Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study.

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

High-density magnetomyography is superior to high-density surface electromyography for motor unit decomposition: a simulation study.

Objective.Studying motor units is essential for understanding motor control, the detection of neuromuscular disorders and the control of human-machine interfaces. Individual motor unit firings are currently identifiedin vivoby decomposing electromyographic (EMG) signals. Due to our body's properties and anatomy, individual motor units can only be separated to a limited extent with surface EMG. Unlike electrical signals, magnetic fields do not interact with human tissues. This physical property and the emerging technology of quantum sensors make magnetomyography (MMG) a highly promising methodology. However, the full potential of MMG to study neuromuscular physiology has not yet been explored.Approach.In this work, we performin silicotrials that combine a biophysical model of EMG and MMG with state-of-the-art algorithms for the decomposition of motor units. This allows the prediction of an upper-bound for the motor unit decomposition accuracy.Main results.It is shown that non-invasive high-density MMG data is superior over comparable high-density surface EMG data for the robust identification of the discharge patterns of individual motor units. Decomposing MMG instead of EMG increased the number of identifiable motor units by 76%. Notably, MMG exhibits a less pronounced bias to detect superficial motor units.Significance.The presented simulations provide insights into methods to study the neuromuscular system non-invasively andin vivothat would not be easily feasible by other means. Hence, this study provides guidance for the development of novel biomedical technologies.

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.

Investigating the spatial resolution of EMG and MMG based on a systemic multi-scale model.

While electromyography (EMG) and magnetomyography (MMG) are both methods to measure the electrical activity of skeletal muscles, no systematic comparison between both signals exists. Within this work, we propose a novel in silico model for EMG and MMG and test the hypothesis that MMG surpasses EMG in terms of spatial selectivity, i.e. the ability to distinguish spatially shifted sources. The results show that MMG provides a slightly better spatial selectivity than EMG when recorded directly on the muscle surface. However, there is a remarkable difference in spatial selectivity for non-invasive surface measurements. The spatial selectivity of the MMG components aligned with the muscle fibres and normal to the body surface outperforms the spatial selectivity of surface EMG. Particularly, for the MMG's normal-to-the-surface component the influence of subcutaneous fat is minimal. Further, for the first time, we analyse the contribution of different structural components, i.e. muscle fibres from different motor units and the extracellular space, to the measurable biomagnetic field. Notably, the simulations show that for the normal-to-the-surface MMG component, the contribution from volume currents in the extracellular space and in surrounding inactive tissues, is negligible. Further, our model predicts a surprisingly high contribution of the passive muscle fibres to the observable magnetic field.

Optimizing NV magnetometry for Magnetoneurography and Magnetomyography applications.

Magnetometers based on color centers in diamond are setting new frontiers for sensing capabilities due to their combined extraordinary performances in sensitivity, bandwidth, dynamic range, and spatial resolution, with stable operability in a wide range of conditions ranging from room to low temperatures. This has allowed for its wide range of applications, from biology and chemical studies to industrial applications. Among the many, sensing of bio-magnetic fields from muscular and neurophysiology has been one of the most attractive applications for NV magnetometry due to its compact and proximal sensing capability. Although SQUID magnetometers and optically pumped magnetometers (OPM) have made huge progress in Magnetomyography (MMG) and Magnetoneurography (MNG), exploring the same with NV magnetometry is scant at best. Given the room temperature operability and gradiometric applications of the NV magnetometer, it could be highly sensitive in the pT / Hz -range even without magnetic shielding, bringing it close to industrial applications. The presented work here elaborates on the performance metrics of these magnetometers to the state-of-the-art techniques by analyzing the sensitivity, dynamic range, and bandwidth, and discusses the potential benefits of using NV magnetometers for MMG and MNG applications.

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue.

The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.

Modelling the electrical activity of skeletal muscle tissue using a multi-domain approach.

Electromyography (EMG) can be used to study the behaviour of the motor neurons and thus provides insights into the physiology of the central nervous system. However, due to the high complexity of neuromuscular control, EMG signals are challenging to interpret. While the exact knowledge of the excitation patterns of a specific muscle within an in vivo experimental setting remains elusive, simulations allow to systematically investigate EMG signals in a controlled environment. Within this context, simulations can provide virtual EMG data, which, for example, can be used to validate and optimise signal analysis methods that aim to estimate the relationship between EMG signals and the output of motor neuron pools. However, since existing methods, which are employed to compute EMG signals, exhibit deficiencies with respect to the physical model itself as well as with respect to numerical aspects, we propose a novel homogenised continuum model that closely resolves the electro-physiological behaviour of skeletal muscle tissue. The proposed model is based on an extension of the well-established bidomain model and includes a biophysically detailed description of the electrical activity within the tissue, which is due to the depolarisation of the muscle fibre membranes. In contrast to all other published EMG models, which assume that the electrical potential field for each muscle fibre can be calculated independently, the proposed model assumes that the electrical potential in the muscle fibres is coupled to the electrical potential in the extracellular space. We show that the newly proposed model is able to simulate realistic EMG signals and demonstrate the potential to employ the predicted virtual EMG signal in order to evaluate the goodness of automated decomposition algorithms.

Characterization of Electromechanical Delay Based on a Biophysical Multi-Scale Skeletal Muscle Model.

Skeletal muscles can be voluntary controlled by the somatic nervous system yielding an active contractile stress response. Thereby, the active muscle stresses are transmitted to the skeleton by a cascade of connective tissue and thus enable motion. In the context of joint perturbations as well as the assessment of the complexity of neural control, the initial phase of the muscle-tendon system's stress response has a particular importance and is analyzed by means of electromechanical delay (EMD). EMD is defined as the time lag between the stimulation of a muscle and a measurable change in force output. While EMD is believed to depend on multiple structures / phenomena, it is hard to separate their contributions experimentally. We employ a physiologically detailed, three-dimensional, multi-scale model of an idealized muscle-tendon system to analyze the influence of (i) muscle and tendon length, (ii) the material behavior of skeletal muscle and tendon tissue, (iii) the chemo-electro-mechanical behavior of the muscle fibers and (iv) neural control on EMD. Comparisons with experimental data show that simulated EMD values are within the physiological range, i.e., between 6.1 and 68.6 ms, and that the model is able to reproduce the characteristic EMD-stretch curve, yielding the minimum EMD at optimal length. Simulating consecutive recruitment of motor units increases EMD by more than 20 ms, indicating that during voluntary contractions neural control is the dominant factor determining EMD. In contrast, the muscle fiber action potential conduction velocity is found to influence EMD even of a 27 cm long muscle by not more than 3.7 ms. We further demonstrate that in conditions where only little pre-stretch is applied to a muscle-tendon system, the mechanical behavior of both muscle and tendon tissue considerably impacts EMD. Predicting EMD for different muscle and tendon lengths indicates that the anatomy of a specific muscle-tendon system is optimized for its function, i.e., shorter tendon lengths are beneficial to minimize the neural control effort for muscles primary acting as motor in concentric contractions.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics.

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Enabling Detailed, Biophysics-Based Skeletal Muscle Models on HPC Systems.

Realistic simulations of detailed, biophysics-based, multi-scale models often require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are typically designed to allow for high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version toward a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment which is based on the MegaMol framework and is capable of handling large amounts of simulated data. We present the results of a number of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieve good scalability on up to 768 cores.

A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation.

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion.

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.

A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin-titin interaction.

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin-myosin interactions, force enhancement based on actin-titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin's free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle's cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle's cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.

Diffusion-weighted magnetic resonance enterocolonography in predicting remission after anti-TNF induction therapy in Crohn's disease.

BACKGROUND: Diffusion-weighted magnetic resonance entero-colonography (DW-MREC) with no rectal distension and with no bowel cleansing is accurate to assess inflammatory activity in ileocolonic Crohn's disease (CD). AIM: To study DW-MREC parameters as predictors of remission (CDAI < 150 and CRP < 5mg/L) after anti-TNF induction therapy. METHODS: Forty consecutive CD patients were prospectively and consecutively included. All the patients underwent DW-MREC with apparent diffusion coefficient (ADC) and MaRIA calculation before starting anti-TNF. Mean ADC was defined as the mean of the segmental ADC. RESULTS: Twenty patients (50.0%) experienced remission at W12. Low mean ADC (2.05 ± 0.22 vs 1.89 ± 0.25, p = 0.03) and high total MaRIA (39.2 ± 16.6 vs 51.7 ± 18.2, p = 0.03) were predictive of remission at W12. Using a ROC curve, we determined a mean ADC of 1.96 as predictive cut-off of remission at W12 (AUC = 0.703 [0.535-0.872]) with sensitivity, specificity, positive predictive value and negative predictive value of 70.0%, 65.0%, 66.7% and 68.4%, respectively. In multivariate analysis, mean ADC < 1.96 (OR = 4.87, 95% CI [1.04-22.64]) and total MaRIA > 42.5 (OR = 5.11, 95% CI [1.03-25.37]), reflecting high inflammatory activity, were predictive of remission at week 12. CONCLUSIONS: DW-MREC using quantitative parameters i.e. ADC, is useful in detecting and assessing inflammatory activity but also to predict efficacy of anti-TNF induction therapy in CD.