Periodic and Dynamical Diseases

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					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”
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 between




The transition
Epileptic seizure occurrence
Manic depressive swings
         Dynamical Disease
• One in which the      • A bifurcation is
  pathology is due to     characterized by a
  a bifurcation           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     33   15   11   11




During     61   18   29   14
         Summary of all neutropenic
                 patients
G-CSF in Cyclical Neutropenia
                                        33   15   11   11
*************************
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        61   18   29   14
*****************************
Increases the average cell counts
Can induce oscillations
          Periodic leukemia

70 days                       83 days




54 days                       43 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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posted:3/29/2008
language:English
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