2. Periodic and Dynamical Diseases Bifurcations at the Bedside

4. Mrs. Reimann’s Knees

5. Outline Examples of periodic and “chaotic” diseases Induction and modification by drugs Dynamical diseases--bifurcation induced Dynamical diseases--bifurcation cures What will Bones be doing in 2503?

6. Periodic Diseases ************** “Constant” to periodic Periodic to new period Periodic to “chaotic”

7. Other knees

8. Periodic hematological disease

9. Periodic Diseases ************** “Constant” to periodic Periodic to new period Periodic to “chaotic”

10. Cheyne Stokes respiration

11. Other breathing patterns

12. Infant apnea

13. Temperature oscillations in Hodgkin’s disease

14. Temperature oscillations after scarlet fever

15. Cardiology Periodic New period--AV block 2:1 4:3

16. Spontaneous change: Atrial fibrillation to sinus rhythm

17. Periodic Diseases ************** “Constant” to periodic Periodic to new period Periodic to “chaotic”

18. Ventricular fibrillation

19. Periodic through chaotic: progression to death

20. Oscillations in the kidney Periodic (normal) vs. Chaotic (hypertension)? Normal rat Spontaneously hypertensive rat

21. Outline Examples of periodic and “chaotic” diseases Induction and modification by drugs Dynamical diseases--bifurcation induced Dynamical diseases--bifurcation cures What will Bones be doing in 2503?

22. Lignocaine induced transition: ventricular tachycardia to atrial fibrillation Before Flipping betweenThe transition

23. Epileptic seizure occurrence

24. Manic depressive swings

25. Dynamical Disease One in which the pathology is due to a bifurcation A bifurcation is characterized by a qualitative change in dynamics

26. Outline Examples of periodic and “chaotic” diseases Induction and modification by drugs Dynamical diseases--bifurcation induced Dynamical diseases--bifurcation cures What will Bones be doing in 2503?

27. Cheyne Stokes breathing Model Data

28. Periodic hematological disease

29. Periodic platelet disease

30. Cyclical Neutropenia & Mrs. “H”

31. Outline Examples of periodic and “chaotic” diseases Induction and modification by drugs Dynamical diseases--bifurcation induced Dynamical diseases--bifurcation cures What will Bones be doing in 2503?

32. Drug alterations of disease dynamics Commonest example: cardiac arrhythmias Next most common: renal hypertension But are they inducing bifurcations to produce a normal state? Cyclical neutropenia

33. Mathematical modeling of cyclical neutropenia predicts: CN is due to an abnormally high rate of cell death (apoptosis) Decreasing rate of death in CN should: Increase amplitude of oscillations Decrease period of oscillations Eventually obliterate oscillations Decreasing death rate in neutropenics will: Induce oscillations

34. Treating cyclical neutropenia with colony stimulating factor

35. Colony stimulating factor induces cycling Before During 331511 61182914

36. Summary of all neutropenic patients G-CSF in Cyclical Neutropenia ************************* Increases the oscillation amplitude Increases the mean value Decreases the oscillation period Stops the oscillation at sufficiently high dose (in grey collies) G-CSF in Non-cycling Neutropenia ***************************** Increases the average cell counts Can induce oscillations 331511 61182914

37. Periodic leukemia 43 days 83 days 70 days 54 days

38. Conclusions Diseases involving: Constant to Periodic Periodic to new period Periodic to “chaotic”

39. Conclusions Diseases involving: Constant to Periodic Periodic to new period Periodic to “chaotic” Dynamical disease: Symptoms  bifurcation

40. Conclusions Diseases involving: Constant to Periodic Periodic to new period Periodic to “chaotic” Dynamical disease: Symptoms  bifurcation Hope: Reverse bifurcation with medication

41. Conclusions Diseases involving: Constant to Periodic Periodic to new period Periodic to “chaotic” Dynamical disease: Symptoms  bifurcation Hope: Reverse bifurcation with medication Mathematics, Modeling & Medicine-2503?

42. That’s All Folks!