acp psentation

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Analysis of Biological Signals using Nonlinear
techniques (Chaos Theory).
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Analysis techniques have evolved for examining
complex physiological rhythms.
Classical approaches - decrease degrees of
freedom, tease apart the system and
test local feedback loops Integrative
approaches - view the whole system -respira
tory control dynamics are expressed in the
rate or period of breathing.
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Bernoulli Eqn. X(n1)2xn(mod 1)
Respirogram from normal infant. (? Equation)
Resting human respiration displays deterministic
chaos. Donaldson,(1992) Respir. Physiol.
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Deterministic systems display rule-obeying,
interactive behaviour.
Hypothesis
That determinism as measured by a chaotic
mathematical tool can quantify health from
disease and delineate physiological state.
Further, noninvasive measures of respiratory
period are adequate primary data sources.
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• How do we detect Chaos?
• It is both deterministic and aperiodic
• Chaotic systems exhibit sensitive dependence on
  initial conditions.
• Chaotic behaviour is bounded.
• Chaotic behaviour has a finite form.

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Recipes for Chaos

• Ignorance if you dont know whats happening
  then results are surprising
• Simple systems interacting
• Single system developing in time
• Some quantum system eg. radioactive decay.

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Phase Plane Plots

• Phase plane plots represent the behaviour of a
  dynamic system in state space.
• Typically, a plot of the variable vs. its first
  derivative.
• Each cycle is called a trajectory.

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Lyapunov Exponent

• Lyapunov Exponents are a measure of the rate of
  divergence of parallel orbits in an attractor.
• gt2 usually denotes a chaotic system

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Measure of Central Tendency (CTM)

• Using difference plots a (n2)-a (n1) vs. a
  (n1) an
• Count no. of points falling within radius r and
  dividing by total no. of points.

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If the system applies the same or similar rules
then response patterns will recur.
I am Sam. That Sam I
am! That Sam I am! I do not like that Sam I am!
. . . I do so like
green eggs and ham ! Thank you! thank you, Sam I
am !
WORD COUNT 512 VOCABULARY 50
Dr. Theodor Seuss Geisel, Beginner Books, Random
House Inc., 1960.
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Applying a Recurrence Quantification Analysis...
GREEN
GREEN
GREEN
GREEN
GREEN
GREEN
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Apply RQA to real data.
Discrete data are lagged and embedded to be
viewed in m dimensional space. The result is
vector with magnitude E SQRT((x(t)2 x(tT)2...
x(t(m-1)T)2)
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A recurrence matrix can then be produced from the
time series data plotted against itself. Local
recurrences denote repetition of a patterned
response by the control system.
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RQA 500 breath time series
REM epoch (Control Infant) REM epoch
(BPD Infant)
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• RQA of Shuffled data.
• Same mean,SD
• Reduced recurrence and determinism.
• Destruction of all patterning

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Mean 95 CI. for resp. period determinism ()
Control and BPD infants in REM and NREM states.
Determinism ()
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Results Summary REM NREM Controls 88 97
pltlt.05 BPD Infants 95 99 plt.05 plt.05 p
gt.05
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• Conclusions
• RQA can delineate physiological states and
  respiratory disease states can be quantified with
  respect to control dynamics.
• Data can be collected noninvasively and
  concurrent with conventional monitoring.

The more chaotic state seen in the healthy group
is consistent with chaotic dynamics of adult
CHF. Poon.et al (1997) Nature
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Summary Chaos can be detected using phase
plane plots, difference plots and recurrence
analysis. Objective measures are Lyapunov
Exponent(s), CTM and determinism/recurrence.
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Further reading CHAOS James Gleick, Cardinal.
1987.