Quantitative analysis of cardiovascular modulation in respiratory neural activity

Abstract

We propose the ‘δ²-statistic’ for assessing the magnitude and statistical significance of arterial pulse-modulated activity of single neurones and present the results of applying this tool to medullary respiratory-modulated units. This analytical tool is a modification of the η²-statistic and, consequently, based on the analysis of variance. The η²-statistic reflects the consistency of respiratory-modulated activity on a cycle-by-cycle basis. However, directly applying this test to activity during the cardiac cycle proved ineffective because subjects-by-treatments matrices did not contain enough ‘information’. We increased information by dividing the cardiac cycle into fewer bins, excluding cycles without activity and summing activity over multiple cycles. The analysed neuronal activity was an existing data set examining the neural control of respiration and cough. Neurones were recorded in the nuclei of the solitary tracts, and in the rostral and caudal ventral respiratory groups of decerebrate, neuromuscularly blocked, ventilated cats (n= 19). Two hundred of 246 spike trains were respiratory modulated; of these 53% were inspiratory (I), 36.5% expiratory (E), 6% IE phase spanning and 4.5% EI phase spanning and responsive to airway stimulation. Nearly half (n= 96/200) of the respiratory-modulated units were significantly pulse modulated and 13 were highly modulated with δ² values exceeding 0.3. In 10 of these highly modulated units, η² values were greater than 0.3 and all 13 had, at least, a portion of their activity during expiration. We conclude that cardiorespiratory interaction is reciprocal; in addition to respiratory-modulated activity in a subset of neuronal activity patterns controlling the cardiovascular system, pulse-modulated activity exists in a subset of neuronal activity patterns controlling the respiratory system. Thus, cardio-ventilatory coupling apparent in respiratory motor output is evident and, perhaps, derived from the neural substrate driving that output.

A statistical tool is not available to characterize the magnitude and statistical significance of cardiac cycle modulated activity of single neurones even though this activity can appear modulated in cardiac cycle-triggered histograms (cCTHs). Generally, cardiovascular control neurones are barosensitive, in that their activity varies with blood pressure. The discharge frequency of these neurones changes with arterial pulse. Cardiac CTHs use the sharp rise in pulse pressure as a reference point to increase the signal-to-noise ratio of activity that is time-locked to the cardiac cycle. Barosensitive activity sums progressively from beat to beat whereas non-modulated activity distributes itself evenly across the cycle.

Even though CTHs are useful in data analysis, they are not a statistical tool because the consistency of activity is assumed and not quantified (Netick & Orem, 1981; Orem & Netick, 1982). CTHs present a picture of total or average activity and not the cycle-to-cycle variability of the pattern. Episodic bursts of activity distort CTHs and may even give them an appearance of being modulated. While consistency and signal strength are related, they are distinct features of an activity pattern. Conclusions regarding signal strength based on CTHs assume consistency that may not exist.

A subjects-by-treatments analysis of variance (ANOVA) can be applied to test significance of the respiratory modulation of neuronal activity and the degree of ‘respiratoriness’ can be quantified by the η² statistic (Orem & Dick, 1983). This statistic is the ratio of the variance across the respiratory cycle to the total variance. Values of η² range from 0.0 to 1.0. ‘Low-η² activity’, values less than 0.2, indicate that only a small proportion of the variability in a cell's activity is attributable to the respiratory cycle. In contrast, ‘high-η² activity’, η² greater than 0.3, indicates activity highly modulated with respiration that is consistent from breath to breath (Orem et al. 1985). So η² values correlate with the strength and consistency of the respiratory modulation of the discharge pattern and, thus, quantify a cell's ‘respiratoriness’ (Orem & Dick, 1983).

The η² statistical analysis was not discriminatory when applied directly to assess the magnitude and statistical significance of pulse modulation of neural activity. We theorized that this occurred because the ANOVA is sensitive to the magnitude of the range of the information. In analysing respiratory neurones, the subjects-by-treatments matrix consists of 50 subjects or breaths and the treatment is the respiratory cycle divided into 20 equal bins. Thus, the number of action potentials for each 5% of the cycle is contained in its respective bin. The incidence of false-negative errors increases when analysing activity with low discharge frequencies. In these cases, the matrix contains a high number of ‘bins’ containing only 0 or 1. The cardiac cycle is much shorter than the respiratory cycle so the bins contain too little information to adequately assess variability results even with active neurones. We hypothesized that increasing the information in each ‘subject’ would enhance the discriminatory power of the ANOVA. We increased information across the treatment by dividing the cardiac cycle into 5 rather than 20 bins, by excluding cardiac cycles which had no activity and by summing activity for multiple cardiac cycles, then entering these values in the matrix (Fig. 1). Thus, we propose the ‘δ² statistic’ as a modification of the η² analysis and as a statistic that essentially analyses the variability in a subjects-by-treatments matrix where the subjects are ‘cCTHs’ rather than single cycles and the treatments are quintiles of the cCTHs.

Figure 1. Relationship between the one-way analysis of variance (ANOVA) and δ² values.

Directly assessing the variability of activity referenced to the cardiac cycle with the ANOVA was ineffective. We modified the ANOVA to assess the variability of activity accumulated from multiple cardiac cycles. Each quintile contains the sum of the activity from every 50th cycle for 10 (shown at bottom for first quintile), 20 and 50 cycles. Thus, the ANOVA assessed the variability in multiple cycle-triggered averages of activity referenced to the cardiac cycle (matrix at bottom). This increased the sensitivity of the statistical analysis by increasing the magnitude of data distributed in each quintile.

We applied this statistic to an existing data set of respiratory-modulated neurones. These single-unit activity recordings were gathered over a 7 year period, were well analysed, and have been incorporated in models of respiratory and cough pattern generators (Shannon et al. 1998,2000; Baekey et al. 2001). The activity patterns were characterized on the basis of their location (recording electrodes were referenced to obex), profile of the CTH, response to airway stimulation and axonal projections. Thus, this activity was from well defined respiratory neurones.

Methods

The database analysed for this study was an existing set of simultaneously recorded medullary single units during which arterial blood pressure was recorded also (Shannon et al. 1998, 2000; Baekey et al. 2001). The methods used to acquire this data set have been previously described (Shannon et al. 1998,2000; Baekey et al. 2001). Recordings (n= 24) were performed in decerebrate, neuromuscularly blocked, ventilated, vagally intact cats (n= 19, adult, 2.5–4.1 kg, either sex) using protocols approved by the University of South Florida's Animal Care and Use Committee. In particular, animals were not neuromuscularly blocked before decerebration so the level of anaesthesia was assessed periodically by evaluating the withdrawal reflex.

Animals were initially anaesthetized with sodium thiopental (22.0 mg kg⁻¹, i.v.). Before surgery, atropine (0.5 mg kg⁻¹, i.m.) and dexamethasone (2.0 mg kg⁻¹, i.v.) were administered to reduce mucus secretion and swelling, respectively. Femoral arteries and veins were catheterized for monitoring arterial blood pressure, acquiring arterial blood samples, and administering fluids and drugs intravenously. If necessary, mean arterial blood pressure was maintained at 100 mmHg by administering (i.v.) 5% dextrose in 0.45% NaCl, 5% dextran, or lactated Ringer solution, if necessary. Arterial P_O2, P_CO2, pH and [HCO₃⁻] were analysed hourly and corrected to normal limits. Rectal temperature was maintained at 38.0 ± 0.5°C.

For the decerebration, the external carotid arteries were ligated bilaterally rostral to the lingual arteries. Animals were positioned in a stereotaxic frame (David Kopf Instruments, Inc, Tujunga, CA, USA.) and a craniotomy was formed in the parietal plates. The brainstem was transected midcollicularly and neural tissue rostral to the transection was aspirated. During and after the decerebration, animals were infused continuously with gallamine triethiodide (4.0 mg kg⁻¹ h⁻¹, i.v.), and ventilated with a phrenic-driven respirator (Charles Ward Enterprises (CWE), Inc.). A bilateral thoracotomy minimized movement associated with ventilation. End-tidal CO₂ was maintained between 4.0 and 5.0%.

At the end of the experiments, the decerebrate cats were killed with an overdose of sodium pentobarbitone (i.v.) followed by potassium chloride (4 m, i.v.).

Whole nerve recordings

The proximal end of the transected left, C5 phrenic nerve root was desheathed and placed on a bipolar silver electrode and covered in mineral oil. Then nerve signal was amplified and filtered (band pass 0.1–5 kHz; Astro-Med, Inc., West Warwick, RI, USA P511). Phrenic nerve activity (PNA) was integrated with a leaky resistor–capacitor circuit (0.2 s τ; CWE, Inc.) and recorded on a polygraph and magnetic tape.

Extracellular recording of single neurones

After an occipital craniotomy was completed, the caudal cerebellum was removed to expose the dorsal medulla. The right side of the medulla was searched with planar electrode (n= 8) arrays (n= 2) of tungsten microelectrodes (Z= 10–12 MΩ). Signals were amplified, filtered (band pass 0.1–5 kHz; P511), monitored and recorded on magnetic tape (Cygnus Technology, Inc.). The medullary surface was covered with a pool of warm mineral oil.

We differentiated the recordings using the stereotaxic coordinates of the electrodes referenced to the obex. Activity was recorded from areas in the dorsomedial and ventrolateral medulla involved in cardiorespiratory control. Recording electrodes in the dorsomedial medulla were located in the nuclei of the solitary tract at the following stereotaxic coordinates: 0.5–1.4 mm rostral to obex, 0.5–2.4 mm lateral to midline, 0.7–3.7 mm below the dorsal surface. Recording electrodes were also located in the rostral and caudal ventrolateral medulla at the following stereotaxic coordinates: 3.0–5.5 mm rostral to obex, 3.0–4.5 mm lateral to midline, 3.0–5.5 mm below the dorsal surface; and 2.0 mm rostral to 4.0 mm caudal to obex, 3.0–4.5 mm lateral to midline, 2.5–4.5 mm below the dorsal surface (Shannon et al. 1998).

Data acquisition, entry and preprocessing

Action potentials of single-unit activity were converted to acceptance pulses and times of occurrence with spike-sorting software (Figs 2 and 3, Datawave Tech. Inc.). Data files were transferred to Hewlett-Packard 9000/735 and c160 computers for subsequent processing and analysis. The signals of efferent nerves were high-pass filtered (40 Hz, 3 dB cut-off) and, along with the common synchronization timing pulses, were digitized (5 kHz) with a 16-bit ADC488/16 analog-to-digital converter hosted by a Hewlett-Packard 9000/380 computer. The program XSCOPE (Lindsey et al. 1992) provided a graphical representation of the times of action potentials and other digital and analog signals. This program was also used to select data segments to be written as separate files for later analysis.

Figure 2. Record (A) and cycle-triggered histograms (CTHs, B) of neuronal activity.

A, acceptance pulses representing discriminated action potentials from five medullary neurones recorded simultaneously. This segment of activity occurred during an expiratory phase as indicated by the decreasing phrenic nerve activity (PNA, 6th trace). Recording electrodes were located in the rostral and caudal ventral respiratory groups (r and cVRG). Activity did not appear to be correlated with arterial pulse (P, 7th trace). B, left column, rCTHs in which the onset of PNA was the triggering event; right column, cCTHs in which the sharp rise in P was the triggering event. The bottom histograms show the autocorrelation for PNA (left) and P (right). The bin duration (at the end of x-axis) in r- and cCTHs was different. The histograms were normalized to the peak action potential discharge frequency (at the top of y-axis). The r- and cCTHs indicated that the activity might be modulated with respiratory and/or cardiac cycles. Even though η² of 0.02 was not significant, these neuronal activities (3rd and 4th tracings) were classified as respiratory modulated because the binary test indicated neural activity in one half of the respiratory cycle was consistently greater than that in the other half. The significance of activity modulated by pulse was based on the δ² values obtained from accumulating activity for 50 cycles. δ² values ranged from 0.01 to 0.44. Activity was not significantly correlated to the cardiac cycle for δ² < 0.04; the top tracing was not significantly modulated. For δ²= 0.04, significance depended on the number of occurrences so one rVRG neurone (4th tracing) was not, but the other (5th tracing) was, significantly modulated. δ² > 0.04 indicated significantly modulated activity; thus the 2nd and 3rd cVRG neurones were modulated. C, in this and subsequent figures. r- and cCTHs of neuronal activity were superimposed on those of integrated PNA and pulse, respectively. The r- and cCTHs on the left were repeated analyses of the activity pattern in the second tracing as recorded (original analysis identified by the dashed box in B). On the right, is the analysis after shuffling the data. The time of the acceptance pulse was shuffled only with respect to the cardiac cycle not the respiratory cycle. Nevertheless, the effect of the shuffling was apparent in the rCTH and η² value. The rCTH showed a spreading of the activity profile and a decrease in the peak frequency of the activity and the η² value decreased from 0.82 to 0.5. Both effects were predictable. Shuffling the data within the cardiac cycle eliminated the relationship of unit activity with respect to pulse.

Figure 3. Action-potential profiles for three ‘single-unit’ recordings from s68m2 in the cVRG.

Action potential profiles did not vary for the isolated (71) or paired (66, grey tracing; 70, black tracing) units during the recording period indicating that neither respiratory nor pulse (P) modulation resulted from either mechanical or electrical deformation of the action potential profile. Calibration bars: 1 ms, horizontal bar; and 1 V, vertical bar. Amplitude of the conditioned signal was adjusted to maximize the signal. Auto-correlation histograms (ACHs) for the unit pair at 0.5 and 2.5 bin widths (100 bins per histogram). The ACHs reveal that the action potential profiles were discriminated without false positive occurrences during the refractory period. Cycle-triggered histograms (CTHs) for the unit pair (20 and 10 ms bin widths and 100 bins per histogram). The CTH for unit 71 is Fig. 4A2. Respiratory (rCTH, left) and cardiac (cCTH, right) CTHs reveal activity time-locked to PNA and P, respectively. The η² (above rCTH), and δ² (above cCTH) values were highly significant. Respiratory-modulated activity was associated with the inspiratory (I) to expiratory (E) (66) and the E-to-I transition (70). Arterial pulse-modulated activity was associated with different phases of the cardiac cycle.

Analysis methods for single neurones

The following measures were computed from a 5–10 min baseline period that preceded the experimental protocols: (1) auto-correlation histograms (ACHs), (2) respiratory CTHs (rCTHs), and (3) cCTHs. With one exception (Fig. 2B), the r- and cCTas of unit activity were superimposed on those PNA or pulse histograms, respectively (Figs 2C, 3 and 4)

Figure 4. Examples of r- and cCTHs of medullary neural activity with high (A), moderate (B) and low (C) δ² values as well as a false positive (D, FP) and false negative (D, FN) δ² value.

The η² values (centred over rCTH) were significant and based on 50 respiratory cycles. The δ² values (centred over cCTH) were from analyses in which 50 cardiac cycles were accumulated (except B2 which was from 20 cycles). Numbers at the end of the axes indicate either bin duration (x-axis, 100 bins per plot) or peak firing frequency (y-axis). Panels bordered with continuous or dashed lines were simultaneously recorded pairs of patterns. A, recordings A1 and 2 were made in the caudal ventral respiratory group (VRG) from two different animals. These neurones were reciprocally active, in that the expiratory–inspiratory (EI) phase transition activity increased with the pulse whereas the IE phase transition activity decreased with the pulse. (A2 was from record 71 in Fig. 3.) Recordings A3 and 4 were made simultaneously in the rostral VRG. Even though these neurones were active in different phases of the respiratory cycle, both increased their activity with the pulse. B, recording B1 was from the caudal nuclei of the solitary tract (nTS), and B2 from the rVRG. The activity in B1 was bi-phasically modulated with the cardiac cycle. The activity patterns in B2 and D, FN were recorded simultaneously. Their respiratory and pulse-modulated activities were reciprocal; one (B2) was I-Dec and increased its activity with the pulse whereas the other (D, FN) was an E-Aug and decreased its activity with the pulse. C, recording C1 was from the caudal nTS, and C2 from the cVRG. D, apparent false positive (D, FP) activity patterns were rare (n= 3), occurring approximately in 1% of the recordings and had δ² values of 0.1. False-negative (D, FN) activity patterns were more common – approximately 5% of the samples.

We generated ACHs for each spike train to evaluate the source of the discriminated action potential. A spike train from an isolated, single neurone will produce an ACH in which a quiescent period follows time zero, the occurrence of the reference spike. With multiunit activity, the occurrence of the correlated spike is not constrained by membrane refractoriness and spurious activity will occur immediately after the reference spike. We analysed units only if the ACH showed a defined interspike interval without false positives (Fig. 3).

For rCTHs, the reference or triggering event was the offset of PNA. Each cycle was divided into 20 equal bins. The number of action potentials that occurred in each 5% of the breath was tabulated for 50 breaths. We evaluated the significance of the respiratory modulation of the activity patterns by the ANOVA and the binary test (Morris et al. 1996). Activity patterns that were not significantly modulated as indicated by the ANOVA were included as respiratory-modulated neurones if the cells were significantly modulated by the binary test (Morris et al. 1996). We subclassified respiratory-modulated activity on the basis of peak-firing frequency, phase of discharge and slope of activity as indicated in their rCTHs.

For cCTHs, the reference event was the sharp rise of arterial blood pressure associated with systole. Spike trains were evaluated for statistically significant modulation with arterial pulse using the subjects-by-treatments design of the ANOVA (Fig. 1). Only cycles in which activity occurred were used in the analysis. Each cycle was divided into five equal bins, quintiles. The number of action potentials that occurred in each quintile was tabulated for 10, 20 and 50 cardiac cycles. These cardiac cycles were not consecutive but separated by 10, 20 and 50 cycles, so no cycle was sampled twice even when accumulating activity for 50 cardiac cycles. Thus, in the subjects-by-treatments matrix, the subjects were tabulated quintiles of 50 composite cardiac cycles and the treatments were the quintiles of the cardiac cycle. We calculated the mean of each quintile and the grand mean (Fig. 1). Two sources of variation were examined, variation across the quintiles and variation within each quintile. If the treatment is a major source of the variation in spike activity, then variance across the quintiles will be high and the variance within the quintiles from composite cycle-to-composite cycle will be low. The F ratio reflects the relative proportions of these two variances. The δ² statistic is between 0 and 1 and is the ratio of the variance across the quintiles to the total variance (Fig. 1). Thus, δ² increases to 1.0 as the magnitude of the variance associated with the treatment increases.

The probability of false positives was assessed by shuffling the time of occurrence of the acceptance pulses (Fig. 2) and minimized by screening the recording for electrical and mechanical artefacts that would modulate the amplitude of a discriminated spike (Fig. 3). A priori we set the probability of false positives at 5%. We assessed for this percentage of occurrence of false positives by shuffling the time of acceptance pulses. When an action potential was detected, the time of occurrence was shuffled by randomly placing the acceptance pulse in a quintile of the cardiac cycle in which it occurred. In this way, the phase within the cardiac cycle rather than the respiratory phase changed (Fig. 2C). The electrical signals-caused by cardiac muscle contractions (e.g. ECG) were filtered. The recorded and accepted action potential waveforms were examined for amplitude changes associated with the pulse pressure or ECG to assure that sorting artefacts did not contribute to signal modulation (Fig. 3).

Results

A total of 246 spike trains were analysed to assess their cardiac and respiratory modulation. All spike trains were recorded in the medulla of decerebrated, vagally intact cats. We classified spike trains as to their location, relationship to respiration and whether or not they were significantly cardiac modulated.

Analysis of recording methodology

Pulse modulation of activity was not apparent in the recording even when it was well modulated in the cCTH (Fig. 2). Consequently, pulse modulation was verified (Fig. 2C) and recordings were examined for artefactual modulation due to either mechanical or electrical deformation of the spike waveform (Fig. 3). Shuffled data trains were analysed to verify pulse modulation (Fig. 2C). Shuffling the data train eliminated the relationship between pulse and activity (Fig. 2C). Overall within the shuffled data set, we had a 5.82% type 1 error which is consistent with an assumption of a 5% false positive error. Further, δ² values were all less that 0.05. Examination of high speed tracings of the recordings indicated that action-potential profiles did not vary (Fig. 3). Both well-isolated single- and pauci-unit recordings were stable during the recording period (Fig. 3). Neither respiratory nor pulse modulation resulted from mechanical or electrical deformation of the action potential profile (Fig. 3).

Respiratory-modulated activity patterns

Overall, 81% of the neurones were identified as respiratory-modulated units (RMU, n= 200/246). Respiratory-modulated activity was recorded preferentially from the ventrolateral medullary respiratory column, i.e. the rostral and caudal ventral respiratory groups (r- and cVRG, respectively), rather than from the nuclei of the solitary tract (nTS) in the dorsomedial medulla. The distribution of the activity patterns was from the nTS (n= 48), rVRG (n= 102) and cVRG (n= 96). Not only were fewer neurones recorded in the nTS, but only 54% (n= 26) of the patterns from the nTS were modulated with respiration and 50% of these were identified by just the binary test. In contrast, 86 and 90% of the spike trains from the r- and cVRG were from RMUs and only 15% of these had non-significant F ratios.

We classified 53% of the RMUs as inspiratory (I), 36.5% as expiratory (E), and 10.5% as phase-spanning (PS); IEPS were 6% and EIPS 4.5%. We subdivided I and E activity into augmenting (Aug) or decrementing (Dec) on the slope of a ramp to or from its peak firing frequency. Activity without a clearly defined ramp was classified simply as either I or E. Using this criterion, I activity subdivided into similarly sized groups of I-Aug (n= 45), I-Dec (n= 32) and I (n= 29) types; similarly, E activity split equally into E-Aug (n= 24), E-Dec (n= 25) and E (n= 24) types.

Types of RMUs were distributed differentially among the medullary respiratory areas. Of the 26 RMUs in the nTS, most (n= 15) had I-modulated activity. In the vl medulla, I activity was recorded preferentially in the rVRG, E in the cVRG.

Pulse-modulated activity patterns

Pooling cycles for the analysis progressively decreased the total number of cells analysed due to insufficient data. Consequently, 220 spike trains were analysed after accumulating counts from 10 cardiac cycles, 201 from 20 cycles, and 130 from 50 cycles. Overall, nearly 50% of the RMUs also expressed significant cardiovascular-modulated activity. Quantitative assessment of spike train patterns identified 113 pulse-modulated neurones from 246 spike trains, with δ² values that ranged from 0.04 to 0.75. Of these, 97 were from respiratory-modulated neurones.

Of the 113 recordings, only 13 had δ² values > 0.3 (Fig. 4A). In these recordings, modulated activity had only a single feature in their cCTHs, i.e. activity could increase (Fig. 4A1) or decrease (Fig. 4A2) following the arterial pulse. Similar (compare Fig. 3 no. 66 and Fig. 4A2) as well as different (Fig. 4A3 and A4) patterns of phase coupling were apparent in the cCTHs of simultaneously recorded single neurones.

Identifying activity patterns that were highly modulated by pulse depended on accumulating activity from multiple cardiac cycles (Fig. 5). The distribution of δ² values across the recorded cells appeared as a Poisson distribution without accumulating cycles and with accumulating 10 and 20 cycles (Fig. 5). After accumulating 50 cycles, a break in the distribution occurred and a separate group of ‘highly modulated’ neurones appeared with δ² values of 0.3 (Fig. 5).

Figure 5. Distribution of δ² values depended on the number of cumulative cycles.

For the histograms of δ² values without cumulating any cycles and with cumulating 10 and 20 cycles, the distribution was skewed with most cycles being non-significant (N.S.). However, with cumulating activity for 50 cycles, even though most patterns were N.S. a break point occurred between the weakly (grey bars) and the strongly (black bars) correlated patterns. There was a single occurrence in which δ² value was between 0.2 and 0.3 (0.26) in the population of recordings in which activity was accumulated over 50 cycles (n= 130).

In the vast majority (100 of 113) of recordings with significant pulse modulation, activity was moderately or weakly modulated with the arterial pulse (Figs 2, 3, and 4B and C). Generally, weakly pulse-modulated activity patterns also only had a single feature in their cCTHs (Figs 2, 3, and 4B and C). However, activity patterns could have more than one feature in their cCTHs (Fig. 4B1).

The δ² values that characterized a recording depended on accumulating activity from multiple cardiac cycles (Fig. 6). Not cumulating activity from multiple cycles resulted in δ² values that were indistinguishable between highly and weakly modulated neurones (circled means, Fig. 6A). When comparing activity patterns with at least one δ² value ≥ 0.3, δ² values increased with increasing cumulated number of cycles (squares, Fig. 6A). The δ² values obtained without and with accumulating activity from 10 and 20 cycles was compared to that when activity was accumulated from 50 cycles (Fig. 6B). As activity was accumulated from more cycles, the slope of the regression line progressively increased toward that of the line of identity and the regression coefficient progressively increased toward 1 (Fig. 6B).

Figure 6. The δ² value depended on the number of cumulative cycles.

A, mean and standard deviation of δ² values for groups of high (▪, continuous line), moderate (♦, continuous line), low (□, continuous line), and non-significant (+, dashed line) activities plotted against number of cumulative cycles used in the analysis. These 4 groups were defined by their highest δ² value, which was obtained after cumulating 50 cardiac cycles for each row (subject) in the matrix. Differences between groups were apparent only after cumulating multiple cycles. Without accumulating any cycles for the analysis (circled region), the means for the groups were not significantly different. Significant differences between high and other types of activity depended on at least cumulating 10 cycles (2-way RM ANOVA). B, δ² values plotted against their δ² values with accumulating activity from 50 cycles. Even though δ² values were significantly correlated, the correlation coefficient progressively increases after accumulating 10 cycles (○, dashed line) and 20 cycles (♦, continuous line). Correlations remained significant after excluding the non-significant δ² values (δ²₅₀ values < 0.04, approximately circled points).

Association between respiratory and pulse-modulated activity

For the 13 spike trains with δ² value ≥ 0.3 (Figs 2, 3 and 4A), one of these neurones was recorded in the nTS, five in the rVRG, and seven in the cVRG (Figs 2 and 4A4). Further, all 13 had a component of their activity in the expiratory phase: four were E-Dec (Figs 4A2 and 3), three E-Aug (Figs 2 and 4A4), three E (Figs 4A1), two IE PS (Fig. 3, no. 66), and one EIPS. Finally, 10 of 13 activity patterns had η² values ≥ 0.3. Thus, activity that was highly modulated to the arterial pulse was also highly modulated to the respiration.

In the population of recordings with δ² value < 0.2, both I- and E-modulated activities were modulated with the cardiac cycle. However, I-Aug neurones had the lowest percentage (27%) whereas activity associated with respiratory phase transitions (both EI and IEPS neurones) had the greatest percentage (67%) of pulse-modulated activity patterns.

Simultaneously recorded activity with significant δ² values displayed phase differences in their activity profiles in their cCTHs (as indicated above) but also in their rCTHs (Figs 2, 3 and 4). For instance compare c- and rCTHs for 66 and 70 in Fig. 3 and 71 in Fig. 4A2; in their cCTHs, for 66 and 71 activity decreased after the up-slope of pulse pressure, but before it for 70. In their rCTHs, these units also displayed reciprocally modulated activity with 66 and 71 having overlapping activity (IEPS or E-Dec activity, respectively) whereas 70 had an I-Dec activity profile. Subtle phase shifts in both c- and rCTHs were evident as well. In comparing Fig. 4A3 and A4, both neurones increased activity during E and with the up-slope in the pulse, but expiratory activity precedes and pulse-modulated activity follows that in Fig. 4A3 compared to A4.

Factors influencing respiratory and pulse-modulated activity

In these recordings, δ² and η² values did not correlate; δ² or η² values ≥0.3 did not preclude nor preferentially associate with one another (Fig. 7A). Discharge frequency did not affect the identification of pulse-modulated but did affect that for respiratory-modulated activity (Fig. 7B). In particular, peak firing rate correlated with η² but not δ² values (Fig. 7B). The magnitude of pulse pressure itself was positively correlated to the percentage of RMU that expressed pulse-modulated activity (Fig. 7C). However, this correlation was weak (r²= 0.22) and depended on a single recording (circled in Fig. 7C).

Figure 7. δ² and η² values varied independently.

A, δ² values plotted against η² values. These values were not correlated; both low and high η² values could be associated with either high or low δ² values. B, calculated discharge rate from the maximal bin in c- and rCTH plotted against δ² (□) and η² (▪) values, respectively. Peak firing rate correlated with η² (continuous line) but not δ² (dotted line) values. C, correlation between arterial pulse pressure (systolic–diastolic) and the percentage of pulse-modulated activity. As pulse pressure increased, more activity patterns were modulated with pulse. However, this relationship depended on a single point; if the circled point was eliminated from the analysis then the correlation was not significant.

In summary, even though we have stressed an association between respiratory- and pulse-modulated activity, δ² and η² values not only varied independently but were affected by different factors.

Discussion

We developed a statistical test to evaluate the significance of the arterial pulse modulation of neuronal activity and a statistic, delta-squared, ‘δ²’, to quantify the magnitude and statistical significance of cardiac-modulated activity. We applied this statistic to evaluate brainstem respiratory-modulated neurones for cardiac cycle modulation and 48% (n= 96/200) of respiratory-modulated neurones were also modulated significantly with the cardiac cycle. Generally, E neurones and subtypes associated with phase transitions (IE and EI) could be highly correlated to both respiratory and cardiac cycles whereas I neurones (I-Aug, I) were, at best, weakly modulated with arterial pulse. The E and pulse-modulated neurones were located preferentially in the cVRG. Finally, various types of pulse modulation were evident in cCTHs of simultaneously recorded neurones. However, we did not subclassify these patterns.

We conclude that pulse modulation is a component of respiratory-related activity. As indicated in the Introduction, we specifically chose to analyse this existing data set because these activity profiles have been well analysed with regards to their role in the control of respiration and cough. However, while the possibility exists that a fraction of these neurones regulate sympathetic nerve activity, the fact that 50% of the population is significantly pulse modulated supports our conclusion. Shuffling the data train and analysis for artefactual modulation failed to reveal a fault in the statistic or a systematic alteration in the spike profile that would predispose the population to appear modulated.

Comparison with the η² statistic

Respiratory modulation of brainstem neurones or the degree of ‘respiratoriness’ can be quantified by the η² statistic (Orem & Dick, 1983). We modified this approach to quantify the magnitude and statistical significance of arterial pulse modulation of neural activity. Similar to η², δ² is a value from 0.0 to 1.0 and is the ratio of the variance across the cardiac cycle to the total variance of activity. Values of δ² correlate with the consistency of the discharge pattern if not from pulse to pulse then from cCTH to cCTH.

Qualitative terms of high or strong and weak have been used to modify modulation on the basis of η² values. The rationale for these descriptions for respiratory modulation was based on a naturally occurring break between 0.2 and 0.3 in the distribution of η² values of respiratory-modulated activity (Orem & Dick, 1983; Orem et al. 1985). In two separate studies analysing the discharge pattern of respiratory-modulated activity (Orem & Dick, 1983; Orem et al. 1985), activity was either greater than 0.3 or less than 0.2. In this study we have observed a similar phenomenon. Little pulse-modulated activity had δ² values between 0.2 and 0.3 and a distinct population of activity patterns had δ² values greater than 0.3. Due to the similarity in distribution patterns and because the upper limit of these values is 1.0, we have adopted the same limits for defining the qualitative terms to describe the degree of pulse modulation.

A critical difference between η² and δ² statistical tests is the necessity to accumulate activity over multiple cycles. Spike counts were accumulated for multiple cardiac cycles – 10, 20 and (when possible) 50 cardiac cycles – to increase bin values (Fig. 1). It was necessary to tabulate activity for multiple cycles into a composite cycle for each ‘subject’ because directly applying η² to measure statistically significant modulation with the cardiac cycle was ineffective in identifying cardiac modulation apparent in the cCTHs. The short cycle period minimizes the range of values in the bins of a subjects-by-treatments matrix and the bursting nature of respiratory-modulated activity allows for many cardiac cycles to contain no activity. Even after dividing the cardiac cycle into quintiles, the bin duration was still too short for multiple occurrences, especially when firing rate was low. A low number of occurrences per bin obfuscates variance across quintiles and favours variance within quintiles.

The δ² statistic depends on the specificity and consistency of cardiac-modulated activity. Specificity of cardiac-modulated activity is related to the range of activity across the cardiac cycle and the dispersion of activity levels over this range. Although the ‘treatments’ in this analysis are cCTHs, their dispersion still directly maps to dispersion of cell activity related to pulse. Consistency of the cardiac-modulated activity is related to the variability in the activity from cardiac cycle to cardiac cycle. Consistency of cCTHs is measured in this treatment and would only occur if the discharge was similar from cycle to cycle.

Even highly cardiac-modulated activity required cycles to be cumulated in order to discriminate statistical significance (Fig. 6). In the sample cells (n= 13) that had δ² values greater than 0.3, without cumulating cycles only three of the spike trains were identified as being significantly correlated to cardiac cycle and the highest δ² value was 0.14. Indeed, without cumulating cycles the mean δ² value of this sample was not statistically different from that of weakly as well as non-modulated activity. However, all the δ² values were significant after cumulating just 10 cycles and increased progressively as the number of cumulative cycles increased (Fig. 6). In only 1 case, δ² values were similar for 20 (δ²= 0.40) and 50 (δ²= 0.44) cumulative cycles.

We did not subclassify patterns of cardiac modulation because we did not determine the latencies between cardiac contraction and the measurement of changes in arterial pressure and between the changes in arterial pressure and the response. Thus, the exact phase relationship between the cardiac cycle and the action potential cannot be stated definitively. However, different patterns of cCTHs occurred within a single animal indicating different types of phase-specific activity.

Limitations of the δ² statistic

Due to the nature of statistical testing both false positives (Fig. 4D) and negatives (Fig. 4D) occur by chance. In this large sample (n= 246), false positives or type 1 errors appeared rarely and only in approximately 1% of the analyses. These examples may have had features in their cCTHs but the profile of their cCTHs or the magnitude of the feature did not correspond with other statistically significant cCTHs with δ² values of this magnitude. Apparent type 2 errors appeared more frequently, in approximately 5% of the spike trains (Fig. 4D). These cCTHs had P-modulated features that were not identified as being statistically significant.

The ANOVA tests and δ² values reflect the consistency of modulation. Both type 1 and type 2 errors may arise from respiratory modulation of the pulse-modulated activity. A type 1 error could be due to differences in the cardiac modulation of activity over the respiratory cycle, which would flatten the cCTH, whereas a type 2 error could be due to cardiac modulation during certain phases of the respiratory cycle, which would diminish the consistency of the signal. In regards to type 2 error, activity of baroreceptor relay neurones in the nTS are modulated over the respiratory cycle (Rogers et al. 1996).

High δ² activity patterns tended to be recorded in the same animals. Although data were recorded from similar medullary areas in 19 animals, high δ² values (i.e. δ² > 0.3) were obtained in only seven animals and one of these had seven spike trains with high δ² values. This distribution was statistically different from random (P < 0.001, χ² analysis). However, the percentage of spike trains with pulse-modulated activity in a recording correlated only weakly with mean pulse pressure and even this correlation depended on one recording (Fig. 7C). While this correlation is consistent with the pulse modulation being determined by baroreceptor input, the differential distribution of high δ² values indicates that other factors such as respiratory modulation of baroreceptor input may play a role.

Cardioventilatory coupling

Brainstem neural networks integrate and coordinate sympathetic and respiratory activities to meet metabolic demands and to maintain homeostatic balance. Respiratory modulation of sympathetic nerve activity may serve this function. On the other hand, the reciprocal relationship, i.e. pulse modulation of respiratory neural activity has not been as recognized. Pulse modulation of respiratory units may coordinate respiratory movements and attendant changes in intrathoracic pressure with heart cycle and sympathetic activity to support cardiac output. In contrast, pulse modulation of respiratory units may act to synchronize bursting patterns of sympatho-respiratory control. Synchrony in activity among neurones has been hypothesized as a mechanism to increase the efficacy of synaptic interaction among oscillators (Gilbey, 2001; Staras et al. 2001).

Previous studies have suggested a cardioventilatory coupling, cardiac modulation of the respiratory cycle or synchronization of respiratory-cycle phase with cardiac-cycle phase. These studies have reported that stimulating carotid baroreceptors decreases integrated phrenic nerve amplitude, prolongs expiration, and facilitates inspiratory termination (Speck & Webber, 1983; Wasicko et al. 1993; Morris et al. 1994; Lindsey et al. 1998; Li et al. 1999a,b; Stella et al. 2001). For example, Speck & Webber (1983) reported that the threshold for intercostal nerve stimulation to terminate inspiration decreased with an increase in mean carotid sinus pressure from 100 to 150 mmHg.

Statistical analyses of the correlation between heart beat and respiration have identified cardioventilatory coupling in animals (Bucher, 1965) and humans (Bucher, 1965; Hinderling & Bucher, 1965; Hinderling et al. 1968; Bucher et al. 1972; Galletly & Larsen, 2001a,b; Larsen & Galletly, 2001). These findings support our analysis, which is the first to detect and quantify beat-to-beat cardiac modulation of neurones within central respiratory networks. The expression of this pulse-modulated activity by respiratory neurones may account for cardioventilatory coupling.