VO2 kinetics in subjects differing in aerobic capacity: investigation by spectral analysis

The power-VO2 transfer functions of 38 subjects differing in aerobic capacity have been determined on the basis of breath-by-breath total oxygen uptake (VO2,t) measurements during light cycle ergometer exercise (lactic acid concentrations below 2 mmol.l-1). At constant pedalling frequency (1 Hz) pseudorandom binary sequences (PRBS) of workload were used as the testing signal. The VO2,t response was analysed by autocorrelating the ergometer power input and crosscorrelating the power input and VO2,t output. From the spectra of these functions the amplitude ratios and phase relationships were computed for the first six harmonics of the PRBS fundamental (14 mrad X s-1). We found that differences in aerobic capacity are associated with significant differences in the amplitude plots of the VO2 transfer function.     

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.     

Frequency domain analysis of ventilation and gas exchange kinetics in hypoxic exercise.

The kinetics of O2 up-take (VO2), CO2 output (VCO2), ventilation (VE), and heart rate (HR) were studied during exercise in normoxia and hypoxia [inspired O2 fraction (FIO2) 0.14]. Eight male subjects each completed 6 on- and off-step transitions in work rate (WR) from low (25 W) to moderate (100-125 W) levels and a pseudorandom binary sequence (PRBS) exercise test in which WR was varied between the same WRs. Breath-by-breath data were linearly interpolated to yield 1-s values. After the first PRBS cycle had been omitted as a warm-up, five cycles were ensemble-averaged before frequency domain analysis by standard Fourier methods. The step data were fit by a two-component (three for HR) exponential model to estimate kinetic parameters. In the steady state of low and moderate WRs, each value of VO2, VCO2, VE, and HR was significantly greater during hypoxic than normoxic exercise (P less than 0.05) with the exception of VCO2 (low WR). Hypoxia slowed the kinetics of VO2 and HR in on- and off-step transitions and speeded up the kinetics of VCO2 and VE in the on-transition and of VE in the off-transition. Frequency domain analysis confined to the range of 0.003-0.019 Hz for the PRBS tests indicated reductions in amplitude and greater phase shifts in the hypoxic tests for VO2 and HR at specific frequencies, whereas amplitude tended to be greater with little change in phase shift for VCO2 and VE during hypoxic tests.(ABSTRACT TRUNCATED AT 250 WORDS)     

大鼠海马神经元对于高频脉冲刺激的暂态响应

闭环刺激是深部脑刺激(deep brain stimulation,DBS)的重要发展方向之一,有望用于治疗多种脑神经系统疾病.与常规开环的长时间持续刺激不同,闭环刺激通常采用短促的高频脉冲序列.而神经元对于高频刺激的响应存在暂态过程,在初期的短时间内会发生很大变化,从而影响闭环刺激的作用.为了研究这种暂态过程,在大鼠...     

Effect of beta-adrenergic blockade on VO2 kinetics during pseudorandom binary sequence exercise

The effect of beta-adrenergic blockade on the dynamic response characteristics of oxygen uptake (VO2) was examined in seven healthy men. Cycle ergometer exercise consisted of a pseudorandom binary sequence (PRBS) with 15 units per sequence, each unit lasting 15 s, for a total period of 225 s. Work rate was either 25 W or 125 W. Six identical sequences were performed continuously in a single exercise test. Each subject was studied on three occasions after 48 h treatment of placebo (CON); a nonselective beta-blocker, propranolol (PROP); and a beta 1-selective blocker, metoprolol (MET). VO2 was measured breath-by-breath. The data were analyzed in the frequency domain by Fourier analysis to yield amplitude and phase shift coefficients for the relationship between the input work rate and output VO2. Time domain analysis was performed on the cross-correlational analysis of VO2 (output).work rate (input) to determine the total lag time. The amplitude of the VO2.W-1 relationship was lower (P less than 0.0022) and the phase shift was greater (P less than 0.0039) with beta-blockade compared to CON; no differences were found between PROP and MET. The total lag time was longer (P less than 0.0053) in PROP (34.3 +/- 2.2 s) and MET (34.4 +/- 1.6 s) compared to CON (29.8 +/- 1.3 s). These data indicate that beta-adrenergic blockade causes a significant slowing of kinetics of the O2 transport system as determined by both frequency and time domain analysis. In addition, the PRBS exercise test is a sensitive indicator of change in function of the O2 transport system.     

Kinetics of ventilation and gas exchange during supine and upright cycle exercise.

The dynamics of ventilation (VE), oxygen uptake (VO2), carbon dioxide output (VCO2), and heart rate (fc) were studied in 12 healthy young men during upright and supine exercise. Responses to maximal and to two different types of submaximal exercise tests were contrasted. During incremental exercise to exhaustion, the maximal work rate, VO2max, VEmax, fc,max, and ventilatory threshold were all significantly reduced in supine compared to upright exercise (P less than 0.01-0.001). Following step increases or decreases in work rate between 25 W and 105 W, both VO2 and VCO2 responded more slowly in supine than upright exercise. Dynamics were also studied in two different pseudorandom binary-sequence (PRBS) exercise tests, with the work rate varying between 25 W and 105 W with either 5-s or 30-s durations of each PRBS unit. In both of these tests, there were no differences caused by body position in the amplitude or phase shifts obtained from Fourier analysis for any observed variable. These data show that the body position alters the dynamic response to the more traditional step increase in work rate, but not during PRBS exercise. It is speculated that the elevation of cardiac output observed with supine exercise in combination with the continuously varying work-rate pattern of the PRBS exercise allowed adequate, perhaps near steady-state, perfusion of the working muscles in these tests, whereas at the onset of a step increase in work rate, greater demands were placed on the mechanisms of blood flow redistribution.     

Effects of prior heavy exercise on VO(2) kinetics during heavy exercise are related to changes in muscle activity.

We hypothesized that the elevated primary O(2) uptake (VO(2)) amplitude during the second of two bouts of heavy cycle exercise would be accompanied by an increase in the integrated electromyogram (iEMG) measured from three leg muscles (gluteus maximus, vastus lateralis, and vastus medialis). Eight healthy men performed two 6-min bouts of heavy leg cycling (at 70% of the difference between the lactate threshold and peak VO(2)) separated by 12 min of recovery. The iEMG was measured throughout each exercise bout. The amplitude of the primary VO(2) response was increased after prior heavy leg exercise (from mean +/- SE 2.11 +/- 0.12 to 2.44 +/- 0.10 l/min, P < 0.05) with no change in the time constant of the primary response (from 21.7 +/- 2.3 to 25.2 +/- 3.3 s), and the amplitude of the VO(2) slow component was reduced (from 0.79 +/- 0.08 to 0.40 +/- 0.08 l/min, P < 0.05). The elevated primary VO(2) amplitude after leg cycling was accompanied by a 19% increase in the averaged iEMG of the three muscles in the first 2 min of exercise (491 +/- 108 vs. 604 +/- 151% increase above baseline values, P < 0.05), whereas mean power frequency was unchanged (80.1 +/- 0.9 vs. 80.6 +/- 1.0 Hz). The results of the present study indicate that the increased primary VO(2) amplitude observed during the second of two bouts of heavy exercise is related to a greater recruitment of motor units at the onset of exercise.     

Blood pressure power within frequency range approximately 0.4 Hz in rat conforms to self-similar scaling following spinal cord transection

This study quantified the effect of interrupting the descending input to the sympathetic preganglionic neurons on the dynamic behavior of arterial blood pressure (BP) in the unanesthetized rat. BP was recorded for approximately 4-h intervals in six rats in the neurally intact state and in the same animals after complete spinal cord transection (SCT) between T(4) and T(5). In the intact state, power within the frequency range of 0.35-0.45 Hz was 1.53 +/- 0.38 mmHg(2)/Hz (mean +/- SD by fast Fourier transform). One week after SCT, power within this range decreased significantly (P < 0.05) to 0.43 +/- 0.62 mmHg(2)/Hz. To test for self-similarity before and after SCT, we analyzed data using a wavelet (i.e., functionally, a digital bandpass filter) tuned to be maximally sensitive to fluctuations with periods of approximately 2, 4, 8, 16, 32, or 64 s. In the control state, all fluctuations with periods of >/=4 s conformed to a "self-similar" (i.e., fractal) distribution. In marked contrast, the oscillations with a period of approximately 2 s (i.e., approximately 0.4 Hz) were significantly set apart from those at lower frequencies. One day and seven days after the complete SCT, however, the BP fluctuations at approximately 0.4 Hz now also conformed to the same self-similar behavior characteristic of the lower frequencies. We conclude that 1) an intact sympathetic nervous system endows that portion of the power spectrum centered around approximately 0.4 Hz with properties (e.g., a periodicity) that differ significantly from the self-similar behavior that characterizes the lower frequencies and 2) even within the relatively high frequency range at 0.4 Hz self-similarity is the "default" condition after sympathetic influences have been eliminated.     

Dynamic characteristics of the human resonance EEG responses to rhythmic photostimulation

The development of the resonance EEG responses of the left and right occipital areas was studied in right-handed men during prolonged (12 or 120 s) rhythmic, photostimulation with the intensity of 0.7 J and frequencies of 6, 10, and 16 Hz. Analysis of the EEG fine spectral structure was applied to compare the accumulated baseline EEG spectra and EEG spectra during photostimulation, to observe the dynamics of the short-term spectra and to detect power changes in the EEG narrow spectral band sharply coincident with the stimulation frequency. The more pronounced EEG responses to photostimulation were observed in subjects with the initially low EEG baseline, α-rhythm. Two-minute flash trains produced a substantial increase in the EEG power within the stimulation frequency with superposed oscillatory processes with different periods. These fluctuations are considered a reflection of intricate interaction between the adaptive and resonance EEG responses to the presented intermittent stimulation. Under 12-s stimulation the resonance EEG responses are steadily recorded within the first 3 s of stimulation and immediately after the flash cessation EEG power at the stimulation frequency returns to the initial level. The resonance EEG responses were more pronounced in the right hemisphere than in the left one, especially, at the stimulation frequencies of 6 and 16 Hz. With increasing the stimulation frequency, the maximum of resonance EEG responses was reached earlier. Under the stimulation frequency of 6 Hz, the maximal response was recorded 9–12 s after the beginning of flashes, at the frequencies of 10 and 16 Hz, it was recorded within 3–6 and 3 s, respectively.     

Salamander morph frequencies do not evolve as predicted in response to 40 years of climate change

The global climate is changing rapidly, yet biotic responses remain uncertain. Most studies focus on changes in species ranges or plastic responses like phenology, but adaptive evolution could be equally important. Studying evolutionary responses is challenging given limited historical data and a poor understanding of genetically variable traits under selection. We take advantage of a historical dataset to test for an adaptive response to climate change in a widespread, polymorphic amphibian, the eastern red‐backed salamander Plethodon cinereus. We resurveyed color morph frequencies across New England to test for an adaptive shift in response to climate change. We modeled historical and present‐day morph proportions as a function of climate and tested the accuracy of predictions both within and across different time periods. Our models showed moderate accuracy when predicting morph frequencies within time periods, but poor accuracy across time periods. Despite substantial changes in climate and significant relationships between morph frequency and climate variables within periods, we found no evidence for the predicted shift in morph frequencies across New England. The relationship between climate and color morph frequencies is likely more complex than originally suggested, potentially involving the interplay of additional factors such as microclimate variation, land use changes, and frequency‐dependent selection. Model extrapolation and changes in the correlation structure of climate variables also likely contributed to poor predictive ability. Evolution could provide a means to moderate the effects of climate change on many species. However, we often do not understand the direct links between climate variation, traits, and fitness. Therefore, forecasting climate‐mediated evolution remains an ongoing and important challenge for understanding climate change threats to species.     

Modulation rate transfer functions in bottlenose dolphins (<Emphasis Type="Italic">Tursiops truncatus</Emphasis>) with normal hearing and high-frequency hearing loss

Envelope following responses were measured in two bottlenose dolphins in response to sinusoidal amplitude modulated tones with carrier frequencies from 20 to 60 kHz and modulation rates from 100 to 5,000 Hz. One subject had elevated hearing thresholds at higher frequencies, with threshold differences between subjects varying from ±4 dB at 20 and 30 kHz to +40 dB at 50 and 60 kHz. At each carrier frequency, evoked response amplitudes and phase angles were plotted with respect to modulation frequency to construct modulation rate transfer functions. Results showed that both subjects could follow the stimulus envelope components up to at least 2,000 Hz, regardless of carrier frequency. There were no substantial differences in modulation rate transfer functions for the two subjects suggesting that reductions in hearing sensitivity did not result in reduced temporal processing ability. In contrast to earlier studies, phase data showed group delays of approximately 3.5 ms across the tested frequency range, implying generation site(s) within the brainstem rather than the periphery at modulation rates from 100 to 1,600 Hz. This discrepancy is believed to be the result of undersampling of the modulation rate during previous phase measurements.     

Spontaneous fluctuations in cerebral blood flow: insights from extended-duration recordings in humans

To determine the dependence of cerebral blood flow (CBF) on arterial pressure over prolonged time periods, we measured beat-to-beat changes in mean CBF velocity in the middle cerebral artery (transcranial Doppler) and mean arterial pressure (Finapres) continuously for 2 h in six healthy subjects (5 men and 1 woman, 18-40 yr old) during supine rest. Fluctuations in velocity and pressure were quantified by the range [(peak - trough)/mean] and coefficients of variation (SD/mean) in the time domain and by spectral analysis in the frequency domain. Mean velocity and pressure over the 2-h recordings were 60 +/- 7 cm/s and 83 +/- 8 mmHg, associated with ranges of 77 +/- 8 and 89 +/- 10% and coefficients of variation of 9.3 +/- 2.2 and 7.9 +/- 2.3%, respectively. Spectral power of the velocity and pressure was predominantly distributed in the frequency range of 0.00014-0.1 Hz and increased inversely with frequency, indicating characteristics of an inverse power law (1/f(alpha)). However, linear regression on a log-log scale revealed that the slope of spectral power of pressure and velocity was steeper in the high-frequency (0.02-0.5 Hz) than in the low-frequency range (0.002-0.02 Hz), suggesting different regulatory mechanisms in these two frequency ranges. Furthermore, the spectral slope of pressure was significantly steeper than that of velocity in the low-frequency range, consistent with the low transfer function gain and low coherence estimated at these frequencies. We conclude that 1) long-term fluctuations in CBF velocity are prominent and similar to those observed in arterial pressure, 2) spectral power of CBF velocity reveals characteristics of 1/f(alpha), and 3) cerebral attenuation of oscillations in CBF velocity in response to changes in pressure may be more effective at low than that at high frequencies, emphasizing the frequency dependence of cerebral autoregulation.     

Effects of prior heavy exercise on phase II pulmonary oxygen uptake kinetics during heavy exercise.

We tested the hypothesis that heavy-exercise phase II oxygen uptake (VO(2)) kinetics could be speeded by prior heavy exercise. Ten subjects performed four protocols involving 6-min exercise bouts on a cycle ergometer separated by 6 min of recovery: 1) moderate followed by moderate exercise; 2) moderate followed by heavy exercise; 3) heavy followed by moderate exercise; and 4) heavy followed by heavy exercise. The VO(2) responses were modeled using two (moderate exercise) or three (heavy exercise) independent exponential terms. Neither moderate- nor heavy-intensity exercise had an effect on the VO(2) kinetic response to subsequent moderate exercise. Although heavy-intensity exercise significantly reduced the mean response time in the second heavy exercise bout (from 65.2 +/- 4.1 to 47.0 +/- 3.1 s; P < 0.05), it had no significant effect on either the amplitude or the time constant (from 23.9 +/- 1.9 to 25.3 +/- 2.9 s) of the VO(2) response in phase II. Instead, this "speeding" was due to a significant reduction in the amplitude of the VO(2) slow component. These results suggest phase II VO(2) kinetics are not speeded by prior heavy exercise.     

Dynamic relationship between sympathetic nerve activity and renal blood flow: a frequency domain approach

Blood pressure displays an oscillation at 0.1 Hz in humans that is well established to be due to oscillations in sympathetic nerve activity (SNA). However, the mechanisms that control the strength or frequency of this oscillation are poorly understood. The aim of the present study was to define the dynamic relationship between SNA and the vasculature. The sympathetic nerves to the kidney were electrically stimulated in six pentobarbital-sodium anesthetized rabbits, and the renal blood flow response was recorded. A pseudo-random binary sequence (PRBS) was applied to the renal nerves, which contains equal spectral power at frequencies in the range of interest (<1 Hz). Transfer function analysis revealed a complex system composed of low-pass filter characteristics but also with regions of constant gain. A model was developed that accounted for this relationship composed of a 2 zero/4 pole transfer function. Although the position of the poles and zeros varied among animals, the model structure was consistent. We also found the time delay between the stimulus and the RBF responses to be consistent among animals (mean 672 +/- 22 ms). We propose that the identification of the precise relationship between SNA and renal blood flow (RBF) is a fundamental and necessary step toward understanding the interaction between SNA and other physiological mediators of RBF.     

Dynamic baroreflex control of blood pressure: influence of the heart vs. peripheral resistance

The aim in the present experiments was to assess the dynamic baroreflex control of blood pressure, to develop an accurate mathematical model that represented this relationship, and to assess the role of dynamic changes in heart rate and stroke volume in giving rise to components of this response. Patterned electrical stimulation [pseudo-random binary sequence (PRBS)] was applied to the aortic depressor nerve (ADN) to produce changes in blood pressure under open-loop conditions in anesthetized rabbits. The stimulus provided constant power over the frequency range 0-0.5 Hz and revealed that the composite systems represented by the central nervous system, sympathetic activity, and vascular resistance responded as a second-order low-pass filter (corner frequency approximately 0.047 Hz) with a time delay (1.01 s). The gain between ADN and mean arterial pressure was reasonably constant before the corner frequency and then decreased with increasing frequency of stimulus. Although the heart rate was altered in response to the PRBS stimuli, we found that removal of the heart's ability to contribute to blood pressure variability by vagotomy and beta(1)-receptor blockade did not significantly alter the frequency response. We conclude that the contribution of the heart to the dynamic regulation of blood pressure is negligible in the rabbit. The consequences of this finding are examined with respect to low-frequency oscillations in blood pressure.     

Response of respiratory exchange ratio (R) to sinusoidal work load in humans

An examination was made of the response of respiratory exchange ratio (R), carbon dioxide output (VCO2) and oxygen uptake (VO2) to sinusoidal work load with periods (T) of 1-16 min in six healthy men to determine whether R response is sinusoidal. The influence of the ratio of the amplitude of VCO2 to that of VO2 and the phase lag between them on R response was also studied by computer simulation. The results and conclusions obtained are as follows: 1) With decrease in the period, the amplitudes of VO2 and VCO2 dropped exponentially, becoming least at T of 1 min (T = 1 min). In contrast, the amplitude of R was largest at T = 4 min and subsequently decreased progressively. 2) The peak amplitude of R at T = 4 min can be explained by the larger phase lag and relatively low of amplitude of VCO2 to VO2. 3) The smallest amplitude of R at T = 1 min was due not to the ratio of amplitude or phase lag, but to remarkably smaller amplitudes of VO2 and VCO2. 4) The phase lag of VO2 to sinusoidal work load was smaller than that of VCO2. Phase lag of R was considerably larger than that of VO2 or VCO2. 5) The response curve of VO2 and VCO2 is a sinusoidal curve with the same period as exercise. However, the response of R is not a real sinusoidal but a deformed biphasic curve with a high crest and low trough. The deformity is determined by the phase lag between VO2 and VCO2 response and also the ratio of amplitude of VCO2 to that of VO2.     

Kinetics of .VO2 and femoral artery blood flow during heavy-intensity, knee-extension exercise.

It has been suggested that, during heavy-intensity exercise, O(2) delivery may limit oxygen uptake (.VO2) kinetics; however, there are limited data regarding the relationship of blood flow and .VO2 kinetics for heavy-intensity exercise. The purpose was to determine the exercise on-transient time course of femoral artery blood flow (Q(leg)) in relation to .VO2 during heavy-intensity, single-leg, knee-extension exercise. Five young subjects performed five to eight repeats of heavy-intensity exercise with measures of breath-by-breath pulmonary .VO2 and Doppler ultrasound femoral artery mean blood velocity and vessel diameter. The phase 2 time frame for .VO2 and Q(leg) was isolated and fit with a monoexponent to characterize the amplitude and time course of the responses. Amplitude of the phase 3 response was also determined. The phase 2 time constant for .VO2 of 29.0 s and time constant for Q(leg) of 24.5 s were not different. The change (Delta) in .VO2 response to the end of phase 2 of 0.317 l/min was accompanied by a DeltaQ(leg) of 2.35 l/min, giving a DeltaQ(leg)-to-Delta.VO2 ratio of 7.4. A slow-component .VO2 of 0.098 l/min was accompanied by a further Q(leg) increase of 0.72 l/min (DeltaQ(leg)-to-Delta.VO2 ratio = 7.3). Thus the time course of Q(leg) was similar to that of muscle .VO2 (as measured by the phase 2 .VO2 kinetics), and throughout the on-transient the amplitude of the Q(leg) increase achieved (or exceeded) the Q(leg)-to-.VO2 ratio steady-state relationship (ratio approximately 4.9). Additionally, the .VO2 slow component was accompanied by a relatively large rise in Q(leg), with the increased O(2) delivery meeting the increased Vo(2). Thus, in heavy-intensity, single-leg, knee-extension exercise, the amplitude and kinetics of blood flow to the exercising limb appear to be closely linked to the .VO2 kinetics.     

Pupillenreaktionen auf sinusförmige Leuchtdichteänderungen

Summary Nonlinear properties of the human pupillary light reflex have been studied using binocular light stimuli of sinusoidally varying intensity. As reported earlier, the pupil responds with a net contraction to the modulation of the light intensity within a wide range of modulation frequencies. Results of the present experiments show that the net contraction does not depend upon the relative phase difference of the binocular light stimuli. However in the lower frequency range, where the in-phase stimuli result in a periodic light reflex, the out-of-phase stimuli fail to do so. These results allow certain conclusions to be drawn regarding the localisation within the photopupil reflex arc of the nonlinearities involved.     

Respiratory response to sinusoidal work load in humans

Present study was undertaken to elucidate possible distortion of phase response and amplitude response of various respiratory parameter such as VO2, VCO2 and VE to sinusoidal work load by comparing model analysis with manual analysis. Also, an attempt was made to determine whether there is any relationship between the characteristics of response of these parameters and the aerobic capacity of subjects. Six healthy male subjects were performed exercise on an electrically braked bicycle ergometer for 32 min. The work load was varied sinusoidally between 30 watts and 60% VO2max being under anaerobic threshold with periods from 1 to 16 min. These parameters were determined in breath-by-breath mode with a computer system and mass spectrometer. In model analysis, amplitude and phase responses were well described by first order exponential model, and strong correlations were observed between magnitude of phase response or time constant of amplitude response and aerobic capacity. Manual analysis revealed that respiratory responses to sinusoidal work load are not completely sinusoidal but somewhat distorted forming saw-tooth waves with steeper downslopes.     

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (g_NaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear?+?quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.