Pulmonary Math Questions (Exam III)

Question 1

Calculate the partial pressure of inspired humidified O₂ .

Answer 1

P_IO₂ = F_IO₂ (P_B - P_H₂O )

P_IO₂ = 0.21 (760mmHg - 47mmHg)

P_IO₂ = 150 mmHg

Question 2

How can alveolar minute volume be calculated?

Answer 2

V̇_A = V̇_T - V̇_D

4200mL/min = 6000mL/min - 1800mL/min

Question 3

What is the percentage of O₂ in a humidified inspiration?

Answer 3

19.69%

↓

149.7 ÷ 760 = 19.69%

Question 4

How much O₂ is in a V_A inspiration?

Answer 4

• 68.9 mL O₂

350mL x [0.1969] = 68.915 mL O₂

Question 5

How much of V_A O₂ (in mLs) leaves per exhaled breath?

Assume P_AO₂ = 104mmHg

Answer 5

P_AO₂ after equilibrium = 104mmHg
↓
104mmHg ÷ 760mmHg = 0.1368 O₂ content.
↓
350mLO₂ x 0.1368 = 47.88 mLO₂
=
47.88 mL O₂ is unabsorbed with each breath.

Question 6

How much of V_A O₂ (in mLs) is absorbed per breath?

Assume P_AO₂ = 104mmHg

Answer 6

Total inspired O₂ per breath = 68.915 mLO₂
↓
Total expired O₂ per breath = 47.88 mL O₂
↓
68.915 - 47.88 mLO₂ = 21.035 mLO₂ absorbed per breath.

Question 7

How much total O₂ is exhaled per breath?

Answer 7

V_A = 350mL
V_D = 150mL
↓
350mL x 0.1368[O₂] = 47.88mLO₂
+
150mL x 0.1969[O₂] = 29.54mLO₂
↓
= 77.42 is the total O₂ (both V_A and V_D) expired per breath.

Question 8

How much CO₂ is exhaled per minute?

Assume the patient has a respiratory rate of 12bpm and give your answer in liters.

Answer 8

P_ACO₂ = 40mmHg
↓
V_D CO₂ content = 0
+
V_A CO₂ = 40mmHg ÷ 760mmHg = .0526
↓
350mL x 0.0526[CO₂] = 18.42mLCO₂
↓
18.42mLCO₂ x 12bpm = 0.221 Liters of CO₂ per minute.

Question 9

Suppose you had a spirometer of 10L with a Helium concentration of 10%.

After being attached to a patient and a respiratory cycle, the helium concentration becomes 8%.

What is the patient’s FRC?

Answer 9

1L He starting out
↓
0.08 * x = 1L He
↓
x = 12.5 (new total volume)
↓
12.5 - 10 = 2.5L = FRC

Question 10

Calculate the normal Minute Alveolar Ventilation rate.

What will Alveolar PO2 be at the calculated Minute Alveolar Ventilation rate?

Answer 10

4.2 L/min

Respiratory Rate x Alveolar Volume
12 breaths/min x 350 mL = 4200 mL/min

At 4.2 L/min, PAO2 will be about 100 mmHg

Question 11

Calculate the normal Minute Dead Space Ventilation rate.

Answer 11

1.8 L/min

Respiratory Rate x Dead Space Volume
12/breaths/min x 150 = 1800 mL/min

1.8 L/min

Question 12

Calculate the oxygen concentration after it has been inspired and displaced by water vapor.

Answer 12

Partial Pressure of O2 = [O2] x Total Pressure
[O2] = Partial Pressure of O2 / Total Pressure
[O2] = 149 mmHg / 760 mmHg
[O2] = 0.1961
[O2]= 19.61%

Question 13

How much O2 is brought into the gas exchange region during each breath?

Answer 13

VA (volume of air for gas exchange) = 350 mL
[Inspired O2] = 19.61%

350 x 0.1961=
68.62 mL of O2 enter the gas exchange region.

Question 14

How much O2 is expired from the gas exchange regions during each breath?

Answer 14

VA (volume of air for gas exchange) = 350 mL
PAO2 (alveolar PO2 after gas exchange) = 100 mmHg
Total Pressure = 760 mmHg

Need to calculate [O2] after equilibrium (gas exchange)
[O2 after equilibrium] = PAO2 / Total Pressure
[O2 after equilibrium ] = 104 / 760
[O2 after equilibrium] = 0.1368

mL of O2 expired = [O2 after equilibrium] x VA
mL of O2 expired = [0.1368] x 350 = 47.89

47.89 mL expired from the gas exchange region during each breath

Question 15

How much O2 is normally absorbed over the course of one breath?

How much O2 is normally absorbed in one minute?

Answer 15

O2 is brought into the gas exchange region during each breath: 68.62 mL

O2 is expired from the gas exchange regions during each breath: 47.89 mL

68.62 - 47.89 =
20.73 mL of O2 absorbed during each breath

20.73 x 12 breaths/min = 248.76 mL absorbed/min

Question 16

How many mL/dL of O₂ return to the heart from systemic circulation?

Answer 16

• 15 mL/dL

Question 17

How many mL/dL of O₂ leave the heart?

Answer 17

• 20 mL/dL

Question 18

Calculate cardiac output from the following parameters:
- V̇O₂ = 240 mLO₂
- Arterial O₂ = 20 mLO₂
- Venous O₂ = 14 mLO₂

Answer 18

4 L/min

Question 19

Calculate the concentration of PCO2 in the lungs at FRC.

Calculate the amount of CO2 in the lungs at FRC.

What will be the new concentration of CO2 if 350 mL of fresh air enters the lung?

What will be the new PCO2 in the lungs?

Answer 19

40 mmHg/ 760 mmHg = 0.05263
[CO2] = 5.26%

0.05263 x 3L = 157.89 mL of CO2

157.89 mL / 3350 mL = 0.0471
New [CO2] = 4.71%

760 mmHg x 0.0471 = 35.7 mmHg
New PCO2 = 36 mmHg

Question 20

If the partial pressure of oxygen is 100 mmHg, how many mL of O2 is dissolved in each dL?

Answer 20

100 mmHg PO2 x 0.003 mL O2/ (mmHg PO2 x dL) = 0.3 mL O2/dL

Question 21

If the partial pressure of oxygen is 40 mmHg, how many mL of O2 is that per dL?

Answer 21

40 mmHg PO2 x 0.003 mL O2/ (mmHg PO2 x dL) = 0.12 mL O2/dL

Question 22

At a saturation of 100%, how much O2 will be bound to Hgb?

What about at 75% saturation?

Answer 22

20.1 mL O2/dL of blood will be bound to Hgb at 100% saturation.

20.1 x 0.75 = 15 mL O2/dL of blood

Question 23

Look at the anemia curve. At a PO2 of 100 mmHg, how much O2 mL will be carried/ dL of blood?

Answer 23

Anemia = 6 g Hgb / dL of blood
1.34 mL of O2/ g Hgb

6 g Hgb/ dL of blood x 1.34 mL of O2/ g Hgb = 8.04 mL of O2/ dL of blood

Even with anemia, there is still enough oxygen to meet the metabolic demand of 5 mL of O2/dL of blood for systemic circulation.

Question 24

Calculate total oxygen in arterial blood.

Answer 24

20.1 + 0.3 = 20.4

CaO2 = 20.4 mL O2/dL of blood
Dr. Schmidt used 100% saturation instead of 97.4% saturation

Question 25

Calculate total oxygen in venous blood.

Answer 25

15.08 + 0.12 = 15.2

CvO2 = 15.2 mL O2/ dL of blood

Question 26

Calculate how much O₂ is dissolved per deciliter of arterial blood.

Answer 26

0.3 mL O₂ / dL of blood

Question 27

Calculate how much O₂ is dissolved per deciliter of venous blood.

Answer 27

(0.003 mL O₂ / 100mL blood x PO₂) x 40 mmHg =

0.12 mL O₂ / dL of blood

Question 28

What would be the carrying capacity of someone who had a hemoglobin of 10 g/dL and Hb carrying capacity of 1.2 mLO₂ /gHb ?

Answer 28

12 mLO₂ / dL of blood

Question 29

What is the CaO₂ assuming an SaO₂ of 97.4%, and PO₂ of 100mmHg?

Answer 29

19.88mL O₂ /dL blood

(dissolved: 0.3 mLO₂) + (Hb-bound 19.58 mLO₂)

Question 30

What is the CvO₂ assuming an SvO₂ of 75%, and PvO₂ of 40mmHg?

Answer 30

15.195 mLCO₂ / dL blood

Dissolved: 0.12 mLCO₂
Bound: 15.075 mLCO₂

Question 31

How much CO₂ is dissolved in arterial blood?

Answer 31

0.06 mLCO₂ x 40 mmHg (PCO₂) = 2.4 mLCO₂ per dL of blood

Question 32

What is the partial pressure of CO₂ in Ē (mixed expired air) ?

Find PCO₂ of Ē

Answer 32

PCO₂ of V_D = 0
PCO₂ of V_A = ?

40mmHg ÷ 760mmHg → [CO₂] of 0.05263 → 350mls (V_A) x 0.05263 = 18.42 mLs CO₂ per breath.

18.42 mLs CO₂ ÷ 500mLs = 0.03684 → 760mmHg x 0.03684 = 27.998mmHg

PCO₂ of Ē = 27.998mmHg

Question 33

How much CO₂ is dissolved in venous blood?

Answer 33

0.06 mLCO₂ x 45 mmHg (PCO₂) = 2.7 mLCO₂ per dL of blood

Question 34

Give an example of a Bohr equation with numbers.

Answer 34

V_TotalDS / V_T = (40mmHg - 28mmHg) ÷ 40mmHg

0.3 = V_TotalDS ÷ 500mL

V_TotalDS = 150mL

Question 35

How would one find alveolar dead space?

Answer 35

V_AlveolarDS = V_TotalDS - V_AnatomicDS

Question 36

How can anatomical dead space be estimated?

Answer 36

1mL of deadspace per 1lb of body weight

(Ex. 200lbs = 200mL anatomic deadspace)

Question 37

Solve for Respiratory System Compliance.

Answer 37

• C_L = 0.2
• C_CW = 0.2
• x = C_RS

(1÷x) = (1÷0.2) + (1÷0.2)
↓
(1÷0.1) = (1÷0.2) + (1÷0.2)
↓
C_{TotalCompliance(RS)} = 0.1L / cmH₂O

Question 38

A 100kg patient presents with a P_ĒCO₂ of 25mmHg, a V_T of 600mls, and a PaCO₂ of 42mmHg. What would the estimated alveolar dead space of this patient be?

Answer 38

V_A = ?
V_T = 600mls
V_Anatomic = 220mls (100kg x 2.2 = 220lbs)

V_D ÷ 600mls = (42 - 25) ÷ 42
V_D = 242.86mls

V_A = 22.86mls (242.86mls - 220mls)

Question 39

What is Fick’s Principle/Equation?

Answer 39

CO = O₂ consumption ÷ (CaO₂ - CvO₂)

Question 40

A patient has the following parameters:

• O₂ consumption of 750 mLO₂ / min
• Hgb of 15g/dL
• SvO₂ of 25%

What is the cardiac output of this patient?

Answer 40

CO = O₂ consumption ÷ (CaO₂ - CvO₂)

CO = 750 mLO₂/min ÷ (20 mLO₂/dL - 5 mLO₂/dL)

CO = 50 dL /min
↓
CO = 5L/min