Non linearity

1. A Non Linear Model to explain
persons with Stroke
K Hari ohm
Professor in PT
MSAJ college of PT
The Indian Centre for Evidence Based
Neuro-Rehabilitation

2. Introduction
• Humans like many
natural systems are
complex
• How do we commonly
study complex systems

3. Reductionism
• Reductionism - understanding
the nature of complex things by
reducing them to simpler or
more fundamental things
• Philosophical position that a
complex system is the sum of its
parts, and that an account of it
can be reduced to accounts of
individual constituents
• Reductionism is the belief that
human behavior can be
explained by breaking it down
into smaller component
parts. Reductionism and Holism in
Psychology by Saul McLeod

4. What is linearity
• Linearity
• Linear systems satisfy the
properties of superposition and
homogeneity.
• Add them up
• Starting state- predictability of
complex system
• Point to point relation

5. Applying reductionism in
understanding and managing stroke

6. Why is not my patient walking?
• Spasticity
Impairments • weakness
• Inability to walk
Disability • unable to eat
• Unable to go to work
• Unable to go to
handicap marriage

7. Paraphrasing Esther Thelen question
WHAT IS THE DIFFERENCE BETWEEN A
PATIENT WHO HAS LEARNED TO WALK
AND WHO HAS NOT?
•IS BIOLOGICAL FACTORS ENOUGH ?
•CAN HUMAN SYSTEM BE SUBJECTED TO
REDUCTIONISM ?

8. Paradigm shift

9. • Will be true if it is a Simple system or Static
1. Human systems are dynamic and complex
2. Variable

10. Understanding variations
• In human biology
– variation is normality
• Behavioural variability
• Movement variability
– Throw darts- for example, we are unable to hit the
‘bull’s eye’ on every attempt.
– When we walk, our footprints never repeat themselves
exactly.
– When we stand quietly, we continuously sway around a
central equilibrium point without ever remaining
exactly still

11. Example of Increased
Stride Time Variability in Elderly Fallers
Quantification of Stride-to-Stride Fluctuations
Time (min) Time (min)

13. Variability or noise
• James Clerk Maxwell (1879), Henri Poincare
(1912), Edward Lorenz 1961

14. Non linearity
• This paradigm has no single name but has
been described in terms of
1. Chaos
2. Nonlinear dynamics (sometimes called
nonlinear dynamical systems theory),
3. Complexity theory
4. Self-organization. Scott Barton January 1994 • American Psychologist
Chaos, Self-Organization, and Psychology

15. What is Non linearity ?
• “Nonlinear dynamics,” can be defined as a
system whose output is not proportional to its
input.
• Nonlinear systems are more complex

16. Nonlinear
• Nonlinear equations are not additive;
therefore, they are often difficult to solve.
• Sometimes a single solution can be obtained,
but often the answer involves a pattern of
solutions.
• Nonlinear systems tend to settle down over
time.

17. • Human beings are nonlinear because a small
change in input can lead to a huge and
unpredictable change in output.
• A minor change in initial conditions may lead
to a significant, abrupt change of behavior

18. Some properties of non-linear
dynamic systems are:
• They do not follow the principle of
superposition (linearity and homogeneity)

19. • Timing and form of such changes are not fully
predictable due to the complexity of the
system
• They may have multiple isolated equilibrium
points (linear systems can have only one)
• They may exhibit properties such as
bifurcation, chaos, self organization
emergence etc.

20. COMPLEX SYSTEM

21. Complex system
• Fundamentally a system is
complex, if its behavior
cannot be easily described.
• System consists of many
components,
• Numerous relationships and
interactions between these
components.
• This is a nonlinear system
because the input does not
lead to a linear change in
output.
Balance control in hemiparetic stroke patients: Main tools
for evaluation Clarissa Barros de Oliveira et al J Rehabil
Res Dev. 2008;45(8):1215-26.

22. Non linearity
• One of the fundamental principles of complex
systems is non linearity
• Complex systems are dynamical systems they
change over time
• Difficult to determine the boundaries of a
complex system

23. • interdependence of variables in a nonlinear
system, along with sensitivity to initial
conditions, lead to the implication that
studying each factor in isolation may not lead
to useful knowledge about the behavior of the
system as a whole

24. IMPLICATION FOR STROKE
MANAGEMENT

25. Model of a
person with
stroke in non
linear complex
system
From Stroke rehabilitation : a functional activity based approach K Hari ohm R Vasanthan

26. Implication for stroke management
• Non linear systems are hard to solve
– They cannot be broken into parts