Title: acp psentation
1Analysis of Biological Signals using Nonlinear
techniques (Chaos Theory).
2Analysis 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.
3Bernoulli Eqn. X(n1)2xn(mod 1)
Respirogram from normal infant. (? Equation)
Resting human respiration displays deterministic
chaos. Donaldson,(1992) Respir. Physiol.
4Deterministic 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.
5- 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.
6Recipes 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.
7 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.
8Lyapunov Exponent
- Lyapunov Exponents are a measure of the rate of
divergence of parallel orbits in an attractor. - gt2 usually denotes a chaotic system
9Measure 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.
10If 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.
11Applying a Recurrence Quantification Analysis...
GREEN
GREEN
GREEN
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12Apply 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)
13A 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.
14RQA 500 breath time series
REM epoch (Control Infant) REM epoch
(BPD Infant)
15- RQA of Shuffled data.
- Same mean,SD
- Reduced recurrence and determinism.
- Destruction of all patterning
16Mean 95 CI. for resp. period determinism ()
Control and BPD infants in REM and NREM states.
Determinism ()
17Results Summary REM NREM Controls 88 97
pltlt.05 BPD Infants 95 99 plt.05 plt.05 p
gt.05
18- 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
19Summary Chaos can be detected using phase
plane plots, difference plots and recurrence
analysis. Objective measures are Lyapunov
Exponent(s), CTM and determinism/recurrence.
20Further reading CHAOS James Gleick, Cardinal.
1987.