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Complexity and pain

Complexity and pain. The problem Definitions and explanations of complex systems, chaos, dynamics and emergence Approaches in pain (and palliative care) with examples. Complexity of pain on the molecular level. Dorsal horn. Neuropeptid system. Opioid system. Cholezystokinin.

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Complexity and pain

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  1. Complexity and pain

  2. The problem • Definitions and explanations of complex systems, chaos, dynamics and emergence • Approaches in pain (and palliative care) with examples

  3. Complexity of pain on the molecular level

  4. Dorsal horn

  5. Neuropeptid system

  6. Opioid system

  7. Cholezystokinin

  8. Transduction (e.g. neurotrophins)

  9. Polysynaptic modulation • Transmitter substances have also effects outside of the synaptic cleft • Increased transmitter concentrations can lead to a rather excitatoric or inhibitoric tone • This regards specially G-protein coupled receptors

  10. Glia as neuromodulator • Astrocytes and glia eksprime receptors similar to neurons (evidence beyond others for NMDA, NK1, P2X4) • They send out transmitter substances (bl.a. SP, CGRP, glutamat), cytokines (bl.a. Il1, Il6, TNF) and modulate elimination of neurotransmitters • Possibly an important function in neuropathic pain Tsuda 2003

  11. Watkins 2002

  12. ?

  13. Santa Fe institute

  14. Principles of Complex Systems • Parts distinct from system. • System displays emergent order. • Not directly related to parts. • Define nature & function of system. • Disappear when whole is broken up. • Robust stability (“basins of attraction”). Emergent order = systemic properties which define health vs. disease.

  15. Principles of Complex Systems • Unpredictable response • Chaos or sensitivity to initial conditions. • Response determines impact to system • Controlled experiments: reproducible results • Uncontrolled patients: unpredictable results Host response is unpredictable, yet it determines outcome.

  16. Some explanations • Chaos (with help of Larry Liebovitch, Florida Atlantic University) • Dynamics (with help of J.C.Sprott, Department of Physics,University of Wisconsin – Madison)

  17. These two sets of data have the same • mean • variance • power spectrum

  18. RANDOM random x(n) = RND Data 1

  19. CHAOS Deterministic x(n+1) = 3.95 x(n) [1-x(n)] Data 2

  20. etc.

  21. RANDOM random x(n) = RND Data 1

  22. CHAOS deterministic x(n+1) = 3.95 x(n) [1-x(n)] Data 2 x(n+1) x(n)

  23. CHAOS Definition predict that value Deterministic these values

  24. CHAOS Definition Small Number of Variables x(n+1) = f(x(n), x(n-1), x(n-2))

  25. CHAOS Definition Complex Output

  26. CHAOS Properties Phase Space is Low Dimensional d , random d = 1, chaos phase space

  27. CHAOS Properties Sensitivity to Initial Conditions nearly identical initial values very different final values

  28. CHAOS Properties Bifurcations small change in a parameter one pattern another pattern

  29. Time Series X(t) Y(t) Z(t) embedding

  30. Phase Space Z(t) phase space set Y(t) X(t)

  31. Phase Space Constructed by direct measurement: Measure X(t), Y(t), Z(t) Z(t) Each point in the phase space set has coordinates X(t), Y(t), Z(t) X(t) Y(t)

  32. Analyzing Experimental Data The Good News: In principle, you can tell if the data was generated by a random or a deterministic mechanism.

  33. Analyzing Experimental Data The Bad News: In practice, it isn’t easy.

  34. Dynamics –the predator-prey example • A dynamic system is a set of functions (rules, equations) thatspecify how variables change over time.

  35. Rabbit Dynamics • Let R = # of rabbits • dR/dt = bR - dR = rR r = b - d Birth rate Death rate • r > 0 growth • r = 0 equilibrium • r < 0 extinction

  36. Exponential Growth • dR/dt = rR • Solution: R = R0ert R r > 0 r = 0 # rabbits r < 0 t time

  37. Logistic Differential Equation • dR/dt = rR(1 - R) 1 R r > 0 # rabbits 0 t time

  38. Effect of Predators • Let F = # of foxes • dR/dt = rR(1 - R - aF) Intraspecies competition Interspecies competition But… The foxes have their own dynamics...

  39. Lotka-Volterra Equations • R = rabbits, F = foxes • dR/dt = r1R(1 - R - a1F) • dF/dt = r2F(1 - F - a2R) r and a can be + or -

  40. Types of Interactions dR/dt = r1R(1 - R - a1F) dF/dt = r2F(1 - F - a2R) + a2r2 Prey- Predator Competition - + a1r1 Predator- Prey Cooperation -

  41. Equilibrium Solutions • dR/dt = r1R(1 - R - a1F) = 0 • dF/dt = r2F(1 - F - a2R) = 0 Equilibria: • R = 0, F = 0 • R = 0, F = 1 • R = 1, F = 0 • R = (1 - a1) / (1 - a1a2), F = (1 - a2) / (1 - a1a2) F R

  42. Stable Focus(Predator-Prey) r1(1 - a1) < -r2(1 - a2) r1 = 1 r2 = -1 a1 = 2 a2 = 1.9 r1 = 1 r2 = -1 a1 = 2 a2 = 2.1 F F R R

  43. Stable Saddle-Node(Competition) a1 < 1, a2 < 1 r1 = 1 r2 = 1 a1 = 1.1 a2 = 1.1 r1 = 1 r2 = 1 a1 = .9 a2 = .9 Node Saddle point F F Principle of Competitive Exclusion R R

  44. Coexistence • With N species, there are 2N equilibria, only one of which represents coexistence. • Coexistence is unlikely unless the species compete only weakly with one another. • Diversity in nature may result from having so many species from which to choose. • There may be coexisting “niches” into which organisms evolve. • Species may segregate spatially. • Purely deterministic (no randomness) • Purely endogenous (no external effects) • Purely homogeneous (every cell is equivalent) • Purely egalitarian (all species obey same equation) • Continuous time

  45. Typical Results

  46. Typical Results

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