KR101190840B1 - Uncertainty estimation method of constraint force in human lower limb using multibody modeling and statiscal methods - Google Patents

Abstract

Uncertainty estimation method of the lower body restraint force using the multi-body modeling and statistical methodology according to the present invention comprises the steps of modeling the lower body part of the human body as a multi-body model; Analyzing the restraint force of the knee joint that occurs during the lower body movement; And analyzing the uncertainty section of the binding force by using statistical methodology. The reliability of the estimation of the binding force on the lower limb of the human body may be increased.

Description

UNCERTAINTY ESTIMATION METHOD OF CONSTRAINT FORCE IN HUMAN LOWER LIMB USING MULTIBODY MODELING AND STATISCAL METHODS}

The present invention relates to a method for estimating the uncertainty of the lower body restraint force using multibody modeling and statistical methodology. More specifically, the anatomical characteristics and statistical methodology of the lower body part of the human body are combined with multibody dynamics to apply pressure to the knee bone. It is about how to predict.

Since the development of modern civilization is fundamentally for human beings, science and technology and science that led the development of civilization are also related to human beings, and there are also various academic fields that are interested in the movement of the human body. In the current era, the field of biomechanical research is gradually expanding and segmenting due to the improvement of living standards, the increase of interest in health, and the demand for high quality products centered on humans. Especially in biomechanical research, the development of mathematical models of musculoskeletal systems has developed into a highly reliable phase over the last few years, and these models are a combination of multibody dynamics theory, muscle mechanics and the geometry of the musculoskeletal system. Often released.

In addition, by using kinematic information of the lower extremity of the human body, it is possible to measure the force generated in muscles and tendons and the restraint force of joints through dynamic dynamics. Using this relationship, dynamic analysis of the lower extremity of the human body is possible, and the standing posture of a person can also be analyzed.

In order to measure muscle-force force, the length of the muscle-gun is very important. However, it is impossible to accurately predict the change in muscle-length length for a particular exercise. Existing studies have measured or estimated changes in muscle- tendon length according to joint rotation angle based on cadaver experiments or magnetic resonance (MR) image analysis. will be.

In the same vein, each parameter value of the Hill-type muscle model must be exactly matched with the physical characteristics of the subject under analysis, but it is practically impossible.

SLDelp defined all muscle-gun parameter values for all 43 muscles involved in lower extremity locomotion based on young carcasses and summarized the muscle-gun geometry with reference to all data reported before 1990. . He also developed SIMM (Software for Interactive Musculoskeletal Modeling, MusculoGraphics Inc.) with these data, and Menelgaldo (2004) based on SIMM based on the The change in the length of the muscle- tendon of the lower extremity of the human body according to the angle change is expressed as a function of the rotation angle of the joint.

Nam (2009), on the other hand, estimated the model parameters of muscle-guns through muscle-gun sensitivity and optimization analysis.

In addition, conventionally, there is a method of estimating joint moments using parameters of human muscle by analyzing and processing neural signals of the brain with an EMG (Electromyogram) signal analysis machine.

However, the EMG signal itself also varies according to the experiment environment and the person, and there is a problem that it is impossible to experiment with all people. In addition, human muscle parameters also have a problem that is impossible to obtain accurate data for each person.

The present invention provides a method for estimating the uncertainty of the lower extremity restraint of the human body using multi-body modeling and statistical methodology, which can estimate the uncertainty by combining the restraint on the knee when a person sits and rises in consideration of the different uncertainty of each person. do.

The present invention estimates the uncertainty of the restraint force acting on the knee joint during lower extremity exercise by applying the muscle-tendon actuator using the characteristics of the hill-type muscle model to the lower extremity muscle strength of the human body. Provide a way to.

Uncertainty estimation method of the lower body restraint force using the multi-body modeling and statistical methodology according to the present invention for achieving the above object, the step of modeling the lower body part of the human body in a multi-body model; Analyzing the restraint force of the knee joint that occurs during the lower body movement; And interpreting the uncertainty section of the binding force by using a statistical methodology.

The modeling may include modeling a multi-body system connected to three links and pin joints in a sagittal plane.

The modeling step is characterized by adding the knee bone, the mass of which is ignored in the link and the joint, including the line of action of the axial force of the muscle-gun.

In the modeling step, the action line is selected as a muscle that affects the knee joint during exercise of the lower extremity of the human body, and the selected muscle is characterized in that the femoral rectus muscle, the central light muscle, the gastrocnemius muscle or the biceps femur.

The step of modeling is characterized by defining the position of the muscle-gun using SIMM (Software for Interactive Musculoskeletal Modeling).

The step of analyzing the restraining force is characterized in that the physical properties of the lower extremity model are obtained based on anatomical data and using a regression equation.

In the step of interpreting the restraining force, the length of the muscle-key is a function of the rotation angle of each joint for all the muscles involved in the lower extremity of the human body using the 3D musculoskeletal motion analysis program (SIMM). It is characterized by the expression.

The step of interpreting the restraining force is characterized in that the muscle-gun actuator (musculo-tendon actuator) is applied to the lower extremity muscle strength of the human body.

The step of analyzing the restraining force is characterized by finding the muscle force according to the desired position using the concept of muscle activity, applying the force to the model, performing linearization and analyzing the natural vibration.

The step of interpreting the uncertainty section is characterized by defining the sum of the horizontal component of the restraining force received by the knee bone by the movement of the shin and thigh as the force to press the knee bone, and set the force to press the knee bone as the response of interest. It is done.

The step of interpreting the uncertainty interval is characterized by setting the maximum isometric muscle strength, which is genetically or physically different for each individual, as a random variable.

The step of analyzing the uncertainty interval is characterized in that the characteristics of the population of the maximum isometric muscle is assumed to be a normal distribution having a standard deviation of 20% from the mean.

The step of interpreting the uncertainty section is characterized by estimating the uncertainty section of the constraint force by extracting a random sample from the population of maximum isometric muscle strength.

The step of interpreting the uncertainty interval derives a pseudostatistic of the response of interest, and the pseudostatistic is an approximation of the mean and standard deviation of the response of interest.

In analyzing the uncertainty interval, the average and standard deviation of the population are included in the upper and lower limits of the response of interest.

As described above, the method of estimating the uncertainty of the lower body restraint force using the multibody modeling and the statistical methodology according to the present invention can know a rough distribution of how much force acts on the human knee bone.

In addition, the present invention can improve the reliability of the results of the restraint analysis of the lower body part by incorporating statistical methodology.

In addition, the present invention can be used for the design of medical aids, rehabilitation treatment, and the like using reliable human data samples.

1 is a view schematically showing a biarticular muscle model of the lower limb of the human body according to the present invention.
2 is a diagram illustrating a hill type muscle model according to the present invention.
3 is a graph illustrating the relationship between dimensionless muscle length-force in accordance with the present invention.
4 is a graph showing the relationship between the force and the length of the gun according to the present invention as a relationship between the dimensionless force and the strain.
5 is a graph showing the relationship between the force and speed of the non-dimensionalized muscle according to the present invention.
6 is a graph showing the restraining force of the knee joint and the pressing force of the knee bone according to the present invention.
7 is a view schematically showing the initial position and the restraining force of the lower body model according to the present invention.
Figure 8 is a graph showing the change over time of the restraining force on the knee joint and the pressing force of the knee bone according to the present invention.
9 is a graph analyzing the sensitivity of the pressing force of the knee bone according to the present invention.
10 is a graph for estimating the mean and variance of the pressing force of the knee bone according to the present invention.

Hereinafter, embodiments according to the present invention will be described in detail with reference to the accompanying drawings. However, the present invention is not limited to or limited by the embodiments. Like reference symbols in the drawings denote like elements.

1 is a view schematically showing a biarticular muscle model of the lower limb of the human body according to the present invention, FIG. 2 is a view showing a hill type muscle model according to the present invention, and FIG. Figure 4 is a graph showing the relationship between the non-dimensionalized muscle length-force according to the present invention, Figure 4 is a graph showing the relationship between the force and the length of the gun according to the present invention as a relationship between the non-dimensionalized force and strain, Figure 5 is the present invention Figure 6 is a graph showing the relationship between the force and speed of the non-dimensionalized muscle according to the present invention, Figure 6 is a graph showing the restraining force and the pressing force of the knee joint according to the invention, Figure 7 is a human lower extremity model of the present invention Figure 8 schematically shows the initial position and the restraining force, Figure 8 is a graph showing the change over time of the restraining force and the pressing force of the knee bones on the knee joint according to the present invention, Figure 9 is pressing the knee bones according to the present invention Force A graph analyzing the sensitivity, Figure 10 is a graph for estimating the mean and variance of the pressing force of the knee bone according to the present invention.

The present invention estimates the uncertainty of restraint force acting on the knee joint during lower extremity exercise by applying the muscle-tendon actuator using the characteristics of the hill-type muscle model to the lower extremity muscle strength of the human body. can do. The muscle parameters used are assumed to be the mean of the population to be interpreted using the data of Dellp, and follow the normal distribution with a standard deviation of 20% of the mean. A sample of this population and its statistical characteristics are then used in the estimation of uncertainty.

The method of estimating the uncertainty of the lower limb restraint of the human body using the multibody modeling and the statistical methodology according to the present invention is expressed biomechanically with respect to the standing posture of the human body and is composed of multibody dynamics, muscle mechanics, and muscle geometric characteristics. Can be.

As shown in FIG. 1, the anatomical model can be modeled as a multibody system connected by three links and pin joints in a typical saggital plane, by adding a pattern of mass bones to the knee bone. And the line of action of the axial force of the muscle-tendon. The line of action of the axial force can be selected as the major muscle that affects the knee joint during lower extremity exercise, and the selected muscle-gun is the rectus femoris, Vastus intermedius, gastrocnemius, Biceps femoris caput longus. In FIG. 1 (a), for convenience of description, the thigh muscle, the central optical muscle, the gastrocnemius muscle, and the biceps femori are indicated as Rf, Vi, Gas, and Bif, respectively. Meanwhile, in FIG. 1B, L1 denotes the length of the shank muscle, L2 denotes the length of the thigh muscle, and trunk may be referred to as a trunk. The position of the muscle-gun of FIG. 1 (b) is defined by referring to software for interactive musculoskeletal modeling (SIMM), where a is 5 cm, b is 10 cm, c is 20 cm, d is 8 cm, and e is 20 cm. can do.

In addition, Fig. 1 (c) schematically represents the force for pressing the knee bone. F ^T is the restraining force on the knee bone due to the thigh movement during the lower body movement, F ^S is the restraining force on the knee bone due to the shank movement. F ^P is the force on the knee bone and can be defined as the sum of the horizontal components of F ^T and F ^S.

In addition, the physical properties such as the length and mass of the lower extremity model can be used based on anatomical data, and the proposed regression equation can be used.

Where the values in parentheses are the regression coefficients, and the rest are the weight of the person, the length of the thighs, and the circumference at the center of length. Details are shown in Table 1 below.

Body

Length (m)

Mass (kg) Moment of
inertia
(kg.m ² )
CG position
(ratio
proximal / distal) One Shank 0.43 0.33 0.00499 0.42 2 Thigh 0.46 0.7 0.01262 0.39 3 Trunk - 4.4 - -

Referring to the CG position of the shank in Table 1, when the total length of the shank is 1, the distance from the side close to the body to the center of gravity of the shank is 0.42.

On the other hand, Figure 2 is a diagram showing a hill type muscle model (Hill type muscle model). In FIG. 2, F ^t is a force transmitted to a bone through a tendon called a tendon, which is a dimensionless expression of isometric maximum muscle force (F _o ^m ), as shown in Equation 2 below. Can be.

와

는 각각 근육의 능동적인 힘(active force)과 수동적인 힘(passive force)을 무차원화한 것이다. 또한, a(t)는 근육 활성화 지수이다.In equation (2)

Wow

Are the non-dimensionalization of the active and passive forces of each muscle. Also, a (t) is the muscle activation index.

의 발생 메커니즘을 모델화한 요소이다. 여기서 액틴과 미오신 사이의 공간에 연결교의 결합이 가장 많을 때를 최적길이(optimal five length, l_o ^m)라 하며 이 상태에서 근육은 가장 큰 힘을 낼 수 있다. 그리고 이 때의 힘이 앞서 언급한 최대 등척 근력(maximum muscle isometric force, F_o ^m )이다. 근육의 길이가 수축 또는 신장되면서 연결교의 결합이 파괴 또는 간섭이 일어나며 앞서 설명한 이유로 근력이 약화되는데 이것을 도 3에 근육 활성화 지수 a(t)와 함께 근 섬유의 무차원화 된 길이의 함수로 도시할 수 있다. 여기서 횡축은

이며 종축은 능동적인 힘을 무차원화 한 힘,

이다.In FIG. 2, the contractile element (CE) is an active contraction element,

The modeling mechanism of the generation of. In this case, the optimal length of the coupling bridge in the space between actin and myosin is called the optimal five length (L _o ^m ). In this state, the muscle can exert the greatest force. The force at this time is the maximum muscle isometric force (F _o ^m ) mentioned above. As the length of the muscle contracts or elongates, the binding of the bridge bridges is broken or interfered, and the muscle strength is weakened for the reasons described above, which can be shown as a function of the non-dimensionalized length of the muscle fiber with the muscle activation index a (t) in FIG. have. Where the horizontal axis is

The vertical axis is the force that is active-dimensionalized,

to be.

이다. 이것은 마치 고무밴드와 같은 성질을 가지고 있어서 휴식시 길이 이하일 경우 즉, 느슨한(slack) 상태에서는 아무런 힘도 작용하지 못한다. 하지만 길이가 그 이상 신장 되면 비선형 스프링처럼 급격히 증가 한다. 이러한 특성은 식 (3)과 같이 지수함수를 사용하여 표현할 수 있다.In FIG. 3, a line including a point is represented as a passive element (PE) in FIG.

to be. It has the same properties as a rubber band so that no force is applied when it is less than the length at rest, i.e. in a slack state. But as it extends further, it grows rapidly like a nonlinear spring. This property can be expressed using an exponential function as shown in equation (3).

Muscles also transmit force between bones through tendons called tendons. Initially, only muscle characteristics were taken into account, but by Zajak (1989), the characteristics of the tendon were also considered. The gun is attached to bone or cartilage, part of it penetrates the periosteum and is in the bone or cartilage, and the mechanical strength is much greater than the muscle to which it is connected, allowing the force to be transmitted to the bone without being damaged by muscle force.

)만큼 기울어져 반대쪽 건과 연결될 수 있다. 근육의 길이가 변화되면 우모각도 이에 따라 변화되며 이러한 기하학적 관계는 식 (4)와 같이 표현될 수 있다.And as shown in Figure 2 and the muscles (pennation angle,

Tilt by) to connect to the opposite gun. As the length of the muscle changes, the right angle also changes accordingly, and this geometric relationship can be expressed as shown in Eq. (4).

는 근육의 길이가

일 때의 우모각이다. 건도 근육의 수동적인 요소의 특성과 같이 건의 길이가 건의 슬랙 길이(tendon slack length,

)보다 클 경우에만 근력을 뼈(골)에 전달할 수 있으며 그 관계는 다음 식 (5) 및 식 (6)으로 주어질 수 있다.here

Is the length of the muscle

It is right angle when. Like the characteristics of the passive elements of the tendon muscle, the length of the gun is the tendon slack length,

Only if greater than) can transfer strength to the bone (bone) and the relationship can be given by the following equation (5) and (6).

In equations (5) and (6), ε represents the strain of the gun, and the relationship between the force and the length of the gun is shown in FIG. 4 as the relationship between the dimensionless force and the strain. We mentioned earlier that the mechanical strength of the gun is greater than that of the muscle, but with reference to Figure 4 it can be seen in more detail. As shown in FIG. 4, the maximum strain produced by the muscle is about 3.3%, the maximum strength is about 3.5 times stronger than the maximum force of the muscle, and the strain is about 10%. And if more force is transmitted, the gun can be destroyed.

On the other hand, if the muscles are contracted or stretched at a constant speed in each direction, the force generated in the muscles will be different from the forces that can be produced in the static state. In this dynamic state, the force transmitted by the muscles to the bone through the gun becomes smaller in the concentric contraction and larger in the eccentric contraction, as compared to that in the static state. do. This effect is represented by f (v) in equation (7) and shown in FIG. There are two reasons why the force decreases as the speed increases during muscle contraction. The first and most important reason is that the linkage linkage between actin and myosin in the contraction element is broken and lost in the process of being replaced with a new contraction state, and the second reason is the fluid viscosity of the contraction element and the connective tissue. It is because of the interpretation. In addition, the expansion movement can be explained by putting down an object without carrying weight when carrying a heavy object. In other words, it tries to contract but is expanded by external force. Looking at the eccentric contraction portion of Figure 5 it can be seen that when the external force is large, the expansion speed is large and if the expansion speed is small, the expansion speed is also small. The characteristics of these muscles can be determined by the following equation (7).

는 f(v)를 결정짓는 파라미터들이다. 본 발명에서는 등척(isomectric) 수의근 최대 수축(maximum voluntary contraction, 이하 MVC) 운동상태에 한하여 설명하므로 f(v)의 값은 a(t) 값과 함께 1이 될 수 있다.In Eq. (7), v is the speed of movement of the muscle and a positive value represents when the muscle contracts. And,

Are parameters that determine f (v). In the present invention, only the maximum voluntary contraction (MVC) state of motion of the isotctric voluntary muscle is described. Therefore, the value of f (v) may be 1 together with the a (t) value.

As a result, combining the results discussed so far, the force acting on the bone through the gun, F ^t , can be derived as shown in Equation (8).

의 4개 파라미터들에 의하여 결정될 수 있다. 이들 파라미터들의 값은 유전적 또는 신체적인 차이로 인하여 개인마다 서로 다를 수 있다. 델프(Delp)는 1990년 이전까지 여러 학자들에 의하여 실험되거나 측정되어 보고된 자료들을 참조하여 젊은 사체를 기준으로 위의 파라미터를 정리하였다.Muscle characteristics

It can be determined by four parameters of. The values of these parameters may differ from person to person due to genetic or physical differences. Delp summarized the above parameters on the basis of young carcasses with reference to data that have been tested or measured by scholars before 1990.

가 알려져 있다면 이 식은

만의 함수가 되기 때문에 건을 통하여 골에 작용하는 힘, F^t는 수치해석적으로 결정될 수 있다.In addition, the length of the muscle- tendon according to each change of the joint in equation (5),

If is known, this expression

Since it is a function of Gulf, the force acting on the goal through the gun, F ^t , can be determined numerically.

에 대해서는 사체를 해부하여 관절의 회전 각도를 조절하면서 실험한 사례들이 여러 차례 보고되어 왔지만 본 발명에서는 메네갈도 (L.L.Menegaldo(2004))등에 의한 연구 결과를 사용하기로 한다. 이들은 델프 등에 의해 개발된 3차원 근골격계 운동해석 소프트웨어인 에스아이엠엠(SIMM: Software for Interactive Musculoskeletal Modeling, MusculoGraphics Inc.)을 이용하여 하지부 운동에 관여하는 모든 근육에 대하여 근육-건의 길이 등을 각 관절의 회전 각도에 대한 함수로 표현할 수 있다.

For example, many cases have been reported while dissecting a carcass and adjusting a rotation angle of a joint, but in the present invention, the result of the research by Menegaldo (LLMenegaldo (2004)) will be used. They used the software for Interactive Musculoskeletal Modeling (SIMM), a 3D musculoskeletal exercise analysis software developed by Delf et al. It can be expressed as a function of the rotation angle of.

)의 회전각도에 대한 함수로 표현될 수 있다. 다시 말해서 Vi근육의 근육-건 길이인

는 미터(meter) 단위로 다음 식 (9)와 같이 표현되며 변화되는 값은 도 6에 도시되어 있다.For example, the Vi muscle as shown in Figure 1 is a knee joint (

It can be expressed as a function of the rotation angle of. In other words, the muscle-to-length of Vi muscle

Is expressed in the following formula (9) in meters, and the changed value is shown in FIG. 6.

는 무릎 관절의 회전각(deg)이며 0도에 가까울수록 무릎은 펴진 상태이며, 120도로 가면서 무릎 관절은 굽혀지는 것을 나타낸다.In equation (9)

Is the rotational angle (deg) of the knee joint and the closer to 0 degrees the knee is in a stretched state, and the knee joint is bent while going to 120 degrees.

에 대한 관심 응답의 민감도를 유한 차분법(Finite Difference Method)으로 해석할 수 있다.In the present invention, as shown in (c) of Figure 1 (c) the force of pressing the patella to the negative value of the sum of the horizontal component of the restraining force received by the patella (patella) by the movement of the shank and thigh (Thigh), respectively defined as the compressive force, which is the maximum isometric muscle force

The sensitivity of the response of interest to can be interpreted by the finite difference method.

7 shows the initial posture of the lower extremity model of the human body (see FIG. 7 (a)) and the restraint force on the knee bone due to the shank and thigh movement during lower extremity movement as F ^S and F ^T , respectively. It is shown.

(A) of FIG. 8 is a graph which analyzes for one second with the motion shown to (b) of FIG. 7, and shows the change of restraint force with respect to it. On the other hand, as shown in (c) of FIG. 7, the sum of the horizontal components of F ^T and F ^S is defined as the compressive force of the knee bone, and the result thereof is shown in FIG. Set the bone pressure to respond to interest, Y = F ^P.

)은 사람마다 다르기 때문에 본 발명에 따른 해석 결과에 대한 신뢰성을 높이기 위해서 본 발명에서는 통계 방법론을 사용한다. On the other hand, maximum isometric muscle strength (

) Varies from person to person, so the present invention uses statistical methodology to increase the reliability of the analysis results.

Assuming that the population of random variables follows a normal distribution, and the design variables and system performance are expressed as in Eq. (10), the average of the system performance is calculated using the sensitivity information of the random variables for the mean and variance and the response of the random variable. Dispersion can be obtained through equations (11) and (12), respectively.

는 확률변수의 평균을 나타내며 E(Y)는 관심응답의 평균을 나타낸다. 그리고, Var(Y)는 관심응답의 분산이며 이것은 확률변수의 분산 Var(b_i)와 관심응답에 대한 확률변수의 민감도를 이용하여 식 (12)를 통해 얻을 수 있다.Here, Y represents the compressive force defined above, and b _i represents the random variable. In equation (11) to find the mean

Represents the mean of the random variable and E (Y) represents the mean of the response of interest. Var (Y) is the variance of the response of interest, which can be obtained through Eq. (12) using the variance Var (b _i ) of the random variable and the sensitivity of the random variable for the response of interest.

)으로 설정하였으며, 델프(Delp)의 자료를 이들 모집단의 평균으로 가정하였다. 또한 모집단의 특성은 평균에서 20%의 표준편차를 갖는 정규분포로 가정하였다. 이러한 가정으로부터 구속력의 불확실성 구간 추정이 가능한데, 이유는

와 같은 인체 해부학적인 데이터를 정확하게 측정하기가 어렵고, 정확하게 측정이 가능하더라도 모집단 전체를 대상으로 실험하기는 불가능하기 때문이다. Using the above method, we can find the mean and variance of the responses of interest when we know the statistical distribution of the design variable population. In the present invention, as the random variable, isometric maximum muscle force, which is genetically or physically different from individual to individual,

) And the data from Delp was assumed as the mean of these populations. The population characteristics were also assumed to be normal distributions with a standard deviation of 20% from the mean. From this assumption, it is possible to estimate the uncertainty interval of the binding force because

This is because it is difficult to accurately measure human anatomical data, and even if accurate measurement is possible, it is impossible to test the entire population.

의 모집단을 10000개를 생성하고 임의로 100의 샘플을 추출하여 구속력의 불확실성 구간을 추정한다. 추출된 샘플의 평균과 표준편차를 각각

라고 한다면, 식 (11)과 식 (12)는 다음 식 (13) 및 (14)와 같이 수정될 수 있다.In the present invention, maximum isometric muscle strength having the above characteristics,

Create a population of 10,000 and randomly sample 100 to estimate the uncertainty interval of the binding force. The mean and standard deviation of the extracted samples

Equation (11) and Equation (12) can be modified as in the following Equations (13) and (14).

와

는 관심응답의 유사통계량(Pseudo statistics)으로 각각 관심응답의 평균과 표준 편차의 근사값을 나타낸다. 한편 구간추정에서 100(1-α)%의 신뢰도를 가진 평균과 분산의 신뢰구간은 다음 식 (15) 및 (16)과 같이 구할 수 있다.here,

Wow

Pseudo statistics show the approximation of the mean and standard deviation of the responses of interest. In the interval estimation, the confidence intervals of the mean and the variance having the reliability of 100 (1-α)% can be obtained as shown in the following equations (15) and (16).

와 s²은 추출된 샘플의 평균과 분산이다. 그리고, n은 샘플의 크기이며

는 Student t 분포,

은 자유도가 n-1인 카이제곱 분포를 나타낸다.Where μ and σ ² are the mean and variance of the responses of interest to be predicted,

And s ² are the mean and variance of the extracted samples. And n is the size of the sample

Is the Student t distribution,

Represents a chi-square distribution with n-1 degrees of freedom.

On the other hand, each time a sample is taken, the statistical properties of the sample will be different, as will the estimated upper and lower limits. This is related to the reliability, which means that the mean and variance of the responses of interest interpreted as the characteristics of the sample extracted are 100 (1-α)% including the mean and variance of the responses of interest interpreted as the characteristics of the population.

To recapitulate the process so far, first obtain the statistics (average, variance) from a sample of system design variables, and use the equations (13) and (14) to derive similar statistics of system performance. Finally, interval estimation is applied to predict the statistical distribution of system performance.

)이 관심응답 해석시 가장 민감하게 작용한다는 것을 알 수 있다. 또한 무릎 관절의 각도에 따라서도 Vi근의 민감도는 변하는데 무릎관절의 각도가 가장 큰 초기위치에서 가장 크며 관절의 각도가 작아질수록 작아짐을 볼 수 있다. 또한 Gas근과 Bif근은 본 발명의 해석 모델에서 중력에 저항하는 힘이 아니므로 그의 민감도는 0에 가깝다고 할 수 있다.In the present invention, the angle θ of the knee joint is interpreted by giving motion such that the angle of the shank is 80 degrees while the knee joint is stretched for 1 second at an initial 120 degrees. 9 is a change in the sensitivity of the response of interest to muscle strength, the isometric maximum muscle force of the Vi muscle,

) Is the most sensitive in interpreting the response of interest. In addition, the sensitivity of the Vi muscle changes according to the angle of the knee joint. The angle of the knee joint is the largest at the initial position, and the smaller the joint angle, the smaller the joint angle. In addition, since the Gas and Bif roots are not forces that resist gravity in the analytical model of the present invention, their sensitivity is close to zero.

10 (a) and 10 (b) are graphs for estimating the mean response mean and standard deviation of the population using the sample of the population by Equation (15) and Equation (16), respectively. In each graph, the dashed line and the dotted line are graphs for estimating the upper and lower limits of the response of interest, and the solid line in the middle is a graph interpreted by the data of Delp assuming the average of the population.

The graphs of (a) and (b) of FIG. 10 in which the mean and the standard deviation are estimated include the mean and the standard deviation of the population, and the size of the estimated interval is smaller as the angle of the knee joint decreases according to the trend of sensitivity analysis. It can be seen that the more the knee is stretched, the smaller the response of interest defined by the force of pressing the patella is also smaller as the angle of the knee joint decreases.

In summary, the method of estimating the uncertainty of the lower body restraint force using the multibody model and the statistical methodology according to the present invention is summarized as follows.

The uncertainty estimation method of the lower body restraint force using the multibody modeling and statistical methodology according to the present invention includes the steps of modeling the lower body part of the human body as a multibody model, analyzing the restraint force of the knee joint generated during the lower body part exercise; Interpreting the uncertainty interval of the binding force using statistical methodology.

Here, the step of modeling the lower body part of the human body as a multi-body model may be modeled as a multi-body system connected with three links and pin joints in the sagittal plane.

In addition, the modeling of the lower body of the human body with a multibody model may be performed by adding a knee bone in which mass is ignored to the link and the joint, and including a line of action of the axial force of the muscle-gun.

In the modeling step, the action line may be selected as a muscle affecting the knee joint during exercise of the lower limb of the human body, and the selected muscle may be the femoral rectus muscle, the central optical muscle, the gastrocnemius muscle, or the biceps femur.

On the other hand, the modeling step may be used to define the position of the muscle-gun using the software for Interactive Musculoskeletal Modeling (SIMM), the step of analyzing the restraint is based on the anatomical data of the physical properties of the lower extremity model It can be obtained by using the regression equation.

In the step of interpreting the restraining force, the length of the muscle-key is a function of the rotation angle of each joint for all the muscles involved in the lower extremity of the human body using the 3D musculoskeletal motion analysis program (SIMM). I can express it.

The step of analyzing the restraining force may be applied to the muscles of the lower extremities of the human body. In the case of applying the muscle-gun actuator to the muscles of the lower extremities of the human body, the concept of muscle activity, a (t) is used to find the force of the muscle according to the desired position through the optimization configuration, and apply the force to the model to perform linearization. This may involve performing and interpreting natural vibrations. That is, in the step of analyzing the restraining force, the muscle force according to the desired position can be found by using the concept of muscle activity, the force can be applied to the model, and the natural vibration can be analyzed.

In addition, the step of interpreting the uncertainty interval may be defined as the sum of the horizontal component of the restraining force received by the knee bone by the movement of the shin and thigh as the force to press the knee bone, and the force to press the knee bone as the response of interest have.

Here, in the step of interpreting the uncertainty interval, the maximum isometric muscle force, which is genetically or physically different for each individual, is set as a random variable.

The step of interpreting the uncertainty interval assumes that the characteristic of the population of maximum isometric muscles is a normal distribution having a standard deviation of 20% from the mean, and extracts an arbitrary sample from the population of the maximum isometric muscles to determine the uncertainty interval of the constraint force. Estimate.

In addition, the step of interpreting the uncertainty interval may derive the similar statistics of the response of interest, wherein the similar statistics may be an approximation of the mean and standard deviation of the response of interest.

In the step of interpreting the uncertainty interval, the uncertainty interval may be estimated to include the mean and standard deviation of the population in the upper and lower limits of the response of interest.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Accordingly, the spirit of the present invention should not be construed as being limited to the embodiments described, and all of the equivalents or equivalents of the claims, as well as the following claims, belong to the scope of the present invention .

Rf: Femoral Muscles Vi: Central muscle
Bif: Biceps Gas: Gastrocnemius
F ^T : restraint on knee bone due to thigh movement
F ^S : restraint on knee bones due to shin movement
F ^P : Sum of horizontal components of F ^T and F ^S
F ^t : Force transmitted to the bone through the gun
l ^m : Length of the gun

Claims (15)

Modeling the lower limb of the human body with a multibody model;
Analyzing the restraint force of the knee joint that occurs during the lower body movement; And
Interpreting the uncertainty interval of the binding force using statistical methodology;
In the step of interpreting the uncertainty interval,
The sum of the horizontal components of the restraint force on the knee bone due to the movement of the shin and the thigh during the movement of the lower leg is defined as the pressing force of the knee bone, and the pressing force of the knee bone is set as an interest response, Multivariate modeling and statistics, wherein a random sample is extracted from the set maximum isometric muscle force, and the uncertainty interval of the constraint force is estimated, and the confidence intervals of the mean and variance of the response of interest are respectively calculated as follows. Uncertainty estimation method of lower limb restraint using methodology.

Where μ and σ ² are the mean and variance of the response of interest to be predicted,

And s ² are the mean and variance of the extracted samples, n is the size of the sample,

Is the Student t distribution,

Is the chi-square distribution with n-1 degrees of freedom.
The method of claim 1,
The modeling step,
A method for estimating the uncertainty of the restraint of the lower extremities of the human body using multibody modeling and statistical methodology, which is modeled as a multibody system connected by three links and pin joints in a sagittal plane.
The method of claim 2,
The modeling step,
Uncertainty of the lower extremity restraint of the human body using multibody modeling and statistical methodology, characterized in that the link and the joint is added to the knee bone, the mass is ignored, including the line of action of the axial force of the muscle-gun Estimation method.
The method of claim 3,
In the modeling step,
The action line is selected as the muscle affecting the knee joint during exercise of the lower extremity of the human body, and the selected muscle is the femoral rectus muscle, the central light muscle, the gastrocnemius muscle, or the biceps femur. Uncertainty estimation method.
The method of claim 4, wherein
The modeling step,
A method for estimating the uncertainty of the lower extremity restraint of the human body using multibody modeling and statistical methodology characterized by defining the position of the muscle-gun using SMMM (Software for Interactive Musculoskeletal Modeling).
The method of claim 5,
Analyzing the binding force,
Physical properties of the lower extremity model is based on anatomical data and is calculated using a regression equation.
The method of claim 6,
In the step of analyzing the binding force,
Using the three-dimensional musculoskeletal exercise analysis program (SIMM) for the muscles involved in the lower extremity movement of the human body characterized in that the length of the muscle-gun as a function of the angle of rotation of each joint Uncertainty estimation method of lower body restraint force using object modeling and statistical methodology.
The method of claim 7, wherein
Analyzing the binding force,
A method of estimating the uncertainty of the lower extremity constraint of the human body using multibody modeling and statistical methodology, characterized by applying a muscle-tendon actuator to the lower extremity muscle strength of the human body.
9. The method of claim 8,
Analyzing the binding force,
Finding the strength of muscle according to the desired position using the concept of muscle activity, applying the force to the model, performing linearization and analyzing the natural vibration Uncertainty estimation method.
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