Periodic and Dynamical Diseases Bifurcations at the Bedside

Mrs. Reimann’s Knees

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?

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

Other knees

Periodic hematological disease

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

Cheyne Stokes respiration

Other breathing patterns

Infant apnea

Temperature oscillations in Hodgkin’s disease

Temperature oscillations after scarlet fever

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

Spontaneous change: Atrial fibrillation to sinus rhythm

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

Ventricular fibrillation

Periodic through chaotic: progression to death

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

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?

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

Epileptic seizure occurrence

Manic depressive swings

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

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?

Cheyne Stokes breathing Model Data

Periodic hematological disease

Periodic platelet disease

Cyclical Neutropenia & Mrs. “H”

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?

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

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

Treating cyclical neutropenia with colony stimulating factor

Colony stimulating factor induces cycling Before During

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

Periodic leukemia 43 days 83 days 70 days 54 days

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

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

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

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?

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