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Modeling the complexity of pain – possibilities and problems

Modeling the complexity of pain – possibilities and problems. Dorsal horn. Nevropeptidergisk system. Opioidergisk system. Cholezystokinin. Transduksjon (ved eksempel av nevrotrofiner). Polysynaptiske modulasjon. Transmittersubstanser diffunderer ogs å ut over det egentlige synapseområdet

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Modeling the complexity of pain – possibilities and problems

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  1. Modeling the complexity of pain – possibilities and problems

  2. Dorsal horn

  3. Nevropeptidergisk system

  4. Opioidergisk system

  5. Cholezystokinin

  6. Transduksjon (ved eksempel av nevrotrofiner)

  7. Polysynaptiske modulasjon • Transmittersubstanser diffunderer også ut over det egentlige synapseområdet • Diffusjonen fører til en heller ekscitatorisk eller inhibitorisk grunnsituasjon • Det gjelder spesielt for G-protein koblede reseptorer

  8. Glia som nevromodulator • Astrozyter og glia ekspremerer reseptorer i lignende omfang som nevroner (påvist bl.a. for NMDA, NK1) • De frisetter nevrotransmitter (bl.a. SP, CGRP, glutamat), cytokiner (bl.a. Il1, Il6, TNF) og modulerer nedbyggningen av nevrotransmitter • Muligens viktig funksjon ved opprinnelse av nevropatiske smerter

  9. Watkins 2002

  10. ?

  11. Santa Fe institute

  12. 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.

  13. 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.

  14. Approaches • The Bottom-Up approach • The hidden signals approach • The Top-down approach

  15. Hidden signals approach • Neurons and other structures do not only communicate by action potential frequencies • “Despite the multitude of physiologic signals available for monitoring, we suggest tha a wealth of potential valuable information that may affect clinical care remains largely an untapped resource” Goldstein 2003

  16. Dopaminergic neurons in Striatum (N. accumbens) can send two different informations, one frequency coded and one pattern (burst activity) coded Fiorillo 2003 • Burst patterns can transport informations over stimulation properties Krahe 2004

  17. Approximate Entropy • Natural information parameter for an approximating Markov Chain; closely related to Kolmogorov entropy • Can be applied to short, noisy series • 100 < N < 5000 data points • Conditional probability that two sequences of m points are similar within a tolerance r • Pincus SM, Goldberger AL, Am J Physiol 1994; 266:H1643 • Other entropy measures: • Cross-ApEn - compare two related time series • Sample entropy - does not count self matches • Richman JS, Moorman JR, Am J Physiol Heart Circ Phys 2000; 278:H2039.

  18. Inflammatory pain model • Identification of WDR Neurons in L4/L5 with their receptive fields • Injection of bee venom • WDR neurons showed different stable ApEN values

  19. ApEN time course of WDR neurons receiving peripheral nociseptive input

  20. Firing rate of WDR neurons receiving nociseptive input: spike number does not correlate with ApEN

  21. Firing rate of WDR neurons after morphine injection: Correlation with ApEN

  22. The bottom-up approach • Models to simulate physiologic and pathophysiologic dynamics • Mathematical models • Network models • Graphical models • Agent based systems

  23. Britton/ Chaplain/ Skevington (1996):The role of N-methyl-D-aspartate (NMDA) receptors in wind-up: a mathematical model • Base assumptions in the model: • One C-fiber, one A-fiber, which are connected to a transmission cell (WDR) in the dorsal horn. • The transmission cells gets input from inhibitory and excitatory interneurons and is sending signals to cells in the midbrain • Midbrain cells again send inhibitory signals directly to transmission cells and excitatory signals to inhibitory interneurons • The firing frequency of a particular cell is a function of ist slow potential

  24. Schematic diagram of the model

  25. Equations • The slow potential is defined as: V(t) = 1/s tt-1 V () d  ( s interval of time) • Frequencies xi, xe, xt, xm are functions of the slow potentials xi = i(Vi), xe= (Ve), xt = t(Vt), xm= m(Vm)

  26. Equations II • The effekt of an input frequency xj to a synapse of a cell of potential Vk will be to raise it by jk: (1) jk = jk t- hjk (t-) gjk (xj ()) d Where jk is equal to 1 for an excitatory synapse and -1 for an inhibitory synapse, hjk is a positive montone decreasing function and gjk is a bounded, strictly monotone increasing function satisfying gjk (0) = 0 • The simplest form for hjk is: (2) hjk (t) = 1/ k exp (- 1/ k)

  27. Equations III • The total effect of all inputs on the potential of cell k gives: (3) Vk = Vk0 +  jk Assuming that the system is linear

  28. Equation IV • Differentiating (3) using (1) and (2) yields: (4) kVk = - (Vk – Vk0) + jkgjk(xj)

  29. Model equations (5) iVi = - (Vi-Vi0) + gli(xI)+gmi(xm) (6) eVe = -(Ve-Ve0) + gse (xs,Ve) (7) tVt = -(Vt-Vt0) + gst(xs) + glt(xl) + get(xe) –git(xi) – gmt (xm) (8) mVm = -(Vm-Vm0) + gtm(xt)

  30. Results I: C fiber stimulation – increase of nociseptive output from the dorsal horn

  31. Results II: Large fiber activation leads to a transient increase, later to a decrease of nociseptive signals from the dorsal horn

  32. Results III: small fiber stimulation with Hz leads to wind-up like phenomena

  33. Top-down approach

  34. K2 K1 Coupling K12 Possible Role of Coupling between the Organs in the Development of Systemic Illnesses: Model of Coupled Stochastic Oscillators Anton Burykin*, Gernot Ernst**, Andrew JE Seely*** * Department of Chemistry, University of Southern California, Los Angeles (bourykin@usc.edu, http://futura.usc.edu/wgroup/people/anton/index.htm) ** Kongsberg Hospital, Norway (gernot.ernst@blefjellsykehus.no) *** Divisions of Thoracic Surgery & Critical Care Medicine, University of Ottawa, Ottawa, Ontario, Canada (aseely@ottawahospital.on.ca) The Approach: Preliminary Results: Stochastic Harmonic Oscillators Motivation The origin of the statistical differences between the patterns of variation of physiological signals (e. g. heart rate or respiratory variability) in health compared to illness states or aging remains a clinically relevant and unsolved problem [1, 2]. A current hypothesis [2] suggests that states involving systemic illness, e.g. multiple organ dysfunction (MOD) or aging, occur due to the uncoupling and/or change in communication between single organs or subsystems. In order to test this hypothesis, we suggest here several possible dynamical models (constructed from the network of coupled elements) of the multiple organ system (the organism) and compare their behavior in different regimes of coupling between their elements. A. Effect of Uncoupling B. Constant Frequency vs. Noisy Mechanical Ventilation Models • “organism” is represented as a system of “organs”; • each “organ” has its own “rhythm” (rate or frequency), which itself is changing with time; • “organs” (and their “rhythms”) are coupled to each other (the physiological examples of coupling include neural, humoral, mechanical, etc…). log(P) Fig 1. Approximate entropy and standard deviation as functions of the coupling coefficient for the case of two (left) and five (right) “organ” systems. log(f) Fig 2. Simulation of the effect of mechanical ventilation with the constant frequency for the case of the “organism” with just two “organs”. (left) Approximate entropy and standard deviation of the first “organ” in the control and during the fixing the frequency of the second one for several values of the coupling between the organs. (right) Change of the slope in log-log representation of the power spectra of the first oscillator. Coupled linear (harmonic) stochastic oscillators: Conclusion These results supports the hypothesis that decreased coupling or fixing the frequency of a single organ leads to decreased complexity of a system. A clinical example of decreased coupling or maintaining a fixed rate of organ oscillation includes certain modes of mechanical ventilation. These mechanisms may represent a mechanism by which clinical deterioration may lead to progressive refractory organ dysfunction. Future investigations regarding the model would include an evaluation of the current hypothesis using non-linear, time-delayed or time-dependent coupling and use of different “treatment functions” (medical devises). Coupled nonlinear (e.g. Van-der-Pol) stochastic oscillators: Acknowledgments: Coupled nonlinear stochastic iterative maps (e.g. logistic map): This work was supported by the grant # GM62674 from the National Institutes of Health to the Santa Fe Institute. We are grateful to Timothy G. Buchman and Lee Segel for useful discussions. - characteristic rate of the organ (e.g. beat-to-beat interval) - oscillators frequency and damping coefficients Ri(t) – random force References: - “treatment function” (the influence of a medical device, e.g. mechanical ventilator) (1). A. L. Goldberger, L. A. N. Amaral, J. M. Hausdorff, P. Ch. Ivanov, C.-K. Peng, and H. E. Stanley, Fractal Dynamics in Physiology: Alterations with Disease and Aging, Proc. Natl. Acad. Sci. 99, 2466-2472 (2002). (2). Godin PJ, Buchman TG. Uncoupling of biological oscillators: a complementary hypothesis concerning the pathogenesis of multiple organ dysfunction syndrome. Crit Care Med. 1996 Jul;24(7):1107-16. (3). Pincus, S. M. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA 1991;88:2297-2301. (4). Seely AJ, Macklem PT. Complex systems and the technology of variability analysis. Crit Care. 2004 Dec;8(6):R367-84. Epub 2004 Sep 22. (5). Pincus, S. M. Greater signal regularity may indicate increased system isolation. Math Biosci. 1994 Aug 122(2):161-81. Fig. 3. Simulation of the effect of mechanical ventilation with the constant frequency for the case of the “organism” with four “organs”. (left) control, (right) effect of the fixing the frequency of the 3rd “organ”. • The time series were analyzed using the following methods: • Power Spectra (Power Law); • Standard Deviation (STD); • Approximate Entropy (ApEn).

  35. Powersim models • Powersim is a graphical system for quantitative dynamical systems • Similar programs include Stella and Vensim

  36. General assumptions for the model • Nociseption and antinociseption are tonically active and in balance • Nociseption can be modeled quantitatively • Subjective pain and emotions can be modeled as VAS between 1 and 100 • To redimension VAS scales to an area from 0 to 100, a logistic differential equation was used

  37. f(x) = 100 * exp ((x-0.4)/12) 100 + exp ((x-0.4)/12)

  38. Submodel for PCA-profile

  39. Submodel for pharmacokinetics

  40. Whole „PCA-model“

  41. Typical result

  42. Summary • Nociseptive systems are complexe systems and share common properties with other complexe (adaptive) systems • There exist three main approaches to get insight in complex systems: Bottom up, Hidden signals, Top down. • While being succseful used in other areas (Neurobiology, Cardiology), the contribution of complex systems theory in pain research sounds promising, but is yet unclear

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