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ENVIRONMENTAL, EXERCISE AND RESPIRATORY PHYSIOLOGY

Chemical activation of pre-Bötzinger complex in vivo reduces respiratory network complexity

Departments of ¹Biomedical Engineering and ²Physiology and Biophysics, State University of New York at Stony Brook

Submitted 22 September 2004 ; accepted in final form 6 January 2005

	ABSTRACT

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In the in vivo anesthetized adult cat model, multiple patterns of inspiratory motor discharge have been recorded in response to chemical stimulation and focal hypoxia of the pre-Bötzinger complex (pre-BötC), suggesting that this region may participate in the generation of complex respiratory dynamics. The complexity of a signal can be quantified using approximate entropy (ApEn) and multiscale entropy (MSEn) methods, both of which measure the regularity (orderliness) in a time series, with the latter method taking into consideration temporal fluctuations in the underlying dynamics. The current investigation was undertaken to examine the effects of pre-BötC-induced excitation of phasic phrenic nerve discharge, which is characterized by high-amplitude, rapid-rate-of-rise, short-duration bursts, on the complexity of the central inspiratory neural controller in the vagotomized, chloralose-anesthetized adult cat model. To assess inspiratory neural network complexity, we calculated the ApEn and MSEn of phrenic nerve bursts during eupneic (basal) discharge and during pre-BötC-induced excitation of phasic inspiratory bursts. Chemical stimulation of the pre-BötC using DL-homocysteic acid (DLH; 10 mM; 10–20 nl; n = 10) significantly reduced the ApEn from 0.982 ± 0.066 (mean ± SE) to 0.664 ± 0.067 (P < 0.001) followed by recovery (1–2 min after DLH) of the ApEn to 1.014 ± 0.067; a slightly enhanced magnitude reduction in MSEn was observed. Focal pre-BötC hypoxia (induced by sodium cyanide; NaCN; 1 mM; 20 nl; n = 2) also elicited a reduction in both ApEn and MSEn, similar to those observed for the DLH-induced response. These observations demonstrate that activation of the pre-BötC reduces inspiratory network complexity, suggesting a role for the pre-BötC in regulation of complex respiratory dynamics.

approximate entropy; network dynamics; inspiratory motor discharge; control of breathing

In the in vivo anesthetized adult cat model, multiple patterns of inspiratory motor discharge have been recorded in response to chemical stimulation and focal hypoxia of the pre-BötC (50, 52, 53), suggesting that this region may participate in the generation of complex respiratory dynamics. The complexity of a signal can be quantified using approximate entropy (ApEn), a statistical index that measures the regularity (orderliness) in a time series (36, 40), thus providing a nonlinear measure for studying the dynamics of complex physiological signals, such as heart rate variability (e.g., 24, 27, 28, 36–38, 40, 46), endocrine function (14, 39, 41, 54), and respiration (4, 11–13, 23, 57). Higher values of ApEn are associated with irregularity and greater randomness and thus reflect less system order (i.e., disorder) or higher system complexity. Conversely, lower values of ApEn are associated with a higher degree of regularity and predictability and thus reflect a more ordered system or lower system complexity. The ApEn method is robust, and it has been used to estimate the complexity of a signal with as few as 100 data points, as well as signals that are corrupted by noise [providing that the threshold (r) is set correctly] or signals that contain spurious large or small artifacts and/or outliers (10, 40). Furthermore, it can be used to analyze signals that are deterministic chaos or stochastic, as well as signals that exhibit a combination of these two behaviors (40). Thus ApEn appears to be well suited for application to experimental data that are often short in data length, corrupted with noise, and in many cases, contain underlying dynamics that may exhibit both deterministic and stochastic behaviors.

The measure of ApEn, however, is based on a single-scale, and therefore, it does not take into account temporal fluctuations in the underlying dynamics, which are inherent in physiological control systems. To overcome this limitation, multiscale entropy (MSEn), which is based on the application of ApEn (or sample entropy, 46) for different timescales, has been recently introduced (22); this new method provides measures of both variation and entropy. To compute MSEn, consecutive coarse-grained sequences, determined by the scale factor (), are constructed from a time series signal, such that the length of each coarse-grained sequence represents the length of the original time series divided by . This is equivalent to smoothing and decimation of the original time series sequence; thus the MSEn approach is essentially a graded low-pass filter with greater smoothing with increasing scales. For a scale factor of 1, the time series is simply the original time series, which effectively yields the value of ApEn.

Although both chemical-induced activation and focal hypoxia of the pre-BötC can produce a marked excitation of phasic phrenic nerve discharge, which is characterized by high-amplitude, rapid-rate-of-rise, short-duration bursts, our previous studies have only assessed the timing (i.e., T_I, T_E) and patterning (i.e., amplitude, rate of rise) characteristics associated with this type of modulation, and therefore, provide no insight into the underlying dynamics contained within the phrenic motor bursts. It, therefore, remains to be determined whether the underlying dynamics contained within the inspiratory (phrenic) discharges are altered under these conditions. Thus the current investigation was undertaken to examine the effects of this pre-BötC-mediated modulation of inspiratory motor discharge on the complexity of the central inspiratory neural controller. We hypothesized that chemical stimulation of the pre-BötC would reduce inspiratory network complexity and that a similar modulation would be elicited by focal hypoxia in this region. To test this hypothesis, we calculated the ApEn and MSEn of phrenic nerve bursts during eupneic (basal) discharge and during pre-BötC-mediated excitation of phasic inspiratory bursts.

	METHODS

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General methods. All data were obtained from chloralose-anesthetized adult cats under protocols approved by the Institutional Animal Care and Use Committee at the State University of New York at Stony Brook in compliance with the Animal Welfare Act and in accordance with The American Physiological Society's "Guiding Principles for Research Involving Animals and Human Beings" (7). Detailed descriptions of the general methods have been published previously (52, 53).

In brief, anesthesia was induced in adult cats (3.0–4.8 kg) with halothane (5%) in oxygen and maintained with intravenous -chloralose (initial 35–50 mg/kg; supplemental 3–5 mg/kg). The adequacy of anesthesia was regularly verified by absence of a withdrawal reflex (in the unparalyzed state) or blood pressure response (during muscular paralysis) to a noxious paw pinch. If the cat withdrew its limb during the absence of paralysis or if an increase in blood pressure was evoked, additional anesthesia was given. The right brachial vein and both brachial arteries were cannulated for administration of drugs, measurement of arterial blood pressure (Statham transducer, P23XL), and sampling of arterial blood. The trachea was cannulated, the cat was vagotomized bilaterally, and the lungs were mechanically ventilated with 40% O₂ in a balance of N₂. Bilateral pneumothoraces were established and the expiratory outlet of the ventilator was placed under 2–3 cm H₂O to prevent collapse of the lungs during expiration. The cat was then paralyzed with vecuronium bromide (0.2–0.4 mg/kg iv), supplemented as needed. The dorsal surface of the brainstem was exposed, and the C₅ rootlet of one or both phrenic nerves was isolated for recording. Raw phrenic nerve discharge was amplified (x10,000), notch-filtered at 60 Hz, and analog-filtered to pass frequencies between 1 Hz and 500 Hz. The filtered signal was rectified, and a moving average was obtained using a third-order Paynter filter with a 100-ms time constant.

Data acquisition and analyses. We calculated the ApEn and MSEn of phrenic nerve bursts during eupneic (basal) discharge and during pre-BötC-mediated chemical-induced excitation of phasic inspiratory bursts. For these experiments, only pre-BötC sites in which unilateral microinjection of DL-homocysteic acid (DLH; 10 mM; 20 nl; n = 10) (Fig. 1) or sodium cyanide (NaCN; 1 mM; 20 nl; n = 2) produced a rapid series of high-amplitude, rapid-rate-of-rise, short-duration phrenic bursts under hyperoxic, normocapnic conditions were selected. All sites in the pre-BötC were initially localized using predetermined stereotaxic coordinates relative to the calamus scriptorius, functionally identified using DLH, and histologically confirmed after completion of the experiment as previously described (52, 53).

View larger version (42K): [in this window] [in a new window]   Fig. 1. A: example showing a rapid series of high-amplitude, short-duration phasic phrenic bursts elicited by microinjection of DL-homocysteic acid (DLH) into the pre-Bötzinger complex (pre-BötC). B: patterning and timing characteristics for phrenic burst data associated with the example in A. Data provided correspond to burst-to-burst amplitude (B1), rate of rise (B2), inspiratory duration (TI) (B3), and expiratory duration (TE) (B4) along with the coefficient of variation (CV) for baseline (BL), DLH-induced, and recovery (Rec) conditions. Note: This trace corresponds to data presented in Figs. 2 and 5.

The calculation of ApEn requires a priori specification of the parameters m, the embedding dimension, and r, the tolerance (threshold) level (which is in effect a noise filter). The value of m can be estimated using the first minimum value of the nonlinear correlation function called average mutual information and subsequent use of the false nearest neighbor approach (1); however, theoretical and varied clinical applications have shown that either m = 1 or 2 and r between 0.1 and 0.25 of the standard deviation (SD) of the data provide good statistical validity of ApEn. For our analysis, we used m = 2 and r = 0.1 SD values, which were determined from a series of simulation experiments and preliminary analyses of our baseline phrenic nerve discharge data. ApEn was calculated as follows (36, 40):

where X(i), X(j) are vectors defined by X(i) = [u(i), u(i + 1), ...,u(i + m – 1)] and X(j) = [u(j), u(j + 1), ..., u(j + m – 1)] from the original time series u(1), u(2), ..., u(N).

Because ApEn depends on the differences between the current m and the next m + 1 embedding dimension, no information is provided about feature patterns on scales other than the scale of 1. To overcome this limitation and evaluate the temporal variability in the underlying dynamics, we used the measure of MSEn, which is based on a simple modification of the ApEn method. For these analyses, MSEn was calculated from the original time series u(1), u(2), ..., u(N) by constructing consecutive coarse-grained time series, w₁, w₂,..., w_N/n, determined by the scale factor , according to the following equation:

Thus the vector W⁽⁾, for any , can then be quantified by the ApEn method. For our analyses, we used up to 20 scales (), and the evaluation of all of the selected was defined as MSEn, with the following relationship: MSEn() = ApEn(W⁽⁾).

For all experiments, ApEn and MSEn of the total inspiratory burst, as well as the 1st half and 2nd half, were examined to characterize the complexity of the central inspiratory network underlying inspiratory motor output, including those associated with generation of early vs. late portions of the inspiratory burst. In addition, we evaluated how much of the inspiratory burst is required to capture the dynamics underlying central inspiratory network complexity. For these analyses, we examined the effects of successive 10% reductions in inspiratory duration (T_I), from the beginning, as well as from the end of the burst (i.e., forward and backward reductions), on ApEn using data obtained during both basal and DLH-induced excitation of phrenic nerve discharge. Finally, because previous studies, predominantly examining heart rate variability, have reported that the ApEn method is fairly insensitive to the number of data points in a time series, as long as there are at least 100 data points (40), we also evaluated the effects of down-sampling the original data set on ApEn of the total inspiratory burst during basal and DLH-induced excitation. For these analyses, the original digitally band pass-filtered data were down-sampled by a factor of 2, 4, and 8 to yield sampling rates of 1 kHz, 500 Hz, and 250 Hz, respectively.

For all analyses, values for ApEn were determined for individual phrenic bursts, and summary data were calculated as an ensemble average derived from analyses of 10 phrenic bursts under baseline conditions and following chemical stimulation of the pre-BötC, as well as during recovery from the effects of chemical stimulation; these summary data are reported as means ± SE. Values for MSEn were determined for individual experiments as an ensemble average derived from analyses of 10 phrenic bursts under baseline conditions and after chemical stimulation of the pre-BötC, as well as during recovery from the effects of chemical stimulation; these data are reported as means ± SD. Summary data for values of MSEn were calculated as an average derived from the analyses of all of the individual DLH experiments, and these data are reported as means ± SE. For ApEn, statistical significance was evaluated using one-way ANOVA with repeated measures, followed by Bonferroni post hoc analyses for multiple comparisons. In addition, correlation analyses between ApEn and phrenic burst amplitude, rate of rise, and inspiratory duration (T_I) were conducted on a burst-to-burst basis. For MSEn, statistical significance was initially evaluated using one-way ANOVA with repeated measures, followed by Dunnett's post hoc analyses for comparisons to scale factor = 1. Once a significant scale factor was identified under baseline, DLH, and recovery conditions, statistical significance was evaluated using one-way ANOVA with repeated measures, followed by Bonferroni post hoc analyses for comparisons among these conditions. For determination of the inspiratory burst duration required to fully capture the dynamics underlying central inspiratory network complexity, statistical significance was evaluated using one-way ANOVA with repeated measures, followed by Dunnett's post hoc analyses for comparisons to the total inspiratory burst. Finally, statistical significance for the effects of down-sampling on ApEn were evaluated using two-way ANOVA with repeated measures, followed by Dunnett's or Bonferroni post hoc analyses for multiple comparisons. The criterion level for determination of statistical significance was set at P < 0.05 for all experiments.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
ApEn of pre-BötC-mediated chemical-induced excitation of phasic phrenic bursts. In the current investigation, we examined the ApEn of inspiratory motor discharge recorded during baseline conditions and in response to pre-BötC-mediated chemical-induced excitation of phasic phrenic nerve discharge in the in vivo anesthetized adult cat model. For our analyses, only DLH- and NaCN-induced elicitation of a rapid series of high-amplitude, rapid-rate-of-rise, short-duration phrenic bursts were studied; an example showing a representative response to unilateral microinjection of DLH into the pre-BötC on phasic phrenic nerve discharge is provided in Fig. 1 (similar modulation was evoked by unilateral microinjection of NaCN into this region; not shown). The quantitative details associated with these patterning and timing changes (e.g., burst amplitude, burst frequency, T_I, T_E, rate of rise) have been characterized in our previous investigations (50, 52, 53) and will not be summarized again here. Included in Fig. 1B1, however, are the patterning and timing characteristics elicited in response to DLH-induced activation of the pre-BötC on a burst-to-burst basis for the experiment presented in panel A. These data are included to demonstrate the degree of variability (coefficient of variation, CV) in the time series data. As can be seen in Fig. 1B1, the magnitude of variability associated with these burst-to-burst patterning and timing variables is small during basal phrenic nerve discharge (i.e., CV 4%, except T_E), and there is a slight reduction in the magnitude of variability (smaller CV) for the DLH-induced high-amplitude bursts and an enhancement in the magnitude of variability (larger CV) for the DLH-induced rate of rise, T_I, and T_E. Correlation analysis between these individual patterning and timing variables and ApEn for both the eupneic and the DLH-induced modified burst patterns (on a burst-to-burst basis) demonstrates that these variables are poorly correlated with ApEn (amplitude, R² < 0.12; rate of rise, R² < 0.14; T_I, R² < 0.08; T_E, not examined), suggesting that even though the patterning and timing characteristics are markedly altered during the DLH-induced modified phrenic bursts, these indexes alone do not directly provide insight into the underlying dynamics contained within the inspiratory burst. Thus we evaluated the ApEn associated with the total inspiratory burst, as well as the 1st half and the 2nd half of the inspiratory burst to provide insight into the complexity of the central neural network generating inspiratory motor output, including the network characteristics associated with early vs. late portions of inspiratory bursts, exhibiting both eupneic and high-amplitude, rapid-rate-of-rise, short-duration burst patterns.

In conjunction with the shift from an augmenting pattern of phrenic nerve discharge, which was observed under baseline conditions, to the high-amplitude, rapid-rate-of-rise, short-duration phrenic bursts elicited by unilateral microinjection of DLH or NaCN into the pre-BötC, there was a marked reduction in ApEn. This decrease in ApEn was maintained throughout the duration of modified phrenic nerve discharge, and returned to (and in some cases, transiently exceeded) baseline values with recovery of phrenic nerve discharge back to the eupneic discharge pattern. Examples showing these burst-to-burst pre-BötC-mediated DLH- and NaCN-induced changes in ApEn are provided in Figs. 2 and 3, respectively, for the total inspiratory burst (Figs. 2A and 3A) and the 1st half and 2nd half of the inspiratory burst (Figs. 3B and 3B). It should be noted that the ApEn data provided in Fig. 2 correspond to the experimental observations shown in Fig. 1. In these examples, the ApEn values for the total inspiratory burst were reduced in response to microinjection of DLH and NaCN into the pre-BötC by 53% and 45%, respectively. A similar reduction in the magnitude of ApEn was observed for the 1st half vs. the 2nd half of the inspiratory burst, and little burst-to-burst variation was noted between the two halves of the inspiratory burst. The overall effect of DLH-induced activation of the pre-BötC on ApEn is summarized in Fig. 4A (total inspiratory burst) and Fig. 4B, (1st half and 2nd half of inspiratory burst) for all 10 experiments using DLH. In each of the experiments conducted, DLH-induced stimulation of this region significantly reduced ApEn, resulting in a decrease of 33% for the total inspiratory burst (P < 0.001) and 39% for both the 1st half and 2nd half of the inspiratory burst (P < 0.001). The reduction in ApEn returned to baseline levels within 1–2 min after DLH microinjection, and this corresponded to the return of the eupneic discharge pattern.

View larger version (21K): [in this window] [in a new window]   Fig. 2. Example demonstrating the effects of DLH-induced activation of the pre-BötC on ApEn of the phasic phrenic bursts. Microinjection of DLH into the pre-BötC elicited a reduction (54%) in ApEntotal (A) and ApEn1st () and ApEn2nd () (B) during the rapid series of DLH-induced high-amplitude, rapid-rate-of-rise, and short-duration phasic phrenic bursts.

View larger version (21K): [in this window] [in a new window]   Fig. 3. Example demonstrating the effects of NaCN-induced activation of the pre-BötC on ApEn of the phasic phrenic bursts. Microinjection of NaCN into the pre-BötC elicited a reduction (44%) in ApEntot (A) and ApEn1st () and ApEn2nd () (B) during the rapid series of DLH-induced high-amplitude, rapid-rate-of-rise, and short-duration phasic phrenic bursts.

View larger version (12K): [in this window] [in a new window]   Fig. 4. Summary data showing the effects of DLH-induced activation of the pre-BötC on ApEn of the phasic phrenic bursts. During the series of DLH-induced high-amplitude, rapid-rate-of-rise, and short-duration phasic phrenic bursts, ApEntotal (A) was reduced by 35% and ApEn1st and ApEn2nd (B) were reduced by 39%. Asterisks represent a statistically significant difference (P < 0.05) between the DLH-induced effect vs. the preinjection baseline (BL) and recovery values (Rec).

View larger version (39K): [in this window] [in a new window]   Fig. 5. Examples demonstrating the effects of DLH- and NaCN-induced activation of the pre-BötC on MSEn of the phasic phrenic bursts. A, B: microinjection of DLH (A) and NaCN (B) into the pre-BötC elicited a marked reduction in MSEntot (A1,B1), MSEn1st (A2, B2), and MSEn2nd (A3, B3); however, the values of MSEn were dependent on the scale factor, with the greatest effect being observed for baseline and recovery data. Further, the effect of increasing scale factor, which was observed for MSEntot, MSEn1st, and MSEn2nd, appeared to be slightly smaller (or delayed in onset) for MSEn2nd. Note. these data correspond to the same data shown in Figs. 2 and 3 for ApEn. Symbols: , DLH/NaCN; , baseline; , recovery. MSEntot, total inspiratory burst; MSEn1st, 1st half of the inspiratory burst; MSEn2nd, 2nd half of the inspiratory burst.

View larger version (36K): [in this window] [in a new window]   Fig. 6. Summary data showing the effects of DLH-induced activation of the pre-BötC on MSEn of the phasic phrenic bursts. A: microinjection of DLH into the pre-BötC elicited a marked reduction in MSEntot (A1), MSEn1st (A2), and MSEn2nd (A3), with the values of MSEn being dependent on the scale factor. For these data, increasing the scale factor to 2 significantly increased the value of MSEn (tot, 1st, and 2nd), with the greatest effects being observed on baseline and recovery values; significant effects for MSEn2nd after DLH microinjection into the pre-BötC were observed at scale 6. Symbols: , DLH; , baseline; , recovery. *P < 0.001 for MSEn at scale factor vs. scale 1. B: summary data demonstrating the effects of DLH-induced activation of the pre-BötC on MSEntot (B1), MSEn1st (B2), and MSEn2nd (B3) at scale factor 1 and the first significant scale factor under BL, DLH, and Rec conditions. MSEn was reduced during DLH-induced phasic phrenic bursts at all scale factors (including scale 1), but the magnitude of this reduction was enhanced at the first significant scale factor. , scale 1; , scale 2; , scale 6. Abbreviations same as in Fig. 5. *P < 0.001 for baseline and recovery vs. DLH-induced responses

View larger version (14K): [in this window] [in a new window]   Fig. 7. Example demonstrating the effects of successive 10% reductions in TI of the total inspiratory burst on ApEn during basal and DLH-induced excitation of phasic phrenic nerve discharge. Under baseline conditions (, backward reductions in TI; , forward reductions in TI), at least 60% of the inspiratory burst is required to fully capture the dynamics underlying network complexity, whereas during DLH-induced excitation of phasic phrenic bursts (, backward reductions in TI; triangles, forward reductions in TI), the extent of the burst required is dependent upon which end of the burst is eliminated. For elimination of successive 10% increments from the beginning and end of the burst, respectively, at least 50% and 80% of TI are required to fully capture the dynamics underlying network complexity. *P < 0.05 for percentage of burst vs. total burst for backward reductions; P < 0.05 for percentage of burst vs. total burst for forward reductions

View larger version (15K): [in this window] [in a new window]   Fig. 8. Example demonstrating the effects of down-sampling the original (digitally band pass filtered) data set on ApEn of the total inspiratory burst during basal and DLH-induced excitation of phasic phrenic nerve discharge. Down-sampling the original (2 kHz sampled) data under baseline conditions () significantly increased ApEn at all sampling intervals examined, with the highest value being observed when the data were down-sampled to 500 Hz. In contrast, during DLH-induced excitation of phasic phrenic bursts (), the highest value of ApEn was observed when the data were down-sampled to 1 kHz, and further down-sampling to 250 Hz significantly reduced ApEn. Further, the ApEn was significantly reduced during the DLH-induced modified phasic phrenic bursts compared with baseline bursts at each sampling interval, except the original 2 kHz sampling rate. *P < 0.001 for baseline vs. DLH-induced phasic phrenic bursts at sampling interval indicated; top (baseline data) and bottom (DLH data) brackets denote P < 0.001 for sampling interval pairs indicated.

	DISCUSSION

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Basal discharge vs. pre-BötC-induced modified phasic phrenic bursts. The findings of the current investigation suggest that the central inspiratory neural network generating the high-amplitude, rapid-rate-of-rise, short-duration phrenic bursts is a less complex network than that producing the eupneic pattern of phrenic nerve discharge. Thus, based on the ApEn and MSEn values calculated, the eupneic pattern of discharge, which is associated with higher values of ApEn and MSEn, reflects an inspiratory neural network with a higher degree of irregularity or greater randomness, while the modified inspiratory burst pattern, which is associated with lower values of ApEn and MSEn, reflects an inspiratory neural network with a higher degree of regularity and predictability. Further, on the basis of the measure of MSEn, the lower entropy values obtained during the modified inspiratory burst pattern are accompanied by lower temporal variability than that seen during the eupneic pattern of discharge. From these observations, we suggest that DLH- and NaCN-induced activation of the pre-BötC reconfigures the inspiratory neural network, resulting in a shift from the eupneic pattern of inspiratory motor discharge to the high-amplitude, rapid-rate-of-rise, short-duration inspiratory motor discharge pattern and that the "less complex network," which produces this modified inspiratory burst pattern, exhibits a higher degree of order or synchrony among the inspiratory brainstem neurons that are responsible for the patterning of inspiratory motor discharge. Consistent with this behavior are preliminary observations from our laboratory demonstrating that high-frequency oscillations (HFO), which serve as an index of short-timescale inspiratory phase synchronization proposed to be generated by medullary inspiratory neurons (17, 18, 20, 21), are enhanced during DLH- and NaCN-induced pre-BötC-mediated modified phasic phrenic bursts compared with HFO activity observed during the eupneic pattern of discharge (51). Our current data, however, do not exclude a potential contribution from phrenic motoneurons to the observed reduction in inspiratory network complexity. In addition, it should be noted that although the patterning changes associated with the DLH-induced modified inspiratory bursts were poorly correlated with ApEn, it is this "less complex network" that generates this modified burst pattern. Thus the patterning characteristics, which are related to the variance of the time series signal, are incorporated into the burst configuration, and therefore in the calculation of ApEn, the latter of which is invariant to the variance of the signal because it evaluates all of the underlying dynamics contained within the inspiratory burst.

In the current investigation, we set out to characterize not only the complexity of the inspiratory neural network generating the entire inspiratory motor burst but also the complexity of the inspiratory neural network generating early vs. late portions of the inspiratory burst. Since early vs. late portions of the inspiratory burst exhibit quite different patterning characteristics, it has become common practice to segment the inspiratory burst for evaluation and characterization of the dynamics underlying the inspiratory neural control system. Numerous studies examining the dynamics of spectral activity during the course of inspiration, for example, have compared the 1st half vs. the 2nd half of the inspiratory burst or smaller segments (e.g., 100 ms or 250 ms) of the inspiratory burst (8, 9, 17, 19, 21, 32, 44, 45, 47, 56) to better characterize differences in network activity underlying these various burst segments. In the current investigation, we compared the ApEn and MSEn of the 1st half vs. 2nd half of the inspiratory burst under baseline conditions and during the modified phasic phrenic bursts to evaluate the complexity of the inspiratory neural network responsible for generation of these early vs. late portions of these two inspiratory burst patterns. On the basis of the measure of ApEn, no differences between the early vs. late portions of the inspiratory burst under either baseline conditions or during the modified phasic phrenic bursts were identified, although the ApEn values for the 1st and 2nd halves of the inspiratory burst were lower than those observed for the total inspiratory burst. This observation suggests that the inspiratory neural network generating the 1st and 2nd halves of the inspiratory burst, although not different in the degree of complexity from each other, may be somewhat less complex than that generating the total inspiratory burst. In addition, in some cases, the magnitude of the reduction in ApEn in response to DLH- or NaCN-induced activation of the pre-BötC was slightly greater for the 1st and 2nd halves of the inspiratory burst compared with the total inspiratory burst. With respect to the MSEn method, some subtle differences between the 1st half vs. the 2nd half of the inspiratory burst were identified, as this method takes into consideration not only the entropy but also the temporal variability in the underlying dynamics (22). Thus, on the basis of the measure of MSEn, as the scale factor increased, a slightly smaller (or delayed onset) effect for the 2nd half of the inspiratory burst compared with the 1st half was observed, suggesting that the inspiratory neural network generating the inspiratory burst exhibits differential temporal variability in the underlying dynamics as the burst progresses.

Dynamics underlying inspiratory network complexity. In addition to the above observations, we have also demonstrated that to adequately capture the dynamics underlying the complexity of the central inspiratory neural controller, it is necessary to consider the extent or duration of the burst to be evaluated and the sampling rate used for data acquisition. Previous studies (focusing predominantly on heart rate variability) have suggested that to estimate the complexity or regularity of a signal, as few as 100 data points (range = 100–5,000) are adequate, as the ApEn method is fairly robust (10, 40). Thus most studies have relied on a specified number of data points (i.e., at least n = 100) for the assessment of ApEn of the signal of interest. As some signals, such as heart rate variability, exhibit relatively slow dynamics (6, 16, 29–31, 35), this approach may be adequate; however, for signals where the underlying dynamics are considerably faster and the sampling rates are therefore considerably higher, this approach may be limited. For our inspiratory burst data, for example, 100 data points correspond to 5–10% of the inspiratory burst; thus it is unlikely that the ApEn value associated with this segment of the burst would accurately reflect the complexity of the inspiratory neural network. In fact, segmenting the inspiratory burst by successive 10% reductions in T_I, revealed that at least 50–60% of the inspiratory burst must be included in the evaluation of ApEn to adequately capture the dynamics underlying inspiratory motor output and characterize the complexity of the inspiratory neural network. These successive 10% reductions in T_I, which were performed from both the beginning and end of the burst, also revealed differences in the network dynamics underlying the early vs. later portions of the DLH-induced, but not basal, phrenic bursts, suggesting that to adequately capture the dynamics of the DLH-induced modified inspiratory neural network, it may be necessary to include even a greater portion of the modified inspiratory burst in the evaluation of ApEn, although the duration to be included will depend upon whether the early vs. late portions of the burst are included. Thus, on the basis of the above observations, it appears that a more appropriate index to evaluate ApEn would be to utilize a specified burst duration (i.e., minimum of 60% of T_I) instead of a specified number of data points to adequately capture the dynamics underlying the inspiratory burst, assuming adherence to the Nyquist theorem.

Further, to adequately capture the dynamics underlying the inspiratory burst, it appears that the data must be sampled in accordance with the Nyquist theorem, as both oversampling and undersampling appear to negatively affect the measure of ApEn. It should be noted, however, that in our experiments, the parameters m and r were held constant for ApEn analyses, and as a result, they may not have been optimal for all sampling rates evaluated. Sampling in excess of the Nyquist theorem appears to be detrimental to the assessment of ApEn, presumably because it adds no new information in the additional data points. Although oversampling does not appear to be detrimental to other aspects of temporal or spectral analyses, in the current investigation, we found that oversampling may mask the real dynamics of the time series by diluting the calculated dynamics. In our experiments, evaluating the effects of down-sampling on ApEn, we found that down-sampling the inspiratory burst data obtained using the original 2-kHz sampling rate to 1 kHz or 500 Hz resulted in an increase in ApEn and that this effect was greater for the more complex signal seen during the basal eupneic pattern of inspiratory motor, as would be expected if the above explanation is correct. Additional support for this detrimental influence of oversampling on ApEn comes from our recent computer simulation experiments, in which we demonstrated that adding data points that contain no information (e.g., zero-padding) reduces the ApEn value (unpublished observations). It should also be noted that undersampling is also detrimental to the assessment of ApEn; however, this affect is presumably due to the inability to adequately capture the underlying dynamics because the low sampling rate does not accurately represent the underlying signal. Thus the sampling parameters used should be appropriate to adequately capture the underlying (fast) dynamics of inspiratory motor output, without oversampling or undersampling the signal. These observations in conjunction with those described above for burst duration suggest that it may be most appropriate to select a specified inspiratory burst duration, with the signal acquired at sampling rate in accordance with the Nyquist theorem, as opposed to selecting a specified number of data points (which is the general practice), for the evaluation of ApEn and network complexity in the inspiratory neural control system.

ApEn vs. MSEn. In the current investigation, two measures of entropy, ApEn and MSEn, were evaluated to characterize the complexity of the central inspiratory neural network generating the basal eupneic pattern of phrenic nerve discharge and the high-amplitude, rapid-rate-of-rise, short-duration phrenic burst pattern elicited by DLH- and NaCN-induced activation of the pre-BötC. The ApEn method was developed by Pincus (36) and introduced as a measure to quantify and describe the complexity of physiological signals in health and disease. This measure of complexity has been used since its introduction in numerous studies focusing on cardiac dynamics (e.g., 24, 27, 28, 36–38, 40, 46), and more recently in studies evaluating respiratory function (3–5, 11–13, 23, 57). For studies examining respiratory function, most have focused on breathing irregularity (i.e., ApEn of respiratory rate and/or tidal volume) among various patient populations [e.g., patients being weaned from mechanical ventilation (23); patients with panic disorder (13, 57); or during waking and various sleep stages (11, 12)], and they have demonstrated greater breathing irregularity (i.e., higher ApEn values) among patient populations vs. control subjects and more regular respiratory movements (i.e., lower ApEn values) during slow-wave (stage IV) sleep than during other stages of consciousness. Three recent studies, however, have focused on the complex dynamics underlying respiratory (phrenic nerve discharge) patterns, and have reported a reduction in respiratory network complexity (i.e., lower ApEn values) with maturation (albeit transient), severe hypoxia, and the early stages of reoxygenation (3–5). Although some of the above studies have suggested that the observed changes in ApEn arise from alterations in the brainstem respiratory neural controller, including the rhythm-generating network (3–5, 13) (although higher centers such as cortical and limbic areas that influence respiration could also exert an effect; Ref. 13, but see Ref . 2), none of these studies directly examined the influence of specific respiratory regions in the brainstem on respiratory network complexity. In the current investigation, we have shown that during pre-BötC-mediated excitation of phasic inspiratory bursts, the ApEn of phrenic nerve bursts is reduced, suggesting a role for this region in the regulation of complex respiratory dynamics; our results, however, provide no insight into the role of this region in the modulation of ApEn observed either in the patients described above or in response to severe hypoxia and reoxygenation during maturation.

Because complex dynamics typically exhibit feature patterns on multiple spatial and temporal scales, which are not taken into consideration by the ApEn method, Costa et al. (22) introduced the MSEn analysis method to overcome the limitations of conventional entropy (e.g., ApEn) calculations. They proposed that the MSEn method would provide a more meaningful assessment of the complexity of physiological dynamics than other entropy approaches because it could be used to quantify the regularity of the physiological signals of interest over multiple timescales. To demonstrate the robustness of the MSEn algorithm, they used this approach to identify differences in heartbeat intervals that were not revealed by the ApEn approach (presumably because it is based on single-scale analysis) between healthy subjects and congestive heart failure (CHF) and atrial fibrillation (AF) patients. On the basis of application of the MSEn method, they found that the AF patients exhibited the highest entropy values for a scale of one (which corresponds to ApEn) and that the lower entropy values corresponding to the healthy and CHF patients overlapped. By increasing the scale factor, the entropy value for the healthy subjects increased, while that of the AF patients fell to the level seen for the CHF patients, resulting in a significantly higher MSEn value for the healthy subjects compared with MSEn values for the AF and CHF patients. The differences in the MSEn values observed at the larger scale factors are consistent with the expected levels of complexity in the underlying physiological dynamics associated with cardiac interbeat intervals (22), as many pathological conditions lead to a loss of complexity in cardiac dynamics (22, 24, 37, 38, 40).

For the current investigation, comparison of the results obtained from the ApEn and MSEn approaches revealed that both entropy measures identified the primary change (i.e., reduction) in inspiratory neural network complexity in response to DLH- and NaCN-induced activation of the pre-BötC, which shifted the augmenting pattern of phrenic nerve discharge to the high-amplitude, rapid-rate-of-rise, short-duration phrenic burst pattern. This is not surprising since the measure of MSEn used in the current investigation was based on a simple modification of the ApEn method; however, the results from the MSEn approach, which were generally similar to those obtained using the ApEn method, did reveal a slightly greater reduction in MSEn between the basal discharge and the DLH- and NaCN-induced modified burst pattern, as well as a reduction in temporal variability during the modified bursts and a slightly smaller (or delayed onset) effect of scale factor for the 2nd half of the inspiratory burst compared with the 1st half. These differences, however, do not appear to be substantial enough to warrant the additional computation time required for the determination of MSEn; thus we believe that our results indicate that evaluation of ApEn alone may have been sufficient to characterize the effects of the pre-BötC-mediated modulation of inspiratory motor discharge on the complexity of the central inspiratory neural network.

Summary and conclusions. In summary, we have demonstrated that both DLH- and NaCN-induced activation of the pre-BötC reduce ApEn and MSEn, two statistical indexes used to represent the complexity of the central neural network generating inspiratory motor output. This reduction in network complexity was associated with the shift from the augmenting pattern of phrenic nerve discharge observed under baseline conditions to the high-amplitude, rapid-rate-of-rise, short-duration phrenic burst pattern elicited by these focal perturbations in the pre-BötC. Our observations further suggest that to adequately capture the dynamics underlying inspiratory motor discharge and the complexity of the inspiratory neural network, it is necessary to evaluate a sufficient duration of the inspiratory burst (e.g., minimum of 50–60% T_I) using appropriate sampling parameters instead of relying on a preset number of data points (e.g., n = 100–5,000) as suggested in previous studies (focusing predominantly cardiac dynamics). Thus our findings indicate that the pre-BötC, which is the primary locus for respiratory rhythm generation, may participate in the regulation of complex respiratory dynamics.

	GRANTS

TOP ABSTRACT METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
This work was supported by National Institutes of Health Grant HL-63175.

	FOOTNOTES

 

Address for reprint requests and other correspondence: I. C. Solomon, Dept. of Physiology and Biophysics, Basic Science Tower T6 Rm. 140, State Univ. of New York at Stony Brook, Stony Brook, NY 11794-8661 (E-mail: ICSolomon{at}physiology.pnb.sunysb.edu

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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