Wellington School of Medicine, PO Box 7343, Wellington, New Zealand*Corresponding author
Accepted for publication: February 7, 2001
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Abstract |
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Br J Anaesth 2001; 86: 77788
Keywords: model, cardioventilatory coupling; heart, heart rate; ventilation, pattern
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Introduction |
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We observed clinically that coupling patterns vary according to the ratio of the heart rate to breathing frequency. However, between subjects, the presence and pattern of coupling may differ despite approximately similar heart/breathing frequency ratios. From these observations, we suggested that patterns and their transitions might be explained by the interaction of three variables; heart rate, intrinsic breathing frequency (the breathing frequency in the absence of coupling) and the strength of interaction between the cardiac afferent signal and a hypothetical brain stem inspiratory pacemaker.5 In this paper we develop and study a simple model of coupling which incorporates these three variables. The model can replicate all of the clinically observed coupling patterns and their associated ventilatory variability.
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Method |
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With cardiac related bursts transiently augmenting (I), inspiration will occur if either (a) the intrinsic
(I) or (b) the cardiac burst transiently augmented
(I) exceeds the inspiratory firing threshold. The slope of the
(I) can, therefore, be divided into alternating sections of exposed intrinsic slope and sections which are in the shadow of a cardiac burst (Fig. 1). The relative size of these sections and, therefore, the likelihood of cardiac versus intrinsic triggering, varies according to the slope of
(I), HR and the cardiac burst magnitude. Although the intrinsic breathing frequency is constant, given a constant
(I) slope, the addition of cardiac bursts causes the ventilatory period to vary if the mechanism of inspiratory triggering changes from one breath to the next. In the presence of coupling therefore, the resulting observed ventilatory frequency (fo) may differ from the intrinsic frequency (fi); it is important to note that fo will always be equal to or greater than fi as a triggered breath will always occur before the expected time of a non-coupled intrinsic breath.
For simplicity, the cardiac pacemaker activity at the sinus node was regarded as equivalent to (I), with a linear cardiac pacemaker function,
(C), rising to a cardiac firing threshold at which cardiac systole is initiated and
(C) is reset to a baseline value.
Noise can be expected in any biological system and variability is assumed to occur in burst magnitude, (I) slope and HR. To avoid undue complexity, we incorporated variability into our model by varying the value of
(I) using a Gaussian distributed random variation. The standard deviation of this Gaussian distribution we will term the
(I) slope variability.
Respiratory sinus arrhythmia (RSA) was not examined in any detail in this preliminary description. However in order to determine whether RSA causes major instability in the model we crudely incorporated RSA by transiently reducing cardiac firing threshold following inspiratory onset. In those simulations, which included RSA, we reduced linearly, the cardiac threshold for firing from 1.0, at inspiratory onset to 0.8, 1.5 s following inspiratory onset, returning this firing threshold, linearly, to 1.0 by the following inspiratory onset.
Input variables
The following variables and parameters define the behaviour of the model.
(a) Inspiratory and cardiac firing thresholds; regarded as constant values=1.0.
(b) (I) slope.
(c) (C) slope.
(d) R wave to cardiac burst interval=0.4 s.
(e) Cardiac burst magnitude, MBc.
(f) Cardiac burst duration=0.1 s.
(g) The magnitude and time course of the cardiac firing threshold lowering by RSA.
(h) (I) slope variability.
Simulation
A computer simulation was written using LabView 5 on a Macintosh PowerBook 1400cs and iterated in time steps of 0.01 s.
Coupling interval (RI) pattern
From simulated time series, we determined the timing of consecutive R waves and inspiratory onsets. Within each breathing cycle (from inspiration to inspiration) we determined the time from each enclosed R wave to the following inspiratory onset. Coupling patterns are observed when these RI intervals are plotted as a time series (the RI plot). Within each breath there will be a number of RI intervals (equal to the entrainment ratio), the shortest of which (RI1) will generally correspond to the coupling interval, although this may vary according to coupling pattern and heart rate.1 5
Model behaviour
Simulation was performed using a range of cardiac burst magnitudes, and for HR/fi values over the general distribution determined for intra-operative anaesthetized, spontaneously breathing subjects.5 Simulations were also performed with variations in (I) slope and with RSA.
(I) slope variations were examined in the region 00.02.
In examining the model behaviour we determined (1) the range of coupling interval patterns generated, (2) the regions of the HR/fi plot associated with each coupling pattern, (3) the difference between intrinsic and observed breathing frequency, and (4) the specific pattern of ventilatory variation associated with each coupling pattern.
Simulation of human time series
Data were taken for study from material used in previous papers on cardioventilatory coupling,5 from subjects showing clear pattern I, II, III, IV, or uncoupled RI interval plots or transitions between coupling patterns. Simulations were performed by using the patients own heart rate time series and adding values for fi and burst magnitude into the model. To remove the effect of RSA the real heart rate time series was first filtered using a simple n beat, boxcar moving averager, where n is the closest integer to mean HR/fo ratio. From this filtered time series, a (C) slope time series was calculated (
(C) slope=60/HR) and this was used to vary heart rate during simulation. For these simulations, we therefore knew both HR and fo, but burst magnitude and fi were unknown. Once we understood the relationship between fi, fo, burst magnitude and the specific coupling pattern (see results below), it was comparatively simple to determine approximate burst magnitude and fi values.
Nomenclature
The plot of HR/fi can be divided into a series of radiating areas between lines of integer relationship. To describe the distribution of coupling patterns on this plot, we term the area between any pair of consecutive integer ratio lines as the domain of the lower integer ratio. Coupling pattern regions within each domain will be termed zones, indicated by an appropriate superscript. Thus, the area between 2:1 and 3:1 integer ratio lines is the 2:1 domain and a zone within this domain in which pattern I is generated is denoted I2.
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Results |
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The smaller zone, C, was observed sandwiched between the zones for pattern III and I. Retrospectively examining epochs of human data, this pattern was found in a number of human time series. Two examples are shown in Figures 2 and 7.
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In Figure 4, we show the RI interval plots for a range of cardiac burst magnitudes and HR/fi ratios. For burst magnitudes in the range 00.2, patterns III and IV will occur commonly in the lower domains (between 2:1 and 4:1 HR/fi) but with increasing HR/fi, these patterns occur less commonly. For any particular burst magnitude there is a critical domain or HR/fi ratio, in which patterns III and IV are no longer apparent and above which only pattern I will occur. The domain in which this occurs will vary directly with burst magnitude.
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These pattern zones may also be represented on the map of HR versus fi. Figure 5A shows the zones as radiations on the HR/fi map for the burst magnitude 0.15. The width and presence of these radiations will vary according to burst magnitude. This figure also illustrates the diminution of III and IV zones, and the invariability of pattern I coupling, at higher domains.
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Starting from the 3:1 integer relationsip line, where fo=fi, the HR/fi relationship moves across the zone. During its passage, the value of fo jumps to and fro between fi and a greater value, with fo increasingly taking on the greater value as HR falls. Mean fo therefore becomes increasingly greater than the starting fi value. The fluctuation in breathing frequency in Figure 5 is seen to be less than the horizontal interval between integer ratio lines. As this horizontal distance corresponds to a variation in ventilatory period of one heart period, pattern IV2hi ventilatory period variability is associated with variations of less than one heart period. It can be seen in Figure 5 that the maximum magnitude of these ventilatory variations are equal to the horizontal width of the pattern I2 zone where the HR/fi will later cut the transition between IV2lo and I2. The variation in breathing frequency will therefore be proportional to burst magnitude (which determines the width of the pattern I zone). Thus, the breathing frequency variation for MBc=0.15 is considerably greater than that for 0.05. In general, the mean breathing frequency during a pattern IV2hi epoch will vary within an area of the 2:1 domain on the HR/fo map, a little below the 3:1 integer ratio line.
Passing through A2, where breathing variation diminishes from that in IV2hi, HR/fi moves into the pattern III2 zone, where breathing rate begins to alternate with consecutive breaths, again with a jump in ventilatory period of less than one heart period. Initially the quantal variability is of similar magnitude to that in the preceding pattern IV2hi zone but decreases as HR falls. When the HR/fi ratio falls to an exact half integer, the breathing rate variation of pattern III2 is zero. On the HR/fo map, the observed breathing frequency variation for pattern III2 is now occupying the central region of the 2:1 domain.
From the pattern III2 zone the HR/fi passes via B2 into pattern IV2lo if MBc=0.05 or directly into C2 if MBc=0.15. The maximum fo variability in B2, IV2lo and C2 are of similar magnitude to that in the IV2hi zone although the specific pattern of variability differs between coupling patterns. In both C2 and IV2lo, fo increasingly takes on the maximum value. On the HR/fo map, the observed breathing frequency variation is now occupying the lowermost region of the 2:1 domain.
As the HR/fi passes into the pattern I2 region, fo is captured by the 2:1 integer relationship line. The fo initially takes on a value equal to the maximum which was observed in the IV2hi and IV2lo zones. The displacement of fo from fi is greatest at this transition and can be seen to be proportional to burst magnitude. Remaining on the integer relationship line the value of fo continues to smoothly decrease as HR falls until HR/fi intersects the 2:1 integer relationship line at which time fo will once again equal fi. Thereafter a sequence of pattern zones in the first domain would be encountered.
From these observations, we can compare the coupling pattern distribution on the maps of HR/fi and HR/fo. The HR/fi map shows radiations corresponding to the four pattern zones, but because fo is altered by the coupling pattern, the pattern distribution on the HR/fo map is different. Pattern I occupies only the integer relationship lines, pattern III occupies the central regions of these domains and pattern IVhi and IVlo occupy regions adjacent to the integer relationship lines. The simulated pattern distribution of the HR/fo map is therefore qualitatively similar to that which is observed in the anaesthetised human subject (Fig. 6).
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As seen in clinical samples, the breathing frequency variability during pattern II coupling was observed in simulation to be characterised by quantal jumps in ventilatory period corresponding to changes in entrainment ratio. Thus, changes in ventilatory period occurred in multiples of the heart period.
The distribution of coupling types seen in the HR/fo map of anaesthetised subjects (Fig. 6) can therefore be entirely explained by our model. Pattern II is invariably present above a critical boundary domain, below which patterns I, III, and IV occur in radiating zones.
Respiratory sinus arrhythmia
Other than the associated increase in HR caused by reducing the cardiac threshold, the addition of RSA had no major qualitative effect on the HR/f distribution of coupling patterns or fo variability (Fig. 4).
Simulation of human time series
Although the qualitative behaviour of our model is similar to that observed in human subjects, it would be of considerable interest to demonstrate whether the model can simulate clinical observations exactly. Unfortunately, in clinical data we observe fo, HR and the RI interval variation, but the two variables fi and burst magnitude are unknown. To simulate the patterns of coupling and fo variability from real data we, therefore, need to choose suitable values for fi and burst magnitude. From the foregoing observations, several pointers are available to guide our choice of values:
Burst magnitude
(1)If there were no sudden transitions in heart rate or ventilatory frequency we could assume that the HR/fi relationship would wander smoothly through regions of the HR/fi versus burst magnitude map. A crude guide to burst magnitude could, therefore, be obtained if some transitions between patterns only occur in certain burst magnitude ranges. Thus, IV2lo only occurs at low burst magnitudes and a rapid transition between IV2hi and I2 via pattern C2, will only occur at high burst magnitudes
(2)Burst magnitude could be inferred from the magnitude of the maximum breathing frequency variation during pattern IV.
(3)The bands in the pattern III RI plot are evenly separated when burst magnitude is small but more closely grouped into pairs as burst magnitude increases. Close groupings therefore suggest a high burst magnitude.
Intrinsic breathing frequency
The longest ventilatory period will correspond to that preceding an intrinsic (I) triggered breath. For those patterns where the mechanism of inspiratory triggering varies between breaths (patterns III, IV, A, B, and C), the lowest breathing frequency will, therefore, correspond to fi. Unfortunately a pure pattern I (or II) epoch gives no obvious clues as to its control variables as all breaths are cardiac triggered and any combination of burst magnitude and fi falling within a pattern I zone gives the same HR/fo.
Using these observations, we could recreate the observed breathing patterns and RI plots of human subjects using the subjects own heart rate time series and inferred fi and burst magnitude values. In all clinical time series, which we have examined, agreement between the real and simulated RI plots could be obtained by appropriate selection of burst magnitude and fi. An example is shown in Figure 7, where the simulation is consistent with the explanation given for this time series in our previous paper.5 In simulations, the required burst magnitude varied between individuals explaining why some clinical time series show a variety of patterns despite similar heart and breathing frequencies. In addition, because these HR time series are RSA filtered, it is clear that RSA, although undoubtedly contributing to minor variations of RI and breathing frequency variation, does not play a critical role in the mechanism of coupling.
In Figure 8, we have modelled a transition between pattern IV and what appears to be uncoupled. The simulation revealed a similar transition but clearly indicates that what appears to be uncoupled may at times be the complex, multiple banded patterns A or B, presumably with the addition of noise.
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Discussion |
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From our clinical observations and from the clinically consistent behaviour of the model we can, therefore, elaborate on the preliminary hypothesis5 put forward for the generation of coupling, coupling patterns and intra-operative breathing irregularity.
In our hypothetical model, inspiration occurs when the activity of an intrinsic pacemaker function reaches an inspiratory firing threshold. The likelihood of this function crossing the firing threshold increases in response to a signal of cardiac origin, and therefore, the exact timing of inspiratory onset will vary according to whether the intrinsic pacemaker function crosses the threshold or whether an earlier cardiac signal causes threshold crossing. Depending upon the ratio of HR to fi, and the magnitude of the afferent cardiac signal, the sequence of consecutive threshold crossings (cardiac triggered versus intrinsic) will vary, and these variations are seen as the observed coupling patterns and corresponding breathing rate irregularities.
Pattern I
Consecutive inspirations are all initiated by the cardiac stimulus and the same number of heart beats occur within each ventilatory period (i.e. the entrainment ratio is constant). Pattern I occurs when HR/fi is in the range where consecutive leading edges of the cardiac burst cause inspiratory threshold crossing. If the magnitude of the cardiac stimulus is low, pattern I coupling only occurs when the HR/fi ratio is equal to, or a little over an integer value. However, as the cardiac stimulus intensity increases, pattern I occurs over a wider range of HR/fi values within a domain. The critical HR/fi above which pattern I is invariable (or because of noise pattern II) occurs, in our model, when the tip of one cardiac burst exceeds the base of the following cardiac burst (Fig. 1). It can be shown from simple geometry that in a simple linear model, this critical boundary occurs at HR/fi=1/burst magnitude. Breathing frequency variability during pattern I coupling is negligible because entrainment ratio is constant and ventilatory period equals the interval between burst related crossings of the inspiratory threshold.
Pattern II
Pattern II is a variant of pattern I in which small variations in (I) slope (and/or HR and burst magnitude) cause variation in the entrainment ratio. The effect of
(I) slope variation is greatest when
(I) slope is least and hence pattern II is most common at high HR/fi ratios or low breathing rates. Varying entrainment ratios cause quantal variation in breathing frequency corresponding to one or more multiples of the heart period.
Pattern III
Consecutive inspirations alternate between intrinsic and cardiac triggering. Ventilatory period also alternates with this variation; the alternate ventilatory periods are (i) from the cardiac burst crossing to intrinsic crossing and (ii) from the intrinsic crossing to cardiac burst crossing. The ventilatory period between a cardiac triggered breath and a following intrinsic breath will correspond to fi, whereas the interval from an intrinsically triggered inspiration to one that is cardiac triggered will be shorter. The magnitude of this variation from breath to breath is less than one heart period. It follows from this that the slowest observed frequency seen during pattern III variation will correspond to the intrinsic breathing frequency (fi).
Pattern IV
Cyclical periods of intrinsic inspiratory triggering follow periods of cardiac burst related triggering. Breathing rate varies according to the phase of this cycle although the largest variation will occur when a cardiac burst related breath changes to an intrinsic triggered breath. The minimum fo during a period of pattern IV coupling will occur during the phase of consecutive intrinsic crossings. Thus, as with pattern III, the intrinsic breathing frequency will correspond to the slowest observed frequency. The magnitude of the breathing frequency variation will be directly proportional to the magnitude of the afferent cardiac signal.
Uncoupled
Apparently uncoupled patterns are generated under two circumstances. (i) If burst magnitude is small and the majority of breaths are initiated by the intrinsic (I). Small degrees of breathing frequency variability under this circumstance may occur because of noise and occasional cardiac burst related triggerings. (ii) At higher burst magnitudes apparently uncoupled time series may be generated during complex patterns A and B which have been disrupted by small variations in HR, burst magnitude, fi and coupling interval.
The described model structure is remarkably similar to that proposed over 20 yr ago by Cohen and Feldman6 in order to explain the effects of electrical stimulation of certain brain regions on inspiratory timing. In their model, the slope of a hypothetical inspiratory function (also ) was increased or decreased by electrical stimulation of the rostral or ventral part of the nucleus parabrachialis, respectively. Delay or shortening of the expiratoryinspiratory phase switch could be achieved by such stimulation. Within the framework of Cohens model, cardioventilatory coupling might be viewed as an example of pulse synchronous rostral stimulation. It may therefore be relevant that the nucleus parabrachialis is the main relay for visceral traffic from the nucleus tractus solitarius to forebrain structures.7 As the nucleus tractus solitarius is the main site of termination of afferent cardiovascular receptors it is conceivable that this region could mediate coupling related cardiovascular stimulus.
An important component of our model is the presence of an intrinsic inspiratory pacemaker. A pacemaker such as this is well recognized, with spontaneous pacemaker activity being measured in isolated brain stem regions associated with respiratory activity. However, it is also known that the frequency of this pacemaker is slower than that in intact animal preparations. The pre-Botzinger complex of the isolated rat brain stem has an intrinsic frequency approximately one third that of the normal breathing rate and, in intact preparations, brain stem de-afferentation reduces breathing frequency.8 If, as many authors believe, the pre-Botzinger complex pacemaker is the origin of the breathing rhythm, a mechanism must exist which augments the intrinsic activity and increases the frequency of the core oscillator. A key feature of our model is the shortening of intrinsic ventilatory period by the cardiac afferent stimulus and therefore this might, in part, explain a mechanism for this augmentation. Furthermore, both somatic stimulation and locomotor activity are also capable of entraining the respiratory rhythm.911 Perhaps therefore cardioventilatory coupling simply represents one aspect of a general mechanism whereby an intrinsic respiratory pacemaker is augmented by a number of afferent inputs. Such a mechanism could relate to a variety of clinical observations including the ventilatory responses to stimulation and exercise.
Although ample evidence suggests the presence of an intrinsic respiratory pacemaker, and the presence of coupling suggests some form of interacting cardiovascular signal, we stress that the described model need not have exact neuroanatomical or electrophysiological correlates. The model is one that behaves in a similar manner to that of the intact anaesthetized human inspiratory timing mechanism, and as such, may be useful for predicting behaviour. It should be used with caution, however, for understanding the detailed underlying mechanisms. The quantity cardiac burst magnitude represents a process whereby the value of (I) and the inspiratory firing threshold are transiently brought closer together. This process could also have been brought about by other means with no change in the overall behaviour. Thus, the afferent cardiac signal could equally reduce inspiratory threshold instead of cardiac bursts augmenting
(I). Each variant does not differ in its overall behaviour and hence could equally be considered as models of inspiratory timing. However, certain features of the model are invariant, that is, present irrespective of how the model is constructed. Perhaps the most important of these is the central idea that a cardiac triggered breath will always be shorter than the intrinsic breath, which would have occurred if the cardiac signal had not been present. The effect of coupling in the model is always to increase the mean observed frequency over the intrinsic. This property has the potential for two clinical implications.
Cardioventilatory overdrive
In some regions of the HR/fi map (especially at high fi, high burst magnitude and at the boundary of patterns IVlo and I), fo may be driven at rates well in excess of fi. From our analysis, as HR/fi crosses from a IVlo to I zone, the HR/fo will be forced, at the same heart rate onto the next lowest integer relationship line. Thus, at HR=80 and fi=30, the HR/fi ratio is 2.66. If cardiac bursts are of sufficient magnitude to place this HR/fi ratio into a pattern I zone the resulting HR/fo would equal int2.66=2. As HR remains at 80 and HR/fo=2, the breathing frequency will increase from 30 to 40 bpm. Unexpectedly high breathing rates such as these are occasionally seen in anaesthetized subjects in the absence of opioids and may in part be a result of this cardioventilatory overdrive. It might be expected that if breathing frequency is driven in this manner for any length of time, with constant tidal volume, there will be a chemoreceptor mediated adjustment of minute ventilation to a lower value. Whether a resetting of intrinsic breathing frequency occurs or whether tidal volume falls in response to a sustained coupling related frequency overdrive, needs to be determined experimentally. However, if a resetting of intrinsic frequency occurred it would be expected that pattern I could not be sustained for long periods as the fi resetting will cause the HR/fi to move back into the IVlo zone and hence reduce mean breathing frequency. In our clinical time series, some subjects were observed to remain in pattern I, locked onto the integer relationship line for periods of 5 min or longer suggesting that minute ventilation is being adjusted in these subjects by changes in tidal volume, rather than through adjustment in fi.
Cardioventilatory support
The potential for excessively high breathing frequencies can be contrasted to the effect of coupling at low intrinsic breathing frequency. At low simulated breathing rates, the (I) slope is comparatively flat, and because all breaths at rates less than 1012 bpm are cardiac burst initiated, coupling is invariably present (as pattern I or II). It follows therefore that at low breathing rates the mean observed breathing frequency will always be greater than the intrinsic frequency. Figure 7 demonstrates this supporting effect of coupling in a human time series. After the administration of fentanyl, the opioid, presumably by an effect on the inspiratory pacemaker, has reduced fi to approximately 15.5 bpm (we can infer fi because, as noted above, the minimum fo will correspond to fi in patterns III, IV, A, B, C). The cardiac triggered breaths however are of higher breathing frequency and, as the breathing frequency jumps between cardiac and intrinsic triggered breaths the mean breathing frequency is increased to approximately 19 bpm. During opioid mediated depression of the intrinsic inspiratory pacemaker, therefore, cardiac afferent activity supports breathing frequency at values greater than that of the intrinsic pacemaker. Whether such support is clinically relevant remains to be determined. As noted above, the regulation of breathing involves the control of minute ventilation by alteration of both rate and tidal volume. However, a mechanism that is relevant to the control of frequency should be of clinical interest as central apnoea is a failure of frequency control. Because cardioventilatory coupling provides a simple non-invasive indication of frequency control which is not otherwise accessible, we suggest that observations of coupling (cardiac, somatic and locomotor) in subjects with abnormal control of respiratory frequency may be helpful.
In previous papers, we have attempted to quantify coupling in terms of the constancy of the RI1 interval (the interval between the inspiration and the preceding R wave). This constancy was measured as the proportional Shannon entropy of the RI1 interval (HRI1). This quantity varies according to coupling pattern, with the most disordered RI plots (i.e. those that are uncoupled) having higher HRI1values than those that are perfectly ordered (pattern I). HRI1 varies with pattern according to the order: I = II < III < IV < uncoupled. Although intuitively HRI1 may be considered a measure of strength of coupling our model clearly indicates that the true strength of coupling must be burst magnitude and that this cannot be directly equivalent to HRI1. Thus, two individuals may have identical burst magnitudes and very similar HR/fi ratios but if one falls into a pattern I zone the HRI1 will be low whereas the other, with a fractionally different HR/fi, may fall into a pattern III or IV zone and hence the HRI1 will be high. As the burst magnitude is identical in these subjects, the underlying strength of interaction between the cardiac afferent and the respiratory pacemaker is the same. Measures based on the RI interval variation such as HRI1, should be distinguished from the true strength of signal interaction (cardiac burst magnitude). Differences in coupling pattern (and hence HRI1) may be caused by minute changes in HR/fi and not by the changes in the strength of interaction between the cardiac afferent and the intrinsic pacemaker. To observe a true alteration in the strength of cardiac afferent/respiratory interaction, or to infer a intrinsic disorder of coupling, demands the observation of altered burst magnitude rather than a simple comparison of coupling pattern or RI plot. We describe several strategies for determining the magnitude of the cardiac afferent signal.
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Acknowledgements |
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References |
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2 Larsen PD, Galletly DC. Cardioventilatory coupling in the anaesthetised rabbit, rat and guinea pig. Pflugers Archiv 1999; 437: 9106[ISI][Medline]
3 Coleman WM. On the correlation of the rate of heart beat, breathing, bodily movement and sensory stimuli. J Physiol 1921; 54: 2137
4 Raschke F. Coordination in the circulatory and respiratory systems. In: Rensing L, an der Heiden U, Mackey MC eds. Temporal Disorder in Human Oscillatory Systems. Berlin: Springer-Verlag 1987; 15275
5 Galletly DC, Larsen PD. Ventilatory frequency variability during spontaneously breathing anaesthesia. Br J Anaesth 1999; 83: 55263
6 Cohen MI, Feldman JL. Models of respiratory phase switching. Fed Proc 1977; 36: 236774[ISI][Medline]
7 Dampney RAL. Functional organisation of central pathways regulating the cardiovascular system. Physiol Rev 1994; 74: 32364
8 Rekling JC, Feldman JL. Prebotzinger complex and pacemaker neurons: hypothesized site and kernel for respiratory rhythm generation. Annu Rev Physiol 1998; 60: 385405[ISI][Medline]
9 Bramble DM, Carrier DR. Running and breathing in mammals. Science 1983; 219: 2516[ISI][Medline]
10 Iscoe S. Respiratory and stepping frequencies in conscious exercising cats. J Appl Physiol 1981; 51: 8359
11 Iscoe S, Palosa C. Synchronization of respiratory frequency by somatic afferent stimulation. J Appl Physiol 1976; 40: 13848