Rate Of Force Change Research Articles

Oscillations in motor unit discharge are reflected in the low-frequency component of rectified surface EMG and the rate of change in force

Common drive to a motor unit (MU) pool manifests as low-frequency oscillations in MU discharge rate, producing fluctuations in muscle force. The aim of the study was to examine the temporal correlation between instantaneous MU discharge rate and rectified EMG in low frequencies. Additionally, we attempted to examine whether there is a temporal correlation between the low-frequency oscillations in MU discharge rate and the first derivative of force (dF/dt). Healthy young subjects produced steady submaximal force with their right finger as a single task or while maintaining a pinch-grip force with the left hand as a dual task. Surface EMG and fine-wire MU potentials were recorded from the first dorsal interosseous muscle in the right hand. Surface EMG was band-pass filtered (5-1,000Hz) and full-wave rectified. Rectified surface EMG and the instantaneous discharge rate of MUs were smoothed by a Hann-window of 400ms duration (equivalent to 2Hz low-pass filtering). In each of the identified MUs, the smoothed MU discharge rate was positively correlated with the rectified-and-smoothed EMG as confirmed by the distinct peak in cross-correlation function with greater values in the dual task compared with the single task. Additionally, the smoothed MU discharge rate was temporally correlated with dF/dt more than with force and with rectified-and-smoothed EMG. The results indicated that the low-frequency component of rectified surface EMG and the first derivative of force provide temporal information on the low-frequency oscillations in the MU discharge rate.

The Threshold Force for Membrane Tether Formation Depends Strongly on Loading Rate

Tethers are thin tubes of lipids (∼20-200 nm in diameter) that form when membranes are subjected to a point force. Tether dynamics are important to a myriad of biological processes including white blood cell adhesion and transport of intracellular material between neighboring cells. To understand the dynamics of tether formation more fully, we investigated the dependence of the force needed to create a tether on the rate of force change (loading rate). To conduct these experiments, a microfabricated magnetic force transducer was used to generate well-controlled and localized magnetic force profiles.

Measurement of cell forces using a microfabricated polymer cantilever sensor

A polymer MEMS sensor was developed for measuring the mechanical forces generated by single adherent cells. Mechanical forces are known to play a role in cell regulation, and measuring these forces is an important step in understanding cellular mechanotransduction. The sensor consisted of four polystyrene microcantilever beams with cell adhesion pads at the end of each beam. Finite element analysis was used to guide the design of a compound cantilever to allow measurement of forces in any direction in the plane of the sensor. The device was used to measure the forces generated by WS1 human skin fibroblasts under a microscope. Single cells were placed on the sensor using a custom micromanipulator. Forces were calculated by optically measuring the deflection of each probe during cell attachment and spreading. Measurements were performed on normal WS1 fibroblast cells and those treated with cytochalasin D to disrupt the actin cytoskeleton. Cytochalasin D treated cells showed a significant decrease in force, with time information about the rate of force change obtained from the sensor. This device can be used to evaluate the mechanical response of cells to a variety of chemical, mechanical, and other environmental stimuli.

The sources of two components of variance: an example of multifinger cyclic force production tasks at different frequencies

In a multifinger cyclic force production task, the finger force variance measured across trials can be decomposed into two components, one that affects the combined force output ("bad variance") and one that does not ("good variance"). Previous studies have found similar time patterns of "bad variance" and force rate leading to an approximately linear relationship between them. Based on this finding and a recently developed model of multifinger force production, we expected the "bad variance" during cyclic force production to increase monotonically with the rate of force change, both within a cycle and across trials at different frequencies. Alternatively, "bad variance" could show a dependence on task frequency, not on actual force derivative values. Healthy subjects were required to produce cyclic force patterns to prescribed targets by pressing on unidimensional force sensors, at a frequency set by a metronome. The task was performed with only the index finger, and with all four fingers. In the task with all four fingers, the "good variance" increased approximately linearly with an increase in the force magnitude. The "bad variance" showed within-a-cycle modulation similar to that of the force rate. However, an increase in the frequency did not lead to an increase in the "bad variance" that could be expected based on the natural relationships between action frequency and the rate of force change modulation. The results have been interpreted in the framework of an earlier model of multifinger force production where "bad variance" is a result of variance of the timing parameter. The unexpected lack of modulation of the "bad variance" with frequency suggests a drop in variance of the timing parameter with increased frequency. This mechanism may serve to maintain a constant acceptable level of variance under different conditions.

Impact of Doublet Discharges on Force Production in Young and Older Humans

Doublet discharges, in which a motor unit fires two action potentials close together in time (inter-spike interval of < 10 ms), have been demonstrated in both animals and humans. However, the functional role of doublets is not yet fully understood in humans. PURPOSE: To determine the functional conditions favorable for the production of doublets. The impact of doublet discharges on the rate of force production was also investigated, and compared between young and older individuals. METHODS: Participants included eightyoung (21.9 ± 3.5 years) and eight older (74.1 ± 8.7 years) individuals. Motor unit activity was recorded from the tibialis anterior during isometric dorsiflexion using a four-wire needle electrode. Subjects performed isometric ramp contractions up to 50% MVC and the occurrence of doublets was identified. A subset of subjects (n=4) also performed a constant force contraction at 50% MVC. The force level and the rate of change in force were assessed 100 ms prior to the first firing of the doublet and 100 ms following the second firing of the doublet. The force and rate of change in force were compared between age groups and pre- vs post-doublet discharge. Similar comparisons were made between constant force and changing force contractions in a subset of individuals. RESULTS: During the ramp contractions the force level prior to the doublet was similar to the force level following the doublet (p=.38). The rate of change of the force was significantly higher following the firing of doublets than prior to the doublets in the older group (p=.008), but not in the young subjects (p=.74). There was a tendency for a greater number of doublets per unit time during ramp contractions (mean=0.66/s) than during constant force contractions (mean=0.14/s). The changes in the level of force and in the rate of change in force from pre-post doublet were also greater during ramp contractions than during constant force contractions, in both young and older subjects. CONCLUSION: These results suggest a role for doublets in increasing both the level and rate of force production in humans, particularly in older individuals. Although data comparing constant force and ramp contractions is limited, the evidence suggests that doublets are more likely to occur, and have a greater impact on force production during changing force conditions.

Linear Lagged Relationship Between Inflation, Unemployment and Labor Force Change Rate in France: Cointegration Test

A linear and lagged relationship between inflation, unemployment and labor force change rate, ?(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+A2 (where A0, A1, and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a root mean square forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study. The VECM approach also allows re-estimation of the coefficients in the individual and generalized relationship between the variables both for cointegration rank 1 and 2. Comparison of the standard cointegration approach to the integral approach to the estimation of the coefficients in the individual and generalized relationships between the studied variables demonstrates the superiority of the latter. The cumulative inflation curve or inflation index, which is the actually measured evolution of price level, is much better predicted in the framework of the integral approach, which is a powerful tool for revealing true relationships between non-stationary variables and can be potentially used for rejection of spurious regression. The cumulative curves allow avoiding obvious drawbacks of the VECM representation and cointegration tests - increasing signal to noise ratio after differentiation and severe dependence on statistical properties of error terms. The confirmed validity of the linear lagged relationship between inflation, unemployment and labor force change indicates that since 1995 the Banque de France has been wrongly applying the policy fixing the monetary growth to the reference value around 4.5%. As a result of the policy, during the last ten years unemployment in France was twice as large as the one dictated by its long-term equilibrium link to labor force change. This increased unemployment compensates the forced price stability.

Inflation as a Function of Labor Force Change Rate: Cointegration Test for the USA

Previously, a linear and lagged relationship between inflation and labor force change rate, π(t)= A1dLF(t-t1)/LF(t-t1)+A2 (where A1 and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for the USA is characterized by A1=4.0, A2=-0.03075, and t1=2 years. It provides a root mean square forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models) and has a perfect parsimony - only one predictor. The relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied - the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations

Afferent Contributions to Digit Force Coupling and Force Level Variation During Performance of Non-lift Pinch

Afferent contributions to the coordination of thumb and index finger forces during non-lift pinch were studied using an anesthetization case study design. Two subjects, one performing with and without digital anesthetization and one with intact sensation, produced dynamic pinch forces against a stable object, with and without visual feedback. Error corrections were less frequent post-anesthetization, and the cross correlation between digit forces was lower when sensation was removed. However, this decrease in cross correlation between digit forces seemed to reflect a loss in the magnitude of tightly coupled error corrections when sensation was removed, rather than more frequent deviations of force magnitude between the digit forces. Force-time output without visual feedback lacked these error corrections, and the correlation between digit forces remained high, irrespective of sensory status. Additionally, with vision occluded, the time rate of force change did not vary in a gradual manner as would be expected from a neural representation of a sinusoidal target, but was instead marked by sudden abrupt reversals of force rate of change, invariant of somatosensory status. The coupling of digit forces and rates of force change during non-lift pinch appear to be controlled primarily with feedforward mechanisms, where the lack of proprioceptive feedback does not seem to disrupt this coupling.

Fast Carbon Nanotube Charging and Actuation

A number of new and established technologies employ electrical stimuli to induce mechanical deformation in materials. Carbon nanotube (CNT) actuators have recently attracted attention due to their low operation voltage (∼ 1 V), high operating load (26 MPa to date), and high tensile strengths (1.8 GPa, and possibly reaching 37 GPa in individual tubes). However, CNT actuators tend to exhibit a full response on a timescale of seconds rather than the milliseconds typical of electromagnetic actuators, piezoceramics, and muscle. A key objective of this work is to push the limits of CNT actuation rates. A second objective is to observe charging rates. CNT papers have been shown to exhibit specific capacitances on the order of 10 F kg and higher. If they can also be shown to charge and discharge rapidly, they will demonstrate particular promise for use as high-power energystorage devices. Previous work presented the use of resistance compensation to increase the rate of actuation in CNT devices. The rate of actuation was found to be limited to 3 % s. At high acceleration rates the inertia of the apparatus appeared to be the limiting rate. In the present work, the rate of change in force is measured while CNT films are held at a fixed length (isometric conditions). The advantage of measuring force changes under isometric conditions is that there are no moving parts, and hence inertia does not limit the peak rates that can be observed. CNTs are formed into porous sheets or fibers which are immersed in electrolyte to form electrodes in an electrochemical cell. The application of potential causes the formation of an electrical double layer at the nanotube/electrolyte interface in which the electronic charge stored in the carbon atoms is balanced by the ionic charge in the electrolyte. The accumulated nanotube charge and the resulting change in band structure is believed to cause a change in the C–C bond length during electron injection due to a number of factors, including Coulomb repulsion. Assuming that these mechanisms are correct, it is the rate at which charge can be injected that determines the strain rate. The key to increasing rate is to increase the current injected per unit volume. Achieving rapid charging rates is a challenge in fibers and sheets composed of CNTs because of the enormous capacitance of CNT electrodes, which is a consequence of the enormous internal surface area. This capacitance is more than six orders-of-magnitude higher than is observed in polyester capacitors, and is similar to that of commercial superand ultracapacitors. Internal resistances and ion-transport rates prevent rapid charging and discharging, limiting the effectiveness of CNTs both as actuators and supercapacitors. Work by Niu and colleagues has shown that it is possible to obtain fast response times by using a combination of relatively thin porous CNT electrodes and high-conductivity electrolytes. Charge and discharge times of 7 ms and specific powers of 8 kW kg were reported. In this paper, it is shown that fast response times can be obtained both for actuation and charging of CNT papers. In order to increase the rates of charging and actuation in thin, porous CNT films, millisecond-long voltage pulses of up to ± 35 V in amplitude are applied. Potentials are much higher than the ∼ 1 V used in charging of CNT paper and fiber actuators and supercapacitors, where such large potential magnitudes would typically lead to parasitic reactions and degradation. However, if the solution resistance and any contact and lead resistance are significantly greater than the CNT paper impedance, most of the voltage drop will initially be across these rather than the double layer within the nanotube films. The use of short pulses ensures that no overcharging of the nanotube double layer will occur, allowing rapid charging without unwanted reactions. The maximum allowable pulse duration is estimated by multiplying the desired potential change at the electrode (for example, 1 V) by the elecC O M M U N IC A TI O N S

The Japanese Economy

The Japanese economic behavior is modeled. GDP evolution is represented as a sum two components: economic tend and fluctuations. The trend is an inverse function of GDP per capita with a constant numerator. The growth rate fluctuations are numerically equal to two thirds of the relative change in the number of eighteen-year-olds. Inflation is represented by a linear function of labor force change rate. The models provide an accurate description for the poor economic performance and deflation separately. Using the models, GDP per capita is predicted for the next ten years and recommendations are given to overcome deflation.

The human central nervous system needs time to organize task-specific covariation of finger forces

We studied how the central nervous system (CNS) organizes outputs of effectors in a redundant motor task. During four-finger ramp force production, finger forces show positive covariations across trials at low forces, which turn into negative covariations at a critical force value ( F CR). Subjects performed such tasks with different target amplitudes and durations of the ramp. F CR showed significant linear relations to the rate of force change. The slopes of the relations varied across subjects corresponding to a critical time ( T CR) ranging from 0.13 to 0.84 s. Across subjects, T CR showed no relation to maximal force production; T CR increased with the ramp duration. We conclude that the CNS needs a certain time to organize stabilization of total force by a negative covariation among finger forces.

The human central nervous system needs time to organize task-specific covariation of finger forces

We studied how the central nervous system (CNS) organizes outputs of effectors in a redundant motor task. During four-finger ramp force production, finger forces show positive covariations across trials at low forces, which turn into negative covariations at a critical force value ( F CR ). Subjects performed such tasks with different target amplitudes and durations of the ramp. F CR showed significant linear relations to the rate of force change. The slopes of the relations varied across subjects corresponding to a critical time ( T CR ) ranging from 0.13 to 0.84 s. Across subjects, T CR showed no relation to maximal force production; T CR increased with the ramp duration. We conclude that the CNS needs a certain time to organize stabilization of total force by a negative covariation among finger forces.

Magnitude estimation of tangential force applied to the fingerpad.

Prior research on large-fibre skin mechanoreceptors in humans and monkeys has demonstrated their sensitivity to perpendicular skin indentation and to the rate of force application. Although some studies have examined skin afferent responses to stretch, relatively few investigations have examined the neural and perceptual correlates of shear forces applied tangentially to the skin. The present study assessed the ability of human subjects to scale different levels of tangential force applied to the distal pad of the index finger. Subjects were instructed to choose their own magnitude estimation scale. Seven force levels ranging from 0.15 to 0.70 N were delivered randomly at rates of 0.10 N/s, 0.15 N/s or 0.30 N/s. Tangential forces were produced with a smooth metal spatula coated with an adhesive to insure a shear force on the underlying skin without slip. The same procedures were also used to generate skin indentation with normal forces. The results showed that most human subjects were able to scale different magnitudes of both tangential and normal forces applied to the tip of the index finger. The rate of force change did not influence the perception of the applied forces. These results highlight the potentially important role of tangential forces in haptic perception.

A component analysis of the generation and release of isometric force in Parkinson's disease.

Paradigms of isometric force control allow study of the generation and release of movement in the absence of complications due to disordered visuomotor coordination. The onset and release of isometric force in Parkinson's disease (PD) was studied, using computerised determinants of latency of response and rate of force generation and release. Components of isometric force control were related to measures of cognitive, affective and clinical motor disability. The effects of treatment were determined by longitudinal study of de novo patients. Patients with PD showed impairment in latency and rate of force change for movement release as well as onset. Rate of force change correlated with depression, clinical motor disability and memory quotient but latency showed no correlation with any of these measures. Treatment improved rate of force release, in concert with clinical motor disability, but not latency. These results suggest dissociations between latency and rate of force change that may be linked to different neurochemical deficits. Further, they demonstrate akinetic deficits in force release that argue against the "neural energy hypothesis" of akinesia.

A portable, easily performed muscle power test and its association with falls by elderly persons

This study developed and evaluated a simple, inexpensive, and safe screening test for assessment of falling risk in elderly persons. Subjects sat in chairs (hips and knees at 90 degrees) with their feet over a force transducer and stood as forcefully as possible. After standing for five seconds, they sat as fast as possible. The rate of change in force (dF/dT) for standing and sitting were calculated from data collected by computer. A group of nonfallers (n = 23, age = 23 to 72 years) and a group of fallers (n = 22, age = 63 to 92 years) were studied. Nonfallers' dF/dT for standing decreased linearly from 4kg.sec-1.kg-1 to 2.5kg.sec-1.kg-1. Values in fallers decreased linearly from 3kg.sec-1.kg-1 to 0.1kg.sec-1.kg-1. The dF/dT for sitting was not dependent on age in either group. Fallers had lower dF/dT than nonfallers (1.3 +/- .6kg.sec-1.kg-1 and 2.3 +/- .01kg.sec-1.kg-1, respectively). Seventeen of 22 fallers were identified by a reduced dF/dT and reduced overshoot force (kg).

Ramp-and-Hold Force Control in the Upper and Lower Lips

The relation among several parameters of the ramp-and-hold force contraction and target force level was quantified for the upper and lower lip in 40 normal adults and in 4 young adults who had sustained traumatic brain injury (TBI). Using visual feedback, subjects produced ramp-and-hold compression lip forces as rapidly and accurately as possible to end-point target levels ranging from 0.25 to 2.00 newtons. In normal adults, significant positive linear relations were found between the parameters of the ramp-and-hold lip force task and target force level, including the peak rate of force change, peak force, and the mean and standard deviation of force during the hold phase. Though males and females have been shown to differ greatly on absolute maximum force-generating capabilities, they are virtually identical on the measures used to quantify the lip force ramp-and-hold task over the range of compression forces studied. Preliminary investigation of lip force control in 4 TBI subjects suggests that these quantitative measures are useful in determining the distribution and nature of motor impairment between the upper and lower lips during a dynamic force control task.

Fine force and position control of select orofacial structures in the upper motor neuron syndrome

A fundamental pathophysiologic feature of patients with the upper motor neuron syndrome is a reduction in the rate of force change associated with generating fine levels of force in the upper lip, lower lip, tongue, and jaw. These measures were highly related to impairments in movement velocity in these same structures. End point accuracy, defined as the ability to generate specified target levels for both force and position, was relatively well preserved in these structures. Moreover, these measures of dynamics in select structures of the oral motor system were found to be highly related to impairments in speech intelligibility. Quantitative physiologic measures of force and movement control are considerably more sensitive than conventional methods in determining the distribution and nature of orofacial motor impairments which degrade fine motor performance.

Effect of external force on relaxation kinetics in single frog atrial cardiac cells.

The effects of external force on relaxation kinetics were investigated in isolated single frog (Rana catesbeiana) atrial cells. We found that force decay occurred at a maximum and constant rate for a significant portion of auxotonic relaxation, and this rate was linearly related to the peak force developed during auxotonic contraction. The slope of the linear relationship between the maximum rate of auxotonic force decay and peak auxotonic force was not affected by changes in the level of contractile activation produced by activating the cell with different stimulus durations. The rate of force change during auxotonic contraction and relaxation in the isolated cell is directly related to the average sarcomere velocity within the cell. Thus, the results indicate that during auxotonic relaxation the velocity of sarcomere extension is directly related to the peak auxotonic force, and sarcomere extension, during relaxation, is therefore affected by external force. The direct effect of external force on relaxation kinetics was confirmed by the observation that force changes imposed on the cell during relaxation immediately altered the velocity of the extending cell from any given length. However, data are also presented which demonstrate that rapid sarcomere extension occurs during relaxation under conditions where external forces are negligible. Thus, rapid sarcomere extension during relaxation does not require large external forces, and internal forces must play a role in sarcomere extension during relaxation. An explanation is given for these apparently contradictory results.

The activity of supplementary motor area neurons during a maintained precision grip

Two monkeys were trained to exert a precision grip of the thumb and forefinger and to maintain constant near-isometric force for a one-second duration. Both animals were trained to perform the task with about equal proficiency with either hand. A total of 134 neurons were recorded from the supplementary motor area (SMA) of the hemisphere contralateral to the performing hand. SMA neurons were identified by either the presence of peripheral fields on the contralateral arm or by consistent changes in discharge frequency during contralateral arm movement. Sixty-one cells demonstrated reliable changes in firing frequency during performance of the maintained precision grip. SMA neurons showed little tendency to discharge at higher frequency during force change rather than during maintained force. Only two neurons significantly increased firing frequency with increased finger force and no modulation of discharge related to rate of force change could be shown. The changes in spike frequency among SMA cells related to the arm were, on the average, about 100 msec after the onset of contraction in the forearm flexors and extensors of the wrist and fingers, although a contingent of cells discharging consistently before the onset of muscular activity was found.

The control of rapid limb movement in the cat. I. Response latency.

A versatile tracking task has been developed to assess the competence of feline subjects in using sensory information to initiate and guide limb movement. In the present study we investigated the response latency and the factors which affect it in order to define temporal constraints on the underlying processing of information. The paradigm makes use of an electromechanical display of the difference between the output of transducers in a manipulandum (controlled by the cat) and a target level (controlled by the experimenter). Because of inertia and friction, a step change in target level required 230 msec to fully shift the display. The animals were trained to match the position of the manipulandum (or the force they applied to it isometrically) to the target level for a food reward. Target perturbations elicited rapid position or force adjustments of appropriate direction and magnitude at short latency. Under isometric conditions, the latency of the response was an inverse function of the extent of display motion and of the peak rate of force change attained during the adjustment. Asymptotic values of the response time, measured from the perturbation to the first change in force applied to the lever, were typically between 50 and 70 msec. Since the motor responses were invariably initiated while the display was still moving, the animals must have used information contained in the derivatives of its motion. In the absence of visual cues, deflection of the vibrissae by the sudden motion of the dispaly provided two of the four animals with sufficient information to initiate and guide their movements without changes in response latency. When vision was allowed, section of the vibrissae produced a persistent increase in response times of 15-20 msec. This difference in latency is compatible with the delays due to retinal transmission. The short time interval elapsing between stimulus and response strongly suggests that the topography and the metrics of the underlying transformations are adjusted by gating and/or biasing processes which precede the stimulus. It is concluded that sensory information can generate purposeful movements through pathways which include only a small number of central relays in series, independently of its modality.