Hill-type Model Research Articles

Development of mapped stress‐field boundary conditions based on a Hill‐type muscle model

Forces generated in the muscles and tendons actuate the movement of the skeleton. Accurate estimation and application of these musculotendon forces in a continuum model is not a trivial matter. Frequently, musculotendon attachments are approximated as point forces; however, accurate estimation of local mechanics requires a more realistic application of musculotendon forces. This paper describes the development of mapped Hill-type muscle models as boundary conditions for a finite volume model of the hip joint, where the calculated muscle fibres map continuously between attachment sites. The applied muscle forces are calculated using active Hill-type models, where input electromyography signals are determined from gait analysis. Realistic muscle attachment sites are determined directly from tomography images. The mapped muscle boundary conditions, implemented in a finite volume structural OpenFOAM (ESI-OpenCFD, Bracknell, UK) solver, are employed to simulate the mid-stance phase of gait using a patient-specific natural hip joint, and a comparison is performed with the standard point load muscle approach. It is concluded that physiological joint loading is not accurately represented by simplistic muscle point loading conditions; however, when contact pressures are of sole interest, simplifying assumptions with regard to muscular forces may be valid.

Exploiting elasticity: Modeling the influence of neural control on mechanics and energetics of ankle muscle–tendons during human hopping

We present a simplified Hill-type model of the human triceps surae-Achilles tendon complex working on a gravitational–inertial load during cyclic contractions (i.e. vertical hopping). Our goal was to determine the role that neural control plays in governing muscle, or contractile element (CE), and tendon, or series elastic element (SEE), mechanics and energetics within a compliant muscle–tendon unit (MTU). We constructed a 2D parameter space consisting of many combinations of stimulation frequency and magnitude (i.e. neural control strategies). We compared the performance of each control strategy by evaluating peak force and average positive mechanical power output for the system (MTU) and its respective components (CE, SEE), force–length (F–L) and –velocity (F–V) operating point of the CE during active force production, average metabolic rate for the CE, and both MTU and CE apparent efficiency. Our results suggest that frequency of stimulation plays a primary role in governing whole-MTU mechanics. These include the phasing of both activation and peak force relative to minimum MTU length, average positive power, and apparent efficiency. Stimulation amplitude was primarily responsible for governing average metabolic rate and within MTU mechanics, including peak force generation and elastic energy storage and return in the SEE. Frequency and amplitude of stimulation both played integral roles in determining CE F–L operating point, with both higher frequency and amplitude generally corresponding to lower CE strains, reduced injury risk, and elimination of the need for passive force generation in the CE parallel elastic element (PEE).

Estimation of muscle and joint forces in the human lower extremity during rising motion from a seated position

Biomechanical models are often employed to predict in vivo muscle or joint forces in the human body because measuring these forces is difficult. Even though the rising motion from a seated position frequently occurs in daily life and the force acting on the knee joints during the motion is important for aged or infirmed people, limited studies related to the motion have been conducted. This study aims to propose a numerical procedure to estimate the muscle and joint forces in the human lower extremity during rising motion from a seated position. The human lower extremity is idealized as a multibody system in which the Hill-type muscle force model is employed. The multibody system consists of four bodies (shank, thigh, pelvis, and upper body), three revolute joints, and ten forces. The motion of the multibody system is assumed constrained to the sagittal plane, and the muscles in the human lower extremity are idealized by nine action/reaction forces. The nine forces are determined by minimizing the metabolic energy, which is consumed during the rising motion. Metabolic energy consists of the energy consumed by heat generation of muscles and the mechanical work done by muscles. For the accuracy validation of the proposed estimation method, numerical results obtained with the proposed method are compared with existing experimental results.

Development of a muscle circumference sensor to estimate torque of the human elbow joint

Many researchers are currently studying and developing various kinds of human–robot systems, as this field requires more accurate and reliable sensing systems to detect the intention behind human motion. This study describes a muscle circumference sensor (MCRS) that was developed to measure the variation in the outline of a muscle as a human–robot interface (HRI), as well as an elbow-joint model to develop an estimation algorithm for human elbow-joint torque. A modular-type MCRS and calibration algorithm were developed to measure the muscle-activation signal, which is represented by the normalization of the calibrated MCRS signal. A Hill-type model was applied to the muscle-activation signal, and the kinematic model of the muscle could be used to estimate the joint torques. Experiments were carried out to evaluate the performance of the proposed algorithm using isotonic contraction motion and KIN-COM® equipment under 5Nm, 10Nm, and 15Nm loads. The algorithm and its feasibility for use as an HRI were verified by comparing the joint load condition and the torque estimated using the algorithm.

A-35 下肢関節まわりの駆動パワーと角運動量解析によるランニング運動の考察(筋骨格系モデリング)

The first purpose of this study considers the degree of burden and degree of fatigue for each muscle by angular momentum of around the lower limb joints during running of the people. This angular momentum of the each muscle represents the severity of muscular exercise. The angular momentum of each muscle worked to produce the driving rotation power around joints. At last, for the final purpose of this study we verify the usability and value of the proposed method from those consideration results. In this case, the muscle mathematics model of the 3D frame model of the lower limbs that was used for inverse dynamics analysis and inverse kinematics analysis is Hill type model. In the future, the usability of the proposed method is verified by comparing with conventional method for evaluating the degree of burden and degree of fatigue for each muscle of muscle activity.

Nonlinear Elasticity of Muscle and Its Role in Motor Control

Holding an object without crushing or dropping it is trivial. But, decades of research in robotics has shown otherwise. Maintaining a static grasp, i.e. postural stability of the fingers, conflicts with the demands of regulating force at the fingertips. We revisit this old problem of stable static contact with simultaneous fingertip force control, and show that the control is greatly simplified by using actuators with well-designed elastic properties. Actuators that produce force as the output, in response to a control input, are well-suited to regulate the fingertip contact force. Such force actuators, like high quality electric motors, maintain a nearly constant force output independent of any displacement imposed upon them, in effect having zero stiffness. This insensitivity of the actuator to displacements induces a postural instability of the finger.We show that the postural instability can be alleviated if the actuators are non-ideal and possess nonlinear elastic properties, namely stiffness that is linearly proportional to the force output. Such an actuator resembles a Hill-type model for muscle, with an ideal force actuator in parallel with a spring that has an exponential force-displacement relationship. Experiments that subject deafferented skeletal muscle to small displacements have shown that the stiffness of muscle scales linearly with its force output, the exact feature that our calculation shows is necessary for postural stability. This nonlinear elastic property of muscle has its roots in the cross-bridge model of muscle function, originally proposed by A.F. Huxley. Our results are not specific to the finger or specific limb, rather they generalize to any appendage such as legs or tentacles, which have more internal degrees of freedom than imposed by the surrounding environment alone.Funding support from WellcomeTrust-DBT India Alliance, HFSP, UKIERI, Simons Foundation, NCBS.

The Distributed Lambda (λ) Model (DLM): A 3-D, Finite-Element Muscle Model Based on Feldman's λ Model; Assessment of Orofacial Gestures

The authors aimed to design a distributed lambda model (DLM), which is well adapted to implement three-dimensional (3-D), finite-element descriptions of muscles. A muscle element model was designed. Its stress-strain relationships included the active force-length characteristics of the λ model along the muscle fibers, together with the passive properties of muscle tissues in the 3-D space. The muscle element was first assessed using simple geometrical representations of muscles in the form of rectangular bars. It was then included in a 3-D face model, and its impact on lip protrusion was compared with the impact of a Hill-type muscle model. The force-length characteristic associated with the muscle elements matched well with the invariant characteristics of the λ model. The impact of the passive properties was assessed. Isometric force variation and isotonic displacements were modeled. The comparison with a Hill-type model revealed strong similarities in terms of global stress and strain. The DLM accounted for the characteristics of the λ model. Biomechanically, no clear differences were found between the DLM and a Hill-type model. Accurate evaluations of the λ model, based on the comparison between data and simulations, are now possible with 3-D biomechanical descriptions of the speech articulators because of the DLM.

Phenomenological models of the dynamics of muscle during isotonic shortening

We investigated the effectiveness of simple, Hill-type, phenomenological models of the force-length-velocity relationship for simulating measured length trajectories during muscle shortening, and, if so, what forms of the model are most useful. Using isotonic shortening data from mouse soleus and toad depressor mandibulae muscles, we showed that Hill-type models can indeed simulate the shortening trajectories with sufficiently good accuracy. However, we found that the standard form of the Hill-type muscle model, called the force-scaling model, is not a satisfactory choice. Instead, the results support the use of less frequently used models, the f-max scaling model and force-scaling with parallel spring, to simulate the shortening dynamics of muscle.

Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Hill-type models are commonly used to estimate muscle forces during human and animal movement—yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation–deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with “differential” activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r2, was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r2=0.26–0.51), and all exhibited some errors (RMSE=9.63–32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.

근 부피 센서를 이용한 인체 팔꿈치 관절의 동작 토크 추정

This study uses a muscle activation sensor and elbow joint model to develop an estimation algorithm for human elbow joint torque for use in a human-robot interface. A modular-type MVS (Muscle Volume Sensor) and calibration algorithm are developed to measure the muscle activation signal, which is represented through the normalization of the calibrated signal of the MVS. A Hill-type model is applied to the muscle activation signal and the kinematic model of the muscle can be used to estimate the joint torques. Experiments were performed to evaluate the performance of the proposed algorithm by isotonic contraction motion using the KIN-COM® equipment at 5, 10, and 15Nm. The algorithm and its feasibility for use as a human-robot interface are verified by comparing the joint load condition and the torque estimated by the algorithm.

Biomechanics of Skeletal Muscles

Part I. Muscle Architecture and Mechanics Chapter 1. Muscle Architecture Muscle Fascicles and Their Arrangements * Parallel Fibered and Fusiform Muscles * Pennate Muscles * Convergent and Circular Muscles Muscle Fascicle Curvature: Frenet Frames Fiber Architecture in the Fascicles Muscle as a Fiber-Reinforced Composite Fiber, Fascicle, and Muscle Length: Length-Length Ratios * Fiber and Fascicle Length * Length-Length Ratios Muscle Path: Muscle Centroids * Straight-Line Representation of Muscle Path * Centroid Model of Muscle Path * Curved and Wrapping Muscles * Twisted Muscles * Muscles Attaching to More Than Two Bones Cross-Sectional Area, Physiological and Anatomical Muscle Attachment Area Summary Questions for Review Literature List Chapter 2. Properties of Tendons and Passive Muscles Biomechanics of Tendons and Aponeuroses * Elastic Behavior * Viscoelastic Behavior of Tendons * Tendon Interaction With Surrounding Tissues Mechanical Properties of Passive Muscles * Muscle Tone: Equitonometry * Mechanical Properties of Relaxed Muscles On Joint Flexibility Summary Questions for Review Literature List Chapter 3. Mechanics of Active Muscle Muscle Force Production and Transmission * Experimental Methods * Transition From Rest to Activity * Transition From Activity to Rest: Muscle Relaxation * Constancy of the Muscle Volume * Force Transmission and Internal Deformations (Strain) * Intramuscular Stress and Pressure * Functional RelationsForce-Length Relations * Force-Velocity Relations * Force-Length-Velocity Relations History Effects in Muscle Mechanics * Force Depression After Muscle Shortening * Effects of Muscle Release: Quick-Release and Controlled-Release Methods: Series Muscle Components Summary Questions for Review Literature List Chapter 4. Muscles as Force and Energy Absorbers Muscle Mechanical Behavior During Stretch * Dynamic Force Enhancement * Residual Force Enhancement Muscle Shortening After Stretch * Work and Power During Shortening After Stretch * Energy Consumption During Stretch and Efficiency of the Muscle Shortening After Stretch Dissipation of Energy Mechanical Muscle Models * Hill-Type Model * Model Scaling Summary Questions for Review Literature List Part II Muscles in the Body Chapter 5. From Muscle Forces to Joint Moments Force Transmission: From Muscle to Bone * From Muscle to Tendon * From Tendon to Bone * Tendon Elasticity and Isometric Force-Length Relation Force Transmission Via Soft Tissue Skeleton (Fascia) * Structure of Fascia * Muscle-Tendon-Fascia Attachments * Fascia as Soft Tissue Skeleton (Ectoskeleton) Muscle Moment Arms * Muscle Moment Arm Vectors and Their Components * Methods for Determination of Muscle Moment Arms * Factors Affecting Muscle Moment Arm * Transformation of Muscle Forces to Joint Moments: Muscle Jacobian Summary Questions for Review Literature List Chapter 6. Two-Joint Muscles in Human Motion Two-Joint Muscles: A Special Case of Multifunctional Muscles * Functional Features of Two-Joint Muscles * Anatomical and Morphological Features of Two-Joint Muscles Functional Roles of Two-Joint Muscles * Kinetic Analysis of Two-Joint Muscles: Lombard's Paradox * Kinematic Analysis of Two-Joint Muscles: Solution of Lombard's Paradox Mechanical Energy Transfer and Saving by Two-Joint Muscles * Tendon Action of Two-Joint Muscles * Saving Mechanical Energy by Two-Joint Muscles Summary Questions for Review Literature List Chapter 7. Eccentric Muscle Action in Human Motion Joint Power and Work as Measures of Eccentric Action * Negative Power and Work at a Joint * Total Negative Power and Work in Several Joints * Negative Power of Center of Mass Motion * Two Ways of Mechanical Energy Dissipation: Softness of Landing Negative Work in Selected Activities * Walking * Stair Descent and Ascent * Level, Downhill, and Uphill Running * Landing Joint Moments During Eccentric Actions * Maximal Joint Moments During Eccentric Actions * Force Changes During and After Stretch * Residual Force Enhancement in Humans Muscle Activity During Eccentric Actions * Surface Electromyographic Activity During Eccentric Actions * Motor Unit Activity During Eccentric Actions * Electromechanical Delay Physiological Cost of Eccentric Action * Oxygen Consumption During Eccentric and Concentric Exercise * Fatigue and Perceived Exertion During Eccentric Action * Muscle Soreness After Eccentric Exercise Reversible Muscle Action: Stretch-Shortening Cycle * Enhancement of Positive Work and Power Production * Mechanisms of the Performance Enhancement in the SSC * Efficiency of Positive Work in SSC Summary Questions for Review Literature List Chapter 8. Muscle Coordination in Human Motion Kinematic Redundancy and Kinematic Invariant Characteristics of Limb Movements * Straight-Line Limb Endpoint Trajectory * Bell-Shaped Velocity Profile8.1.3 Power Law * Fitts' Law * Principle of Least Action Kinetic Invariant Characteristics of Limb Movements * Elbow-Shoulder Joint Moment Covariation During Arm Reaching * Minimum Joint Moment Change * Orientation and Shape of the Arm Apparent Stiffness Ellipses Muscle Redundancy * Sources of Muscle Redundancy * Invariant Features of Muscle Activity Patterns The Distribution Problem * Static Optimization * Dynamic Optimization * Inverse Optimization * On Optimization Methods in Human Biomechanics and Motor Control Summary Questions for Review Literature List

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force–length–velocity relationship and the tendon force–strain relationship. This study was aimed at investigating the influence of subject-specific tendon force–strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration–prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.

Pharmacodynamics and Dose-Response Relationships of Liposomal Amphotericin B against Different Azole-Resistant Aspergillus fumigatus Isolates in a Murine Model of Disseminated Aspergillosis

The management of invasive aspergillosis (IA) has become more complicated due to the emergence of acquired azole resistance in Aspergillus fumigatus, which is associated with treatment failure and a mortality rate of 88%. Treatment with liposomal amphotericin B (L-AmB) may be a useful alternative to improve therapeutic outcome in azole-resistant IA. Four clinical A. fumigatus isolates obtained from patients with proven IA were studied in a nonneutropenic murine model of infection: a wild-type isolate without mutations in the cyp51A gene and three azole-resistant isolates harboring a single mutation at codon 220 (M220I) and tandem repeat mutations (a 34-bp tandem repeat mutation in the promoter region of the cyp51A gene in combination with substitutions at codon L98 [TR(34)/L98H] and a 46-bp tandem repeat mutation in the promoter region of the cyp51A gene in combination with mutation at codons Y121 and T289 [TR(46)/Y121F/T289A]), respectively. Female CD-1 mice were infected intravenously 24 h prior to the start of therapy. Groups of 11 mice were treated at days 1, 2, and 5 postchallenge with increasing 4-fold doses of L-AmB ranging from 0.004 to 16 mg/kg/day and observed for 14 days. Survival for all 4 isolates at day 14 was significantly better than that of controls. A dose-response relationship was observed independent of the azole resistance mechanism. The Hill-type model with a variable slope fitted the relationship between the dose and 14-day survival well for all isolates, with R(2) values of 0.95 (wild-type), 0.97 (M220I), 0.85 (TR(34)/L98H), and 0.94 (TR(46)/Y121F/T289A), respectively. Multiple logistic regression analysis confirmed that there was no significant difference between groups. The results of these experiments indicate that L-AmB was able to prolong survival in vivo in disseminated IA independent of the presence of an azole resistance mechanism in a dose-dependent manner, and therefore, they support a role for L-AmB in the treatment of azole-resistant IA.

Pharmacodynamic Variability beyond That Explained by MICs

Monte Carlo simulations (MCS) present a powerful tool to evaluate candidate regimens by determining the probability of target attainment. Although these assessments have traditionally incorporated variability in pharmacokinetic (PK) parameters and MICs, consideration of interstrain pharmacodynamic (PD) variability has been neglected. A population PK/PD model was developed for doripenem using murine thigh infection data based on 20 bacterial strains. PK data were fit to a linear two-compartment model with first-order input and elimination processes and an absorption lag time from a separate site (r(2) > 0.96). PK parameters were utilized to simulate free-drug profiles for various regimens in PD studies, from which the percentage of the dosing interval for which free-drug concentrations exceed the MIC of the targeted strain (%fT>MIC) was calculated. Doripenem PD was excellently described with Hill-type models (r(2) > 0.98); significant differences between mean PD estimates determined using a two-stage approach versus population analyses were not observed (P > 0.05); however, the variance in 50% effective concentration (EC50) and maximum effect (Emax) among strains was much greater using the two-stage approach. Even using the population approach, interstrain variability in EC50 (coefficient of variation expressed as a percentage [CV%] = 29.2%) and H (CV% = 46.1%) parameters was substantive, while the variability in Emax (CV% = 19.7%) was modest. This resulted in extensive variability in the range of %fT>MIC targets associated with stasis to those associated with a 2-log10 reduction in bacterial burden (CV% ∼ 50%). It appears that MCS, based on the assumption that PD variability is due to MIC alone, underestimates variability and may consequently underestimate treatment failures.

Hill-type muscle model parameters determined from experiments on single muscles show large animal-to-animal variation.

Models built using mean data can represent only a very small percentage, or none, of the population being modeled, and produce different activity than any member of it. Overcoming this "averaging" pitfall requires measuring, in single individuals in single experiments, all of the system's defining characteristics. We have developed protocols that allow all the parameters in the curves used in typical Hill-type models (passive and active force-length, series elasticity, force-activation, force-velocity) to be determined from experiments on individual stick insect muscles (Blümel et al. 2012a). A requirement for means to not well represent the population is that the population shows large variation in its defining characteristics. We therefore used these protocols to measure extensor muscle defining parameters in multiple animals. Across-animal variability in these parameters can be very large, ranging from 1.3- to 17-fold. This large variation is consistent with earlier data in which extensor muscle responses to identical motor neuron driving showed large animal-to-animal variability (Hooper etal. 2006), and suggests accurate modeling of extensor muscles requires modeling individual-by-individual. These complete characterizations of individual muscles also allowed us to test for parameter correlations. Two parameter pairs significantly co-varied, suggesting that a simpler model could as well reproduce muscle response.

Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error

Hill-type parameter values measured in experiments on single muscles show large across-muscle variation. Using individual-muscle specific values instead of the more standard approach of across-muscle means might therefore improve muscle model performance. We show here that using mean values increased simulation normalized RMS error in all tested motor nerve stimulation paradigms in both isotonic and isometric conditions, doubling mean simulation error from 9 to 18 (different at p<0.0001). These data suggest muscle-specific measurement of Hill-type model parameters is necessary in work requiring highly accurate muscle model construction. Maximum muscle force (F (max)) showed large (fourfold) across-muscle variation. To test the role of F (max) in model performance we compared the errors of models using mean F (max) and muscle-specific values for the other model parameters, and models using muscle-specific F (max) values and mean values for the other model parameters. Using muscle-specific F (max) values did not improve model performance compared to using mean values for all parameters, but using muscle-specific values for all parameters but F (max) did (to an error of 14, different from muscle-specific, mean all parameters, and mean only F (max) errors at p≤ 0.014). Significantly improving model performance thus required muscle-specific values for at least a subset of parameters other than F (max), and best performance required muscle-specific values for this subset and F (max). Detailed consideration of model performance suggested that remaining model error likely stemmed from activation of both fast and slow motor neurons in our experiments and inadequate specification of model activation dynamics.

Elastic recoil can either amplify or attenuate muscle–tendon power, depending on inertial vs. fluid dynamic loading

Frog jumps exceed muscle power limits. To achieve this, a muscle may store elastic energy in tendon before it is released rapidly, producing ‘power amplification’ as tendon recoil assists the muscle to accelerate the load. Do the musculoskeletal modifications conferring power amplification help or hinder frog swimming? We used a Hill-type mathematical model of a muscle–tendon (MT) with contractile element (CE) and series elastic element (SEE) properties of frogs. We varied limb masses from 0.3 to 30g, foot-fin areas from 0.005 to 50cm2 and effective mechanical advantage (EMA=in-lever/out-lever) from 0.025 to 0.1. ‘Optimal’ conditions produced power amplification of ∼19% greater than the CE limit. Yet, other conditions caused ∼80% reduction of MT power (power attenuation) due to SEE recoil absorbing power from (rather than adding to) the CE. The tendency for elastic recoil to cause power amplification vs. attenuation was load dependent: low fluid drag loads, high limb mass and EMA=0.1 caused power amplification whereas high drag, low mass and low EMA (=0.025) caused attenuation. Power amplification emerged when: (1) CE shortening velocity is 1/3Vmax, (2) elastic energy storage is neither too high nor too low, and (3). peak inertial-drag force ratio≥∼1.5. Excessive elastic energy storage delayed the timing of recoil, causing power attenuation. Thus our model predicts that for fluid loads, the benefit from a compliant tendon is modest, and when the system is ‘poorly tuned’ (i.e., inappropriate EMA), MT power attenuation can be severe.

Optimizing Locomotion Controllers Using Biologically-Based Actuators and Objectives.

We present a technique for automatically synthesizing walking and running controllers for physically-simulated 3D humanoid characters. The sagittal hip, knee, and ankle degrees-of-freedom are actuated using a set of eight Hill-type musculotendon models in each leg, with biologically-motivated control laws. The parameters of these control laws are set by an optimization procedure that satisfies a number of locomotion task terms while minimizing a biological model of metabolic energy expenditure. We show that the use of biologically-based actuators and objectives measurably increases the realism of gaits generated by locomotion controllers that operate without the use of motion capture data, and that metabolic energy expenditure provides a simple and unifying measurement of effort that can be used for both walking and running control optimization.

A neuromechanical computational model of spinal control of locomotion

We developed a neuromechanical computational model of cat locomotion that simulated the locomotor movements of cat hindlimbs controlled by spinal locomotor central pattern generators (CPGs, one per limb). In the closed-loop model, CPG operation was adjusted by afferent feedback from the hindlimbs. The CPG model was based on the previous two-level model [4] and included a half-center rhythm generator (RG), producing alternating flexor and extensor activities, and a pattern formation (PF) network operating under control of RG and controlling the synergetic activities of different hindlimb motoneuron pools. This basic model [4] was extended by incorporating additional neural circuits at the PF level allowing the CPG to generate the complex activity patterns of motoneurons controlling two-joint muscles. The model included reflex circuits, mediating reciprocal inhibition between antagonistic motoneurons, recurrent inhibition of motoneurons via Renshaw cells, and di-synaptic excitation of extensors by extensor afferents during stance phase of locomotion. The hindlimbs with the pelvis and trunk were modeled as a 10 degree-of-freedom sagittal plane system of rigid segments interconnected by frictionless revolute joints. The hindlimb interactions with the ground and other body segments were modeled as linear springs and dampers [1,2]. The two hindlimbs were driven by 18 muscle actuators representing major hindlimb muscles in the cat. The dynamics of each muscle-tendon unit was described by a Hill-type model extended to account for muscle mass, pennation angle, and force-length-velocity properties of muscle and tendon [1,2]. All muscles generated motion-dependent afferent signals which were calculated as functions of muscle length, velocity and force using modified regression equations from [3]. Parameters of the musculoskeletal model were identified by minimizing a mismatch between the computed (based on the recorded hindlimb muscle activity) and experimentally recorded changes in the joint angles, joint moments and ground reaction forces using the simulated annealing optimization algorithm [1,2]. The developed neuromechanical model demonstrated stable locomotion and exhibited realistic patterns of muscle activation, limb kinematics, and ground reaction force dynamics. The model was used for investigation of the role of afferent feedback and the CPG in control of locomotion under different conditions.

A Muscle’s Force Depends on the Recruitment Patterns of Its Fibers

Biomechanical models of whole muscles commonly used in simulations of musculoskeletal function and movement typically assume that the muscle generates force as a scaled-up muscle fiber. However, muscles are comprised of motor units that have different intrinsic properties and that can be activated at different times. This study tested whether a muscle model comprised of motor units that could be independently activated resulted in more accurate predictions of force than traditional Hill-type models. Forces predicted by the models were evaluated by direct comparison with the muscle forces measured in situ from the gastrocnemii in goats. The muscle was stimulated tetanically at a range of frequencies, muscle fiber strains were measured using sonomicrometry, and the activation patterns of the different types of motor unit were calculated from electromyographic recordings. Activation patterns were input into five different muscle models. Four models were traditional Hill-type models with different intrinsic speeds and fiber-type properties. The fifth model incorporated differential groups of fast and slow motor units. For all goats, muscles and stimulation frequencies the differential model resulted in the best predictions of muscle force. The in situ muscle output was shown to depend on the recruitment of different motor units within the muscle.