deformation and cannot describe the evolutionary path of the mechanical process. Due to the lack of characterization of post-yield mechanical behavior, existing risk models can only perform macroscopic classification or grade prediction, failing to reveal the true damage potential of different individuals under dynamic loading.

[0003] Specifically, while magnetic resonance imaging (MRI) can provide high temporal resolution dynamic images, it currently lacks the capability to extract the softening behavior of tissues in the post-yield stage from image sequences. Soft tissues exhibit typical viscoelastic and time-dependent softening characteristics under high stress, a process that often follows a nonlinear decay law and is difficult to express using linear or static models. Furthermore, existing image analysis workflows lack a mechanism to identify this dynamic stage; that is, they cannot determine when the post-yield response region is entered, nor are there corresponding parameters to quantify the softening rate. Therefore, risk models cannot utilize the time-series information recorded by MRI during training and can only rely on static indicators or empirical thresholds, resulting in limited model generalization ability and prediction accuracy. Summary of the Invention

[0004] This invention provides a system for constructing a risk model for female pelvic floor dysfunction, which solves the technical problem mentioned in the background: how to use observable tissue time-series changes in magnetic resonance imaging sequences to quantitatively characterize the softening pattern of the female pelvic floor in the post-yield stage, thereby achieving dynamic prediction and modeling of disease risk.

[0005] This invention provides a system for constructing a risk model for female pelvic floor dysfunction, comprising: The data acquisition module acquires dynamic magnetic resonance data of the supine position, including the resting, contraction, exertion, and emptying phases, and records the time information of each phase. The reference coordinate establishment module determines the pubococcygeal line in the midsagittal position, establishes fixed reference coordinates based on the pubococcygeal line registration data, generates the functional region corresponding to the pubococcygeal line in the resting phase, and maps it to each frame. The displacement feature extraction module obtains the relatively resting displacement field through registration within the reference coordinates and functional areas of each frame. It extracts the regional displacement features along the tail side of the pubococcygeal line and normalizes them by the length of the pubococcygeal line to obtain the displacement curve over continuous time. The critical moment detection module takes the start of the force application phase as the starting point and detects the position where the first slope of the displacement curve changes the most in the logarithmic time domain as the critical moment. The softening index calculation module performs a weighted fitting of the logarithmic relationship between displacement increment and time within the critical window, and uses the fitted second slope as the critical power-law softening index; wherein, the critical window is determined based on the critical moment. The risk prediction module constructs a risk prediction model for female pelvic floor dysfunction using the post-critical power-law softening index, outputting individual risk probabilities, including: The input is the post-critical power-law softening exponent; The model training data consists of multiple sample pairs. Each sample pair contains the critical post-power-law softening exponent of the j-th sample and the event indicator of the j-th sample. The event indicator takes the value of zero or one, j is a positive integer representing the sample number, and the total number of samples is a positive integer. The linear predictor is defined as the product of the model intercept parameter, the model slope parameter, and the critical post-power-law softening exponent of the j-th sample. A logic function is defined as a function that maps any real number to the range between zero and one. The logic function is calculated by dividing one by one and raising the negative linear predictor of the natural exponential function to the power of one. The individual risk probability of the j-th sample is calculated using the aforementioned logical function; The objective function is defined as the negative log-likelihood based on the individual risk probability. Specifically, it is calculated by multiplying the event indication of each sample by the negative logarithm of the risk probability of that sample, and adding the negative logarithm of the difference between the event indication and the risk probability of that sample to obtain the sample parameter for each sample. The sample parameters of all samples are then summed to obtain the objective function. Adjust the values ​​of the model intercept parameter and the model slope parameter to minimize the value of the objective function, thereby obtaining the optimal model intercept parameter and the optimal model slope parameter; For any individual to be evaluated, the linear predictor is calculated using the corresponding critical post-power-law softening exponent, the optimal model intercept parameter, and the optimal model slope parameter. The risk probability of the individual is then obtained through the aforementioned logic function and used as the model output.

[0006] The beneficial effects of this invention include: by establishing a fixed reference coordinate system based on the pubococcygeal line and achieving multi-stage image registration, this invention can accurately extract continuous displacement curves of pelvic floor soft tissues throughout the entire process of rest, contraction, exertion, and emptying, overcoming the limitations of traditional MRI, which relies solely on static indicators and struggles to identify tissue dynamic characteristics. Through slope analysis of the displacement curves in the logarithmic time domain, this invention can automatically identify the critical moment after tissue yielding and extract a power-law softening index as a quantitative parameter, truly reflecting the degree of mechanical degradation of tissues under abdominal pressure loading. The logistic function established based on this index can output individualized risk probabilities, significantly improving the sensitivity and interpretability of disease risk assessment, achieving a breakthrough from anatomical structure measurement to mechanical behavior modeling. Attached Figure Description

[0007] Figure 1 This is a flowchart of a system for constructing a risk model for female pelvic floor dysfunction according to the present invention. Detailed Implementation

[0008] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0009] like Figure 1 As shown, a system for constructing a risk model for female pelvic floor dysfunction includes: The data acquisition module acquires dynamic magnetic resonance data of the supine position, including the resting, contraction, exertion, and emptying phases, and records the time information of each phase. The reference coordinate establishment module determines the pubococcygeal line in the midsagittal position, establishes fixed reference coordinates based on the pubococcygeal line registration data, generates the functional region corresponding to the pubococcygeal line in the resting phase, and maps it to each frame. The displacement feature extraction module obtains the relatively resting displacement field through registration within the reference coordinates and functional areas of each frame. It extracts the regional displacement features along the tail side of the pubococcygeal line and normalizes them by the length of the pubococcygeal line to obtain the displacement curve over continuous time. The critical moment detection module takes the start of the force application phase as the starting point and detects the position where the first slope of the displacement curve changes the most in the logarithmic time domain as the critical moment. The softening index calculation module performs a weighted fitting of the logarithmic relationship between displacement increment and time within the critical window, and uses the fitted second slope as the critical power-law softening index; wherein, the critical window is determined based on the critical moment. The risk prediction module constructs a risk prediction model for female pelvic floor dysfunction using the post-critical power-law softening index, outputting individual risk probabilities, including: The input is the post-critical power-law softening exponent; The model training data consists of multiple sample pairs. Each sample pair contains the critical post-power-law softening exponent of the j-th sample and the event indicator of the j-th sample. The event indicator takes the value of zero or one, j is a positive integer representing the sample number, and the total number of samples is a positive integer. The linear predictor is defined as the product of the model intercept parameter, the model slope parameter, and the critical post-power-law softening exponent of the j-th sample. A logic function is defined as a function that maps any real number to the range between zero and one. The logic function is calculated by dividing one by one and raising the negative linear predictor of the natural exponential function to the power of one. The individual risk probability of the j-th sample is calculated using the aforementioned logical function; The objective function is defined as the negative log-likelihood based on the individual risk probability. Specifically, it is calculated by multiplying the event indication of each sample by the negative logarithm of the risk probability of that sample, and adding the negative logarithm of the difference between the event indication and the risk probability of that sample to obtain the sample parameter for each sample. The sample parameters of all samples are then summed to obtain the objective function. Adjust the values ​​of the model intercept parameter and the model slope parameter to minimize the value of the objective function, thereby obtaining the optimal model intercept parameter and the optimal model slope parameter; For any individual to be evaluated, the linear predictor is calculated using the corresponding critical post-power-law softening exponent, the optimal model intercept parameter, and the optimal model slope parameter. The risk probability of the individual is then obtained through the aforementioned logic function and used as the model output.

[0010] In one embodiment of the present invention, dynamic magnetic resonance data of the supine position including resting, contraction, exertion, and emptying phases are acquired, and the time information of each phase is recorded, including: Determine the start and end times of the rest, contraction, exertion and emptying phases to form time information for each phase; Dynamic magnetic resonance data is generated by acquiring image frames corresponding to the resting, contraction, exertion, and emptying phases at fixed time intervals.

[0011] Resting phase: The patient lies supine with knees flexed, body relaxed, and maintains natural breathing. There is no active contraction or exertion of the pelvic floor muscles. This phase is used to obtain baseline anatomical data.

[0012] Contraction phase: Under the guidance of a physician, the patient performs anal contraction exercises, that is, actively tightens the muscles around the anus and holds for several seconds until a relaxation instruction is received. This is used to assess the contraction function of the pelvic floor muscles.

[0013] Exertion phase: The patient performs actions to increase abdominal pressure, that is, after taking a deep breath, holding it and forcefully pressing the abdominal wall inward and downward (similar to the straining state before defecation), and maintains the position until the action is stable.

[0014] Emptying phase: For rectal or bladder function assessment, if assessing the rectum, the patient attempts to expel simulated feces from the rectum (such as a balloon containing ultrasound coupling agent). If assessing the bladder, the patient attempts to expel urine from the bladder until there is no obvious expulsion or the equipment shows that the organ is close to emptying. This phase should be followed by the exertion phase.

[0015] The data were collected continuously in the order of resting → contraction → exertion → emptying. After the previous phase ended, the patient needed to briefly adjust to the starting state of the next phase. The adjustment time should not exceed ten seconds to ensure the continuity of dynamic data.

[0016] End of resting state: The moment when the patient completes the preparation for resting state, the image signal displayed by the device stabilizes (such as the signal noise value drops to a preset low level), and the physician issues the command to start contraction is taken as the start of the contraction phase.

[0017] The start time of each stage: The start time of the contraction, exertion and emptying stages is the instant when the physician issues the corresponding action command; the equipment synchronously records the system time when the command is issued, as the official start time of that stage.

[0018] The time information consists of the start and end times of each stage. The end time is the instant when the patient completes the action of the stage (such as relaxation of contraction, release of exertion, and cessation of emptying) and the physician issues the end instruction of the stage.

[0019] The fixed time interval needs to be set in conjunction with the rapid scanning capability of the magnetic resonance equipment. The usual choice is an interval corresponding to acquiring two to three frames per second, that is, the acquisition time difference between two adjacent frames is between one-third and half a second.

[0020] A fixed time interval must meet two conditions, specifically: 1. It can fully capture the dynamic changes of pelvic floor tissues at each stage (such as the tissue displacement process during the exertion stage). 2. Avoid excessively small intervals that could lead to data redundancy and increased storage burden on the equipment. The specific intervals can be adjusted according to the equipment model; this range applies to both 1.5T and 3.0T MRI machines.

[0021] Preoperative preparation: If assessing rectal emptying function, 100 to 120 ml of diluted ultrasound coupling agent (temperature close to body temperature) needs to be injected into the rectum before the examination to simulate the state of normal stool; if assessing bladder emptying function, the bladder needs to be in a semi-full state (hold urine until there is no feeling of distension or pain) before the examination.

[0022] Instructions: After the straining phase, the patient should immediately attempt to empty their bowels or bladder as they normally would, while remaining supine to avoid shifting their body position. The physician will observe changes in organ morphology through real-time imaging until the images show a significant reduction in the contents of the organ or the patient indicates that they are unable to continue emptying their bowels, at which point the emptying phase is considered complete.

[0023] In one embodiment of the present invention, the pubococcygeal line is determined in the midsagittal plane, a fixed reference coordinate is established based on the pubococcygeal line registration data, and a functional region corresponding to the pubococcygeal line in the resting phase is generated and mapped to each frame, including: In the image frame during the resting phase, the lower edge of the pubis and the end point of the coccyx are determined, and the straight line connecting the lower edge of the pubis and the end point of the coccyx is taken as the pubococcygeal line. Using the image frame corresponding to the start of the resting state as the reference image frame, for any image frame at any time, a rigid body transformation including rotation and translation is constructed. By adjusting the rotation and translation parameters, the lower edge of the pubis and the end point of the coccyx in the image frame are aligned with the lower edge of the pubis and the end point of the coccyx in the reference image frame, respectively, so as to establish a fixed reference coordinate. After rotating the direction vector from the lower edge of the pubis to the end of the coccyx counterclockwise by 90 degrees, normalize it to obtain the unit normal vector pointing to the caudal half-plane. On the reference image frame, the set of pixels located at the tail of the pubococcygeal line and whose unit normal vector and the projection of the line connecting each point in the region to the lower edge of the pubis are less than or equal to zero are defined as the functional region. By using the inverse transformation of rigid body transformation, the functional regions on the reference image frame are mapped to the corresponding image frames at each time point, thus obtaining the functional regions in each image frame.

[0024] Identification of the inferior pubic margin: On a resting midsagittal image frame, locate the lowest edge of the pubic symphysis (a high-density bony structure, shown as a bright white area in the image), and take the midpoint or the point of maximum curvature of this edge as the inferior pubic margin. If pubic symphysis osteophyte formation is present, use the lower edge of the normal cortical bone below the osteophyte area as the reference point.

[0025] Identification of the distal point of the coccyx: trace the coccyx (which has a beaded bony structure) from top to bottom to the last coccyx segment and take the distal end of that segment; if there is fusion or bending variation of the coccyx, take the distal edge of the last coccyx joint that can be clearly identified as the reference point.

[0026] Landmark confirmation requirements: It must be identified by two physicians with more than 3 years of experience in pelvic floor MRI diagnosis. If the coordinate error between the two points exceeds 1 pixel, the final position of the point shall be determined by joint review of the image to ensure the consistency of the landmark.

[0027] The rigid body transformation parameters are adjusted as follows: Adjustment target: The optimization target is to minimize the sum of the straight-line distances between the two marker points of the target image frame and the corresponding points of the reference frame. The distance unit is the image pixel spacing (e.g., 1.5 mm / pixel).

[0028] Operation method: Use an automatic optimization algorithm (such as gradient descent) to adjust the parameters. First, fix the rotation parameters and adjust the translation amount to initially align the two points. Then, simultaneously fine-tune the rotation and translation parameters until the sum of the distances is less than 0.5 pixels.

[0029] Stop condition: When the sum of distances changes by less than 0.1 pixels after 3 consecutive parameter iterations, or when the preset maximum number of iterations (e.g., 50 times) is reached, the adjustment will stop and the current parameters will be saved.

[0030] The unit normal vector is generated as follows: Definition of reference coordinate system: Based on the conventional display orientation of MRI images, that is, the upper part of the image corresponds to the patient's head side, the lower part corresponds to the patient's foot side, the left side corresponds to the patient's right side, and the right side corresponds to the patient's left side.

[0031] Rotation operation: First, determine the direction vector from the lower edge of the pubis to the end of the coccyx (as shown in the image, from the upper left to the lower right). Rotate this vector 90 degrees around the starting point (lower edge of the pubis) according to the rule that clockwise is to the right and counterclockwise is to the left to form the initial normal vector.

[0032] Normalization: Calculate the length of the initial normal vector (i.e., the straight-line distance between the two endpoints of the vector), divide each directional component of the initial normal vector by this length, and obtain a unit normal vector with a length of 1, ensuring that it only represents the direction and does not contain length information.

[0033] Projection calculation and functional area delineation, including: Projection operation: For each pixel on the tail side of the pubococcygeal line in the reference image frame, first draw a line from the lower edge of the pubis to the pixel (i.e., the line from the point to the lower edge of the pubis). Then determine the direction relationship between this line and the unit normal vector. If the line is inclined in the direction pointed to by the unit normal vector or is perpendicular to the normal vector, the projection result is less than or equal to zero; if it is inclined in the opposite direction, the projection result is greater than zero.

[0034] Functional region filtering rules: First, retain all pixels located below (towards) the pubococcygeal line, then remove pixels whose projection results are greater than zero. The set of remaining pixels is the functional region. This can be simply understood as: taking the pubococcygeal line as the boundary, selecting the pixel region below it and facing the unit normal vector direction.

[0035] Region verification: The functional region must include pixels corresponding to pelvic floor support structures such as the levator ani muscle and the anterior rectal wall. If the region deviates significantly from the actual anatomy, the rotation direction of the normal vector must be rechecked.

[0036] The inverse transform region mapping is as follows: Inverse transformation parameters: The rigid body transformation parameters (rotation angle, translation amount) of each frame image are calculated in reverse to obtain the inverse transformation parameters. The rotation angle is taken as the opposite number, and the translation amount is taken as the same distance in the opposite direction.

[0037] Pixel mapping rule: Substitute the coordinates of each pixel in the functional area of ​​the reference frame into the inverse transform parameters of the corresponding frame to calculate the corresponding position of the pixel in the target frame; if the calculation result is a non-integer coordinate, the nearest neighbor interpolation method is used to take the nearest integer coordinate pixel.

[0038] Edge processing: If scattered and isolated pixels (area less than 3 pixels) appear at the edge of the functional area after mapping, they are removed; if there is a break in the area, the adjacent pixels of the same type at the break point (i.e., the pixels on the tail side and whose projection meets the conditions) are filled to ensure the continuity and integrity of the functional area in each frame.

[0039] In one embodiment of the present invention, within the reference coordinates and functional regions of each frame, a relatively resting displacement field is obtained through registration. Regional displacement features are extracted along the tail-side direction of the pubococcygeal line and normalized by the length of the pubococcygeal line to obtain a continuous-time displacement curve, including: Use the grayscale of the reference image frame as the reference image grayscale; For each image frame at each time point, based on rigid body transformation, the image frame is converted into a rigid body registration image aligned to the reference coordinates; By using non-rigid registration, the grayscale difference between the rigid registration image and the reference image frame is minimized. At the same time, a smoothing term for the deformation field is added to determine the deformation field from the pixel in the reference coordinates to the corresponding position at each time step. The displacement field in the relative resting phase is obtained by subtracting the deformation field from the pixel position in the reference coordinates. The functional regions of each frame and the caudal unit direction pointing to the caudal direction are determined, and the distance between the lower edge of the pubis and the end point of the coccyx is defined as the length of the pubococcygeal line. Within each frame's functional region, calculate the average value of the projection of the displacement field onto the tail side unit direction after rigid body transformation, and normalize this average value by dividing it by the length of the tail line to obtain the single-frame region displacement corresponding to each moment. By associating each moment with the corresponding single-frame region displacement, a displacement curve over continuous time is formed.

[0040] The reference image grayscale only takes the grayscale values ​​of all pixels within the functional region of the reference image frame during the resting phase, excluding irrelevant areas outside the functional region (such as the background and intestinal gas region). Specifically, the functional region (the caudal functional region of the pubococcygeal line) is first determined on the resting reference frame, and then the grayscale value of each pixel within this region is extracted to form a reference grayscale dataset, which is used for subsequent grayscale difference comparison in non-rigid registration.

[0041] The smoothing settings for non-rigid body registration are as follows: Smoothing term type: Gaussian smoothing term is used. By applying Gaussian filtering to the deformation field, local severe deformation is suppressed to ensure that the deformation conforms to the physiological movement law of the pelvic floor soft tissue (such as the gradual deformation of the levator ani muscle contraction).

[0042] Smoothing weight values: Adjusted according to the MRI equipment field strength. For 1.5T equipment, the smoothing weight is 0.1-0.3, and for 3.0T equipment, it is 0.05-0.2 (the higher the field strength, the higher the image resolution, and the smoothing weight can be appropriately reduced). Weight adjustment principle: The goal is to achieve a gray-level difference of less than 5% within the registered functional area and no obvious local protrusions in the deformation field. If the gray-level difference is too large, the weight is reduced; if abnormal protrusions appear in the deformation field, the weight is increased.

[0043] The caudal unit direction is determined based on the pubococcygeal line: using the pubococcygeal line (connecting the lower edge of the pubis to the distal end of the coccyx) as a reference, the direction perpendicular to the pubococcygeal line and pointing downwards towards the pelvic floor (towards the patient's foot) is taken as the caudal unit direction. Specifically, the pubococcygeal line is considered a horizontal baseline, and the caudal unit direction is vertically downwards (consistent with the caudal aspect in human anatomy), which can be confirmed using image coordinates. If the MRI image shows the patient's head at the top and the foot at the bottom, then the caudal unit direction is the vertically downwards direction of the image.

[0044] Rigid body transformation of the displacement field involves transforming the displacement field of image frames at each time step to align it with the reference coordinates. The specific steps are as follows: First, obtain the rigid body transformation parameters (rotation angle, translation amount, rigid body transformation parameters) corresponding to the image frame at that time step. Then, adjust the displacement vector of each pixel in the displacement field according to the inverse transformation of the rigid body transformation (i.e., reverse rotation and reverse translation) to eliminate the influence of body motion on the displacement field, ensuring that the adjusted displacement field only reflects the active deformation of the pelvic floor soft tissue and remains consistent with the reference coordinates.

[0045] The pubococcygeal line length is fixed as the straight-line distance between the lower edge of the pubis and the distal end of the coccyx in the resting reference image frame, not the real-time length of each frame. Reason: The pubococcygeal line length in the resting frame represents the baseline dimension of the pelvic floor bony structures. Slight changes in the relative positions of bony landmarks may occur in each frame due to body movement or soft tissue deformation. Using the real-time length would cause fluctuations in the normalized baseline, affecting the comparability of displacement characteristics. Measurement method: On the resting reference frame, the straight-line distance between two points is directly measured using an image measurement tool (such as the distance measurement function built into the MRI equipment), with the unit uniformly set to millimeters.

[0046] The rules for calculating the mean of displacement projection include: Abnormal pixel elimination: First, remove non-soft tissue pixels (such as bone structure pixels, pixels with gray values ​​higher than 200 HU; noise pixels, pixels with gray values ​​lower than 0 HU) within the functional area, and only retain soft tissue pixels (gray values ​​between 0 and 200 HU).

[0047] Mean calculation: For the remaining soft tissue pixels, calculate the projection value of their displacement field in the unit direction on the tail side after rigid body transformation, and then calculate the arithmetic mean of all projection values ​​to obtain the mean displacement of the region at that moment. If the number of soft tissue pixels in the functional region is less than 100 at a certain moment (due to image cropping or changes in organ position), it is necessary to recheck whether the functional region mapping is correct to ensure that the sample size meets the reliability of the mean calculation.

[0048] The time intervals of the continuous-time displacement curve are relative to the start time of the resting phase, rather than the absolute time of the device acquisition. Specifically: the time of the first frame acquired at the start of the resting phase is taken as time 0. The time of each subsequent frame is calculated as (the acquisition sequence of that frame - 1) × a fixed time interval (e.g., if the fixed interval is 0.5 seconds, then the time of the 3rd frame is 1 second). The time axis unit is uniformly set to seconds. The horizontal axis of the curve represents relative time, and the vertical axis represents the displacement (in millimeters) of the single-frame region at the corresponding time.

[0049] In one embodiment of the present invention, taking the start time of the force application phase as the starting point, the position where the first slope of the displacement curve in the logarithmic time domain changes to a maximum is taken as the critical moment, including: Set a small positive constant; Add the small constant to the difference between each moment and the moment when force is applied, and then take the logarithm to obtain the logarithmic time corresponding to each moment; The logarithmic displacement at each moment is obtained by adding the small constant to the difference between the displacement value of the displacement curve at each moment and the displacement value of the displacement curve at the moment of force application, and then taking the logarithm. Calculate the difference in logarithmic displacement between two adjacent time points, divide it by the difference in logarithmic time between these two adjacent time points, and obtain the logarithmic time domain slope between the two adjacent time points. Calculate the difference between the slopes of two adjacent logarithmic time domains to obtain the slope change; The absolute value of the slope change is obtained by taking the absolute value of the slope change. All positions that satisfy the first preset condition are selected to form a set of local maxima of the absolute value of the slope change; wherein, the first preset condition is: the absolute value of the previous slope change is less than the absolute value of the current slope change, and the absolute value of the current slope change is greater than or equal to the absolute value of the next slope change. The earliest position corresponding to the local maximum position is selected from the set of local maximum positions as the first maximum position, and the time corresponding to the first maximum position is determined as the critical time.

[0050] The positive small constant needs to be determined by combining the actual magnitude of the pelvic floor displacement data and the accuracy of the MRI device. The specific value range is 0.1 - 0.5 mm (corresponding to the typical small change in pelvic floor tissue displacement): If a 1.5T MRI device (displacement measurement accuracy is about 0.3 mm) is used, the small constant is taken as 0.3 mm; if a 3.0T MRI device (displacement measurement accuracy is about 0.1 mm) is used, the small constant is taken as 0.1 mm; Value-taking principle: Ensure that the result of the displacement difference + the small constant is greater than 0 (to avoid the logarithm being meaningless), and at the same time, the value of this constant is much smaller than the normal pelvic floor displacement difference (usually 2 - 10 mm), so as not to interfere with the authenticity of the displacement change trend.

[0051] Each moment is only limited to the moments corresponding to all image frames after the start moment of the forced phase and before the end moment of the evacuation phase. Specifically, two types of moments are excluded: Moments before the start moment of the forced phase (such as the resting and contraction phases): No abdominal pressure is applied in this phase, and there is no active force-induced deformation of the pelvic floor tissue. The data has nothing to do with the critical moment (the mechanical turning point after abdominal pressure loading); Moments after the end of the evacuation phase: The tissue has completed the evacuation action in this phase, the deformation tends to be stable, and there is no effective mechanical turning point information; During operation, first screen out all frame moments within the above-defined range from the time series of dynamic MRI, and then perform subsequent logarithmic transformation.

[0052] Two adjacent moments specifically refer to the moments corresponding to two continuously acquired image frames of dynamic MRI, that is, adjacent frame moments arranged in sequence according to the fixed acquisition interval of the device (such as 0.3 s / frame, 0.5 s / frame). It is not allowed to skip intermediate frames and select interval moments. For example, if the device acquires at an interval of 0.5 s / frame, the first frame moment after the start moment of the forced phase is t1, the second frame is t2, and the third frame is t3, then the adjacent moments are only continuous frame combinations such as (t1, t2), (t2, t3); specifically, the deformation of the pelvic floor tissue is a continuous time process, and continuous frame moments can fully reflect the continuity of the slope change, avoiding information loss caused by interval frames.

[0053] Both the previous and the next in the first preset condition specifically refer to 1 moment point directly adjacent to the current moment, rather than multiple moments. Specifically, taking the current moment t0 as an example, the previous moment is the previous frame moment t - 1 of t0 (continuously adjacent to t0), and the next moment is the next frame moment t + 1 of t0 (continuously adjacent to t0); only when the absolute value of the slope change corresponding to t - 1 < the absolute value of the slope change corresponding to t0, and the absolute value of the slope change corresponding to t0 ≥ the absolute value of the slope change corresponding to t + 1, will t0 be included in the local maximum position set; to avoid the complexity of the judgment standard and misjudgment caused by multi-neighborhood comparison (such as the previous 2 and the next 2).

[0054] To avoid misjudging small slope changes caused by noise as local maxima, a minimum threshold for the absolute value of slope changes needs to be set. The arithmetic mean of all absolute slope changes within a defined range (from the start of the exertion phase to the end of the emptying phase) is calculated and denoted as Savg. A threshold of 1.5-2 times Savg (denoted as Sth) is set. Only when the absolute value of the slope change at a certain moment is ≥ Sth and meets the first preset condition is that moment included in the set of local maxima locations. For example, if Savg = 0.2, then Sth is 0.3 (1.5 times). Although a moment with an absolute slope change of 0.25 satisfies the condition of smaller values ​​at the beginning and larger values ​​at the end, it is not included in the set of local maxima because it is below 0.3. It should be noted that 2 times Savg is used for 1.5T MRI equipment (slightly higher image noise), and 1.5 times Savg is used for 3.0T equipment (lower noise), balancing noise filtering and effective signal preservation.

[0055] The critical moment for judgment must conform to the physiological and mechanical characteristics of the pelvic floor tissues. The verification criteria are as follows: The critical moment must be within 0.5-5 seconds after the start of the exertion phase. That is, after the pelvic floor tissue is loaded by abdominal pressure, the elastic deformation usually lasts for 0.5 seconds. After 0.5 seconds, it enters the viscoelastic softening phase. After 5 seconds, the deformation tends to stabilize. If the critical moment exceeds this range, the data processing process needs to be re-examined. Before the critical moment, the logarithmic time domain slope of the displacement curve is usually stable at around 1.0 (approximately elastic deformation, with displacement and time having a linear relationship); after the critical moment, the slope drops to 0.3-0.8 (viscoelastic softening, and the rate of displacement increase slows down). If the slope change does not conform to this trend, the small constant or threshold needs to be readjusted.

[0056] In one embodiment of the present invention, within the post-critical window, a weighted fitting of the logarithmic relationship between displacement increment and time is performed to obtain a second slope as the post-critical power-law softening index, including: Starting from the critical moment, a positive time interval for avoiding the critical transient and a positive duration of the continuous time window are set. The time period from the critical moment plus the positive time interval for avoiding the critical transient to the critical moment plus the positive duration of the continuous time window is defined as the post-critical window. Take the logarithm of the difference between each time point within the critical window and the critical time point to obtain the logarithmic time of that time point relative to the critical time point; Calculate the difference between the displacement value of the displacement curve at this moment and the displacement value of the displacement curve at the critical moment, add the small constant to the difference and take the logarithm to obtain the logarithmic displacement increment at this moment relative to the critical moment. Calculate the ratio of the pixel area of ​​the functional region in each frame to the pixel area of ​​the functional region at the critical moment, and use this ratio as the weight for each frame. Construct an objective function with a constant term and the slope to be determined as variables. The objective function is the weight corresponding to each time point within the critical window, multiplied by the logarithmic displacement increment at that time point minus the constant term, and then subtracted by the sum of the squares of the product of the slope to be determined and the logarithmic time at that time point. Adjust the values ​​of the constant term and the slope to be determined so that the objective function reaches its minimum value, thus obtaining the second slope. Use the second slope as the critical post-power-law softening exponent.

[0057] This time interval needs to match the duration of transient fluctuations in the pelvic floor tissues after the critical point, and its value ranges from 0.3 to 1 second, specifically determined according to the following rules: If the patient is a young person (≤45 years old, with good elasticity of pelvic floor tissues), the transient fluctuation is shorter, and 0.3-0.5 seconds is taken; If the patient is a middle-aged or elderly person (>45 years old, with tissue elasticity deterioration), the transient fluctuation is relatively long, so take 0.6-1 seconds; During operation, a preliminary experiment can be conducted to observe: after the critical moment, if the logarithmic displacement increment of the displacement curve does not fluctuate significantly for 3 consecutive frames (according to the equipment acquisition interval, such as 1.5 seconds for 0.5 seconds / frame), the interval between the stable starting point and the critical moment is taken as the final value.

[0058] The duration must be sufficient to ensure that the data volume is sufficient and only includes the stable softening phase, with a value range of 2-4 seconds. Specific requirements: The minimum duration must include at least 5 frames (based on a minimum acquisition interval of 0.3 seconds per frame, 5 frames correspond to 1.5 seconds, and 2 seconds is used to ensure sufficient data volume) to avoid insufficient degrees of freedom during fitting. The duration cannot exceed 1 / 2 of the time from the critical moment to the end of the emptying phase. For example, if there are 6 seconds left from the critical moment to the end of the emptying phase, the duration can be up to 3 seconds to prevent the inclusion of data from the stable displacement phase (non-softening phase) in the later stage of emptying. Typical values ​​include: 3 seconds (6 frames) for a 1.5T MRI device (0.5 seconds / frame acquisition interval), and 2.4 seconds (8 frames) for a 3.0T MRI device (0.3 seconds / frame acquisition interval).

[0059] The pixel area of ​​the functional region is calculated based on the grayscale threshold and the determination of complete pixels. The steps are as follows: Based on the average gray value of the functional area of ​​the reference frame during the resting phase, half of this value is taken as the threshold. Any pixel in the functional area with a gray value greater than or equal to the threshold is considered a valid pixel. If the center point of a pixel is located within the boundary line of the functional area (according to the outline of the functional area), the area is included regardless of whether the grayscale meets the standard; if only part of the pixel is within the boundary (such as a pixel with blurred edges), the area ratio of the pixel within the boundary needs to be calculated. If the ratio is ≥50%, it is included in the area; if it is <50%, it is excluded. The actual pixel area of ​​the functional region is obtained by counting the number of all valid pixels and multiplying it by the actual area of ​​a single pixel (e.g., if the pixel pitch of an MRI device is 1.2 mm × 1.2 mm, then the area of ​​a single pixel is 1.44 square millimeters).

[0060] The gradient descent method is used to adjust the constant term and the slope to be determined, specifically including: Initial value settings: The initial value of the constant term is the average value of the logarithmic displacement increment within the window after the critical point, and the initial value of the slope to be determined is 0.5 (a typical empirical value for the slope of pelvic floor tissue softening). Learning rate setting: The learning rate is set to 0.01-0.05. If the objective function decreases slowly, increase the learning rate (e.g., 0.05); if oscillations occur, decrease the learning rate (e.g., 0.01). Iteration stopping condition: When the change in the objective function is less than 0.0001 after 100 consecutive iterations, or when the number of iterations reaches 1000 (to prevent infinite iteration), the adjustment is stopped, and the current constant term and the slope to be determined are taken. Verification: If the correlation coefficient (linear correlation between logarithmic shift increment and logarithmic time) after fitting is ≥0.85, the fitting is considered effective; if it is <0.85, the window duration or small constant needs to be readjusted and the fitting repeated.

[0061] The second slope obtained from the fitting (the critical post-power-law softening exponent) must meet the following physiological and data standards to be considered valid: Numerical range: The softening index of normal pelvic floor tissue is usually 0.2-0.8. If the slope is <0.2, it indicates that the tissue softens very slowly (which may be due to data acquisition error, such as insufficient abdominal pressure); if the slope is >0.8, it indicates that the tissue softens too quickly (which may be due to incorrect functional area division, such as including pixels that do not support tissue), and the data needs to be checked again. Residual requirement: The minimum value of the objective function (i.e., the sum of squared residuals) must be less than 1 / 10 of the maximum value of the logarithmic shift increment within the critical window. For example, if the maximum value of the logarithmic shift increment is 2, then the sum of squared residuals must be less than 0.2 to ensure that the fitting error is small. Clinical relevance: If the patient has a history of pelvic floor dysfunction (such as uterine prolapse), the softening index is usually >0.5; if the patient is healthy, it is usually <0.4. This clinical pattern can be used to help verify the effectiveness of the slope.

[0062] The specific clinical definition of an event indicator includes: Event time window: uniformly set to start from the time the MRI examination is completed, with a follow-up period of 24 months, and only events occurring within this window are counted.

[0063] Event determination criteria (meeting any one of these criteria is sufficient to mark an event as indicator = 1): Prolapse recurrence / progression: POP-Q stage improves by ≥1 stage compared to MRI examination (e.g., progressing from stage II to stage III), confirmed by clinical examination by a gynecologist or pelvic floor surgeon; Reoperation: If a second surgery is performed due to pelvic floor dysfunction (such as uterine prolapse, anterior or posterior vaginal wall prolapse), the surgical record shall prevail. Symptoms worsened: The patient reported a significant worsening of pelvic floor discomfort symptoms (such as a feeling of heaviness and urinary incontinence), and the physician's assessment confirmed that this was related to the degeneration of the pelvic floor support structures; Event indication = 0: No of the above events occurred during the 24-month follow-up period, and there was no change in the POP-Q stage or worsening of symptoms.

[0064] The criteria for constructing sample pairs specifically include: Sample inclusion criteria: Female patients aged 18-75; The patient has been diagnosed with pelvic floor dysfunction (such as POP-Q stage I-IV) and has completed a supine dynamic MRI examination and calculated the critical post-power-rate softening index. Able to cooperate in completing 24-month follow-up (unless there are serious underlying diseases leading to loss to follow-up).

[0065] Sample exclusion criteria: Patients with concurrent pelvic malignant tumors or severe neurological diseases (such as spinal cord injury); Incomplete MRI data (e.g., missing segments, failed index calculation); Patients who died or went missing during the follow-up period due to non-pelvic floor disorders.

[0066] Sample size and balance requirements: The total sample size should be at least 100 cases (to ensure that the model has enough data to learn). The ratio of positive to negative samples should be controlled between 1:1 and 1:3. If the number of cases is small (e.g., only 20 cases), the balance should be adjusted by oversampling positive samples (replicating a small number of positive samples) or undersampling negative samples (randomly deleting some negative samples).

[0067] Setting the initial values ​​of model parameters includes: The model intercept parameter is initially set to 0 (corresponding to a default risk probability of 0.5 when there is no feature input, which is consistent with the initial neutral assumption). The initial value of the model slope parameter was set to 0.1 (referring to the preliminary correlation trend between the risk of pelvic floor dysfunction and the softening index, to avoid optimization oscillations caused by an excessively large initial value). If the proportion of events with an indicator value of 1 in the sample is high (e.g., >40%), the initial intercept value can be adjusted to 0.2; if the proportion is low (<20%), it can be adjusted to -0.2 to help optimize faster convergence.

[0068] Definition of the natural exponential function: The base of the natural exponential function here is uniformly a mathematical constant e (approximately equal to 2.71828), which is the industry-standard natural exponential base and does not require additional adjustment.

[0069] Specifically, the numerical precision control is as follows: the linear predictor is calculated to retain 4 decimal places, the natural index is calculated to retain 6 decimal places, and the final risk probability is retained to retain 3 decimal places (e.g., 0.325, which is 32.5%), so as to facilitate the understanding of clinicians.

[0070] Sample weighting for negative log-likelihood includes: If the sample is imbalanced (e.g., the proportion of positive samples is <30%), weights need to be assigned to different samples. The adjusted objective function calculation rules are as follows: Calculate sample weights: Let the number of positive samples be N1 and the number of negative samples be N0. The weight of a positive sample = (N1 + N0) / (2 × N1), and the weight of a negative sample = (N1 + N0) / (2 × N0). Weighted negative log-likelihood: Objective function = Σ[sample weights × (event indication × (-ln(risk probability)) + (1 - event indication) × (-ln(1 - risk probability)))]; For example, if N1=30 and N0=70, then the weight of the positive sample = 100 / (2×30)≈1.667 and the weight of the negative sample = 100 / (2×70)≈0.714, and the contribution of the two types of samples to the objective function is balanced by the weights.

[0071] The specific algorithm and stopping conditions for parameter adjustment include: Parameter tuning algorithm: Batch gradient descent method is used (suitable for small to medium sample sizes, computationally stable). Specific steps: During each iteration, the partial derivatives of the objective function with respect to the intercept and slope are calculated using all training samples; Update the parameters according to the formula: new parameter value = old parameter value - learning rate × partial derivative; Parameter settings: Learning rate: fixed at 0.01 (balancing optimization speed and stability; if the objective function oscillates, reduce to 0.005; if convergence is slow, increase to 0.02). Stopping conditions: After 50 consecutive iterations, the change in the objective function is less than 0.0001 (i.e., the difference between the objective functions of two adjacent iterations is less than one ten-thousandth), or the total number of iterations reaches 1000 (to prevent infinite iteration). Optimization process monitoring: Output the current objective function value and parameter value every 10 iterations to facilitate timely detection of anomalies (such as an increase in the objective function, which requires checking the learning rate or initial value).

[0072] After the model is trained, its effectiveness needs to be evaluated using an independent test set (accounting for 20%-30% of the total samples, which is not used for parameter training). The core criteria are: Key performance indicator: AUC (Area Under Receiver Operating Characteristic) ≥ 0.75. A higher AUC indicates a stronger ability of the model to distinguish between events that have occurred and those that have not. Accuracy (number of correctly predicted samples / total number of test samples) ≥ 0.7; Recall rate (number of correctly predicted positive samples / actual number of positive samples) ≥ 0.65 (to avoid missing high-risk patients); If the evaluation fails to meet the target (e.g., AUC < 0.75), the sample construction needs to be re-examined (e.g., supplementing samples) or the initial parameter values ​​need to be adjusted, and training should be performed again.

[0073] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A system for constructing a risk model for female pelvic floor dysfunction, characterized in that, include: The data acquisition module acquires dynamic magnetic resonance data of the supine position, including the resting, contraction, exertion, and emptying phases, and records the time information of each phase. The reference coordinate establishment module determines the pubococcygeal line in the midsagittal position, establishes fixed reference coordinates based on the pubococcygeal line registration data, generates the functional region corresponding to the pubococcygeal line in the resting phase, and maps it to each frame. The displacement feature extraction module obtains the relatively resting displacement field through registration within the reference coordinates and functional areas of each frame. It extracts the regional displacement features along the tail side of the pubococcygeal line and normalizes them by the length of the pubococcygeal line to obtain the displacement curve over continuous time. The critical moment detection module takes the start of the force application phase as the starting point and detects the position where the first slope of the displacement curve changes the most in the logarithmic time domain as the critical moment. The softening index calculation module performs a weighted fitting of the logarithmic relationship between displacement increment and time within the critical window, and uses the fitted second slope as the critical power-law softening index; wherein, the critical window is determined based on the critical moment. The risk prediction module constructs a risk prediction model for female pelvic floor dysfunction using the post-critical power-law softening index, outputting individual risk probabilities, including: The input is the post-critical power-law softening exponent; The model training data consists of multiple sample pairs. Each sample pair contains the critical post-power-law softening exponent of the j-th sample and the event indicator of the j-th sample. The event indicator takes the value of zero or one, j is a positive integer representing the sample number, and the total number of samples is a positive integer. The linear predictor is defined as the product of the model intercept parameter, the model slope parameter, and the critical post-power-law softening exponent of the j-th sample. A logic function is defined as a function that maps any real number to the range between zero and one. The logic function is calculated by dividing one by one and raising the negative linear predictor of the natural exponential function to the power of one. The individual risk probability of the j-th sample is calculated using the aforementioned logical function; The objective function is defined as the negative log-likelihood based on the individual risk probability. Specifically, it is calculated by multiplying the event indication of each sample by the negative logarithm of the individual risk probability of that sample, and adding the negative logarithm of the difference between the event indication and the difference between the individual risk probabilities of that sample to obtain the sample parameter for each sample. The sample parameters of all samples are then summed to obtain the objective function. Adjust the values ​​of the model intercept parameter and the model slope parameter to minimize the value of the objective function, thereby obtaining the optimal model intercept parameter and the optimal model slope parameter; For any individual to be evaluated, the linear predictor is calculated using the corresponding critical post-power-law softening exponent, the optimal model intercept parameter, and the optimal model slope parameter. The risk probability of the individual is then obtained through the aforementioned logic function and used as the model output.

2. The system for constructing a risk model for female pelvic floor dysfunction according to claim 1, characterized in that, Acquire dynamic magnetic resonance imaging (MRI) data in the supine position, including the resting, contraction, exertion, and emptying phases, and record the time information for each phase, including: Determine the start and end times of the rest, contraction, exertion and emptying phases to form time information for each phase; Dynamic magnetic resonance data is generated by acquiring image frames corresponding to the resting, contraction, exertion, and emptying phases at fixed time intervals.

3. The system for constructing a risk model for female pelvic floor dysfunction according to claim 2, characterized in that, The pubococcygeal line is determined in the midsagittal plane. Based on the pubococcygeal line registration data, a fixed reference coordinate system is established. The functional regions corresponding to the pubococcygeal line during the resting phase are generated and mapped to each frame, including: In the image frame during the resting phase, the lower edge of the pubis and the end point of the coccyx are determined, and the straight line connecting the lower edge of the pubis and the end point of the coccyx is taken as the pubococcygeal line. Using the image frame corresponding to the start of the resting state as the reference image frame, for any image frame at any time, a rigid body transformation including rotation and translation is constructed. By adjusting the rotation and translation parameters, the lower edge of the pubis and the end point of the coccyx in the image frame are aligned with the lower edge of the pubis and the end point of the coccyx in the reference image frame, respectively, so as to establish a fixed reference coordinate. After rotating the direction vector from the lower edge of the pubis to the end of the coccyx counterclockwise by 90 degrees, normalize it to obtain the unit normal vector pointing to the caudal half-plane. On the reference image frame, the set of pixels located at the tail of the pubococcygeal line and whose unit normal vector and the projection of the line connecting each point in the region to the lower edge of the pubis are less than or equal to zero are defined as the functional region. By using the inverse transformation of rigid body transformation, the functional regions on the reference image frame are mapped to the corresponding image frames at each time point, thus obtaining the functional regions in each image frame.

4. The system for constructing a risk model for female pelvic floor dysfunction according to claim 3, characterized in that, Within the reference coordinates and functional regions of each frame, the relatively resting displacement field is obtained through registration. Regional displacement features are extracted along the tail side of the pubococcygeal line and normalized by the length of the pubococcygeal line to obtain continuous-time displacement curves, including: Use the grayscale of the reference image frame as the reference image grayscale; For each image frame at each time point, based on rigid body transformation, the image frame is converted into a rigid body registration image aligned to the reference coordinates; By using non-rigid registration, the grayscale difference between the rigid registration image and the reference image frame is minimized. At the same time, a smoothing term for the deformation field is added to determine the deformation field from the pixel in the reference coordinates to the corresponding position at each time step. The displacement field in the relative resting phase is obtained by subtracting the deformation field from the pixel position in the reference coordinates. The functional regions of each frame and the caudal unit direction pointing to the caudal direction are determined, and the distance between the lower edge of the pubis and the end point of the coccyx is defined as the length of the pubococcygeal line. Within each frame's functional region, calculate the average value of the projection of the displacement field onto the tail side unit direction after rigid body transformation, and normalize this average value by dividing it by the length of the tail line to obtain the single-frame region displacement corresponding to each moment. By associating each moment with the corresponding single-frame region displacement, a displacement curve over continuous time is formed.

5. The system for constructing a risk model for female pelvic floor dysfunction according to claim 4, characterized in that, Starting from the moment of the force application phase, the critical moment is defined as the location of the first maximum change in the slope of the displacement curve detected in the logarithmic time domain, including: Set a small positive constant; Add the small constant to the difference between each moment and the moment when force is applied, and then take the logarithm to obtain the logarithmic time corresponding to each moment; The logarithmic displacement at each moment is obtained by adding the small constant to the difference between the displacement value of the displacement curve at each moment and the displacement value of the displacement curve at the moment of force application, and then taking the logarithm. Calculate the difference in logarithmic displacement between two adjacent time points, divide it by the difference in logarithmic time between these two adjacent time points, and obtain the logarithmic time domain slope between the two adjacent time points. Calculate the difference between the slopes of two adjacent logarithmic time domains to obtain the slope change; The absolute value of the slope change is obtained by taking the absolute value of the slope change. All positions that satisfy the first preset condition are selected to form a set of local maxima of the absolute value of the slope change; wherein, the first preset condition is: the absolute value of the previous slope change is less than the absolute value of the current slope change, and the absolute value of the current slope change is greater than or equal to the absolute value of the next slope change. The earliest position corresponding to the local maximum position is selected from the set of local maximum positions as the first maximum position, and the time corresponding to the first maximum position is determined as the critical time.

6. The system for constructing a risk model for female pelvic floor dysfunction according to claim 5, characterized in that, Within the critical window, a weighted fit is performed on the logarithmic relationship between displacement increment and time. The second slope obtained from the fit is used as the power-law softening exponent after the critical period, including: Starting from the critical moment, a positive time interval for avoiding the critical transient and a positive duration of the continuous time window are set. The time period from the critical moment plus the positive time interval for avoiding the critical transient to the critical moment plus the positive duration of the continuous time window is defined as the post-critical window. Take the logarithm of the difference between each time point within the critical window and the critical time point to obtain the logarithmic time of that time point relative to the critical time point; Calculate the difference between the displacement value of the displacement curve at this moment and the displacement value of the displacement curve at the critical moment, add the small constant to the difference and take the logarithm to obtain the logarithmic displacement increment at this moment relative to the critical moment. Calculate the ratio of the pixel area of ​​the functional region in each frame to the pixel area of ​​the functional region at the critical moment, and use this ratio as the weight for each frame. Construct an objective function with a constant term and the slope to be determined as variables. The objective function is the weight corresponding to each time point within the critical window, multiplied by the logarithmic displacement increment at that time point minus the constant term, and then subtracted by the sum of the squares of the product of the slope to be determined and the logarithmic time at that time point. Adjust the values ​​of the constant term and the slope to be determined so that the objective function reaches its minimum value, thus obtaining the second slope. Use the second slope as the critical post-power-law softening exponent.

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