ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

solve all the governing equations.
Fig. 2 Transient velocity load.
4. RESULTS
Fig. 3 presents the flow rate through ostia during respiration. Since the flow through
ostia of sinus III was zero due to the incompressible assumption, we calculated the
absolute airflow rate passing through the ostium with the following equation:
F
v n dA
A (1)
where F is the rate of airflow entering the ostium, v is the velocity vector of the
airflow, n is the normal vector of the cross section of maxillary ostium and A is the area
of the cross section. The net volume flow rate in sinuses I and II were calculated as
2
F v ndA
(2)
A
In sinus I at 15 L/min, airflow through NO and AO2 was in opposite directions and
equal in magnitude during inspiration. Flow rates through both NO and AO2 increased
to a maximum within the first 0.4 second, and remained elevated throughout the whole
inspiration until the last 0.4 second. The inspiratory flow rate through AO1 was almost
zero. Compared to inspiration, during expiration, flow directions through NO and AO2
reversed, and flow through AO1 became significant. Flow rates through all three ostia
had the same pattern seen during inspiration: rapid early increase, peaking in the
middle, and decrease during the second half. Unlike inspiration, where AO1 had no
flow, during expiration, flow through NO was opposite in direction, and equal in
magnitude to, the summation of flows through AO1 and AO2. In both phases, flow
through AO1 was less than through the other two ostia. In sinus II at 15 L/min, the
airflow pattern during both inspiration and expiration was very similar to that of AO2
and NO in sinus I. The only difference from sinus I was that the direction of flow
through the NO was opposite in the two sinuses during inspiration, and that sinus II had
two short periods of low magnitude flow reversal, in both NO and AO, at the beginning
of both inspiration and expiration, a feature not seen in sinus I. In sinuses III, with no
AO, at 15 L/min, flow rates through the NO were markedly lower.