Vol. 85, Issue 3, 787-788, September 1998
INVITED EDITORIAL
Invited Editorial on "Irregularities and power law distributions
in the breathing pattern in preterm and term infants"
Eugene N.
Bruce
Center for Biomedical Engineering, University of Kentucky,
Lexington, Kentucky 40506-0070
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ARTICLE |
THERE HAS BEEN A LONGSTANDING DESIRE to develop an
index that concisely describes the breath-to-breath irregularity of
breathing. Such an index might be useful for distinguishing potentially
pathological respiratory arrhythmias from "normal" variability in
the breathing pattern or for describing the maturational development of
respiratory control mechanisms in neonates. Early approaches (see Refs.
4, 5) were based on simple statistics of breath-by-breath values of
respiratory pattern variables, e.g., SD of tidal volume. More recent
studies have used power spectral analysis, comb filtering, and
autoregressive modeling to characterize breathing pattern variability
(6, 8, 9, 10, 12). However, although one can detect components of
respiratory variations that meet the criteria of these analyses, often
the detected components either appear to change unexpectedly with time
or account for only a small percentage of total respiratory
variability.
Contemporary methods of variability analysis derived from the fields of
stochastic systems and nonlinear dynamics (2, 11, 15) often utilize a
global index that is capable (theoretically) of characterizing the
variability in a signal over broad frequency and/or time
ranges. The paper by Frey et al. (7) applies the concept of power law
distributions to the analysis of breathing patterns of preterm and term
infants and concludes that a simple index 
, the slope of a log-log
plot of a type of histogram of respiratory intervals, can characterize
variability in breathing pattern in a global sense. Furthermore, this
index increases with postconceptional age (PCA) in both preterm and
term infants and, therefore, may be an indicator of maturation of the
respiratory rhythm generator. As the authors note, because of large
interindividual variability is not useful as an indicator of
maturation in individual infants, but its ability to represent the
relative likelihood of occurrence of long hypopneas in an infant may be
clinically noteworthy.
The analysis method developed by Frey et al. (7) identifies the
intervals between breaths, the tidal volumes for which exceed a
threshold specified as the mean tidal volume + 1 SD. [The
descriptor "interbreath intervals (IBIs)" is somewhat misleading, since most intervals encompass more than one breath.] These IBIs are expressed as a normalized histogram, and a linear fit is made to
the "tail" of a log-log plot of the histogram. The slope of this
line is . The paper is convincing in that the authors' data are
well fit by a straight line (average squared correlation coefficient of
the fitted data points was 0.973 ± 0.025), and the paper notes that
normally distributed IBIs would yield a large negative value for .
One might ask, however, how the observed values for compare with
these expected for a null hypothesis based on a breathing pattern that
is regular, except for some default uncorrelated noise. For example,
one null hypothesis might be a breathing pattern in which respiratory
rate is constant and tidal volume exhibits uncorrelated random
variations. It is easy to demonstrate from simulations that this latter
pattern yields logarithmic histograms having tails that are
approximately linear with slopes near the same range as seen in the
data of the paper discussed. There are important differences, however;
e.g., the IBI range of the apparently linear relation seems to be
significantly smaller in the simulated data, and may be independent
of the SD of the simulated data (implying that it might be difficult to
explain changes in ). These results derived from a simplistic model
do not dispute the findings of the paper but do substantiate the need
to define the statistical limits of the method of Frey et al. A related
question is whether the computation of exhibits a bias that depends
on the number of data points available. This point may be important if
the length of data records differs between studies.
To substantiate their experimental findings, the authors (7) also
analyzed the output of a mathematical model of respiratory rhythm
generation (3) subjected to noise disturbances. Arguably, other, more
recent models of this type (1, 14) better represent the present
thinking of the field, although the model used may provide helpful
insights. It should be noted, however, that Botros and Bruce
(3) did not test and validate their model for the low
values of tonic neural input to first neuronal group
(TNI1) that are invoked by Frey
et al. (7) to explain the generation of power law IBI data by the
model. One also must consider whether the disturbance effect of noisy
physiological afferent inputs that are distributed asynchronously
across a population of physiological ramp-inspiratory neurons (I
neurons) would be comparable to adding a large noise stimulus in a
model having only one TNI1 input
and one I neuron.
In the original paper of Botros and Bruce (3), vagal stretch-receptor
afferent input directly influenced two neuronal pools, the
early-inspiratory and the postinspiratory neurons. The hypothesis of
Frey et al. (7) that vagal afferents might be the source of the noisy
disturbances to the I neurons contradicts the original structure of the
model and needs to be evaluated further on the basis of physiological
results. Generally, pulmonary stretch afferents have not been thought
to directly affect I neurons.
There is an interesting parallel between the hypothesis that small
values of tonic input to I neurons may combine with noisy disturbances
to produce irregular breathing (7) and another recent hypothesis
regarding the genesis of apneas in neonates; Paydafar and Buerkel (13)
have suggested that at low levels of respiratory drive the expiratory
trajectory of the respiratory oscillator passes near a singularity in
its behavior. Thus a small noisy disturbance potentially can drive the
oscillator close to the singularity and produce a prolonged arrhythmic
period or, during this arrhythmic period, drive the oscillator back
toward its natural rhythm. Consequently, both hypotheses suggest that at low respiratory drives the influence of noisy disturbances on
respiratory rhythm is magnified by the dynamic properties of the
respiratory oscillator. In the model of Paydafar and Buerkel, contraction of the phase plot toward the singularity is assumed to be
due to decrease of chemoreceptor drive, and the possible role of
chemoreceptor afferents as a source of disturbances to TNI1 should be examined.
To address the specific mechanisms underlying these new findings (7),
it is probably necessary to develop an animal model that exhibits
similar behavior. Then a simple experiment would be to assess the
distribution of IBIs before and after vagotomy at various PCA.
Similarly, one could determine the influence of changing chemoreceptor
drive on IBIs. In addition, it may be possible to determine the role of
specific afferent inputs, or of the specific configuration of the
respiratory rhythm generator, by modifying neurotransmission at various
loci in the brain stem.
The authors have been appropriately cautious about inferring mechanisms
on the basis of observing a power law distribution of IBIs. Although
one would like to draw inferences about the temporal structure of the
breathing pattern, such speculations are premature. For example, the
occurrence of long IBIs could result from occasional grouping of
breaths having tidal volumes that are too low relative to metabolic
demand or from the presence of occasional very large breaths that cause
the tidal volume threshold to be artificially high relative to
metabolic demand. The types of mechanisms that might generate these two
types of data may be very different. In fact, it may be difficult to
attribute the power law behavior to a single mechanism. Because of the
existence of multiple feedback loops that control breathing,
variability generated at one site may reverberate throughout the
respiratory control system, creating multiple interactions encompassing
multiple time scales (4). Furthermore, the temporal relationships of breath-to-breath variations of respiratory pattern variables seem to be
at least as important as the magnitude of their fluctuations. Clearly,
this interesting paper will motivate a variety of future studies.
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