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Phase plane analysis of physical working capacity Boyd, William Robert 1967

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A PHASE PLANE ANALYSIS OF PHYSICAL WORKING CAPACITY by WILLIAM ROBERT BOYD B.P.E. The U n i v e r s i t y of B r i t i s h Columbia, 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION  i n the School of PHYSICAL EDUCATION AND RECREATION  We accept t h i s t h e s i s as coriforming t o t h e required standard:  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1967  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements  for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that che L i b r a r y s h a l l make i t f r e e l y available f o r reference study,  and  I further agree that permission f o r extensive copying of t h i s  thesis f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives.  I t i s understood that copying  or p u b l i c a t i o n of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8;, Canada  ABSTRACT The purpose of t h i s study was t o determine the r e l a t i o n s h i p of s e l e c t e d measurements from the phase plane loop of the b r a c h i a l pulse wave t o p h y s i c a l working capacity as measured on a b i c y c l e ergometer. The s e l e c t e d measurements were: 1. +p(x) which i n d i c a t e s the pulse pressure^when maximum p o s i t i v e r a t e of change o f pressure occurs* 2  »  + p ( y ) which i s a measure of the maximum p o s i t i v e r a t e of change of pressure.  3.  -p(x) which i n d i c a t e s t h e pulse pressure when maximum negative r a t e of change of pressure occurs.  4*  - p ( y ) which i s a measure o f maximum negative r a t e of change of pressure.  5*  +P/-P which i s the r a t i o of maximum p o s i t i v e r a t e o f change of pulse pressure t o maximum negative r a t e of change of pulse pressure.  6*  Pr./Pr. which i s t h e r a t i o of pulse pressure t o maximum r a t e o f change of pulse pressure* Thirty-two young male a d u l t s underwent a b i c y c l e ergometer t e s t i n g  procedure i n which p h y s i c a l working capacity  (PWC^-Q)  was determined.  On the t e s t i n g day a r e s t i n g phase plane loop was f i r s t recorded* FWC^_Q  The  t e s t was then administered, followed by the immediate recording  of a post-exercise l o o p .  Two subsequent loops were then recorded a t  recovery i n t e r v a l s of f i v e and t e n minutes.  Thus, twenty-four d i r e c t  loop measurements were obtained from each s u b j e c t .  I n a d d i t i o n , the  d i f f e r e n c e between each p o s t - e x e r c i s e l o o p measurement and t h e corresponding  r e s t i n g v a l u e was c a l c u l a t e d making a t o t a l o f f o r t y - t w o  loop v a r i a b l e s per subject. A l a r g e c o r r e l a t i o n m a t r i x was c o n s t r u c t e d i n which a l l l o o p v a r i a b l e s as w e l l as  PWC-^Q,  and t h e s l o p e o f t h e  PWGJ^Q  FWC-^Q  d i v i d e d by body w e i g h t , body weight,  p l o t t e d l i n e ( s e e Appendix A) were i n c l u d e d .  The f o l l o w i n g r e s u l t s were o b s e r v e d .  PWC-^Q  correlated significantly  with: 1.  immediate p o s t - e x e r c i s e  -p(y).  2.  immediate p o s t - e x e r c i s e +p/-p.  3.  immediate p o s t - e x e r c i s e - r e s t  Pr./Pr.  No l o o p v a r i a b l e s c o r r e l a t e d s i g n i f i c a n t l y w i t h FWC^^ d i v i d e d by body weight.  However, body weight a l o n e  correlated significantly  1.  immediate p o s t - e x e r c i s e +p/-p.  2.  immediate p o s t - e x e r c i s e - r e s t +p/-p.  The s l o p e o f t h e  PWC-^Q  plotted line correlated significantly  1.  immediate p o s t - e x e r c i s e +p/-p.  2.  immediate p o s t - e x e r c i s e  3.  resting -p(y).  with:  with:  -p(y).  A stepwise m u l t i p l e r e g r e s s i o n a n a l y s i s c a l c u l a t e d by computer i n d i c a t e d t h a t t h e sum o f t h e independent c o n t r i b u t i o n s o f t h r e e v a r i a b l e s a c c o u n t e d f o r 42.7$ o f t h e t o t a l v a r i a n c e o f 1.  immediate p o s t - e x e r c i s e  -rest  2.  immediate p o s t - e x e r c i s e  -p(y).  3.  5 minute p o s t - e x e r c i s e + p ( x ) .  Pr./Pr.  PWCL^Q.  These were:  The multiple R between these three loop variables and FViKL  1  was  .65  The term "pulse pressure" as used here does not have the conventional meaning, i . e . the difference between systolic and diastolic pressures, but refers to any given point along the range between systolic and diastolic pressures.  ACKNOWLEDGEMENTS  ,  The author would like to extend his thanks to  Dr. S.R. Brown who acted as advisor for this study. His helpful guidance and assistance was very much appreciated. The author also wishes to extend his thanks to Miss Rozika Kogal for her help with the testing programme.  TABLE OF CONTENTS CHAPTER I  II  PAGE INTRODUCTION  1  Statement of the Problem  1  Definitions  1  Limitations  2  Delimitations  2  Justification  2 4  REVIEW OF THE LITERATURE  4  Pulse Wave Analysis . . The Relationship of the Cardiovascular Physical Working Capacity III  .  System t o . . . . .  METHODS AND PROCEDURES  4 8  Introduction  3  The FWC^-Q Test and I t s Administration  9  Recording the Phase Plane Loops i n Relation t o the PWC  170  Test  Apparatus and Formation of Loops  12  Description of the Loop  13  Measuring the Loops .  IV V  11  . . . . .  15  Heart Rate Determination  16  S t a t i s t i c a l Methods  16  RESULTS  19  DISCUSSION  28  Correlations of Loop Variables with FWC^.  . . .  28  Correlations of Loop Variables with the P W ^ - Q Plotted Line  31  CHAPTER  PAGE Correlations of Loop Variables with Body Weight and PWC  31  Divided by Weight  170 32  The Stepwise Regression VI  36  SUMMARY AND CONCLUSIONS Summary  36  Conclusions  33 39  BIBLIOGRAPHY APPENDICES  42  A.  Sample  B.  Sample Phase Plane Loop Data Sheet.  43  C.  PWC  44  F W C ^ Q  Data Sheet  Raw Scores  170 D.  Phase Plane Loop Raw Scores  45  E.  PWC ^ /Body Weight, Slope, and Body Weight Raw Scores . . .  49  F.  Means and Standard Deviations of the Loop Variables . . . .  50  G.  Means and Standard Deviations of  1  0  F W C - ^ Q ,  Weight, Slope, and Body Weight H.  Intercorrelations of Loop Variables  FWC-^Q/  B o d  y 52 53  LIST OF TABLES TABLE I  PAGE Correlation of PWC^YQ  PWC-^Q,  PWC^yBody Weight, Slope of  Plotted Line, and Body Weight with Phase  Plane Loop Variables II  Intercorrelations of  FWC^Q,  19 PWO^^Body Weight,  Slope of P W ^ - Q Plotted Line, and Body Weight. . . III IV  23  b Coefficients from a Stepwise Regression Contribution of Three Loop Variables to the Total  24  Variance of PWC V  A Series of Resting Phase Plane Loops from Subject  25  J.T VI  The Ratio of Intra-Individua! to Inter-Individual Variance of the Resting Phase Plane Loop . . . . .  VII  22  Result of Practice and Experimental PWC  Test. . .  26 27  LIST OF FIGURES  FIGURE  '  PAGE  1  The Brachial Pulse Wave and I t s Derivative . . . . .  13  2  The Phase Plane Loop  14  CHAPTER  I  INTRODUCTION  I  STATEMENT OF THE PROBLEM  The purpose o f t h i s s t u d y i s t o determine t h e r e l a t i o n s h i p o f s e l e c t e d measurements from t h e phase p l a n e l o o p o f t h e b r a c h i a l p u l s e wave t o p h y s i c a l working c a p a c i t y measured on a b i c y c l e ergometer.  II  Phase Plane A n a l y s i s ;  DEFINITIONS  The phase r e l a t i o n s h i p between p u l s e p r e s s u r e and  r a t e o f change o f p r e s s u r e i s d i s p l a y e d as a l o o p o r a s t o r a g e  oscilloscope.  Measurements o b t a i n e d from a phase p l a n e l o o p may be a n a l y s e d i n terms o f cardiovascular condition. P h y s i c a l Working C a p a c i t y :  I n t h i s s t u d y , p h y s i c a l working c a p a c i t y i s  d e f i n e d a s t h e work l o a d r e q u i r e d t o produce a h e a r t r a t e o f 170 b e a t s p e r minute on a b i c y c l e ergometer a t a steady Steady S t a t e :  C o n s o l a z i o , Johnson, and Pecora  state. (1) d e f i n e s t e a d y s t a t e as  a c o n d i t i o n i n which t h e r e i s a b a l a n c e between oxygen requirement  and  oxygen s u p p l y under c o n d i t i o n s such t h a t oxygen consumption, carbon d i o x i d e production, l a c t i c  a c i d c o n c e n t r a t i o n , body temperature,  p u l s e and  r e s p i r a t i o n r a t e s a r e a t a f a i r l y constant l e v e l r e g a r d l e s s o f t i m e . Pulse Pressure:  The t e r m " p u l s e p r e s s u r e " as used here does not have  t h e c o n v e n t i o n a l meaning, i . e . t h e d i f f e r e n c e between s y s t o l i c and d i a s t o l i c p r e s s u r e s , b u t r e f e r s t o any g i v e n p o i n t a l o n g t h e range between s y s t o l i c and d i a s t o l i c p r e s s u r e s .  2 III  LIMITATIONS  The subjects of t h i s study do not constitute a random sample. Twenty-nine were male undergraduate  students from a tests and measurements  course i n the School of Physical Education and Recreation at The University of B r i t i s h Columbia.  Three were male graduate students i n  Physical Education from the same i n s t i t u t i o n .  The ages of a l l subjects  ranged from 20 to 30 years with a mean of 22.5  years.  IV  DELIMITATIONS  The study i s confined to an i n v e s t i g a t i o n of the r e l a t i o n s h i p of phase plane measurements of the b r a c h i a l pulse wave t o physical working capacity as measured i n young men.  I t does not cover the range of  possible measurements of cardiovascular condition nor i s i t concerned with the possible application of the phase plane measurements to the measurement of other groups of people such as women.  V  JUSTIFICATION  Nothing has been published about the b r a c h i a l pulse wave under conditions of simultaneous p l o t t i n g of pulse pressure and rate of change of pressure.  An unpublished study has indicated that the r a t i o s of various  loop dimensions may be considered p o t e n t i a l l y valuable as measures of physical condition (2).  I t i s f e l t that the present study may  m a t e r i a l l y to the evidence f o r or against t h i s point of view.  add  3  REFERENCES 1.  Consolazio, C.F., Johnson, R.E., and Pecora, L.J., Physiological Measurements of Metabolic Functions i n Man, McGraw H i l l , New York, Toronto, London (1963) pp. 396-397.  2. Brown, S.R., Banister, E.W., and Dower, G.E., Time Derivatives of the Carotid Pulse Wave and Phase Plane Analysis of Cardiovascular Condition. (Unpublished paper), The University of British Columbia, 1966.  CHAPTER II REVIEW OP THE LITERATURE I  PULSE WAVE ANALYSIS  Analyses of pulse pressure waves have been utilized i n physical education for some time* Cameron Heartometer  Most analyses have been carried! out using the  (1,2,3)•  More recently the development of an  electronic differentiating device has added new dimensions to pulse wave analysis.  Instantaneous plotting of the f i r s t and second derivatives of  the curves of pulse pressure waves has provided investigators with a more accurate measure of the velocity and acceleration characteristics of these curves.  Discussions of the usefulness of such a device have been  published by Neal et a l * (4) and Bobskii et a l * (5)*  Gleason and  Braunwald (6) and Dohtas and Cottas (7) have studied pulse wave characteristics i n normal male adults while Butelar (8) and Starr and Ogawa (9) have analysed pressure curves for c l i n i c a l purposes.  At present,  interest i s being expressed i n the development of a phase plane loop (10) which graphically displays the phase relationship of pulse pressure to i t s f i r s t derivative. II  As yet, nothing has been published on this subject.  THE RELATIONSHIP OF THE CARDIOVASCULAR SYSTEM TO PHYSICAL WORKING CAPACITY  Working capacity i s usually referred to either as work accomplished at a given steady state heart rate or as maximum aerobic capacity* The following evidence lends support to the probability of some cardiovascular variables being related to working capacity.  5  Sjostrand  (11), Wahlund (12),  and others  (13,14,15,1A7,1S) 6  have  demonstrated a linear relationship between the intensity of doing work and heart rate. Others have shown a linear relationship between work intensity and oxygen consumption  (19,20).  Tests of working capacity have  been constructed u t i l i z i n g these principles (21,22). Very l i t t l e information i s available concerning the influence of cardiac efficiency on working capacity alone.  However, Balke (23) and  D i l l (24) have both shown that lack of sufficient oxygen i n inhaled a i r w i l l reduce working capacity.  Astrand (25) has stated that both central  and peripheral blood circulation probably act as contributing factors limiting oxygen consumption. Wahlund (26) also states that circulatory factors can impose limits on oxygen consumption.  It i s therefore logical  to assume that high cardiac efficiency w i l l contribute to higher oxygen consumption and thus to higher working capacity.  6  REFERENCES 1.  Cureton, T.K., "The Nature of Cardiovascular Condition i n Normal Humans", J . of the Assn. for Physical and Men. Rehab., Vol 11, (Nov-Dec 1957), pp. 186-196. ~~'  2.  Cureton, T.K., Physical Fitness Appraisal and Guidance. C.V. Mosby Co., St. Louis, 1947»  3.  Cureton, T.K., and Massey, R.H., "Brachial Peripheral Pulse Waves Related to Altitude Tolerance and Endurance", Amer. J . Physiol.. Vol 159 (Dec. 1949), p. 566.  4*  Neal, N.J., Halpern, W., and Reeves, T.J., "Velocity and Acceleration Pressure Changes i n Heart and Arteries", J . Appl. Physiol.. Vol 15, No. 4 (July I960), pp. 747-749.  5.  Bobskii, E.B., Karpman, V.L., Petrov, G.M., and Sachkova, A.I., "Use of an Electronic Differentiating Device i n Physiological Studies", Biophysics. Vol 4, No. 6 (1959). p. 102.  6.  Gleason, W.L., and Braunwald, E., "Studies on the First Derivative of the Ventricular Pressure Pulse i n Man", J . Clin. Inves., Vol 41, No. 1 (1962), pp. 80-91.  7.  Dontas, A.S., and Cottas, C.S., "Arterial Volume and Pressure Pulse Contours i n Young Human Subjects", Amer. Heart J . . Vol 61, No. 5 (May I960), pp. 676-683.  8.  Butelar, B.C., "The Relation of Systolic Upstroke Time and Pulse Pressure i n Aortic Stenosis", Brit. Heart J.. Vol 24, No. 4 (1962), pp. 657-660.  9.  Starr, I., and Ogawa, J., "A Clinical Study of the First Derivative of the Brachial Pulse Wave", Amer. Heart J.. Vol 65, No. 4 (April 1962), pp. 482-484.  10.  Brown, S.R., Banister, E.W., and Dower, G.E., Time Derivatives of the Carotid Pulse Wave and Phase Plane Analysis of Cardiovascular Condition. (Unpublished paper), The University of British Columbia, 1966.  11.  Sjostrand, T., "Changes i n the Respiratory Organs of Workmen at an Ore Smelting Works", Acta Med. Scand., Vol 128, (Supplementum 196) (1947), pp. 687-699.  12.  Wahlund, H., "Determination of Physical Working Capacity", Acta Med. Scand.. Vol 132,  (Supplementum 215) (1948), pp. 5-78.  7 13.  Adams, F.H., Linde, L.M., and Miyake, H., "The P h y s i c a l Working Capacity of Normal School C h i l d r e n " , ( C a l i f o r n i a ) ,  P e d i a t r i c s . V o l 28, No. 1 ( J u l y 1961), pp. 55-64.  14*  Adams, H.A., Bengtsson, £•£., Birwen, H., and Wegelius, C , "The P h y s i c a l Working Capacity of Normal School C h i l d r e n " , (Swedish c i t y and town), P e d i a t r i c s . V o l 28, No. 2 (August 1961), pp. 243-257.  15.  Astrand, P.O., "Human P h y s i c a l F i t n e s s w i t h S p e c i a l Reference t o Sex and Age", P h y s i o l o g i c a l Reviews. V o l 36, No. 3 ( J u l y 1956), pp. 307-335.  16.  Bengtsson, Ji;., "The Working Capacity i n Normal C h i l d r e n Evaluated by Submaximal E x e r c i s e i n the B i c y c l e Ergometer and Compared w i t h A d u l t s " , Acta Med. Scand.. V o l 154, Fasc. 2,  (1956), pp. 91-109.  17*  Cumming, G.R., and Cumming, P.M., "Working Capacity of Normal Children Tested on a B i c y c l e Ergometer", Canad. Med. Assn. J . ,  Vol 88, No. 7 (Feb. 1963), pp. 351-355.  18.  Cumming, G.R., and Danzinger, R«, " B i c y c l e Ergometer Studies i n C h i l d r e n " , P e d i a t r i c s . V o l 32, No. 2 (Aug. 1963), pp. 202-208.  19.  Astrand, I . , "Aerobic Work Capacity i n Men and Women w i t h S p e c i a l Reference t o Age", Acta P h y s i o l . Scand.. V o l 49 (Supplementum 169) (I960), pp. 1-92.  20. Astrand, P.O., Experimental Studies of P h y s i c a l Working Capacity i n R e l a t i o n t o Sex and Age. Enjar Munksgaard, Copenhagen,  1952.  21. Astrand, P.O., Work Tests w i t h the B i c y c l e Ergometer. Dept. of Physiology, Gymnastika C e n t r a l - i n s t i t u e t , Stockholm, Sweden. 22. Wahlund, l o c . c i t . 23.  Balke, B., "Work Capacity and I t s L i m i t i n g Factors a t High A l t i t u d e " , Reprinted from The Symposium on t h e P h y s i o l o g i c a l E f f e c t s of High A l t i t u d e , I n t e r l a k e n , Sept. 1962, Pergamon Press, Oxford, London, New York, P a r i s , I963.  24.  D i l l , D.B., and Perrod, K.E., "Man*s C e i l i n g as Determined i n the A l t i t u d e Chamber", J . Appl. P h y s i o l . . V o l 1, No. 6 (Dec. 1948),  pp. 409-417.  25. Astrand, P.O., Experimental Studies of P h y s i c a l Working Capacity i n R e l a t i o n t o Sex and Age. Enjar Munksgaard, Copenhagen, 1952, p. 121. 26. Wahlund, l o c . c i t .  CHAPTER III METHODS AND PROCEDURES I  INTRODUCTION  Thirty-two male physical education students from The University of British Columbia underwent a series of tests i n which physical working capacity was determined and various resting and post-exercise brachial pulse wave tracings were recorded.  Twenty-nine of the subjects  were undergraduate students enrolled i n a tests and measurements course and three were graduate students included to increase the number of subjects. The  PWC^_Q  test, carried out on a Monark bicycle ergometer  was used to determine physical working capacity. A detailed description of this test i s included later i n the chapter. Brachial pulse wave signals were obtained by means of a pressure transducer applied with a cuff over the brachial artery. The transducer was fed into an amplifier and displayed on an oscilloscope face. Using a conventional RC network, this pulse signal could be immediately differentiated and also displayed on the oscilloscope face. During the testing, three types of signals were displayed and photographed.  Only  the f i r s t of the following three types was used i n this study: 1. The pulse wave and i t s f i r s t derivative were plotted simultaneously so that the pulse wave was displayed as the abscissa and the f i r s t derivative pulse wave was displayed as the ordinate. Thus the phase relationship between the pulse pressure and rate of change of pressure  was displayed as a loop and photographed. This was  9 termed a phase plane loop (see figure 2 ) . 2.  The pulse wave and i t s f i r s t derivative were displayed conventionally and the two resulting curves were photographed (see figure 1 ) .  3.  The pulse wave and an EGG recording were both plotted and the two resulting curves were photographed. The testing was carried out during the f a l l of 1 9 6 6 , Each subject  was tested on two different days. On the f i r s t day a practice test was administered.  P W C ^ Q  On the second testing day the sequence of testing  was as follows: 1.  A resting phase plane loop was recorded and photographed.  2.  The  3*  An immediate post-exercise phase plane loop was recorded and  P W C ^ Q  test was administered.  photographed. 4»  5 and 1 0 minute recovery phase plane loops were recorded and photographed.  A l l phase plane loop recordings were obtained with the subject i n supine position. Various measurements from these loops were correlated with physical working capacity and with other related variables as described under "Statistical Methods". II  THE PWC^ TEST AND ITS ADMINISTRATION  A test of physical working capacity must involve large muscle groups. Different and sufficiently heavy loads must be used i n a stepwise progression i n order to estimate the maximum steady state. The working time should not be over twenty to thirty minutes ( 1 ) .  A test  which apparently meets these requirements i s the P W C ^ Q test.  Here  physical working capacity i s defined as the intensity of work (Kgm/min) that i s performed at a frequency of 170 heart beats per minute (2). In this study a l l subjects rode the Monark bicycle ergometer (3) at three progressively increasing work loads designed to produce steady state heart rates f a l l i n g within the intervals of 115 to 130, 140 to 150, and 160 to 170 beats per minute respectively.  Each man worked for six  1'  minutes at each of the three levels, i . e . for 18 minutes i n a l l without stopping.  The average heart rate of the f i f t h and sixth minute of each  level was considered to conform to the requirements of the steady state i f the difference between the f i f t h and sixth minute rates was less than five beats per minute. I f i t was more than this amount, the subject continued pedalling at the same level until the steady state was reached. The value of FiiC^^ was determined for each subject i n the following manner. For each test a graph was prepared with steady state heart rate plotted against work load at each of the three levels of work. The best f i t t i n g straight line was drawn through the three points and the estimated work corresponding to a heart rate of 170 beats per minute was obtained by either interpolation or extrapolation. This procedure was, of course, not necessary i f the heart rate levelled off at exactly 170 beats per minute during the last work level. The test was performed twice.  The f i r s t test served as a practice  t r i a l and was used to predict the loads which would produce the required pulse rates at the three levels on the second test.  During the f i r s t  tests i t was noted that a work load which produced a steady state heart rate of 130 rather than 115 beats per minute during the f i r s t work level  11 was more satisfactory i n terms of obtaining a straight line through the three points, i . e . a point plotted on the graph corresponding to 130 beats per minute lined up with the plotted points of the second and third work levels more consistently than did a point corresponding to 115 beats per minute. Thus, i n the second series of PWC-j_~o tests, a work load was designed to produce a heart rate of approximately 130 beats per minute. The estimated work necessary to produce a heart rate of 130 beats per minute was obtained from the f i r s t  FWC^_Q  test by interpolation from the  graph plotted at that,time. It was also noted that a line drawn through the plotted points of the f i r s t and second work levels gave a f a i r l y accurate prediction of the work load necessary to obtain a steady state heart rate of 170. The f i r s t test was carried out with no attempt made to control pre-test eating or smoking. Conditions of the second test were more carefully controlled.  The test was administered at least an hour after  a light breakfast or lunch. Subjects were asked to refrain from drinking tea or coffee or from smoking at least an hour before the test. Ill  RECORDING THE PHASE PLANE LOOPS IN RELATION TO THE PWCp-Q TEST  Prior to performing the actual  FWC^_Q  test, chest electrodes for  telemetric transmission of the precordial electrocardiogram were applied to the subject who then rested supine for 10 minutes. The resting phase plane loop, f i r s t derivative, and EGG recordings were photographed respectively i n that order, and the subject then moved to the bicycle. The height of the bicycle seat was adjusted to a comfortable level (lower extended knee should be slightly flexed with the b a l l of the foot placed on the pedal). The PWC  _ test was then carried out after which  12  the subject was rapidly transferred back to supine position and an immediate post-exercise loop was recorded and photographed. The average time lapse between the end of the ride and the recording of the immediate post-exercise loop was one minute forty-three seconds, the range being from forty-five seconds to three minutes. Two subsequent loops were then recorded and photographed at recovery intervals of five and ten minutes. IV  APPARATUS AND FORMATION OF LOOPS (4)  Pulse wave signals are derived by means of a pressure transducer feeding into a Type 3C66 (Tektronix) amplifier and displayed on an oscilloscope face as the abscissa. Simultaneously the pulse signal voltage i s amplified and differentiated using a conventional RC network and the f i r s t derivative pulse curve i s displayed as the ordinate. Thus, the phase relationship between the pulse pressure and the rate of change of pressure may be obtained and displayed i n the phase plane. The resultant loop i s displayed and stored i n a storage oscilloscope (Tektronix Type 564) and photographed. Two channels are used for the phase plane loops - the horizontal display for the pressure signal and the vertical display for the differential signal from the amplifier which amplifies the pressure signal after differentiation.  This i s necessary as the differentiating  circuit reduces the signal by 20 to 100 times.  Low pass f i l t e r s i n both  circuits remove sixty cycle interference but pass the signals unreduced i n amplitude.  The oscilloscope i s calibrated so that an input sine wave  signal of 5 cps. w i l l yield a circular phase plane loop.  13 V  DESCRIPTION OF THE LOOP  As previously described, the loop i s formed by simultaneously plotting the pulse pressure curve as the abscissa and the rate of change of pressure curve as the ordinate. The following diagram describes the pulse pressure curve and i t s corresponding derivative curve i n terms of the variables used i n this study: Fig. 1 The Brachial Pulse Wave and Its Derivative  T/M£  1.  "a™ corresponds to +p = maximum positive rate of change of pressure.  2. b " corresponds to -f> = maximum negative rate of change of pressure. n  3»  "B" i s the base l i n e of the derivative curve.  The derivative curve  cuts the base l i n e when the rate of change of pulse pressure changes from positive to negative, or vice versa.  14 The simultaneous plotting of the above curves form the following loop: Fig. 2 The Phase Plane Loop  V-AX/S  y-AX/s  5 PRESSURE  Key: 1. Pr.  width of loop (the pressure range for one heart beat),  2. Pr.  height of loop,  3.  +P  highest point,  4.  -p  lowest point. The following variables were utilized:  1.  The ratio of the maximum positive rate of change of pulse pressure to the maximum negative rate of change (+p(y)/-p(y)).  2.  The ratio of systolic pulse pressure to the rate of change of pressure (Pr./Pr.).  3*  The points of maximum positive rate of change of pressure (+p) and maximum negative rate of change of pressure (-p). Other measures were derived from the variables mentioned above.  15 These were t h e d i f f e r e n c e s between a l l t h e immediate, 5 and 10 minute p o s t - e x e r c i s e phase p l a n e l o o p measurements and t h e i r r e s p e c t i v e resting values.  S i n c e t h e s e d e r i v e d v a r i a b l e s show t h e d i f f e r e n c e s o r  changes i n t h e l o o p measurements a t d i f f e r e n t stages o f r e c o v e r y , i t was thought t h a t t h e r e l a t i o n s h i p o f t h e s e v a r i a b l e s t o p h y s i c a l working c a p a c i t y might be o f c o n s i d e r a b l e i n t e r e s t .  VI  MEASURING THE LOOPS  Dimensions o f t h e l o o p s were measured w i t h V e r n i e r c a l i p e r s t o t h e nearest tenth of a m i l l i m e t e r . between photographs.  T h e r e f o r e , a l l dimensions were measured from t h e  c e n t e r o f each t r a c i n g . 1.  The t h i c k n e s s o f t h e l o o p t r a c i n g s v a r i e d  The measuring procedure was as f o l l o w s :  P r . was measured a l o n g t h e X - a x i s .  The X - a x i s was a h o r i z o n t a l l i n e  which passed through t h e extreme r i g h t and l e f t hand p o i n t s o f t h e loop perimeter.  T h i s l i n e was c o n s t r u c t e d through t h e l o o p which was  t e m p o r a r i l y s t o r e d on t h e o s c i l l o s c o p e f a c e by u n b a l a n c i n g gauge b r i d g e system so t h a t no s i g n a l from t h e p r e s s u r e c o u l d produce v e r t i c a l displacement  of the ordinate.  the s t r a i n  transducer  I n t h i s way t h e  time base was i n s c r i b e d h o r i z o n t a l l y a c r o s s t h e scope f a c e . 2.  A p e r p e n d i c u l a r l i n e ( Y - a x i s ) was c o n s t r u c t e d b i s e c t i n g P r . Thus a c o - o r d i n a t e system was c r e a t e d . to Pr./lO.  U n i t s i n t h i s system were e q u a l  A l l v a r i a b l e s were expressed  i n these  units.  3.  +p(x) was t h e p e r p e n d i c u l a r d i s t a n c e from +p t o t h e Y - a x i s .  4»  -p(x) was t h e p e r p e n d i c u l a r d i s t a n c e f r o m -p t o t h e Y - a x i s .  5»  +p(y) was t h e p e r p e n d i c u l a r d i s t a n c e from +p t o t h e X - a x i s .  6.  -p(y) was t h e p e r p e n d i c u l a r d i s t a n c e from -p t o t h e X - a x i s .  16 7.  P r . was  t h e sum  of t h e a b s o l u t e v a l u e s of +p(y)  VII  D u r i n g t h e PWC  One  was  170  t e s t t h e h e a r t r a t e was Two  Telemetering  t o a Sanborn 500 VIII  The  each minute  e l e c t r o d e s were  T r a n s m i t t e r (Model 27-1)  which was  attached  E l e c t r i c a l i m p u l s e s were p i c k e d up  an ECG R a d i o Telemetry R e c e i v e r (Model  1.  monitered  p l a c e d on the upper sternum and t h e o t h e r on t h e  t o a b e l t worn around t h e w a i s t .  connected  N  Beckman s k i n e l e c t r o d e s were used i n t h i s  f i f t h i n t e r c o s t a l space under t h e l e f t n i p p l e . w i r e d t o an ECG  -p(y).  HEART RATE DETERMINATION  on an e l e c t r o c a r d i o g r a m . procedure.  and  RC-27).  This, i n turn,  by  was  Viso-Cardiette. STATISTICAL METHODS  The r e s u l t s of t h e second  P W C ^ Q  t e s t and the phase plane  measurements were i n t e r c o r r e l a t e d by computer.  loop  I n c l u d e d i n the  m a t r i x were p h y s i c a l working c a p a c i t y d i v i d e d by body weight i n k i l o g r a m s , body w e i g h t , and t h e s l o p e of the  FW  C  -J^Q  plotted  T h i s s l o p e i s d e f i n e d as t h e acute angle produced by t h e of a h o r i z o n t a l l i n e and t h e 2.  plotted  intersection  line.  The means and s t a n d a r d d e v i a t i o n s o f a l l t h e above v a r i a b l e s were a l s o c a l c u l a t e d by  3.  P W C ^ Q  line.  computer.  M u l t i p l e p r e d i c t i o n e q u a t i o n s were c a l c u l a t e d w i t h  F W C - ^ Q  a c t i n g as  t h e dependent v a r i a b l e and a l l phase p l a n e l o o p v a r i a b l e s a c t i n g as t h e independent v a r i a b l e s .  These were o b t a i n e d by computer u s i n g  a s t e p w i s e r e g r e s s i o n method. 4.  An e s t i m a t e o f t h e i n t r a - i n d i v i d u a l v a r i a b i l i t y of t h e s i x l o o p  17  variables was obtained from measurements made on a series of twelve resting loops taken on one subject over a period of four days. Means, standard deviations, and standard errors of the means were computed. The variance of the repeated measurements obtained from this subject was compared with the sample variance (one test only) by means of a ratio of the intra-individual variance over the inter-individual variance.  18  REFERENCES 1.  Wahlund, H., "Determination of P h y s i c a l Working Capacity", Acta Med. Scand.. V o l 132, (Supplement— 215) (1948),  pp. 17-18.  2.  Doroschuk, E.V., "A Short Tes% of Submaximal Working Capacity",  C A H P E R. V o l 32, No. 2 (Dec. 1965-Jan. 1966), p. 10. 3.  Astrand, P.O., Work Tests w i t h a B i c y c l e Ergometer. Dept. of Physiology, Gymnastika C e n t r a l - i n s t i t u e t , Stockholm, Sweden.  4.  Brown, S.R., B a n i s t e r , E.W., and Dower, G.E., Time D e r i v a t i v e s of the C a r o t i d Pulse Wave and Phase Plane A n a l y s i s of Cardiovascular Condition. (Unpublished paper). The U n i v e r s i t y of B r i t i s h Columbia, 1966.  CHAPTER IV RESULTS The r e s u l t s of t h i s study are summarized i n Tables I t o IV. The  v  0.05 l e v e l of confidence was used t o t e s t the s t a t i s t i c a l s i g n i f i c a n c e of the c o r r e l a t i o n c o e f f i c i e n t s .  A l l c o r r e l a t i o n c o e f f i c i e n t s of 0.349 or  l a r g e r were s t a t i s t i c a l l y s i g n i f i c a n t . The r e l a t i o n s h i p s between the loop v a r i a b l e s and  ^  FWC-J^Q,  d i v i d e d by body weight, slope of the ^ 0 ^ ^ p l o t t e d l i n e , and body weight are shown i n Table I . TABLE  I  CORRELATION OF F W C ^ , P W O ^ B O D I WEIGHT, SLOPE OF P W C ^ PLOTTED LINE, AND BODY WEIGHT WITH PHASE PLANE LOOP VARIABLES  Time Rest  Immediate postexercise  PWC /Weight  Loop Variable  170  Slope  Weight +.078  +p(x)  +.186  -.020  +p(y)  -.309  -.160  -.043 +.018  -P(x)  -.008  +.030  +.072  -.036  -p(y)  +.177  +.067  -.416*  +.177  itTP Pr Pr  +.075  -.150  +.084  +.092  +.308  +.115  +.052  +.191  +P« +p(y) -P(x)  -.083 +.094 +.044 +.459*  , -.124 +.186  -.042 -.060  +.041 +.247  +.138  +.100 -.150 +.005  -.393*  +.285  -.402*  -.124  +.381*  -.389*  -.330  -.292  +.287  -.025  -«7)  -P Pr • Pr  (Cont'd),  -.158  Time 5 minute postexercise  Loop Variable  Weight  . ~P Pr ~ Pr_: +p(x) +£( ) _£( ) -p(y)  +.098  +.104  +.136  -.301  +.109  -.003  +.076  +.242  -.041 -.321 +.091 +.149'  -.041 -.185 +.090 -.038  -.053 -.001 -.014 -.329  -.111 -.225 +.075 +.187  -.345  -.114  +.154  -.293  +.211  +.169  +.142  +.109  -.078 +.227 +.035 +.213 -.241  -.080 +.242 +.000 +.152 +.127  +.000 -.063 +.027 +.081 +.218  +.017* -.063 +.033 +.065 -.365*  -.478*  -.305  +.176  -.161  ...269  -.165  +.137  -.138  X  y  x  BE +p(x) +p( ) _£(-) _£(-) +p" y  +j( )  -  x  .  + 104  -•  G08  162  +.098  -.165  -.130  +.284  -.096  +.008  +.119  +.007  -.267  -|£  -.154  -.098  +.027  +.064  +p(x)  -.038  +.039  +.063  -.124  ^ -f>() (y) x  -p(y)  --° «°95 G6  +  ^° +.064  54  +.068  -  +.036 f$(y)  minute e -Srrecsitse  Slope  R  -.089 -.288 -.064 +.117  - rest  10  o  +.124 +.005 +.170 -.i69  Pr .  exSlse  /Weight 70  -.223 +.038 +.165 -.122  • -P  5 minute  1  ' -.312 -.110 +.038 +-006  +L.  Immediate Postexercise - rest  FWC  +p (x) +|(y) _J( ) -p(y)  _p_  10 minute postexercise  FWG\ ^  -.018  --.069  "' +.101  02G  10k  -.116  -.110  +.286  -.090  -.147  +.081  +.013  -.286  +.089  +.121  -.060  +__  -P -.056 • s i g n i f i c a n t a t 0.05 l e v e l 1  21 There are three statistically significant correlations  PWC^-Q.  between the loop variables and  FWCL^Q.  These are:  1«  -p(y) during immediate post-exercise (positive).  2.  +p/-p  3»  The difference i n Pr/Pr between immediate post-exercise and rest  during immediate post-exercise (negative).  (negative). PWC^Yo/body weight. FW^yo/body weight does not correlate significantly with the loop variables. Slope.  There are three statistically significant correlations  between the slope of the  PWCJ^Q  plotted line and the loop variables.  These are: 1.  -p(y) during rest (negative).  2»  -p(y) during immediate post-exercise (negative).  3»  +P/-P  during immediate post-exercise (positive).  It should be noted that the last two of the above variables also correlated significantly with  PWCJ^Q.  Body weight. The following two loop variables correlate significantly with body weight: 1.  +p/-p  during immediate post-exercise (negative).  2.  The difference i n +p/-p  values between immediate post-exercise  and rest (negative). Again i t should be noted that +p/-p correlates with  during immediate post-exercise also  FWC-^Q.  Thus, from a total of six loop measurements, only -p(y), and Pr/Pr correlate significantly with the selected c r i t e r i a .  Also, only  measurements derived from immediate post-exercise and resting variables  22  correlate significantly with these criteria.  Of the four criteria, only  PWC^yQ/body weight does not correlate significantly with any loop variable. Table II shows the intercorrelations between PWC  , PWC  170  170  divided by body weight, the slope of the FWC^y plotted line, and body 0  weight. There are statistically significant intercorrelations between a l l four variables except for correlations of PWC-j^c/ body weight with slope and body weight. In fact, PWC^Q i s the only variable that correlates significantly with PWC^ /body weight. This includes the 70  loop variables as well. TABLE II INTERCORRELATIONS OF SLOPE OF  F W C ^ Q  PWOJ^Q,  P W C ^ Q / B O D Y  WEIGHT,  PLOTTED LINE, AND BODY WEIGHT  PWC^yQ  Slope  PWC /Weight 170  PW(^ /weight 7G  +.648*  Slope  -.626*  -.306  Weight  +.472*  -.305  -.490*  *significant at 0.05 level A stepwise regression analysis by computer with  FWC^Q  as the  dependent variable and a l l loop measurements as the independent variables show that there are three loop variables which contribute the most to predicting 1.  P W C ^ Q .  These variables are:  +£/-£ during immediate post-exercise.  23  2.  +p(x) during 5 minute post-exercise.  3.  The difference i n Pr./Pr. between rest and immediate post-exercise. Table I I I l i s t s the b c o e f f i c i e n t s f o r each corresponding loop  variable• TABLE I I I  b COEFFICIENTS FROM A STEPWISE REGRESSION  Time  Variable  b coefficients  Immediate post-exercise  +P/-P  -74.0039  5 minute post-exercise  +P(x)  -68.8175  Immediate post-exercise - rest  Pr./Pr.  -415.0021  Using these c o e f f i c i e n t s and a constant term of 1060.1684, the following p r e d i c t i o n equation may be used i n which the standard error of estimate i s +167.8983. Predicted P W C ^ Q = 1060.1684 + (-74.0039)(X ) + (-68.8175)(X ) x  2  +  (-415.0021)(Xo)  X^, X^, and X^ represent the i n d i v i d u a l raw scores of the variables i n Table I I I . The b c o e f f i c i e n t shows how many units  FWC^_0  increases f o r  every unit increase i n the corresponding loop variable when the effects of the other two loop variables have been n u l l i f i e d or held constant.  24  Table IV gives the corresponding B c o e f f i c i e n t f o r each of the three loop v a r i a b l e s and the independent c o n t r i b u t i o n of each one t o the t o t a l variance of PWG^Q i n terms of a percentage. TABLE  IV  CONTRIBUTION OF THREE LOOP VARIABLES TO THE TOTAL VARIANCE OF FWC,„„  Time  Variable  Immediate post-exercise  +p/-P  5 minute post-exercise  +P(x)  Immediate post-exercise - rest  Pr./Pr.  % contribution  J3 c o e f f i c i e n t  11.8  -.461  8.8  -.294  22.1  -.285  The t o t a l c o n t r i b u t i o n of the three v a r i a b l e s i n Table IV i s 42.7$ r e s u l t i n g i n a m u l t i p l e R of  /.427 = .65.  Approximately 57$ of the t o t a l  variance of PWC,„^ i s not accounted f o r . The scores i n Table V represent the r e s u l t s of a s e r i e s of phase plane loops taken from subject J.T. and obtained under the r e s t i n g conditions as described i n Chapter I I I *  These measurements, i n u n i t  scores, are obtained from twelve observations taken over a period of four days, three times each day.  The standard d e v i a t i o n s and standard e r r o r s  i n d i c a t e the amount of v a r i a b i l i t y t h a t can be expected from each loop v a r i a b l e obtained under r e s t i n g c o n d i t i o n s .  25  TABLE, V A SERIES OF RESTING PHASE PLANE LOOPS FROM SUBJECT J.T. Test No.  +p(x)  +p(y)  -p(x)  -p(y) ~  +*>/-£  Pr./Pr.  Day .  1  -.55  4.74  3.17  1.69  2.79  1.55  Dec.19  9:30 AM  2  -.20  6.73  2.67  1.41  4.75  1.22  19  2:30 PM  3  -.48  4.95  2.52  1.54  3.20  1.57  19  3:45 PM  4  -.55  5.02  2.28  1.83  2.73  1.45  Dec.20  9:30 AM  5  -.82  4.60  1.94  1.78  2.57  1.56  20  2:30 PM  6  -1.19  4.35  1.86  1.74  2.51  1.64  20  3:45 PM  7  -.89  4.35  1.45  2.07  2.10  1.55  Dec.21  9:30 AM  8  -1.12  5.59  3-05  1.62  3.43  1.38  21  2:30 PM  9  -1.25  3.97  2.27  1.77  2.24  1.70  21  3:45 PM  10  -.68  4.53  1.52  ,1.45  3-L1  1T06  Dec.22  9:30 AM  11  -1.18  5.03  .71  1.86  2.70  1.45  22  2:30 PM  12  -.79  4.87  1.36  2.51  2.38  1.48  22  3:45 PM  Total  -9.70  58.73  24.80  21.27  34.51  18.21  Mean  .81  4.89  2.06  1.77  2.87  1.52  S.D.  .33  .71  .73  .30  .71  .13  SE M  .030  .207  .213  .086  .205  .038  7  Table VI indicates the relationship between intra-individual and inter-individual resting phase plane loop variables.  This relationship  Time  26  was indicated by dividing the variance of the loop variables from the twelve r e l i a b i l i t y rides of subject J.T. by the variance of the thirtytwo subjects of this study. TABLE VI THE RATIO OF INTRA-INDIVIDUAL TO INTER-INDIVIDUAL VARIANCE OF THE RESTING PHASE PLANE LOOP  +p(y)  .133  1.496  -P(X)  -p(y)  +p/-p  Fr£r  .265  .263  .636  .966  An analysis of Table VI shows that i n several cases the ratio of intra-individual variance to inter-individual variance i s very close to one.  In one instance, intra-individual variance i s actually larger than  inter-individual variance, i . e . for +p(y). The size of the intraindividual variance, as shown here, tends to decrease the likelihood of a significant correlation occurring between loop variables and other related scores.  The resulting correlation coefficients may be very  inaccurate estimates of the real relationship which may exist between true scores.  I t i s interesting to note that the smallest ratios were  those of variables +p(x) and -p(y); +p(x) was an important factor i n predicting PWC^Q and -p(y) correlated significantly with PWC-^Q. An estimate of the r e l i a b i l i t y of the PWC Table VII.  170  test i s given i n  27 TABLE. VII RESULT OF PRAGTIGE AND EXPERIMENTAL PWC^Q. TEST  Mean scores  Standard deviation  Test 1  1124.6  246.6  Test 2  II5O.6  210.8  Correlation coefficient  .869  Mean Standard difference error of difference +26.0  19.16  t  I.36  A mean increase of 26 kgm/min i n physical working capacity between the practice test and experimental test i s not statistically significant (0.05 level of confidence, one tailed test).  The correlation coefficient  of +.869 indicates a relatively high degree of relationship between the results of the two tests.  CHAPTER V DISCUSSION I  CORRELATIONS OF LOOP VARIABLES WITH PWG,_ 170  The recording of phase plane loops from the b r a c h i a l a r t e r y by means o f an e x t e r n a l recording device has c e r t a i n l i m i t a t i o n s . For example, varying amounts and types o f t i s s u e around the b r a c h i a l a r t e r y could conceivably cause considerable d i s t o r t i o n of pulse pressure contours. A l s o , the shape o f the contour may p o s s i b l y be changed by varying the t e n s i o n o f the pressure c u f f around the arm. The extent that these f a c t o r s a c t u a l l y change t h e loop co-ordinates used i n t h i s study i s not known. The s e r i e s of phase plane loops obtained from subject J.T. gives some i n d i c a t i o n o f how the co-ordinates can vary w i t h t h e same i n d i v i d u a l . Despite t h e above l i m i t a t i o n s , c e r t a i n c h a r a c t e r i s t i c s i n the phase plane loops seem"to show common variance with p h y s i c a l working c a p a c i t y . Three v a r i a b l e s , - p ( y ) , +p/-p, and Pr./Pr., c o r r e l a t e s i g n i f i c a n t l y w i t h 170  As explained i n Chapter I I I , values of -p(y) i n d i c a t e the maximum negative r a t e of change of blood pressure, i . e . the r a t e of d e c l i n e of pressure.  A p o s i t i v e c o r r e l a t i o n o f +.459 between -p(y) immediately a f t e r  exercise and H f C ^ i n d i c a t e s t h a t t h e subjects w i t h high working c a p a c i t i e s tend t o have a greater maximum negative r a t e of change of blood pressure than the subjects w i t h low working c a p a c i t i e s . Under c e r t a i n conditions a r a p i d d e c l i n e i n blood pressure f o l l o w i n g peak s y s t o l i c pressure i n d i c a t e s a l a c k of a r t e r i a l d i s t e n s i b i l i t y  29  as occurs, for example, i n arteriosclerosis. characteristic of aortic insufficiency (1).  This i s also a However, the subjects of this  study are, i n general, young and active individuals.  Moreover, i t i s highly  unlikely that the subjects with the highest working capacities should suffer from any such disorder. Hence, there must be some other explanation. It i s well known that peripheral resistance i s a chief factor i n maintaining diastolic pressure ( 2 ) .  Burton considers the decline i n  pressure during diastole an index of total peripheral resistance ( 3 ) .  Thus,  i n subjects with high working capacities, lower peripheral resistance causing a more rapid run off of blood from the arteries through the peripheral resistance may explain, i n part, their rapid decline i n pressure during diastole. A second loop variable which correlates with WC^^  i s +p/-p  immediately after exercise* The negative correlation of - . 4 0 2 between i t and WGyjQ indicates that the subjects with high working capacities tend to have low immediate post-exercise values of +p/-p. As previously explained, +$/-f> i s the ratio of maximum positive rate of change of pressure to maximum negative rate of change of pressure.  One value of a ratio l i e s  i n i t s showing whether the numerator or the denominator w i l l predominate under given conditions. In this case, since high PWCj_70  i s  a  s  s  o  c  i  a  t  e  (  i  with low +p/-p, the denominator predominates. This i s i n accordance with the previously discussed negative correlation of - . 4 0 2 between -p(y) and PWC^_Q.  Further support i s added by an insignificant correlation of +.094  between +p(y) and PWC^_Q. Basically, +p/-p and -£(y) measure much the same characteristics as i s evidenced by their high intercorrelation of - . 7 8 8 .  30 At this point, i t may be worthwhile to briefly discuss the term, immediate post-exercise. There may be some question as to whether phase plane loops recorded at this time are indications of circulatory reaction during stress or whether they are indications of circulatory recovery following stress.  In this experiment, a l l subjects were stressed to the  same point before completing their work task, i . e . heart rates were close to 170 beats per minute. Since there was a time lapse of one minute forty-three seconds between the end of exercise and  the recording of the  f i r s t loop, i t seems probable that loop variables obtained at this time were indications of circulatory recovery following stress. The fact that the difference between Pr./Pr. immediately after exercise and Pr./Pr. at rest correlates negatively with  FWC^Q  indicates  that the subjects with high working capacities recover the fastest i n terms of Pr./Pr.  It i s an accepted fact that cardiovascular fitness i s  associated with speedy recovery from exercise and Pr./Pr. i s no exception ( 4 ) . The variable Pr./Pr. gives an indication of the relationship of pulse pressure to rate of change of pressure. A low value of Pr./Pr. indicates that, relative to pulse pressure, the rate of change of pressure i n a positive and/or negative direction i s rapid. at rest and -.308  Correlations of  -.330  immediately after exercise with FWC^Q give some  indication that this occurs i n the subjects with high working capacities. Of course, these correlation coefficients are not statistically significant and no real conclusions can be drawn here.  31  II  CORRELATIONS OF LOOP VARIABLES WITH THE PWC  PLOTTED LINE  170 The negative c o r r e l a t i o n c o e f f i c i e n t of  -.626 between  PWC^_Q  and  the slope of the PWC^_ plotted l i n e indicates that the subjects with high 0  working capacities tend t o have a more horizontal plotted l i n e .  It i s ,  therefore, not s u r p r i s i n g that -p(y) and +p/-p, both immediately a f t e r exercise, correlate with the slope of the with  However, an explanation  PWC-^-Q.  c o e f f i c i e n t of not evident PWC  1 7 0  plotted l i n e as w e l l as  PWC^_Q  as to why there i s a c o r r e l a t i o n  -.4-6 between -p(y) at rest and the  PWC^_Q  plotted l i n e i s  since -p(y) at r e s t does not correlate s i g n i f i c a n t l y with  .  ILL  CORRELATIONS  BODY  WEIGHT  OF LOOP  AND P W C ^  VARIABLES  DIVIDED  BY  WITH  WEIGHT  The lack of any s i g n i f i c a n t correlations between  PWC-^_Q  d  i'"-  d e o  ^  by body weight and any of the loop variables indicates that t h i s i s a l e s s valuable  c r i t e r i o n than  PWC^_Q  itself.  Since i n the  PWC-^-Q  test  body weight i s supported by the b i c y c l e ergometer, i n d i v i d u a l differences i n working capacity w i l l , t o some extent, r e f l e c t differences i n muscular strength.  Muscular strength w i l l be r e f l e c t e d i n the muscle mass which,  i n turn, i s r e l a t e d to the body weight.  Dividing  PWC^_Q  by body weight  i s designed t o take i n t o account the differences i n working capacity values which are due t o differences i n body s i z e . c o r r e l a t i o n obtained between body weight and PWC  However, the ^ (r =  +.472) indicates  that the common variance shared by these two variables i s only 22$. The amount of unshared variance between PWC^__ and body weight (78$)  32  i n d i c a t e s subjects  that are  i n c l u d i n g  not  i n d i v i d u a l  l a r g e l y  d i f f e r e n c e s  r e l a t i o n s h i p weight  the  has  between  due  i n  t o  body  f i t n e s s .  PWC  introduced  d i f f e r e n c e s  ^ and  weight  Thus,  the  a d i f f e r e n t  i n  working but  t o  r a t h e r  l o o p  other  than  v a r i a b l e s ,  e f f e c t  which  capacity  between  d i f f e r e n c e s ,  i n c r e a s i n g d i v i d i n g  tends  t o  the  by  body  reduce  t h i s  r e l a t i o n s h i p .  IV  The values  of  PWC-^yQ.  P W C - ^ Q  i n  i s  t h a t  the  the  f l o w  of  the  with  of  change  toward  high  the  r a t e  of  of  variance i t  p h y s i c a l  change  of  normal  computer,  exercise  of  and  of  heart.  5  are  i  minutes  occur  i n  Rushmer  l e f t  v e n t r i c l e  of  l e f t  v e n t r i c u l a r  the  e a r l y  +p(x)  IV).  "At  the  r i s e s root  onset  develops  abruptly of  the  k i n e t i c  outflow  i s  the  of  s y s t o l e  t o  exceed  a o r t a .  imparts i n  r a p i d l y  i n  s y s t o l e  a p t l y terms  energy  part  the  of  f l o w  t o  the  s y s t o l e . r a t e  s y s t o l e , the  pressure  r a p i d l y  i n  s y s t o l e ,  i s ,  of  blood  that  i . e .  course, the  pressure  myocardial pressure  pressure gradient  contained t o  The  maximum  describes of  v e n t r i c u l a r  g r e a t l y  Ahigh  a c c e l e r a t e d  f i r s t  and  and  suggests  (5).  t e n s i o n  t o  l o o p .  e a r l y  the  r e l a t e d  p o s t - e x e r c i s e  Table  c a p a c i t i e s , t o  a l s o  negative  s  that  between  (see  PWC-^Q  the  pressure  shows  -.312  at  P W C ^ Q  tends  side  of  +p(x)  working  pressure hand  i n  a f t e r  s i g n i f i c a n t ,  l e f t  by  c o e f f i c i e n t  between  of  the  s y s t o l e  minutes  t o t a l  high  REGRESSION  c a l c u l a t e d  c o r r e l a t i o n  c o r r e l a t i o n  r a t e  of  f i v e  s t a t i s t i c a l l y  c h a r a c t e r i s t i c  character  the  8.8$  f o r  moves A  a  not  STEPWISE  r e g r e s s i o n ,  recorded  subjects  p o s i t i v e +p(x)  +p(x)  Although  accounts f a c t  stepwise  THE  blood  a very  During  d e c e l e r a t e s . "  the  high  at  the  r a p i d l y and peak  remainder  and  33  Although  one must be c a r e f u l n o t t o confuse f l o w r a t e i n t h e a r t e r i e s  w i t h r a t e o f change o f p r e s s u r e , both o f t h e s e p a t t e r n s r e f l e c t , t o some degree,  t h e magnitude o f t h e impulse generated by t h e c o n t r a c t i n g l e f t  v e n t r i c l e d u r i n g t h e i n i t i a l s t a g e o f e j e c t i o n (6).  Thus, i t would appear  t h a t t h e maximum impulse generated by t h e c o n t r a c t i n g l e f t  ventricle  d u r i n g e j e c t i o n tends t o o c c u r e a r l i e r i n s y s t o l e i n t h e s t u d e n t s w i t h h i g h e r working c a p a c i t i e s t h a n i n t h o s e w i t h lower working (Impulse  i s t h e product  capacities.  o f f o r c e and t i m e ) .  The o t h e r two l o o p v a r i a b l e s t h a t appear i n t h e stepwise r e g r e s s i o n a r e P r . / P r . and +p/-p and have been p r e v i o u s l y c o n s i d e r e d . +p(x)  account f o r  42.7$  of t h e t o t a l variance o f FWC-^Q.  These two p l u s The a d d i t i o n o f  o t h e r l o o p v a r i a b l e s does n o t s i g n i f i c a n t l y i n c r e a s e t h i s p r o p o r t i o n . m u l t i p l e R o f .65  i s produced  when t h e y a r e c o r r e l a t e d w i t h F W C - ^ Q .  A  This  suggests t h a t s u b j e c t s w i t h h i g h working c a p a c i t i e s tend t o be c h a r a c t e r i z e d , i n terms o f b l o o d p r e s s u r e changes i n t h e b r a c h i a l a r t e r y , by: 1.  A speedy r e t u r n a f t e r e x e r c i s e toward t h e r e s t i n g v a l u e s f o r maximal p o s i t i v e and/or n e g a t i v e r a t e s o f change o f b l o o d p r e s s u r e .  2.  A r a p i d d e c l i n e i n b l o o d p r e s s u r e d u r i n g d i a s t o l e immediately  after  exercise* 3.  The maximum p o s i t i v e r a t e o f change o f p r e s s u r e o c c u r r i n g e a r l y i n s y s t o l e w h i l e r e c o v e r i n g from e x e r c i s e ( a t 5 minute p o s t - e x e r c i s e ) . The m u l t i p l e R o f .65  o b t a i n e d f o r F W C - ^ Q and t h r e e  independent  v a r i a b l e s (+£/-$, P r . / P r . , and +p(x)) i n d i c a t e s t h a t t h e percentage r e d u c t i o n i n t h e e r r o r o f p r e d i c t i o n o f P W C - ^ Q i s o n l y 24$ of A l i e n a t i o n ) .  Thus, knowledge o f t h e v a l u e s o f t h e t h r e e  (1-  Coefficient  independent  34  loop variables yields a prediction of F W C ^ Q which i s only 24$ better than assigning the mean of the sample  PWC-^Q  values as the best estimate  of any individual's true score. Therefore, R = .65, while of some use, has no great value i n predicting PWC  i n this study.  3  35  REFERENCES 1.  Burton, A.C, Physiology and Biophysics of the Circulation, Tear Book Medical Publishers, Inc., (1965), p. 152.  2.  Langley, L.L., Outline of Physiology. McGraw-Hill Book Co., Inc., New York, Toronto, London (1961), p. 240.  3.  Burton, op. c i t . . p. 154.  4.  Consolazio, C.F., Johnson, R.E., and Pecora, L.J., Physiological Measurements of Metabolic Functions i n Man. McGraw-Hill, New York, Toronto, London (1963), p. 341.  5.  Rushmer, R.F., " I n i t i a l Ventricular Impulse", Circulation. Vol XXIX (February 1964), p. 270.  6.  Ibid., p. 271.  CHAPTER VI SUMMARY AND CONCLUSIONS I  SUMMARY  The purpose of this study was to determine the relationship of selected measurements from the phase plane loop of the brachial pulse wave to physical working capacity as measured on a bicycle ergometer* The selected measurements were: 1.  +p(x) which indicates the pulse pressure when maximum positive rate of change of pressure occurs.  2. +p(y) which i s a measure of the maximum positive rate of change of pressure. 3*  -p(x) which indicates the pulse pressure when maximum negative rate of change of pressure occurs.  4*  -p(y) which i s a measure of maximum negative rate of change of pressure.  5.  +p/-p which i s the ratio of maximum positive rate of change of pulse pressure to maximum negative rate of change of pulse pressure.  6.  Pr./Pr. which i s the ratio of pulse pressure to maximum rate of change of pulse pressure. Thirty-two young male adults underwent a bicycle ergometer testing  procedure i n which physical working capacity ( ^ C ^ )  V S l S  determined.  On the testing day a resting phase plane loop was f i r s t recorded. The PWC ~ test was then administered, followed by the immediate recording 1  n  37  of a post-exercise loop.  Two subsequent loops were then recorded at  recovery i n t e r v a l s of f i v e and ten minutes.  Thus, twenty-four d i r e c t  loop measurements were obtained from each subject.  In addition, the  difference between each post-exercise loop measurement and i t s corresponding r e s t i n g value was calculated making a t o t a l of forty-two loop variables per subject, A large c o r r e l a t i o n matrix was constructed i n which a l l loop variables as w e l l as  FWC^Q,  F W C ^  Q  divided by body weight, body weight,  and the slope of the PWC ^ p l o t t e d l i n e (see Appendix A) were included. The following r e s u l t s were observed.  PWC correlated 170  s i g n i f i c a n t l y with: 1.  immediate post-exercise -p(y).  2.  immediate post-exercise +p/-p.  3.  immediate post-exercise - r e s t Pr./Pr.  No loop variables correlated s i g n i f i c a n t l y with PWC ^ divided by body weight.  However, body weight alone correlated s i g n i f i c a n t l y with:  ...  1.  immediate post-exercise +p/-p.  2.  immediate post-exercise - r e s t +p/-p.  The slope of the  PWC^Q  p l o t t e d l i n e correlated s i g n i f i c a n t l y with:  1.  immediate post-exercise +p/-p.  2.  immediate post-exercise -p(y).  3.  r e s t i n g -p(y). A stepwise multiple regression calculated by computer indicated  that the sum of the independent contributions of three variables accounted f o r 42.7$ of the t o t a l variance of FWC-^Q. 1.  immediate post-exercise - r e s t  Pr./Pr,  These were:  38 2.  immediate post-exercise -p(y).  3«  5 minute post-exercise +p(x).  The multiple R between these three loop variables and JWC  was .65.  1/0  i  ;  II  CONCLUSIONS  The results of this study indicate that the phase plane loops of the subjects with high working capacities tend to exhibit the following characteristics: 1.  Relatively large values of -p(y) immediately after exercise.  2.  Relatively small values of +p/-p immediately after exercise.  3.  A tendency for +p(x) to move toward the l e f t hand side of the loop five minutes after exercise.  4.  A speedy return of Pr./Pr. immediately after exercise toward resting values. An analysis of these results and of the nature of the phase plane  loop indicates that the subjects with higher working capacities have certain characteristics i n terms of changing pulse pressures. These subjects tend to show a rapid decline i n blood pressure during diastole immediately after exercise. Five minutes after exercise there i s a tendency for the maximum rate of change of blood pressure to occur early i n systole.  Finally, there i s a tendency for the large rates of change  of pressure,caused by exercise, to rapidly return=to resting values.  BIBLIOGRAPHY  BIBLIOGRAPHY BOOKS Astrand, P.O., Experimental Studies of P h y s i c a l Working Capacity i n R e l a t i o n t o Sex and Age. Enjar Munkgaard, Copenhagen, 1952. Astrand, P.O., Work Tests with the B i c y c l e Ergometer. Dept. of Physiology, Gymnastiska C e n t r a l i n s t i t u e t , Stockholm, Sweden. Brouha, L», and Radford, E.P., "The Cardiovascular System i n Muscular A c t i v i t y " , Science and Medicine o f Exercise and Sports. Edited by W.R. Johnson, Harper and Brothers, New York, I960. Burton, A . C , Physiology and Biophysics o f the C i r c u l a t i o n . Year Book Medical P u b l i s h e r s , Inc., Chicago, 1965. Consolazio, C.F., Johnson, R.E., and Pecora, L . J . , P h y s i o l o g i c a l Measurements of Metabolic Functions i n Man. McGraw-Hill Book Company, Inc., New York, Toronto, London, 1963* Cureton, T.K., P h y s i c a l F i t n e s s A p p r a i s a l and Guidance, C.V. Mosby Co., S t . L o u i s , 1947. G u i l f o r d , J.P., Fundamental S t a t i s t i c s i n Psychology and Education, 2nd Ed., McGraw-Hill Book Company, Inc., New York, Toronto, London, 1950. Langley, L.L., Outline o f Physiology, McGraw-Hill Book Company, Inc., New York, Toronto, London, 1961. Rushmer, R.F., Cardiovascular Dynamics. 2nd Id., W.B. Saunders Co., P h i l a d e l p h i a and London, 1961. PERIODICALS Adams, F.H., Linde, L.M., and Miyake, H., "The P h y s i c a l Working Capacity o f Normal School C h i l d r e n " ( C a l i f o r n i a ) , P e d i a t r i c s . V o l 28, No. 1 ( J u l y 1961), pp. 55-64. Adams, H.A., Bengtsson, E.B., Birwan, H., and Wegelius, C , "The P h y s i c a l Working Capacity of Normal School C h i l d r e n " (Swedish c i t y and town), P e d i a t r i c s . V o l 28, No. 2 (August 1961), pp. 243-257. Astrand, I . , "Aerobic Work Capacity i n Men and Women with S p e c i a l Reference t o Age", Acta P h y s i o l . Scand.. V o l 49 (Supplementum 169)  (I960), pp. 1-92.  Astrand, P.O., "Human P h y s i c a l F i t n e s s w i t h S p e c i a l Reference t o Sex and Age", P h y s i o l o g i c a l Reviews. V o l 36, No. 3 ( J u l y 1956), pp. 307-335.  40  Balke, B., "Work Capacity and I t s JJ.mi.ting Factors a t High A l t i t u d e " , Reprinted from The Symposium on the P h y s i o l o g i c a l E f f e c t s of High A l t i t u d e , I n t e r l a k e n , Sept. 1962, Pergamon Press, Oxford, London, New l o r k , P a r i s , 1963. Bengtsson, E., "The Working Capacity i n Normal C h i l d r e n Evaluated by Submaximal Exercise on the B i c y c l e Ergometer and Compared with A d u l t s " , Acta Med. Scand.. V o l 154, Fasc 2, (1956), pp. 91-109. B o b s k i i , E.B., Karpman, V.L., Petrov, G.M., and Sachkova, A . I . , "Use o f an E l e c t r o n i c D i f f e r e n t i a t i n g Device i n P h y s i o l o g i c a l Studies", Biophysics. V o l 4, No. 6 (1959), p. 102. Brown, S.R., B a n i s t e r , E.W., and Dower, G.E., Time Derivations of the Carotid Pulse Wave and Phase Plane A n a l y s i s of Cardiovascular Condition. (Unpublished paper), The U n i v e r s i t y o f B r i t i s h Columbia, 1966. B u t e l a r , B.S., "The R e l a t i o n o f S y s t o l i c Upstroke Time and Pulse Pressure i n A o r t i c S t e n o s i s " , B r i t . Heart J . . V o l 24, No. 4 (1962), pp. 657-660. Cumming, G.R., and Cumming, P.M.,"Working Capacity of Normal C h i l d r e n Tested on a B i c y c l e Ergometer", Canad. Med. Assn. J . . V o l 88, No. 7 (Feb 1963), pp. 351-355. Cumming, G.R., and Danzinger, R., " B i c y c l e Ergometer Studies i n C h i l d r e n " , P e d i a t r i c s . V o l 32, No. 2 (Aug 1963), pp. 202-208. Cureton, T.K., "The Nature of Cardiovascular Condition i n Normal Humans", J . of the Assn. f o r P h y s i c a l and Men. Rehab., V o l 11, (Nov-Dec 1957), pp. 186-196. Cureton, T.K., and Massey, R.H., " B r a c h i a l P e r i p h e r a l Pulse Waves Related t o A l t i t u d e Tolerance and Endurance", Amer. J . P h y s i o l . . V o l 159, (Dec 1949), p. 566. D i l l , D.B., " E f f e c t s o f P h y s i c a l S t r a i n and High A l t i t u d e s on t h e Heart and C i r c u l a t i o n " , Amer. Heart J . . V o l 23, No. 4 ( A p r i l 1942), pp. 441-454. D i l l , D.B., and Perrod, K.E., "Man's C e i l i n g as Determined i n the A l t i t u d e Chamber", J . Appl. P h y s i o l . . V o l 1, No. 6 (Dec 1948), pp. 409-417. Dontas, A.S., and Cottas, C.S., " A r t e r i a l Volume and Pressure Pulse Contours i n Young Human Subjects", Amer. Heart J . . V o l 61, No. 5 (May I960), pp. 676-683. Doroschuk, E.V., "A Short Test of Submaximal Working Capacity", CARPER. V o l 32, No. 2 (Dec-Jan 1966)., p. 10.  41  Gleason, W.L., and Braunwald, E., "Studies on the F i r s t D e r i v a t i v e of the V e n t r i c u l a r Pressure Pulse i n Man", J . C l i n . Inves.. V o l 4 1 , No. 1 ( 1 9 6 2 ) , pp. 8 0 - 9 1 .  Neal, N.J., Halpern, W., and Reeves, T.J., " V e l o c i t y and A c c e l e r a t i o n Pressure Changes i n Heart and A r t e r i e s " , J . A p p l . P h y s i o l . . V o l 1 5 , No. 4 ( J u l y I 9 6 0 ) , pp. 7 4 7 - 7 4 9 . Rushmer, R.F., " I n t r a l V e n t r i c u l a r Impulse", C i r c u l a t i o n . V o l XXIX, February, 1 9 6 4 ) , pp.  268-283.  S a l t i n , B., "Aerobic Work Capacity and C i r c u l a t i o n a t Exercise i n Man", Acta P h y s i o l . Scand.. V o l 6 2 (Supplementum 2 3 0 ) ( 1 9 6 4 ) , pp. 6 - 5 2 . Sjostrand, T., "Changes i n the R e s p i r a t o r y Organs of Workmen a t an Ore Smelting Works", Acta Med. Scand.. V o l 1 2 8 , (Supplementum 1 9 6 ) (1947), PP. 687-699.  S t a r r , I . , and Ogawa, J . , "A C l i n i c a l Study of t h e F i r s t D e r i v a t i v e of the B r a c h i a l Pulse Wave", Amer. Heart J . . V o l 6 5 , No. 4 ( A p r i l 1962), pp. 4 8 2 - 4 9 4 . Wahlund, H., "Determination of P h y s i c a l Working Capacity", Acta Med. Scand.. V o l 1 3 2 , (Supplementum 2 1 5 ) ( 1 9 4 8 ) , pp. 5 - 7 8 .  42  APPENDIX A  NAME  John Smith  AGE  22  WEIGHT  80  DATE  Sept. 25  SCHOOL Test 1 Min. 1 2 3 4 5 6  time rate time rate time rate time rate time rate time rate mean  KP = 2  Test 2 Min.  time rate time rate time rate time rate time rate time rate  1  107  2  118  3  119  4  121  5  121  6  122  mean  121.5  Test 3  KP = 2.75  Min.  136  1 2  135  3  138  4  139  5  142  6  144  time rate time rate time rate time rate time rate time rate mean  143,  KP - 3.75 149 157 162  164 164 168 166  /so  too  /30  J60  S40  Z20  900  /080  WOtfK COAO fAfm/wh)  /260  Z+J-O  43  APPENDIX  B  OSCILLOSCOPE DATA SHEET  NAME  DATE  TEST NO.  PHASE PLANE LOOP  Co-ordinates Strain P r . Unit * u l t . • Time Gauge B.P. P.P. mm Pr/10 LO Pr ,+P -P Pre  X  Exercise y Immediate Post Exercise 5 Min. Post Exercise 10 Min. Post Exercise  X  y X  y X  y  mm units mm units mm units mm units  mm units mm units mm units mm units  mm units mm units mm units mm units  mm units mm units mm units ns& units  -P Pr.  Pr/. Pr  44  APPENDIX  PWC  SUBJECT  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  1 7 0  RAW  C  SCORE-  PRACTICE TEST  1460 1210 1285 760 675 1235 955 1240 845 1230 1010 810 1285 1015 1555 840 935 1195 1210 1135 1470 1215 875 960 1030 1350 810 1125 1140 1710 1020 1395  EXPERIMENTAL TEST  1395 1230 1185 950 720 1110 980 1320 1020 1135 1140 990 1405 1035 1560 840 920 1215 1270 1170 1485 1190 1080 970 1120 1270 820 1295 1260 1640 1035 1065  45  APPENDIX  D  PHASE PLANE LOOP RAW SCORES  Rest  ;  Subject  +p(x)  +p(y)  1 2 3 4 5 6 7 8 9 10 11 12  -0.58 -2.09 -1.98 0.00 -0.67 -1.54 -1.92 -0.46 0.00 1.25 0.00 -1.48 -1.23 0.00  4.40 3.69 4.64 4.34 4.06 4.56 4.18 4.80  13  14 15 16 17 18 19 20 21 22 23 24 25 26  27 28 29 30  31 32  -1.32  -2.69 1.06 -0.71 -1.21 -0.89 -0.42 -0.95 -1.31 -2.40 -0.91 -1.19 -0.51 -0.64 -1.72 0.23 -1.15 -1.52  4.70  4.62 4.09 4.50 5.69 4.16 5.80 3.71 4.26 5.70  5.15 4.31 4.95 5.60 4.90 3.83 3.97 5.25 4.48 4.78 3.88 4.20 4.64 4.27  -p(x)  2.06 -0.86 3.39 3.76 0.55 -0.21 0.72 0.70  2.29 3.28 1.42 3.20 -0.30 3.20 2.13 0.00 4.30 1.85 2.78 0.54 1.63 2.86 2.62 3.50 3.42 3.30 0.23 1.63 2.09 3.33 3.07 3.78  •  -p(y)  +P/-P  Pr/Pr  1.54 1.60 1.41 1.23 1.54 1.90 1.37 1.44  2.84 2.31  1.68 1.88  3.51 2.63 2.33 3.05 3.32 2.26 3.17 2.96 3.04 3.55 2.64 4.29 2.04 5.21 4.46 2.63 3.15 4.50 2.67 5.03 2.35 2.48 4.45 2.69 5.06 3.88 3.35  1.79 1.78 1.53 1.80 1.60 1.47 1.64 1.83 1.67 1.37  2.07  1.45 1.38 1.47 1.59 1.57 -1.35 1.81: 0.81 1.27 1.95 1.36 1.10 2.09 0.97 1.63 1.60 1.18 1.66 0.94  1.07  1.25 1.15 1.23  3.30  4.03  3.46  1.65  1.70  1.39 1.81 1.97 1.43 1.41 1.76 1.65 1.30 1.70  1.83 1.79 1.55 1.62 1.74 2.01 1.83 1.72 1.81  46  Immediate post-exercise Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  +p(x)  +p(y)  -1.10 -1.55 0.85 -1.56 -0.93 -1.12 -1.43 -1.13 -0.28 -0.77 0.00 -1.59 -0.84 -1.38 -1.80 -0.62 -0.35 -1.03 1.03 -1.42 -1.04 -0.97 -1.97 -1.57 -0.51 -1.13 -1.30 2.40 -1.93 -1.34 -1.09 -1.45  8.67 4.87 6.57 5.29 7.44 5.30 6.82 6.24 5.97 6.84 9.84 7.92 6.87 7.60 6.20 8.34 6.83 7.38 8.44 7.09 8.22 8.38 5.97 7.18 7.35 7.65 7.30 5.33 5.68 7.00 7.72 8.13  -p(x) 1.87 1.08 -0.66 1.88 1.02 0.00 0.56 0.00 0.00 0.35 -1.37 -0.22 0.00 0.31 2.66 0.18 1.33 1.32 0.82 2.44 1.04 0.97 2.51 0.00 -0.85 0.36 1.21 -1.31 1.60 0.75 2.41 1.77  -ky)  +P/-P  Pr/Pr  2.41 1.65 1.85 1.37 2.31 2.41 2.39 1.88 2.54 2.77 1.78 2.33 2.64 2.63 1.26 2.38 2.26 2.41 2.92 2.25 2.08 2.28 1.27 3.12 2.57 2.50 2.67 3.52 2.49 2.47 2.07 2.62  3.31 2.94 3.53 3.83 3.22 2.19 2.85 3.31 2.34 2.46 5.51 3.47 2.60 2.88 4.90 3.49 3.01 3.06 2.88 3.14 3.94 3.67 4.68 2.30 2.87 3.05 2.73 1.51 2.28 2.04 3.72 2.73  0.96 1.53 1.18 1.50 1.02 1.29 1.08 1.22 1.17 1.04 0.84 0.98 1.05 0.98 1.33 0.93 1.10 1.02 0.69 1.07 0.97 0.94 1.37 0.97 1.01 0.98 1.10 1.13 1.03 1.10 1.02 1.02  47  r  5 min  post-exercise  Subject  +p(x)  +p(y)  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  -0.69 -1.31 0.62 -1.24 -1.12 -1.84 -1.33 -1.25 0.00 -0.84 -0.74 -1.75 -1.00 -1.85 -1.37 0.58 1.34 -0.94 -1.25 -1.76 -0.50 -1.24 -1.85 -2.02 -0.40 -1.42 -0.64 -2.47 -2.42 -0.83 -0.96 -2.46  5.15 5.59 4.74 4.98 5.43 4.26 5.41 4.23 4.88 4.97 7.29 5.25 4.62 5.36 5.98 4.56 3.96 6.62 6.68 5.10 5.37 5.89 4.85 4.76 5.12 5.97 4.47 3.34 4.75 5.00 4.82 4.40  -P(X)  1.36 0.99 2.18 2.07 0.00 -0.34 -0.80 -0.29 1.84 -1.09 1.03 1.64 -1.22 -0.86 0.85 0.00 -0.40 1.71 -0.46 1.35 1.12 0.00 3.27 2.40 -0.81 0.00 0.00 2.57 2.97 -0.33 2.22 1.22  -p(y)  +p/-p  Pr/Pr  1.73 2.02 1.92 1.64 2.60 2.24 2.09 1.65 2.04 2.42 1.67 1.6? 1.91 2.25 1.85 2.06 2.09 1.63 2.56 2.09 2.66 1.26 1.44 1.99 2.41 2.47 2.13 1.47 1.48 2.22 1.82 1.83  2.96 2.76 2.45 3.03 2.08 1.90 2.58 2.55 2.39 2.05 4.36 3.14 3.00 2.38 3.25 2.20 1.89 3.86 2.60 2.44 2.01 3.15 3.36 2.39 2.12 2.41 1.55 2.27 3.21 2.25 2.63 2.46  1.45 1.31 1.53 1.51 1.24 1.53 1.33 1.70 1.44 1.35 1.11 1.44 1.30 1.31 1.28 1.51 1.65 1.21 1.08 1.39 1.24 1.29 1.59 1.48 1.33 1.18 1.51 2.07 1.60 1.38 1.50 1.57  48  10 min Subject . +p(x) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  -0.97 -0.79 0.99 -0.52 0.00 -1.78 -1.23 -1.03 0.00 -0.44 -0.93 -1.49 -1.24 -1.41 -1.38 -0.54 -2.77 -1.89 -1.13 -1.41 -0.74 -1.11 -1.66 -1.66 -1.07 -1.23 -1.47 -1.05 1.12 -0.54 -0.93 -1.62  post-exercise +p(y) 4.58 3.75 4.19 4.79 4.70 4.98 4.79 4.84 4.54 4.68 5.96 5.22 5.41 4.47 5.25 4.02 4.00 5.88 6.11 4.52 5.09 5.31 4.76 4.48 4.78 5.73 4.32 3.65 3.40 4.23 4.19 4.31  -p(x) 1.66 0.24 -0.44 1.66 -0.42 -0.55 -1.02 0.54 0.00 1.26 1.22 2.01 1.55 1.48 1.60 0.39 9.49 1.07 -0.54 0.53 1.68 0.22 2.39 2.20 0.19 0.35 0.64 1.42 2.17 0.00 1.58 0.00  •  -kr)  +P/-P  Pr/Pr  2.00 1.87 1.65 1.82 2.64 2.20 2.28 1.99 2.31 2.53 1.71 1.74 2.18 2.40 1.35 2.10 2.04 1.92 2.61 2.13 1.96 2.05 1.53 1.90 1.98 1.77 2.11 1.30 1.54 1.93 1.77 1.79  2.29 2.00 2.53 2.62 1.78 2.26 2.10 2.43 1.96 1.84 3.48 2.98 2.48 1.80 3.88 1.92 1.96 3.07 3.82 2.12 2.59 2.59 3.10 2.36 2.42 3.24 2.05 2.81 2.20 2.18 2.37 2.41  1.51 1.75 1.71 1.51 1.36 1.39 1.41 1.46 1.45 1.38 1.30 1.43 1.31 1.44 1.51 1.63 1.65 1.22 0.93 1.50 1.41 1.36 1.58 1.57 1.48 1.33 1.55 2.02 2.02 1.62 1.68 1.64  *  49 APPENDIX  PWO.  Subject  1 2 3 4 5 6 7 8 9 10 11 12 13  14 15 16 17 18 19 20 21 22 23  24 25 26 27 28 29 30 31 32  E  /BODY WEIGHT, SLOPE, AND BODY WEIGHT RAW SCORES  PWC  170  /Weight  13.20 16.61 10.78 11.99 13.88 10.63 9.50 14.65 16.43 14.41 14.43 20.00 14.49 18.54 14.54 16.19 13.44 16.83 14.87 18.04 16.10 15.57 11.48 15.40 16.92 11.13 15.25 15.27 19.49 13.79 16.21 ... 17.25  Slope  36 35 42 55 43 43 39 39 36 39 48 32 35 28 55 45 38 38 28 37 34 39 33 43 39 . 40 ' 36 40 32 39 56 40  Weight  93.21 72.24 88.91 60.56 78.70 93.10 95.37 72.46 70.65 79.37 67.10 71.21 71.90 82.32 59.42 56.24 89.81 75.41 78.69 84.82 73.02 68.83 85.62 72.80 75.18 73.48 85.40 82.50 84.00 75.00 65.40 80.28  50  APPENDIX  F  MEANS AND STANDARD DEVIATIONS OF THE LOOP VARIABLES  Time  Variable  Rest  +p(x)  0 . 9 0 5  +P(y)  4 . 5 6 6  0 . 5 8 1  -PU)  2 . 0 7 1  1.417  -P(y)  1 . 3 5 2  0 . 5 8 5  3.332  0 . 8 9 0  1 . 6 7 8  0 . 1 7 5  +p(x)  1 . 1 4 2  0 . 7 5 1  1 . 0 7 4  2.316  0 . 4 9 8  + P /  3 . 1 3 9  0 . 8 3 4  1 . 0 8 2  0 . 1 7 6  - 1 . 0 9 2  0 . 8 7 4  7  P  +p(x) +p(y) -p(x) -£(y) 7  +p(x) +p(y) -£(x) -P(y) + P /  7  P  Pr/Pr Immediate p o s t exercise - r e s t  0.915  7 . 0 7 6  +p/ p Pr/Pr 1 0 minute post-exercise  - 0 . 9 0 4  +P(y) -p(x) -p(y) Pr/Pr  5 minute post-exercise  S.D.  - 0 . 9 0 5  +p/rP Pr/Pr Immediate postexercise  Mean  +p(x) +P(y) -P(x) -P(y) +p/ p Pr/Pr 7  5 . H 9  0 . 8 0 8  0 . 7 5 6  1 . 2 8 4  1 . 9 7 8  0 . 3 6 2  2.615  0 . 5 9 6  1 . 4 1 9  0 . 1 9 5  - 0 . 9 9 8  0 . 7 7 2  4.717  0 . 6 6 3  1 . 0 8 0  1 . 7 9 3  1 . 9 7 2  0 . 3 2 8  2 . 4 8 9  0 . 5 5 8  1 . 5 0 3  0.210  0 . 0 0 1  1 . 1 9 3  2.510  1 . 2 6 3  -1.320  1.717  0 . 9 6 3  0 . 5 8 7  - 0 . 1 9 4  1 . 1 1 5  0 . 2 3 4  - 0 . 5 9 7  (Cont*d)  51  Time 5 minute post-exercise - rest  Variable +p(x) +p(y) -PU)  -*(y) + P /  7  P  Pr/Pr 10 minute post-exercise - rest  +PU)  +p(y) -P(x)  r*(7) +p/ P Pr/Pr 7  Mean  S.D.  -0.188 0.553 -1.315 0.626 -0.718 -0.259  1.075  -0.093 0.151 -0.990 0.619 -0.844 -0.175  1.261 0.554 1.840 0.474 0.860 0.173  0.86? 1.722 0.641 0.981 0.213  52  A P P E N D I X  MEANS  AND  STANDARD  W E I G H T ,  D E V I A T I O N S  S L O P E ,  Variable FWGJ^Q  (kgm/min)  PWC /weight 170  (m/min)  Slope  (degrees)  Weight  (kg)  A N D  G  O F  BODY  P W C ^ Q ,  P W C ^ Q / B O D I  WEIGHT  Mean 1 1 5 1  S.D. 2 1 0 . 8  1 4 . 9 2  2 . 5 4 9  3 9 . 4 4  6 . 8 1 1  7 6 . 9 7  9 . 8 5 3  APPENDIX H INTERCORRELATIONS OF LOOP VARIABLES i  Rest +p(x)  Immediate post-exercise  -kr)  +o(y)  +P/-P  Pr/Pr  +p(x)  +p(y)  -p(x)  -p(y)  +P/-P  Pr/Pr  +J(x)  -  +p(y)  +.116  -p(y)  -.050  +.046 -.298  +p/rP Pr/Pr  +.256 -.011  +.435* +.300 -.872* +.107  -.621 -.023  +.140. +.061  +p(y) -J>(x) - . 0 0 3  +.121 +.036  +.049 +.178  +.158  +.033 +P/7P -.015 Pr/Pr - . 0 3 1  -.095 +.196 -.035  +.069 +.058. +.038 -.186  +.173 +.207 -.408* +.421*  +p(x) +.270 +P(y) +.000 -*(x) -.272 -p(y) +.154 +P/-P - . 1 1 3 Pr/Pr -.024  -.044 +.254 -.061 -.172 +.286 -.211  -P(x) +.324 • * •  +p(x)  -P(y)  -  -.166  —  +.039  -  -  +.088 -.180  -.130 -.107  +.295 -.175 -.385* +.165 +.161 -.317  +.008 -.103 +.107  -.096 +.432* +.161 -.438* +.372* +.260 -.213 -.294 -.833* +.269  +.066 +.021  +.100 -.036  -.054 -.150  +.007 -.306  +.257 -.102  +.190 -.055 +.027 +.050  -.211 +.148 -.216 -.091  +.335 -.253 +.175 +.305  +.231 +.021  -.016 +.063 -.142 +.228  • s i g n i f i c a n t a t 0.05 l e v e l  -.015  -.154 +.343  +.073 -.588*  -  +.212 +.503* -.230 +•162 +.186 -.507*  -  -.141 -.053 +.249 -.118 -.096 -.065  -  -.788* -.576*  +.055  -.179 -.271 -.222 +.246  +.193 +.529* +.182 -.222  -.427* +.174  (Cont'd)  —  -.079 -.336  +.255 -.251 +.573* - . 0 1 3 -.364* +.362*  10 minute post-exercise  5 minute post- Immediate postexercise - rest exercise - rest •?  c f  »c(«  VjL Q'x  jnj *no» s  *< 'x  i •I •l +• •I •l • O UJ H Q O H O UJ O -3 N  UJ UJ UJ  H CO  +  Ui-s3 vO  + 1 + 1 I I • • • • • • M H o {H  •+ •I +•  IO ^ H Ui  vO  -*3  .00 UJ UJ P"  U)  I I I •I I• +• • • • O  to H  O  O  IO  P P g  +  1  +  I  H OV o  + +  I  * * •i •i Ui H H to QvO  + • O UJ U  + UJ  H  H  O I  I H  M  O  O  +  + +  .020  i  8  w  %  + • +• O UJ TO Q ^ O  I  I  O ui IO UJ  H  I  NJ  O  I  +  • • • •  •  $ 3 8 +  I  g  MU) O O ON vO o +  H  +  k H  •+  +  vo K5 o oo o u i  {0 H .p- u i  +  +  SI  O  + •  + •  (2  I + Nj IO O N O W O 00 vO  H H 00  I  + •  S 3 +  O VA> — I -s3 O O IO H U J U J 00 1  * * •*  I  I  I  +  Q 00 UJ  +  I  •+ •1  W Q O N5 *~ ' H  I  +  +  -pO 00  O H  O g> H Q  I •  + •  + •  & g §g  •  Ul UJ 00->3 +  I I  •I •I +• •I  UJ vO IO o  +  UJ H IO -J -p- O  + 1 + 1  OOP-  00  I •  • • • • • •  HIO H tOUJ vO U O t-  I  +1 i i • • +• +• • •  £  ;+  k  1 +  1  +  vO * +  H  UJ  b  # +  1  Ul  UJ UJ o  •3 *  o + o  I  +  IO UJ O O UJ -J  Ul Ul 00  Ul ->J  + I • •  •I H 00 UJ  + 1 • • UJ O TO U l IO ->3  • •  O*QUJ vO O  +  •  •  I  •  Q O  >o  •I  +  N> UJ IO  O -P-P- O UJ O  •  •I  I + • • O R O H  I • ^  + • IO  I • H O Ui  I • UH i Ui  I  I  I  +  • to  O  vUl  g  +  I  +  +  NJ CO P-  H O vO  fM ^  io I  +  I  O O O00 vo-<}  I  I  +  N H Ul -O IO I  H U J -vl < N Ul U J H -a  00 +  I 1 4 ?  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X *< X  O O O I  UJ b -P~ VjO 00 UJ  I  at  Rest  Immediate post-exercise  -p<*)'  -p(y)  -.219 -.320 -.068 +.289  +.118  -.069 +.358*  +p(x) +>  1 -P  CO CD  u 1  •*PCX)  +P(7)  o p. a> a 0) -p(y) a Pr/Pr  -pU)  + P /  7  P  38  -.794 -.008 +.135 +.243 -.358* -.203  +P/-D  •  Pr/Pr  +p(x)  +p(y)  -p(x)  -p(y)  +P/-P  Pr/Pr  -.263 -.017 -.418* +.076  -.098 -.327 +.341 - . 4 6 7 * +.130 +.302 +.232 -.193 -.829* +.381* -.098  -.009 -.108 -.084 -.209  -.072  +.359* - . 7 9 7 * +.280 -.289  -.033 +.149  -.026 +.302 +.077 +.279 +.156 -.197  +.043 -.379* +.192 +.156  -.187 -.069  -.093 -.137 +.519* - . 2 9 1 -.179 +.141 +.450 -.094 +.321 -.294 -.472* -.069  -.323 -.272  5 min post-exercise +p(x)  -p(x)  +a  CO Q> O CO O  +p(y) -PU)  -p(y) +P/ P :  Pr/Pr  .000 -.273 +.271 -.255 -.132  -  -  -.103 +.118 -.564* +.602* +.387* -.876* +.380*  * s i g n i f i c a n t a t 0.05 l e v e l  -.251 +.375*  10 min post-exercise -p(y)  +p/-p  Pr/Pr  +p(x) +p(y) -p(x) -p(y) +p/-p  +p(x)  1  .3  +p(y)  -.047 -.128 -.299 +.022 +.235  -  -.641* -.458*  -.283  (Cont'd)  Pr/Pr  5 min post-exercise +p(x) i +»  CO O  <D  P<  CO  •ri  C o  l  -P  CO  CD  a CD  ?  -P  a  a> co  CO  43  co  +p(x) +.088 +p(y) -.021 -p(x) +.301 -P(y) +.233 • • -.209 +P/7P Pr/Pr -.118 +p(x) +p(y) -p(x) -P(y) +P/.P Pr/Pr  I  -.143 -.252 +.187 -.065  +o(y)  -p(x)  -p(y)  +P/-P  Pr/Pr  +p(x)  +.006 +.727* -.264 +.139 +.542* -.650*  +.244 -.285 +.119 -.666* +.226 +.510*  +.011 +.137 -.174 +.623* -.221 -.397*  +.022 +.437* +.009 -.412* +.585* -.157  +.004 -.697* +.294 -.436* -.277 +.759*  -.310 -.413* -.028 -.192 +.298  -.207 +.214 -.217 +.667* -.096 -.895* +.251  -.452* -.609*  -.078 +.338 +.016 -.194 +.516 -.023  +.194 -.180  -.068 +.226  +.209 -.035  -.060 +.141  -.335 -.023  -.194 +.263  -.001 +.022 -.013 -.019  -.028 +.061 +.056 -.204  -.192 -.023 +.363* - . 3 6 2 * +.377* -.082 +.238 -.147 +.288 -.516* +.105 +.015  -.055 -.199 +.140 -.085  -.087 -.128 +.324 +.231  -.173 +.256 -.355* -.204  +.105 -.313 +.233 -.118  -.674* +.257 -.176  +.177 +.154 +.224 +.115  -.097 +.268 -.234 +.056  -.087 -.223 -.209 +.203  -.160 +.449* -.449* -.437* -.132 +.633*  +.224 -.118  -.273 -.096  -.491* +.003  +p(x) +.586* -.001 +.761* +p(y) +.029 -P(x) -.258* - . 0 9 5 -p(y) +.062 +.100 +P/-P  UN.  -.008 +.212  Pr/Pr  -.088 -.127  10 min post-exercise  +.502* -.550*  -.088 +.091 +.225 -.369 -.055 +.266 +.589* -.375* -.126 +.430* -.165 +.007  -.069 +.175  -.087  +p(y)  —  -p(x)  -p(y)  -  +P/-P  Pr/Pr  _  -.353*  —  +.253 -.083 -.146 +.227 +.084 +.229  +.145 -.233 +.013 +.262 -.396* -.157  -.031 +.206 -.343 -.183  -.052 +.111 +.012 +.274  +.053 -.316 +.354* +.011  +.256 -.248  +.023 +.106  -.334 +.193  * s i g n i f i c a n t a t 0.05 l e v e l (Cont'd)  10 min post-exercise  5 min post-exercise  CO  •ri U  U  +pU) +p(y)  -P(x)  8 +» o, CO  -My) +P/-P  o no-  Pr/Pr  Pr/Pr  +p(y)  -p(x)  -p(y)  +P/-P  Pr/Pr  +p(x)  -.140 +.022 +.242 +.038  +.003 +.345 +.602* - . 2 7 7 -.274 -.031 -.200 +.140  -.103  +.095 +.222 -.012 -.018  +.020 -.611* +.248 -.190  +.702* -.258 -.536* -.205 -.017 +.376* +.181 -.138 +.556* - . 2 1 2 -.192 +.696* -•076 -.363* -.222 +.118 +.257 +.227 -.183 -.033  +.309 -.616* +.220  -.083 -.150  +.118 +.507* - . 2 0 0 - . 4 8 0 * +.386* - . 5 0 2 *  +.198  -.496* +.574*  +.270 +.013  -.501*  -.035  +.115 +.212  +.343 -.127 +.248  +p(y)  -p(x)  +p/-p  +p(x)  +.442* - . 5 9 6 * -.421* - . 0 2 1  -p(y)  +.284 -.555*  n s i g n i f i c a n t a t 0.05 l e v e l  (Cont'd)  -.103 +.597*  5 min postexercise - rest  LO min postexercise - rest  *  CO H  © o H CD  *?  *rt»  "C(  •v* ^v,  ••o* • t t » C ^ « •5* *rt» "ci» •cj»»ck 'rt. •F >tt.»o.»cj. •it'it. ,  »~v W«l «4 •J X) • v-/ I  <-v *—» <-v X «{ x v-^ v_x I I  NJ "  NJ NO  O  O  Ui  ON  -5  NO  I >  + •  ui  UJ  ^ {8 + • G H O  i • O UJ O  UJ  U l -v? -o i i +  Ul  UJ  K5  i • • O• • NJ H NJ H  09  +  O  H < *  +  I  NO  \  *-V  *<  rj  « w  T) •  +  +  ^ NJ  O NJ  »IO H.  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