The Abbreviated Alveolar Air Equation Revisited

1. The ewnt immediately followed two separate unsuccessful attempts to advance tbe endotracheal tube through

the laryu. While attempting to gain access to the epig]ottis area with the aid of the laryngoscope blade, the tongue and soft tissues were lifted and placed to the left of the mouth, thereby eliminating these sbuctures as potential factors of airway obstruction. 2. Ventilation with a face mask was attempted with the neck in hyperextension and with mandibular support, thus minimizing the possibility that tongue and soft tissues would interfere with airway patency. 3. Although the epiglottis was identified, bnt the vocal cords were not visua1ized. one cannot rule ont with certainty that the inability to effectively ventilate the patient was the result of other than laryngospasm, eg, bronchospasm.

4. We are, of course, fully aware of the various steps recommended for the treatment of laryngospasm, including the administration of oxygen under positive airway pressure, and the use of succinylcholine to induce paralysis of the muscles of adduction of the vocal cords. In our patient, the initial treatment of laryngospasm followed precisely these rules and only when the patient failed to respond promptly were aminophylline and epinephrine administered, since the possibility of a bronchospastic component could not be ignored. We would like to clarify a statement made by Dr. Poulton regarding analysis of arterial blood gas levels "within three minutes" of the episode of airway obsbuction. The blood gases were obtained not three minutes after the onset of respiratory obsbuction, but rather three minutes after the administration of the medication, which means that at least 8 to 10 minutes had elapsed from the onset of ventilatory difliculties until arterial blood gases were analyzed. We also think that further clarification is required regarding our patient's acuity during the event. She was indeed conscious during this episode and remained conscious for several hours following its onset. Dr. Poulton's comments are well taken, though not applicable in this case. Fredric N. ]oclcson, M.D., Pulrnontuy FeUow, and Guenter Consen, M.D. ChtJitman, Deptmment of Anesthesiology, Maricopa County General HospittJl, Phoenu Reprint reque&ta: Dr. Consen, Deptmment of Health Serofcu, 2601 East Boo.sevelt, PhoenU 85003

The Abbreviated Alveolar Air Equation Revisited To the Editor:

The reports by Raymond 1 and Helmholzt concerning abbreviation of the alveolar air equation to encourage more general use still result in a rather formidable algebraic expression. The clinician without a bandy programmable pocket calculator remains without a truly simpli&ed approach to estimate the P(A-a)Oll. Wasserman• proposed such an approach based on the equality of PAC0ll and PaCO. for the evaluation of patients breathing room air. He advised merely subtracting the sum of the measured arterial tensions of Oll and C02 from the normal sum of the respective alveolar tensions to yield a clinically useful approximation of the 0 2 tension difference, the P(A-a)0 2

CHEST, 80: 6, DECEMBER, 1981

( approx). Once determined, this altitude-dependent normal sum of the alveolar t:ensioos remains constant and aerves as the baseline for a simple subtraction leading directly to the approximation. An uncomplicated calculation of this baseline, as weD as an error analysis of the P(A-a)02 (appro:.:) follows from analysis of the algebraic repteam.tatioD of Wasserman's technique:

P(A-a)02 (approx) =alveolar sum(baseline) - arterial sum = (PA02 + PAC02 ) - (Pa0 2 + PaCO:a) (I)

The first term (PA02 + PAC02 ) is the baseline number, PA02 is the normal ideal alveolar 0:t tension, and PAC02 (equal to PaCOll) is the normal alveolar COli tension for any given altitude. PAO:t is calculated from the alveolar air equation with R = 0.8 using the mean barometric pressure (mm Hg) for the given altitude, (PB), and PAC02 • Substituting the altitude-dependent function' PaC02 = 40- .042 (760-PB)

(2)

and consolidating terms with the alveolar air equation, the

baseline simplifies to:

A parabolic &t to the US Standard Abnosphere tables& allows the baseline to be expressed as a function of altitude: (PAOli+ PACOll) = 141.8- 5.495XIO·•h + 7.135X10·Bht

(4)

where h is altitude in feet. Thus, the sea level baseline ( PB = 760, h = 0) calculated from equation ( 3) or ( 4) is 142, while the baseline for Denver ( PB = 626, h = 5280) is 115. The P(A-a)Oll (approx) of a patient in Denver breathing room air with arterial gases Pa02 = 60 and PaCOll = 30 is easily calculated: 115- (60 + 30) = 25 Exact calculation of room air P(A-a)O. using the ideal alveolar air equation with R = 0.8 at PB reduces to: P(A-a)02 (ideal) = 0.21 PB(Pa02 + 1.198 PaC02) - 9.87

(5)

By rearranging and simplifying, the error of the approximation is seen to be: P(A-a)02 (approx-ideal) = .1975 PaC02 8.295XI0-8 PB- 1.596

-

(6)

and is, therefore, a function of both altitude and PaCOll. In the 6gure, the dashed line represents zero error and

intersects the PaC02 isopleths at the corresponding normal PaCO:t for given altitude. The figure demonstrates that the sign and magnitude of the error are in the same direction and proportional to the PaC02 variation from normal, I mm Hg error developing for every 5 mm Hg change in the PaCO:t. Because of the simplicity and minimal error of this method, its use as a bedside approximation of P(A-a)02

COMMUNICATIONS TO THE EDITOR 783

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ALTITUDE (teet a 1,000) FIGURE

1

bas been encouraged by our hou.sestaff for the evaluation of hypoxemia in patients breathing room air. The following altitude-baseline table can he used for convenience in place of equation ( 4). Altitude (Feet)

Baseline

0 500 1000 1500

142 139 136 134 131 129 126 123 121 119 116 114 111 109 107 105 10.2 100 98 96 94

2000

2500 3000

3500 4000

4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000

PulmontBv

.Reprint requem:

Diset.ue

The Dolovich Reaction To the Editor:

Seroice.

Fbimonl Amari Medical Center. Aurora, Colorado 80045

784 COMMUNICATIONS TO THE EDITOR

The difference between ideal alveolar Po2 and arterial ( P( A-a )0 2 )is a measure of the severity of the pathophysiological mechanisms which cause hypoxemia. I am pleased that Perry et al agree that the mental arithmetic simple expedient for calculating P(A-a)02 by summing arterial Pco2 and Po2 and subtracting from 142 (at sea level; lower value for higher altitude) described in reference 3 is "correct enough" and practical for clinical use. The difference between the exact and the expedient calculation is small. We would rather have the housestaff approximate the difference by the summing technique rather than not make any estimation in their patients because of the complexity of the "exact" calculation. The recognition of pulmonary insufliciency without an increase in P(A-a)02 can quickly alert the house officer to a defect in respiratory control (example: primary or drug induced) or respiratory muscle failure (example: myasthenia gravis or Guillain Barre syndrome) from primary disorders of the lungs which characteristically give an increased P(A-a)02 • Po 2

Medical Center. TorrtJnCIJ. CDllfomitJ

Fitsaimom Amari MedictJl Center, Aurora, Colotodo

PulmontBv

To the Editor:

Karlman Wasserman. M.D .• F.C.C.P. UCLA School of Medicine. Harbor-UCLA

Michael E. Pem;. LTC. MC; Robert ]. Browning. B.S.; tmd NBDl B. KJndlg, Ph.D., INet.ue/Clinical IntJeltlgation Seroice,

Dt. Pem;.

1 Raymond LW. The alveolar air equation abbreviated. Chest 1978; 74:675 2 HeJmhoJz HF. The abbreviated alveolar air equation. Chest 1979; 75:748 3 Wasserman K. Summing PaCO,.~ and PaOt: A simple expedient for determining alveolar-arterial Po2 difference. Am Rev Resp Dis 1976; 113:707 4 Fenn wo. Rahn H. Handbook of physiology, Sec 3. Respiration, Vol1. Washington D.C.; American Physiological Society. 1964:520 5 US Standard Atmosphere. 1976. Washington D.C.; 1\IASA. 1976:53

We have recently undertaken a study on the prevalence of allergic reactions in people exposed to animal allergens by virtue of their employment either as full-time or parttime animal handlers or as animal experimentalists. We found asthma. rhinitis and contact allergy as the main allergic symptoms. with a high degree of correlation between animal induced asthma and a positive immediate skin prick test to the animal species inducing the asthmatic reaction.1 Of the 17 subjects with animal asthma and positive immediate skin prick test reactions. three developed late skin reactions around the test site. These late reactions were maximal at about six hours and were large. red. warm. tender edematous areas involving about half the forearm and resolving by the following day. The serum of these individuals did not contain specific lgG antibody to the eliciting animal materials (serum and male urine) as determined by both the enzyme-linked immunosorbant assay (ELISA) and by double gel diffusion. On the basis of the time course of this reaction there is an undoubted parallel with the Arthus (type m) reaction which does involve specific IgG antibody to the antigen; however. in view of the absence of detectable speci&c IgG and the minute amount of allergen introduced by the skin

CHEST, 80: 6, DECEMBER, 1981