An optimal control model for maximum-height human jumping

To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).     

Vestibular postural control model

Current models for physiological components and a posture control experiment conducted with three normal subjects form the basis for a model which seeks to describe quantitatively the control of body sway when only vestibular motion cues are used. Emphasis is placed on delineating the relative functional roles of the linear and the angular acceleration sensors and on modeling the functional interface between these sensors and the initiation of compensatory responses at the ankle joint.The model predicts the form of the postural response to a small sway disturbance; including initial detection of sway, characteristics of the transient correction, and maintenance of stability. The model suggests that postural stability requires a short time constant integration of semicircular canal output. Separation of semicircular canal and utricular otolith function into sway motion detector and static reference sensors respectively is demonstrated.This work was supported by NASA under Grant NGR-22-009-156.     

Evaluation of the lambda model for human postural control during ankle strategy

An accurate modeling of human stance might be helpful in assessing postural deficit. The objective of this article is to validate a mathematical postural control model for quiet standing posture. The postural dynamics is modeled in the sagittal plane as an inverted pendulum with torque applied at the ankle joint. The torque control system is represented by the physiological lambda model. Two neurophysiological command variables of the central nervous system, designated and , establish the dynamic threshold muscle at which motoneuron recruitment begins. Kinematic data and electromyographic signals were collected on four young males in order to measure small voluntary sway and quiet standing posture. Validation of the mathematical model was achieved through comparison of the experimental and simulated results. The mathematical model allows computation of the unmeasurable neurophysiological commands and that control the equilibrium position and stability. Furthermore, with the model it is possible to conclude that low-amplitude body sway during quiet stance is commanded by the central nervous system.     

A double-inverted pendulum model for studying the adaptability of postural control to frequency during human stepping in place

In order to analyze the influence of gravity and body characteristics on the control of center of mass (CM) oscillations in stepping in place, equations of motion in oscillating systems were developed using a double-inverted pendulum model which accounts for both the head-arms-trunk (HAT) segment and the two-legged system. The principal goal of this work is to propose an equivalent model which makes use of the usual anthropometric data for the human body, in order to study the ability of postural control to adapt to the step frequency in this particular paradigm of human gait. This model allows the computation of CM-to-CP amplitude ratios, when the center of foot pressure (CP) oscillates, as a parametric function of the stepping in place frequency, whose parameters are gravity and major body characteristics. Motion analysis from a force plate was used to test the model by comparing experimental and simulated values of variations of the CM-to-CP amplitude ratio in the frontal plane versus the frequency. With data from the literature, the model is used to calculate the intersegmental torque which stabilizes the HAT when the Leg segment is subjected to a harmonic torque with an imposed frequency. Received: 24 February 1997 / Accepted in revised form: 30 June 1998     

A model of optimal voluntary muscular control

Summary In the absence of detailed knowledge of how the CNS controls a muscle through its motor fibers, a reasonable hypothesis is that of optimal control. This hypothesis is studied using a simplified mathematical model of a single muscle, based on A. V. Hill's equations, with series elastic element omitted, and with the motor signal represented by a single input variable.Two cost functions were used. The first was total energy expended by the muscle (work plus heat). If the load is a constant force, with no inertia, Hill's optimal velocity of shortening results. If the load includes a mass, analysis by optimal control theory shows that the motor signal to the muscle consists of three phases: (1) maximal stimulation to accelerate the mass to the optimal velocity as quickly as possible, (2) an intermediate level of stimulation to hold the velocity at its optimal value, once reached, and (3) zero stimulation, to permit the mass to slow down, as quickly as possible, to zero velocity at the specified distance shortened. If the latter distance is too small, or the mass too large, the optimal velocity is not reached, and phase (2) is absent. For lengthening, there is no optimal velocity; there are only two phases, zero stimulation followed by maximal stimulation.The second cost function was total time. The optimal control for shortening consists of only phases (1) and (3) above, and is identical to the minimal energy control whenever phase (2) is absent from the latter.Generalization of this model to include viscous loads and a series elastic element are discussed.     

A structurally relevant coarse-grained model for cholesterol

Detailed atomistic computer simulations are now widely used to study biological membranes, including increasingly mixed lipid systems that involve, for example, cholesterol, which is a key membrane lipid. Typically, simulations of these systems start from a preassembled bilayer because the timescale on which self-assembly occurs in mixed lipid systems is beyond the practical abilities of fully atomistic simulations. To overcome this limitation and study bilayer self-assembly, coarse-grained models have been developed. Although there are several coarse-grained models for cholesterol reported in the literature, these generally fail to account explicitly for the unique molecular features of cholesterol that relate to its function and role as a membrane lipid. In this work, we propose a new coarse-grained model for cholesterol that retains the molecule's unique features and, as a result, can be used to study crystalline structures of cholesterol. In the development of the model, two levels of coarse-graining are explored and the importance of retaining key molecular features in the coarse-grained model that are relevant to structural properties is investigated.     

A deep learning model for predicting optimal distance range in crosslinking mass spectrometry data

Macromolecular assemblies play an important role in all cellular processes. While there has recently been significant progress in protein structure prediction based on deep learning, large protein complexes cannot be predicted with these approaches. The integrative structure modeling approach characterizes multi-subunit complexes by computational integration of data from fast and accessible experimental techniques. Crosslinking mass spectrometry is one such technique that provides spatial information about the proximity of crosslinked residues. One of the challenges in interpreting crosslinking datasets is designing a scoring function that, given a structure, can quantify how well it fits the data. Most approaches set an upper bound on the distance between Cα atoms of crosslinked residues and calculate a fraction of satisfied crosslinks. However, the distance spanned by the crosslinker greatly depends on the neighborhood of the crosslinked residues. Here, we design a deep learning model for predicting the optimal distance range for a crosslinked residue pair based on the structures of their neighborhoods. We find that our model can predict the distance range with the area under the receiver-operator curve of 0.86 and 0.7 for intra- and inter-protein crosslinks, respectively. Our deep scoring function can be used in a range of structure modeling applications.     

Tools for analyzing and predicting N-terminal protein modifications

The vast majority of the proteins encoded in any genome naturally undergo a large number of different N-terminal modifications, hindering their characterization by routine proteomic approaches. These modifications are often irreversible, usually cotranslational and are crucial, as their occurrence may reflect or affect the status, fate and function of the protein. For example, large signal peptide cleavages and N-blocking mechanisms reflect targeting to various cell compartments, whereas N-ligation events tend to be related to protein half-life. N-terminal positional proteomic strategies hold promise as a new generation of approaches to the fine analysis of such modifications. However, further biological investigation is required to resolve problems associated with particular low-abundance or challenging N-terminal modifications. Recent progress in genomics and bioinformatics has provided us with a means of assessing the impact of these modifications in proteomes. This review focuses on methods for characterizing the occurrence and diversity of N-terminal modifications and for assessing their contribution to function in complete proteomes. Progress is being made towards the annotation of databases containing information for complete proteomes, and should facilitate research into all areas of proteomics.     

Evaluation of a generalized model of human postural dynamics and control in the sagittal plane

A two-step identification method is used to evaluate a generalized model of human postural control in the sagittal plane. Postural dynamics are represented as a planar open-chain linkage system supported by a triangular foot. The control mechanism is modeled as a state feedback element in which the torque acting at a given link is an arbitrary function of the state variables — angles and angular velocities. To validate the approach, six normal subjects underwent two series of experiments. The first series were used to determine an appropriate model of the system dynamics. The second series were used to estimate the parameters of the feedback model. A computer simulation of the complete system shows that the model predictions closely match the observed responses. These results suggest that the proposed model provides a useful framework for analysis of postural control mechanisms.This work was supported by the National Institutes of Health under Grant NS 21363     

A model for predicting masking-period patterns

Information calculations were performed using different codes for the same neuronal impulse data. Under various stimulus conditions the data were obtained from first, second and fourth order neurons (muscle spindles, neurons of the dorsal spino-cerebellar tract and principal cells of the lateral geniculate body of the cat) which had different transneuronal couplings between input and output. A code matched approximately to the signal transfer properties of the investigated neuronal systems was applied. This code was realized by performing a time-weighted average of the input signal with the weighting function being derived from the cross-correlation between the neuronal input and output. Computations of the transinformation using this weighted-average code and the rate code (frequency code) were carried out to show the loss of transinformation due to restrictions in these codes. This loss was determined by comparison with calculations without code restrictions (signal code). In all computations the weighted-average code yielded results ranging from 90 to 99% of those of the signal code. This demonstrates that nearly all information is transmitted by the linear part of the coupling. The results of the rate code did not approximate those of the signal code as closely (5–92%) as in the case of the weighted-average code indicating an unreliability in the rate code when applied to transneuronal signal transmission. Reasons for this unreliability are discussed.     

A dynamic model for finger interphalangeal coordination

In this paper a dynamic model to investigate interphalangeal coordination in the human finger is proposed. Suitable models which describe the relationship between the tendon displacement and the joint angles have been chosen and incorporated into the skeletal dynamic model. A kinematic and kinetic model for interphalangeal coordination is suggested. Digital computer simulations are carried out to study interphalangeal (IP) flexion. Moreover, the effect of two different optimization methods is contrasted. The two optimization algorithms are employed to obtain a set of feasible values for the forces in the tendons or muscles of the finger.     

A single muscle's multifunctional control potential of body dynamics for postural control and running

A neuromechanical approach to control requires understanding how mechanics alters the potential of neural feedback to control body dynamics. Here, we rewrite activation of individual motor units of a behaving animal to mimic the effects of neural feedback without concomitant changes in other muscles. We target a putative control muscle in the cockroach, Blaberus discoidalis (L.), and simultaneously capture limb and body dynamics through high-speed videography and a micro-accelerometer backpack. We test four neuromechanical control hypotheses. We supported the hypothesis that mechanics linearly translates neural feedback into accelerations and rotations during static postural control. However, during running, the same neural feedback produced a nonlinear acceleration control potential restricted to the vertical plane. Using this, we reject the hypothesis from previous work that this muscle acts primarily to absorb energy from the body. The conversion of the control potential is paralleled by nonlinear changes in limb kinematics, supporting the hypothesis that significant mechanical feedback filters the graded neural feedback for running control. Finally, we insert the same neural feedback signal but at different phases in the dynamics. In this context, mechanical feedback enables turning by changing the timing and direction of the accelerations produced by the graded neural feedback.     

A multi-phase optimal control technique for the simulation of a human vertical jump

A multi-phase optimal control technique is presented that can be used to solve dynamic optimization problems involving musculoskeletal systems. The biomechanical model consists of a set of differential equations describing the dynamics of the multi-body system and the generation of the dynamic forces of the human muscles. Within the optimization technique, subintervals can be defined in which the differential equations are continuous. At the boundaries the dimension of the state- and control vector as well as the dimension of the right-hand side may change. The problem is solved by a multiple shooting approach which converts the problem into a non-linear program. The method is applied to simulate a human jump movement.     

Biomechanical modeling and optimal control of human posture

The present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open-loop raising-up movements from a squatting position. The biomechanical model comprises 10 equivalent musculotendon actuators, based on a 40 muscles model, and three links (shank, thigh and HAT-Head, Arms and Trunk). Optimal control solutions are achieved through algorithms based on the Consistent Approximations Theory (Schwartz and Polak, 1996), where the continuous non-linear dynamics is represented in a discrete space by means of a Runge-Kutta integration and the control signals in a spline-coefficient functional space. This leads to non-linear programming problems solved by a sequential quadratic programming (SQP) method. Due to the highly non-linear and unstable nature of the posture dynamics, numerical convergence is difficult, and specific strategies must be implemented in order to allow convergence. Results for control (muscular excitations) and angular trajectories are shown using two final simulation times, as well as specific control strategies are discussed.     

Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1–0.7 Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.     

An optimal control model of diabetes mellitus

Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.     

A balance control model of quiet upright stance based on an optimal control strategy

Models of balance control can aid in understanding the mechanisms by which humans maintain balance. A balance control model of quiet upright stance based on an optimal control strategy is presented here. In this model, the human body was represented by a simple single-segment inverted pendulum during upright stance, and the neural controller was assumed to be an optimal controller that generates ankle control torques according to a certain performance criterion. This performance criterion was defined by several physical quantities relevant to sway. In order to accurately simulate existing experimental data, an optimization procedure was used to specify the set of model parameters to minimize the scalar error between experimental and simulated sway measures. Thirty-two independent simulations were performed for both younger and older adults. The model's capabilities, in terms of reflecting sway behaviors and identifying aging effects, were then analyzed based on the simulation results. The model was able to accurately predict center-of-pressure-based sway measures, and identify potential changes in balance control mechanisms caused by aging. Correlations between sway measures and model parameters are also discussed.