A regression model predicting isometric shoulder muscle activities from arm postures and shoulder joint moments

Tissue overloading is a major contributor to shoulder musculoskeletal injuries. Previous studies attempted to use regression-based methods to predict muscle activities from shoulder kinematics and shoulder kinetics. While a regression-based method can address co-contraction of the antagonist muscles as opposed to the optimization method, most of these regression models were based on limited shoulder postures. The purpose of this study was to develop a set of regression equations to predict the 10th percentile, the median, and the 90th percentile of normalized electromyography (nEMG) activities from shoulder postures and net shoulder moments. Forty participants generated various 3-D shoulder moments at 96 static postures. The nEMG of 16 shoulder muscles was measured and the 3-D net shoulder moment was calculated using a static biomechanical model. A stepwise regression was used to derive the regression equations. The results indicated the measured range of the 3-D shoulder moment in this study was similar to those observed during work requiring light physical capacity. The r² of all the regression equations ranged between 0.228 and 0.818. For the median of the nEMG, the average r² among all 16 muscles was 0.645, and the five muscles with the greatest r² were the three deltoids, supraspinatus, and infraspinatus. The results can be used by practitioners to estimate the range of the shoulder muscle activities given a specific arm posture and net shoulder moment.     

A reduced muscle model and planar musculoskeletal model fit for the simulation of whole-body movements

Musculoskeletal models are made to reflect the capacities of the human body in general, and often a specific subject in particular. It remains challenging to both model the musculoskeletal system and then fit the modelled muscles to a specific human subject. We present a reduced muscle model, a planar musculoskeletal model, and a fitting method that can be used to find a feasible set of active and passive muscle parameters for a specific subject. At a minimum, the fitting method requires inverse dynamics data of the subject, a scalar estimate of the peak activation reached during the movement, and a plausible initial estimate for the strength and flexibility of that subject. While additional data can be used to result in a more accurate fit, this data is not required for the method solve for a feasible fit. The minimal input requirements of the proposed fitting method make it well suited for subjects who cannot undergo a maximum voluntary contraction trial, or for whom recording electromyographic data is not possible. To evaluate the model and fitting method we adjust the musculoskeletal model so that it can perform an experimentally recorded stoop-lift of a 15 kg box.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

A model for insect locomotion in the horizontal plane: Feedforward activation of fast muscles, stability, and robustness

We develop a neuromechanical model for running insects that includes a simplified hexapedal leg geometry with agonist-antagonist muscle pairs actuating each leg joint. Restricting to dynamics in the horizontal plane and neglecting leg masses, we reduce the model to three degrees of freedom describing translational and yawing motions of the body. Muscles are driven by stylized action potentials characteristic of fast motoneurons, and modeled using an activation function and nonlinear length and shortening velocity dependence. Parameter values are based on measurements from depressor muscles and observations of kinematics and dynamics of the cockroach Blaberus discoidalis; in particular, motoneuronal inputs and muscle force levels are chosen to approximately achieve joint torques that are consistent with measured ground reaction forces. We show that the model has stable double-tripod gaits over the animal's speed range, that its dynamics at preferred speeds matches those observed, and that it maintains stable gaits, with low frequency yaw deviations, when subject to random perturbations in foot touchdown and lift-off timing and action potential input timing. We explain this in terms of the low-dimensional dynamics.     

Alterations of musculoskeletal models for a more accurate estimation of lower limb joint contact forces during normal gait: A systematic review

Musculoskeletal modelling is a methodology used to investigate joint contact forces during a movement. High accuracy in the estimation of the hip or knee joint contact forces can be obtained with subject-specific models. However, construction of subject-specific models remains time consuming and expensive. The purpose of this systematic review of the literature was to identify what alterations can be made on generic (i.e. literature-based, without any subject-specific measurement other than body size and weight) musculoskeletal models to obtain a better estimation of the joint contact forces. The impact of these alterations on the accuracy of the estimated joint contact forces were appraised.The systematic search yielded to 141 articles and 24 papers were included in the review. Different strategies of alterations were found: skeletal and joint model (e.g. number of degrees of freedom, knee alignment), muscle model (e.g. Hill-type muscle parameters, level of muscular redundancy), and optimisation problem (e.g. objective function, design variables, constraints). All these alterations had an impact on joint contact force accuracy, so demonstrating the potential for improving the model predictions without necessarily involving costly and time consuming medical images. However, due to discrepancies in the reported evidence about this impact and despite a high quality of the reviewed studies, it was not possible to highlight any trend defining which alteration had the largest impact.     

A predictive model of moment-angle characteristics in human skeletal muscle: application and validation in muscles across the ankle joint

In the present work, a generic model for the prediction of moment-angle characteristics in individual human skeletal muscles is presented. The model's prediction is based on the equation M = V x Lo(-1)sigma c cos phi x d, where M, V, and Lo are the moment-generating potential of the muscle, the muscle volume and the optimal muscle fibre length, respectively, and sigma, phi and d are the stress-generating potential of the muscle fibres, their pennation angle and the tendon moment arm length, respectively, at any given joint angle. The input parameters V, Lo, sigma, phi and d can be measured or derived mechanistically. This eliminates the common problem of the necessity to estimate one or more of the input parameters in the model by fitting its outcome to experimental results often inappropriate for the function modelled. The model's output was validated by comparisons with the moment-angle characteristics of the gastrocnemius (GS) and tibialis anterior (TA) muscles in six men, determined experimentally using voluntary contractions at several combinations of ankle and knee joint angles for the GS muscle and electrical stimulation for the TA muscle. Although the model predicted realistically the pattern of moment-angle relationship in both muscles, it consistently overestimated the GS muscle M and consistently underestimated the TA muscle M, with the difference gradually increasing from dorsiflexion to plantarflexion in both cases. The average difference between predicted and measured M was 14% for the GS muscle and 10% for the TA muscle. Approximating the muscle fibres as a single sarcomere in both muscles and failing to achieve complete TA muscle activation by electrical stimulation may largely explain the differences between theory and experiment.     

A model of myogenesis in vivo,derived from detailed autoradiographic studies of regenerating skeletal muscle,challenges the concept of quantal mitosis

Summary We have recently shown that myogenesis following severe injury is prolonged compared with minor injury (McGeachie and Grounds 1987). In this previous autoradiographic study 44 mice were injected with tritiated thymidine at various times after muscle injury (0 to 120 h), and samples were taken 9d after injury to determine the percentage of labelled myotube nuclei. In the present study the same experimental data are analysed in detail to reveal how many times labelled muscle precursors divided before fusing to form myotubes.Additional mice were prepared and samples removed 1 h after injection of tritiated thymidine to determine the maximum grain counts of premitotic nuclei. When a labelled premitotic nucleus divides, each of the two daughter nuclei will contain half of the original label. The grain counts of nuclei resulting from sequential divisions of a maximally labelled premitotic nucleus, forms the basis for our detailed analysis which can reveal how many times a muscle precursor has divided after labelling.Nine days after injury the autoradiographic grain counts of labelled myotube nuclei were analysed in detail. The results describe an in vivo model of myogenesis which we use to evaluate quantitatively observations derived from tissue culture studies. The analysis shows that, at the onset of myogenesis in regenerating muscle (30 h after injury), muscle precursors divide only twice before fusing to form myotubes. This observation challenges the concept of quantal mitosis as defined by the tissue culture studies of Quinn et al. (1984, 1985).     

A parametric model of muscle moment arm as a function of joint angle: Application to the dorsiflexor muscle group in mice

A parametric model was developed to describe the relationship between muscle moment arm and joint angle. The model was applied to the dorsiflexor muscle group in mice, for which the moment arm was determined as a function of ankle angle. The moment arm was calculated from the torque measured about the ankle upon application of a known force along the line of action of the dorsiflexor muscle group. The dependence of the dorsiflexor moment arm on ankle angle was modeled as r=R sin(a+Δ), where r is the moment arm calculated from the measured torque and a is the joint angle. A least-squares curve fit yielded values for R, the maximum moment arm, and Δ, the angle at which the maximum moment arm occurs as offset from 90°. Parametric models were developed for two strains of mice, and no differences were found between the moment arms determined for each strain. Values for the maximum moment arm, R, for the two different strains were 0.99 and 1.14 mm, in agreement with the limited data available from the literature. While in some cases moment arm data may be better fitted by a polynomial, use of the parametric model provides a moment arm relationship with meaningful anatomical constants, allowing for the direct comparison of moment arm characteristics between different strains and species.     

A biomechanical model to simulate the effect of a high vertical loading on trunk flexural stiffness

A human trunk model was developed to simulate the effect of a high vertical loading on trunk flexural stiffness. A force–length relationship is attributed to each muscle of the multi-body model. Trunk stiffness and muscle forces were evaluated experimentally and numerically for various applied loads. Experimental evaluation of trunk stiffness was carried out by measuring changes in reaction force following a sudden horizontal displacement at the T10 level prior to paraspinal reflexes induction. Results showed that the trunk stiffness increases under small applied loads, peaks when the loads were further increased and decreases when higher loads are applied. A sensitivity analysis to muscle force–length relationship is provided to determine the model's limitations. This model pointed out the importance of taking into account the changes in muscle length to evaluate the effect of spinal loads beyond the safe limit that cannot be evaluated experimentally and to predict the trunk instability under vertical load.     

A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle

A conventional five-step chemo-mechanical cycle of the myosin–actin ATPase reaction, which implies myosin detachment from actin upon release of hydrolysis products (ADP and phosphate, Pi) and binding of a new ATP molecule, is able to fit the [Pi] dependence of the force and number of myosin motors during isometric contraction of skeletal muscle. However, this scheme is not able to explain why the isometric ATPase rate of fast skeletal muscle is decreased by an increase in [Pi] much less than the number of motors. The question can be solved assuming the presence of a branch in the cycle: in isometric contraction, when the force generation process by the myosin motor is biased at the start of the working stroke, the motor can detach at an early stage of the ATPase cycle, with Pi still bound to its catalytic site, and then rapidly release the hydrolysis products and bind another ATP. In this way, the model predicts that in fast skeletal muscle the energetic cost of isometric contraction increases with [Pi]. The large dissociation constant of the product release in the branched pathway allows the isometric myosin–actin reaction to fit the equilibrium constant of the ATPase.     

A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle

We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.     

Dissociation coefficients of protein adsorption to nanoparticles as quantitative metrics for description of the protein corona: A comparison of experimental techniques and methodological relevance

Protein adsorption to nanoparticles is described as a chemical reaction in which proteins attach to binding sites on the nanoparticle surface. This process is defined by a dissociation coefficient, which tells how many proteins are adsorbed per nanoparticle in dependence of the protein concentration. Different techniques to experimentally determine dissociation coefficients of protein adsorption to nanoparticles are reviewed. Results of more than 130 experiments in which dissociation coefficients have been determined are compared. Data show that different methods, nanoparticle systems, and proteins can lead to significantly different dissociation coefficients. However, we observed a clear tendency of smaller dissociation coefficients upon less negative towards more positive zeta potentials of the nanoparticles. The zeta potential thus is a key parameter influencing protein adsorption to the surface of nanoparticles. Our analysis highlights the importance of the characterization of the parameters governing protein–nanoparticle interaction for quantitative evaluation and objective literature comparison.     

A DIGE approach for the assessment of rat soleus muscle changes during unloading: effect of acetyl-L-carnitine supplementation

After hind limb suspension, a remodeling of postural muscle phenotype is observed. This remodeling results in a shift of muscle profile from slow-oxidative to fast-glycolytic. These metabolic changes and fiber type shift increase muscle fatigability. Acetyl-L-carnitine (ALCAR) influences the skeletal muscle phenotype of soleus muscle suggesting a positive role of dietary supplementation of ALCAR during unloading. In the present study, we applied a 2-D DIGE, mass spectrometry and biochemical assays, to assess qualitative and quantitative differences in the proteome of rat slow-twitch soleus muscle subjected to disuse. Meanwhile, the effects of ALCAR administration on muscle proteomic profile in both unloading and normal-loading conditions were evaluated. The results indicate a modulation of troponin I and tropomyosin complex to regulate fiber type transition. Associated, or induced, metabolic changes with an increment of glycolytic enzymes and a decreased capacity of fat oxidation are observed. These metabolic changes appear to be counteracted by ALCAR treatment, which restores the mitochondrial mass and decreases the glycolytic enzyme expression, suggesting a normalization of the metabolic shift observed in unloaded animals. This normalization is accompanied by a maintenance of body weight and seems to prevent a switch of fiber type.     

Glycogen phosphorylase from flight muscle of the hawk moth,Manduca sexta: purification and properties of three interconvertible forms and the effect of flight on their interconversion

Glycogen phosphorylase (EC 2.4.1.1) of Manduca sexta flight muscle was separated into three distinct peaks of activity on diethylaminoethyl-Sephacel. The three fractions of phosphorylase activity were further purified by affinity chromatography on AMP-Sepharose and shown to have the same relative molecular mass (=178000) on polyacrylamide gradient gel electrophoresis under non-denaturating conditions and to produce subunits of molecular mass =92000 on SDS gelelectrophoresis. On the basis of their kinetic properties with respect to the activator AMP and the inhibitor caffeine, the three fractions of phosphorylase activity were assigned as follows: peak 1=phosphorylase b (unphosphorylated form), peak 3=phosphorylase a (phosphorylated form); peak 2 represented a phospho-dephospho hybrid in which only one subunit of the dimeric enzyme was phosphorylated. This hypothesis was corroborated as the various forms could be interconverted in vitro by either dephosphorylation by an endogenous protein phosphatase producing the b form, or by phosphorylation catalyzed by purified phosphorylase kinase from rabbit muscle producing phosphorylase ab and a. From muscle of resting moths more phosphorylase was isolated in the b form (41%) than in the forms ab (28%) and a (31%), respectively. This proportion was changed in favour of the fully phosphorylated a form after a brief interval of flight when 68% of the phosphorylase activity was represented by the a form and only 13% by the b form. Unlike the phosphorylated forms a and ab of phosphorylase, the b form had low affinities for the substrates and for the activator AMP, and was virtually inactive if near-physiological concentrations of substrates and effectors were employed in the assays. The results demonstrate that in Manduca flight muscle three forms of phosphorylase coexist and that their interconversion is a mechanism for regulating phosphorylase activity in vivo.Abbreviations DEAE diethylaminoethyl - EDTA ethylenediamine tetraacetate - EGTA ethyleneglycol-bis(-aminoethylether)N,N-tetra-acetic acid - M _r relative molecular mass - NMR nuclear magnetic resonance - PAGGE polyacrylamide gradient gel electrophoresis - P_i morganic phosphate - SDS sodium dodecylsulphate - TRIS tris(hydroxymethyl)-aminomethane - V _max maximum activity     

A model for the generation of localized transient [Na] elevations in vascular smooth muscle

We present a stochastic computational model to study the mechanism of signaling between a source and a target ionic transporter, both localized on the plasma membrane (PM). In general this requires a nanometer-scale cytoplasmic space, or nanodomain, between the PM and a peripheral organelle to reflect ions back towards the PM. Specifically we investigate the coupling between Na⁺ entry via the transient receptor potential canonical channel 6 (TRPC6) and the Na⁺/Ca²⁺ exchanger (NCX), a process which is essential for reloading the sarcoplasmic reticulum (SR) via the sarco/endoplasmic reticulum Ca²⁺ATPase (SERCA) and maintaining Ca²⁺ oscillations in activated vascular smooth muscle. Having previously modeled the flow of Ca²⁺ between reverse NCX and SERCA during SR refilling, this quantitative approach now allows us to model the upstream linkage of Na⁺ entry through TRPC6 to reversal of NCX. We have implemented a random walk (RW) Monte Carlo (MC) model with simulations mimicking a diffusion process originating at the TRPC6 within PM-SR junctions. The model calculates the average Na⁺ in the nanospace and also produces profiles as a function of distance from the source. Our results highlight the necessity of a strategic juxtaposition of the relevant ion translocators as well as other physical structures within the nanospaces to permit adequate Na⁺ build-up to initiate NCX reversal and Ca²⁺ influx to refill the SR.     

A proposed model for dragline spider silk self‐assembly: Insights from the effect of the repetitive domain size on fiber properties

Dragline spider silk has been intensively studied for its superior qualities as a biomaterial. In previous studies, we made use of the baculovirus mediated expression system for the production of a recombinant Araneus diadematus spider silk dragline ADF4 protein and its self‐assembly into intricate fibers in host insect cells. In this study, our aim was to explore the function of the major repetitive domain of the dragline spider silk. Thus, we generated an array of synthetic proteins, each containing a different number of identical repeats up to the largest recombinantly expressed spider silk to date. Study of the self‐assembly properties of these proteins showed that depending on the increasing number of repeats they give rise to different assembly phenotypes, from a fully soluble protein to bona fide fibers with superior qualities. The different assembly forms, the corresponding chemical resistance properties obtained as well as ultrastructural studies, revealed novel insights concerning the structure and intermolecular interactions of the repetitive and nonrepetitive domains. Based on these observations and current knowledge in the field, we hereby present a comprehensive hypothetical model for the mechanism of dragline silk self‐assembly and fiber formation. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 458–468, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

A model for estimating abundance of cattle grub (Diptera: Oestridae) from the proportion of uninfested cattle as determined by serology*

A model is presented for determining the abundance of cattle grubs in the backs of calves from the proportion of uninfested calves in a herd. The distribution of grubs in calves' backs was compared with the negative binomial, but no relationships were found among the distribution parameters, suggesting that the negative binomial is an inappropriate choice for the basis of a sampling model. The relationship between the mean number of grubs per animal (mean), variance (delta 2), and proportion of uninfested calves (p0) in a herd was determined and used as the basis for the sampling model. The relationship between p0 and p0e [determined using serology (ELISA)] was evaluated. The variance of estimates of mean grubs per animal based on the regression model and uncertainty due to using p0e as an estimate of p0 was examined. A test of the model indicated that p0e could be used to obtain a reliable estimate of mean grubs per animal and that the method would be applicable for monitoring grub populations, assessing chemical control programmes, and determining release rates of sterile insects for control.     

CoMFA study of distamycin analogs binding to the minor-groove of DNA: a unified model for broad-spectrum activity

A 3D-QSAR analysis has been carried out by comparative molecular field analysis (CoMFA) on a series of distamycin analogs that bind to the DNA of drug-resistant bacterial strains MRSA, PRSP and VSEF. The structures of the molecules were derived from the X-ray structure of distamycin bound to DNA and were aligned using the Database alignment method in Sybyl. Statistically significant CoMFA models for each activity were generated. The CoMFA contours throw light on the structure activity relationship (SAR) and help to identify novel features that can be incorporated into the distamycin framework to improve the activity. Common contours have been gleaned from the three models to construct a unified model that explains the steric and electrostatic requirements for antimicrobial activity against the three resistant strains. Figure A unified CoMFA model for broad-spectrum DNA minor-groove binders     

A model for an early stage of tomato fruit development: cell multiplication and cessation of the cell proliferative activity

Changes in cell number during the early period of tomato fruit development were analysed by means of a deterministic model of cell multiplication. The period commenced at the seed stage with one theoretical cell undergoing intensive cell division, and ended when the cell number became nearly constant. The model takes into consideration the proliferative activity of the fruit cell population which, a few days before flower anthesis, begins to decrease progressively after each mitotic cycle. Model parameters, namely the time at which proliferative activity diminishes, its rate of decrease and the length of the cell cycle, were estimated by fitting the model to observed cell population dynamics in tomato fruits growing in three different positions on the truss. It is hypothesized that the molecular mechanism responsible for the cessation of mitosis in growing fruits is associated with shortening of telomeric ends of nuclear DNA, as suggested previously for other growing cell populations.