Principles of ultrasonic flow meter. Flow and molar mass of the inhaled and
exhaled gas were measured with the ultrasonic flow meter (13). Figure 1 shows a
schematic cross-section of the flow meter. The instrument simultaneously measures
flow and molar mass by transmitting an ultrasonic pulse from transducer Tr1 and
receiving the pulse at transducer Tr2. Shortly afterwards an ultrasonic pulse is transmitted from transducer Tr2 and received by Tr1. Both upstream and downstream
transit times are electronically measured. The flow can be computed using the
formulas for the upstream and downstream ultrasonic transit times, tu and td:
tu =
L
;
c + u cos
td =
L
c u cos
[1]
where L is the length of the sound transmission path, c is the sound velocity of the
medium, u is the mean flow velocity in the flow tube and
is the angle between the
flow and the sound path. Using the formulas [1] the speed of sound can be eliminated
and the flow can be computed independent of the gas composition.
The following formula for ideal gases can be used to compute the molar mass of the
gas:
c=
where
R T
M
[2]
is the relation of the specific heat capacities cp/cv, R is the gas constant, T the
temperature and M the molar mass. By combining formulas [1] and [2] the molar
mass can be computed as follows:
M =
4
R T 2
L
tu t d
tu + t d
2
If , R and L are constant the molar mass can be computed using the measured transit
times tu and td and the temperature T of the gas. In the ultrasonic flow meter the
upstream- and downstream transit times are measured each 5 ms with a resolution of
[3]
10 ns. The temperature T along the sound transmission path, however, must also be
determined with high accuracy. Due to the rapid temperature changes, pressure
transients and high humidity, measuring the mean temperature along the sound
transmission path is an extremely complex task. The software of the ultrasonic flow
meter uses a combination of relatively simple temperature measurements and a
mathematical model to estimate the temperature profile along the sound transmission
path. The mathematical temperature model uses the measured flow, instrument dead
space volumes, preset inspiratory and expiratory temperatures, and the temperature of
the flow sensor housing to estimate the mean temperature along the sound
transmission path. We have previously shown that the molar mass signal is strongly
linearly related to the SF6 concentration of the breathing gas (6). The ultrasonic
transducers of the flow meter are placed inside chambers which are separated by gas
permeable filters from the flow channel. Due to these side chambers the molar mass
of the flow channel is not identical to the mean molar mass along the entire sound
transmission path. In order to compensate for this effect the molar mass inside the
side chambers must be determined and proportionally subtracted from the mean molar
mass signal measured by the instrument. This additional compensation is achieved by
a simple mathematical model that simulates the diffusion of gas through the filters
into the side chambers.
In the present study we used 5 % SF6 and 95 % oxygen as the washout gas rather
than 100% oxygen, because 5 % SF6 results in a greater change of molar mass than
using pure oxygen alone (changes in molar mass are 7.3 and 3.15 g . mol-1,
respectively), and the gas mixture has a higher signal-to-noise ratio. The molar mass
of the gas can be measured with a resolution of 0.01 g . mol-1. Using the molar mass
signal, the difference between the instantaneous inspiratory SF6-O2 fraction and the
SF6- O2 fraction at the end of the washin was obtained and the SF6-O2 flow was
calculated as the product of instantaneous airflow and the difference. The SF6-O2 flow
was then integrated over time to give the inspired SF6-oxygen volume. The FRC of
the SF6-O2 washin was obtained by dividing the measured inspired SF6-O2 volume
with the end tidal SF6-O2 concentration of the SF6-O2 at the end of the washin.