Biomedical Engineering Reference
In-Depth Information
the other objects in the MDS map. Although well grouped, the nuclei of the CF lie
within the surface of the other two groups (healthy children and asthma). Our results
suggest that MDS may not be able to distinguish between pathologies with similar
manifestations (both asthma and cystic fibrosis show presence of mucus, etc.). In
children, the difficulty of diagnostic remains more pronounced than in adults. This
conclusion is supported by Fig.
8.17
depicting the corresponding dendrogram tree.
8.3 Revealing the Hidden Information in Breathing at Rest
8.3.1 Pressure-Volume Loops, Work of Breathing and Fractal
Dimension
A delay differential equation is a description where the evolution of a system at a
certain time, depends on the state of the system at an earlier time. Such a relation
is usually graphically analyzed by means of phase-plots. Hence, intuitively, there
must exist a relationship between the information extracted from the phase-plots and
fractional calculus. This motivates our interest in evaluating the dynamic patterns of
the breathing, since it may provide useful insight into relating the changes in airway
structure and tissue properties with the changes in the respiratory dynamics.
The pseudo-phase space is used to analyze signals with nonlinear behavior. For
the two-dimensional case it is called pseudo-phase plane (PPP) [
104
]. To reconstruct
the PPP it is necessary to find the adequate time lag between the signal and one de-
layed image of the original signal. Since PPP proved successful in various technical
applications, we propose the use of PPP tools to analyze data from lung function
tests in healthy subjects and in patients with respiratory disorders. The novelty of
the proposed methodology is to combine the information from PPP with the corre-
sponding fractal dimension computed using the box-counting method. In this way,
the fractal dynamics of the respiratory system can be assessed and further analyzed.
One of the most common clinical features extracted from lung function tests is
the air-pressure and the airflow variation during forced breathing or during breathing
at rest. A standard measure of the work of breathing in lung function analysis is
obtained by means of pressure-volume loops acquired during spirometry (i.e. by
means of forced breathing maneuvers).
In clinical terms, the air-pressure and air-volume variations in one breathing cycle
plotted against each other form a closed loop known as the PV loop [
112
]. The area
inside this loop, and the slope of the axis of the minimal-to-maximal points in the PV
loop are used to evaluate the respiratory mechanics of the patient. The interpretation
of the PV loop is then made with respect to inspiratory and expiratory parameters,
such as airflow resistance and work of breathing.
The PV loops are defined by
T
T
Area
=
V(t)dP(t)
=
P(t)dV(t)
(8.17)
0
0
