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Feed Sideward Applications to Biological Biomedical Systems Session 2

Jim HolteUniversity of Minnesota. 2. 2/7/02. Sessions. Session 1 - Feed Sideward Concepts and Examples, 1/15Session 2 Feed Sideward Applications to Biological

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Feed Sideward Applications to Biological Biomedical Systems Session 2

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    1. Jim Holte University of Minnesota 1 2/7/02 Feed Sideward Applications to Biological & Biomedical Systems Session 2 Jim Holte 2/7/2002

    2. Jim Holte University of Minnesota 2 2/7/02 Sessions Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 2/7 Session 3 Chronobiology, 2/21 ? Franz Hallberg and Germaine Cornelissen

    3. Jim Holte University of Minnesota 3 2/7/02 Biomedical Devices Pacemakers - Companies are introducing circadian rhythm based pacemakers. The pacing strategy (amplitude & timing of pacing stimulus) for effective cardiac capture depends on the time of day. (eg. work & sleep). Drug Delivery - Medtronic/Minimeds insulin pump has a drug delivery strategy. It is preprogrammed for continuous insulin delivery which depends on exercise, food intake, patient endogenous performance, may now use adjustment of dose as a function of time of day.

    4. Jim Holte University of Minnesota 4 2/7/02 Summary Dynamical systems analysis provides a technique for designing rate-control biomedical devices for therapeutic diagnosis & intervention. Rate-control provides direct access to bio-rhythms. Rate control techniques can apply the extensive knowledge of heart rate variability without requiring knowledge of the causes. The above builds on the extensive modeling of controllability and extensibility - opaque-box techniques.

    5. Jim Holte University of Minnesota 5 2/7/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    6. Jim Holte University of Minnesota 6 2/7/02 Introduction Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 feeds values of other variables into the specified variable Feed Sideward #2 feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    7. Jim Holte University of Minnesota 7 2/7/02 References Colin Pittendrigh & VC Bruce, An Oscillator Model for Biological Clocks, in Rhythmic and Synthetic Processes in Growth, Princeton, 1957. Theodosios Pavlidis, Biological Oscillators: Their mathematical analysis, Princeton, 1973, Chapter 5, Dynamics of Circadian Oscillators J.D. Murray, Mathematical Biology, Springer-Verlag, 1993, Chapter 8 Perturbed and Coupled Oscillators Arthur Winfree, The Timing of Biological Clocks, Scientific American Books, 1987

    8. Jim Holte University of Minnesota 8 2/7/02 Inherent Biological Rhythms Biosystems Rhythms second cycles (sec) - cardiac circadian (day) - sleep cycle) - melatonin (pineal) circaseptan (week) - mitotic activity of human bone marrow, balneology, bilirubin cycle neonatology circalunar cycles (month) - menstrual cycle annual (year) cycles - animals coats weight loss & gain by the season.

    9. Jim Holte University of Minnesota 9 2/7/02 Synchronizers Exogenous (external) stimulated by light, temperature & sleep/wake, barometric pressure & headaches/joint aches, Endogenous (internal): heart rates escape beats preventricular contractions - ectopic beats Sino-atreal node (associations of myocardial fibers on basis of enervation by vagus nerve) SA node beats spontaneously, governed by nerve & chemical, SA node stimulates the AV node providing a time delay. AV node sends excitation through conduction system to the purkinje fibers which stimulate the heart walls to contract. EEG rhythms (4-30 Hz, alpha, beta, theta & delta)

    10. Jim Holte University of Minnesota 10 2/7/02 Mathematics Mathematical linkage to synchronizers Endogenous rhythms refer to the eigenvectors. Exogenous rhythms refer to the particular integrals (forcing function). dX/dt = AX +B, B provides a forcing function. AX provides the eigenvectors.

    11. Jim Holte University of Minnesota 11 2/7/02 Viewpoint Challenge Traditional view biological rhythms are exogenous Focus on particular integrals (heterogenous eqn, x=ax+b) Blood pressure variation is interpreted as an activity variation, thus external. Now, many claim that biological rhythms are endogenous Focus on eigenvectors (homogeneous eqn, x=ax). Chronobiology viewpoint Blood pressure variation is interpreted as a hormonal variation, thus internal.

    12. Jim Holte University of Minnesota 12 2/7/02 Nollte Model Variation of Pavlidis, Eqns 5.4.1 & 5.4.2 Dynamical System r=r-cs+b, r>=0 s=r-as s>=0 r is heart rate, r is dr/dt s is blood pressure, s is ds/dt b is ambient temperature * Coupling* Coupling

    13. Jim Holte University of Minnesota 13 2/7/02 Dynamical System Circuit Map

    14. Jim Holte University of Minnesota 14 2/7/02 Limit Cycle Limit Cycle, Limit Cycle,

    15. Jim Holte University of Minnesota 15 2/7/02 Effect of Increased Heart Rate Stable limit cycle Stable limit cycle

    16. Jim Holte University of Minnesota 16 2/7/02 Effect of Decreased Heart Rate Stability Stability

    17. Jim Holte University of Minnesota 17 2/7/02 Effect of Critical Heart Rate & Pressure Equilibrium point Unstable - Eigenvalues have positive real partEquilibrium point Unstable - Eigenvalues have positive real part

    18. Jim Holte University of Minnesota 18 2/7/02 Effect of Perturbed Equilibrium Reduce sReduce s

    19. Jim Holte University of Minnesota 19 2/7/02 Biomedical Devices Pacemakers - Companies are introducing circadian rhythm based pacemakers. The pacing strategy (amplitude & timing of pacing stimulus) for effective cardiac capture depends on the time of day. (eg. work & sleep). Drug Delivery - Medtronic/Minimeds insulin pump has a drug delivery strategy. It is preprogrammed for continuous insulin delivery which depends on exercise, food intake, patient endogenous performance, may now use adjustment of dose as a function of time of day.

    20. Jim Holte University of Minnesota 20 2/7/02 Summary Dynamical systems analysis provides a technique for designing rate-control biomedical devices for therapeutic diagnosis & intervention. Rate-control provides direct access to bio-rhythms. Rate control techniques can apply the extensive knowledge of heart rate variability without requiring knowledge of the causes. The above builds on the extensive modeling of controllability and extensibility - opaque-box techniques.

    21. Jim Holte University of Minnesota 21 2/7/02 Next Session Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 2/7 Session 3 Chronobiology, 2/21 ? Franz Hallberg and Germaine Cornelissen

    22. Jim Holte University of Minnesota 22 2/7/02

    23. Jim Holte University of Minnesota 23 2/7/02 Backup

    24. Jim Holte University of Minnesota 24 2/7/02 Solution

    25. Jim Holte University of Minnesota 25 2/7/02 Nollte Model: Continuous Extension

    26. Jim Holte University of Minnesota 26 2/7/02 ODE Architect Models

    27. Jim Holte University of Minnesota 27 2/7/02 References Colin Pittendrigh & VC Bruce, An Oscillator Model for Biological Clocks, in Rhythmic and Synthetic Processes in Growth, Princeton, 1957. Theodosios Pavlidis, Biological Oscillators: Their mathematical analysis, Princeton, 1973, Chapter 5, Dynamics of Circadian Oscillators J.D. Murray, Mathematical Biology, Springer-Verlag, 1993, Chapter 8 Perturbed and Coupled Oscillators Arthur Winfree, The Temporal Morphology of a Biological Clock, Amer Math Soc, Lectures on Mathematics in the Life Sciences, Gerstenhaber, 1970, p 111-150 Arthur Winfree, Integrated View of Resetting a Circadian Clock, Journ Theoretical Biology, Vol 28, pp 327-374, 1970 Arthur Winfree, The Timing of Biological Clocks, Scientific American Books, 1987

    28. Jim Holte University of Minnesota 28 2/7/02 Feed Sideward - Topics (60 min) Session 1 (14 slides) Background Concepts & Examples Phase Space (1 slide) Singularities (2 slides) * Coupled Oscillators (2 slides) Phase Resetting (2 slides) * Oscillator Entrainment (1 slide) Feed Sideward as modulation (3 slides) ** Summary (1 slide)

    29. Jim Holte University of Minnesota 29 2/7/02 Feed Sideward Understanding Biological Rhythms Session 1 Jim Holte 1/15/2002

    30. Jim Holte University of Minnesota 30 2/7/02 Sessions Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 1/31 Session 3 Chronobiology, 2/12 Franz Hallberg and Germaine Cornalissen

    31. Jim Holte University of Minnesota 31 2/7/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    32. Jim Holte University of Minnesota 32 2/7/02 Introduction Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 feeds values of other variables into the specified variable Feed Sideward #2 feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    33. Jim Holte University of Minnesota 33 2/7/02 Phase Space Laws of the physical world Ordinary differential equations Visualization of Solutions Understanding

    34. Jim Holte University of Minnesota 34 2/7/02 Phase Space The Lotka-Volterra Equations for Predator-Prey Systems H' = b*H - a*H*P P' = -d*P + c*H*P H = prey abundance, P = predator Set the parameters b = 2 growth coefficient of prey d = 1 growth coefficient of predators a = 1 rate of capture of prey per predator per unit time c = 1 rate of "conversion" of prey to predators per unit time per predator.

    35. Jim Holte University of Minnesota 35 2/7/02 Phase Space

    36. Jim Holte University of Minnesota 36 2/7/02 Coupled Oscillators Model x and y represent the "phases of two oscillators. Think of x and y: angular positions of two "particles" moving around the unit circle a1 = 0 x has constant angular rate a2 = 0 y has constant angular rate. Coupling when a1 or a2 non-zero

    37. Jim Holte University of Minnesota 37 2/7/02 Example Uncoupled Oscillators

    38. Jim Holte University of Minnesota 38 2/7/02 Example Coupled Oscillators

    39. Jim Holte University of Minnesota 39 2/7/02 Phase Resetting

    40. Jim Holte University of Minnesota 40 2/7/02 Example Phase Resetting

    41. Jim Holte University of Minnesota 41 2/7/02 Oscillator Entrainment

    42. Jim Holte University of Minnesota 42 2/7/02 Oscillator Entrainment Example

    43. Jim Holte University of Minnesota 43 2/7/02 Singularities

    44. Jim Holte University of Minnesota 44 2/7/02 Example - Singularities

    45. Jim Holte University of Minnesota 45 2/7/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    46. Jim Holte University of Minnesota 46 2/7/02 Feed Sideward Example

    47. Jim Holte University of Minnesota 47 2/7/02 Summary Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 feeds values of other variables into the specified variable Feed Sideward #2 feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    48. Jim Holte University of Minnesota 48 2/7/02 Next Session Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 1/31 Session 3 Chronobiology, 2/12 Franz Hallberg and Germaine Cornelissen

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