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Inserting Eq. (2.26) and Eq. (2.27) into Eq. (2.25) and rearranging gives an expression
for calculating the fluctuating flow velocity in HADT:
1 M aVMa dPM
uT [ m P 0.985 2 Ma
( ABH nBH ) PM sign( PM
)] (2.28)
A R T dt
Ta Tcs ugc Ma
2.4 Reverse flow and air transportation
2.4.1 Reverse flow calculation
Reverse flow occurs when the volumetric flow rate of the patient’s exhalation is greater
than the bias vent flow rate so the pressure in the mask increases. When it is higher than
that in the humidifier chamber, some of the air will be pushed back into the HADT.
Reverse flow can be calculated by integrating the possible negative part of the HADT
velocity in each breath cycle:
DRF uT dt
(2.29)
Where uT 0 , and integration range is repetitive within n tc t ( n 1) tc
for each
breath cycle while n 0,1,2,...
Flow and reverse flow in the HADT is simplified by assuming that they displace each
other. Although mixing near the interface of fresh air and exhaled air produces a
gradient of concentration, it is not expected to significantly influence the condensation
and CO 2 in the re-breath.
2.4.2 Varying transport delay analysis
For dynamic and reverse flow situations, tube air flow velocity is fluctuating with time
and can be negative when reverse flow occurs. That is to say, within a breath cycle, air
is mainly flowing from the chamber towards the mask then the patient. However, for a
short fraction of time within the cycle, air is pushed back by exhalation from the mask
towards the chamber. For analysing and mimicking the humid air, the HADT is divided
into 30 lumps with each lump of 5.75 cm (1.725 m/30). Due to the varying airflow
velocity, time for air flowing over one lump’s length is also fluctuating. This fluctuating
time may be derived as follow:
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