Respiratory activity, which may either be at fixed-rate or
random-intervals [1], is modeled in terms of
. Fixed-rate
is represented by a pure
sinusoid, which is characterized by tidal volume (
) and
respiratory period (
), as well as a DC offset representing the
functional reserve volume of the lungs (
). Each respiratory
cycle of random-interval
is also represented by one period
of a sinusoid with the DC offset
. However, the period is not
constant here but rather determined based on the outcome of a
probability experiment (which ranges from one to 15 seconds with a
mean of five seconds), and the tidal volume is set such that the
instantaneous alveolar ventilation rate (which considers the dead
space in the airways (
)) is identical to that of fixed-rate
breathing.
In order to account for the mechanical effects of on
and
, the simple model of ventilation,
illustrated in Figure 6 in terms of its electrical circuit
analog, is also incorporated in the model. The electrical components
may be interpreted similarly to those in Figure 1 by
considering air here rather than blood. Hence, the resistor
(
) may be thought of as a conduit for airflow between the
atmosphere and the lungs, while the capacitor may be interpreted as an
air volume container representing the lung compartment, which is
parametrized by an unstressed volume (
) in addition to
.
The systemic effects of the autoregulation of local vascular beds is
represented with an exogenous disturbance to which is defined
by a bandlimited Gaussian white noise process. This process is
created by convolving Gaussian white noise of zero mean and stdwr standard deviation with a lowpass filter (truncated unit-area
sinc function) of desired frequency cutoff (fco). Higher brain
center activity impinging on the ANS is modeled with a 1/f
exogenous, Gaussian disturbance to
convolved with a filter
defined by a linear combination of
(
-sympathetic
sublimb) and
. The 1/f Gaussian disturbance is created by
convolving Gaussian white noise of zero mean and stdwf standard
deviation with a unit-area filter of 1/f
magnitude
squared frequency response from
Hz to 1 Hz, where alpha is set to one. Each of these exogenous disturbances are
treated as unobservable quantities.