A control theoretic model of the forearm

In this paper, a control theoretic model of the forearm is developed and analyzed, and a computational method for predicting muscle activations necessary to generate specified motions is described. A detailed geometric model of the forearm kinematics, including the carrying angle and models of how the biceps and the supinator tendons wrap around the bones, is used. Also, including a dynamics model, the final model is a system of differential equations where the muscle activations play the role of control signals. Due to the large number of muscles, the problem of finding muscle activations is redundant, and this problem is solved by an optimization procedure. The computed muscle activations for ballistic movements clearly recaptures the triphasic ABC (Activation-Braking-Clamping) pattern. It is also transparent, from the muscle activation patterns, how the muscles cooperate and counteract in order to accomplish desired motions. A comparison with previously reported experimental data is included and the model predictions can be seen to be partially in agreement with the experimental data.     

A 'cheap' optimal control approach to estimate muscle forces in musculoskeletal systems

This paper shows a new method to estimate the muscle forces in musculoskeletal systems based on the inverse dynamics of a multi-body system associated optimal control. The redundant actuator problem is solved by minimizing a time-integral cost function, augmented with a torque-tracking error function, and muscle dynamics is considered through differential constraints. The method is compared to a previously implemented human posture control problem, solved using a Forward Dynamics Optimal Control approach and to classical static optimization, with two different objective functions. The new method provides very similar muscle force patterns when compared to the forward dynamics solution, but the computational cost is much smaller and the numerical robustness is increased. The results achieved suggest that this method is more accurate for the muscle force predictions when compared to static optimization, and can be used as a numerically 'cheap' alternative to the forward dynamics and optimal control in some applications.     

A general-purpose framework to simulate musculoskeletal system of human body: using a motion tracking approach*

Computation of muscle force patterns that produce specified movements of muscle-actuated dynamic models is an important and challenging problem. This problem is an undetermined one, and then a proper optimization is required to calculate muscle forces. The purpose of this paper is to develop a general model for calculating all muscle activation and force patterns in an arbitrary human body movement. For this aim, the equations of a multibody system forward dynamics, which is considered for skeletal system of the human body model, is derived using Lagrange–Euler formulation. Next, muscle contraction dynamics is added to this model and forward dynamics of an arbitrary musculoskeletal system is obtained. For optimization purpose, the obtained model is used in computed muscle control algorithm, and a closed-loop system for tracking desired motions is derived. Finally, a popular sport exercise, biceps curl, is simulated by using this algorithm and the validity of the obtained results is evaluated via EMG signals.     

Airway obstruction in asthma: does the response to a deep inspiration matter?

Airway hyperresponsiveness in asthma may not be a problem of too much airway smooth muscle strength. Rather, it may be a problem of too little of the factors that oppose muscle shortening. The weight of available evidence seems to support the idea that loss of the dilating response to a deep inspiration may play a central role in this process, and that the locus of the response is within the airway smooth muscle cell. Bridge dynamics and plastic reorganization of the smooth muscle cytoskeleton are the focus of this commentary; how these factors interact and details about underlying mechanisms remain unclear.     

On the role of myoglobin in muscle respiration

The presence of myoglobin in red muscle tissue has a marked effect on its respiration because it combines reversibly with oxygen and hence gives rise to facilitated diffusion. In this paper we consider the role of myoglobin in facilitating oxygen diffusion and give quantitative results for the oxygen concentration within a typical muscle fibre. Simple expressions are derived for the critical metabolism for the onset of oxygen debt and the growth and size of the region in oxygen debt when the muscle metabolism exceeds this critical value.The general principle, enunciated by Murray &; Wyman (1971), that the macromolecule, myoglobin here, can only function as a carrier if it is unsaturated in some region of the system is again shown to hold.A singular perturbation procedure is used to analyze the model, the effect of which is to reduce the mathematical problem to that of trivially solving a quadratic algebraic equation for the oxygen concentration in the muscle fibre. Physically one condition which causes this phenomenon to be singular in the mathematical sense is that the relaxation times of the myoglobin-oxygen reaction are small compared with the diffusion time of the myoglobin-oxygen complex.     

Investigation of the Peculiarities of Two-joint Muscles Using a 3 DOF Model of the Human Upper Limb in the Sagittal Plane: an Optimization Approach

Abstract

The purpose of this paper is an investigation of the peculiarities of biarticular muscles by means of modelling and analytical solution of the indeterminate problem. The basic model includes 10 muscle elements performing flexio/extensio in the shoulder, elbow and wrist. Four of them are biarticular muscles. Two modifications of the model with only monoarticular muscles are developed. The indeterminate problem is solved analytically using the objective criterion σc_iF_i ² where F( is the module of the i-th muscle force and Cj is a weight coefficient. The predicted muscle forces, joint reactions and moments are compared in-between the basic model and its two modifications for different joint angles, external loading and weight coefficients. The main conclusions are: it is impossible to formulate strict advantages of the biarticular muscles under quasistatical conditions, their peculiarities depend on limb position, external loading and neural control; in general, monoarticular muscles are more powerful than biarticular ones; the biarticular muscles fine tune muscle coordination, their control is more precise and graceful; the presence of biarticular muscles leads to an increase of the joint reactions and moments, thus stabilizing the limb.     

A physiology-based inverse dynamic analysis of human gait using sequential convex programming: a comparative study

This paper presents an enhanced version of the previously proposed physiological inverse approach (PIA) to calculate musculotendon (MT) forces and evaluates the proposed methodology in a comparative study. PIA combines an inverse dynamic analysis with an optimisation approach that imposes muscle physiology and optimises performance over the entire motion. To solve the resulting large-scale, nonlinear optimisation problem, we neglected muscle fibre contraction speed and an approximate quadratic optimisation problem (PIA-QP) was formulated. Conversely, the enhanced version of PIA proposed in this paper takes into account muscle fibre contraction speed. The optimisation problem is solved using a sequential convex programing procedure (PIA-SCP). The comparative study includes PIA-SCP, PIA-QP and two commonly used approaches from the literature: static optimisation (SO) and computed muscle control (CMC). SO and CMC make simplifying assumptions to limit the computational time. Both methods minimise an instantaneous performance criterion. Furthermore, SO does not impose muscle physiology. All methods are applied to a gait cycle of six control subjects. The relative root mean square error averaged over all subjects, ε(RMS), between the joint torques simulated from the optimised activations and the joint torques obtained from the inverse dynamic analysis was about twice as large for SO (ε(RMS) = 86) as compared with CMC (ε(RMS) = 39) and PIA-SCP (ε(RMS) = 50). ε(RMS) was at least twice as large for PIA-QP (ε(RMS) = 197) than for all other methods. As compared with CMC, muscle activation patterns predicted by PIA-SCP better agree with experimental electromyography (EMG). This study shows that imposing muscle physiology as well as globally optimising performance is important to accurately calculate MT forces underlying gait.     

磁场辐照对美国青蛙蝌蚪肌蛋白氨基酸的影响

适量磁场辐照水生动物的促生长机理是一复杂的研究课题,本文从营养学、生物化学角度对该课题做了阶段性的初浅分析。我们发现适量的磁场辐照在美国青蛙蝌蚪期肌蛋白氨基酸方面的效应是有益的,它不会引起氨基酸组份的改变,而且能使氨基酸含量增加３０％以上。     

A dynamic optimization technique for predicting muscle forces in the swing phase of gait

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.     

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.     

Biomechanical model calculation of muscle contraction forces: a double linear programming method

This paper presents a novel scheme for the use of linear programming to calculate muscle contraction forces in models describing musculoskeletal system biomechanics. Models of this kind are frequently found in the biomechanics literature. In most cases they involve muscle contraction force calculations that are statically indeterminate, and hence use optimization techniques to make those calculations. We present a linear programming optimization technique that solves a two-objective problem with two sequential linear programs. We use the technique here to minimize muscle intensity and joint compression force, since those are commonly used objectives. The two linear program model has the advantages of low computation cost, ready implementation on a micro-computer, and stable solutions. We show how to solve the model analytically in simple cases. We also discuss the use of the dual problem of linear programming to gain understanding of the solution it provides.     

Propagation of shear waves in the muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. The muscle is modelled by an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. Two types of shear waves in an infinite medium have been established. The waves of the second type (transverse) propagate without attenuation even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer has been investigated numerically. The values of the problem parameters have been found for which the active tension or muscle tonus is easily estimated from the characteristics of standing waves. This value is informative for the diagnosis of muscle state.     

Static and dynamic optimization solutions for gait are practically equivalent

The proposition that dynamic optimization provides better estimates of muscle forces during gait than static optimization is examined by comparing a dynamic solution with two static solutions. A 23-degree-of-freedom musculoskeletal model actuated by 54 Hill-type musculotendon units was used to simulate one cycle of normal gait. The dynamic problem was to find the muscle excitations which minimized metabolic energy per unit distance traveled, and which produced a repeatable gait cycle. In the dynamic problem, activation dynamics was described by a first-order differential equation. The joint moments predicted by the dynamic solution were used as input to the static problems. In each static problem, the problem was to find the muscle activations which minimized the sum of muscle activations squared, and which generated the joint moments input from the dynamic solution. In the first static problem, muscles were treated as ideal force generators; in the second, they were constrained by their force-length-velocity properties; and in both, activation dynamics was neglected. In terms of predicted muscle forces and joint contact forces, the dynamic and static solutions were remarkably similar. Also, activation dynamics and the force-length-velocity properties of muscle had little influence on the static solutions. Thus, for normal gait, if one can accurately solve the inverse dynamics problem and if one seeks only to estimate muscle forces, the use of dynamic optimization rather than static optimization is currently not justified. Scenarios in which the use of dynamic optimization is justified are suggested.     

Critical analysis of musculoskeletal modelling complexity in multibody biomechanical models of the upper limb

The inverse dynamics technique applied to musculoskeletal models, and supported by optimisation techniques, is used extensively to estimate muscle and joint reaction forces. However, the solutions of the redundant muscle force sharing problem are sensitive to the detail and modelling assumptions of the models used. This study presents four alternative biomechanical models of the upper limb with different levels of discretisation of muscles by bundles and muscle paths, and their consequences on the estimation of the muscle and joint reaction forces. The muscle force sharing problem is solved for the motions of abduction and anterior flexion, acquired using video imaging, through the minimisation of an objective function describing muscle metabolic energy consumption. While looking for the optimal solution, not only the equations of motion are satisfied but also the stability of the glenohumeral and scapulothoracic joints is preserved. The results show that a lower level of muscle discretisation provides worse estimations regarding the muscle forces. Moreover, the poor discretisation of muscles relevant to the joint in analysis limits the applicability of the biomechanical model. In this study, the biomechanical model of the upper limb describing the infraspinatus by a single bundle could not solve the complete motion of anterior flexion. Despite the small differences in the magnitude of the forces predicted by the biomechanical models with more complex muscular systems, in general, there are no significant variations in the muscular activity of equivalent muscles.     

Four-state models and regulation of contraction of smooth muscle. II. Properties of the solutions and identification.

We analyze the behavior and the identification problem of cyclic four-state models. We find that for any state, or a weighted combination of two states, there can be at most one maximum, or one minimum, and two inflection points. We obtain necessary conditions for overshoot and undershoot and give examples. We describe procedures to estimate all the rate constants and discuss certain experimental aspects of the identification problem. Finally, we give an example of identification by obtaining the 10 model parameters from experimental data on skinned fibers from smooth muscle. These results, in conjunction with the results of the previous paper, can help in testing four-state models of regulation of contraction of smooth muscle and of a variety of other physiological and biochemical phenomena.     

Activation of human arm muscles during flexion/extension and supination/pronation tasks: A theory on muscle coordination

Generally the number of muscles acting across a joint exceeds the number of degrees of freedom available to the joint. This redundancy raises a problem regarding the ratio in which these muscles are activated during a particular motor task. In this paper we present a theory to explain the activation patterns of muscles used during voluntary and reflex induced contractions. The basic assumptions underlying the theory are that 1) coordination of muscles is based on synergistic muscle activities, 2) the synergisms involved satisfy certain transformations of muscle spindle signals to muscle activation signals and 3) muscle spindle output is proportional to the ratio of muscle stretch and muscle length in lengthening muscles, and is zero in shortening muscles. The theory is used to predict the recruitment threshold of motor units in six arm muscles during voluntary isometric contractions. All theoretical predictions are in reasonable agreement with the experimentally observed behavior of a large population of motor units within each muscle. However, within a single muscle sometimes motor-unit populations have been found to have different types of recruitment behavior. This deviating behavior is discussed in the light of the theory presented here.     

The MusIC method: a fast and quasi-optimal solution to the muscle forces estimation problem

The present paper aims at presenting a fast and quasi-optimal method of muscle forces estimation: the MusIC method. It consists in interpolating a first estimation in a database generated offline thanks to a classical optimization problem, and then correcting it to respect the motion dynamics. Three different cost functions – two polynomial criteria and a min/max criterion – were tested on a planar musculoskeletal model. The MusIC method provides a computation frequency approximately 10 times higher compared to a classical optimization problem with a relative mean error of 4% on cost function evaluation.     

In vivo parameter identification in arteries considering multiple levels of smooth muscle activity

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.

     

Generating dynamic simulations of movement using computed muscle control

Computation of muscle excitation patterns that produce coordinated movements of muscle-actuated dynamic models is an important and challenging problem. Using dynamic optimization to compute excitation patterns comes at a large computational cost, which has limited the use of muscle-actuated simulations. This paper introduces a new algorithm, which we call computed muscle control, that uses static optimization along with feedforward and feedback controls to drive the kinematic trajectory of a musculoskeletal model toward a set of desired kinematics. We illustrate the algorithm by computing a set of muscle excitations that drive a 30-muscle, 3-degree-of-freedom model of pedaling to track measured pedaling kinematics and forces. Only 10 min of computer time were required to compute muscle excitations that reproduced the measured pedaling dynamics, which is over two orders of magnitude faster than conventional dynamic optimization techniques. Simulated kinematics were within 1 degrees of experimental values, simulated pedal forces were within one standard deviation of measured pedal forces for nearly all of the crank cycle, and computed muscle excitations were similar in timing to measured electromyographic patterns. The speed and accuracy of this new algorithm improves the feasibility of using detailed musculoskeletal models to simulate and analyze movement.