(Circulation. 1999;100:1065-1070.)
© 1999 American Heart Association, Inc.
Clinical Investigation and Reports |
Origin of Oscillatory Kinetics of Respiratory Gas Exchange in Chronic Heart Failure
From the National Heart & Lung Institute, Imperial College of Science, Technology and Medicine, London, UK; Piacenza Hospital (M.P.), Piacenza, Italy; and Klinik Innere Medizin III/Kardiologie, Martin-Luther-Universität Halle, Germany (M.R.).
Correspondence and reprint requests to Dr D.P. Francis, Heart Failure Unit, Royal Brompton Hospital, National Heart & Lung Institute, Imperial College of Science, Technology and Medicine, Sydney St, London SW3 6NP, UK. E-mail d.francis{at}cheerful.com
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Abstract |
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Background—Respiratory gas exchange measurements in patients with chronic heart failure (CHF) at rest and during exercise commonly reveal prominent slow oscillations in ventilation (
E), measured oxygen uptake
(O2), and carbon dioxide
production (CO2), whose origin
is not clear. Voluntary simulation of periodic breathing (PB) in
normals has been reported to generate a different pattern of
oscillations in gas exchange from that seen in spontaneous
PB. This necessitates hypothesizing that PB is caused by a primary
oscillation in tissue metabolism or in cardiac
output.
Methods and Results—We developed an automated method by which
normal controls could be guided to breathe according to a PB pattern.
The resultant metabolic oscillations closely
matched those seen in spontaneous PB and had several interesting
properties. At low workloads (including rest), the
oscillations in O2 were as
prominent as those in E in both spontaneous PB
(
VO2/VE=0.92±0.04) and voluntary PB
(0.93±0.07). However, at increased workload, the
oscillations in O2 because
less prominent than those in E in spontaneous PB
(intermediate workload 0.63±0.05, high workload 0.57±0.04;
P<0.001) and voluntary PB (intermediate 0.66±0.03, high
0.48±0.03; P<0.001). There was no difference in the
relative size of metabolic oscillations between
voluntary and spontaneous PB at matched workloads (P>0.05
at low, intermediate, and high workloads). Furthermore,
O2 peaked before E in
both spontaneous and voluntary PB. This time delay varied from 6.4±0.4
s at low ventilation, to 11.3±0.9 s at high ventilation
(P<0.0001).
Conclusions—The magnitude and phase pattern of oscillations in gas exchange of spontaneous PB can be obtained by adequately matched voluntary PB. Therefore, the gas exchange features of PB are explicable by primary ventilatory oscillation.
Key Words: heart failure • ventilation • metabolism
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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During exercise testing of some chronic heart failure (CHF) patients, marked periodic oscillations in measured oxygen uptake (
O2), measured carbon
dioxide production (CO2), and
ventilation (E) have been recognized, with a period
of approximately one minute,1 a manifestation of periodic
breathing (PB). The origin of these oscillations is
unclear. There are several possibilities, and these may be
conveniently grouped into (1) ventilatory and (2)
metabolic- hemodynamic.
The ventilatory hypothesis is that there is a primary cyclic
fluctuation in the homeostatic systems which regulate ventilation,
which results from the time delay between detection of a
disturbance and its correction. Fluctuating ventilation causes
variations in the body's gas stores, which manifest as
oscillations in O2 and
CO2 as determined by respiratory gas
exchange.
Three lines of evidence oppose this hypothesis. First, it has been
reported that the amplitude of O2
oscillation in spontaneous PB during exercise is more
prominent than the concomitant oscillation in
ventilation.2 This has been given as evidence of an
underlying oscillation in metabolism, driving
that in ventilation. Second, the metabolic
oscillations do not coincide in time with those in
ventilation. The third (and most persuasive) finding opposing a
ventilatory origin is that control subjects who volitionally simulated
PB failed to reproduce the magnitude and phase of the
metabolic oscillations seen in spontaneous
PB.2 This can be viewed as proof that primary ventilatory
oscillations cannot be the cause of the
oscillations observed in O2
and CO2 in patients with PB.
The alternative metabolic-hemodynamic
hypothesis is, therefore, that the fluctuations in
O2 and
CO2 in patients with spontaneous PB
result not from fluctuations in ventilation but instead from true
fluctuations in gas exchange of the tissues of the body.2
Because tissue O2 is equal to blood flow
multiplied by arteriovenous difference in oxygen content, there must be
either an underlying oscillation in cardiac output or in
tissue metabolic rate. Changes in either of these can
modulate ventilation3 through the action of
chemoreceptors4 and metaboreceptors,5 thus
causing periodic fluctuations in ventilation.
The rejection of the ventilatory hypothesis is based on the failure of voluntary PB to adequately match spontaneous PB. However, one drawback is that voluntary PB is difficult to perform and therefore may not match spontaneous PB well. A second drawback is that without appropriate guidance, controls find it difficult to simulate PB at low mean ventilation rates. It has been assumed that volitional simulation of the qualitative pattern of PB forms an adequate control group, even if the mean ventilation and workload are much higher than those of patients with spontaneous PB. There has been no study to date which assesses the effect of changing workload on the inter-relationships between metabolism and ventilation.
We therefore developed a computer program that could visually guide controls to simulate PB at different ventilation rates to suit rest and different exercise levels. We could thus examine the effect of different workloads on the interrelationship between ventilatory and measured metabolic oscillations.
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Methods |
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Subjects
We studied 13 patients with CHF who exhibited oscillatory breathing at rest and during clinical exercise testing (spontaneous PB) and 8 normal controls who performed voluntary PB at rest and during exercise. Patients had an average left ventricular ejection fraction of 34±10%. Six had ischemic heart disease, 1 had primary valvular disease, and the remaining 6 had idiopathic dilated cardiomyopathy. The patients were aged 52±20 years, and controls were aged 31±4 years. All subjects gave informed consent.
Exercise Studies
Patients and controls were studied for a short period at rest
and then during treadmill exercise, which followed a Bruce protocol
modified by the insertion of an initial stage of 0.5 mph at 5%
gradient. An Amis 2000 metabolic monitoring system
(Innovision), which used a heated pneumotachograph and respiratory mass
spectrometer, obtained breath-by-breath on-line calculations of
E, oxygen uptake O2
and carbon dioxide production
CO2.
Voluntary Periodic Breathing
To enable volunteers to simulate PB, the signal from the
pneumotachograph was also monitored by a second computer system
(Carrera) with custom-designed software which displayed, for the
volunteer, a moving bar representing their breathing in
association with a target. We could program this system with a
fluctuating ventilatory pattern, whose tidal volume varied sinusoidally
with a period of oscillation of 1 minute, and with a
controllable mean and amplitude. The software compared the volunteer's
respiratory rate and tidal volume with those of the programmed target.
It continuously computed and cumulated the difference between intended
and actual ventilation. It used this information to modify the target
presented to the volunteer. Thus the subject was guided to
correct undershoots or overshoots (of rate and/or volume). The result
achieved was a close approximation to a sinusoidal ventilation
pattern.
Quantification of Oscillation
For each cycle of oscillation, we calculated the
mean and amplitude (half the difference between peak and trough). We
defined the relative amplitude of the oscillation () as
the ratio between amplitude and mean. For example, if ventilation
varied between 15 and 25 L/min with mean 20 L/min, then the amplitude
would be 5 L/min and the relative amplitude, VE, would
be 5/20=0.25. We calculated VO2 and VCO2
in a similar manner.
Ventilatory oscillations in spontaneous PB become less
prominent (lower VE) at higher workloads. This must be
taken into account when comparing the sizes of metabolic
oscillations at different workloads. We therefore
calculated the ratio between VO2 and VE.
For example, if VE is 0.25 and VO2 is
0.20, then the size of the metabolic
oscillation in comparison to the ventilatory
oscillation is VO2/VE=0.8.
This ratio was also calculated for oscillations in
CO2.
Statistics
The distribution of continuous variables is described by
their mean and SD. When means of samples are being compared, each mean
is qualified by its standard error (SE). Statistical analysis
was carried out using Statview 4.5 (Abacus Concepts). Comparisons
between patients and controls, and/or across different workloads, were
made using ANOVA. P<0.05 was significant.
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Results |
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Examples of the ventilatory and metabolic data obtained are shown in Figure 1A
(spontaneous PB) and Figure 1B (voluntary PB). The fine line indicates
ventilation, whereas the thick line shows measured oxygen uptake. The
13 patients demonstrated a total of 84 cycles of PB, and the normal
controls performed a total of 170 cycles of voluntary PB. Overall
workload and ventilation rates were comparable between the 2 groups, as
shown in Table 1.
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The mean workload of each cycle was categorized into low
(O2 <6 mL ·
kg-1 · min-1, which included the
resting state), intermediate (6–12 mL · kg-1
· min-1), and high (>12 mL ·
kg-1 · min-1), so that similar numbers
of cycles of spontaneous PB were in each group. The same categorization
was applied to the cycles of voluntary PB.
Magnitude of Oscillations in
O2
The relative size of the oscillations in oxygen
uptake, in comparison to those in ventilation
(VO2/VE) averaged 0.74 (SE 0.03) in the
spontaneous PB of the patients. It was not significantly different in
the controls performing voluntary PB (mean
VO2/VE 0.71, SE 0.03, P>0.5).
However, the means of VO2/VE for all
subjects at different workloads were 0.93 (SE 0.05) at low, 0.67 (SE
0.03) at intermediate, and 0.52 (SE 0.03) at high workload (Figure 2A). The differences in
VO2/VE were all significant (low versus
intermediate, P<0.0001; intermediate versus high,
P=0.003; low versus high, P<0.0001).
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Considering the spontaneous and voluntary PB cycles separately (Figure 2B
) revealed a similar pattern. Among the spontaneous cycles, the means
of VO2/VE were 0.92 (SE 0.04) at low,
0.69 (SE 0.05) at intermediate, and 0.57 (SE 0.04) at high workload.
The differences were significant for low versus intermediate
(P=0.0003) and low versus high (P<0.0001) and
close to significant for intermediate versus high (P=0.057).
Among the voluntary cycles, the means of
VO2/VE were 0.93 (SE 0.07) at low, 0.66
(SE 0.03) at intermediate, and 0.48 (SE 0.03) at high workload. All the
differences were significant: low versus intermediate,
P<0.0001; intermediate versus high, P=0.01; low
versus high, P<0.0001.
Magnitude of Oscillations in
CO2
The relative size of the oscillations in
CO2 production, in comparison to those in
ventilation (VO2/VE) was greater overall
than the corresponding measure for oxygen uptake: mean
VCO2/VE 0.87 (SE 0.02) versus mean
VCO2/VE 0.72 (SE 0.02),
P<0.0001. This difference persisted across different
workloads: at low workload, 1.04 (SE 0.05) versus 0.93 (SE 0.05),
P<0.0001; at intermediate 0.83 (SE 0.02) versus 0.67 (SE
0.03), P<0.0001; at high 0.70 (SE 0.03) versus 0.52 (SE
0.03), P<0.0001. There was no significant difference in
VCO2/VE between spontaneous (0.81, SE
0.03) and voluntary PB (0.89, SE 0.03), P>0.05. Figure 3A shows the variation of
VCO2/VE with workload. Its mean value was
1.04 (SE 0.05) at low, 0.83 (SE 0.02) at intermediate, and 0.70 (SE
0.03) at high workload. These differences were all significant: low
versus intermediate, P<0.0001; intermediate versus high,
P=0.009; low versus high, P<0.0001. Again, this
difference in VCO2/VE was seen when
spontaneous and voluntary cycles were considered separately (Figure 3B).
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Timing of Oscillations in
O2
The peak in O2 preceded rather than
coincided with the peak in E. This
O2
E time delay
(TVO2VE) averaged 8.3 (SD 4.5) seconds over all the
cycles and was significantly different from zero
(P<0.0001), although there was a wide dispersion. This wide
dispersion in TVO2VE was seen both in spontaneous PB
cycles (mean TVO2VE 6.7, SD 4.4 seconds) and in
voluntary PB cycles (mean TVO2VE 9.1, SD 4.4 seconds) as
shown in Figure 4, although both were
significantly different from zero (P<0.0001 for both).
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No relationship was seen between TVO2VE and workload.
However, there was a clear relationship between TVO2VE
and ventilation level, as shown in Figure 5A. At low ventilation levels (<300
mL · kg-1 · min-1)
TVO2VE averaged 6.4 s (SE 0.4), at intermediate
(300–600 mL · kg-1 · min-1) it
was 9.1 s (SE 0.4), and at high (>600 mL ·
kg-1 · min-1) it was 11.3 s (SE
0.9). The comparisons between these are all statistically significant:
low versus intermediate, P<0.0001; intermediate versus
high, P=0.011; low versus high, P<0.0001.
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Separate analysis of spontaneous and voluntary PB cycles also
showed a similar result (Figure 5B). For spontaneous cycles, the
TVO2VE at the 3 ventilation levels averaged 4.8 (SE
0.7), 7.3 (SE 0.6), and 10.8 (SE 1.4) s, respectively. These
differences were all significant: low versus intermediate,
P=0.008; intermediate versus high, P=0.015; low
versus high, P<0.0001. For voluntary cycles, the
TVO2VE means were 7.3 (SE 0.5), 9.8 (SE 0.5) and 11.5
(SE 1.1). The differences between low and intermediate
(P=0.0005) and low and high (P=0.0002) were
significant, although that between intermediate and high ventilation
was not (P=0.11).
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Discussion |
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Periodic breathing, the waxing and waning of ventilation with a period of about one minute, has been a recognized feature of CHF for almost 2 centuries.6 7 Lately the development of on-line respiratory gas exchange analysis has demonstrated associated fluctuations in measured metabolic rates (
O2 and
CO2). Whether these fluctuations in
O2 and
CO2 are cause or effect of the
ventilatory oscillations is as yet an unresolved
question.1
Under the metabolic-hemodynamic hypothesis,
the O2 and
CO2 oscillate because of a primary
fluctuation in tissue metabolism or in cardiac output. In
support of this are echocardiographic8 and
radionuclide9 studies which demonstrate fluctuations in
stroke volume. CHF is associated with weakened baroreflex regulation of
heart rate,10 and experimental interference with
baroreflex function has been shown to enhance the natural fluctuations
in arterial blood pressure.11 Indeed, blood
pressure12 and even cerebral blood flow13
have been shown to oscillate during PB. Moreover, there is a potential
animal model in the Mayer wave phenomenon seen with experimental
hemorrhage: ventilation and blood pressure, as well as
directly-measured sympathetic and phrenic nerve activity are all seen
to oscillate together.14 In fact, many lines of evidence
support the concept of simultaneous ventilatory and
metabolic-hemodynamic fluctuations during
PB.15 But the most important clinical evidence showing
that the ventilatory oscillations could not be the prime
mover has been the failure of voluntary PB to reproduce the pattern of
metabolic oscillation seen in spontaneous
PB.
Our study is, to our knowledge, the first in which volunteers had not
simply an oscillatory target but also automated feedback of the
cumulative error in their ventilation, so that they could adapt their
rate and depth appropriately. It is also unique in that it considered
the effect of different workloads upon the observed
metabolic oscillations, in both patients and
controls. The central finding is that as workload increases, there is a
marked decline in size of the measured metabolic
oscillations in relation to the ventilatory ones (a falling
VO2/VE ratio). This occurs both in
patients with spontaneous PB and in normal controls with voluntary PB.
This key VO2/VE ratio does not differ
between patients and controls whether all cycles are considered
together or grouped by workload level. The other available measure of
metabolic rate, CO2, also
undergoes oscillations during periodic breathing. Again,
the relative size of these oscillations
(VCO2/VE ratio) is comparable between
spontaneous and voluntary PB and reduces with increasing workload in
both groups. The phase of the metabolic
oscillations also changes with level of ventilation; as
mean ventilation rises, the O2 peak
moves to a progressively earlier time with respect to the ventilatory
peak in both spontaneous PB and voluntary PB.
How can we reconcile these findings with the previous clinical
studies2 of voluntary PB which showed that the
metabolic oscillations measured during
voluntary PB differ dramatically from those occurring in spontaneous
PB? We propose that in fact there is no contradiction. In previous
work, the spontaneous PB cycles occurred at a relatively low workload,
with average oxygen uptake of about 8.7 mL ·
kg-1 · min-1 (obtained by calculating
an average of 653 mL/min from the published data and dividing by a
notional weight of 75 kg). In contrast, nearly 3-fold higher a workload
(approximately 23.9 mL · kg-1 ·
min-1) was applied to the normal controls carrying out
their voluntary PB cycles. Those volunteers manifested a relatively
smaller oscillation in O2
(in comparison to the oscillation in VE) than did the
patients; this was interpreted as a sign of an underlying
metabolic oscillation driving spontaneous PB.
Our study now offers an alternative explanation for the lower value of
VO2/VE seen in volunteers in previous
work: their workload was far higher, which we have now shown leads to
smaller VO2/VE ratios in both patients
and controls. When workload is instead matched,
VO2/VE is higher and equivalent in
patients and controls.
The same study also reported a large 39-degree phase discordance
(equivalent to 
6.5 seconds) between spontaneous and voluntary PB
with regard to timing of metabolic oscillation
in relation to ventilatory oscillation. This has also been
interpreted as evidence against a purely ventilatory origin for
spontaneous PB. Yet it can now be explained by the marked difference in
ventilation between those patients (which can be estimated at 387
mL · kg-1 · min-1) and their
controls (740 mL · kg-1 ·
min-1). The evidence from our study shows that such higher
ventilation can itself cause the observed metabolic
fluctuations to move earlier in phase in relation to the ventilatory
fluctuations. The difference in phase between low and high ventilation
in our patients alone was as high as 6 s.
Our study demonstrates that the metabolic oscillations seen in association with spontaneous PB can be closely emulated by voluntary PB. It removes the need to hypothesize an underlying hemodynamic or metabolic oscillation. Application of Occam's razor (the preference for minimal complexity in scientific explanations) obliges us to consider pure ventilatory oscillation an adequate primary driving force for spontaneous PB. Ventilation is dependent on arterial blood and tissue gas tensions, which in turn (after a circulation-time lag) are determined by lung gas concentrations whose levels themselves fluctuate according to ventilation.16 This sequence of relationships forms a closed circuit which may develop self-sustaining oscillations if the gains of the various linkages are high enough and the time-delays are adequate.17 In CHF, there is enhanced ventilatory sensitivity to both central18 and peripheral19 chemoreceptor stimulation. Chronically increased ventilation results in reduction in arterial concentration of both CO2 and bicarbonate,20 which weakens the blood's power to buffer against changes in CO2 levels so that the same change in ventilation yields a larger change in arterial pCO2 and pH. Circulation time is also prolonged in CHF. CHF patients with spontaneous PB manifest more severe forms of these abnormalities of chemoreflex control,21 circulation time,22 and blood buffering capacity.20 Modifying the levels of inspired oxygen23 and CO224 have been found to attenuate PB, as have procedures that may shorten circulation time such as valve operations,25 heart transplantation,26 and administration of cardioactive drugs such as milrinone27 or theophylline.28 Thus a wide body of observational, interventional, and theoretical studies support the concept of a primary oscillation in ventilation resulting from harmonic interactions between reflexes of the ventilatory control system and cardiopulmonary physiology.22 The cardiovascular fluctuations that have been documented to occur during PB may well exist, in both patients and controls, as a consequence of this primary oscillation in respiratory physiological control.
Why does the relationship between measured metabolism and
ventilation change as exercise progresses? We speculate that at low
workloads and associated low ventilations, lung O2 stores
are relatively stable. Consequently, periodic fluctuations in
ventilation produce proportional changes in respiratory exchange of
oxygen (VO2/VE close to unity). As
ventilation approaches its peak, the difference in O2
concentration between air and the lung begins to fall. Because
O2 is the product of alveolar
ventilation and O2 concentration difference between air and
lung, it peaks slightly before ventilation. This explains the small but
significant time delay between peak O2
and peak E, which in our study averaged 6 s at
rest and minimal exercise. With gradually increasing exercise, the mean
ventilation rises, generating swifter changes in lung gas stores in
response to cyclic fluctuations in ventilation. The nadirs in air-lung
O2 concentration difference more closely match the peaks in
ventilation. This has 2 effects. First, the peak in
O2 (which is related to the product
of the 2) occurs even sooner (because the air-lung O2
concentration difference falls more rapidly). In our study, at high
ventilation rates, the time difference between peak
O2 and peak E
extended to 11 s. Second, the amplitude of oscillation
of O2 is attenuated, because the 2
contributory components are almost in antiphase. Carbon dioxide has a
slightly different quantitative physiology; whereas oxygen can be
considered to be extracted from the lung into pulmonary blood
at a relatively constant rate irrespective of lung O2
fluctuations, carbon dioxide is effectively buffered by the passage of
pulmonary blood, whose CO2 concentration can vary
in response to lung CO2 concentration. The result is that
end-tidal CO2 is relatively more stable in the face of
irregular breathing than is end-tidal O2. For the reasons
given above, this leads to relatively larger oscillations
in CO2 than in
O2, particularly at the higher workloads
where the pulmonary blood flow (and consequently the buffering
effect on CO2 levels) is greater.
One important implication of this study is that planning of future investigations of the periodic breathing phenomenon should incorporate the knowledge that workload affects not only the overall size of the ventilatory oscillations1 but also the magnitude and phase of the observed relationships. Studies focusing purely on resting patients or exercising patients may thus have reason to demonstrate divergent results. Furthermore, when control subjects are involved, they should be matched with the patient group for workload and ventilation, if the comparison is to be appropriate.
In conclusion, this study shows for the first time that the oscillations measured in oxygen uptake and CO2 production in patients with spontaneous periodic breathing can be reproduced by appropriate voluntary periodic breathing in normal controls. We make the novel observations that the relative size of the metabolic oscillations becomes smaller with increasing workload, and that rising ventilation leads to a shift of oxygen uptake to a phase further ahead of that of ventilation itself. Finally, these changes occur not only in spontaneous periodic breathing but also in voluntary periodic breathing, which explains discrepancies observed in previous studies of this phenomenon. It is therefore not necessary to hypothesize a primary metabolic oscillation in the genesis of spontaneous periodic breathing of CHF. Harmonic fluctuations in reflex control, resulting from enhancement of chemoreflex sensitivity, slowed hemodynamics, and increased instability of blood gas stores, are an adequate explanation.
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Acknowledgments |
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Dr Francis is supported by the Estate of the late Mabel Grace Parker and by the British Heart Foundation (FS 98005); Dr Davies is supported by the Robert Luff Fellowship, Prof Coats, by the Viscount Royston Trust, and Dr Rauchhaus, by the Deutsche Herzstiftung e.V.
Received February 18, 1999; revision received June 1, 1999; accepted June 14, 1999.
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 M. Guazzi, J. Myers, M. A. Peberdy, D. Bensimhon, P. Chase, and R. Arena Exercise oscillatory breathing in diastolic heart failure: prevalence and prognostic insights Eur. Heart J., November 2, 2008; 29(22): 2751 - 2759. [Abstract] [Full Text] [PDF]
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 P. Agostoni, A. Apostolo, and R. K. Albert Mechanisms of Periodic Breathing During Exercise in Patients With Chronic Heart Failure Chest, January 1, 2008; 133(1): 197 - 203. [Abstract] [Full Text] [PDF]
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 M. Guazzi, R. Raimondo, M. Vicenzi, R. Arena, C. Proserpio, S. Sarzi Braga, and R. Pedretti Exercise oscillatory ventilation may predict sudden cardiac death in heart failure patients. J. Am. Coll. Cardiol., July 24, 2007; 50(4): 299 - 308. [Abstract] [Full Text] [PDF]
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 C. H. Manisty, K. Willson, R. Wensel, Z. I. Whinnett, J. E. Davies, W. L. G. Oldfield, J. Mayet, and D. P. Francis Development of respiratory control instability in heart failure: a novel approach to dissect the pathophysiological mechanisms J. Physiol., November 15, 2006; 577(1): 387 - 401. [Abstract] [Full Text] [PDF]
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P. Dall'Ago, G. R.S. Chiappa, H. Guths, R. Stein, and J. P. Ribeiro Inspiratory Muscle Training in Patients With Heart Failure and Inspiratory Muscle Weakness: A Randomized Trial J. Am. Coll. Cardiol., February 21, 2006; 47(4): 757 - 763. [Abstract] [Full Text] [PDF]
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J. J. Leite, A. J. Mansur, H. F. G. de Freitas, P. R. Chizola, E. A. Bocchi, M. Terra-Filho, J. A. Neder, and G. Lorenzi-Filho Periodic breathing during incremental exercise predicts mortality in patients with chronic heart failure evaluated for cardiac transplantation J. Am. Coll. Cardiol., June 18, 2003; 41(12): 2175 - 2181. [Abstract] [Full Text] [PDF]
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D. P Francis, K. Willson, P. Georgiadou, R. Wensel, L C. Davies, A. Coats, and M. Piepoli Physiological basis of fractal complexity properties of heart rate variability in man J. Physiol., July 15, 2002; 542(2): 619 - 629. [Abstract] [Full Text] [PDF]
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 W. Huang, M. P Kingsbury, M. A Turner, J.L. Donnelly, N. A Flores, and D. J Sheridan Capillary filtration is reduced in lungs adapted to chronic heart failure: morphological and haemodynamic correlates Cardiovasc Res, January 1, 2001; 49(1): 207 - 217. [Abstract] [Full Text] [PDF]
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 D. P. Francis, K. Willson, L. C. Davies, A. J.S. Coats, and M. Piepoli Quantitative General Theory for Periodic Breathing in Chronic Heart Failure and its Clinical Implications Circulation, October 31, 2000; 102(18): 2214 - 2221. [Abstract] [Full Text] [PDF]
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