THE FOUR MOST IMPORTANT

EQUATIONS IN CLINICAL

PRACTICE

by Lawrence Martin, M.D., FACP, FCCPAssociate Professor of MedicineCase Western Reserve University School of MedicineCleveland, Ohio

WHY?

These formulas are only briefly taught in medicalschool but the concepts are of paramountimportance to the safety of the patient.

RT’s need to be expert on the qualitativerelationships expressed by these formulas

1) CO2 EQUATION

PaCO2 =(VCO2)(0.863)

VA.

ALVEOLAR MINUTE VOLUME

Ve = ( f )(Vt)

VA = ( f )(Vt-Vd)

“Slow/deep” Example:

6.0 L/m = (12)(.5L)

4.2 L/m = (12)(.5L-.15L)

.

.

ALVEOLAR MINUTE VOLUME

Ve = ( f )(Vt)

VA = ( f )(Vt-Vd)

“Fast/Shallow” example:

6.0 L/m = (24)(.25L)

2.4 L/m = (24)(.25L-.15L)

.

.

1) CO2 EQUATION

PaCO2VCO2

VA

PaCO2 is directly proportional to CO2 production andinversely proportional to alveolar ventilation

.

.

PaCO2 VA

HOW MUCH VENTILATION?

(Current Ve)(Actual CO2)

Desired CO2=Needed Ve

..

HOW MUCH VE: EXAMPLE

Patient Settings: f = 12, Vt = 500ml

ABG: pH = 7.28, PaCO2 = 55

(6.0 L/m)(55 mmHg)

40 mmHg=

40

330= 8.25 L/m

2) HENDERSON-HASSELBALCH EQUATION

pH =HCO3-

H2CO3

pK + log

CABONIC ACID

H2CO3 H+ HCO3-

CO2 + H2O H2CO3

CO2 forms Carbonic Acid

2) HENDERSON-HASSELBALCH EQUATION

pHHCO3-

CO2

pH is directly proportional to HCO3- andinversely proportional to CO2.

CO2 AND PH

Lawrence Martin MD http://www.globalrph.com/martin_4_most.htm#top

COMPENSATION

pHHCO3-

CO2pH

HCO3-

CO2

pH = 7.20CO2 = 60

HCO3- = 24

pH = 7.40CO2 = 60

HCO3- = 32

COMPENSATION

pH HCO3-

CO2pH

HCO3-

CO2

pH = 7.20CO2 = 40

HCO3- = 18

pH = 7.40CO2 = 25

HCO3- = 18

DO ALKALOSIS COMPENSATE?

CompensatedRespiratory Alkalosis

pH - 7.50

CO2 – 25

HCO3- 22

CompensatedMetabolic Alkalosis

pH – 7.55

CO2 – 40

HCO3- 28

ANION GAP

Cations (Positively charged ions Na+, K+

Anions (Negatively charged ions HCO3-, Cl-

<11 meq/L Normal

>11 meq/L High (Metabolic acidosis)

[(Na+) + (K+)] – [(HCO3-) + (Cl-)]

3) ALVEOLAR AIR EQUATION TO ARTERIAL

PO2 GRADIENT:

PAO2 = (PB – PH2O)FIO2 - PaCO2(1.25)

Or A-a gradient

PaO2 = Arterial oxygen

ALVEOLAR AIR EQUATION

PB = 760

PH2O = 47

PaCO2 = 40

FIO2 = 40%

(760 – 47).40 40(1.25)

(713)(.40) 50

285 50

235

ASSESSING OXYGENATION

A-a Gradient

Lower numbers are better

Example: Patient on 40% PaO2 is 66

PAO2 = 240 - 66 = 174

Later: Patient on 50% PaO2 is 87

PAO2 = 310 - 87 = 223

a/A Ratio

66/240 = 28%

87/310 = 28%

4) O2 CONTENT EQUATION

(Hb)(1.34)(SaO2)+

(PaO2)(.003)

(14)(1.34)(.97) = 18.2+

(85)(.003) = .26

ANEMIA VS. HYPOXIEMA: WHO’S WORSE?

(12)(1.34)(.88) = 14.2+

(56)(.003) = .17

Hypoxemia, normal Hb

Norm oxygen, Anemia(8)(1.34)(.99) = 10.6

+(200)(.003) = .6

BONUS EQUATION: FICK PRINCIPLE

VO2CaO2 – CvO2

Q =