A comparison of static and dynamic optimization muscle force predictions during wheelchair propulsion

The primary purpose of this study was to compare static and dynamic optimization muscle force and work predictions during the push phase of wheelchair propulsion. A secondary purpose was to compare the differences in predicted shoulder and elbow kinetics and kinematics and handrim forces. The forward dynamics simulation minimized differences between simulated and experimental data (obtained from 10 manual wheelchair users) and muscle co-contraction. For direct comparison between models, the shoulder and elbow muscle moment arms and net joint moments from the dynamic optimization were used as inputs into the static optimization routine. RMS errors between model predictions were calculated to quantify model agreement. There was a wide range of individual muscle force agreement that spanned from poor (26.4% F_max error in the middle deltoid) to good (6.4% F_max error in the anterior deltoid) in the prime movers of the shoulder. The predicted muscle forces from the static optimization were sufficient to create the appropriate motion and joint moments at the shoulder for the push phase of wheelchair propulsion, but showed deviations in the elbow moment, pronation–supination motion and hand rim forces. These results suggest the static approach does not produce results similar enough to be a replacement for forward dynamics simulations, and care should be taken in choosing the appropriate method for a specific task and set of constraints. Dynamic optimization modeling approaches may be required for motions that are greatly influenced by muscle activation dynamics or that require significant co-contraction.     

Prediction of applied forces in handrim wheelchair propulsion

Researchers of wheelchair propulsion have usually suggested that a wheelchair can be properly designed using anthropometrics to reduce high mechanical load and thus reduce pain and damage to joints. A model based on physiological features and biomechanical principles can be used to determine anthropometric relationships for wheelchair fitting. To improve the understanding of man-machine interaction and the mechanism through which propulsion performance been enhanced, this study develops and validates an energy model for wheelchair propulsion. Kinematic data obtained from ten able-bodied and ten wheelchair-dependent users during level propulsion at an average velocity of 1m/s were used as the input of a planar model with the criteria of increasing efficiency and reducing joint load. Results demonstrate that for both experienced and inexperienced users, predicted handrim contact forces agree with experimental data through an extensive range of the push. Significant deviations that were mostly observed in the early stage of the push phase might result from the lack of consideration of muscle dynamics and wrist joint biomechanics. The proposed model effectively verified the handrim contact force patterns during dynamic propulsion. Users do not aim to generate mechanically most effective forces to avoid high loadings on the joints.     

A new dynamic model of the wheelchair propulsion on straight and curvilinear level-ground paths

Independent-roller ergometers (IREs) are commonly used to simulate the behaviour of a wheelchair propelled in a straight line. They cannot, however, simulate curvilinear propulsion. To this effect, a motorised wheelchair ergometer could be used, provided that a dynamic model of the wheelchair–user system propelled on straight and curvilinear paths (WSC) is available. In this article, we present such a WSC model, its parameter identification procedure and its prediction error. Ten healthy subjects propelled an instrumented wheelchair through a controlled path. Both IRE and WSC models estimated the rear wheels' velocities based on the users' propulsive moments. On curvilinear paths, the outward wheel shows root mean square (RMS) errors of 13% in an IRE vs 8% in a WSC. The inward wheel shows RMS errors of 21% in an IRE vs 11% in a WSC. Differences between both models are highly significant (p < 0.001). A wheelchair ergometer based on this new WSC model will be more accurate than a roller ergometer when simulating wheelchair propulsion in tight environments, where many turns are necessary.     

Nonlinear numerical analysis of the structural response of the intervertebral disc to impact loading

The analysis of intervertebral disc dynamics under impact loading, using computational simulation, is scarcely reported. In this study, the contribution of the characteristic structure of the disc to its dynamic response has been evaluated. The influence of several model features on the dynamic response was investigated. A hyperelastic large deformation formulation was used to describe the nonlinear behaviour of the soft tissues. The material parameters were determined by the fitting of experimental data from the literature. The model demonstrated pressure wave propagation and reflection through the disc, with a periodic oscillation of the system in response to a single impulse load, and highlighted a potential primary role played by the collagen fibre reinforcement. Their tensioning contributes to changing the stress propagation and oscillation, with a faster reduction in the internal pressure peak. The natural frequency of the disc was predicted to be approximately 9.8 Hz for the vertical oscillation.     

A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts

In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibroblasts. Beyond the simulation (from a quantitative, parametrized model) of the experimentally observed oscillatory cell deformations, a final goal of this work is to underline that a set of common assumptions regarding intracellular actin dynamics and associated cell membrane local motion allows us to describe a wide variety of cell morphologies and protrusive activity. The model proposed describes cell membrane deformations as a consequence of the endogenous cortical actin dynamics where the driving force for large-amplitude cell protrusion is provided by the coupling between F-actin polymerization and contractility of the cortical actomyosin network. Cell membrane movements then result of two competing forces acting on the membrane, namely an intracellular hydrostatic protrusive force counterbalanced by a retraction force exerted by the actin filaments of the cell cortex. Protrusion and retraction forces are moreover modulated by an additional membrane curvature stress. As a first approximation, we start by considering a heterogeneous but stationary distribution of actin along the cell periphery in order to evaluate the possible morphologies that an individual cell might adopt. Then non-stationary actin distributions are considered. The simulated dynamic behaviour of this cytomechanical model not only reproduces the small amplitude rotating waves of deformations of round-shaped cells such as keratinocytes [as proposed in the original model of Alt and Tranquillo (1995, J. Biol. Syst. 3, 905–916)] but is furthermore in very good agreement with the protrusive activity of cells such as fibroblasts, where large amplitude contracting/retracting pseudopods are more or less periodically extended in opposite directions. In addition, the biophysical and biochemical processes taken into account by the cytomechanical model are characterized by well-defined parameters which (for the majority) can be discussed with regard to experimental data obtained in various experimental situations.     

Structural identifiability of systems biology models: a critical comparison of methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided.     

An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Numerical optimization is the key to estimate the values of kinetic parameters so that the dynamic model reproduces the behaviors of the existing experimental data. It is required to develop general strategies for the optimization of complex biochemical networks with a huge space of search parameters, under the condition that kinetic and quantitative data are hardly available. We propose an integrative and practical strategy for optimizing a complex dynamic model by using qualitative and incomplete experimental data. The key technologies are the divide and conquer method for reducing the search space, handling of multiple objective functions representing different types of biological behaviors, and design of rule-based objective functions that are suitable for qualitative and error-prone experimental data. This strategy is applied to optimizing a dynamic model of the yeast cell cycle to demonstrate the feasibility of it.     

The push force pattern in manual wheelchair propulsion as a balance between cost and effect

We investigate the hypothesis that the direction of the propulsion force in manual wheelchair propulsion can be interpreted as a result of the balance between the mechanical task requirements and the driver's biomechanical possibilities. We quantify the balance at the joint level in the form of an effect-cost criterion, from which we predict the force direction that results in an optimal compromise. Kinematic and dynamic data were collected from nine habitual wheelchair users driving at four velocities (0.83, 1.11, 1.39, 1.67 m/s) and three external power levels (10, 20, 30 W). Experimental data and predictions are in good agreement in the middle and final part of the push; the effect-cost value in this region approximates the achievable maximum. Early in the push the effect-cost criterion predicts an upwards propulsion force whereas the experimental force is downwards, the difference probably being mainly attributable to the force generation dynamics of the muscles. As a result of the geometric features of large-rim manual wheelchairs, the mechanically required and biomechanically preferred force directions are not in accordance during a substantial part of the push, making even the best compromise a poor one. This may contribute to the low mechanical efficiency of manual wheelchair propulsion and the high incidence of shoulder complaints.     

A coarse-grained model for PCL: conformation,self-assembly of MePEG-b-PCL amphiphilic diblock copolymers

Poly-ε-caprolactone (PCL) is a biodegradable hydrophobic polyester that has been widely used in medical devices, tissue engineering and nanoparticle-based drug delivery. Coarse-grained molecular dynamics (CGMD) has been employed to study and gain insights into the conformational, structural and self-assembly behaviour of polymers, lipids and amphiphilic macromolecules. In this work, we developed a model for PCL within the framework of the MARTINI coarse-grained force field. The non-bonded interactions were based on the existing MARTINI bead types, while the bonded interactions were mapped onto a PCL rendition obtained from atomistic simulations. The model accurately reproduces the structural and dynamic properties of the PCL homopolymer and shows very reasonable temperature and solvent transferability. We also studied self-assembly of MePEG-b-PCL linear diblock copolymers using an existing MARTINI model for MePEG (Methoxy Polyethylene glycol), by analysing the critical micelle concentration (CMC), as well as the shape, size and morphology of the nano-polymeric micelles. We obtained excellent agreement of the CMC, while the size was under-predicted compared to experimental data. This robust model paves the way for CGMD modelling of PCL and serves as a starting point for future designs of PCL-related polymeric systems .     

Two dynamic processes for the induction of long-term potentiation in hippocampal CA1 neurons

This work sets out to investigate fast and slow dynamic processes and how they effect the induction of long-term potentiation (LTP). Functionally, the fast process will work as a time window to take a spatial coincidence among various inputs projected to the hippocampus, and the slow process will work as a temporal integrator of a sequence of dynamic events. Firstly, the two factors were studied using a “burst” stimulus and a “long-interval patterns” stimulus. Secondly, we propose that, for the induction of LTP, there are two dynamic processes, fast and slow, which are productively activated by bursts and long-interval patterns. The model parameters, a time constant of short dynamics and one of long dynamics, were determined by fitting the values obtained from model simulation to the experimental data. A molecular factor or cellular factors with these two time constants are likely to be induced in LTP induction. Received: 3 November 1997 / Accepted in revised form: 18 August 1999     

Generalized Linear Dynamics of a Plant-Parasitic Nematode Population and the Economic Evaluation of Crop Rotations

In 1-year experiments, the final population density of nematodes is usually modeled as a function of initial density. Often, estimation of the parameters is precarious because nematode measurements, although laborious and expensive, are imprecise and the range in initial densities may be small. The estimation procedure can be improved by using orthogonal regression with a parameter for initial density on each experimental unit. In multi-year experiments parameters of a dynamic model can be estimated with optimization techniques like simulated annealing or Bayesian methods such as Markov chain Monte Carlo (MCMC). With these algorithms information from different experiments can be combined. In multi-year dynamic models, the stability of the steady states is an important issue. With chaotic dynamics, prediction of densities and associated economic loss will be possible only on a short timescale. In this study, a generic model was developed that describes population dynamics in crop rotations. Mathematical analysis showed stable steady states do exist for this dynamic model. Using the Metropolis algorithm, the model was fitted to data from a multi-year experiment on Pratylenchus penetrans dynamics with treatments that varied between years. For three crops, parameters for a yield loss assessment model were available and gross margin of the six possible rotations comprising these three crops and a fallow year were compared at the steady state of nematode density. Sensitivity of mean gross margin to changes in the parameter estimates was investigated. We discuss the general applicability of the dynamic rotation model and the opportunities arising from combination of the model with Bayesian calibration techniques for more efficient utilization and collection of data relevant for economic evaluation of crop rotations.     

Shoulder model validation and joint contact forces during wheelchair activities

Chronic shoulder impingement is a common problem for manual wheelchair users. The loading associated with performing manual wheelchair activities of daily living is substantial and often at a high frequency. Musculoskeletal modeling and optimization techniques can be used to estimate the joint contact forces occurring at the shoulder to assess the soft tissue loading during an activity and to possibly identify activities and strategies that place manual wheelchair users at risk for shoulder injuries. The purpose of this study was to validate an upper extremity musculoskeletal model and apply the model to wheelchair activities for analysis of the estimated joint contact forces. Upper extremity kinematics and handrim wheelchair kinetics were measured over three conditions: level propulsion, ramp propulsion, and a weight relief lift. The experimental data were used as input to a subject-specific musculoskeletal model utilizing optimization to predict joint contact forces of the shoulder during all conditions. The model was validated using a mean absolute error calculation. Model results confirmed that ramp propulsion and weight relief lifts place the shoulder under significantly higher joint contact loading than level propulsion. In addition, they exhibit large superior contact forces that could contribute to impingement. This study highlights the potential impingement risk associated with both the ramp and weight relief lift activities. Level propulsion was shown to have a low relative risk of causing injury, but with consideration of the frequency with which propulsion is performed, this observation is not conclusive.     

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.     

Possible effects of the influence of dynamic disorder of biological systems on characteristics of intramolecular mobility, determined by Mossbauer spectroscopy]

A model for describing dynamic properties of proteins is proposed. The model involves the distribution over amplitudes and correlation times of intramolecular dynamics. It has been shown that distribution parameters and its temperature dependence have a great influence upon the values of experimental dynamic characteristics. Besides the discrepancy between the real and experimental temperature, dependence of characteristics on intramolecular dynamics can be observed.     

Flow of a blood analogue fluid in a compliant abdominal aortic aneurysm model: Experimental modelling

The aim of this work is to develop a unique in vitro set-up in order to analyse the influence of the shear thinning fluid-properties on the flow dynamics within the bulge of an abdominal aortic aneurysm (AAA). From an experimental point of view, the goals are to elaborate an analogue shear thinning fluid mimicking the macroscopic blood behaviour, to characterise its rheology at low shear rates and to propose an experimental device able to manage such an analogue fluid without altering its feature while reproducing physiological flow rate and pressure, through compliant AAA. Once these experimental prerequisites achieved, the results obtained in the present work show that the flow dynamics is highly dependent on the fluid rheology. The main results point out that the propagation of the vortex ring, generated in the AAA bulge, is slower for shear thinning fluids inducing a smaller travelled distance by the vortex ring so that it never impacts the anterior wall in the distal region, in opposition to Newtonian fluids. Moreover, scalar shear rate values are globally lower for shear thinning fluids inducing higher maximum stress values than those for the Newtonian fluids. Consequently, this work highlights that a Newtonian fluid model is finally inadequate to obtain a reliable prediction of the flow dynamics within AAA.     

Modeling peptide formation during the hydrolysis of β-casein by Lactococcus lactis

Hydrolysis of milk proteins by lactic acid bacteria leads to the formation of a large number of peptides. In this work, the hydrolysis of β-casein by the protease PrtP_I of Lactococcus lactis was studied. Experiments were carried out at different initial enzyme/substrate ratios. Identification and quantification of peptides were performed by MS and RP-UHPLC analyses. Nine low molecular weight (LMW) peptides were quantified absolutely. Additionally, semi-quantification of six high molecular weight peptides (HMW) was provided. To describe the dynamics of peptides concentrations, an aggregated model was developed. This model links peptide formation to the breakdown of intact protein by introducing the concept of virtual intermediate peptides (VIP). The model represented the experimental data with an average error of 14% (comparable with the experimental error). By using the model, three dynamic pools of peptides were identified. The model suggests that LMW peptides have similar dynamic characteristics as their counterpart HMW peptides in the β-casein sequence. This study indicates that the presence and structure of micelles affect the hydrolysis dynamics and that, for some peptides, the enzyme/substrate ratio appears to affect the hydrolysis stoichiometry. The model developed is parsimonious and has a basic mechanistic component. It allows for a rational study of protein hydrolysis.     

Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage

Abstract

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.