Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

The reaction-diffusion system of the neuromuscular junction has been modeled in 3D using the finite element package FEtk. The numerical solution of the dynamics of acetylcholine with the detailed reaction processes of acetylcholinesterases and nicotinic acetylcholine receptors has been discussed with the reaction-determined boundary conditions. The simulation results describe the detailed acetylcholine hydrolysis process, and reveal the time-dependent interconversion of the closed and open states of the acetylcholine receptors as well as the percentages of unliganded/monoliganded/diliganded states during the neuro-transmission. The finite element method has demonstrated its flexibility and robustness in modeling large biological systems.     

Inners and biocontrol models

Techniques of modelling and simulation are discussed as they relate to bioengineering systems. The advantages and disadvantages of different analytical engineering methods utilized to gather information concerning the behavior of complex physiological and neuromuscular control mechanisms are explained. An Inners Criterion is developed to determine if the roots of a model lie within a certain “biologically realistic region” Γ_B, in the complex plane which contains the roots of linearized models for a large variety of neuromuscular systems. Several algorithmic methods based on the Jury Inners Test are described which specify whether the model roots lie within the desired region, thereby providing an indication as to the validity of the proposed model. This technique can help to eliminate tedious simulation on an unrealistic model with roots lying far outside this region. An exemplary model for control of vergence eye movements is presented and shown to satisfy the Γ_B criterion; several counter-examples are also discussed. The Inners approach can be adapted to other classes of bioengineering systems by specifying the region based on models that are contained in the class of interest.     

Analysis of Zebrafish Larvae Skeletal Muscle Integrity with Evans Blue Dye

The zebrafish model is an emerging system for the study of neuromuscular disorders. In the study of neuromuscular diseases, the integrity of the muscle membrane is a critical disease determinant. To date, numerous neuromuscular conditions display degenerating muscle fibers with abnormal membrane integrity; this is most commonly observed in muscular dystrophies. Evans Blue Dye (EBD) is a vital, cell permeable dye that is rapidly taken into degenerating, damaged, or apoptotic cells; in contrast, it is not taken up by cells with an intact membrane. EBD injection is commonly employed to ascertain muscle integrity in mouse models of neuromuscular diseases. However, such EBD experiments require muscle dissection and/or sectioning prior to analysis. In contrast, EBD uptake in zebrafish is visualized in live, intact preparations. Here, we demonstrate a simple and straightforward methodology for performing EBD injections and analysis in live zebrafish. In addition, we demonstrate a co-injection strategy to increase efficacy of EBD analysis. Overall, this video article provides an outline to perform EBD injection and characterization in zebrafish models of neuromuscular disease.     

A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45–7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.     

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.     

The role of apoptosis in neuromuscular diseases and prospects for anti-apoptosis therapy

Although genetic mutations that are responsible for most of the inherited neuromuscular diseases have been identified, the molecular and cellular mechanisms that cause muscle and nerve depletion are not well understood and therapies are lacking. Histological studies of many neuromuscular diseases indicated that loss of motor-nerve and/or skeletal-muscle function might be due to excessive cell death by apoptosis. Recent studies have confirmed this possibility by showing that pathology in mouse models of amyotrophic lateral sclerosis, congenital muscular dystrophy, oculopharyngeal muscular dystrophy and collagen-VI deficiency, but not Duchenne muscular dystrophy, is significantly ameliorated by genetic or pharmacological interventions that have been designed to inhibit apoptosis. Thus, apoptosis greatly contributes to pathology in mouse models of several neuromuscular diseases, and appropriate anti-apoptosis therapy might therefore be beneficial for the corresponding human diseases.     

Statistical multi‐path exposure method for assessing the whole‐body SAR in a heterogeneous human body model in a realistic environment

Assessing the whole‐body absorption in a human in a realistic environment requires a statistical approach covering all possible exposure situations. This article describes the development of a statistical multi‐path exposure method for heterogeneous realistic human body models. The method is applied for the 6‐year‐old Virtual Family boy (VFB) exposed to the GSM downlink at 950 MHz. It is shown that the whole‐body SAR does not differ significantly over the different environments at an operating frequency of 950 MHz. Furthermore, the whole‐body SAR in the VFB for multi‐path exposure exceeds the whole‐body SAR for worst‐case single‐incident plane wave exposure by 3.6%. Moreover, the ICNIRP reference levels are not conservative with the basic restrictions in 0.3% of the exposure samples for the VFB at the GSM downlink of 950 MHz. The homogeneous spheroid with the dielectric properties of the head suggested by the IEC underestimates the absorption compared to realistic human body models. Moreover, the variation in the whole‐body SAR for realistic human body models is larger than for homogeneous spheroid models. This is mainly due to the heterogeneity of the tissues and the irregular shape of the realistic human body model compared to homogeneous spheroid human body models. Bioelectromagnetics 34:240–251, 2013. © 2012 Wiley Periodicals, Inc.     

Computation of hemodynamics in the left coronary artery with variable angulations

The purpose of this study was to investigate the hemodynamic effect of variations in the angulations of the left coronary artery, based on simulated and realistic coronary artery models. Twelve models consisting of four realistic and eight simulated coronary artery geometries were generated with the inclusion of left main stem, left anterior descending and left circumflex branches. The simulated models included various coronary artery angulations, namely, 15°, 30°, 45°, 60°, 75°, 90°, 105° and 120°. The realistic coronary angulations were based on selected patient's data with angles ranging from narrow angles of 58° and 73° to wide angles of 110° and 120°. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics. The wall shear stress, wall shear stress gradient, velocity flow patterns and wall pressure were measured in simulated and realistic models during the cardiac cycle. Our results showed that a disturbed flow pattern was observed in models with wider angulations, and wall pressure was found to reduce when the flow changed from the left main stem to the bifurcated regions, based on simulated and realistic models. A low wall shear stress gradient was demonstrated at left bifurcations with wide angles. There is a direct correlation between coronary angulations and subsequent hemodynamic changes, based on realistic and simulated models. Further studies based on patients with different severities of coronary artery disease are required to verify our results.     

An integrative approach to the biomechanical function and neuromuscular control of the fingers

The exquisite mechanical functionality and versatility of the human hand emerges from complex neuro-musculo-skeletal interactions that are not completely understood. I have found it useful to work within a theoretical/experimental paradigm that outlines the fundamental neuro-musculo-skeletal components and their interactions. In this integrative paradigm, the laws of mechanics, the specifications of the manipulation task, and the sensorimotor signals define the interactions among hand anatomy, the nervous system, and manipulation function. Thus, our collaborative research activities emphasize a firm grounding in the mechanics of finger function, insistence on anatomical detail, and meticulous characterization of muscle activity. This overview of our work on precision pinch (i.e., the ability to produce and control fingertip forces) presents some of our findings around three Research Themes: Mechanics-based quantification of manipulation ability; Anatomically realistic musculoskeletal finger models; and Neural control of finger muscles. I conclude that (i) driving the fingers to some limit of sensorimotor performance is instrumental to elucidating motor control strategies; (ii) that the cross-over of tendons from flexors to extensors in the extensor mechanism is needed to produce force in every direction, and (iii) the anatomical routing of multiarticular muscles makes co-contraction unavoidable for many tasks. Moreover, creating realistic and clinically useful finger models still requires developing new computational means to simulate the viscoelastic tendinous networks of the extensor mechanism, and the muscle-bone-ligament interactions in complex articulations. Building upon this neuromuscular biomechanics paradigm is of immense clinical relevance: it will be instrumental to the development of clinical treatments to preserve and restore manual ability in people suffering from neurological and orthopedic conditions. This understanding will also advance the design and control of robotic hands whose performance lags far behind that of their biological counterparts.     

Synthesis and neuromuscular blocking activity of 16-(2- and 3-pyridylmethylene) dehydroepiandrosterone derivatives

The interonium distance plays a major role in neuromuscular blocking activity of bis-quaternary ammonium compounds. In this study we tried to alter the distance between two quaternary nitrogens in some of the steroidal derivatives synthesized and evaluated them for neuromuscular blocking activity using in vivo (in chicks) and in vitro models (rectus abdominus and chick biventer cervis muscle) for their mechanism of action. All the synthesized compounds have shown to possess good depolarizing, competitive neuromuscular blocking activity, particularly the 17-acetoxy derivative and the increase in the distance between two quaternary nitrogens decreased the activity.     

Segmental motion of forefoot and hindfoot as a diagnostic tool

Segmental motions derived from non-invasive motion analysis are being used to investigate the intrinsic functional behavior of the foot and ankle in health and disease. The goal of this research was to examine the ability of a generic segmented model of the foot to capture and differentiate changes in internal skeletal kinematics due to neuromuscular disease and/or trauma. A robotic apparatus that reproduces the kinematics and kinetics of gait in cadaver lower extremities was employed to produce motion under normal and aberrant neuromuscular activation patterns of tibialis posterior and/or tibialis anterior. Stance phase simulations were conducted on 10 donor limbs while recording three-dimensional kinematic trajectories of (1) skin-mounted markers used clinically to construct segmented foot models, and (2) bone-mounted marker clusters to capture actual internal bone motion as the gold standard for comparison. The models constructed from external marker data were able to differentiate the kinematic behaviors elicited by different neuromuscular conditions in a manner similar to that using the bone-derived data. Measurable differences between internal and externally measured kinematics were small, variable and random across the three axes of rotation and neuromuscular conditions, with a tendency toward more differences noted during early and late stance. Albeit slightly different, three-dimensional motion profiles of the hindfoot and forefoot segments correlated well with internal skeletal motion under all neuromuscular conditions, thereby confirming the utility of measuring segmental motions as a valid means of clinical assessment.     

Overview of mathematical computer models of striated sphincter muscles

The present paper compares current mathematical striated sphincter models. Current models are subdivided in four categories: (1) simple models, (2) implementations of the urethral resistance relation, (3) models with realistic muscle dynamics and (4) finite element models. In our research group a neural network model, representing Onuf's nucleus, the spinal motor nucleus that innervates the external urethral and anal sphincters, was developed. A realistic sphincter model is needed to test the neural network. To decide whether or not a model is applicable in our research two requirements should be fulfilled: (1) the presence of realistic muscle dynamics preferably by implementation of a Huxley type muscle model and (2) the model should consist of more than one muscle unit to form a more dimensional model. Reviewing the literature, if a myogenic sphincter is modelled, mainly the Hill-equation is applied. Moreover, single muscle unit models are published. In general a multi-unit muscle model of the sphincter is lacking, prohibiting the study of the inherent properties of sphincter muscles, which could give information on the realistic behaviour of elements in circular muscles. It is concluded that the functionality of current sphincter models is limited for our purpose.     

Optimal fishery policy: An equilibrium solution with irreversible investment

Optimal fishery policy has been derived using several different models of varying biological realism. Policy has either been assumed to be non-time-varying and static optimization techniques have been applied or dynamic techniques have been used and have in some cases resulted in constant policy. Botsford (1981) showed by applying dynamic optimization techniques to several biologically realistic models (i.e. models that included size structure and either density or food dependent growth and recruitment rates) that the constant policy solution found for simpler, less realistic models was not possible. He concluded that optimal policy was a time-varying, possibly pulse-fishing policy. We show here that when the maximum allowed fishing mortality is low enough a different kind of constant policy is optimal for these realistic models. Interpretation of this condition requires explicit consideration of fixed capital costs in addition to operating costs. Practical considerations indicate that this constant policy would apply only to fisheries with high fixed capital costs.     

The Classical Assortative Mating Process when more than one Continuous Characteristic is Considered

In this article we give a general proof for the existence of the equilibrium position for the joint phenotypic distribution of several continuous characteristics, in a population which reproduces assortatively, and wherein generations are overlapping. This model is a more realistic one for human populations, compared with models arising from consideration of a single characteristic. By placing realistic conditions on the assortation process in the equilibrium position it is found that the consequences are even less realistic and less satisfactory compared with conclusions from single (continuous) characteristic models involving assortative mating. This suggests that a different approach to modelling the assortation process may be required, and this is discussed alsewhere (WILSON, 1981).     

Cascading extinctions and community collapse in model food webs

Species loss in ecosystems can lead to secondary extinctions as a result of consumer–resource relationships and other species interactions. We compare levels of secondary extinctions in communities generated by four structural food-web models and a fifth null model in response to sequential primary species removals. We focus on various aspects of food-web structural integrity including robustness, community collapse and threshold periods, and how these features relate to assumptions underlying different models, different species loss sequences and simple measures of diversity and complexity. Hierarchical feeding, a fundamental characteristic of food-web structure, appears to impose a cost in terms of robustness and other aspects of structural integrity. However, exponential-type link distributions, also characteristic of more realistic models, generally confer greater structural robustness than the less skewed link distributions of less realistic models. In most cases for the more realistic models, increased robustness and decreased levels of web collapse are associated with increased diversity, measured as species richness S, and increased complexity, measured as connectance C. These and other results, including a surprising sensitivity of more realistic model food webs to loss of species with few links to other species, are compared with prior work based on empirical food-web data.     

Calculating spatial statistics for velocity jump processes with experimentally observed reorientation parameters

Mathematical modelling of the directed movement of animals, microorganisms and cells is of great relevance in the fields of biology and medicine. Simple diffusive models of movement assume a random walk in the position, while more realistic models include the direction of movement by assuming a random walk in the velocity. These velocity jump processes, although more realistic, are much harder to analyse and an equation that describes the underlying spatial distribution only exists in one dimension. In this communication we set up a realistic reorientation model in two dimensions, where the mean turning angle is dependent on the previous direction of movement and bias is implicitly introduced in the probability distribution for the direction of movement. This model, and the associated reorientation parameters, is based on data from experiments on swimming microorganisms. Assuming a transport equation to describe the motion of a population of random walkers using a velocity jump process, together with this realistic reorientation model, we use a moment closure method to derive and solve a system of equations for the spatial statistics. These asymptotic equations are a very good match to simulated random walks for realistic parameter values.     

Predator model recognition and response habituation in shoaling minnows

Minnows in shoals used a spectrum of behaviours to discriminate stalking models of pike. Predator recognition was initially based on model shape and size, with identification being confirmed using information on markings gathered by minnows during predator inspection visits. Minnow behaviour indicated that shoals regarded the most realistic model as the greates threat. Conversely, habituation of the anti-predator response in repeated stalks was most evident with the least realistic model. Implications for the design of models used in predation experiments are discussed.     

A Distinct Perisynaptic Glial Cell Type Forms Tripartite Neuromuscular Synapses in the Drosophila Adult

Previous studies of Drosophila flight muscle neuromuscular synapses have revealed their tripartite architecture and established an attractive experimental model for genetic analysis of glial function in synaptic transmission. Here we extend these findings by defining a new Drosophila glial cell type, designated peripheral perisynaptic glia (PPG), which resides in the periphery and interacts specifically with fine motor axon branches forming neuromuscular synapses. Identification and specific labeling of PPG was achieved through cell type-specific RNAi-mediated knockdown (KD) of a glial marker, Glutamine Synthetase 2 (GS2). In addition, comparison among different Drosophila neuromuscular synapse models from adult and larval developmental stages indicated the presence of tripartite synapses on several different muscle types in the adult. In contrast, PPG appear to be absent from larval body wall neuromuscular synapses, which do not exhibit a tripartite architecture but rather are imbedded in the muscle plasma membrane. Evolutionary conservation of tripartite synapse architecture and peripheral perisynaptic glia in vertebrates and Drosophila suggests ancient and conserved roles for glia-synapse interactions in synaptic transmission.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.