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Chapter 6 – High Frequency Percussive Ventilator characterization
The following mathematical equation, known as motion equation, describes its behaviour
P
rs
= K + E ⋅V
+ R ⋅V&
rs rs + Irs
⋅V&
where P
rs
is the pressure applied to the respiratory system, V is the pulmonary volume, V & is
the airflow and V & its derivative that represents flow acceleration; K represents the mouth
pressure when V , V & and V & are zero.
P
rs
and V & may be measured directly at the patient’s
mouth with a pressure transducer and a pneumotacograph, respectively. Volume and airflow
derivative are mathematically obtained from the airflow wave as its integral and its first
derivative, respectively. From the motion equation the values of the four unknown quantities
K (pressure offset),
E
rs
(elastance),
fitting the equation using the sampled values of
R
rs
(resistance) and I
rs
(inertance) can be estimated by
P
rs
, V , V & and V & . The term
Ers
⋅V
corresponds to the pressure necessary to balance elastic forces; it depends on both the volume
insufflated in excess of resting volume and the elastance of the respiratory system. On the
other hand the term
R
rs
⋅V&
corresponds to the pressure necessary to balance frictional forces; it
is mainly due to the resistance offered to the airflow. Lastly, the product
I
rs
⋅V&
corresponds to
the pressure necessary to overcome the system’s inertia (i.e. the inertance of the respiratory
system) which depends on the airflow derivative. Finally,
the resistive, elastic and inertial pressure drops of the respiratory system.
Prs − K corresponds to the sum of
6.2 Model parameters estimation
In order to estimate the three parameters of the respiratory system model we use the
multiple linear regression approach [Kaczka et al 1995]. The n acquired flow samples
together with their integral V
i
and derivative V & i
are used to build the first three columns of a
[n x 4] matrix A, whose fourth column is composed by 1’s. The corresponding n acquired
samples of pressure P
i
are used to create a [n x 1] vector B:
V &
i
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