Resting Physiologic Perturbations

Respiratory activity, which may either be at fixed-rate or random-intervals [1], is modeled in terms of $Q_{lu}(t)$. Fixed-rate $Q_{lu}(t)$ is represented by a pure sinusoid, which is characterized by tidal volume ($Q_{t}$) and respiratory period ($T_r$), as well as a DC offset representing the functional reserve volume of the lungs ($Q_{fr}$). Each respiratory cycle of random-interval $Q_{lu}(t)$ is also represented by one period of a sinusoid with the DC offset $Q_{fr}$. 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 ($Q_{ds}$)) is identical to that of fixed-rate breathing.

In order to account for the mechanical effects of $Q_{lu}(t)$ on $P_{th}(t)$ and $P_{alv}(t)$, 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 ($R_{air}$) 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 ($Q_{lu}^0$) in addition to $C_{lu}$.

  

Figure 6: Electrical circuit analog of the human ventilatory mechanics model.

The systemic effects of the autoregulation of local vascular beds is represented with an exogenous disturbance to $R_a(t)$ 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 $F(t)$ convolved with a filter defined by a linear combination of $s(t)$ ($\beta$-sympathetic sublimb) and $p(t)$. 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 $^{\,alpha}$ magnitude squared frequency response from $10^{-4}$ Hz to 1 Hz, where alpha is set to one. Each of these exogenous disturbances are treated as unobservable quantities.