The relationship between absolute disparity and ocular vergence

The relationship between disparity and ocular vergence was investigated under closed-loop as well as under open-loop viewing conditions. First we examined whether vergence responded similarly to disparity presented under open-loop and closed-loop conditions. Similar response were observed in both conditions. The direct relationship between disparity and vergence was examined by presenting constant disparities between 0.2° and 4° under open-loop viewing conditions. Such vergence responses are described as the outputs of first-order low-pass filters with different filter characteristics for each amplitude of disparity. By analyzing the latency of vergence responses induced by constant disparities with help of the transfer function of disparitycontrolled vergence, the time delay of disparity processing in the vergence loop was estimated. We suggested that the time delay was approximately between 80 and 120 ms instead of 160 ms as is generally assumed. The relationship between the rate of disparity change and vergence was examined by comparing responses to ramp and stepwise changes in target vergence. From the similar responses to ramp and staircase changes in disparity we concluded that vergence is not sensitive to the velocity of target vergence as such. On the basis of these findings we developed a model of disparity-controlled vergence. In this model disparity is processed through several parallel, imperfect integrators with slightly different low-pass filter characteristics, each of them susceptible to a limited range of disparities. Gains as well as phase lags of vergence responses to sinusoidal disparities are accurately simulated by this model. As a consequence of the limited working range of the low-pass filters, the model correctly simulates the alterations of fast and slow phases in response to step and ramps of target vergence, which are characteristic of real vergence responses.     

Muscle dynamics: Dependence of muscle length on changes in external load

A phenomenological theory of muscle dynamics has been elaborated on the basis of data obtained in experiments on hind limb extensor muscles of narcotized cat. Functional dependence of muscle length on external load was explored in conditions of a constant frequency of the efferent stimulation. It was shown that the system under study could be presented for a rather wide class of input signals as a system with nonlinear statics and linear dynamics. The nonlinear statics was shown to be determined mainly by the hysteretical effects of muscle contraction, whereas dynamic element was described by the first order linear differential equation corresponding to the traditional three-component mechanical model of the muscle. A hypothesis was proposed to explain the hysteresis in active muscle on the basis of functioning of the troponin-tropomyosin regulatory complex. Elaborated mathematical model of muscle dynamics can be used to predict and evaluate changes in the muscle length evoked by arbitrary changes in the external load.     

Recruitment of single human low-threshold motor units with increasing loads at different muscle lengths.

We investigated the recruitment behaviour of low threshold motor units in flexor digitorum superficialis by altering two biomechanical constraints: the load against which the muscle worked and the initial muscle length. The load was increased using isotonic (low load), loaded dynamic (intermediate load) and isometric (high load) contractions in two studies. The initial muscle position reflected resting muscle length in series A, and a longer length with digit III fully extended in series B. Intramuscular EMG was recorded from 48 single motor units in 10 experiments on five healthy subjects, 21 units in series A and 27 in series B, while subjects performed ramp up, hold and ramp down contractions. Increasing the load on the muscle decreased the force, displacement and firing rate of single motor units at recruitment at shorter muscle lengths (P<0.001, dependent t-test). At longer muscle lengths this recruitment pattern was observed between loaded dynamic and isotonic contractions, but not between isometric and loaded dynamic contractions. Thus, the recruitment properties of single motor units in human flexor digitorum superficialis are sensitive to changes in both imposed external loads and the initial length of the muscle.     

Cross-bridge attachment and stiffness during isotonic shortening of intact single muscle fibers.

Equatorial x-ray diffraction pattern intensities (I10 and I11), fiber stiffness and sarcomere length were measured in single, intact muscle fibers under isometric conditions and during constant velocity (ramp) shortening. At the velocity of unloaded shortening (Vmax) the I10 change accompanying activation was reduced to 50.8% of its isometric value, I11 reduced to 60.7%. If the roughly linear relation between numbers of attached bridges and equatorial signals in the isometric state also applies during shortening, this would predict 51-61% attachment. Stiffness (measured using 4 kHz sinusoidal length oscillations), another putative measure of bridge attachment, was 30% of its isometric value at Vmax. When small step length changes were applied to the preparation (such as used for construction of T1 curves), no equatorial intensity changes could be detected with our present time resolution (5 ms). Therefore, unlike the isometric situation, stiffness and equatorial signals obtained during ramp shortening are not in agreement. This may be a result of a changed crossbridge spatial orientation during shortening, a different average stiffness per attached crossbridge, or a higher proportion of single headed crossbridges during shortening.     

Motion control of musculoskeletal systems with redundancy

Motion control of musculoskeletal systems for functional electrical stimulation (FES) is a challenging problem due to the inherent complexity of the systems. These include being highly nonlinear, strongly coupled, time-varying, time-delayed, and redundant. The redundancy in particular makes it difficult to find an inverse model of the system for control purposes. We have developed a control system for multiple input multiple output (MIMO) redundant musculoskeletal systems with little prior information. The proposed method separates the steady-state properties from the dynamic properties. The dynamic control uses a steady-state inverse model and is implemented with both a PID controller for disturbance rejection and an artificial neural network (ANN) feedforward controller for fast trajectory tracking. A mechanism to control the sum of the muscle excitation levels is also included. To test the performance of the proposed control system, a two degree of freedom ankle–subtalar joint model with eight muscles was used. The simulation results show that separation of steady-state and dynamic control allow small output tracking errors for different reference trajectories such as pseudo-step, sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against system parameter and controller parameter variations. A possible application of this control algorithm is FES control using multiple contact cuff electrodes where mathematical modeling is not feasible and the redundancy makes the control of dynamic movement difficult.     

Impulse frequency encoding of the dynamic aspects of excitation

Like receptors, neurones of the mammalian CNS react to both the static and the dynamic features of the input signals. The quantitative aspect of the current-to-frequency transduction during input transients were analyzed in spinal motoneurones and in corticospinal neurones by the technique of injecting intracellularly either ramp of sine-wave currents. It was found that, in both types of neurones, the instantaneous firing frequency is linearly correlated, within definite ranges, both to the intensity and to the velocity of change of the input currents. By recording the isometric mechanogram of the muscle units innervated by the impaled motoneurones, it was disclosed that the motoneurones discharges produced by the ramp currents develop tension changes, whose average velocity is proportional to the ramp slope. For both types of neurones, results are consistent with the hypothesis that the major determinants of the double sensitivity, to the intensity and to the velocity, are the kinetics of the potassium conductance system responsible for the spike afterhyperpolarization.     

Autonomic energy conversion. I. The input relation: phenomenological and mechanistic considerations

The differences between completely and incompletely coupled linear energy converters are discussed using suitable electrochemical cells as examples. The output relation for the canonically simplest class of self-regulated incompletely coupled linear energy converters has been shown to be identical to the Hill force-velocity characteristic for muscle. The corresponding input relation (the “inverse” Hill equation) is now derived by two independent methods. The first method is a direct transformation of the output relation through the phenomenological equations of the converter; Onsager symmetry has no influence on the result. The second method makes use of a model system, a hydroelectric device with a regulator mechanism which depends only on the operational limits of the converter (an electro-osmosis cell operated in reverse) and on the load. The inverse Hill equation is shown to be the simplest solution of the regulator equation. An interesting and testable series of relations between input and output parameters arises from the two forms of the Hill equation. For optimal regulation the input should not be greatly different in the two limiting stationary states (level flow and static head). The output power will then be nearly maximal over a considerable range of load resistance, peak output being obtained at close to peak efficiency.     

Fatigue from incompletely fused tetanic contractions in skeletal muscle in situ

The purpose of this study was to investigate the contractile response of skeletal muscle in situ when stimulation results in an unfused tetanic contraction. The left gastrocnemius-plantaris muscle group of anesthetized (pentobarbital sodium) dogs (n = 16) was connected to an isometric lever and stimulated indirectly for 30 min. During 10-Hz stimulation, total tension (the peak of each oscillation in tension) increased during the first 2 min of stimulation (staircase), then decreased during the remaining 28 min of stimulation. Since relaxation was incomplete at this rate of stimulation, the developed tension, the difference between peak tension and the lowest tension between successive contractions, did not follow the same pattern of staircase and fatigue as the peak tension did. Developed tension (delta T) decreased during the staircase response then increased from 2 to 10 min before finally decreasing again during the last 20 min, ending at 56 +/- 15 (mean +/- SE) % of the initial (first contraction) delta T. At 2 min of 10-Hz contractions, half-relaxation time (1/2 RT) was too long to measure (insufficient relaxation between contractions), but later, 1/2 RT decreased from greater than 65 ms to less than 40 ms. Increased 1/2 RT has been associated with reduced energy availability. If an increased 1/2 RT is an indication of insufficient energy, then it can be concluded that fatigue continued in spite of a recovery of energy supplies. This suggests a possible dissociation of fatigue and energy availability.     

Calcium currents in normal and dystrophic human skeletal muscle cells in culture

Human muscle cells obtained from biopsy specimens were grown in a primary culture system and electrophysiologically studied. Whole cell patch-clamp recordings revealed the presence of two types of calcium currents: (i) a low-threshold (-60 mV) one (ICa, T) with fast activation and inactivation kinetics (time-to-peak: 39 ms at -30 mV); and (ii) a high-threshold (-10 mV) one (ICa,L) with slower kinetics (time-to-peak: 550 ms at 20 mV). These two types of calcium currents could be also distinguished by their pharmacological characteristics since ICa,L was sensitive to the antagonist and agonist dihydropyridine derivatives contrary to ICa,T which was completely resistant to these compounds. These functional calcium channels existed both in normal and Duchenne dystrophic (DMD) human skeletal muscle cells in culture. We discuss a possible role of these two types of calcium channels in the myoplasmic calcium accumulation observed in the Duchenne muscular dystrophy.     

Revealing threshold criteria of biostimulation for dye-laden wastewater treatment using immobilized cell systems

This study provides a first attempt from a process dynamic perspective to put forward, in general terms and explanations, threshold criteria of dye-laden wastewater treatment using immobilized cell systems (ICSs). Porites corals were selected as packing matrices of ICSs in demonstration of immobilized cell treatment for dye decolorization. With a staircase ramp input of dye in the inlet stream, significant losses of biodecolorization activity were gradually emerged when dye concentrations went over critical loadings for treatment. Design equations also disclosed that the decay rate constant decreased from infinity to a finite value directly caused an operation failure in ICS. According to mean value theorem, the proposed threshold criteria (e.g., maximal allowable treatment capacity) in ICSs could be determined by the method of a constant-slope isocline family, directly indicating treatment limits at various nutrient media in biostimulation.     

Effects of slip severity on muscle activation of the trailing leg during an unexpected slip

Falls and injuries due to falls are a major health concern, and accidental slips are a leading cause of falls during gait. Understanding how the body reacts to an unexpected slip can aid in developing intervention techniques to reduce the number of injuries due to falls. In this study, muscle activation patterns, specifically those of the trailing (non-slipping) limb, were studied in unexpected slips of 24 young and 24 middle-aged adults. The typical reaction of the trailing limb is swing phase interruption in an attempt to arrest the slip. Variables examined were the reactive muscle activation onset, peak electromyography (EMG) magnitude, and time-to-peak of the vastus lateralis and medial hamstring of the trailing limb. Statistical analysis was performed to determine the effects of slip severity, quantified by peak slip velocity, and age on outcome variables. As slip severity increased, the reactive activation onset of the medial hamstring was significantly faster and there was a trend approaching significance for the onset of the vastus lateralis. Additionally, the peak magnitude and time-to-peak of the vastus lateralis increased with slip severity. No significant effects of age were found on any of the output variables. These findings may aid in development of perturbation-based paradigms, as it may be possible to “tune” the postural control system to generate an appropriate response to unexpected slips.     

Reverse correlation analysis of the stretch response of primary muscle spindle afferent fibers

The nonlinear responses of deefferented primary muscle spindle afferent fibers to muscle stretching consisted of a train of action potentials which was analyzed when random changes in muscle length (band-limited gaussian white noise) were applied in cats. The upper cutoff frequency of the applied noise (the source stimulus) was varied between 1.6 and 570 Hz; the amplitude of the random input was varied between 0.002 and 1.2 mm. In a previous report the reverse correlation of 1st and 2nd order was studied for its ability to analyze data of a continuous input signal and pulsatile events in the output. Computations of the Wiener kernelsh ₁ andh ₂ or their equivalents, the perispike averages of the 1st and 2nd order, were computed from the random stretch responses of muscle-spindle afferents. Then the 1st- and the 2ndorder predictions and the summation of both to random muscle stretch was estimated. A general finding was that the 1st-order component was approximately 10 times that of the 2nd-order component, when both were combined in approximation procedures to give the closest prediction of observed responses to random test stimuli. The approximation was poor when the source stimulus was less than 0.03 mm and improved when it was greater. With the increase in the upper cutoff frequency of the random source input, the approximation worsened continuously. Predictions to ramp-and-hold stimuli were computed, as well as responses to random stimulation. Limiting the upper cutoff frequency did not diminish the value of the techniques applied.     

Comparison of three methods for beat-to-beat-interval extraction from continuous blood pressure and electrocardiogram with respect to heart rate variability analysis.

In recent years the analysis of heart rate variability (HRV) has become a suitable method for characterizing autonomous cardiovascular regulation. The aim of this study was to investigate the differences in HRV estimated from continuous blood pressure (BP) measurement by different methods in comparison to electrocardiogram (ECG) signals. The beat-to-beat intervals (BBI) were simultaneously extracted from the ECG and blood pressure of 9 cardiac patients (10 min, Colin system, 1000-Hz sampling frequency). For both data types, slope, peak, and correlation detection algorithms were applied. The short-term variability was calculated using concurrent 10-min BP and ECG segments. The root mean square errors in comparison to ECG slope detection were: 1.74 ms for ECG correlation detection; 5.42 ms for ECG peak detection; 5.45 ms for BP slope detection; 5.75 ms for BP correlation detection; and 11.96 ms for BP peak detection. Our results show that the variability obtained with ECG is the most reliable. Moreover, slope detection is superior to peak detection and slightly superior to correlation detection. In particular, for ECG signals with higher frequency characteristics, peak detection often exhibits more artificial variability. Besides measurement noise, respiratory modulation and pulse transit time play an important role in determining BBI. The slope detection method applied to ECG should be preferred, because it is more robust as regards morphological changes in the signals, as well as physiological properties. As the ECG is not recorded in most animal studies, distal pulse wave measurement in combination with correlation or slope detection may be considered an acceptable alternative.     

Linear and quadratic models of point process systems: Contributions of patterned input to output

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike.     

Cross bridge slippage in skinned frog muscle fibres

Mechanically skinned single fibres of the semitendinosus muscles of Rana esculenta were investigated at ca. 4 degrees C. The fibres were activated by a Ca2+ jump technique, which allowed the development of a steady isometric tension within several seconds of entering a calcium rich solution at 4 degrees C. Sequences of length changes of different duration and amplitude were applied to the fibre. It could be demonstrated that the fibre behaved as a Hookean spring in the case of small amplitude length changes (up to 0.5% L0, ramp duration 0.5 ms) and that a sequence of length changes induced reversible changes in fibre state. In contrast, large stretches (greater than 1% L0) induced a muscle "give" if the stretch were not immediately preceded by a release. The data was interpreted on the basis of a strain induced detachment of cross bridges in combination with a rapid reattachment of presumably the same cross bridges in a discharged position. The rates of strain induced detachment and reattachment depended on the stretch amplitude. At amplitudes exceeding 2% L0 the rates were estimated to be at least several thousands per second.     

Time domain analysis of oxygen uptake during pseudorandom binary sequence exercise tests.

Pseudorandom binary sequence (PRBS) exercise tests involve repeated switching between two work rates (WR) according to a computer-generated pattern. This paper presents an approach to analysis of O2 uptake (VO2) in the time domain. First, the autocorrelation function (ACF) of the input WR was recognized to be a triangular-shaped pulse that can be taken to be equivalent to a ramp increase followed by a ramp decrease in WR. Then the cross-correlation function of the input (WR) and the output (VO2) was treated as if it were the response to a triangular-shaped pulse. The cross-correlation function was analyzed by fitting a linear summation of the ramp form of a two-component exponential function to this triangular pulse. VO2 responses of eight subjects were obtained from two different PRBS tests, as well as step changes in WR. The first PRBS test consisted of 15 units, each 30 s in duration. Its ACF had a base width of 60 s. The ramp increase-ramp decrease model fit the data throughout the range of response. The second PRBS test had 63 units, each 5 s in duration; thus its ACF base width was 10 s. Again, the ramp model fit adequately. The data from the second PRBS test could be fit by the impulse form of the two-component exponential equation, although the fit in the first 30 s tended to be poorer. The time constants of VO2 dynamics estimated from step and PRBS tests were not significantly different. PRBS tests can be analyzed in the time domain, and the indicators of system dynamics reflect physiological properties similar to those investigated during step changes in WR.     

Use of ultrasound to make noninvasive in vivo measurement of continuous changes in human muscle contractile length.

Continuous measurement of contractile length has been traditionally achieved using animal preparations in which the muscle and tendon are exposed. More modern methods, e.g., sonomicroscopy, are still invasive. There is a widely perceived need for a noninvasive, in vivo method of measuring continuous changes of human muscle contractile length. Ultrasonography has been used for several years to measure relatively static, discrete changes in tendon, aponeurosis, and muscle fascicle length. We have recently developed this technique to continuously track changes in muscle contractile length during quiet standing. Here, we present the tracking algorithm and use externally applied perturbations to establish the spatial and temporal resolution of the technique. Subjects maintained a low level of ankle torque while a pneumatic actuator applied rapid, square-pulse ankle rotations of defined magnitude and 0.2-s duration. Tracked changes in gastrocnemius and soleus contractile length follow the temporal profile of the perturbations and scale progressively (5-400 microm) with the size of the ankle rotation (0.03-0.7 degrees ). In a second experiment, we tracked a wire oscillating in water with known peak to peak amplitudes of 1.5 microm to 8 mm. The ultrasound tracking procedure had near 100% accuracy at all amplitudes for frequencies up to 3 Hz and showed attenuation at higher frequencies consistent with an effective sampling frequency of 12 Hz and sampling time of 80 ms. This noninvasive technique is sensitive, without averaging, to changes as small as 1 microm and is suitable for observing neuromotor activity in posture and locomotion.     

Caffeine and length dependence of staircase potentiation in skeletal muscle

Skeletal muscle sensitivity to Ca2+ is greater at long lengths, and this results in an optimal length for twitch contractions that is longer than optimal length for tetanic contractions. Caffeine abolishes this length dependence of Ca2+ sensitivity. Muscle length (ML) also affects the degree of staircase potentiation. Since staircase potentiation is apparently caused by an increased Ca2+ sensitivity of the myofilaments, we tested the hypothesis that caffeine depresses the length dependence of staircase potentiation. In situ isometric twitch contractions of rat gastrocnemius muscle before and after 10 s of 10-Hz stimulation were analyzed at seven different lengths to evaluate the length dependence of staircase potentiation. In the absence of caffeine, length dependence of Ca2+ sensitivity was observed, and the degree of potentiation after 10-Hz stimulation showed a linear decrease with increased length (DT = 1.47 - 0.05 ML, r2 = 0.95, where DT is developed tension). Length dependence of Ca2+ sensitivity was decreased by caffeine when caffeine was administered in amounts estimated to result in 0.5 and 0.75 mM concentrations. Furthermore, the negative slope of the relationship between staircase potentiation and muscle length was diminished at the lower caffeine dose, and the slope was not different from zero after the higher dose (DT = 1.53 - 0.009 ML, r2 = 0.43). Our study shows that length dependence of Ca2+ sensitivity in intact skeletal muscle is diminished by caffeine. Caffeine also suppressed the length dependence of staircase potentiation, suggesting that the mechanism of this length dependence may be closely related to the mechanism for length dependence of Ca2+ sensitivity.     

A quantitative method for the detection of edges in noisy time-series

A modification of the edge detector of Chung & Kennedy is proposed in which the output provides confidence limits for the presence or absence of sharp edges (steps) in the input waveform. Their switching method with forward and backward averaging windows is retained, but the output approximates an ideal output function equal to the difference in these averages divided by the standard deviation of the noise. Steps are associated with peak output above a pre-set threshold. Formulae for the efficiency and reliability of this ideal detector are derived for input waveforms with Gaussian white noise and sharp edges, and serve as benchmarks for the switching edge detector. Efficiency is kept high if the threshold is a fixed fraction of the step size of interest relative to noise, and reliability is improved by increasing the window width W to reduce false output. For different steps sizes D, the window width for fixed efficiency and reliability scales as 1/D2. Versions with weighted averaging (flat, ramp, triangular) or median averaging but the same window width perform similarly. Binned above-threshold output is used to predict the locations and signs of detected steps, and simulations show that efficiency and reliability are close to ideal. Location times are accurate to order square root of W. Short pulses generate reduced output if the number of data points in the pulse is less than W. They are optimally detected by choosing W as above and collecting data at a rate such that the pulse contains approximately W data points. A Fortran program is supplied.     

The effects of β motor stimulation on the interpretation of signals from muscle spindles

A previously proposed method for the interpretation of the signals in sensory nerve fibres is extended to incorporate activation of muscle spindles. Simulations, based on previous experimental observations, of muscle spondles subjected to ramp and hold stretches are used as input to an interpreter, where the simulated trains of action potentials are reconverted to a length change interpretation. The interpreted signals are compared with the original length change inputs to observe the effects of -stimulation and stochastic variability.