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Individuality of breathing patterns in patients under noninvasive mechanical ventilation evidenced by chaotic global models
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10.1063/1.4794435
/content/aip/journal/chaos/23/1/10.1063/1.4794435
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4794435

Figures

Image of FIG. 1.
FIG. 1.

Excerpts of the time series recorded in a patient-ventilator system with inefficient inspiratory efforts inducing NT.

Image of FIG. 2.
FIG. 2.

Phase portraits reconstructed from the airflow measured in our patients using delay coordinates. The value of the high ventilatory pressure —reported for each subject—is the value for which the rate of untriggered cycles was the smallest. The time delay is .

Image of FIG. 3.
FIG. 3.

Shannon entropy SP versus Shannon entropy ST for the data sets recorded during the protocol. Integers i ( ) designate subjects Si for the six mesurements at different values. Letters A, B, and C designate subjects , and S 12, respectively. The dashed lines represent the threshold beyond which the events become significant (see the main text).

Image of FIG. 4.
FIG. 4.

Chaotic solution to the RBF model obtained from breathing data of subject S 3 with . Measured data (grey disks) used for estimating the model and the Poincaré section (red—online only—thick line) are also represented. Width of the RBF function: .

Image of FIG. 5.
FIG. 5.

First-return map to a Poincaré section of the model attractor for subject S 3 defined by for decreasing Pt (see Fig. 4 ). Qn is the nth value of the flow in this Poincaré section.

Image of FIG. 6.
FIG. 6.

Bifurcation diagram of the RBF model, flow Qn , versus parameter . The attractor in Fig. 4 is obtained for , which lies outside of this plot period-doubling cascade.

Image of FIG. 7.
FIG. 7.

First-return map to a Poincaré section of the attractor reconstructed from the data measured in subject S 3. The section is defined by for decreasing Pt . Qn is the nth value of the flow in this Poincaré section.

Image of FIG. 8.
FIG. 8.

Unimodal chaotic solution to the RBF model obtained from breathing data. Parameter: .

Image of FIG. 9.
FIG. 9.

First-return map to a Poincaré section of the unimodal chaotic model attractor shown in Fig. 8 .

Image of FIG. 10.
FIG. 10.

Two unstable periodic orbits embedded within the unimodal chaotic model attractor. Four positive crossings—not clearly distinguished in this projection—and two negative crossings are identified. The linking number is equal to +1.

Image of FIG. 11.
FIG. 11.

Template of the unimodal chaotic attractor.

Image of FIG. 12.
FIG. 12.

Toroidal chaos solution to the model estimated from the data measured in subject S 9 ventilated with . The Poincaré section was defined by . Width: .

Image of FIG. 13.
FIG. 13.

Phase portrait solution to the model estimated from the data measured in subject S 1 ventilated with . The Poincaré section was defined by . Width: .

Image of FIG. 14.
FIG. 14.

Phase portrait solution to the model estimated from the measured data in subject S 11 ventilated with . The Poincaré section was defined by . Width: .

Image of FIG. 15.
FIG. 15.

Phase portrait solution to the model estimated from the data measured in subject S 5 ventilated with . Width: .

Image of FIG. 16.
FIG. 16.

Phase portrait solution to the model estimated from the data measured in subject S 4 ventilated with . Width: .

Image of FIG. 17.
FIG. 17.

A 150 data points realization of yk . Five thousand realizations like this one were used to estimate in Eq. (A1) .

Image of FIG. 18.
FIG. 18.

Five thousand iterations of model (A2) .

Image of FIG. 19.
FIG. 19.

Histogram of values estimated for in Eq. (A1) using least squares.

Image of FIG. 20.
FIG. 20.

Inverted unimodal folded chaos solution to Sprott D system (B1) . Parameter value: .

Image of FIG. 21.
FIG. 21.

Branched manifold describing the topology of the chaotic attractor solution to the Sprott D system. The direct branched manifold—with the global torsion (a)—can be transformed into a simpler template (b).

Tables

Generic image for table
Table I.

Individual data (demographic, antropometric, and functional characteristics) of subjects included in the study. It is specified whether the subject was trained or not to breath assisted by a noninvasive mechanical ventilation. The rate of untriggered cycles is also reported. (Gender: F = female and M = male. BMI = body mass index, Patients with a chronic respiratory failure will be designated by “patient” and the normal subjects by “subject.” COPD = chronic obstructive pulmonary disease and OHS = obesity hypoventilation syndrome.)

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/content/aip/journal/chaos/23/1/10.1063/1.4794435
2013-03-08
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Individuality of breathing patterns in patients under noninvasive mechanical ventilation evidenced by chaotic global models
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4794435
10.1063/1.4794435
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