Predicting optimal electrical stimulation for repetitive human muscle activation.

Functional electrical stimulation is the use of electrical currents to activate paralyzed muscles to produce functional movements. Muscle force output must meet or exceed the external load to maintain a posture or produce movements. A mathematical force-fatigue modeling system that predicts muscle force responses during repetitive electrical stimulation has been developed in our laboratory to help identify stimulation patterns that optimize force output for individual subjects. This study tests how well this model predicts the number of contractions that can be maintained above a required force level (successful contractions) during repetitive activation of a muscle. Healthy human quadriceps muscles were tested isometrically on 12 subjects. Data were first collected and used to parameterize the model. Next, the model was used to predict the number of successful contractions that were produced by trains with frequencies ranging from 5 to 100 Hz while the pulse durations and amplitudes were held constant. Finally, three clinically relevant stimulation frequencies were selected and tested to verify the model's predictions. Under these conditions, the model accurately predicted the number of successful contractions for clinically relevant stimulation frequencies. Furthermore, the model appears to have the potential to identify the stimulation frequency that maximizes muscle force output and minimizes fatigue for each subject.     

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.     

Study of Biomechanical Response of Human Hand-Arm to Random Vibrations of Steering Wheel of Tractor

This paper reports a study on the biomechanical response of a human hand-arm model to random vibrations of the steering wheel of a tractor. An anatomically accurate bone-only hand-arm model from TurboSquidTM was used to obtain a finite element (FE) model to understand the Hand-arm vibration syndrome (HAVS), which is a neurological and vascular disorder caused by exposure of the human hand-arm to prolonged vibrations. Modal analysis has been done to find out the first few natural frequencies and mode shapes of the system. Coupling of degrees of freedom (DOF) had to be done in the FE idealization to do modal analysis, as the bones were not attached to each other in the TurboSquidTM model. The shoulder bone, scapula, has been constrained at one end for eigenvalue analysis. It was observed that the first five natural frequencies were in the range of 0-250 Hz, which is the range in which the effect of HAVS is the highest. Harmonic analysis was done by giving a swept sine excitation in the frequency range 0 to 200 Hz. For this, a force input of 25 N was imparted at nodes perpendicular to the hand, the force value chosen being the nominal force in most applications involving powered hand-held tools and steering wheels of tractors. The nodes chosen for force application were determined experimentally from observations made by gripping the steering wheel. The frequency response function (FRF) plots were obtained in the x, y and z directions. Random vibration analysis was done next by giving force power spectral densities (PSD) in the form of nodal excitation as input to the FE model of hand-arm, and computing the output acceleration PSDs. The input force PSDs were measured using FlexiForce® sensors along the three axes. The acceleration responses at the steering wheel were also measured using tri-axial accelerometers for validating the computed results. The output acceleration PSDs were then weighted using the frequency weighting curves for hand-arm vibration and the total daily exposure A(8), computed using ISO 5349-1 standards, was compared with the vibration action and limit values. The A(8) values obtained are found to be higher than the vibration limit values.     

Manufacture and Performance of Ionic Polymer-Metal Composites

Ion-exchange Polymer Metal Composites （IPMC） are a new class of intelligent material that can be used effectively as actuators and artificial muscles. IPMC was fabricated and its displacement and force characteristics were investigated with respect to voltage, frequency and waveform of the controlling signal. A square waveform input generated slightly larger displacement and force than sinusoidal or triangular waveform. When the voltage was increased and the frequency was decreased, displacement and force were both increased. However, although the bending deformation of IPMC was large, the output force was much lower than we expected. Improvement of the force output is key and is the main obstacle to be overcome in order to make IPMC of practical use.     

Computer simulations of synchrony and oscillations evoked by two coherent inputs

Coherent oscillations have been reported in multiple cortical areas. This study examines the characteristics of output spikes through computer simulations when the neural network model receives periodic/aperiodic spatiotemporal spikes with modulated/constant populational activity from two pathways. Synchronous oscillations which have the same period as the input are observed in response to periodic input patterns regardless of populational activity. The results confirm that the output frequency of synchrony is essentially determined by the period of the repeated input patterns. On the other hand, weak periodic outputs are observed when aperiodic spikes are input with modulated populational activity. In this case, higher firing rates are necessary to input for higher frequency oscillations. The spike-timing-dependent plasticity suppresses the spikes which do not contribute to the synchrony for periodic inputs. This effect corresponds to the experimental reports that learning sharpens the synchrony in the motor cortex. These results suggest that spatiotemporal spike patterns should be entrained on modulated populational activity to transmit oscillatory information effectively in the convergent pathway.     

Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons

Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.     

Smooth muscle stiffness variation due to external longitudinal oscillations

This research focuses on an in vitro investigation of the stiffness changes of contracted airway smooth muscles (ASM) subjected to external longitudinal oscillations. ASM tissues were dissected from excised pig tracheas and stimulated by a chemical stimulus (acetylcholine, 10(-3) M) to produce maximum contractions. The tissues were then systematically excited with external oscillations. Various frequencies, amplitudes and durations were used in the experiments to determine stiffness changes in response to these variations. Force changes were recorded to reflect the muscle stiffness changes. Two stiffness definitions were used to quantify the results, dynamic stiffness to reflect variations during oscillation and static stiffness to reflect the net effect of oscillation. Under isometric contractions, these two stiffnesses were determined before, during and after oscillations. Incorporating an empirical stiffness equation, a two-dimensional finite element model (FEM) was developed to generalize the tissue responses to oscillation. The main outcomes from this work are: the dynamic stiffness has the tendency to decrease as the frequency and/or amplitude of external oscillation increases; the static stiffness has the tendency of decreasing with an increase in the frequency and/or amplitude of excitation until it reaches almost a constant value for frequencies at and above 25 Hz. The difference in the behavior of the dynamic and static stiffness changes may be attributed to the effect of elasticity and mass inertia that are involved in the dynamic motion. The findings of this research are in agreement with the hypothesis that oscillations exert a direct action on the contractile processes by causing an increased rate of actin-myosin detachments.     

Dependency analysis of frequency and strength of gamma oscillations on input difference between excitatory and inhibitory neurons

It has been found that gamma oscillations and the oscillation frequencies are regulated by the properties of external stimuli in many biology experimental researches. To unveil the underlying mechanism, firstly, we reproduced the experimental observations in an excitatory/inhibitory (E/I) neuronal network that the oscillation became stronger and moved to a higher frequency band (gamma band) with the increasing of the input difference between E/I neurons. Secondly, we found that gamma oscillation was induced by the unbalance between positive and negative synaptic currents, which was caused by the input difference between E/I neurons. When this input difference became greater, there would be a stronger gamma oscillation (i.e., a higher peak power in the power spectrum of the population activity of neurons). Further investigation revealed that the frequency dependency of gamma oscillation on the input difference between E/I neurons could be explained by the well-known mechanisms of inter-neuron-gamma (ING) and pyramidal-interneuron-gamma (PING). Finally, we derived mathematical analysis to verify the mechanism of frequency regulations and the results were consistent with the simulation results. The results of this paper provide a possible mechanism for the external stimuli-regulated gamma oscillations.     

Hystereses in the force-length relation and regulation of cross-bridge recruitment in tetanized rat trabeculae

Various mechanisms have been suggested to explain cardiac force-length Ca2+ relations. The existence of a cooperativity mechanism, whereby cross-bridge (XB) recruitment is affected by the number of active XBs, suggests that the force response to length oscillations should lag length oscillations. Consequently, the oscillatory force response should be larger during shortening than during lengthening. To test this prediction, force responses to large-sarcomere length (SL) oscillations (36.7 +/- 16.0 nm) at different SLs (n = 6) and frequencies (n = 7) were studied in intact tetanized trabeculae dissected from rat right ventricle (n = 13). Stable tetani were obtained by utilizing 30 microM cyclopiazonic acid in Krebs-Henseleit solution containing 6 mM extracellular Ca(2+) at 25 degrees C. SL was measured by laser diffraction techniques (Dalsa). Force was measured by silicone strain gauge. Instantaneous dynamic stiffness during large oscillations was measured by superimposing additional fast (50 or 200 Hz) and small-amplitude (2.25 +/- 0.25 nm) oscillations. The force responses lagged the SL oscillations at slow frequencies (112 +/- 41 ms at 1 Hz), and counterclockwise hystereses were obtained in the force-length plane: the force was higher during shortening than during lengthening. The delay in the force response decreased as the frequency of the SL oscillation was increased. Clockwise hysteresis, where the force preceded the SL, was obtained at frequencies >4 Hz. Similar hysteresis characteristics were obtained in the force-SL and stiffness-SL planes. Maximal lag was observed at the shortest SL, and the delay decreased with sarcomere elongation: 131.1 +/- 31.7 ms at 1.78 +/- 0.03 microm vs. 14.7 +/- 18.5 ms at 1.99 +/- 0.015 microm. The results establish the ability of cardiac fiber to adapt XB recruitment to changes in prevailing loading conditions. This study supports the stipulated existence of a cooperativity mechanism that regulates XB recruitment and highlights an additional method to characterize regulation of the force-length relation.     

Time series modeling of neuromuscular system

The dynamic response of the human ankle joint to a bandlimited random torque perturbation superimposed on a constant bias torque is observed in normal human subjects. The applied torque input, the joint angular rotation output, and the electromyographic activity using surface electrodes from the extensor and the flexor muscles of the ankle joint were recorded. Transfer function models using time series techniques were developed for the torque — angular rotation input-output pair and for the angular rotation — electromyographic activity input-output pair. A parameter constraining technique was applied to develop more reliable models. It is shown that the asymptotic behavior of the system must be taken into account during parameter optimization to develop better predictive models.This work was supported in part by National Science Foundation grant ENG-7608754 and grants from the National Institutes of Health NS-12877 and NS-00196     

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: curvature as an indicator of the torque

ATP synthase (F-ATPase) operates as an electrochemical-to-mechanical-to-chemical energy transducer with an astounding 360 degrees rotary motion of subunits epsilongammac(10-14) (rotor) against delta(alphabeta)(3)ab(2) (stator). The enzyme's torque as a function of the angular reaction coordinate in relation to ATP-synthesis/hydrolysis, internal elasticity, and external load has remained an important issue. Fluorescent actin filaments of micrometer length have been used to detect the rotation as driven by ATP hydrolysis. We evaluated the viscoelastic dynamics of actin filaments under the influence of enzyme-generated torque, stochastic Langevin force, and viscous drag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (approximately 100 ms), power strokes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretical background for the alternative use of the filament as a spring balance. The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Pertinent experiments were analyzed in the companion paper.     

A computer analysis of EEG intersignal reactions during the the acquisition of conditioned motor-food reflexes in dogs]

Background electric activity was studied of different neocortex areas in interstimulus intervals at the stage of generalization during elaboration of motor alimentary conditioned reflexes in dogs. For this stage the appearance is typical of short-term (0.1-0.3 s) packs of high frequencies (above 40 osc./s) significantly exceeding the adjacent initial background by frequency and amplitude (along side with motor interstimulus reactions). The index of specific variation, elaborated by us, allowed to single out this EEG pattern in the initial realizations of the background activity during their input in the computer. With the purpose of further evaluation of the above phenomenon parameters non-standard approaches of computer analyses were used, directed to decomposition of the EEG curve into the system of oscillations and receipt of corresponding amplitudes frequencies distributions (maps). It was shown, the described high frequencies packs were localized on these maps in definite sufficiently compact places.     

Cyclic stress at mHz frequencies aligns fibroblasts in direction of zero strain

Recognition of external mechanical signals is vital for mammalian cells. Cyclic stretch, e.g. around blood vessels, is one such signal that induces cell reorientation from parallel to almost perpendicular to the direction of stretch. Here, we present quantitative analyses of both, cell and cytoskeletal reorientation of umbilical cord fibroblasts. Cyclic strain of preset amplitudes was applied at mHz frequencies. Elastomeric chambers were specifically designed and characterized to distinguish between zero strain and minimal stress directions and to allow accurate theoretical modeling. Reorientation was only induced when the applied stretch exceeded a specific amplitude, suggesting a non-linear response. However, on very soft substrates no mechanoresponse occurs even for high strain. For all stretch amplitudes, the angular distributions of reoriented cells are in very good agreement with a theory modeling stretched cells as active force dipoles. Cyclic stretch increases the number of stress fibers and the coupling to adhesions. We show that changes in cell shape follow cytoskeletal reorientation with a significant temporal delay. Our data identify the importance of environmental stiffness for cell reorientation, here in direction of zero strain. These in vitro experiments on cultured cells argue for the necessity of rather stiff environmental conditions to induce cellular reorientation in mammalian tissues.     

The effects of different stretch amplitudes on electromyographic activity during drop jumps

The purpose of this study was to investigate the effects of different stretch amplitudes (angular displacements) on the performance and electromyographic (EMG) activity during drop jumps (DJs). The AMTI force platform, the Biovision electrical goniometer, and EMG system were used to record the ground reaction forces, knee angular displacement, and the EMG signals of the rectus femoris. The EMG data were treated by different data-processing methods: the biphase and triphase data-processing methods. The results revealed that the short-stretch DJs had a larger passive force, a higher eccentric end force, a higher concentric average force, and a faster eccentric angular velocity showing a more efficient stretch-shortening cycle (SSC) mechanism in using elastic energy and reactive properties than the long-stretch DJs. Therefore, the short-stretch DJs are recommended in training for the SSC movement. However, the results of biphase data-processing EMG method did not support this conclusion because there was no significant difference between long-stretch DJs and short-stretch DJs by using the biphase data-processing method, whereas the triphase method did support this conclusion and demonstrated that short-stretch DJs are more efficient.     

A model of visual detection of angular speed for bees

A fly or bee's responses to widefield image motion depend on two basic parameters: temporal frequency and angular speed. Rotational optic flow is monitored using temporal frequency analysers, whereas translational optic flow seems to be monitored in terms of angular speed. Here we present a possible model of an angular speed detector which processes input signals through two parallel channels. The output of the detector is taken as the ratio of the two channels’ outputs. This operation amplifies angular speed sensitivity and depresses temporal frequency tuning. We analyse the behaviour of two versions of this model with different filtering properties in response to a variety of input signals. We then embody the detector in a simulated agent's visual system and explore its behaviour in experiments on speed control and odometry. The latter leads us to suggest a new algorithm for optic flow driven odometry.     

Alternating electric fields stimulate ATP synthesis in Escherichia coli

External alternating electric fields of low intensity stimulated membrane bound ATP synthesis in starving Escherichia coli cells with electric field amplitudes of 2.5-50 V/cm and a frequency optimum at 100 Hz. The model of electrocon-formational coupling was used to analyze the frequency and amplitude responses of ATP synthesis. Two relaxation frequencies of the system were obtained at 44 Hz and 220 Hz, and an estimate of roughly 12 was obtained as the effective charge displacement for the catalytic cycle of ATP synthesis.     

Simulation of vestibular semicircular canal responses during righting movements of a freely falling cat

The righting maneuver of a freely falling cat was filmed at 1000 pictures per second, and the head position about the roll axis was digitized from each film frame using a graphics input tablet. The head angular velocity and acceleration were computed from the roll axis position trajectory. Head acceleration trajectories approximated two periods of a damped sinusoid at a frequency of 26 Hz. Head acceleration peak amplitudes exceeded 120,000 deg/s². These trajectories were used as stimuli for the horizontal semicircular canals in a computer simulation of first-order afferent responses during the fall. Linear system afferent response dynamics, characterized in a previous study of the cat horizontal canal using pseudorandom rotations, provided the basis for linear predictions of falling cat afferent responses. Results showed predicted single afferent firing rates that exceeded physiological values; and variations in afferent sensitivities and phase were predicted among different neurons. Fast head movement information could be carried by ensemble populations of vestibular neurons, and a phase-locking encoding hypothesis is proposed which accomplishes this. Implications for central program versus peripheral vestibular feedback strategies for motor control during falling are presented and discussed.     

Classification of oscillatory states of blood pressure after bleeding in cats (author's transl)]

Blood pressure and heart rate responses were recorded on bleeding of blood volume of 1 ml/kg body weight (test input) from the abdominal aorta of cat. Forward path gain, backward path gain and minification were determined from blood pressure responses to test input. Oscillations in blood pressure were elicited spontaneously or artificially after bleeding of blood volume of 5 ml/kg body weight (conditioning input). The oscillatory states are classified into latent state, underdamped oscillatory state and harmonic oscillatory state. Open loop gain decreased in the latent state but increased in the other states. Therefore, oscillation was hard to elicit in the latent state. Minification, however, enlarged in the latent state, making the system irritable to disturbances and reducing its control accuracy. In the latent state, an insensible disturbance increased backward path gain and open loop gain to induce the oscillations. There was an increase of heart rate at an elicitation of oscillation in any state and a decrease of heart rate made it damped. Therefore, the heart rate regulatory system plays a main role in the feedback path of the blood pressure regulatory system and an increase of heart rate by an insensible disturbance or test input increases backward path gain.     

Analysis of the coding of a periodic movement of stretch receptors of an insect

A study has been made of the input-output relationships of the in situ stretch receptor organs at the tibio-femoral joint of the locust. Sinusoidal deformations of variable amplitudes and frequencies were applied at different angular levels of the tibia. Three units were mainly recorded with silver electrodes on the lateral femoral nerve of the insect. The experimental conditions for which the discharge was periodically abolished are described. The shape and the amplitude of the impulse frequency modulation signal were studied also in relation to the stimulus gradation applied at the input. This response was highly temperature dependent. A graphical representation of the gain is given by a Bode plot (1·7 dB/octave), but over the range of stimulus cycle frequencies the phase-advance of impulse frequency modulation was constant. In successive cycles, there was no phase relation for each spike, except when the response was limited to a single one. In this condition, the response seemed locked in phase over a small range of relatively high frequencies.     

Oscillatory processes in lymph microcirculation in the human skin

This study was the first to use laser Doppler flowmetry followed by wavelet analysis in order to estimate oscillations in lymph microcirculation in 30 subjects with (n = 13) or without (n = 17) edema of the distal part of the upper limb. Lymph flow in the human skin exhibited clear dominance of pacemaker phase oscillations in the frequency ranges of 0.021–0.042 and 0.016–0.035 Hz in the skin of the palm surface of the finger nail bone and in the skin of the forearm, respectively. Edema was associated with an increase in the peak frequencies and normalized maximum amplitudes (Al/Ml, where Al is the mean value of the maximum amplitude of phase oscillations, and Ml is the value of the averaged lymph flow expressed in perfusion units). Low-amplitude oscillations were recorded rarer in the myogenic, endothelial, and respiratory ranges. We did not find any cardiac pulse rhythm in the wavelet spectrum of the lymph flow. We did not find any interaction between the Al/Ml value and the skin temperature. In the group of subjects without edema, under physiological conditions only, we found a negative correlation between the Al/Ml value and the amplitudes of myogenous proper blood flow oscillations, which reflected the number of functional capillaries and activity of oxidative metabolism in the tissue. In the group with edema, we did not find any correlations between the indices of lymph flow and blood flow. The values of normalized amplitude and frequency of phase oscillations may be used as efficient diagnostic tools in the studies on lymph microcirculation.