eLFH - Preoxygenation and 'e'

Question 1

How is alveolar ventilation usually modelled

Answer 1

As a continuous process rather than the tidal nature of alveolar ventilation

Therefore made into an approximation as it is treated as continuous flow

Question 2

Assumptions made with preoxygenation to predict FAO2 with fall in FAN2

Answer 2

Oxygen replaces Nitrogen molecule for molecule i.e Rise in FAO2 is equal to fall in FAN2

Preoxygenation is perfect with no leak

Tidal ventilation can be approximated with continuous flow

Ignore marginal impact of tissue stores of nitrogen

Question 3

Table highlighting ratio of de-nitrogenation with FAN2 and FAO2 as number of breaths in given time period increases

Answer 3

Question 4

Formula for proportional dilution for given time period with n as number of breaths

Answer 4

Proportional dilution = (n/n+1)^n

Question 5

Why is time period of 30 seconds used for this modelling

Answer 5

It is the time constant (flashcard later on this)

As using values of FRC = 2L and alveolar ventilation 4L/min

Therefore in 30 seconds, FRC and alveolar ventilation are both 2L so the flow matches the container volume for this time period

Time period chosen should reflect the flow required to fill the container being used

Question 6

What happens as number of breaths per cycle ‘n’ increases

Answer 6

Proportional dilution increases at a decreasing exponential to a plateau

As n tends to infinity, the value reaches the limit

Question 7

e definition

Answer 7

Constant denoting the limit of (n+1/n)^n as n tends to infinity

n+1 > n, therefore e is >1

Question 8

e value

Answer 8

2.71828

Question 9

Limit for proportional dilution in preoxygenation

Answer 9

Proportional dilution with breaths = (n/n+1)^n
e is limit for equation y = (n+1/n)^n

Therefore limit for proportional dilution with breaths in cycle = 1/e
= e^-1
= 0.3678

Therefore with each cycle (30 seconds) FAN2 falls to 37% of value at start of previous cycle

Question 10

Value for e^-1

Answer 10

0.3678

Question 11

Assumption made when using e^-1 for dilutional proportion

Answer 11

Continuous rather than tidal flow

Question 12

Error margin when assuming continuous rather than tidal flow of alveolar ventilation

Answer 12

Eg. 6 breaths per cycle
(6/7)^6 = 0.3965
1/e = 0.3678

Low margin of error therefore acceptable to approximate with 1/e

Question 13

How long (with assumptions and measurements made thus far) will it take to achieve goal of FAO2 of 0.95

Answer 13

Starting values: FAN2 0.8, FAO2 0.15, FACO2 0.05
FACO2 will remain at 0.05

After first 30s FAN2 = 0.8 x 0.37 = 0.29
(FAO2 therefore = 0.15 + (0.8 - 0.29) = 0.65

After second 30s FAN2 = 0.29 x 0.37 = 0.11
(FAO2 therefore = 0.7 + (0.29 - 0.11) = 0.84

After third 30s FAN2 = 0.11 x 0.37 = 0.04
(FAO2 therefore = 0.89 + (0.11 - 0.04) = 0.91

After fourth 30s FAN2 = 0.04 x 0.37 = 0.01
(FAO2 therefore = 0.91 + (0.04 - 0.01) = 0.94

So would take 2 mins with all the assumptions made

Question 14

Equation for simple exponential wash out process

Answer 14

y = value of substance in question after wash out for period of time
(in these examples y = FAN2)

A = starting value prior to wash out (eg 0.8)
t = time period being studied (usually in minutes)
k = rate constant in a time dependent process

Here k = 2 as 2 cycles of 30 seconds occurs per 1 minute unit time

Question 15

Equation for standard exponential wash in process

Answer 15

Question 16

k rate constant for flow-container systems

Answer 16

k = Q / V

Ratio of flow to container volume

k is large if flow is large relative to container volume

Question 17

Time constant (tau)

Answer 17

Time taken for the flow to fill the container

Reciprocal of rate constant (k)

In this example, k = 4/2 = 2

Therefore tau = 1/2 = 1/2 minute = 30 seconds

Question 18

Approximate tissue store of nitrogen in adults

Answer 18

Same as volume of nitrogen in FRC

I.e 2 x 0.8 = 1.6 L

Question 19

Time constant for washout of tissue N2

Answer 19

~ 30 minutes

Compared with 30 seconds for FRC

Question 20

Why can we ignore tissue stores of Nitrogen with our modelling

Answer 20

Because the time constant is so much greater for tissues so minimal impact