HANDBOOK OF RESPIRATORY DAY A IN ACIATION Prepared under the direction of the Subcomm.t ee on Oxygen and Anoxia of the Committee Aviat.on Medicine Div «... of Meoicat Sciences, National Research Council Acting for the v/-va: iE£ ..>s Medical Research wf Scientific Research and Deveiou Wasnington, D. C. 1944 HANDBOOK OF RESPIRATORY DATA IN AVIATION Prepared under the direction of the Subcommittee on Oxygen and Anoxia of the Committee on Aviation Medicine Division of Medical Sciences, National Research Council Acting for the Committee on Medical Research Office of Scientific Research and Development Washington, D. C. 1944 INTRODUCTION It is the purpose of this Handbook to make available in concise and usable form physiological data of value in the study of high altitude physiology and in the design of oxygen equipment for aviators. It has been compiled to meet the needs of the many physiologists, flight surgeons and engineers who, through research, development and training, are endeavoring to make flight at high altitudes safer and more effective. Much of this material has been collected from published scientific papers and from reports issued by gov- ernment organizations or service laboratories in the United States, England and Canada. Where significant omissions existed, the necessary information has been obtained by special investigations carried out under con- tracts with the Committee on Medical Research of the Office of Scientific Research and Development. Whenever possible, data have been presented graphically in order that they may be more readily used. With each chart there is a brief description explaining its use, together with a statement of the sources from which it has been constructed and a definition of its limitations. Algebraic formulations of the data are also given in many instances, to provide general equations applicable to the solution of specific problems. The Handbook has been prepared under the direction of the Subcommittee on Oxygen and Anoxia of the National Research Council. But the expeditious publication of this material has required that the authors of the sections which bear their signatures assume responsibility for the data and their interpretation. The Subcommittee is indebted especially to Doctor John R. Pappenheimer for most of the editorial work, for the details of publication and for the preparation of many of the charts. The rapid development of Aviation Physiology makes it difficult to provide a collection of data such as this, which will be either complete or adequate for more than a brief time. It is, therefore, presented in loose- leaf form so as to facilitate the inclusion of additional material and the elimination of that which may be found inadequate. The Subcommittee will welcome useful additions or corrections from the many workers in this active field of scientific research and application. THE SUBCOMMITTEE ON OXYGEN AND ANOXIA Detlev W. Bronk Chairman Carl F, Schmidt Secretary Walter M. Boothby Eaton MacKay Frank W. Maurer RESTRICTED TABLE OF CONTENTS Section Introduction P . . . Physical Data Essay P Measurement of Barometric Pressure. Table P-2 Table of Functions Based on the U. S. Standard Atmosphere. Temperature, total pressure, pressure of gases saturated with water vapor at 370 C., frac- tions of oxygen in inspired air saturated at 370 C. to equal 0,5000, and 10,000 foot equivalents. Chart P-3 Positive Pressures Required to Attain Stated Effective Altitudes. Table P-4 Properties of Oxygen. A . . . Composition of Respiratory Gases Essay A Calculations Relating to the Composition of Respiratory Gases. Chart A-i Alveolar Oxygen and Carbon-Dioxide Pressures Breathing Air at Altitude. Chart A-2 Equivalent Altitudes Breathing Gas Mixtures. Chart A-3 Comparison of Standards for Calculating Oxygen Requirements. Chart A-4 Composition of Inspired Gas Required to Maintain Stated Alveolar Oxygen Pressures at Altitude. Chart A-5 Gas Mixtures Required to Simulate Altitudes at Sea-Level. R . . . Respiratory and Metabolic Data Chart R-i Components of Respiratory Minute Volume. Chart R-2 Respiratory Requirements During Exercise. Chart R-3 Metabolic Requirements During Exercise. Chart R"4 Respiratory Response to Carbon Dioxide. Chart R-5 Peak Inspiratory Velocities. Chart R-6 Resistance to Breathing. B . . . Properties of Blood Chart B-i a. & b. .. Oxygen Dissociation Curves of Normal Human Blood. Chart B-3 Arterial Oxygen Saturation at Altitude. Chart B-4 Arterial Oxygen Saturation at Altitude (Statistical Analysis). E . . . Oxygen Supply Systems Chart E-ia & b Calculated Economies of Ideal Oxygen Systems. M . . . Carbon Monoxide Chart M-i Equilibria Between O2, CO and Hb02 in Normal Human Blood. Chart M-2 Concentration of CO in Inspired Air Required to Bring Arterial Oxygen Saturation to 85% at Stated Altitudes and in Stated Periods of Time. Chart M-3 CO Standards for Use With Auto-Mix Systems, C . . . Circulation RESTRICTED CONTRIBUTORS Walter M. Boothby Aero-Medical Unit Mayo Foundation Frank Brink, Jr. Johnson Research Foundation University of Pennsylvania W. G. Brombacher National Bureau of Standards J. S. Hart R. C. A. F., No. i Clinical Investigation Unit H. F. Helmholz, Jr. Consolidated Aircraft Corporation and Aero-Medical Unit Mayo Foundation John C. Lilly Johnson Research Foundation University of Pennsylvania Glenn A. Millikan Johnson Research Foundation University of Pennsylvania John R. Pappenheimer Johnson Research Foundation University of Pennsylvania Arthur J. Rawson Johnson Research Foundation University of Pennsylvania Carl F. Schmidt Department of Pharmacology University of Pennsylvania SECTION P Physical Data MEASUREMENT OF BAROMETRIC PRESSURE ESSAY P RESTRICTED December, 1943 Measurement of Barometric Pressure Essay P Mercury Manometers and Barometers. To define pressure in terms of the height of a mercury column standard conditions as to temperature and gravity must be specified. The U. S. standard values are OcC and 980.665 cm/sec2. Barometers and manometers divide into two classes: (a) those in which the height of the mercury column is measured directly, as in U-tube manometers and Fortin barometers, and (b) those in which the read- ing is made essentially only at the top of the column and in which the scale is graduated to take care of the shifting position of the lower mercury surface; examples are fixed cistern manometers and barometers where the scale is foreshortened to compensate for the changing mercury level in the cistern. For class (a) instruments, the correction to the measured height of the mercury column for deviations from the standard temperature is given in the following table as the percent of the measured height. To obtain the subtractive correction to be applied, multiply the given correction by the column height. In com- puting the correction the scales are assumed to read correctly at 0°C. The temperature effect on the invar scale is assumed to be zero. Temperature Corrections for Mercury Manometers and Fortin Barometers Temperature Invar scale Steel scale Brass scale °C Correction % Correction % Correction % o 0 0 0 IO —.18 —•17 —.16 15 —.27 —.26 —•25 20 —•36 —•34 —•33 25 —45 —.42 —.41 30 —•55 —•5i —49 For class (b) instruments the temperature error is greater than given in the table, dependent on the relative bores of the cistern and tube. For both classes of instruments the corrections, expressed as a percentage of the height of the liquid col- umn, corrected for temperature error, to be applied for variation in gravity from the standard value are given below for various latitudes at sea level. Positive values are to be added to the column height at 0°C, and negative values subtracted, to obtain the true pressure. The effect of station altitude is -fo.oi percent per 1000 feet, an amount ordinarily negligible. RESTRICTED RESTRICTED Gravity Corrections for Manometers and Barometers Gravity Gravity Latitude correction Latitude correction degrees % degrees % o —.27 45 0 20 —.21 50 +.04 30 —.14 60 +•13 40 —•05 70 +.20 45 0 90 +.26 Water Manometers. No one temperature has been generally adopted as standard for water manom- eters. In aeronautics, the standard temperature is generally accepted as 15°C; standard gravity is 980.665 cm/sec2. On this basis the temperature error in percent of column height is as follows, in which minus corrections are subtracted from, and plus corrections are added to, the indication to obtain the column height at 15°C. In computing the correction the scales are assumed to read correctly at o°C. Water Column Temperature Correction temperature Invar Scale Steel Scale Brass Scale °C % % % 10 +.06 +•05 +.04 i5 0 —.02 —•03 20 —.09 —.11 —•13 25 —.21 —.24 —•25 30 —•35 —•39 —.40 The gravity corrections are the same as those given for mercury barometers and manometers. Altimeters. The readings of the altimeter are not affected by changes in the acceleration of gravity. The effects of temperature changes on the altimeter readings cannot be calculated; they must be deter- mined by test. Present specifications (AN-GG-A-461 dated Sept. 27, 1941) permit the following maximum errors in 50,000 foot altimeters; in general the errors are less, especially for selected altimeters. Pressure Altitude Maximum Errors in feet 1000 feet + 20°C —5°°C 0 50 100 6 150 250 18 275 550 25 375 750 35 525 1050 40 600 ■— 50 750 1500 Reference: Smithsonian Metereological Tables, 5th revised edition, 1939. “Barometers and Manometers,” Dictionary of Applied Physics, vol. 3, pp. 140-192, 1923. W. G. B. RESTRICTED RESTRICTED December, 1943 Table P-2 Explanation: I. Temperature: In the United States standard atmosphere a simple altitude-temperature relation is assumed which approximates the yearly average of the observed relation at latitude 40°N. Up to the iso- thermal layer (35,332 ft.) the relation is given by, T — T0 —aZ =15 — 0.0019812 Z degrees centigrade where T = air temperature in degrees centigrade. T0 — standard temperature at sea-level = I5°C. Z = altitude in feet above sea-level, a = standard lapse rate of temperature with altitude. = o.ooi98i2°C. per foot or 6.5°C. per kilometer. The mean temperature of the air column below the isothermal layer (Tma) is given by the relation— aZ Tma (degrees absolute) = 288 2.303 log 288 — aZ II. Pressure Altitude: Up to the isothermal layer ' 760 Z = 221.15 Tma log PB where PB is the barometric pressure (mm. Hg) at altitude Z feet above sea-level. U5-9 In the isothermal layer Z — 35,332 -f- 48211 log PB III. Fractions of oxygen to maintain constant pressure of oxygen in inspired air saturated with water vapor at 37 °C. -Cisl _ -209 (760 — 47) cisooo _ -209 (632 — 47) cuoooo -209 (523 — 47) J- 02 — > 02 — > I02 — pb ~ 47 PB ~ 47 PB — 47 The fractions of oxygen so calculated are useful in the design of oxygen equipment for maintaining altitude equivalents of o, 5000 or 10,000 feet. The fractions given are based on physical standards of alti- tude equivalence and are slightly greater (never more than 5% o2) than similar fractions calculated from physiological standards based on identity of alveolar gas composition (cf. Chart A-3). Limitations. 1) The Standard Atmosphere. In the design of oxygen equipment it may be necessary to consider deviations from the standard atmos- phere which occur at different latitudes and in different seasons. Observed values for the altitude and tem- perature of the tropopause vary from 56,000 feet and —8o°C. at the equator to 30,000 feet and —42°C. at the North Pole. In the north temperate zone the seasonal variations of temperature about the standard values given in the table rarely exceed -f-200 or —30 °C. Detailed data concerning the variation of air tem- perature with altitude may be found in reference (2) cited below, 2) Fractions of Oxygen in Inspired Air. Use of these oxygen fractions in relation to quantitative physiological investigations at altitude should be considered only after examination of the assumptions implicit in the equations given above. A discussion of these assumptions is given in Essay A, Section V. Sources: 1) W. G. Brombacher, N. A. C. A. Report #538, 2) E. M. Walsh, Airesearch Mfg, Co. Report 3) W. M. Boothby, Mayo Aero Medical Unit. F. B., Jr. and J. R. P. Table of Functions RESTRICTED TABLE P-2 TABLE OF FUNCTIONS Based on U. S, Standard Atmosphere Altitude (feet) Temper- ature0 C P.S.I. mm.Hg PB-47 mm.Hg Based on Physical Standard of Con- stant Po£ in Saturated Inspired Gas To*- Fo25000 Fo21000° 0 15.0 14.69 760.0 713.0 0.21 .17 .14 500 14.0 14.43 746.4 699.4 0.21 .18 .14 1000 13.0 14.17 732.9 685.9 0.22 .18 .14 1500 12.0 13.91 719.7 672.7 0.22 .18 .15 A 2000 11.0 13.66 706.6 659.6 0.23 .19 .15 0 2500 10.0 13.41 693.8 646.8 0.23 .19 .15 3000 9.1 13.17 681.1 634.1 0.24 .19 .16 3500 8.1 12.93 668.6 621.6 0.24 .20 .16 4000 7.1 12.69 656.3 609.3 0.25 .20 .16 4500 6.1 12.45 644.2 597.2 0.25 .21 .17 5000 5.1 12.22 632.3 585.3 0.25 .21 .17 5500 4.1 12.00 620.6 573.6 0.26 .21 .17 6000 3.1 11.77 609.0 562.0 0.27 .22 .18 6500 2.1 11.55 597.6 550.6 0.27 .22 .18 cr 7000 1.1 11.34 586 .4 539.4 0.28 .23 .19 5 7500 0.1 11.12 575.3 528,3 0.28 .23 .19 8000 —0.8 10.91 564.4 517.4 0.29 .24 .19 8500 -1.8 10.70 553.7 506.7 0.29 .24 .20 9000 -2.8 10.50 543.2 496.2 0.30 .25 .20 9500 -3.8 10.30 532.8 485.8 0,31 .25 .20 10000 -4.8 10.10 522.6 475.6 0.31 .26 .21 10500 -5,8 9.91 512.5 465.5 0.32 .26 .21 11000 -6.8 9.72 502.6 455.6 0.33 .27 .22 11500 -7.8 9,53 492.8 445.8 0.33 .27 .22 4 12000 —8,8 9.34 483.3 436.3 0.34 .28 .23 10 12500 -9.8 9.16 473.8 426.8 0.35 .29 .23 13000 -10.8 8.98 464.5 417.5 0,36 .29 .24 13500 -11.7 8.80 455,4 408.4 0.37 .30 .24 14000 -12.7 8.63 446.4 399.4 0.37 .31 .25 14500 -13.7 8.53 437.5 390.5 0.38 .31 ,25 15000 -14.7 8.29 428.8 381.8 0.39 .32 .26 15500 -15.7 8.12 420.2 373.2 0.40 ,33 .27 16000 -16.7 7.96 411.8 364.8 0.41 .34 .27 16500 -17.7 7,80 403.5 356.5 0.42 .34 .28 15 17000 -18.7 7.64 395.3 348.3 0.43 .35 .29 17500 -19.7 7.49 387.3 340.3 0.44 .36 .29 18000 -20.7 7.33 379.4 332.4 0.45 .37 .30 18500 -21.7 7.18 371.7 324.7 0.46 .38 .31 19000 -22.6 7.03 364.0 317.0 0.47 .39 .31 19500 -23.6 6.89 356.5 309.5 0.48 .40 .32 20000 -24.6 6.75 349.1 302.1 0.49 .41 .33 20500 -25.6 6.61 341.9 294.9 0.51 .42 .34 21000 -26.6 6.47 334.7 287.7 0.52 .43 .35 21500 -27.6 6.33 327.7 280.7 0.53 .44 .35 O A 22000 -28.6 6.20 320.8 273.8 0.55 .45 .36 du 22500 -29.6 6.07 314.1 267.1 0.56 .46 .37 23000 -30.6 5.94 307.4 260.4 0.57 .47 .38 23500 -31.6 5.82 300.9 253.9 0.59 .48 .39 24000 -32.5 5.69 294.4 247.4 0.60 .50 .40 24500 -33.5 5.57 288.1 241.1 0.62 .51 .41 25000 -34.5 5.45 281.9 234.9 0.63 .52 .42 25500 -35.5 5.33 275.8 228.8 0.65 .54 .44 25 26000 -36.5 5.22 269.8 222.8 0.67 .55 .45 26500 -37.5 5.10 263.9 216.9 0.69 .57 .46 27000 -38.5 4.99 258.1 211.1 0.71 .58 .47 27500 -39.5 4.86 252,5 205.5 0.72 .60 .49 TABLE OF FUNCTIONS Based oa U. 3, Standard Atmosphere Altitude (feet) Temper- ature4^ P.S.I. mm.Hg PB-47 mm.Hg Based on Physical Standard of Con- stant Pog in Saturated Inspired Gas Fo|L Fo2500< 1 „„ 10000 Fo2 28000 -40.5 4.77 246.9 199.9 0.75 .61 .50 28500 -41.5 4.67 241.4 194.4 0.77 ,63 .51 29000 -42.5 4.56 236.0 189.0 0.79 .65 .53 29500 -43.4 4.46 230.7 183.7 0.81 .67 .54 30000 -44,4 4.36 225.6 178.6 0.84 .69 .56 30500 -45.4 4.26 220.5 173.5 0.86 .71 .57 31000 -46.4 4.17 215.5 168.5 0.89 .73 .59 31500 -47.4 4.07 210.6 163.6 0.91 .75 .61 -,n 32000 -48.4 3.98 205.8 158.8 0.94 .7? .63 0 0 32500 -49.4 3,89 201.0 154.0 0.97 .80 .65 33000 -50.4 3.80 196.4 149.4 1.00 .82 .67 33500 -51.4 3.71 191.8 144.8 .85 .69 34000 -52.4 3.62 187.4 140.4 .87 .71 34500 -53.4 3.54 183.0 136.0 .90 .73 35000 -54.3 3.46 178.7 131.7 .93 .76 35332 -55.0 3.40 175.9 128.9 .95 .77 35500 -55.0 3.37 174.5 127.5 .96 .78 36000 -55.0 3.29 170.4 123.4 .99 .81 36100 -55.0 3.28 169.6 122.6 1.00 .81 36500 -55.0 3.22 166.4 119.4 .83 -r37000 -55.0 3.14 162.4 115.4 .86 3 v) 37500 -55.0 3.07 158.6 111.6 .90 38000 -55.0 3.00 154.9 107.9 .92 38500 -55.0 2.92 151.2 104.2 .95 39000 -55.0 2.85 147.6 100.6 .99 39500 -55.0 2.79 144.1 97.1 1.00 40000 -55.0 2.72 140.7 93.7 40500 -55.0 2.66 137.4 90.4 41000 -55.0 2.59 134.2 87.2 41500 -55.0 2.53 131.0 84.0 AC\ 42000 -55.0 2.47 127.9 80.9 TU 42500 -55.0 2.42 124.9 77.9 43000 -55.0 2.36 122.0 75.0 43500 -55.0 2.30 119.1 72.1 44000 -55.0 2.25 116.3 69.3 44500 -55.0 2.19 113.5 66.5 45000 -55.0 2.14 110.8 63.8 45500 -55.0 2.09 108.2 61.2 46000 -55.0 2.04 1C5.7 58.7 46500 -55.0 2.00 103.2 56.2 4r 47000 -55.0 1.95 100.7 53.7 W 47500 -55.0 1.90 98.38 51.38 48000 -55.0 1.86 96.05 49.05 48500 -55.0 1.81 93.79 46.79 49000 -55.0 1.77 91.57 44.57 49500 -55.0 1.73 89.41 42.41 50000 -55.0 1.69 87.30 40.30 51000 -55.0 1.61 82,22 36.22 52000 -55 .0 1.53 79.34 32.34 53000 -55.0 1.46 75.64 28.54 54000 -55 .0 1.39 72.12 25.12 5 0 55000 -55.0 1.33 68.76 21.76 56000 -55.0 1.27 65.55 18.55 57000 -55.0 1.21 62.49 15.49 58000 -55*0 1.15 59.58 12.58 59000 -55.0 1.10 56.80 9.80 60000 -55.0 1.05 54.15 7.15 POSITIVE PRESSURES REQUIRED TO ATTAIN STATED EFFECTIVE ALTITUDES CHART P-3 RESTRICTED November, 1943 Positive Pressures Required to Attain Stated Effective Altitudes Chart P-3 This nomogram provides a rapid means for calculating the pressure differential required to maintain any given effective altitude at any given altitude. The chart is useful for problems involving pressurized equipment of all types. It contains no physiological data. It is constructed from the relation— Effective pressure (altitude) = Ambient pressure (altitude) -j- Applied pressure differential. Use of the chart is illustrated by the following examples: 1) A pressurized aircraft is flying at 20,000 feet. What pressure is reouired to maintain the cabin at an effective altitude of 12,000 feet?—A straight line drawn through 20,000 ft. and 12,000 ft. (sam- ple, Range 1) intersects the Applied Pressure axis at 2.75 lbs/in2. Ans. 2) A pressure of 8" of water is applied to the mask of an individual flying at 44,000 feet. What is the effective pressure altitude inside the mask?—A straight line drawn through 44,000 feet and 8" of water (sample on Range #2) intersects the Effective Altitude axis at 41,500 feet. Ans. Limitations: It should be emphasized that the nomogram is based solely on physical data and that the “effective pressure altitudes’’ obtained from it do not necessarily correspond with “physiologically equivalent alti- tudes.’’ This limitation is especially important in connection with pressure breathing where the application of pressure in the mask may produce physiological changes in addition to those brought about by the change of “effective pressure altitude.” Source: N. A. C. A. Report #538 J. R. P. RESTRICTED APPLIED PRESSURE DIFFERENTIAL POSITIVE PRESSURES REQUIRED TO ATTAIN STATED EFFECTIVE ALTITUDES APPLIED PRESSURE DIFFERENTIAL RESTRICTED December 1943 Properties of Oxygen Table P-4 I. Specific Weight (density) of gaseous oxygen subjected to standard gravity at one atmosphere pressure. Temperature °C grams/liter Ibs./cu. ft. Ibs./cu. inch x 104 —40 1.674 .1045 .604 —30 1.605 .1002 •579 —20 1.542 .0962 •557 —10 1.484 .0926 •536 *0 1.429 .0892 .516 10 1-378 .0861 .498 20 1-331 .0832 .481 30 1.287 .0804 •465 40 1.246 .0778 •450 * values at 0 degrees from Int. Crit. Tables; other values computed. Table A II. Weight of Oxygen in supply cylinders at pressures greater than one atmosphere. W = Pxdx V/K where P — gage pressure of cylinder in atmospheres. W = weight of oxygen in lbs. d = specific weight of oxygen at one atmosphere and at temperature at which P is meas- ured (Table A, above). V = volume of cylinder in cubic inches. K = compressibility factor given in Table B below. Table B Pressure K Ibs./sq. inch atmospheres o°C. 20° C. 450 30.6 ■973 .981 900 61.3 .946 .962 1800 122.5 .915 (approx.) .938 (approx.) III. Weight in Ibs./hr. of an oxygen flow of one liter per minute at o°C. and at ambient pressure. Altitude (thousands of ft.) o 10 20 25 30 35 40 Oxygen, Ibs./hr. .189 .130 .086 .070 .056 .044 .035 IV. Oxygen from Tank Supply required to produce stated fractions (Fo2) of oxygen in air-oxygen mixtures. Fraction of oxygen from tank = (Fo2 — .21)7.79 Fraction of oxygen in mixture .21 .30 .40 .50 .60 .70 .80 .90 1.00 Fraction of total volume drawn from tank o2 supply o .11 .24 .37 .49 .62 .75 .87 1.00 V. Miscellaneous Properties of Liquid and Solid Oxygen Melting point —2i8.4°C. Boiling point at 760 mm. Hg = —i83°C. at 493 mm, Hg = —i87°C. at 162 mm. Hg = —195.5°C. Specific Weight at —i83°C. = 1.14 g/cc. = 71.2 Ib./cu. ft. = .0412 Ib./cu. inch. One liter of liquid oxygen weighs 1140 grams or 2.52 lbs. It is equivalent to 797 liters of gaseous oxygen measured at o°C, at a pressure of 1 atmosphere. One pound of liquid oxygen yields 317 liters of gaseous oxygen at o°C, 1 atmosphere. Heat of Vaporization at —183° C. — 50.9 cal./gram, at —i88°C. = 52.0 cal./gram. Specific Heat liquid oxygen at —200°C. = 0.394 cal./gram solid oxygen at —222°C. = 0.336 cal./gram Surface Tension at —i83°C. = 13.2 dynes/cm. W. G. B. RESTRICTED SECTION A Composition of Respiratory Gases CALCULATIONS RELATING TO THE COMPOSITION OF RESPIRATORY GASES ESSAY A Calculations Relating to the Composition of Respiratory Gases Purpose: To present detailed derivation of equations used to construct Charts A-2, A-3, A-4, A-5 and M-2. Knowledge of the contents of this essay is not essential to the practical application of the charts. Essay A Page I. Definition of Symbols I II. Introduction I III. Derivation of Basic Equation 2 IV. Special Applications of Basic Equation 3 1) To Calculate R. Q. from Expired Gas 2) To Calculate R. Q. from Alveolar Gas 3) To Calculate Alveolar po2 from Composition of Inspired Gas 4) To Calculate Fo2 required to maintain constant p02 5) To Calculate Altitude-equivalents V. Approximate Calculations for Regulator Design 4 VI. Non-steady State of Respiratory Exchange 5 VII. Summary of Equations 6 I. Definition of Symbols PB = barometric pressure Px = pressure of gas X in inspired gas P'x = pressure of gas X in expired gas pX = pressure of gas X in alveolar gas R. Q. = metabolic respiratory quotient Ex = fraction of gas X in dry inspired gas Fsl = fraction of oxygen in inspired gas required to maintain Po2 in any portion of in lung gases equal 02 • • • • • I to that at sea level when breathing air. Similar designation for 5000 feet would be Jh 02 * — specific for quantities associated with breathing air. II. Introduction In principle it is obvious that the composition of exhaled gas can be calculated in terms of the composi- tion of inhaled gas and any additions or subtractions of molecules by the body. It is the object of this essay to develop equations relating the composition of dry inspired gas containing oxygen and nitrogen to the com- position of any portion of this gas after it has been saturated with water vapor and has exchanged oxygen for carbon dioxide in the body. The derived equations are employed to construct Charts A-2, A~3, A-4, A-5 and M-2. A simplified form of the general equation which considers only the effect of water vapor on the com- position of inspired gas is employed to calculate the oxygen content of inspired gas that supply systems should deliver at altitude (Table P-2). In the following derivations several terms are frequently used which require special definition. 1) Steady state of respiratory exchange.f The steady state of exchange is such that following each inspi- ration there is expired a volume of gas which leaves the volume and composition of gas remaining in the lungs and trachea identical with that at the end of the preceding expiration. In practice this condition rarely applies to successive respiratory cycles, but is characteristic of the volume and composition of the respiratory gases when these are averaged over reasonable intervals of time under constant physiological conditions. 2) The Respiratory Quotient, R. Q. The metabolic processes of the body are such that in a steady state of respiratory exchange the number of molecules of C02 given off by the blood is less than the number of molecules of 02 absorbed per unit time and the ratio of these two quantities is known as the metabolic respira- tory quotient. The value of this ratio is ordinarily calculated from the measured difference between the com- position of dry inspired air and gas which has been expired during a steady state period of respiratory ex- change. When a particular portion of gas exhaled during part of a single expiration is analyzed, the ratio of C02 added to oxygen removed is not necessarily equal to the average metabolic R. Q, The value of this ratio for alveolar air samples calculated from the average data of Chart A-i by equation 8 is about 0.85. This is comparable with the nominal value of 0.82 for the average metabolic R. Q. Therefore, in the calculations relating to the composition of alveolar air samples collected as described in Chart A-i the metabolic R. Q. may be employed. f In Section VI the non-steady state of respiratory exchange is discussed. Contents 3) Alveolar Gas. In the following derivation the term alveolar gas is employed to designate a sample of expired gas obtained as described in the legend of Chart A-i. No attempt is made to define the relations between the partial pressures of gases in such a sample and the partial pressures of gases in the arterial blood because this subject is unsettled at present and is being reinvestigated. It is important to recognize, however, that estimations of equivalent altitudes based on equivalence of alveolar gas composition agree closely with similar estimations made on the basis of equivalent arterial oxygen saturations as determined experimentally (Charts A-2, B-4). III. Derivation f If the inspired gas contains only oxygen and nitrogen,ft then by definition— M'co2 1) R. Q. = Mo2 —M'o2 Where: M'co2 = number of C02 molecules exhaled per breath. M'o2 = number of 02 molecules exhaled per breath. Mo2 = number of 02 molecules inhaled per breath. The only limitation of this definition of the metabolic R. O. is that a steady state of respiratory exchange is assumed. The number of carbon dioxide molecules in the expired air can be expressed in terms of their partial pressure and the volume of expired gas V'. A similar law holds for the oxygen content of inspired and ex- pired gas. The volumes of gas (V and V') considered, are not identical even when dry because the amount of C02 added is not equal to amount of 02 taken away. Thus— P'co2 M'co2 = X V' RT P'o2 2) M'o2 = X V' RT Pn2 M'n2 = X V' RT Po2 Mo2 = X V RT Pn2 Mn2 = X V RT Since nitrogen is an inert gas the number of molecules exhaled equals the number inhaled. Mn2 = M'n2 Therefore— P'n2 Vn2 3) Pn2 V'n2 The relations (2) and (3) can be substituted in equation 1 to give equation (4). 4) P'co2 R. Q. = P'n2 Po2 P'o2 Pn2 The various equations to be derived in the several forms in which they have actually been employed are special cases of equation (4). t This derivation contains the essential features of similar derivations by A. C. Burton, Toronto, Canada, D. B. Dill, War Department Report #Exp-M-6S3-i03A, W. A. Wildhack, J. Aeronautical Sc., Vol. 9, 1942, J. S. Gray, Report #131, School of Aviation Medicine, Randolph Field, and Major J. Berkson, Office of The Air Surgeon, Washington, D. C. ft The presence of 0.04 percent CO2 in the inspired gas will not change the values calculated from these equations to an important degree. Equations including inspired CO2 will be given in a separate section. If it is desired to estimate R. Q. to three figures the .04 percent CO2 in air must be employed. IV. Special Applications 1. To calculate R. Q. from Analysis of Expired Gas. Divide each member of the right side of equation (4) by the barometric pressure (PB) and introduce the definition, Px Fx = PB The equation becomes— F'co2 5) R. Q. F'n2 Fo2 F'o2 Fn2 This is the form usually employed to calculate R. Q. from analysis of expired gas. 2. To calculate the R. Q. from analysis of alveolar gas. The results of alveolar gas analysis are usually presented in terms of the partial pressures of oxygen and of C02 so the equation is employed in form (4). Here the symbols refer to that portion of expired gas which is defined as alveolar gas. Since the partial pressures of nitrogen are always obtained by subtraction from the barometric pressure, it is convenient to introduce this change explicitly. Thus for dry inspired gas— Pn2 = PB — P°2 and for the moist alveolar gases containing oxygen and carbon dioxide— pN2 = PB — pC02 — p02 — pH2Q The nitrogen pressures differ since the inspired dry gas is saturated at 37° within the lungs as well as being affected by exchanged C02 and 02. The quantity pH20 is assumed to be 47 mm. Hg, for alveolar gas at body temperature. Making these substitutions (PB — P°2) pC02 6) R.Q. = Po2 (PB — 47 — pC02) — PBpQ2 The composition of inspired gas is usually given as the fraction of oxygen in the dry gas. Thus substituting the definition Po2 Fo2 = PB equation (6) becomes (1 — Fo2) pC02 7) R.Q. = Fo2(Pb — pH2Q — PC02) — p02 If the inspired gas is air, this equation becomes: 0.791 pco2 8) R.Q. = 0.209 (PB 47 — pC02) — po2 The calculation of the R. Q. from analysis of alveolar gas is done by substitution in equation (8). 3 .To Calculate Alveolar Oxygen Tensions From Knowledge of the Composition of Inspired Gas. i_Fo2(i-R.Q.) 9) p02 = Fo2 (Pb — 47) — pC02 R. Q. 4 .To Calculate the Oxygen Composition of Inspired Dry Gas Required to Maintain Constant Alveolar pO% at Altitude. pCC2 p02 H R.Q. 10) Fo2 = pC02 PB — 47 — Pco2 -| R.Q. The use of this equation is illustrated in Section V and in Chart A~4. 5. To Calculate Altitudes Breathing Gas Mixtures Physiologically Equivalent to Altitudes Breathing Air. Another use (see Chart A-2) is to calculate altitudes when breathing a gas mixture that are physiologically equivalent to various altitudes when breathing air. Equivalent altitudes are defined by n) a) pC>2 = pO*2 b) PC02 = pCO*2 For this purpose the quantities associated with air breathing may be marked with an asterisk: Thus— i — 0.209 (1 — R. Q.) 12) pO*2 + pCO*2 = 0.209 (P*B — 47) R. Q. For other gas mixtures 1 —Fo2 (i —R. Q.) 13) po2 + pco2 = f°2 (pb — 47) R. Q. Using relation (a) equations 12 and may be combined, thus 1 Fo2 (i —R. Q.) 14) Fo2 (Pb — 47) —pC02 = R.Q. 1 —0.209(1 — R. Q.) 0.209 (P*B — 47) — pCO*2 R.Q. From relation (b) 0.209 (Fo2—0.209) (Fo2— 0.209) (1 — RQ) 15) PB = P*B H 47 — pCO*2 X Fo2 Fo2 Fo2 R. Q. The equation (4) is therefore of great usefulness in analyzing relations between composition of alveolar gas and that of the inspired gas at any altitude. But the same equation is equally applicable to calculation based upon analyses of total expired gas. In brief, when employing the equation to calculate alveolar pC>2 we need to know the alveolar pCC>2 or vice versa. This is the sole unique connection between symbols in the equation and the alveolar gas composition. Correspondingly when the value of P'c02 in expired gas is used the value of P'o2 in expired gas is calculated. V. Approximate Calculations for Regulator Design The equation (10) can be simplified for the purpose of specifying the composition of gas to be supplied by an oxygen supply system. These simplifications are desirable for two principal reasons. First, the variation in alveolar p02 and pCC>2 observed in the population is considerable, making necessary the use of statistical values for these quantities. Second, oxygen supply systems (unlike the mask) are not designed for the individual but must be constructed with a sufficient factor of safety to fit the population. At sea level the respiration is adjusted to maintain an approximately constant alveolar carbon dioxide pressure. Though experiments show this value to vary from 35-45 mm. Hg in the population, by far the largest number have a value close to 40 mm. Hg. Experiment also shows that the metabolic R. Q. calculated from (8) is about 0.85 for the analyses reported in Chart A-i. These two nominal values substituted into equation (9) give a corresponding average pC>2 of 104 mm. Hg. Therefore, to maintain the alveolar oxygen pressure equal to that at sea level the fraction of oxygen in inspired air is given by _ 151 16) FSl2 PB—40 Evaluation of available data on alveolar CO2 analyses (see Chart A-2) indicates that a man breathing air at 5000 feet altitude will have, on the average, an alveolar pCC>2 of 38 mm. Hg. Using this value in equation (9) indicates a corresponding pC>2 of 79 mm. of Hg. To maintain this oxygen pressure in the alveoli at higher altitudes the fraction of oxygen in the inspired gas is 124 17) FoT -—— pB—40 At an altitude of 10,000 feet breathing air the experimental average pCC>2 is 35 mm. Hg. For this con- dition the alveolar pC>2 is 59 mm. Hg. To maintain these conditions at altitude 101 T o N TTUOOOO r«) to2 — PB—41 The numerical values appearing in Equations 16, 17 and 18 depend upon average values of R. Q. and pC02 determined experimentally on a large number of individuals (Chart A-i). The equations therefore represent approximations based on the best data available at the present time, but they are subject to such revision as may be indicated by further data. Another form of approximation leads to a practical standard suggested by Dr. W. M. Boothby. If the R. Q. is assumed to be 1.0, then equation (14) becomes 19) Fo2 (Pb — 47) = -209 (PB* — 47) The quantity on the right side of this equation is the oxygen tension Po2 in saturated inspired gas when breathing air. Thus Po2 — 0.2094 (PB* — 47) Therefore, according to these assumptions, the Fo2 values calculated from (19) depend only upon physical quantities and the oxygen required at altitude is defined in terms of the Po2 in inspired gas saturated with water vapor at 37 °C. From (19) we have— 149.3 20) Fo2 = -209 (760 — 47)/Pb — 47 = Pb-47 122.6 TT'5000 21) too =- PB —47 99.6 rr =—— Pb-47 The numerical relations between the two methods of approximation are shown in Chart A~3. The differences are not sufficiently large to be of practical importance in present-day regulator design although they may be of importance in the interpretation of research work involving equivalent altitudes (Chart A-2). Fo2 values based on equations 20, 21 and 22 are given in Table P-2. A summary of the approximate equations is given in § VII. VI. The Non-Steady State of Respiratory Exchange In developing the equations in Section II it was stressed that the results applied only to steady states of respiratory exchange. This restriction is necessary in order to permit a definite interpretation of the quantity R. Q. introduced in equation 1, page 2. In the steady state this quantity may be identified with the metabolic respiratory quotient, but in the non-steady state it is merely the ratio of the quantity of carbon dioxide in ex- pired air to the difference in oxygen content of expired and inspired air. During a non-steady state of respiratory exchange, when the pC02 and p02 are changing with time, this ratio may be designated simply as R to distinguish it from the true R. Q. With this change in interpretation the derivation can be made as before. However, the relations between pC02 and p02 are now between instantaneous value? of quantities which are continuously changing as the respiratory exchange passes from one steady state to another. The limited data available indicate that the transient change from one steady state of respiratory exchange to another takes approximately 45 minutes. During this time the value of R rises rapidly to a maximum and falls again to its original value, as indicated in Table I, Changes in Alveolar Tension During One Hour Stay at 18,000 Feet (Lutz & Schneider) (Amer. J. Physiol. 50, 280, 1919) Minutes at 18,000 ft. po2 Pco2 Calculated R 0 38-5 30.8 0.98 10 36.5 304 0.88 20 35-2 3i-5 0.89 30 35-o 31.0 0.86 40 33-9 30-3 0.81 50 344 29.1 0.78 60 35-i 29.0 0.80 In research on respiratory problems these transient phenomena are of utmost importance because many experiments have been carried out in too short a time to achieve steady state conditions. The calculation of R, by equation (7) offers a convenient criterion for stating that a set of data apply to steady states of respiratory exchange. The data from the control period of the experiment provide a reference value of R. The subject will be in a new steady state following some change when R again approaches this control value. Thus in the experiment illustrated in Table I, R has returned to the control level of .80 in about 40 minutes. In this instance the analyses were made on alveolar air. As a general control measure of this sort the values of R calcu- a lated from a series of expired air samples would serve the same purpose in experiments not specifically con- cerned with collecting alveolar gas samples. The deviations from normal respiration expected in aviation are hyperventilation from excitement or mild anoxia. This raises the pC>2 in the alveolar gas by lowering the pCC>2. Therefore, if the composition of inspired gas has been set at a value which insures an adequate alveolar pC>2 at a given altitude during normal respiration the change during transient hyperventilation will be to increase this pC>2. Thus far only short-time transient changes have been considered since these are probably most important in aviation. If mild anoxia lasted a week or more, the degree of hyperventilation would increase very grad- ually. This prolonged adjustment to altitude, called acclimatization, is associated with rather insignificant changes in composition of alveolar gas relative to those accomplished during the first hour of exposure. VII. Summary of Equations General Equations (Definition of Symbols on Page 1) 1 — F02 (1 — R. Q.) ' Reference in essay A) p02 = Fo2 (Pb — 47) — pC02 R. Q. Eq. 9, p. 3 pC02 p02 H R.Q. B) Fo2 = Eq. 10, p. 3 PB — 47 + PCO2/ 1 — R. Q. \ \ R- Q. / .209 / 1 — R. Q.\/Fo2 — .209\ C) PB = PB* — 47 — pCC2* I )( ) + 47 Eq. 15, p. 4 Fo2 |_ \ R. Q. A .209 / Approximate Equations By “Maximum error” in the following table is meant the largest discrepancy between the results of direct substitution in the approximate equations and values obtained from Equations A), B) and C), where R. Q. is taken = 0.85, and the pCC>2 values of Chart A-2 are used. The “maximum errors” refer to altitudes breathing air (denoted by asterisk) up to 20,000 feet. These errors may be exceeded at higher altitudes. Quantity Simple graphical solution with best fit Maxi- mum error Equations based on physical standard: equal oxygen pressures in inspired gas, 37°C, saturated Maxi- mum error Fraction of oxygen in inspired air to maintain stated equivalent altitude D) 150 Jr ©2 Pb~40 E) FoT = 125 PB —40 IOO F>Fr= pB—40 .01 .01 .01 149 K) F°s = P 47 — 47 123 T v T75000 _ 0 ro2 ~~ „ Pb 47 IOO M) FiT = PB —47 •05 •05 •05 Alveolar oxygen pressure, breathing air (mm. Hg) G) p02* = .185 PB — 37 2 mm. Barometric pressure breathing oxygen equivalent to given barometric pressure breathing air (mm. Hg) H) PB = .206 PB* + 34 1 mm. N) PB =: .209 (PB*—47) + 47 = 209 PB* + 37 5 mm. Altitude breathing oxygen equivalent to given alti- tude breathing air (in feet) J) Alt = 33,700 -f- .6 Alt* 200 feet O) Alt = 33,000 + .6 Alt* 800 \ feet F. B., Jr. October, 1943 Alveolar Oxygen and Carbon-Dioxide Pressures While Breathing Air at Altitude Chart A-1 The data in this chart were obtained by analyses of the fractions of C02 and 02 in alveolar air samples collected over mercury by the Haldane-Priestley method of sampling aided by a specially constructed valve. In the average values indicated by an open circle there are 1025 observations at various elevations, 836 of which were obtained on 30 male and 189 on 5 female subjects. In addition 288 observations have been put on the chart which were obtained by various other methods of obtaining alveolar air samples, both at rest and at work. These are indicated on the chart by separate signs. The alveolar air samples were obtained as a rule in the forenoon after a normal breakfast and less frequently in the afternoon after an average lunch. On an average flight alveolar samples were obtained usually on the way up at six or seven different eleva- tions although occasionally they were obtained on the way down after a rapid ascent. The runs lasted there- fore about three to three and a half hours. Before the first alveolar air sample was taken ten minutes were allowed to elapse after arrival at each elevation for the subject to become partially stabilized to that altitude. A second alveolar air sample at each altitude was taken after another five minutes. The subjects were at sitting rest and care was taken that they remain quiet without talking during the preliminary and alveolar air sampling periods. Curve A Curve A is a smoothed curve drawn to represent the average experimental alveolar oxygen pressure (Ap02) at different altitudes shown by a large O circle for averages containing 45 or more and by a small 0 circle for averages of a smaller number of observations. Curve C Curve C is also a smoothed curve drawn to represent the average experimental alveolar C02 pressures (ApC02) shown similarly by large and small circles. Curve E Curve E is likewise a similar smoothed curve drawn to represent the corresponding average experimental alveolar pressure ratio (APR). Curves B, D and F Curves B, D and F are straight lines drawn in to indicate what the hypothetical p02, pC02 and APR values would be if the body in no way compensated for the anoxia produced by a slowly increasing altitude. These curves are valuable as indicating the degree of oxygen deficiency that must be compensated for by addition of oxygen. The curves and the individual experimental points are algebraically related as follows: AfCOs (Pb-47) ApC02 APR = or APR = and If02 (Pb-47) - AfQ2 (Pb-47) Ip02 - ApQ2 AfCQ2 (Pb-47 pC02 ApQ2 — If02 (Pb-47) or ApQ2 = 0.2094 (PB-47) APR APR where PB indicates barometric pressure, p indicates partial pressure of gas, f indicates volumetric fraction of dry gas, A indicates alveolar air, I indicates inspired air, 47 is the vapor pressure water at 370 C., and 0.2094 is the fraction of 02 to be inserted if pure dry air is inspired. The alveolar pressure ratio (APR) is the alveolar C02 pressure divided by the difference between the oxygen pressure in the inspired air (ambient pressure 37°C. Sat.) and the alveolar oxygen pressure. The respiratory quotient (RQ), in the sense of the combustion quotient, is the relation of the volume of C02 given off to the volume of 02 absorbed obtained by analysis of the total expired gas collected over a period of time during which the subject is in a steady state (and calculated by allowing both for any change in volume of the expired air from the inspired air that may have occurred and for the amount of C02 present in the in- spired air). Sometimes the term “respiratory quotient” has been used (either deliberately or unconsciously) to represent what might be called a “ventilation quotient”, that is, the relationship obtained by analysis of total expired gas collected from a subject over a period in which he is in an unsteady state. In the table on the chart, also reproduced in Table I, are the average values for the various altitudes of the 1025 observations by the Haldane-Priestley alveolar air method while at rest. The averages in which more than 45 observations were made are indicated in the plots by the large circle and the averages containing less than 45 observations are indicated by the small circle. The standard deviation was calculated for those aver- ages that contain more than 45 observations. (The pC02 for females is usually 3 or 4 mm. less than the pC02 for males but there is no corresponding significant difference in the p02 for males and females.) RESTRICTED TABLE I Alveolar 02 and C02 Pressures and Alveolar Ratios at Various Altitudes While Breathing Air Subjects Acclimatized to a Ground Altitude of 1,000 Feet Averages: Haldane-Priestley Method at Rest O 45 observations or more 0 37 observations or less Elevation in feet Number of Observations Alveolar C02 Mean Standard mm. Deviation Alveolar 02 Mean Standard mm. Deviation Alveolar Ratio Mean 1,000 Ground 186 36-7 2.7 102.3 5-5 0.889 2,000 8 38.1 95-5 0.892 3,000 45 36.2 2.9 89.2 5-2 0.830 4.000 8 38.5 84.8 0.902 5,000 62 36-5 2.8 81.6 4-5 0.892 6,ooo 54 36.2 3-i 74.2 5-2 0.832 7,000 3 40.0 67.0 0.871 8,ooo 10 37-4 64.8 0.860 9,000 50 35-4 3-2 61.2 5-5 0.829 10,000 92 35-8 2.6 60.9 4.6 0.923 11,000 12 36.8 53-3 0.872 12,000 61 34-8 3-2 507 5-4 0.857 13,000 15 36.5 44.9 0.857 14.000 26 35-4 44.0 0.894 15.000 M5 32-9 2.8 44.2 5-i 0.919 16,000 9 33-8 38.8 0.899 17,000 37 30-7 38.1 0.882 18,000 55 31.8 2.5 37-9 3-8 1.006 19,000 11 29.4 36-5 0.983 20,000 81 29.4 2.6 35-3 4.6 1.054 21,000 5 24.8 30.0 0.818 22,000 45 28.1 2.7 30.2 2.9 1-033 23,000 1 29.0 30.0 1.189 24,000 2 25.0 32.0 1.269 25,000 2 23-5 32.5 1.407 Individual Observations Total number = 1313 Sign Number Method Condition • 1025 Haldane-Priestley Rest * 22 Haldane-Priestley Rest (Work Series) X 65 Haldane-Priestley Work 0 106 Bag-Rebreathing Rest 0 40 Bag-Rebreathing Rest (Work Series) * 55 Bag-Rebreathing Work Chart includes all data obtained between 12-21-39 and 3-18-43. Both the CO2 and 0-2 content of all alveolar air samples were determined volumetrically in calibrated Haldane gas analyzer. W. M. B. RESTRICTED ALVEOLAR 02 and C02 PRESSURES and ALVEOLAR RATIOS at VARIOUS ALTITUDES WHILE BREATHING AIR MAYO AERO MEDICAL UNIT ALTITUDE - THOUSANDS OFFSET SUBJECTS ACCLIMATIZED TO A OROUND ALTITUDE OF 1,000 FEET Averages: HaIdane-Priestly Method at Rest O 45 observations or more O 37 observations or less Alveolar C©2 Alveolar O2 Elevation in feet Number of Observation Mean Standard Deviation Standard Deviation Alveolar Ratio Mean 1,000, Ground 186 36.7 2.7 102.3 5.5 0.889 2,000 8 3«.l 95.5 0.892 3,000 45 36.2 2.9 89.2 5.2 0.830 4,000 8 38.5 84.8 0.902 5,000 62 36.5 2.8 81.6 4.5 0.892 6,000 54 36.2 3. 1 74.2 5.2 0.832 7,000 3 40.0 67.0 0.871 8,000 10 37.4 64.8 0.860 9,000 50 35.4 3.2 61.2 5.5 0.829 10,000 92 35.8 2.6 60.9 4.6 0.923 11,000 12 36.8 53.3 0.872 12,000 61 34.8 3.2 50.7 5.4 0.-857 13,000 15 36.5 44.9 0.857 14,000 26 35.4 44.0 0.894 15,000 145 32.9 2.8 44.2 5.1 0.919 16,000 9 33.8 38.8 0.899 17,000 37 30.7 38.1 0.882 18,000 55 31.8 2.5 37.9 3.8 1.006 19,000 11 29,4 36.5 0.983 20,000 81 29.4 2.6 35.3 4.6 1.054 21,000 5 24.8 30.0 0.818 22,000 45 28.1 2.7 30.2 2.9 1.033 23,000 I 29.0 30.0 1.189 24,000 2 25.0 32.0 1.269 25,000 2 2 3.5 32.5 1.407 INDIVIDUAL OBSERVATIONS Sign Number Method Condition • 1025 Haldane-Priaatly Reat t 22 Hnldnna—Prloatly Reat (Work Seriea) X 65 Bnldnne-Priaatly Work O 106 Bng-Rebrenthintf' Reat 0 40 Bn£-R«brenthin£ Reat (Work Sorlea) * 55 Bng-Rabranthing Work ALVEOLAR Og PRESSURE mm. Both the C02 and 02 content of all alveolar air .ample* were determined t. ■ netrloally In calibrated Haldane ffa. analyser. DESCRIPTION OF CURVES CURVE A - EXPERIMENTAL ALVEOLAR 02 PRESSURE (Ap02) CURVE C - EXPERIMENTAL ALVEOLAR C02 PRESSURE (ApC02) CURVE E - EXPERIMENTAL ALVEOLAR PRESSURE RATIO (APR) A. C and E are .moothed curve, representing the experimental^data. APR m AfC02 (B-47) or AJ)R _ XpC02 If02 (B-47) - Af02 (B-47) Ip02 - Ap02 AfC02 (B-47) , pC02 Ap02 - If02 (B—47J or Ap02 - 0.2094 (B-47) - alveolar air, I Indicate, in.plred air, 47 i. the vapor prenure water at 37® C., and 0.2094 i. the fraction of 02 in pure dry in.plred air. CURVE B - THEORETICAL ALVEOLAR 02 PRESSURE. It 1. assumed that there i. no compensation by the body to the anoxia resulting from the decrease in partial pressure of oxygen in Inspired air at increasing altitudes. CURVE D - THEORETICAL ALVEOLAR C02 PRESSURES. (No compensation for anoxia.) CURVE P - THEORETICAL ALVEOLAR RATIO. (Ho compensation for anoxia.) ALVEOLAR C02 PRESSURE mm ALVEOLAR PRESSURE RATIO EQUIVALENT ALTITUDES BREATHING GAS MIXTURES CHART A-2 RESTRICTED November, 1943 Equivalent Altitudes Breathing Gas Mixtures Chart A-2 This chart shows the relation between physiologically equivalent altitudes for persons breathing gas mix- tures containing various concentrations of oxygen. Equivalent altitudes are defined in terms of identity of alveolar gas composition. Thus altitude A breathing gas mixture X is equivalent to altitude B breathing gas mixture Y when the composition of alveolar gas is identical in the two cases. Equivalent altitudes calculated in this way would be expected to correspond with equivalent altitudes defined in terms of equal arterial oxygen saturations. Comparison of Chart A-2 with Chart B-4 shows that this is indeed the case. Construction of Chart: Each curve on the chart was constructed by calculating for a given gas mixture the altitudes physiologi- cally equivalent to various altitudes breathing air. The equation defining this relation is given in Section IV (Equation 15) of the Essay on the Composition of Respiratory Gases. It may be written in the form .209 ( (1— R. Q.) (Fo2 — .209) j PB — ] Pr* — 47 —pC02* X [ ~h 47 Fo2 ( R. Q. .209 \ where the quantities marked with an asterisk denote values breathing air. 1. The Value of R. Q.—The value of R. Q. used for the calculation was 0.85. 2. The Value of Alveolar pCO2—To make the calculations it is necessary to adopt a nominal value for alveolar pCC>2 at each altitude while breathing air. The exact value chosen is not critical owing to the fact that we are equating two altitudes under conditions in which the alveolar carbon dioxide pressures are by defi- nition the same. The actual values used are shown in Table I below; they were obtained from the smoothed data of Boothby (Chart A-i) and of Lutz & Schneider. TABLE I Altitude (Thousand feet) o 5 10 12 14 16 18 20 22 24 Alveolar pC02 mm. Hg 40 38 36 35 34 33 32 30 28 25 The small effect of large variations of CO2 on the calculation of equivalent altitudes is illustrated in the following example: What altitude breathing 100% oxygen is equivalent to breathing air at 16000 ft. (PB = 412 mm. Hg) ? a) Let pCC>2* on air = 33 mm. as assumed for chart. .209 ( (1 — .85) (1.0 — .209) 1 PB = ' 412 — 47 — 33 > + 47 = 117 mm. Hg or 43870 feet 1.0 / .85 .209 ) b) Let pCC>2* on air = 28 mm. i (1 — .85) (1.0 — .209) ) PB = .209 < 412 — 47 —28 > -f 47 = 118 mm. Hg or 43690 ft. ( .85 .209 ) Thus a change of 5 mm. pCC>2 produces a change of only 180 feet in the calculated equivalent altitude. Limitations. The values shown in Chart A-2 are valid only under the defined conditions of equality of alveolar gas composition. If, as a result of fear, pain or other factors, an individual hyperventilates in such a way that the alveolar pCC>2 varies independently of the alveolar PO2, then the values shown in the Chart do not apply. Sources: 1) Boothby, W. M. Chart A-i 2) Lutz and Schneider, Am. J. Physiol. 50, 280, (1919) J. R. P. and F. B., Jr. RESTRICTED Thousands of feet ALTITUDE BREATHING GAS MIXTURES EQUIVALENT ALTITUDES thousands of feet EQUIVALENT ATTITUDE BREATHING AIR COMPARISON OF STANDARDS FOR CALCULATING OXYGEN REQUIREMENTS (5000 FT. EQUIVALENT) CHART A-3 RESTRICTED Comparison of Standards for Calculating Oxygen Requirements (5000 ft. Equivalent) Chart A-3 Purpose of Chart: To compare the results of two methods commonly employed to specify the fractions of oxygen in dry inspired gas at altitude which are required to simulate a given altitude breathing air. Explanation: Curve I is based on the equivalence of Po2 in inspired air saturated with water vapor at 370 C. It is defined by the approximation formula given in Essay A, Section V, Equation 21 122.6 •*•02 Pb - 47 Curve II is based on the equivalence of p02 and pC02 in alveolar air. It 4s defined by the approxima- tion formula given in Essay A, Section V, Equation 19 Fsooo I24 o2 — PB — 40 The maximum difference between the two methods of specifying oxygen requirements at altitude is less than 5%. This difference is considerably less than variations in composition of gas delivered by present- day dilutor-demand regulators. Lirnitatiofis: Curve I is based on physical standards which are unaffected by physiological variables. It specifies a slightly greater fraction of oxygen at each altitude than does Curve II which is based on equiva- lence involving physiological variables as discussed above. Curve I is suitable for defining specifications for oxygen equipment; it is the basis of the Fo2 values presented in Table P-2. The method of calculation em- ployed in constructing Curve II should be considered in connection with quantitative physiological research work at altitude. F. B., Jr. RESTRICTED COMPARISON OF STANDARDS FOR CALCULATING OXYGEN REQUIREMENTS (5,000 ft. equivalent) REQUIRED PERCENT OXYGEN IN INSPIRED GAS ALTITUDE (Thousands of feet) THE COMPOSITION OF INSPIRED GAS REQUIRED TO MAINTAIN A CONSTANT ALVEOLAR p02 CHART A-4 RESTRICTED August, 1943 The Composition of Inspired Gas Required to Maintain a Constant Alveolar pC>2 Chart A-4 Use of Chart: Determination of oxygen requirements at altitude. In order to calculate the fraction of oxygen in inspired air required to maintain a constant alveolar gas tension at altitude it is necessary to know the metabolic R. Q. and the alveolar pCCV The equation is P©2 pC©2 Fo2 = pco2 PB — 47 — PC02 H R. Q. (Equation 10, p. 5, Essay A) 1. The Value of Alveolar Pressure of Carbon Dioxide. In the absence of anoxia, respiration is adjusted to maintain a relatively constant CO2 pressure in the lung gases and arterial blood. The nominal value of this pressure for healthy young men is 40 mm. of Hg. One recent set of data obtained by alveolar gas analysis on 16 young men gave an average PCO2 of 40.5 mm. of Hg. Another set obtained in another laboratory by arterial blood analysis gave 39.6 mm. of Hg. Exam- ination of these data indicates that all the PCO2 values for these subjects were between 35 and 45 mm. of Hg. These values, therefore, were used as the limits to employ in estimating the changes in composition of inspired gas required to maintain a constant alveolar oxygen tension when the barometric pressure is changed. The shaded areas in the chart represent the spread in Fo2 values due to this range of alveolar carbon dioxide pres- sures found in tested subjects. These values are assumed to apply except when the respiration is altered by anoxic drive. This does not occur significantly in young men in the range of alveolar oxygen tensions covered in this chart. 2. The Value of R. Q. In the steady state of respiratory exchange the R. Q. in equation (10) is the metabolic respiratory quotient (R. Q.). All values are therefore confined between 0.7 and 1.0. For most people during most of the day this value is 0.82. The effect of R. Q. on the calculation of F02 is small enough to be neglected in specifications for oxygen regulators since inspired gas mixtures provided by aviation oxygen equipment are not adjusted to better than 0.01. The values of F02 given in Chart A-4 may therefore be assumed applicable for all values of R. Q. between 0.8 and 1.0. There are two important conditions which may cause a prolonged deviation from a steady state: first, hyperventilation due to anoxia and, second, that due to excitement. With adequate oxygen equipment most flying can be done without anoxia. Thus deviations from the above predictions will affect only the small number of men who must go to extreme altitudes for short times. A prolonged condition of anoxia, over 40 minutes, will lead to a new steady state of respiratory exchange and the above equations are again valid. Although the pCC>2 will now be lower than usual this merely means that the pC>2 is higher, i. e. the deviation from prediction is in a safe direction. The same conclusion applies to hyperventilation due to emotional stimuli. The expected deviations from predicted steady state conditions, therefore, are not in a dangerous direction insofar as alveolar oxygen pressure is concerned. The scale on the right hand side of Chart A-4 was calculated as in Table P-4, Section IV. From the respiratory minute volume it is possible to estimate, using this scale, the fraction of oxygen taken from the supply per minute at any altitude when the regulator is designed to maintain one of the indicated alveolar oxygen tensions. Thus problems of economy and of design requirements for oxygen regulators can be solved by using this chart. F. B., Jr. RESTRICTED OXYGEN REQUIRED TO MAINTAIN STATED ALVEOLAR OXYGEN PRESSURES AT ALTITUDE CALCULATED % OXYGEN IN INSPIRED GAS (dry) FRACTION OF INSPIRED GAS (dry) DRAWN FROM OXYGEN -ALTITUDE - thousands o£ Feet Barometric Pressure, mm.Hq OXYGEN-NITROGEN MIXTURES REQUIRED TO SIMULATE ALTITUDES CHART A-5 RESTRICTED November, 1943 Oxygen-Nitrogen Mixtures Required to Simulate Altitudes Chart A-5 Use of Chart: Experiments in which altitudes are to be simulated by breathing oxygen-nitrogen mixtures at sea-level. Explanation: The curve is calculated from Equation 15, Section IV in Essay A .209 (Fo2 — .209) (Fo2 — .209) (1 — RQ) Pb — Pb* H X 47 — pC02 — Fo2 Fo2 Fo2 RQ At sea-level, PB — 760 mm. Hg. Let R. Q. = 0.85. Substituting these values in (15) and solving for Fo2 we have— •209 (PB* — 47 + -i77 PC02) Fo2 = (713 + .177 pco2) The pC02 corresponding to each PB* is defined in Table I, Chart A-2. However, the values of R. Q. and pC02 chosen for the calculation are not critical. Within the range of equivalent altitudes shown in the chart the Fo2 values do not differ by more than 0.1% 02 from similar values calculated on the basis of equal Po2 in inspired air saturated at 370 C. (cf. also Chart A-3). Limitations: It should be emphasized that the chart applies only to steady state conditions. Evidence ob- tained from the rate of fall of arterial oxygen saturation while breathing gas mixtures indicates that 5-15 min- utes are required to bring the oxygen saturation to a steady level (cf. also Essay A, Section VI “Non-Steady State”). F. B., Jr. and J. R. P. RESTRICTED GR3 MIXTURES REQUIRED TO SIMULATE ALTITUDES EQUIVALENT ALTITUDE BREATHING AIR (Thousands oFEeet.) SECTION R Respiratory and Metabolic Data COMPONENTS OF RESPIRATORY MINUTE VOLUME CHART R-l RESTRICTED November, 1943 Components of Respiratory Minute Volume Chart R-i Use of Chart: 1) Definition of components of respiratory minute volume. 2) Calculation of consumption of dry gas at O0 C., 760 mm. Hg corresponding to any given respiratory minute volume. 3) Calculation of respiratory minute volume from measurement of consumption of dry gas at O0 C, 760 mm. Hg. Explanation: The respiratory minute volume is defined as the sum of the increases (or decreases’}-) of lung volume which take place in one minute by successive inspiratory (or expiratoryf) movements. It is equal to the volume of inspired (or expired-}-) air measured at body temperature, 370 C., ambient pressure and saturated with water vapor (abbreviated throughout these charts as BTPS). At sea-level the corrections for water vapor and tem- perature are relatively small and are frequently omitted in presenting respiratory data. At altitude, however, the water vapor and temperature corrections become increasingly important and large errors are introduced if the respiratory minute volume is considered equal to the volume of gas inspired from or collected in a spiro- meter at ambient temperature and pressure. The chart is intended to show the sources from which the dif- ferent components of lung volume increase are derived and the relative fraction of each as a function of alti- tude. The fractions are independent of the absolute value of the respiratory minute volume and apply equally well to the gas components of a single inspiration. Example of Use: Consider an altitude of 32,600 feet (PB — 200 mm. Hg). The chart shows that at this altitude only a small fraction (0.18) of the total respiratory minute volume is derived from dry gas measured at O0 C., 760 mm. Hg. Isothermal expansion of this gas to ambient pressure brings the volume to 0.67 of the total and further isoharic expansion to body temperature increases the value to 0.77 of the total. The remaining fraction (0.23) is contributed by saturation of the dry gas with water vapor in the respiratory passages. Conversely, if the consumption of dry gas (O0 C., 760 mm. Hg) is L liters per minute then at 32,600 feet the respiratory minute volume is L/0.18 liters per minute BTPS. Equations used for calculating chart: PB —47, 273 (PB —47), 273 (PB —47) Upper (heavy) = Middle — X Lower — X curve PB curve 310 PB curve 310 760 t The inspiratory minute volume (BTPS) is not exactly equal to the expiratory minute volume (BTPS) owing to the fact that less CO2 is produced than O2 consumed. This difference may amount to 0.15 liters/min. thereby intro- ducing a discrepancy of 1.5% when the respiratory minute volume is 10 liters/min. H. F. H., Jr. RESTRICTED COMPONENTS OF RESPIRATORY MINUTE VOLUME BAROMETRIC PRESSURE TRACTION OF VOLUME NT B.T.FS. - RESPIRATORY REQUIREMENTS DURING EXERCISE CHART R-2 RESTRICTED November, 1943 Respiratory Requirements During Exercise Chart R-2 Explanation: The data include 224 observations on 123 individuals. No classification according to age, height and weight has been made although the majority of subjects were less than 30 years old. The measurements were made several minutes after the beginning of exercise when “steady state” conditions were attained. Observations at altitude were made under conditions in which no serious anoxia would be expected, but actual data regarding alveolar oxygen pressures or arterial saturations were not obtained. The center line indicates average values and the boundary lines include more than 90% of the observa- tions. Respiratory volumes have been corrected to body temperature and pressure, saturated with water vapor at 370 C. (BTPS) Limitations: The data apply only to conditions in which the respiratory minute volume has been altered as a result of exercise uncomplicated by anoxia, COo accumulation, cold or other factors. There is evidence that an increase of metabolism produced by shivering results in a greater increase of respiratory minute volume than that indicated by the chart for exercise. Sources: 1) Harvard Fatigue Laboratory, Miscellaneous Data 2) Dill, D. B., Manuscript from Wright Field (1942) 3) Dill, D. B., et al. J. Physiol. 7/, 47 (1931) 4) Christensen, E. H. Sk. Arch. f. Physiol. y6, 88 (1937) 5) Taylor, C, Am. J. Physiol. 135, 27 (1941) J. R. P. RESTRICTED RESPIRATORY REQUIREMENTS DURING EXERCISE RESPIRATORY MINUTE VOLUME- B.T.P.S.- METABOLIC OXYGEN CONSUMPTION-Liters/min. 5.T.ED: OXYGEN REQUIREMENT DURING EXERCISE CHART R-3 RESTRICTED November, 1943 Oxygen Requirement During Exercise Chart R-3 Use of Chart: 1) Design of closed oxygen supply systems 2) Efficiency of different types of work Explanation: This chart shows the oxygen requirements associated with three forms of work load—lifting weights, climbing on a treadmill, and pedalling on a bicycle ergometer. Experimental points are shown only for the bicycle ergometer when pedalled at the rate of 70 r. p. m. The experimental scatter about the lines shown on the chart is about the same for the three types of work. The dashed part of the weight lifting curve is extrapolated. The points include observations on 11 individuals and were obtained in three laboratories. The points represent steady state conditions. The slope of each line on the chart is the reciprocal of the efficiency. The efficiency is defined as follows: Work done (calories/min.) Efficiency = Calorimetric equivalent of increase in oxygen consumption (calories/min.) For any given type of work the efficiency varies with the velocity of muscular movement. There is in general an optimum velocity; in the case of the bicycle ergometer this occurs at 70 r. p. m. at which velocity the efficiency averages 22% at all work loads. The efficiency falls to 15% at velocities of 20 r. p. m. or 170 r. p. m. The upper limit of efficiency for muscular work is about 25% and for most forms of exercise is of the order of 15%. It is the opinion of experienced investigators that the subjective sensation of degree of work load depends on the metabolic oxygen consumption rather than on the actual work load. Thus a work load of 500 kg. meters/min. on the bicycle ergometer would be subjectively classified as “moderate” whereas a similar work load lifting weights would be subjectively classified as “hard” or “severe.” Sources: 1) Christensen, E. H., Sk. Arch. f. Physiol. 76, 88 (1937) 2) Dickinson, S., J. Physiol. 67, 242 (1929) 3) Schneider, E. C, Am. J. Physiol. 97, 353 (1931) 4) Taylor, C, Am. J. Physiol. 135, 27 (1941) 5) Harvard Fatigue Laboratory, Miscellaneous data 6) Mayo Aero-Medical Unit, Miscellaneous data J. R. P. RESTRICTED OXYGEN REQUIREMENTS DURING EXERCISE METABOLIC OXYGEN CONSUMPTION Liters 0^/min. (5.T.PD.) Revere work Hard. work Moderate work Light work Rest 2Z00 Kgm. meters /min 8,000 Toot Ubs./772in. WORK LOAD RESPIRATORY RESPONSE TO CARBON DIOXIDE CHART R-4 RESTRICTED August, 1943 Respiratory Response to Carbon Dioxide Chart R-4 The experiments were performed on 23 male college students ranging in age from 18 to 28 years, lying at rest (supine) and breathing through a Siebe-Gorman half mask and egg-shell valves a mixture containing 21% 02 (balance N2) plus o, 1, 2. and 4% C02, all at sea level (Berkeley, Calif.). Each inhalation period lasted long enough for respiratory volume to become stabilized and volume of air expired into delicately balanced spirometers was measured over this period. Assumptions used: Average curve for volume of expired air is extrapolated back to zero from the level reached while breathing 1% C02. Some of the increases produced by this mixture were so small (4%) as to justify the tentative conclusion that 1% C02 is about the weakest concentration in inspired air by which breath- ing is likely to be stimulated significantly under these conditions. The part of the curve between this and the zero point should be evaluated accordingly. Limitations: 1. The results apply only to subjects lying supine at rest, breathing 21% 02 at sea level. High concentra- tions (96-99%) of 02 at sea level will markedly increase the response to each of these percentages of CG2 (Shock & Soley). Corresponding data at higher altitudes are lacking. The effect of position'alone would probably not be great. 2. Subjective discomfort would probably not be produced by C02 until respiratory minute volume is in- creased by at least 50% over the control level (subjects lying supine at rest and at sea level). 3. Other factors such as exercise, anoxia, cold, and excitement would unquestionably increase the respira- tory response to a given C02 concentration in the inspired air, but pertinent data are not available at present. Source of Data: Shock and Soley (Am. J. Physiol. 130, 777, 1940) C. F. S. RESTRICTED RESPIRATORY RESPONSE TO CARBON DIOXIDE AT SEA LEVEL % INCREASE IN RESPIRATORY MINUTE VOLUME ■ Partial Pressure, mm.Kq C0Z IN INSPIRED AIR PEAK INSPIRATORY VELOCITIES DURING EXERCISE AT SEA-LEVEL CHART R-5 March, 1943 Peak Inspiratory Velocities During Exercise at Sea-level Chart R-5 Explanation: (1) Vertical lines indicate boundaries which include the standard deviation about the mean, (2) Solid Circles show the mean values from 27 subjects breathing without inspiratory resistance to flow. Open Circles are mean values from same subjects breathing against a constant inspiratory resistance of 1.20 mm. H20 per liter/min. (3) The term constant resistance refers to a device in which the pressure drop is proportional to the rate of flow. Charcoal canisters having this characteristic were used to provide resistance to inspiration. (4) A resistance of 1.20 mm. H20 per liter per minute (shown in chart) is sufficient to cause discomfort even at low flows (10 Hters/min.). Lesser values of resistance yielded results which are included between the extremes shown in the chart. (5) Respiratory minute volumes given in the chart have been recalculated from the original data to body temperature and pressure, saturated (BTPS), Limitations: (i.) The minute volumes were varied by exercising on a bicycle ergometer at sea-level (cf. Chart Other stimuli to increased respiration (anoxia, cold or COo) may not give comparable results. (2) The results may not be applicable to variable resistances to inspiration. Orifices or complex resistances from demand regulators are examples of this type. More data are needed in this connection. (3) The data may be applied only to sea-level conditions. For the same respiratory minute volume (BTPS) the volume of dry inspired gas is greatly reduced at altitude (Chart #R-i) and the peak velocity may therefore be altered. Source: Harvard Report OSRD No. 1222 J. C. L. PEAK INSPIRATORY VELOCITIES DURING EXERCISE AT SEA LEVEL INSPIRATORY PEAK PLOW RATESI Hers/min. at Zo°-Z5°C.,room humidity, at sea level RESPIRATORY MINUTE VOLUMES Sea Level, B.TP.S. RESISTANCE TO BREATHING CHART R-6 November, 1943 Resistance to Breathing Chart R-6 The data shown on the accompanying chart were obtained by plotting the mask suction pressures against the corresponding peak instantaneous rates of airflow. The instantaneous rates of airflow were determined by recording the instantaneous pressure changes during breathing in oxygen masks modified to hold various cali- brated orifices. The subjects breathed both ways through these orifices, the characteristics of which were such that inspiratory and expiratory pressure fluctuations were approximately equal. The magnitude of the pressure fluctuations for a given air flow velocity was varied by changing the size and number of orifices used. The resistance to breathing was brought about by sudden reduction in orifice area by plugging one or more in the mask. The pressure fluctuations were recorded optically with a segment capsule manometer. The records were taken on eleven subjects seated quietly, and immediately after light, moderate and heavy exercise. Light exercise consisted of sitting down and standing up once every 5 seconds for three minutes. Moderate exercise consisted of jog trotting 100 yds. Heavy exercise was a 100 yd. dash. At the conclusion of each exercise, various orifice combinations were used, and the subject was asked his opinion of the resistance of each combination. The grades of resistance to breathing were as follows: Resistance unnoticed—Subjects not conscious of resistance to breathing (open circles). Resistance noticed—(closed circles and triangles). (1) Light—resistance noticed but not uncomfortable. (2) Moderate—resistance not uncomfortable for a short while but one which (in the opinion of the sub- ject) would become uncomfortable after a long period, (3) Heavy (triangles)—resistance uncomfortable and too high for a short period; occasional desire to remove mask for relief. On the chart, curve A is a line which has only unnoticed resistances to the left of it. Curve B has approxi- mately an equal number of unnoticed and noticed resistances on either side of it, and it has no heavy resistances to the left of it. Source: Report B-25, January, 1943. Canadian N. R. C. No. C2428 J. S. H. RESISTANCE TO BREATHING INSPIRATION MAXIMUM RATE OF INSPIRATION, LITRES/ MIN. 20°C. DRV. UNNOTICED SUBJECTIVE RESISTANCE NOTICED SUBJECTIVE RESISTANCE HEAVY SUBJECTIVE RESISTR NICE NEGATIVE- PRESS. IN MASK AT MAX. RATE OF INSPIRATION SECTION B Properties of Blood November, 1943 Oxygen Dissociation Curves for Human Blood at 37°C. Chart B-i a & b Under given conditions of temperature and hydrogen ion concentration the oxygen dissociation curves of blood from different individuals do not vary greatly. A comparison of the data given in the following two charts with data obtained from the blood of three individuals is shown in Table I. TABLE I Comparison of Individual Oxygen Dissociation Curves Arterial Oxygen Saturations in Percent of Oxygen Capacity (02-cap.) at pH = 7.40 (pC02 = 40 mm. Hg) pOs mm. Hg Blood of A. V. B. 02-cap. =: 20 vpc Blood of G. S. A. 02-cap. = 18 vpc Blood of T. J.F. 02-cap. = 17 vpc Data in Charts (Dill) 10 15 11 13 H 20 40 34 36 35 25 50 46 — 47 30 60 59 57 58 40 76.5 77 73 74 50 86 87 84 84-5 60 9i 9i-5 90 89 70 94-5 95-5 93-5 93 80 96 97 96 95 100 98 98 98.5 97-5 Sources: i) Curves based on data of D. B. Dill, Wright Field Aero-Medical Unit. 2) Bock, A. V. & Adair, G. S.—J. B. C. LIX 353 (1924). 3) Henderson, L. J.—Blood Yale University Press (1928) p. 132. Prepared by J. R. P. %0Z ; MM. Hg. S' pH = 2 -6 pH -2-A "N pH = 7-2, 2 1,7 2,1 2.6 4 3.0 3.8 4.6 6 4.4 5.5 6.8 10 6.5 8.2 10.5 15 8.7 10.9 13.5 20 10.7 13.4 16.5 30 14.2 17.9 22.1 40 17.5 22.0 27.1 50 20.9 26.3 32.3 60 24.7 31.1 38.2 70 28.7 36.1 44.3 80 36.3 45.7 56.2 85 41.1 51.7 63.6 90 48.7 61.4 77.2 94 59.5 75.0 92.1 96 69.7 87.7 108.0 98 89.8 113.0 139,0 OXYGEN DISSOCIATION CURVES FOR HUMAN BLOOD OXYGEN PRESSURE PERCENTAGE SATURATION %0r Saturation p02:nrnirtg ptlffi ptm pm 2 17 2.1 2 £ 4 5j0 33 4.6 6 4.4 5.5 6.8 10 63 a 2 103 15 az 103 13.5 20 10.7 13.4 163 30 14.2 17.9 22.1 40 17.5 223 27.1 50 2 OS 263 32.3 60 24.7 31.1 3a2 70 28.7 36.1 443 ao 363 45.7 saz 85 41.1 51.7 63.6 90 4&7 614 77.2 94 593 75.0 92.1 96 69.7 87.7 100.0 9fl 89.8 113.0 139.0 : OXYGEN DISSOCIATION CURVES: ' TOR HUNAN BLOOD : ~ Curves based on data of Major Dill Wright Held Aero-Medical Unit. - flayo Aero-rtedical Unit Lt. fl.MaaonGuest 6-9-4Z HE'5A ~m2 pressures Tor varimts pti. values have, been..... calculated from ~ equation? using o pKj value of tulO amL assuming a cans Ian £ Blood bicaA&nafe content (mingi ARTERIAL OXYGEN SATURATION AT ALTITUDE CHART B-3 November, 1943 Arterial Oxygen Saturation at Altitude Chart B-3 Modified from Physiology of Flight, Aero-Medical Laboratory, Wright Field, p. 13, Fig. 8 Explanation: Open circles are data from gasometric analysis of arterial blood drawn by puncture. Dots are values ob- tained with the oximeter. Analytical errors of the two methods are approximately ±1% and ± 5% satura- tion respectively. Subjects were seated at rest or engaged in light activity. Oximeter readings were average steady values obtained during a stay of at least ten minutes at any given altitude. Points obtained in the range 0-5000 feet have been omitted owing to doubt as to the validity of conventional methods for determining the oxygen saturation in this region. The normal arterial oxygen saturation as determined by gas analysis of blood drawn by puncture is usually stated to be 93-95%. Recent evidence indicates that this value is too low and that the true oxygen saturation of arterial blood at sea-level is 97-98%. Qualitative indications of the handicap associated with any particular oxygen saturation (“appreciable,” “considerable,” etc.) are based upon the opinions of investigators rather than upon analytical data. The extent to which the arterial oxygen saturation may be reduced without impairing physiological functions varies con- siderably from one individual to another and in the same individual from day to day. There is evidence that interference with visual mechanisms may take place at arterial saturations as high as 92-3% (5000 feet breath- ing air). Most performance tests of the “pursuit meter” type do not indicate changes of performance until the saturation has dropped below 80-85%. Limitations: 1) The data included in the chart were obtained from resting individuals. Evidence has been obtained by Dill, MR#EXP-M-54~653-39A Wright Field, June 10, 1941, that the data are also valid under conditions of light work (1500 ft-lbs/min., cf. Chart #R-3). Use of the data for heavier grades of work is not yet justified by experiment. 2) The observed scatter greatly exceeds the errors of analysis and, therefore, represents a real variation of arterial oxygen saturation among individuals at any given altitude. Due consideration of this scatter should be made in the application of mean values to any specific problem. There is evidence that the day to day variation of any one individual is considerably less than the scatter of the population. A statistical treatment of the data is given in a separate chart (#6-4). Sources: a) Arterial puncture data—Physiology of Flight (cited above) b) Oximeter data—Johnson Foundation, unpublished. J. R. P. ARTERIAL OXYGEN SATURATION AT ALTITUDE ARTERIAL OXYGEN SATURATION AT ALTITUDE STATISTICAL ANALYSIS CHART B-4 December, 1943 Arterial Oxygen Saturation at Altitude Statistical Analysis Use of Chart: Standards for problems involving arterial oxygen saturation as a function of altitude. Explanation: This chart depicts the variations of arterial oxygen saturation which occur among individuals breathing air or oxygen at selected altitudes. The data were taken.from the points shown in Chart B-3 and are subject to the limitations outlined in that chart. The solid bars show' the standard error of the mean and the cross- hatching shows the standard deviation about the mean. The central lines are drawn by eye as smooth curves which are as close as possible to the mean values at each altitude. Individual points are given where the data were considered too incomplete to warrant statistical treatment. Estimations of oxygen saturation made by the oximeter and by gas analysis of arterial blood are treated alike. Separate data are shown in Table II for altitudes at which five or more analyses by each method are available; the mean values obtained by the two methods are in close agreement except at one altitude (18.000 ft.). An important use of the data is the experi- mental verification of calculated “equivalent altitudes.” It may be noted that equal arterial oxygen saturations breathing air and breathing oxygen are found at the same altitude “pairs” as those calculated on the basis of equivalence of alveolar gas composition in Chart A-2. Chart B-4 TABLE I Mean Arterial Oxygen Saturation Pressure Altitude Total no. of subjects Mean Smoothed Mean Standard Error of Mean Standard Deviation Breathing air 15,000 ft. 12 78.5% 78.3% ±1.1% ±3.6% 16,000 if 75-5 75-5 1-7 5-5 17,000 12 74-5 72-3 1.8 6.1 18,000 12 68.0 68.5 1.8 6.2 19,000 6 64.7 63.8 2.9 7.2 Breathing oxygen 40,000 16 88.0 88.5 1.0 4-0 41,000 5 85.0 85.8 0.8 1.8 42,000 15 834 82.3 i-9 7-5 43,000 14 774 78.1 i-7 6-5 44,000 14 74-7 73-5 2.0 7-5 44.8—45,000 13 67.6 68.2 2.2 7-9 TABLE II Pressure Altitude No. of subjects Oximeter Puncture Mean oxygen Oximeter saturation Puncture 15,000 5 7 79.0 dr 1.8 78.0 dr 1.3 18,000 6 6 64.3 dr 1.9 72.1 dr 2.1 40,000 13 9 88.0 dr 1.5 88.0 ± 1.3 43,000 9 5 77.3 dr 2.9 77.6 dr 2.7 44.8—45,000 5 8 694 dr 3.8 66.5 dr 2.8 Comparison of Oximeter and Arterial Puncture Data Limitations: The data given in this chart may be useful as standards for discussions involving arterial oxygen satura- tion as a function of altitude. With the accumulation of new data, however, the present figures will almost certainly be subject to minor revision. Source: Chart 6-3 J. R. P. ARTERIAL OXYGEN SATURATION AT ALTITUDE SECTION E Oxygen Supply Systems November, 1943 Calculated Economies of Ideal Oxygen Systems Charts No. E-i a and No. E-i b Explanation: These are calculated values of oxygen consumption. Because of factors of safety, manufacturing toler- ances, and leaks, no actual system will give economies as good as those indicated. However, the curves do indicate the relative economies attainable by various systems if all are brought to the same degree of mechanical perfection. Demand valve curves are based on the computation of components of respiratory volume as presented in Chart No. R-i. Diluter demand curves are based on the values of percentage oxygen for various equivalent altitudes as given in Chart No. A-2. The curves for demand systems with rebreather are computed for a rebreather bag capacity of 35% of the tidal air volume. Experiments have shown that the economy changes very slightly with considerable in- crease of bag volume over this value. The oxygen consumption indicated for the closed system with CO2 absorber is assumed as .58 liters SPTD for a Respiratory Minute Volume of 15 liters BTPS. (See Chart R-2.) It should be noted that oxygen con- sumption in demand systems depends only on ventilation rate, while in closed systems it depends primarily on metabolic rate. There is a large spread in the ratio of ventilation rate to metabolic rate as shown in Chart R-2. The curve for the closed system is therefore not strictly comparable to those for the demand systems. Definition of symbols: Vr = Respiratory minute volume BTPS Vo = Oxygen consumption from supply system per min. STPD PB = Barometric pressure, mm. Hg. pHsO — Vapor pressure of water Fo2 — .21 Fs = Fraction of inspired gas which comes from the oxygen supply system = •79 Fo2 = Fraction of oxygen in inspired air required to produce desired equivalent altitude as obtained from Table P-2 T = Absolute temperature Vb = Effective volume of rebreather bag (if any) Vt = Average tidal volume Vo PB — pH20 273 , ( Vb :: x XFsX I \ Vr 760 T V t General equation used: Specific equations used: For demand systems Vo PB — 47 273 = X — Vr 760 310 For demand diluter systems: Vo PB — 47 273 Fo2 —.21 = X X Vr • 760 310 .79 For demand diluter rebreather systems: Vo PB —47 273 Fo2 —.2i = X X X 0.65 Vr 760 310 .79 Source: Boothby, Special Report #1, August 4, 1942 A. J. R. and G. A. M. CALCULATED ECONOMIES OF IDEAL OXYGEN SYSTEMS CALCULATED ECONOMIES OF IDEAL OXYGEN SYSTEMS SECTION M Carbon Monoxide EQUILIBRIA BETWEEN OXYGEN CARBON MONOXIDE AND HEMOGLOBIN IN NORMAL HUMAN BLOOD CHART M-l RESTRICTED November, 1943 Equilibria Between Oxygen, Carbon Monoxide and Hemoglobin in Normal Human Blood Chart M-i Symbols: p(02) = partial pressure of oxygen in blood. p(CO) — partial pressure of carbon monoxide in blood. %Hb02 = percentage of total hemoglobin in form of oxyhemoglobin. %HbCO = percentage of total hemoglobin in form of carboxy-Hb. K = Haldane constant. F = a function defined by the oxygen dissociation curve of normal human blood at 37°C, pC02 = 40 mm. Hg. The laws governing the equilibria between oxy-, carboxy- and reduced hemoglobin in the presence of known partial pressures of oxygen and carbon monoxide were first described by Douglas, Haldane & Haldane (1). The laws may be stated in the following way— %HhCO Kp(CO) %Ub02 p(02) (1) %Hb02+ %HbC0 = F[p(02) H-Kp(CO)] Equations (1) and (2) may be combined and solved for either Hb02 or for HbCO. Thus— F[p(02) + Kp(C0)] %Hb02 — X p02 p02 -(- KpCO (3) or F[p(02) -j- Kp(CO)] %HbCO = X KpCO P(02) + Kp(CO) (4) In normal human blood equilibriated with known values of p(CO) and p(02) Douglas et al. found excellent agreement between the %HbCO found by analysis and the values obtained from equation (4). Further ex- perimental evidence confirming the validity of the equations has recently been obtained by Roughton & Dar- ling (2). The curves shown in Chart M-i are obtained from equation (3;, A graphical solution of this equation may be made in the following way— a) Lety =p(02) + Kp(CO) (5) From the oxygen dissociation curve of normal human blood (Chart B-ia) a graph is constructed relating F(y)/y to y. Sample values are given below— Table I. y F(y) F(y)/y 50 84-5 1.69 70 93 i-33 90 97-5 1.08 b) From equations (3) and (5), F (y)/y = %Hb02/p(02) (6) For any given values of %Hb02 and p(02), F(y)/y and hence y are determined. Whence Kp(CO) = y—p(02) c) Example: Let %Hb02 = 80, p(02) = 60 mm. Hg. Find Kp(CO). From (6) F(y)/y = 80/60 = 1.33 From graph constructed in (a) or Table I we find that when F(y)/y — 1.33, y = 70. Whence, KpCO = 70 — 60 = 10 If K = 210 (cf below), p(CO) = 0.0475 as shown in chart. The Value of K: The value of K for human hemoglobin has been variously reported to range from 200-290. However, Sendroy et al. (3) found an avearge value of 210 ±: 5 in six individuals and this value has been employed in constructing the ordinates in the Chart. Sources: 1) Douglas, Haldane & Haldane, J. Physiol. 44, 275, 1912 2) Roughton & Darling, C. A. M. Report #93, 1942 3) Sendroy, Liu, & Van Slyke, Amer. J. Physiol. 90, 511, 1929 J. R. P. RESTRICTED EQUILIBRIA BETWEEN OXYGEN, CARBON MONOXIDE AND OXYHEMOGLOBIN IN NORMAL HUMAN BLOOD. November, 1943 Standards for Carbon Monoxide Chart M-2 I. Definition of Symbols PB = barometric pressure. Po2 = partial pressure of oxygen in dry inspired air. Pco = partial pressure of CO in dry inspired air. p(02) = partial pressure of oxygen in arterial blood. p(CO) = partial pressure of CO in arterial blood, p(CO)i = partial pressure of CO in arterial blood, initially. pCO — partial pressure of CO in alveolar air. k = time constant of rate of uptake of CO by the blood, t rr time in hours required to reach dangerous p(CO). II. Equilibrium Conditions—Concentrations of CO in dry inspired air required to bring the arterial oxygen saturation to 85% at different altitudes. The p(CO) required to bring Hb02 to 85% at any given p(02) is shown in Chart M-i. The altitude corresponding to any given p(02) and the % CO in dry inspired air corresponding to any given p(CO) and altitude determine the curve marked “indefinitely” in Chart M-2. The values were obtained in the following way— A. pC>2 as a junction of altitude. The exact relations between p(02) and altitude are unknown. The p(02) in arterial blood calculated in the conventional way from the arterial oxygen saturation (Chart B- la) is less than that in alveolar air by an amount which decreases with decreasing oxygen saturation (Table I). The values chosen for the preparation of Chart M-2 were calculated from the average arterial oxygen saturations at different altitudes (Chart B-3) ; they are shown in Table I. TABLE I Values of p02 Used in Construction of Chart M-2 Altitude— breathing air (Ft.) Po2 in dry inspired air Alveolar po2 (Chart A-i) Arterial p(02)— values used for Chart M-2 0 159 103 87 2000 148 94 83 4000 137 85 78 6000 127 76 69 8000 118 66 62 10000 109 57 55 12000 101 50 49 Continued on back of Chart M-2 Standards for Carbon Monoxide Chart M-2 Factors Considered 1) Equilibrium values of oxyhemoglobin in the presence of known partial pressures of oxygen and car bon monoxide. 2) Pressure of oxygen in arterial blood as a function of altitude. 3) Equilibrium relations between the partial pressure of carbon monoxide in alveolar air and in dry inspired air. 4) The rate at which carbon monoxide enters the blood as affected by the respiratory minute volume and the concentration in dry inspired air. 5) The effects of initial concentrations of carbon monoxide in the blood. Limitations of Chart M-2: The standards for CO shown in Chart M-2 depend largely upon the choice of numer- ical values for 3 physiological variables. 1) Choice of 85% saturation as that value which may be safely tolerated: This value corresponds approximately with that which obtains while breathing air free from CO at 12,000 ft. (Chart B-4). The exact value chosen critically affects the calculated standards. Thus if 88% Hb02 is chosen instead of 85% the permissible CO at 6,000 ft. would be reduced from 0.0065% to 0.0041%. 2) Choice of values of p02 as a function of altitude:—Recent evidence indicates that p(02) may be con- siderably nearer to alveolar p©2 at all altitudes than has been assumed in the construction of the Chart (Table I above). If this is in fact the case then the permissible CO at lower altitudes may considerably exceed the values shown in the Chart. Thus at sea-level 0.013% CO instead of 0.0083% would be required to bring Hb02 to 85%. 3) Time standards: If the respiratory minute volume exceeds 10 Hter/min. then the rate of uptake of CO may exceed the standards shown in the chart. A margin of safety should be provided under conditions in which prolonged activity is expected. The margin of safety should be proportional to the percentage increase in minute volume (cf. Chart R-3). STANDARDS FOR CARBON MONOXIDE B. %C0 in dry inspired air as a junction of pCO. At equilibrium CO is neither taken up nor given off by the blood; under these conditions pCO = p(CO) and the ratio p(CO)/Pco is the same as that for nitrogen or for any other neutral gas (Haldane & Smith (3)). The value of this ratio is defined by Equations (4) and (9) in the Essay on “Composition of Respiratory Gases” in this manual. Solving Equations (1) above, and (4) and (9) in the Essay, we have, p(CO)/Pco = PN2/Pn2 (i) P(CO) _ PB—47 pC02 (1 -RQ) Pco ” PB PbXRQ whence, Pco X 100 loop (CO) %CO = = PB PC02 (1 —RQ) PB — 47 H RQ (2) For practical purposes variations of pC02 and RQ have a negligible effect (less than 1%) on the % CO cal- culated from (2). Using nominal values of pC02 = 39 mm. Hg and R. Q. = 0.85 (2) becomes— 100 p(CO) %CO = PB —40 (3) and this form was used in the preparation of Chart M-2. Sample Calculation: What concentration of CO is required to bring PIb02 to 85% at 6000 ft.? Refer- ence to Table I shows that at this altitude p©2 in arterial blood is 69 mm, Hg. Reference to Chart M-i shows that this corresponds with a blood p(CO) of 0.03 mm. Then from (3) we have— %CO = 100 X -037/609 — 40 = 0.0065 Ans. IV. Dynamic Conditions: The rate at which CO is taken up by the blood The uptake of CO by the blood may be expressed by the exponential equation— Pco — p(CO)i log = kt Pco —p(CO) (5) Under conditions of light activity (respiratory minute volume 10 L./min.) the value of k is approximately 0.12 when t is expressed in hours. Thus 90% of the experimentally obtained values of Forbes et al. (2) lie within the boundary defined by this equation. Example: How many hours are required to reduce the arterial oxygen saturation to 85% while breathing 0.02% CO at 6000 ft.? a) Pco = %CO X PB — 0.02% X 609 = 0.122 mm. Hg b) p(O2) at 6000 ft. is 69 mm, Hg (Table I above) c) p(CO) (when p02 = 69, Hb02 = 85%) is 0.038 mm. Hg (Chart M-i) d) Assume p(CO)i = 0.01 mm. (usual in blood of cigarette smokers) whence, .122 .010 log = .12 t whence t — 1.05 hours .122 — .038 Ans. Sources: 1) Chart M-i 2) Forbes, Sargent & Roughton, C. A. M. Report #97 (1942) 3) Haldane & Smith, J. Physiol. 20, 497 (1896) J. R. P. CARBON MONOXIDE STANDARDS FOR USE WITH AUTO-MIX SYSTEMS CHART M-3 Carbon Monoxide Standards for Use With Auto-Mix Systems November, 1943 Chart M-3 The use of an Auto-mix system alters the standards shown in Chart M-2 in two ways— 1) Alteration of Po2 in inspired gas as a function of altitude. 2) Alteration of fraction of inspired gas breathed from cabin and containing carbon monoxide. Calculations: 1) For any given value of Po2 the value of p(CO) required to bring Hb02 to 85% saturation was calculated as in Chart M-2. The %CO corresponding to each value of p(CO) at any altitude is then, ioop(CO)/f %CO = PB — 40 (1) cf. Equation (3) Chart M-2 where f is the fraction of cabin air in inspired air. But, (1 — Fo2) f — = 1.26 (1 — Fo2) (1— .21) 00 Combining (1) and (2) we have, ioop(CO) i % CO= X PB — 40 1.26(1 — Fo2) The values of Fo2 used for the chart are shown in the following table— Altitude A-12 Pioneer Regulator Ideal-Regulator Sea-level Equiv. Ideal Regulator 5000 ft. Equiv. o •35 .21 .21 5000 — •25 .21 10000 4i •3i .27 15000 — •39 •33 20000 .60 •49 •41 25000 — •63 •52 J. R. P. CARBON MONOXIDE STANDARDS FOR USE WITH AUTO-NIX SYSTEMS SECTION C Circulation