Hip replacement postoperative gait dynamics prediction method based on discrete optimal control

Abstract

The invention discloses a hip replacement postoperative gait dynamics prediction method based on discrete optimal control, and belongs to the field of clinical medical auxiliary prediction. The implementation method comprises the steps that kinematics data are collected through a preoperative gait motion capture experiment, muscle activation signals are collected through a surface myoelectricity system, and on this basis, a neuromuscular control strategy of a patient is obtained through a neural network; predicting the gait motion characteristics of the postoperative patient based on discrete mechanics and an optimal control method, and predicting the postoperative muscle activation degree by using the neuromuscular control strategy; by comparing the muscle activation degrees before and after the operation, the influence of the replacement operation on the muscle force change of the hip joint of the patient is investigated. According to the method, discrete optimal control and the neural network are combined, the learning characteristics of human nerve-muscle control are considered while the physical characteristics of the system are not deviated, personalized muscle control strategies better conforming to different patients can be found, and personalized prediction of postoperative gait dynamic characteristics is achieved.

Description

Technical Field

[0001] The invention relates to a method for predicting gait dynamics after hip replacement based on discrete optimal control, and belongs to the field of clinical medical auxiliary prediction. Background Art

[0002] Total hip arthroplasty (THA) is one of the main technical means to treat end-stage hip joint diseases such as degenerative osteoarthritis and femoral head necrosis. According to statistics, 16.3% of patients still experience prosthesis dislocation and prosthesis infection after surgery, which further leads to gait instability, difficulty squatting and other gait abnormalities. The root cause of the change in the patient's motor function lies in the change in the biomechanical properties of the patient's hip joint soft tissue. The muscle structure around the hip joint is complex, which can not only drive joint movement, but also maintain the stability of the hip joint together with static structures such as joint capsule and ligaments. Hip joint lesions and the resulting movement compensation reduce the patient's muscle activity ability; artificial joint implantation will remove and loosen part of the soft tissue, change the surrounding muscle force arm of the hip joint, and then affect the working efficiency of the soft tissue around the hip joint, which is the main cause of postoperative joint instability. The traditional prosthesis implantation scheme does not take into account the change in the patient's muscle force pattern after surgery, resulting in insufficient muscle force in the patient's muscles after surgery, limiting the patient's postoperative gait function recovery effect.

[0003] There are existing invention patents, which often use electromyography and optimized coupled muscle force calculation models to obtain muscle force distribution results corresponding to human movement. However, this method can only provide muscle biomechanical information for surgical treatment based on preoperative gait experiments, lacks postoperative muscle force prediction, and does not take into account the learning characteristics of human neuromuscular control, and cannot complete the analysis of changes in muscle force patterns. Summary of the invention

[0004] The main purpose of the present invention is to solve the problem that the existing technology cannot consider the postoperative muscle strength changes before hip replacement surgery, resulting in unsatisfactory postoperative exercise rehabilitation effect. The present invention provides a method for predicting gait dynamics after hip replacement based on discrete optimal control; the method uses preoperative gait motion capture experiments to collect kinematic data, and uses a surface electromyography system to collect muscle activation signals, and on this basis, obtains the patient's neuromuscular control strategy through a neural network; further, based on discrete mechanics and optimal control methods, the postoperative patient's gait motion characteristics are predicted, and the postoperative muscle activation is predicted using the above neuromuscular control strategy; by comparing the preoperative and postoperative muscle activation, the effect of replacement surgery on the patient's hip joint muscle strength changes is examined, providing guidance for clinical prosthesis implantation surgery planning, and solving the problem that postoperative muscle mechanical function changes cannot be considered before surgery.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] The present invention discloses a method for predicting gait dynamics after hip replacement based on discrete optimal control, comprising the following steps:

[0007] Step 1: Perform motion capture and surface electromyography (EMG) signal acquisition during motion simultaneously; build a motion capture system with an infrared camera, attach infrared reflective markers to the subject's lower limbs, and collect gait kinematics data; at the same time, attach electrodes to the skin surface that drives the hip joint muscles, and the electrodes are used to collect the surface electromyography (EMG) signal of the affected side of the subject; the surface electromyography (EMG) signal includes the surface electromyography (EMG) signal during gait. 1 And the maximum force electromyographic signal EMG of each muscle group during the maximum voluntary contraction 2 .

[0008] Step 2: Establish a personalized musculoskeletal model for the patient, including a skeletal model and a joint model; the skeletal model includes the pelvis, left and right thighs, left and right calves, and feet; the joints include the hip joint, knee joint, and ankle joint, where the hip joint connects the pelvis and thigh, the knee joint connects the thigh and calf, and the ankle joint connects the calf and foot. Since only the movement in the sagittal plane of the joint is considered, the above joints are all regarded as single-degree-of-freedom rotation pairs; the control equation of this musculoskeletal model is a typical set of differential algebraic equations:

[0009]

[0010] Among them, q m is the generalized coordinate of the musculoskeletal system, M represents the generalized mass matrix of the musculoskeletal system, Q = Q ext +Q joint represents the generalized force, including the external force Q ext and joint torque Q joint C represents the constraint force related to generalized coordinates and time, C q is the Jacobian matrix of the constraint force. λ is the conjugate Lagrange multiplier of the constraint equation, which represents the normal force corresponding to the constraint surface spanned in generalized coordinates. Considering the difference between the musculoskeletal model and the real human anatomy, as well as the elasticity and damping properties of the human skin and muscle tissue under the marker points, a spring-damper connection is established between the measured marker points and the coordinates of the bony marker points corresponding to the musculoskeletal model, thereby converting equation (1) into a problem of minimizing elastic potential energy. By solving the problem of minimizing elastic potential energy, the joint angles q of the hip and knee joints in a single gait cycle before surgery are obtained. pre .

[0011] Step 3: Calculate preoperative muscle activation a pre .

[0012] First, the surface electromyography signal EMG 1 and EMG 2Perform rectification and filtering to obtain the filtered surface electromyography signal and And use right After normalization, the smooth signal u is obtained, which is called the muscle excitation signal. The muscle excitation signal u is used as the input of the first-order time-delay differential equation to solve the muscle activation degree a EMG ;

[0013] Secondly, the joint angle q pre As input, substitute into formula (1) to get the joint torque The deep muscle activation a will be solved SO The problem is regarded as an optimization problem for solution, that is, the static optimization method:

[0014]

[0015] in, Represents muscle activation, N mus is the number of hip joint muscles, and represents the muscle force associated with muscle activation, R mus Represents the force arm of the muscle force relative to the joint center. The optimization target is the muscle activation degree a of each muscle i The sum of squares, with weight w i Take 1.

[0016] Finally, the preoperative muscle activation degree a was obtained through the above-mentioned myoelectric mixed inverse dynamics analysis. pre =a EMG +a SO .

[0017] Step 4: Construct a mapping strategy based on reinforcement learning to calculate joint kinematics and muscle activation.

[0018] In the human musculoskeletal model, the joint angles in step 2 are As input, the muscle activation in step 3 For the output, build a neural network, where N q is the number of joints, and the proximal strategy optimization algorithm is used to train the optimal control strategy for muscle activation, and obtain the mapping strategy π from joint angles to muscle activation:

[0019]

[0020] Where r represents the reward function. To match the experimental results, the present invention maximizes the joint angle and muscle activation The matching degree with the experimental results pre and a preDetermine the optimal strategy for the goal, ω q represents the joint posture tracking reward coefficient, ω a Represents the muscle activation tracking reward coefficient.

[0021] Step 5: Prediction of the patient's postoperative gait kinematics.

[0022] Construct a two-dimensional human body model, including bones and joints; the bones include the trunk, thigh, calf and foot, and the joints include the hip joint, knee joint and ankle joint, which are modeled as single-degree-of-freedom hinges; define the generalized coordinates in the two-dimensional model as the joint angles of each joint:

[0023] q=[x 1 y 1 q 1 q 2 q 3 q 4 q 5 q 6 q 7 ] T (4)

[0024] In order to drive the two-dimensional plane model to produce gait motion, the joint angle motion of the two-dimensional plane model is driven by joint torque, including:

[0025] u=[u 1 u 2 u 3 u 4 u 5 u 6 ] T (5)

[0026] To describe the foot-ground contact relationship, the foot is modeled as a rigid body, and different support states are defined according to the geometric contact relationship between the toe and heel and the ground, including full foot contact FHC, heel contact HC, and toe contact FC. When the right side is the support side and the left side is the swing side, the single gait cycle is divided into the following four stages:

[0027] ① The first double-foot support phase: the moment when the right foot heel touches the ground is defined as the initial moment of the gait cycle. In this gait phase, the right heel and the left toe keep in contact with the ground, and at the end moment, the right toe touches the ground, and the supporting foot changes from the heel-touch HC phase to the full-foot-touch FHC phase; ② The second double-foot support 2: In this phase, the right foot keeps the full-foot touch the ground, the left toe leaves the ground at the end moment, and the left foot enters the swing phase swing; ③ The first single-foot support phase: In this phase, the left foot keeps the swing state and has no contact with the ground; the right heel leaves the ground at the end moment, and the supporting foot changes from the full-foot support phase FHC to the toe-touch FC, and the heel constraint is released at the end moment; ④ The second single-foot support phase: In this phase, the right foot keeps the toe-touch state, the left foot swings to the front of the right foot at the initial moment, and through the heel touches the ground, the support state changes from the single-foot support phase to the double-foot support phase.

[0028] The processing method for the four-stage transition is as follows: to ensure the continuity of joint movement in adjacent stages, the terminal posture of the previous stage is kept consistent with the initial posture of the next stage; further, to ensure left-right symmetry in the complete gait cycle, the initial posture and terminal posture of the entire single gait cycle satisfy an antisymmetric relationship.

[0029] The human gait motion control problem can be regarded as an optimal control problem to be solved. For the two-dimensional plane model, the joint angle q(t) is a generalized coordinate and must satisfy the Euler-Lagrange equation. At the same time, the human joint motion trajectory must meet the optimization goal, that is, the function J(u) of the generalized force u(t) to ensure the minimum joint torque. Considering the above foot-ground contact relationship, the optimal control problem of the constrained system is in continuous form:

[0030]

[0031] in, is the Lagrangian of the system, f(t) represents the force applied to the system; represents the Jacobian matrix of the constraint function Ω(q), where the constraint function Ω(q) is defined based on the foot-ground contact relationship, G T (q)·λ represents the foot-ground geometric contact constraint force;

[0032] Discretize equation (6) and give the optimal result in discrete form:

[0033] First, the generalized coordinate q that changes with time is discretized, and the discrete time node [t 0 ,...,t n =t 0 +n△t,...,t N =t 0 +N△t], N is the number of discrete time nodes, △t is the time interval, and the nth time node t nThe corresponding discrete generalized coordinates are q n .

[0034] Formula (6b) restricts the system motion to the interior of the constraint manifold Based on QR decomposition, we introduce T (q)·(G T The null space matrix P(q) with (q)λ)=0 eliminates redundant constraints; so far, the discrete mechanics and optimal control problem of the constrained system is described as:

[0035]

[0036] Among them, q d and u d denote the discrete generalized coordinates and generalized forces corresponding to discrete time nodes, J d (q d ,u d ) represents the discretized objective function. The interior point method is used to numerically solve equation (7) to obtain the optimal joint motion trajectory q that satisfies the patient's minimum joint torque. opt .

[0037] Step 6: The optimal joint angle trajectory q obtained in step 5 opt As input, the mapping strategy π obtained in step 4 is used as the muscle control strategy, and the corresponding postoperative muscle activation degree a is output. opt ; Compare the preoperative experimental muscle activation a in step 3 pre and postoperative predicted muscle activation opt , analyzed the changes in the force mechanism of the main muscles of the hip joint after surgery, and obtained the prediction results of the changes in the muscle force pattern after surgery.

[0038] Beneficial effects:

[0039] 1. The present invention discloses a method for predicting gait dynamics after hip replacement based on discrete optimal control theory. By establishing a method for predicting gait after hip replacement based on a physical model, the method provides the changes in the gait dynamics characteristics of the patient after surgery before surgery, thereby being able to consider the muscle compensation problems caused by postoperative muscle weakness or imbalance of muscle strength on the surgical side before surgery, which helps to improve the accuracy and efficiency of preoperative artificial prosthesis implantation.

[0040] 2. The present invention discloses a method for predicting gait dynamics after hip replacement surgery based on discrete optimal control theory. It uses a neural network to obtain the patient's muscle control strategy. Compared with traditional muscle recruitment strategies such as static optimization, it takes into account the learning characteristics of human neuromuscular control, which helps to find personalized muscle control strategies that are more suitable for different patients and realize personalized prediction of postoperative gait dynamics characteristics.

[0041] 3. The present invention discloses a method for predicting gait dynamics after hip replacement based on discrete optimal control theory, which uses the discrete mechanics and optimal control for constrained systems (DMOCC) method to predict postoperative gait motion. For complex systems with multiple degrees of freedom such as the human musculoskeletal system, the DMOCC model can keep the physical characteristics of the system from deviating during the discrete process, and is more in line with the physical laws of motion of the human musculoskeletal dynamics system than traditional indirect and direct methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Flow chart of the method for predicting gait dynamics after hip replacement based on discrete optimal control theory of the present invention;

[0043] Figure 2 Schematic diagram of infrared points for gait motion capture before surgery, where: Figure 2 (a) is the front view, Figure 2 (b) is a rear view;

[0044] Figure 3 Schematic diagram of the human skeleton model with foot-ground constraints, where: Figure 3 (a) is a schematic diagram of the planar bipedal model and its generalized coordinates. Figure 3 (b) is a schematic diagram of the foot-ground geometric relationship during the heel contact phase. Figure 3 (c) is a schematic diagram of the foot-ground geometric relationship during the toe contact phase. Figure 3 (d) is a schematic diagram of the foot-ground geometric relationship during the full foot contact phase;

[0045] Figure 4 Schematic diagram of phase division of a single gait cycle and the relationship between foot and ground constraints;

[0046] Figure 5 The optimal joint angle after surgery predicts outcomes. DETAILED DESCRIPTION

[0047] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0048] Embodiment 1:

[0049] like Figure 1 As shown, the method for predicting gait dynamics after hip replacement surgery based on discrete optimal control theory disclosed in this embodiment has the following specific implementation steps:

[0050] Step 1: Patient kinematic data and electromyographic signal collection experiment.

[0051] A male patient with femoral head necrosis was selected. His main symptoms were hip pain and lameness. Conservative treatment was ineffective and he received unilateral total hip replacement. Infrared reflective markers were attached to the lower limbs of the subject. The template for the markers was as follows: Figure 2 As shown. At the same time, electrodes were attached to the skin surface of the muscles that drive hip flexion and extension (gluteus maximus, gluteus medius, rectus femoris, vastus intermedius, biceps femoris, gastrocnemius, tibialis anterior) to collect surface electromyography (EMG). The subjects walked back and forth at a self-selected speed, and the trajectory of the markers was captured by an infrared camera as the patient's kinematic data. The surface electromyography signals of the hip joint muscles during walking were synchronously collected and recorded as EMG. 1 The patients were also asked to repeat the Maximum Voluntary Contraction (MVC) trajectory three times to obtain the maximum force capacity of each muscle group, and the corresponding electromyographic signals were recorded as EMG. 2 .

[0052] Step 2, including bones and joints; the bones include pelvis, left and right thighs, left and right calves and feet; the joints include: hip joint, knee joint and ankle joint, where the hip joint connects the pelvis and thigh, the knee joint connects the thigh and calf, and the ankle joint connects the calf and foot. Since only the movement in the sagittal plane of the joint is considered, the above joints are all regarded as single-degree-of-freedom rotation pairs; the control equation of this musculoskeletal model is a typical differential algebraic equation system:

[0053]

[0054] Among them, q m is the generalized coordinate of the musculoskeletal system, M represents the generalized mass matrix of the musculoskeletal system, Q = Q ext +Q joint represents the generalized force, including the external force Q ext and joint torque Q joint C represents the constraint force related to generalized coordinates and time, C q is the Jacobian matrix of the constraint force. λ is the conjugate Lagrange multiplier of the constraint equation, which represents the normal force corresponding to the constraint surface spanned in generalized coordinates. Considering the difference between the musculoskeletal model and the real human anatomy, as well as the elasticity and damping properties of the human skin and muscle tissue under the marker points, a spring-damper connection is established between the measured marker points and the coordinates of the bony marker points corresponding to the musculoskeletal model, thereby converting equation (1) into a problem of minimizing elastic potential energy. By solving the problem of minimizing elastic potential energy, the joint angles q of the hip and knee joints in a single gait cycle before surgery are obtained. pre .

[0055] Step 3: Calculate preoperative muscle activation a pre .

[0056] First, the surface electromyography signal EMG 1 and EMG 2 Perform rectification and filtering to obtain the filtered surface electromyography signal and And use right After normalization, the smooth signal u is obtained, which is called the muscle excitation signal. The muscle excitation signal u is used as the input of the first-order time-delay differential equation to solve the muscle activation degree a EMG ;

[0057] Secondly, the joint angle q pre As input, substitute into formula (1) to get the joint torque The deep muscle activation a will be solved SO The problem is regarded as an optimization problem for solution, that is, the static optimization method:

[0058]

[0059] in, Represents muscle activation, N mus is the number of hip joint muscles, and represents the muscle force associated with muscle activation, R mus Represents the force arm of the muscle force relative to the joint center. The optimization target is the muscle activation degree a of each muscle i The sum of squares, with weight w i Take 1.

[0060] Finally, the preoperative muscle activation degree a was obtained through the above-mentioned myoelectric mixed inverse dynamics analysis. pre =a EMG +a SO ;

[0061] Step 4: Calculate the mapping strategy between joint kinematics and muscle activation based on reinforcement learning;

[0062] In the human musculoskeletal model, the joint angles in step 2 are As input, the muscle activation in step 3 For the output, build a neural network, where N q is the number of joints, and the proximal strategy optimization algorithm is used to train the optimal control strategy for muscle activation, and obtain the mapping strategy π from joint angles to muscle activation:

[0063]

[0064] Where r represents the reward function. To match the experimental results, the present invention maximizes the joint angle and muscle activation The matching degree with the experimental results pre and a pre Determine the optimal strategy for the goal, ω q represents the joint posture tracking reward coefficient, ω a Represents the muscle activation tracking reward coefficient.

[0065] Step 5: Prediction of the patient's postoperative gait kinematics. Construct a two-dimensional human body model, including bones and joints; the bones include the trunk, thigh, calf and foot, and the joints include the hip joint, knee joint and ankle joint, which are modeled as single-degree-of-freedom hinges, such as Figure 3 As shown in (a), through the reconstruction of the patient's medical images, the geometric parameters such as the length and center of mass of each bone segment and the inertial parameters such as mass and moment of inertia can be obtained (as shown in Table 1). The generalized coordinates in the two-dimensional plane model are defined as the joint angles of each joint:

[0066] q=[x 1 y 1 q 1 q 2 q 3 q 4 q 5 q 6 q 7 ] T (4)

[0067] Among them, x 1 ,y 1 They represent the horizontal and vertical coordinates of the heel of the supporting foot, q i (i=1,...,7) represents the angle between each segment and the vertical direction.

[0068]

[0069] In order to drive the two-dimensional plane model to produce gait motion, the joint angle motion of the two-dimensional plane model is driven by the joint torque, and the generalized force includes:

[0070] u=[u 1 u 2 u 3 u 4 u 5 u 6 ] T (5)

[0071] To describe the foot-ground contact relationship, the foot is modeled as a rigid body, and different support states are defined according to the geometric contact relationship between the toe and heel and the ground, including: full foot contact (FHC, such as Figure 3(d)), heel contact (HC, such as Figure 3 (b) and forefoot contact (FC, such as Figure 3 (c)); When the right side is the support side and the left side is the swing side, the single gait cycle is divided into the following four stages (such as Figure 4 shown):

[0072] ① The first double-foot support phase: the moment when the right foot heel touches the ground is defined as the initial moment of the gait cycle. In this gait phase, the right foot heel and the left foot toe keep in contact with the ground, and at the end moment, the right foot toe touches the ground, and the supporting foot changes from the heel-touching HC phase to the full-foot-touching FHC phase; ② The second double-foot support 2: In this phase, the right foot keeps the full-foot touching the ground, the left foot toe leaves the ground at the end moment, and the left foot enters the swing phase swing; ③ The first single-foot support phase: In this phase, the left foot keeps the swinging state and has no contact with the ground; the right foot heel leaves the ground at the end moment, and the supporting foot changes from the full-foot support phase FHC to the toe-touching FC, and the heel constraint is released at the end moment; ④ The second single-foot support phase: In this phase, the right foot keeps the toe-touching state, the left foot swings to the front of the right foot at the initial moment, and through the heel touches the ground, the support state changes from the single-foot support phase to the double-foot support phase;

[0073] The processing method for the four-stage conversion is as follows: to ensure the continuity of joint motion in adjacent stages, the terminal posture of the previous stage is consistent with the initial posture of the next stage; further, to ensure left-right symmetry in the complete gait cycle, the initial posture and terminal posture of the entire single gait cycle satisfy an antisymmetric relationship;

[0074] The human gait motion control problem can be regarded as an optimal control problem to be solved. For the two-dimensional plane model, the joint angle q(t) is a generalized coordinate and must satisfy the Euler-Lagrange equation. At the same time, the human joint motion trajectory must meet the optimization goal, that is, the function J(u) of the generalized force u(t) to ensure the minimum joint torque. Considering the above foot-ground contact relationship, the optimal control problem of the constrained system is in continuous form:

[0075]

[0076] in, is the Lagrangian of the system, f(t) represents the force applied to the system; G represents the Jacobian matrix of the constraint function Ω(q(t)), where the constraint function Ω(q(t)) is defined based on the foot-ground contact relationship. T (q(t))·λ represents the foot-ground geometric contact constraint force;

[0077] Discretize equation (6) and give the optimal result in discrete form:

[0078] First, the generalized coordinates q(t) that vary with time are discretized, and the discrete time nodes [t 0 ,...,t n =t 0 +n△t,...,t N =t 0 +N△t], N is the number of discrete time nodes, △t is the time interval, and the nth time node t n The corresponding discrete generalized coordinates are q n .

[0079] Formula (6b) restricts the system motion to the interior of the constraint manifold Based on QR decomposition, we introduce T (q)·(G T The null space matrix P(q) with (q)λ)=0 eliminates redundant constraints; so far, the discrete mechanics and optimal control problem of the constrained system is described as:

[0080]

[0081] Among them, q d and u d denote the discrete generalized coordinates and generalized forces corresponding to discrete time nodes, J d (q d ,u d ) represents the discretized objective function. The interior point method is used to numerically solve equation (7) to obtain the optimal joint motion trajectory q that satisfies the patient's minimum joint torque. opt ; The results are as follows Figure 5 As shown, the predicted joint angles are basically consistent with the standard human gait phase. ;

[0082] Step 6: Use the mapping relationship in step 4 to obtain the postoperative muscle force distribution

[0083] The optimal joint angle trajectory q obtained in step 5 opt As input, the mapping strategy π obtained in step 4 is used as the muscle control strategy, and the corresponding postoperative muscle activation degree a is output. opt ; Compare the preoperative experimental muscle activation a in step 3 pre and postoperative predicted muscle activation opt ;

[0084] Step 7. By comparing the changes in muscle activation before and after surgery, a prosthesis implantation plan can be formulated before surgery based on the changes in muscle strength after surgery: on the one hand, avoid loosening the main force-generating muscles, and on the other hand, adjust the prediction model to find a prosthesis implantation angle that is more conducive to the patient's postoperative recovery. After surgery, further observe the patient's recovery, evaluate the degree of gait rehabilitation, and verify the preoperative prediction results.

[0085] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting gait dynamics after hip replacement based on discrete optimal control, characterized by: The following steps are included: Step 1: Perform motion capture and surface electromyography signal collection during action simultaneously; build a motion capture system with infrared cameras, attach infrared reflective markers to the lower limbs of the subject, and collect gait kinematics data; at the same time, attach electrodes to the skin surface that drives the hip joint muscles, and the electrodes are used to collect the surface electromyography signal EMG of the affected side of the subject; the surface electromyography signal EMG includes the surface electromyography signal EMG1 during gait and the maximum force electromyography signal EMG2 during the maximum voluntary contraction of each muscle group; Step 2: Establish a personalized musculoskeletal model for the patient, including a skeletal model and a joint model; the skeletal model includes the pelvis, left and right thighs, left and right calves, and feet; the joints include the hip joint, knee joint, and ankle joint, wherein the hip joint connects the pelvis and thigh, the knee joint connects the thigh and calf, and the ankle joint connects the calf and foot; since only the movement in the sagittal plane of the joint is considered, the above joints are all regarded as single-degree-of-freedom rotation pairs; the gait kinematics data of step 1 is input into the musculoskeletal model, and the preoperative lower limb joint angle q is calculated using inverse kinematics. pre Step 3: Calculate preoperative muscle activation a pre : First, the surface electromyographic signals EMG1 and EMG2 are rectified and filtered to obtain the filtered surface electromyographic signals. and And use right After normalization, the smooth signal u is obtained, which is called the muscle excitation signal. The muscle excitation signal u is used as the input of the first-order time-delay differential equation to solve the muscle activation degree a EMG ; Secondly, the joint angle q pre As input, the control equation of the musculoskeletal model is used to obtain the joint torque The deep muscle activation degree a will be solved SO The problem is regarded as an optimization problem for solution, that is, the static optimization method: in, Represents muscle activation, N mus is the number of hip joint muscles, and represents the muscle force associated with muscle activation, R mus Represents the force arm of the muscle force relative to the joint center; the optimization target is the muscle activation degree a of each muscle i The sum of squares, with weight w i Take 1; The preoperative muscle activation degree a was obtained through the above-mentioned myoelectric mixed inverse dynamics analysis. pre =a EMG +a SO ; Step 4: Construct a mapping strategy based on reinforcement learning to calculate joint kinematics and muscle activation; In the human musculoskeletal model, the joint angles in step 2 are As input, the muscle activation in step 3 For the output, build a neural network, where N q is the number of joints, and the proximal strategy optimization algorithm is used to train the optimal control strategy for muscle activation, and obtain the mapping strategy π from joint angles to muscle activation: Among them, r represents the reward function, which is to match the experimental results to maximize the joint angle and muscle activation The matching degree with the experimental results pre and a pre Determine the optimal strategy for the goal, ω q represents the joint posture tracking reward coefficient, ω a Represents the muscle activation tracking reward coefficient; Step 5: Prediction of the patient's postoperative gait kinematics; Construct a two-dimensional human body model, including bones and joints; the bones include the trunk, thigh, calf and foot, and the joints include the hip joint, knee joint and ankle joint, which are modeled as single-degree-of-freedom hinges; define the generalized coordinates in the two-dimensional model as the joint angles of each joint: q=[x1 y1 q1 q2 q3 q4 q5 q6 q7] T (4) In order to drive the two-dimensional plane model to produce gait motion, the joint angle motion of the two-dimensional plane model is driven by joint torque, including: u=[u1 u2 u3 u4 u5 u6] T (5) The foot is modeled as a rigid body, and different gait phases are defined according to the geometric relationship between the toe and heel and the ground. The foot-ground contact constraints at different phases are defined, including full foot contact FHC, heel contact HC, and toe contact FC. When the right side is the support side and the left side is the swing side, the single gait cycle is divided into the following four phases: ① The first double-foot support period: the moment when the right foot heel touches the ground is defined as the initial moment of the gait cycle. In this gait stage, the right foot heel and the left foot toe keep in contact with the ground, and the right foot toe touches the ground at the end, and the supporting foot changes from the heel-touching HC stage to the full-foot-touching FHC stage; ② The second double-foot support period: In this stage, the right foot keeps the full-foot touching the ground, the left foot toe leaves the ground at the end, and the left foot enters the swing stage swing; ③ The first single-foot support period: In this stage, the left foot keeps the swinging state and has no contact with the ground; the right foot heel leaves the ground at the end, and the supporting foot changes from the full-foot support stage FHC to the toe-touching FC, and the heel constraint is released at the end; ④ The second single-foot support period: In this stage, the right foot keeps the toe-touching state, the left foot swings to the front of the right foot at the initial moment, and through the heel touches the ground, the support state is converted from the single-foot support period to the double-foot support period; The human gait motion control problem is regarded as an optimal control problem to be solved. For the two-dimensional plane model, the joint angle q(t) is a generalized coordinate and must satisfy the Euler-Lagrange equation. At the same time, the human joint motion trajectory must meet the optimization goal, that is, the function J(u) of the generalized force u(t) to ensure the minimum joint torque. Considering the above foot-ground contact relationship, the optimal control problem of the constrained system is in continuous form: in, is the Lagrangian of the system, f(t) represents the force applied to the system; represents the Jacobian matrix of the constraint function Ω(q), where the constraint function Ω(q) is defined based on the foot-ground contact relationship, G T (q)·λ represents the foot-ground geometric contact constraint force; Discretize equation (6) and give the optimal result in discrete form: First, the generalized coordinate q that changes with time is discretized, and the discrete time nodes [t0,...,t n =t0+n△t,...,t N =t0+N△t], N is the number of discrete time nodes, △t is the time interval, and the nth time node t n The corresponding discrete generalized coordinates are q n ; Formula (6b) restricts the system motion to the interior of the constraint manifold Based on QR decomposition, we introduce T (q)·(G T The null space matrix P(q) with (q)λ)=0 eliminates redundant constraints; so far, the discrete mechanics and optimal control problem of the constrained system is described as: Among them, q d and u d denote the discrete generalized coordinates and generalized forces corresponding to discrete time nodes, J d (q d ,u d ) represents the discretized objective function. The interior point method is used to numerically solve equation (7) to obtain the optimal joint motion trajectory q that satisfies the patient's minimum joint torque. opt ; Step 6: The optimal joint angle trajectory q obtained in step 5 opt As input, the mapping strategy π obtained in step 4 is used as the muscle control strategy, and the corresponding postoperative muscle activation degree a is output. opt ; Compare the preoperative experimental muscle activation a in step 3 pre and postoperative predicted muscle activation opt , analyzed the changes in the force mechanism of the main muscles of the hip joint after surgery, and obtained the prediction results of the changes in the muscle force pattern after surgery.

2. The method for predicting gait dynamics after hip replacement based on discrete optimal control according to claim 1, characterized in that: In step 2, The governing equations of the musculoskeletal model are a system of differential algebraic equations: Among them, q m is the generalized coordinate of the musculoskeletal system, M represents the generalized mass matrix of the musculoskeletal system, Q = Q ext +Q joint represents the generalized force, including the external force Q ext and joint torque Q joint ; C represents the constraint force related to generalized coordinates and time, C q is the Jacobian matrix of the constraint force. λ is the conjugate Lagrange multiplier of the constraint equation, which represents the normal force corresponding to the constraint surface spanned in generalized coordinates. Considering the difference between the musculoskeletal model and the real human anatomy, as well as the elasticity and damping properties of the human skin and muscle tissue under the marker points, a spring-damper connection is established between the measured marker points and the coordinates of the bony marker points corresponding to the musculoskeletal model, thereby converting equation (1) into a problem of minimizing elastic potential energy. By solving the problem of minimizing elastic potential energy, the joint angles q of the hip and knee joints in a single gait cycle before surgery are obtained. pre .

3. The method for predicting gait dynamics after hip replacement based on discrete optimal control as claimed in claim 2, characterized in that: In step five, The processing method for the four-stage transition is as follows: to ensure the continuity of joint movement in adjacent stages, the terminal posture of the previous stage is consistent with the initial posture of the next stage; to ensure left-right symmetry in the complete gait cycle, the initial posture and terminal posture of the entire single gait cycle satisfy an antisymmetric relationship.

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