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Why is the PaCO2 equation the most important equation in all of clinical medicine?

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### Why is the PaCO2 equation the most important equation in all of clinical medicine?

### Why is the PaCO2 equation the most important equation in all of clinical medicine?

Lawrence Martin, M.D.

Clinical Professor of MedicineCase Western Reserve University School of MedicineCleveland, OHIO USA

September 17, 2009

Because your understanding the PaCO2 equation will:

Save lives!

Improve patient care!

Help wean patients off the ventilator!

Shorten length of stay!

PaCO2 Equation: PaCO2 reflects ratio of metabolic CO2production (VCO2) to alveolar ventilation (VA)

VCO2 x 0.863 VCO2 = CO2 production

PaCO2 = ------------------- VA = VE – VD

VA VE = minute (total) ventilation = f (tidal volume)VD = dead space ventilation = f (dead space volume)

0.863 converts VCO2 and VA units to mm Hg

Condition State of

PaCO2 in blood alveolar ventilation

> 45 mm Hg Hypercapnia Hypoventilation

35 - 45 mm Hg Eucapnia Normal ventilation

< 35 mm Hg Hypocapnia Hyperventilation

PaCO2 Equation: PaCO2 reflects ratio of metabolic CO2 production (VCO2) to alveolar ventilation (VA)

VCO2 x 0.863 VCO2 = CO2 production

PaCO2 = ------------------- VA = VE – VD

VA VE = minute (total) ventilation = f (tidal volume)VD = dead space ventilation = f (dead space volume)

0.863 converts VCO2 and VA units to mm Hg

Normal Resting

VCO2 = 200 ml/minute

f(tidal volume) = 12 (500 ml) = 6 l/min

f(dead space vol.) = 12 (150 ml) = 1.80 l/min

VA = 6 – 1.80 = 4.2 l/min

200 x 0.863

PaCO2 = ----------------- = 41 mm Hg

4.2

PaCO2 Equation: PaCO2 reflects ratio of metabolic CO2 production (VCO2) to alveolar ventilation (VA)

VCO2 x 0.863 VCO2 = CO2 production

PaCO2 = ------------------- VA = VE – VD

VA VE = minute (total) ventilation = f (tidal volume)VD = dead space ventilation = f (dead space volume)

0.863 converts VCO2 and VA units to mm Hg

Rapid Breathing, normal tidal volume

VCO2 = 200 ml/minute

f(tidal volume) = 24 (500 ml) = 12 l/min

f(dead space vol.) = 24 (150 ml) = 3.60 l/min

VA = 12 – 3.60 = 8.4 l/min

200 x 0.863

PaCO2 = ----------------- = 20.5 mm Hg

8.4

PaCO2 Equation: PaCO2 reflects ratio of metabolic CO2 production (VOC2) to alveolar ventilation (VA)VA VE = minute (total) ventilation = f (tidal volume)VD = dead space ventilation = f (dead space volume)

VCO2 x 0.863 VCO2 = CO2 production

PaCO2 = ------------------- VA = VE – VD

0.863 converts VCO2 and VA units to mm Hg

Rapid Breathing, Shallow Tidal Volume

VCO2 = 200 ml/minute

f(tidal volume) = 20 (300 ml) = 6 l/min

f(dead space vol.) = 20 (150 ml) = 3.00 l/min

VA = 6 – 3 = 3 l/min

200 x 0.863

PaCO2 = ----------------- = 57.5 mm Hg

3

PaCO2 Equation: PaCO2 reflects ratio of metabolic CO2production (VCO2) to alveolar ventilation (VA)VA VE = minute (total) ventilation = f (tidal volume)VD = dead space ventilation = f (dead space volume)

VCO2 x 0.863 VCO2 = CO2 production

PaCO2 = ------------------- VA = VE – VD

0.863 converts VCO2 and VA units to mm Hg

Rapid breathing, increased dead space (severe COPD)

VCO2 = 200 ml/minute

f(tidal volume) = 16 (500 ml) = 8 l/min

f(dead space vol.) = 16 (300 ml) = 4.80 l/min

VA = 8 – 4.8 = 3.2 l/min

200 x 0.863

PaCO2 = ----------------- = 54 mm Hg

3.2

PaCO2 is the center of the blood gas universe; without understanding PaCO2 you can’t understand oxygenation or acid-base balance.

OxygenationAcid-Base

PAO2 = FIO2 (BP-47) – 1.2 (PCO2) HCO3 pH ~ ------------ PaCO2

PaO2

- VCO2 x .863
- PaCO2 = --------------------
- VA where VA = VE - VD

Note: PaCO2 is from ABGs. HCO3 is calculated from ABG measurement of pH and PaCO2or measured in venous blood as part of electrolytes. When measured in venous blood it is variously labeled ‘bicarbonate’, ‘HCO3’ or ‘CO2’ (the latter NOT to be confused with PaCO2).

Arterial blood – blood gases

Venous blood - BMP

You can’t learn this material from a lecture!!

Review:

www.lakesidepress.com/pulmonary/index-phys.html

index to web sites on pulmonary physiology

www.lakesidepress.com/ABGQuiz2009-Questions.htm

multiple-choice blood gas quiz

www.lakesidepress.com/pulmonary/papers/eq/tablecontents.html

4 Most Important Equations in Clinical Practice

www.lakesidepress.com/pulmonary/ABG/MixedAB.htm

Diagnosing mixed acid-base disorders

www.lakesidepress.com/pulmonary/ABG/PO2.htm

PaO2, SaO2 & CaO2 – What’s the Difference?

Hypercapnia – PaCO2 > 45 mm Hg

VCO2 x 0.863

PaCO2 = ------------------

VA where VA = VE – VD

Hypercapnia is a serious respiratory problem. The PaCO2 equation shows that the only physiologic reason for elevated PaCO2 is inadequate alveolar ventilation (VA) for the amount of metabolic CO2 production (VCO2).

Since alveolar ventilation (VA) equals minute ventilation (VE) minus dead space ventilation (VD), hypercapnia can arise from insufficient VE, increased VD, or a combination of both.

Hypercapnia(cont)

VCO2 x 0.863

PaCO2 = ------------------

VA where VA = VE – VD

VA = f(tidal vol.) –

f(dead space vol.)

- Examples of inadequate VE leading to decreased VA and hypercapnia: sedative drug overdose; respiratory muscle paralysis; central hypoventilation
- Examples of increased VD leading to decreased VA and hypercapnia: chronic obstructive pulmonary disease; severe restrictive lung disease (with shallow, rapid breathing)

Dangers of Hypercapnia

Besides indicating a serious derangement in the respiratory system, elevated PaCO2 poses a threat for three reasons:

- An elevated PaCO2 will lower the PAO2(see Alveolar gas equation) and as a result will lower the PaO2.

2) An elevated PaCO2 will lower the pH (see Henderson-Hasselbalch equation) and as result lead to acidosis.

3) The higher the baseline PaCO2, the more it will rise for a given fall in alveolar ventilation, e.g., a given decrease in VA will raise the PaCO2 more when PaCO2 is 50 mm Hg than when it is 40 mm Hg.

Dangers of Hypercapnia – lowers PAO2 & PaO2

An elevated PaCO2 will lower the PAO2 and as a result will lower the PaO2

Alveolar Gas Equation determines the alveolar PO2 (PAO2). PAO2 is one of two main factors that determine PaO2. (The other is ventilation-perfusion relationships within in the lungs.)

PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)

PaO2

Dangers of Hypercapnia – lowers PAO2 & PaO2

An elevated PaCO2 will lower the PAO2 and as a result will lower the PaO2

PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)

=.21 (760-47) – 1.2 (40)

= 150 – 48 = 102

Assuming 10 mm (A-a) O2 difference,

PaO2 = 92 mm Hg

PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)

=.21 (760-47) – 1.2 (60)

= 150 – 72 = 78

Assuming 10 mm (A-a) O2 difference,

PaO2 = 68 mm Hg

Dangers of Hypercapnia – lowers the pH

An elevated PaCO2 will lower the pH, as predicted by the Henderson-Hasselbalch Equation.

HCO3

pH ~ ------------

PaCO2

Dangers of Hypercapnia – lowers the pH

An elevated PaCO2 will lower the pH, as predicted by the Henderson-Hasselbalch Equation.

HCO3

pH ~ ------------

PaCO2

Normal

24 mEq/l

7.40 ~ ------------

40 mm Hg

Respiratory Acidosis

24 mEq/l

7.23 ~ ------------

60 mm Hg

Basic Metabolic Panel from venous blood (BMP)

Na+ 140 mEq/L

K+ 4.0 mEq/L

Cl 95 mEq/L

HCO3 35 mEq/L

BUN 20 mg%

Creatinine 1.1 mg%

HCO3 and PaCO2 are 2 of 3 components in the H-H equation:

What does HCO3 by itself reveal about PaCO2?

HCO3

pH ~ ------------

PaCO2

Any venous HCO3 can

reflect virtually any

value of PaCO2.

Shown here is venous

HCO3 of 35 mEq/L ,

plotted on graph of H-H

equation.

The range of

possible PaCO2

values is below 20 to

above 100.

Abbreviated H-H equation:

Knowing just one parameter doesn’t tell you the acid-base state; you need at least two of the three values in H-H equation!

HCO3

pH ~ ------------

PaCO2

Dangers of Hypercapnia –

less reserve if there is

further hypoventilation

Effect of 1 liter decreases in alveolar ventilation on PaCO2, when VCO2 = 200 ml/min

High PaCO2 increases the slope of change for any further decrease in VA

VCO2 x 0.863

PaCO2 = ---------------

VA

A one-liter decrease in VA when PaCO2 is 40 mm Hg will increase PaCO2 to 52 mm Hg.

The next one-liter decrease in VA will increase PaCO2 to 75 mm Hg…

And the next 1 liter decrease in VA will increase PaCO2 to 133 mm Hg!

High PaCO2 is dangerous!

PaCO2

VA (l/min)

Dangers of Hypercapnia – summary

PaCO2 of 60 mm Hg is not ‘just 50% higher’ than 40mm Hg. A high PaCO2 also:

- Lowers PaO2 at any given Bar. Press.

PAO2 = PIO2 – 1.2(PaCO2)

PAO2 > PaO2

- Makes patient acidotic

pH ~HCO3

PaCO2

- Increases the slope of change for any further decrease in VA.

Graph of:

VCO2 x 0.863

PaCO2 = -------------

VA

For VCO2 of 200 and 300 ml/min

PaCO2

VA (l/min)

You cannot assess PaCO2 clinically – Why not?

50-year-old man with COPD:

respiratory rate 35/minute;

agitated

BP 170/104 mm Hg

Pulse 105/minute

Good breath sounds

Is he hyperventilating? Hypoventilating? No way to tell clinically.

At bedside can’t determine if PaCO2 high or low because:

VCO2 x 0.863

PaCO2 = ------------------------

VA

= f(tidal vol. –

f(dead space vol.)

You don’t know:

- VCO2

- tidal volume

- dead space volume

Trying to assess PaCO2 clinically can lead to fatal or near fatal errors!

(continued)

Check of her lab work shows that 2 days earlier, on hospital admission, her venous HCO3 was 35 mEq/L (normal up to 29).

ERROR

Intern didn’t think of hypoventilation in setting of agitation.

VCO2

PaCO2 =---------

VA = f(tidal vol.) – f(dead space vol.)

The only parameter known to intern was frequency of breathing (fast). Knowing just ‘f’, it is impossible to reliably gauge if patient is hyperventilating or hypoventilating. High HCO3 (not noted by intern) was certainly consistent with latter. Without check of ABG, Valium should not have been given!

Case – 73 yo woman in hospital

- Intern called to bedside at 11 pm because “she is agitated.” She was previously calm all day.
- Respiratory rate 20 (mild tachypnea). Lungs clear. Intern assess “hypreventilation” and prescribes Valium to “calm her down.”
- 45 minutes later patient stops breathing, is emergently intubated.

(continued)

Cannot reliably assess PaCO2 clinically

- The ONLY clinical parameter in PaCO2 equation is frequency of breathing!!!
- There is nothing in PaCO2 equation about respiratory effort, mental status, body habitus, etc.
- If all you know at bedside is resp. rate, you can’t possibly discern patient’s PaCO2!!
- You cannot determine at bedside if patient’s PaCO2 is high or low.

PaCO2 is determined only by factors in the PaCO2 equation:

VCO2 x 0.863

PaCO2 = --------------------

VA = f(tidal vol. – f(dead space vol.)

VCO2 = metabolic CO2 production/min

VA = alveolar ventilation

f = frequency of breathing

0.863 converts units to mm Hg

PaCO2 is key to the blood gas universe; without understanding PaCO2 you can’t understand oxygenation or acid-base.

OxygenationAcid-Base

HCO3

PAO2 = FIO2 (BP-47) – 1.2 (PCO2) pH ~ ------------

PaCO2

PaO2

- VCO2 x .863
- PaCO2 = --------------------
- VA where VA = VE = VD
- = f(VT) – f(VD)

PaCO2 and Alveolar Ventilation: Test Your Understanding

1. What is the PaCO2 of a patient with respiratory rate 24/min, tidal volume 300 ml, dead space volume 150 ml, CO2 production 300 ml/min? The patient shows some evidence of respiratory distress.

.

PaCO2 and Alveolar Ventilation: Test Your Understanding

1. What is the PaCO2 of a patient with respiratory rate 24/min, tidal volume 300 ml, dead space volume 150 ml, CO2 production 300 ml/min? The patient shows some evidence of respiratory distress.

.

- First, you must calculate the alveolar ventilation.
- VE = 24 x 300 = 7.2 L/min
- VD = 24 x 150 = 3.6 L/min
- VA = 3.6 L/min. Then
- 300 ml/min x .863
- PaCO2 = -----------------------
- 3.6 L/min
- PaCO2 = 71.9 mm Hg

PaCO2 and Alveolar Ventilation: Test Your Understanding

2. What is the PaCO2 of a patient with respiratory rate 10/min, tidal volume 600 ml, dead space volume 150 ml, CO2 production 200 ml/min? The patient shows some evidence of respiratory distress.

PaCO2 and Alveolar Ventilation: Test Your Understanding

2. What is the PaCO2 of a patient with respiratory rate 10/min, tidal volume 600 ml, dead space volume 150 ml, CO2 production 200 ml/min? The patient shows some evidence of respiratory distress.

- VA = VE – VD
- = 10(600) - 10(150) = 6 - 1.5 = 4.5 L/min
- 200 ml/min x .863
- PaCO2 = ---------------------- = 38.4 mm Hg
- 4.5 L/min

PaCO2 and Alveolar Ventilation: Test Your Understanding

3. A man with severe chronic obstructive pulmonary disease exercises on a treadmill at 3 miles/hr. His rate of CO2 production increases by 50% but he is unable to augment alveolar ventilation. If his resting PaCO2 is 40 mm Hg and resting VCO2 is 200 ml/min, what will be his exercise PaCO2?

PaCO2 and Alveolar Ventilation: Test Your Understanding

3. A man with severe chronic obstructive pulmonary disease exercises on a treadmill at 3 miles/hr. His rate of CO2 production increases by 50% but he is unable to augment alveolar ventilation. If his resting PaCO2 is 40 mm Hg and resting VCO2 is 200 ml/min, what will be his exercise PaCO2?

Exercise increases metabolic CO2 production. People with a normal respiratory system are always able to augment alveolar ventilation to meet or exceed the amount of VA necessary to excrete any increase in CO2 production. As in this example, patients with severe COPD or other forms of chronic lung disease may not be able to increase their alveolar ventilation, resulting in an increase in PaCO2. This patient’s resting alveolar ventilation is

VCO2 x .863 200 ml/min x .863

PaCO2 = --------------- VA = 4.32 L/min = -----------------------

VA 40 mm Hg

Since CO2 production increased by 50% and alveolar ventilation not at all, his exercise PaCO2 is

300 ml/min x .863

-------------------------- = 59.9 mm Hg

4.32 L/min

You can’t learn this material from a lecture!!

Review:

www.lakesidepress.com/pulmonary/index-phys.html

index to web sites on pulmonary physiology

www.lakesidepress.com/ABGQuiz2009-Questions.htm

multiple-choice blood gas quiz

www.lakesidepress.com/pulmonary/papers/eq/tablecontents.html

4 Most Important Equations in Clinical Practice

www.lakesidepress.com/pulmonary/ABG/MixedAB.htm

Diagnosing mixed acid-base disorders

www.lakesidepress.com/pulmonary/ABG/PO2.htm

PaO2, SaO2 & CaO2 – What’s the Difference?

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