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Temporal variation in the Vt -Ti relationship in humans
Respiration Phys~logy (1982) 47, 97-106 Elsevier Biomedical Press
97
T E M P O R A L V A R I A T I O N IN T H E VT-TI R E L A T I O N S H I P IN H U M A N S *
J. A N D R E W
D A U B E N S P E C K a n d M A R K W. F A R N H A M
Department of Physiology, Dartmouth Medical School, Hanover, NH 03755, U.S.A.
Abstract. The variation with time of the relationship between tidal volume (VT) and inspiratory dura-
tion (T0 was assessed by analysis of 34 breathing sequences, nominally of 300 breath duration, during eupnea and hypercapnic hyperpnea in 6 human subjects. Two approaches were used: (l) each sequence was divided into consecutive 50-breath blocks and standard regression techniques used to characterize VT as a function of Ti; and (2) a piecewise linear regression technique was applied to cluster consecutive breaths into regression regimes. Analysis of covariance was used with the results of both approaches to determine the likelihood that a single regression line was adequate to describe the entire data set. Similar results obtained regardless of the approach used. In only 4 of the 34 experiments would the hypothesis of regression slope homogeneity be accepted (P >0.05) using the clustering approach; in 27 experiments, it was indicated that the regression slope estimates of VT on TI should not be considered homogeneous. Changes in the VT-TI slope were not correlated with changes in mean levels of VT, TI, minute ventilation ('~), mean inspiratory flow (VT/TI), nor alveolar Pco2 (PAco2)' Thus it is apparent that the VT-TI relation cannot be considered temporally invariant, but changes with time over periods ranging from less than 20 to more than 100 breaths. Alveolar carbon dioxide Breathing pattern Hypercapnia
Inspiratory flow Periodic respiration Ventilation
V a r i a t i o n in the v o l u m e a n d t i m i n g c o m p o n e n t s o f the h u m a n b r e a t h i n g p a t t e r n is well d o c u m e n t e d ( P r i b a n , 1963; D e j o u r s et al., 1966) a n d oscillations in v a r i o u s aspects o f the b r e a t h i n g p a t t e r n have been r e p o r t e d (Lenfant, 1967; Hlastala et al., 1973; Brusil et al., 1980). N e w s o m Davis a n d Stagg (1975) showed that the correlation between VT a n d TI was positive a n d significant d u r i n g resting b r e a t h i n g sequences o f m o r e t h a n 200 breaths d u r a t i o n a n d further, that the regression o f VT o n TI passed close to the origin. They p o i n t e d o u t that this c o u p l i n g between VT a n d TI p e r m i t t e d m e a n i n s p i r a t o r y flow (VT/TI) to be m a i n t a i n e d relatively c o n s t a n t
Accepted for publication 28 September 1981 * This study was supported by National Institutes of Health Grant HL 19248 and Research Career Development Award HL 00280 to J.A. Daubenspeck. 0034-5687/82/0000-0000/$ 02.75 © Elsevier Biomedical Press
98
J.A. DAUBENSPECKAND M.W. FARNHAM
in the face of variations in the breath-by-breath values of VT and TI. These authors felt that the central control of ventilation operated by regulation of mean inspiratory airflow in accordance with the model of Clark and von Euler (1972). This model postulated that central respiratory drive determines the rate of lung inflation, approximated on the average by the mean inspiratory flow, which interacts with an inspiratory-terminating threshold to set both the inspiratory duration and volume of a given breath. Brusil et al. (1980) used a filtering technique to show that not only were oscillations in breath volume and timing apparent in their subjects at high altitude, but the interrelationship between the filtered volume and total breath duration components of the pattern, as characterized by the correlation coefficient, changed dramatically over the course of a hundred or so breaths. The goal of the present investigation was to determine the temporal stability of the VT:TI relationship reported by Newsom Davis and Stagg (1975).
Methods
Six normal human volunteers in good health served as subjects for this study (5 male, 1 female; ages 22-33 years). The responses during resting eupnea and hypercapnia to be reported here were measured using techniques and procedures explained in more detail elsewhere (Daubenspeck, 1979, 1981) and therefore only a brief description will be given here. A closed-circuit breathing apparatus was used that permitted elevation of the inspired CO2 by adjustment of the amount of expired gas that could bypass a CO z absorption canister. Inspired airflow was measured with a wire-screen pneumotachometer and this flow was monitored by an on-line minicomputer, which measured and stored breath-by-breath values for VT (from digital integration of inspiratory airflow) and phase durations (TI and TE). Eupneic breathing was measured while subjects inspired mildly hyperoxic (PIo2 -250-280 Torr) gas containing no CO2. Hypercapnic data were obtained on separate occasions when FIco: was elevated sufficiently to produce a hyperpnea of 20-40 1 per min. The eucapnic and hypercapnic tests were randomly selected and at least 2 tests were performed in each condition for each subject. Subjects were permitted to acclimate to the apparatus for about 15 min prior to the start of data collection. During this period, inspired CO 2 was elevated if hypercapnia was to be applied. Data collection then commenced for a nominal 300 breath span; later editing of cough and swallow artifacts often resulted in fewer breaths available for analysis. A total of 34 experiments, each containing from 232 to 300 breaths (average 290 + 2 SE), were subjected to analysis procedures to be described.
TEMPORAL VARIATION IN HE VT-T1 INTERRELATIONSHIP
99
Results
The initial approach was to simply subdivide each data set into consecutive blocks of.sequential breaths (nominally 50) and separately subject each block to regression analysis. The resulting set of estimates of the regression relation of VT on TI for the 5-6 separate regimes was assessed for homogeneity using analysis of covariance techniques (Brownlee, 1965). A typical set of regression lines is shown in fig. 1 for one experiment so analyzed. The results of analysis of covariance of these data indicate that a single regression equation is not adequate to describe all breath values and that it is unlikely that the set of estimated slopes from the 50-breath blocks reflects a steady, underlying value holding over the entire experiment. Inhomogeneity of the regression slopes was indicated in 21 of the 34 experiments and in only 2 experiments was it reasonable to accept a single regression relation to describe the responses. It is obvious that separation of the data into fixed length blocks for analysis is arbitrary and unsynchronized with whatever changes may have occurred in the control processes. Therefore a more general procedure was adopted using a piecewise linear regression technique described by McGee and Carleton (1970). This technique assembles the (VT, TI) data pairs into clusters of consecutive breaths in a stepwise fashion according to the effect of each operation upon the quality of the regression (goodness-of-fit) pertaining to the cluster under consideration. This procedure is briefly outlined in Appendix A. The clustering procedure begins with the unclustered data set of separate points and proceeds to the final clustering step where all data are analyzed together, identical to the usual regression analysis of the entire data set. Information is provided at each step concerning not only the regression parameters of the particular clusters, but also concerning the likelihood
1.5 ~
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Fig. l. Comparisonof regression linescomputed for 6 consecutive50-breath sequencesfrom one experiment in eucapnia. Analysisof covariance indicated that the null hypothesisof slope homogeneityshould not be accepted (P < 0.001). This conclusionholds for 21 of 34 experiments.
100
J.A. DAUBENSPECK AND M.W. FARNHAM
that a statistically consistent regression regime results from the current clustering operation. The results of such piecewise regression are generally assessed starting from the clustering level where all but some predetermined number of breaths have been included into regression clusters, and working toward the final point. A solution is identified based upon the probability that a statistically consistent regression regime has been created by the clustering operation at a given level. For the purposes of the present analysis, it seemed reasonable to permit no more than 15 breaths ( 5 ~ of the total) to be unincorporated into a regression regime for a solution to be acceptable; a probability greater than 0.05 for a particular clustering procedure was assumed to indicate consistency and attention was directed principally to those clustering procedures which joined two clusters (and involved many points) rather than those which merely added a single point to an existing cluster (and thus involved fewer points). The interpretation procedure is described in more detail by McGee and Carleton (1970). A drawback to this piecewise approach is that a globally optimal solution is not guaranteed by the selection of an optimal clustering operation at each level since once a cluster is formed, it cannot later be broken apart. Some assessment of the stability of a solution can be gained by altering the minimal size permitted for a cluster and repeating the analysis as described by McGee and Carelton. Normally the minimum cluster was set to include 10 breaths; at times this was reduced to 5 breaths, the analysis redone, and the solutions compared as will be shown. The results of such clustering analysis of an experimental data set are demonstrated in fig. 2A, which shows the breath limits and regression slopes for each cluster identified in the solution. A very similar solution (fig. 2B) was determined using a minimum cluster size of 5 instead o f the normal 10 breaths a n d this was true in most, but not all analyses. It was usually true that the general features of the clustering were apparent regardless of the minimum cluster size selected. It was always true that if multiple regimes were identified in the solution using a 10-breath minimum cluster, then more than one regime would be identified using the smaller minimum cluster size. Multiple regression regimes were indicated in 31 of the 34 experiments. Analysis of covariance supported the clustering results in 30 of those 31 situations, showing a single regression relation to be inadequate to describe the responses. In 27 of those 30 experiments, it was possible to reject the null hypothesis that the slope estimates were homogeneous. It frequently appeared that clusters tended to form between extreme values of VT and/or TI. In order to remove the influence of such outliers upon the clustering, the data sets were reanalyzed after deletion of any breath having a VT or Tl value more than 4 SD from the mean of the preceding 10 breaths. This editing removed an average of 23 breaths (range 3 to 49) from each data set and significantly reduced the numbers of separate clusters determined in each analysis from 6.56 + 0.51 (SE) to 3.91 + 0.38 (P < 0.001). Thus the solutions for the edited data often differed
TEMPORAL VARIATION IN THE VT-TI INTERRELATIONSHIP
101
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Fig. 2. Comparison of regression slopes fitted to breath sequences identified using piecewise linear regression. The numbers inside each bar indicate the limits of each regression regime by breath number. The results are shown when the minimum regression size was set to 10 breaths in panel A; panel B shows results using a minimum size of 5 breaths for the regression. Note that the majority of breaths (240 of 289) are included in identical clusters regardless of the choice of the minimum cluster size. Covariance analysis indicates that the null hypothesis of slope homogeneity should not be accepted (P < 0.001).
considerably from those of the unedited data, not a surprising result since the data sets differed by the numbers of breaths deleted. Even so, solutions with more than one regression regime were identified in 29 of 34 edited experiments and the hypothesis of homogeneity of the regression slope could be rejected in those experiments. The comparison between fitted regression lines and the edited (VT, TI) observations from one experiment is shown in fig. 3. It is apparent that the mean VT/TI does not differ greatly a m o n g clusters as the regression lines tend to pivot around a c o m m o n point and this was frequently seen. Figure 4 shows the regression slopes found during hypercapnia for one subject. More than one regression regime was found in 16 of the 17 hypercapnic tests as compared to the same result on 14 of the 17 eupneic tests. The number of hypercapnic tests demonstrating regression slope inhomogeneity was 14 of the 16 for comparison to the same conclusion in 13 of the 14 eupneic tests in which a single regression regime was found inadequate. Thus no influence of hypercapnic hyperpnea upon the temporal changes in the regression lines was apparent. In order to determine whether the fluctuations in the VT-TI relationship were related to changes in ventilatory performance, mean values for VT, TI, ~', VT/TI, and PETco~ were computed for each regression regime identified in the solution. No pattern between changes in the mean levels of these variables and changes in the regression parameters could be identified using rank correlation coefficients.
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Fig. 3. Comparison of fitted regression lines to actual data for regression regimes identified by piecewise linear regression. The data shown have been edited by deletion of 22 breaths identified as outliers prior to regression analysis as described in the text. Panels A, B, and C show each of the separate regimes with the previous regimes' regression line dashed; panel D shows all the data together with the separate regression lines. Covariance analysis indicates that the null hypothesis of slope homogeneity should not be accepted (P < 0.001).
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Fig. 4. Comparison of regression slopes fitted to breath sequences identified using piecewise linear regression on data obtained during hypercapnic hyperpnea of 19.8 LPM. Null hypothesisof slope homogeneity should not be accepted (P < 0.001).
Discussion The main finding o f these analyses is that changes in the relationship between VT and TI often occur with time and the assumption of a fixed VT-TI relationship is often not valid over more than a few breaths. Clustering analysis demonstrates the e,xistence of separate regression regimes having spans from less than 20 to more than 100 breaths. That these results are not simply an artifact of the clustering technique is indicated from the results of the fixed block analysis, which arbitrarily separated the data into fixed clusters and supports the same conclusion. Thus the VT-TI relationship predicted over the span of 40-50 breaths is not necessarily representative o f the average VT-TI relationship estimated over several hundred breaths. It may be that neither of these data collection spans is a satisfactory window through which to assess the VT-TI relationship over shorter spans. The mechanisms responsible for the changes in the VT-TI relationship are not established. It is known that the average VT/TI is depressed by both elastic loads (Daubenspeck, 1979) and flow resistive loads, (Zechman et aL, 1957; Altose et al., 1979; Daubenspeck, 1981). Spontaneous oscillation in canine tracheal smooth muscle tone has been reported by Beinfield and Seifter (1980) and such variation ought to produce alterations in internal mechanics. Such alterations may influence the average VT/TI as do external loads but it is not known how such internal loading changes may alter the VT-TI variation about this mean VT/TI. Significant correlations between the mean levels of the separate pattern parameters, minute ventilation, mean inspiratory flow, or end-tidal CO2 and changes in the VT-TI were rarely found. It is not possible to assess a possible connection between changes in estimated respiratory drive and changes in the slope of the VT-T! relation, since this would require continuous estimation of changes in respiratory mechanics or workrate and such measurements were not performed here.
104
J.A. DAUBENSPECK AND M.W. FARNHAM
Newsom Davis and Stagg (1975) noted that the VT-TI correlation was decreased from the awake state value by sleep in the one subject for whom both measurements were available. In the present study we requested that subjects keep their eyes open during the tests and most subjects read and/or listened to music during the experiments. Tests were not included in the analysis if there was any question about whether or not the subject was awake. Within these constraints upon allowable alterations in the level o f consciousness, it is still possible that small changes in the level of alertness could alter the VT-TI relationship. Reduction in the mean level of ventilation has been noted upon simply closing the eyes (Asmussen, 1977) and thus we cannot rule out influences of alterations in the level of alertness upon the VT-TI relation over the span of each experiment ( ~ 3 0 min). It is likely that a change in the state of cortical activity is not the sole factor influencing the VT-TI relation since changes in this relationship occurred commonly during moderate hypercapnic hyperpnea when the concommitant arousal would have minimized spontaneous lapses toward sleep. Without concurrent measurements o f the EEG, we cannot rule out the possibility that changes in the E E G occur spontaneously with time during hypercapnic hyperpnea and may influence the variation in VT-TI that we observe. The next steps in elucidating the mechanisms responsible for the observed changes in the VT-TI relation should include concurrent monitoring of the EEG and breath-by-breath measurement of respiratory mechanics. Whatever the cause of these changes in the VT-TI relationship that were observed, the implication is that the long period oscillations demonstrated with respect to other aspects of the breathing pattern (Priban, 1963 ; Dejours et al., 1966 ; Lenfant, 1967; Hlastala et al., 1973) may also be reflected in the changing relationship between VT-TI. Alteration in the pattern relationship between VT and TT has been shown to occur with time in some subjects during altitude acclimatization (Brusil et al., 1980). The present results indicate that variation in the VT-TI relation is the rule in normal subjects during normoxia.
Acknowledgements The authors express their sincere thanks to Prof. Victor McGee for his kind advice concerning the analysis of the data.
Appendix A PIECEWISE LINEAR REGRESSION SCHEME The piecewise linear regression scheme used in this study follows the procedures set forth by McGee and Carleton (1970), which is briefly outlined here. The data are considered to be sequentially ordered with respect to time and points are incorporated into regression clusters according to the particular
T E M P O R A L VARIATION IN THE VT-TI I N T E R R E L A T I O N S H I P
105
clustering operation producing the best linear fit of the potential operations possible at any given point in the stepwise clustering. Once the minimum allowable size of a regression regime has been selected (and here we have chosen the minimum cluster size to be 5 or 10 breaths), then at any clustering level one of three operations will be selected: (1) a single breath may be incorporated into an existing adjacent cluster; (2) two adjacent clusters may be conjoined to form a single regression cluster; or (3) a new cluster o f the designated minimum size may be formed from separate, but adjacent breaths. The selected option of these three possibilities depends upon which results in the best fit judged by a standard least-squares criterion applied to the breaths included in the new regression cluster. McGee and Carleton (1970) provide appropriate F statistics by which to assess the reasonableness o f the selected operation by comparison of the sum of the squared deviations before and after the particular clustering operation. Using the probabilities associated with the computed F statistics, decisions can be made about where to halt the clustering process once the number o f breaths yet unincorporated into a cluster is less than a preselected maximum. We have chosen this level to be 5 ~ of the total number of breaths when the minimum cluster size was 10 breaths, and reduced this to 2.5% when the minimum cluster size was reduced to 5 breaths since the smaller minimum cluster size permits more breaths to be unincorporated at any stage of the clustering. A flow chart of the clustering procedure has been adapted directly from McGee and Carleton (1970) and is listed below: (1) input data and minimum cluster size to be used; (2) identity all potential clusters for the next clustering level and compute the goodness-of-fit for each potential cluster using the sum-of-squared deviations about the potential regression line; (3) identify the best-fit cluster as that with the smallest mean square residual; (4) if the number o f unincorporated breaths is less than the preselected maximum, then go to 5; otherwise go to 2; (5) if the newest cluster is a newly-formed cluster of minimum size, then go to 2 ; otherwise compute the appropriate F statistic for this clustering operation; (6) print the clustering details at this level and determine whether this is the final level o f clustering (all breaths included into a single regression regime). If so, then stop; otherwise go to 2. We have implemented this flowchart in a subset of the computer language PL/I that runs on our laboratory minicomputer. A listing with documentation will be provided for the cost of postage upon request to the authors.
References Altose, M . D . , S.G. Kelsen and N.S. Cherniak (1979). Respiratory responses to changes in airflow resistance in conscious man. Respir. Physiol. 36: 249-260. Asmussen, E. (1977). Regulation of respiration: 'The Black Box'. Acta Physiol. Scand. 99: 85-90. Beinfield, W. H. and J. Seifter (1980). Spontaneous mechanical activities of dog trachealis muscle in vivo. J. Appl. Physiol. 48: 320-328. Brownlee, K.A. (1965). Statistical Theory and Methodology in Science and Engineering. New York, J. Wiley, pp. 376-388. Brusil, P. J., T. B. Waggener, R. E. Kronauer and P. Gulesian, Jr. (1980). Methods for identifying respiratory oscillations disclose altitude effects. J. Appl. Physiol. 48:545 556. Clark, F.J. and C. von Euler (1972). On the regulation of depth and rate of breathing. J. Physiol. (London) 222: 267-295. Daubenspeck, J.A. (1979). Ventilatory responses to elastic loading at constant PAco 2 in hypercapnic hyperpnea. J. Appl. Physiol. 47: 778-786. Daubenspeck, J.A. (1981). Influence of small mechanical loads on variability o f breathing pattern. J. Appl. Physiol. 50: 299-306.
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Dejours, P., R. Puccinelli, J. Armand and M. Dicharry (1966). Breath-to-breath variations of pulmonary gas exchange in resting man. Respir. Physiol. 1 : 265-280. Hlastala, M.P., B. Wranne and C. J. Lenfant (1973). Cyclical variations in FRC and other respiratory variables in resting man. J. Appl. Physiol. 34: 670-676. Lenfant, C. (1967). Time-dependent variations of pulmonary gas exchange in normal man at rest. J. Appl. Physiol. 22: 675~i84. McGee, V.E. and W.T. Carleton (1970). Piecewise regression. J. Am. Star. Assoc. 65:1109-1124. Newsom Davis, J. and D. Stagg (1975). Interrelationships of the volume and time components of individual breaths in resting man. J. Physiol. (London) 245:481-498. Priban, I.P. (1963). An analysis of some short-term patterns of breathing in man at rest. J. Physiol. (London) 166: 425-434. Zechman, F., F. G. Hall and W. E. Hull (1957). Effects of graded resistance to tracheal airflow in man. J. Appl. Physiol. 10: 356-362.
97
T E M P O R A L V A R I A T I O N IN T H E VT-TI R E L A T I O N S H I P IN H U M A N S *
J. A N D R E W
D A U B E N S P E C K a n d M A R K W. F A R N H A M
Department of Physiology, Dartmouth Medical School, Hanover, NH 03755, U.S.A.
Abstract. The variation with time of the relationship between tidal volume (VT) and inspiratory dura-
tion (T0 was assessed by analysis of 34 breathing sequences, nominally of 300 breath duration, during eupnea and hypercapnic hyperpnea in 6 human subjects. Two approaches were used: (l) each sequence was divided into consecutive 50-breath blocks and standard regression techniques used to characterize VT as a function of Ti; and (2) a piecewise linear regression technique was applied to cluster consecutive breaths into regression regimes. Analysis of covariance was used with the results of both approaches to determine the likelihood that a single regression line was adequate to describe the entire data set. Similar results obtained regardless of the approach used. In only 4 of the 34 experiments would the hypothesis of regression slope homogeneity be accepted (P >0.05) using the clustering approach; in 27 experiments, it was indicated that the regression slope estimates of VT on TI should not be considered homogeneous. Changes in the VT-TI slope were not correlated with changes in mean levels of VT, TI, minute ventilation ('~), mean inspiratory flow (VT/TI), nor alveolar Pco2 (PAco2)' Thus it is apparent that the VT-TI relation cannot be considered temporally invariant, but changes with time over periods ranging from less than 20 to more than 100 breaths. Alveolar carbon dioxide Breathing pattern Hypercapnia
Inspiratory flow Periodic respiration Ventilation
V a r i a t i o n in the v o l u m e a n d t i m i n g c o m p o n e n t s o f the h u m a n b r e a t h i n g p a t t e r n is well d o c u m e n t e d ( P r i b a n , 1963; D e j o u r s et al., 1966) a n d oscillations in v a r i o u s aspects o f the b r e a t h i n g p a t t e r n have been r e p o r t e d (Lenfant, 1967; Hlastala et al., 1973; Brusil et al., 1980). N e w s o m Davis a n d Stagg (1975) showed that the correlation between VT a n d TI was positive a n d significant d u r i n g resting b r e a t h i n g sequences o f m o r e t h a n 200 breaths d u r a t i o n a n d further, that the regression o f VT o n TI passed close to the origin. They p o i n t e d o u t that this c o u p l i n g between VT a n d TI p e r m i t t e d m e a n i n s p i r a t o r y flow (VT/TI) to be m a i n t a i n e d relatively c o n s t a n t
Accepted for publication 28 September 1981 * This study was supported by National Institutes of Health Grant HL 19248 and Research Career Development Award HL 00280 to J.A. Daubenspeck. 0034-5687/82/0000-0000/$ 02.75 © Elsevier Biomedical Press
98
J.A. DAUBENSPECKAND M.W. FARNHAM
in the face of variations in the breath-by-breath values of VT and TI. These authors felt that the central control of ventilation operated by regulation of mean inspiratory airflow in accordance with the model of Clark and von Euler (1972). This model postulated that central respiratory drive determines the rate of lung inflation, approximated on the average by the mean inspiratory flow, which interacts with an inspiratory-terminating threshold to set both the inspiratory duration and volume of a given breath. Brusil et al. (1980) used a filtering technique to show that not only were oscillations in breath volume and timing apparent in their subjects at high altitude, but the interrelationship between the filtered volume and total breath duration components of the pattern, as characterized by the correlation coefficient, changed dramatically over the course of a hundred or so breaths. The goal of the present investigation was to determine the temporal stability of the VT:TI relationship reported by Newsom Davis and Stagg (1975).
Methods
Six normal human volunteers in good health served as subjects for this study (5 male, 1 female; ages 22-33 years). The responses during resting eupnea and hypercapnia to be reported here were measured using techniques and procedures explained in more detail elsewhere (Daubenspeck, 1979, 1981) and therefore only a brief description will be given here. A closed-circuit breathing apparatus was used that permitted elevation of the inspired CO2 by adjustment of the amount of expired gas that could bypass a CO z absorption canister. Inspired airflow was measured with a wire-screen pneumotachometer and this flow was monitored by an on-line minicomputer, which measured and stored breath-by-breath values for VT (from digital integration of inspiratory airflow) and phase durations (TI and TE). Eupneic breathing was measured while subjects inspired mildly hyperoxic (PIo2 -250-280 Torr) gas containing no CO2. Hypercapnic data were obtained on separate occasions when FIco: was elevated sufficiently to produce a hyperpnea of 20-40 1 per min. The eucapnic and hypercapnic tests were randomly selected and at least 2 tests were performed in each condition for each subject. Subjects were permitted to acclimate to the apparatus for about 15 min prior to the start of data collection. During this period, inspired CO 2 was elevated if hypercapnia was to be applied. Data collection then commenced for a nominal 300 breath span; later editing of cough and swallow artifacts often resulted in fewer breaths available for analysis. A total of 34 experiments, each containing from 232 to 300 breaths (average 290 + 2 SE), were subjected to analysis procedures to be described.
TEMPORAL VARIATION IN HE VT-T1 INTERRELATIONSHIP
99
Results
The initial approach was to simply subdivide each data set into consecutive blocks of.sequential breaths (nominally 50) and separately subject each block to regression analysis. The resulting set of estimates of the regression relation of VT on TI for the 5-6 separate regimes was assessed for homogeneity using analysis of covariance techniques (Brownlee, 1965). A typical set of regression lines is shown in fig. 1 for one experiment so analyzed. The results of analysis of covariance of these data indicate that a single regression equation is not adequate to describe all breath values and that it is unlikely that the set of estimated slopes from the 50-breath blocks reflects a steady, underlying value holding over the entire experiment. Inhomogeneity of the regression slopes was indicated in 21 of the 34 experiments and in only 2 experiments was it reasonable to accept a single regression relation to describe the responses. It is obvious that separation of the data into fixed length blocks for analysis is arbitrary and unsynchronized with whatever changes may have occurred in the control processes. Therefore a more general procedure was adopted using a piecewise linear regression technique described by McGee and Carleton (1970). This technique assembles the (VT, TI) data pairs into clusters of consecutive breaths in a stepwise fashion according to the effect of each operation upon the quality of the regression (goodness-of-fit) pertaining to the cluster under consideration. This procedure is briefly outlined in Appendix A. The clustering procedure begins with the unclustered data set of separate points and proceeds to the final clustering step where all data are analyzed together, identical to the usual regression analysis of the entire data set. Information is provided at each step concerning not only the regression parameters of the particular clusters, but also concerning the likelihood
1.5 ~
SLOPE.Ts2t 3 ....
V T(L)
,~
~/®
.486~ HO: SLOPE ESTIMATESHOMOGENEOUS THIS EXPT,: F(5,287)=i3.0, p<.OOI
~
~:~" h~ \%~/~'~'-~
Ioo HOTACCEPTHol
~
1.0
'~ ~
\b\ "C~'~
SUBJ 04
o(
.5
i.'o
=:~
2'.o
Tz (S)
Fig. l. Comparisonof regression linescomputed for 6 consecutive50-breath sequencesfrom one experiment in eucapnia. Analysisof covariance indicated that the null hypothesisof slope homogeneityshould not be accepted (P < 0.001). This conclusionholds for 21 of 34 experiments.
100
J.A. DAUBENSPECK AND M.W. FARNHAM
that a statistically consistent regression regime results from the current clustering operation. The results of such piecewise regression are generally assessed starting from the clustering level where all but some predetermined number of breaths have been included into regression clusters, and working toward the final point. A solution is identified based upon the probability that a statistically consistent regression regime has been created by the clustering operation at a given level. For the purposes of the present analysis, it seemed reasonable to permit no more than 15 breaths ( 5 ~ of the total) to be unincorporated into a regression regime for a solution to be acceptable; a probability greater than 0.05 for a particular clustering procedure was assumed to indicate consistency and attention was directed principally to those clustering procedures which joined two clusters (and involved many points) rather than those which merely added a single point to an existing cluster (and thus involved fewer points). The interpretation procedure is described in more detail by McGee and Carleton (1970). A drawback to this piecewise approach is that a globally optimal solution is not guaranteed by the selection of an optimal clustering operation at each level since once a cluster is formed, it cannot later be broken apart. Some assessment of the stability of a solution can be gained by altering the minimal size permitted for a cluster and repeating the analysis as described by McGee and Carelton. Normally the minimum cluster was set to include 10 breaths; at times this was reduced to 5 breaths, the analysis redone, and the solutions compared as will be shown. The results of such clustering analysis of an experimental data set are demonstrated in fig. 2A, which shows the breath limits and regression slopes for each cluster identified in the solution. A very similar solution (fig. 2B) was determined using a minimum cluster size of 5 instead o f the normal 10 breaths a n d this was true in most, but not all analyses. It was usually true that the general features of the clustering were apparent regardless of the minimum cluster size selected. It was always true that if multiple regimes were identified in the solution using a 10-breath minimum cluster, then more than one regime would be identified using the smaller minimum cluster size. Multiple regression regimes were indicated in 31 of the 34 experiments. Analysis of covariance supported the clustering results in 30 of those 31 situations, showing a single regression relation to be inadequate to describe the responses. In 27 of those 30 experiments, it was possible to reject the null hypothesis that the slope estimates were homogeneous. It frequently appeared that clusters tended to form between extreme values of VT and/or TI. In order to remove the influence of such outliers upon the clustering, the data sets were reanalyzed after deletion of any breath having a VT or Tl value more than 4 SD from the mean of the preceding 10 breaths. This editing removed an average of 23 breaths (range 3 to 49) from each data set and significantly reduced the numbers of separate clusters determined in each analysis from 6.56 + 0.51 (SE) to 3.91 + 0.38 (P < 0.001). Thus the solutions for the edited data often differed
TEMPORAL VARIATION IN THE VT-TI INTERRELATIONSHIP
101
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Fig. 2. Comparison of regression slopes fitted to breath sequences identified using piecewise linear regression. The numbers inside each bar indicate the limits of each regression regime by breath number. The results are shown when the minimum regression size was set to 10 breaths in panel A; panel B shows results using a minimum size of 5 breaths for the regression. Note that the majority of breaths (240 of 289) are included in identical clusters regardless of the choice of the minimum cluster size. Covariance analysis indicates that the null hypothesis of slope homogeneity should not be accepted (P < 0.001).
considerably from those of the unedited data, not a surprising result since the data sets differed by the numbers of breaths deleted. Even so, solutions with more than one regression regime were identified in 29 of 34 edited experiments and the hypothesis of homogeneity of the regression slope could be rejected in those experiments. The comparison between fitted regression lines and the edited (VT, TI) observations from one experiment is shown in fig. 3. It is apparent that the mean VT/TI does not differ greatly a m o n g clusters as the regression lines tend to pivot around a c o m m o n point and this was frequently seen. Figure 4 shows the regression slopes found during hypercapnia for one subject. More than one regression regime was found in 16 of the 17 hypercapnic tests as compared to the same result on 14 of the 17 eupneic tests. The number of hypercapnic tests demonstrating regression slope inhomogeneity was 14 of the 16 for comparison to the same conclusion in 13 of the 14 eupneic tests in which a single regression regime was found inadequate. Thus no influence of hypercapnic hyperpnea upon the temporal changes in the regression lines was apparent. In order to determine whether the fluctuations in the VT-TI relationship were related to changes in ventilatory performance, mean values for VT, TI, ~', VT/TI, and PETco~ were computed for each regression regime identified in the solution. No pattern between changes in the mean levels of these variables and changes in the regression parameters could be identified using rank correlation coefficients.
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Fig. 3. Comparison of fitted regression lines to actual data for regression regimes identified by piecewise linear regression. The data shown have been edited by deletion of 22 breaths identified as outliers prior to regression analysis as described in the text. Panels A, B, and C show each of the separate regimes with the previous regimes' regression line dashed; panel D shows all the data together with the separate regression lines. Covariance analysis indicates that the null hypothesis of slope homogeneity should not be accepted (P < 0.001).
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Fig. 4. Comparison of regression slopes fitted to breath sequences identified using piecewise linear regression on data obtained during hypercapnic hyperpnea of 19.8 LPM. Null hypothesisof slope homogeneity should not be accepted (P < 0.001).
Discussion The main finding o f these analyses is that changes in the relationship between VT and TI often occur with time and the assumption of a fixed VT-TI relationship is often not valid over more than a few breaths. Clustering analysis demonstrates the e,xistence of separate regression regimes having spans from less than 20 to more than 100 breaths. That these results are not simply an artifact of the clustering technique is indicated from the results of the fixed block analysis, which arbitrarily separated the data into fixed clusters and supports the same conclusion. Thus the VT-TI relationship predicted over the span of 40-50 breaths is not necessarily representative o f the average VT-TI relationship estimated over several hundred breaths. It may be that neither of these data collection spans is a satisfactory window through which to assess the VT-TI relationship over shorter spans. The mechanisms responsible for the changes in the VT-TI relationship are not established. It is known that the average VT/TI is depressed by both elastic loads (Daubenspeck, 1979) and flow resistive loads, (Zechman et aL, 1957; Altose et al., 1979; Daubenspeck, 1981). Spontaneous oscillation in canine tracheal smooth muscle tone has been reported by Beinfield and Seifter (1980) and such variation ought to produce alterations in internal mechanics. Such alterations may influence the average VT/TI as do external loads but it is not known how such internal loading changes may alter the VT-TI variation about this mean VT/TI. Significant correlations between the mean levels of the separate pattern parameters, minute ventilation, mean inspiratory flow, or end-tidal CO2 and changes in the VT-TI were rarely found. It is not possible to assess a possible connection between changes in estimated respiratory drive and changes in the slope of the VT-T! relation, since this would require continuous estimation of changes in respiratory mechanics or workrate and such measurements were not performed here.
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Newsom Davis and Stagg (1975) noted that the VT-TI correlation was decreased from the awake state value by sleep in the one subject for whom both measurements were available. In the present study we requested that subjects keep their eyes open during the tests and most subjects read and/or listened to music during the experiments. Tests were not included in the analysis if there was any question about whether or not the subject was awake. Within these constraints upon allowable alterations in the level o f consciousness, it is still possible that small changes in the level of alertness could alter the VT-TI relationship. Reduction in the mean level of ventilation has been noted upon simply closing the eyes (Asmussen, 1977) and thus we cannot rule out influences of alterations in the level of alertness upon the VT-TI relation over the span of each experiment ( ~ 3 0 min). It is likely that a change in the state of cortical activity is not the sole factor influencing the VT-TI relation since changes in this relationship occurred commonly during moderate hypercapnic hyperpnea when the concommitant arousal would have minimized spontaneous lapses toward sleep. Without concurrent measurements o f the EEG, we cannot rule out the possibility that changes in the E E G occur spontaneously with time during hypercapnic hyperpnea and may influence the variation in VT-TI that we observe. The next steps in elucidating the mechanisms responsible for the observed changes in the VT-TI relation should include concurrent monitoring of the EEG and breath-by-breath measurement of respiratory mechanics. Whatever the cause of these changes in the VT-TI relationship that were observed, the implication is that the long period oscillations demonstrated with respect to other aspects of the breathing pattern (Priban, 1963 ; Dejours et al., 1966 ; Lenfant, 1967; Hlastala et al., 1973) may also be reflected in the changing relationship between VT-TI. Alteration in the pattern relationship between VT and TT has been shown to occur with time in some subjects during altitude acclimatization (Brusil et al., 1980). The present results indicate that variation in the VT-TI relation is the rule in normal subjects during normoxia.
Acknowledgements The authors express their sincere thanks to Prof. Victor McGee for his kind advice concerning the analysis of the data.
Appendix A PIECEWISE LINEAR REGRESSION SCHEME The piecewise linear regression scheme used in this study follows the procedures set forth by McGee and Carleton (1970), which is briefly outlined here. The data are considered to be sequentially ordered with respect to time and points are incorporated into regression clusters according to the particular
T E M P O R A L VARIATION IN THE VT-TI I N T E R R E L A T I O N S H I P
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clustering operation producing the best linear fit of the potential operations possible at any given point in the stepwise clustering. Once the minimum allowable size of a regression regime has been selected (and here we have chosen the minimum cluster size to be 5 or 10 breaths), then at any clustering level one of three operations will be selected: (1) a single breath may be incorporated into an existing adjacent cluster; (2) two adjacent clusters may be conjoined to form a single regression cluster; or (3) a new cluster o f the designated minimum size may be formed from separate, but adjacent breaths. The selected option of these three possibilities depends upon which results in the best fit judged by a standard least-squares criterion applied to the breaths included in the new regression cluster. McGee and Carleton (1970) provide appropriate F statistics by which to assess the reasonableness o f the selected operation by comparison of the sum of the squared deviations before and after the particular clustering operation. Using the probabilities associated with the computed F statistics, decisions can be made about where to halt the clustering process once the number o f breaths yet unincorporated into a cluster is less than a preselected maximum. We have chosen this level to be 5 ~ of the total number of breaths when the minimum cluster size was 10 breaths, and reduced this to 2.5% when the minimum cluster size was reduced to 5 breaths since the smaller minimum cluster size permits more breaths to be unincorporated at any stage of the clustering. A flow chart of the clustering procedure has been adapted directly from McGee and Carleton (1970) and is listed below: (1) input data and minimum cluster size to be used; (2) identity all potential clusters for the next clustering level and compute the goodness-of-fit for each potential cluster using the sum-of-squared deviations about the potential regression line; (3) identify the best-fit cluster as that with the smallest mean square residual; (4) if the number o f unincorporated breaths is less than the preselected maximum, then go to 5; otherwise go to 2; (5) if the newest cluster is a newly-formed cluster of minimum size, then go to 2 ; otherwise compute the appropriate F statistic for this clustering operation; (6) print the clustering details at this level and determine whether this is the final level o f clustering (all breaths included into a single regression regime). If so, then stop; otherwise go to 2. We have implemented this flowchart in a subset of the computer language PL/I that runs on our laboratory minicomputer. A listing with documentation will be provided for the cost of postage upon request to the authors.
References Altose, M . D . , S.G. Kelsen and N.S. Cherniak (1979). Respiratory responses to changes in airflow resistance in conscious man. Respir. Physiol. 36: 249-260. Asmussen, E. (1977). Regulation of respiration: 'The Black Box'. Acta Physiol. Scand. 99: 85-90. Beinfield, W. H. and J. Seifter (1980). Spontaneous mechanical activities of dog trachealis muscle in vivo. J. Appl. Physiol. 48: 320-328. Brownlee, K.A. (1965). Statistical Theory and Methodology in Science and Engineering. New York, J. Wiley, pp. 376-388. Brusil, P. J., T. B. Waggener, R. E. Kronauer and P. Gulesian, Jr. (1980). Methods for identifying respiratory oscillations disclose altitude effects. J. Appl. Physiol. 48:545 556. Clark, F.J. and C. von Euler (1972). On the regulation of depth and rate of breathing. J. Physiol. (London) 222: 267-295. Daubenspeck, J.A. (1979). Ventilatory responses to elastic loading at constant PAco 2 in hypercapnic hyperpnea. J. Appl. Physiol. 47: 778-786. Daubenspeck, J.A. (1981). Influence of small mechanical loads on variability o f breathing pattern. J. Appl. Physiol. 50: 299-306.
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Dejours, P., R. Puccinelli, J. Armand and M. Dicharry (1966). Breath-to-breath variations of pulmonary gas exchange in resting man. Respir. Physiol. 1 : 265-280. Hlastala, M.P., B. Wranne and C. J. Lenfant (1973). Cyclical variations in FRC and other respiratory variables in resting man. J. Appl. Physiol. 34: 670-676. Lenfant, C. (1967). Time-dependent variations of pulmonary gas exchange in normal man at rest. J. Appl. Physiol. 22: 675~i84. McGee, V.E. and W.T. Carleton (1970). Piecewise regression. J. Am. Star. Assoc. 65:1109-1124. Newsom Davis, J. and D. Stagg (1975). Interrelationships of the volume and time components of individual breaths in resting man. J. Physiol. (London) 245:481-498. Priban, I.P. (1963). An analysis of some short-term patterns of breathing in man at rest. J. Physiol. (London) 166: 425-434. Zechman, F., F. G. Hall and W. E. Hull (1957). Effects of graded resistance to tracheal airflow in man. J. Appl. Physiol. 10: 356-362.