The fundamental problem of myoskeletal inverse dynamics and its implications.

The validity of current inverse dynamics models utilized for motion analysis is investigated. It is shown that observables generated by the real biosystem, such as ground reaction forces, are incompatible with comparable responses of skeletodynamical inverse models currently in use. This implies that results obtained with such models are erroneous to varying degrees while a quantification of these errors is difficult or impossible. This phenomenon is termed the fundamental myoskeletal inverse dynamics problem. A model fidelity indicator is proposed which, for a specific inverse dynamics model applied to a particular motion, provides a dimensionless numerical measure for the replicative validity of that model and the fidelity of its input data. A practical example demonstrates the usefulness of this indicator. It is suggested that the development of structurally sufficiently complex and biologically more realistic skeletomechanical models as well as substantial error reductions in data measuring and processing procedures will be necessary to improve the accuracy of inverse dynamics model computations.     

The escape of Tritonia: dynamics of a neuromuscular control mechanism.

The results of photosynthesis experiments with ¹⁸O labelled water and carbon dioxide are commonly regarded as the strongest arguments for a light-induced water oxidation. In these experiments, however, several sources of error have not been adequately considered. The peculiarities of natural H₂OCO₂ mixtures and their enzymatically enhanced equilibration are discussed. The unequal distribution of the oxygen isotopes is considered. Relevant data are presented on the CO₂ storage in green plant cells and the oxygen burst which is often observed during the beginning of the light period. After the statement of the necessary precautions for isotope experiments data of former measurements of the oxygen isotope discrimination by photosynthetic and respiratory processes are discussed. The data laid down in the literature together with the results of some experiments with deuterated water are taken as disproof of the hypothesis of water oxidation.     

Computation of inverse dynamics for the control of movements

 Accuracy of movements requires that the central nervous system computes approximate inverse functions of the mechanical functions of limb articulations. In vertebrates, this is known to be achieved within the cerebellar pathways, and also in the cerebral cortex of primates. A cybernetic circuit achieving this computation allows accurate simulation of fast movements of the eye or forearm. It is consistent with anatomy, and with the classical view of the cerebellum as permanently supervised by the inferior olive. The inferior olive detects over- or under-shoots of movements, and the resulting climbing fiber activity corrects ongoing movements, regulates the function of cerebellar cortex and nuclei, and sets the gains of the sensorimotor reactions. Received: 25 September 1995/Accepted in revised form: 9 May 1996     

The inverse problem for DNA

The DNA distribution function for a given section of DNA of a given length depends on the nucleotide composition. It can be expressed in terms of other functions, such as specific heat, optical density, etc., if they are measured in the vicinity of the DNA melting point.     

Static optimal estimation of joint accelerations for inverse dynamics problem solution

In inverse dynamics computations, the accuracy of the solution strongly depends on the accuracy of the input data. In particular, estimated joint moments are highly sensitive to uncertainties in acceleration data. The aim of the present work was to improve classical inverse dynamics computations by providing an accurate estimation of accelerations. Accelerations are usually calculated from noise-polluted position data using numerical double differentiation, which amplifies measurement noise. The objective of the present paper is to use all available imperfect position and force measurements to extract optimum acceleration estimations. A weighted least-squares optimisation approach is used to provide optimal acceleration distributions most consistent with position and force data, and which account for the propagation of measurement uncertainties. The task chosen for comparing the solution methodology with other classical methods is a typical experimental postural movement, consisting in upper limb swings from an upright stance. The proposed method delivers a set of optimal accelerations well consistent with all available measurements. It also leads to an accurate prediction of ground reactions and it produces no residual moment at the top-most segment.     

The neuromuscular control of birdsong.

Birdsong requires complex learned motor skills involving the coordination of respiratory, vocal organ and craniomandibular muscle groups. Recent studies have added to our understanding of how these vocal subsystems function and interact during song production. The respiratory rhythm determines the temporal pattern of song. Sound is produced during expiration and each syllable is typically followed by a small inspiration, except at the highest syllable repetition rates when a pattern of pulsatile expiration is used. Both expiration and inspiration are active processes. The oscine vocal organ, the syrinx, contains two separate sound sources at the cranial end of each bronchus, each with independent motor control. Dorsal syringeal muscles regulate the timing of phonation by adducting the sound-generating labia into the air stream. Ventral syringeal muscles have an important role in determining the fundamental frequency of the sound. Different species use the two sides of their vocal organ in different ways to achieve the particular acoustic properties of their song. Reversible paralysis of the vocal organ during song learning in young birds reveals that motor practice is particularly important in late plastic song around the time of song crystallization in order for normal adult song to develop. Even in adult crystallized song, expiratory muscles use sensory feedback to make compensatory adjustments to perturbations of respiratory pressure. The stereotyped beak movements that accompany song appear to have a role in suppressing harmonics, particularly at low frequencies.     

Physical parameter estimation from porcine ex vivo vocal fold dynamics in an inverse problem framework

This study presents a framework for a direct comparison of experimental vocal fold dynamics data to a numerical two-mass-model (2MM) by solving the corresponding inverse problem of which parameters lead to similar model behavior. The introduced 2MM features improvements such as a variable stiffness and a modified collision force. A set of physiologically sensible degrees of freedom is presented, and three optimization algorithms are compared on synthetic vocal fold trajectories. Finally, a total of 288 high-speed video recordings of six excised porcine larynges were optimized to validate the proposed framework. Particular focus lay on the subglottal pressure, as the experimental subglottal pressure is directly comparable to the model subglottal pressure. Fundamental frequency, amplitude and objective function values were also investigated. The employed 2MM is able to replicate the behavior of the porcine vocal folds very well. The model trajectories’ fundamental frequency matches the one of the experimental trajectories in \(98.6\%\) of the recordings. The relative error of the model trajectory amplitudes is on average \(9.5\%\). The experiments feature a mean subglottal pressure of 10.16 (SD \(= 2.31\)) \({\text {cmH}}_2{\text {O}}\); in the model, it was on average 7.61 (SD \(= 2.40\)) \({\text {cmH}}_2{\text {O}}\). A tendency of the model to underestimate the subglottal pressure is found, but the model is capable of inferring trends in the subglottal pressure. The average absolute error between the subglottal pressure in the model and the experiment is 2.90 (SD \(= 1.80\)) \({\text {cmH}}_2{\text {O}}\) or \(27.5\%\). A detailed analysis of the factors affecting the accuracy in matching the subglottal pressure is presented.     

The ion channel inverse problem: neuroinformatics meets biophysics

Ion channels are the building blocks of the information processing capability of neurons: any realistic computational model of a neuron must include reliable and effective ion channel components. Sophisticated statistical and computational tools have been developed to study the ion channel structure–function relationship, but this work is rarely incorporated into the models used for single neurons or small networks. The disjunction is partly a matter of convention. Structure–function studies typically use a single Markov model for the whole channel whereas until recently whole-cell modeling software has focused on serial, independent, two-state subunits that can be represented by the Hodgkin–Huxley equations. More fundamentally, there is a difference in purpose that prevents models being easily reused. Biophysical models are typically developed to study one particular aspect of channel gating in detail, whereas neural modelers require broad coverage of the entire range of channel behavior that is often best achieved with approximate representations that omit structural features that cannot be adequately constrained. To bridge the gap so that more recent channel data can be used in neural models requires new computational infrastructure for bringing together diverse sources of data to arrive at best-fit models for whole-cell modeling. We review the current state of channel modeling and explore the developments needed for its conclusions to be integrated into whole-cell modeling.     

The inverse relationship between protein dynamics and thermal stability

Protein powders that are dehydrated or mixed with a glassy compound are known to have improved thermal stability. We present elastic and quasielastic neutron scattering measurements of the global dynamics of lysozyme and ribonuclease A powders. In the absence of solvation water, both protein powders exhibit largely harmonic motions on the timescale of the measurements. Upon partial hydration, quasielastic scattering indicative of relaxational processes appears at sufficiently high temperature. When the scattering spectrum are analyzed with the Kohlrausch-Williams-Watts formalism, the exponent beta decreases with increasing temperature, suggesting that multiple relaxation modes are emerging. When lysozyme was mixed with glycerol, its beta values were higher than the hydrated sample at comparable temperatures, reflecting the viscosity and stabilizing effects of glycerol.     

An inverse problem in neural processing

Any neural network aimed at the coding sensory events must contain computational properties which generally allow the organism to reconstruct the input signals with some degree of accuracy-else the association between stimulus and response would, at best, be uncertain. In this paper we investigate the problem of reconstructing external input signals to neural networks when the activity profiles of only some of its member cells are known. The evolution and activities of such cells are defined by an earlier formulation of one of us (Ouztöreli 1979) and, here, we restrict our application to local curcuits within the vertebrate retina. Solutions to this inverse coding problem are presented for specific network equations and examplified with 1, 3, and 5 neuron cases.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and grant A-4395 to T.M.C. through the University of Alberta     

The molecular dynamics of pain control

Pain is necessary for survival, but persistent pain can result in anxiety, depression and a reduction in the quality of life. The discriminative and affective qualities of pain are both thought to be regulated in an activity-dependent fashion. Recent studies have identified cells and molecules that regulate pain sensitivity and the parallel pathways that distribute nociceptive information to limbic or sensory areas of the forebrain. Here, we emphasize the cellular and neurobiological consequences of pain, especially those that are involved in the generation and maintenance of chronic pain. These new insights into pain processing will significantly alter our approach to pain control and the development of new analgesics.     

The dynamics of recycled acetylcholine receptors at the neuromuscular junction in vivo

At the peripheral neuromuscular junction (NMJ), a significant number of nicotinic acetylcholine receptors (AChRs) recycle back into the postsynaptic membrane after internalization to intermingle with not-yet-internalized ;pre-existing' AChRs. However, the way in which these receptor pools are maintained and regulated at the NMJ in living animals remains unknown. Here, we demonstrate that recycled receptors in functional synapses are removed approximately four times faster than pre-existing receptors, and that most removed recycled receptors are replaced by new recycled ones. In denervated NMJs, the recycling of AChRs is significantly depressed and their removal rate increased, whereas direct muscle stimulation prevents their loss. Furthermore, we show that protein tyrosine phosphatase inhibitors cause the selective accumulation of recycled AChRs in the peri-synaptic membrane without affecting the pre-existing AChR pool. The inhibition of serine/threonine phosphatases, however, has no effect on AChR recycling. These data show that recycled receptors are remarkably dynamic, and suggest a potential role for tyrosine dephosphorylation in the insertion and maintenance of recycled AChRs at the postsynaptic membrane. These findings may provide insights into long-term recycling processes at less accessible synapses in the central nervous system in vivo.     

The neuromuscular demands of toe walking: a forward dynamics simulation analysis

Toe walking is a gait deviation with multiple etiologies and often associated with premature and prolonged ankle plantar flexor electromyographic activity. The goal of this study was to use a detailed musculoskeletal model and forward dynamical simulations that emulate able-bodied toe and heel-toe walking to understand why, despite an increase in muscle activity in the ankle plantar flexors during toe walking, the internal ankle joint moment decreases relative to heel-toe walking. The simulations were analyzed to assess the force generating capacity of the plantar flexors by examining each muscle's contractile state (i.e., the muscle fiber length, velocity and activation). Consistent with experimental measurements, the simulation data showed that despite a 122% increase in soleus muscle activity and a 76% increase in gastrocnemius activity, the peak internal ankle moment in late stance decreased. The decrease was attributed to non-optimal contractile conditions for the plantar flexors (primarily the force-length relationship) that reduced their ability to generate force. As a result, greater muscle activity is needed during toe walking to produce a given muscle force level. In addition, toe walking requires greater sustained plantar flexor force and moment generation during stance. Thus, even though toe walking requires lower peak plantar flexor forces that might suggest a compensatory advantage for those with plantar flexor weakness, greater neuromuscular demand is placed on those muscles. Therefore, medical decisions concerning whether to reduce equinus should consider not only the impact on the ankle moment, but also the expected change to the plantar flexor's force generating capacity.     

The inverse Womersley problem for pulsatile flow in straight rigid tubes

In this study a numerical solution for the problem of pulsating flow in rigid tubes is described. The method applies to the case of known flow rate waveform, as opposed to Womersley solution where the pressure gradient was the known quantity. The solution provides the pressure gradient and wall shear stress waveforms as well as the instantaneous velocity profiles. Results show that the method can be used to study the blood flow characteristics in large arteries.     

Acetylcholinesterase dynamics at the neuromuscular junction of live animals

At cholinergic synapses, acetylcholinesterase (AChE) is critical for ensuring normal synaptic transmission. However, little is known about how this enzyme is maintained and regulated in vivo. In this work, we demonstrate that the dissociation of fluorescently-tagged fasciculin 2 (a specific and selective peptide inhibitor of AChE) from AChE is extremely slow. This fluorescent probe was used to study the removal and insertion of AChE at individual synapses of living adult mice. After a one-time blockade of AChEs with fluorescent fasciculin 2, AChEs are removed from synapses initially at a faster rate (t(1/2) of approximately 3 days) and later at a slower rate (t(1/2) of approximately 12 days). Most of the removed AChEs are replaced by newly inserted AChEs over time. However, when AChEs are continuously blocked with fasciculin 2, the removal rate increases substantially (t(1/2) of approximately 12 h), and most of the lost AChEs are not replaced by newly inserted AChE. Furthermore, complete one-time inactivation of AChE activity significantly increases the removal of postsynaptic nicotinic acetylcholine receptors (AChRs). Finally, time lapse imaging reveals that synaptic AChEs and AChRs that are removed from synapses are co-localized in the same pool after being internalized. These results demonstrate a remarkable AChE dynamism and argue for a potential link between AChE function and postsynaptic receptor lifetime.     

Molecular seismology: an inverse problem in nanobiology

The density profile of an elastic fiber like DNA will change in space and time as ligands associate with it. This observation affords a new direction in single molecule studies provided that density profiles can be measured in space and time. In fact, this is precisely the objective of seismology, where the mathematics of inverse problems have been employed with success. We argue that inverse problems in elastic media can be directly applied to biophysical problems of fiber-ligand association, and demonstrate that robust algorithms exist to perform density reconstruction in the condensed phase.     

Modeling locomotion of a soft-bodied arthropod using inverse dynamics

Most bio-inspired robots have been based on animals with jointed, stiff skeletons. There is now an increasing interest in mimicking the robust performance of animals in natural environments by incorporating compliant materials into the locomotory system. However, the mechanics of moving, highly conformable structures are particularly difficult to predict. This paper proposes a planar, extensible-link model for the soft-bodied tobacco hornworm caterpillar, Manduca sexta, to provide insight for biologists and engineers studying locomotion by highly deformable animals and caterpillar-like robots. Using inverse dynamics to process experimentally acquired point-tracking data, ground reaction forces and internal forces were determined for a crawling caterpillar. Computed ground reaction forces were compared to experimental data to validate the model. The results show that a system of linked extendable joints can faithfully describe the general form and magnitude of the contact forces produced by a crawling caterpillar. Furthermore, the model can be used to compute internal forces that cannot be measured experimentally. It is predicted that between different body segments in stance phase the body is mostly kept in tension and that compression only occurs during the swing phase when the prolegs release their grip. This finding supports a recently proposed mechanism for locomotion by soft animals in which the substrate transfers compressive forces from one part of the body to another (the environmental skeleton) thereby minimizing the need for hydrostatic stiffening. The model also provides a new means to characterize and test control strategies used in caterpillar crawling and soft robot locomotion.     

Infinite number of solutions to the hemodynamic inverse problem

Investigators have had much success solving the "hemodynamic forward problem," i.e., predicting pressure and flow at the entrance of an arterial system given knowledge of specific arterial properties and arterial system topology. Recently, the focus has turned to solving the "hemodynamic inverse problem," i.e., inferring mechanical properties of an arterial system from measured input pressure and flow. Conventional methods to solve the inverse problem rely on fitting to data simple models with parameters that represent specific mechanical properties. Controversies have arisen, because different models ascribe pressure and flow to different properties. However, an inherent assumption common to all model-based methods is the existence of a unique set of mechanical properties that yield a particular pressure and flow. The present work illustrates that there are, in fact, an infinite number of solutions to the hemodynamic inverse problem. Thus a measured pressure-flow pair can result from an infinite number of different arterial systems. Except for a few critical properties, conventional approaches to solve the inverse problem for specific arterial properties are futile.