automatic parameter range estimation for cardiac cells
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Automatic Parameter-Range Estimation for Cardiac Cells Radu Grosu SUNY at Stony Brook Joint work with Ezio Bartocci, Gregory Batt, Flavio H. Fenton, James Glimm, Colas Le Guernic, and Scott A. Smolka Excitable Cells Generate action

  1. Automatic Parameter-Range Estimation for Cardiac Cells Radu Grosu SUNY at Stony Brook Joint work with Ezio Bartocci, Gregory Batt, Flavio H. Fenton, James Glimm, Colas Le Guernic, and Scott A. Smolka

  2. Excitable Cells • Generate action potentials (elec. pulses) in response to electrical stimulation – Examples: neurons, cardiac cells, etc. • Local regeneration allows electric signal propagation without damping • Building block for electrical signaling in brain, heart, and muscles

  3. Excitable Cells – Examples: neurons, cardiac cells, etc. Neurons of a squirrel University College London Artificial cardiac tissue University of Washington

  4. Excitable Cells Neurons of a squirrel • Local regeneration allows electric signal University College London propagation without damping Artificial cardiac tissue University of Washington

  5. Excitable Cells Neurons of a squirrel University College London • Building block for electrical signaling in brain, heart, and muscles Artificial cardiac tissue University of Washington

  6. Single Cell Reaction: Action Potential Membrane’s AP depends on: Schematic Action Potential • Stimulus (voltage or current): – External / Neighboring cells • Cell’s state (excitable or not): voltage – Parameters value Threshold Resting potential time

  7. Single Cell Reaction: Action Potential Schematic Action Potential • Cell’s state (excitable or not): voltage – Parameters value Threshold Resting potential time

  8. Single Cell Reaction: Action Potential Schematic Action Potential voltage Threshold failed initiation Resting potential time

  9. Single Cell Reaction: Action Potential Schematic Action Potential nonlinear voltage Threshold failed initiation Resting potential time

  10. Single Cell Reaction: Action Potential Schematic Action Potential nonlinear voltage Threshold Tissue: Reaction / diffusion  u failed initiation  t  R ( u )   ( D  u ) Resting potential time

  11. Single Cell Reaction: Action Potential Schematic Action Potential nonlinear voltage Threshold Tissue: Reaction / diffusion  u failed initiation  t  R ( u )   ( D  u ) Resting potential time Behavior In time

  12. Single Cell Reaction: Action Potential Schematic Action Potential nonlinear voltage Threshold Tissue: Reaction / diffusion  u failed initiation  t  R ( u )   ( D  u ) Resting potential time Reaction

  13. Single Cell Reaction: Action Potential Schematic Action Potential nonlinear voltage Threshold Tissue: Reaction / diffusion  u failed initiation  t  R ( u )   ( D  u ) Resting potential time Diffusion

  14. Lack of Excitability: Implications Stimulus: bottom row, every 300ms Obstacle of UT No Obstacle

  15. Problem to Solve • What circumstances lead to a loss of excitability? • What parameter ranges reproduce loss of excitability?

  16. Problem to Solve • What parameter ranges reproduce loss of excitability?

  17. Problem to Solve • What parameter ranges reproduce loss of excitability? Experimental Minimal Minimal Data Resistor Model Conductor Model RoverGene Minimal Analysis Tool Multi-Affine Model

  18. Biological Switching  u   1 0   u   1 R  ( u ,  1 ,  2 ,0,1)  else   2   1  1  S  ( u ,  , k ,0,1)  u   2 1  1  e  2 k ( u   )   0.5 k  16  0 u   H  ( u ,  ,0,1)   1 u    

  19. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))

  20. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Voltage Rate

  21. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Diffusion Laplacian

  22. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Fast input current

  23. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Slow input current

  24. Minimal Resistor Model: Voltage ODE u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Slow output current

  25. MRM: Currents Equations u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )

  26. MRM: Currents Equations Heaviside u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) (step)   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )

  27. MRM: Currents Equations Constant u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u )) Resistanc e   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )

  28. MRM: Currents Equations u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) Piecewise Nonlinear J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )

  29. MRM: Currents Equations u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si Piecewise  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u ) Bilinear

  30. MRM: Currents Equations u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u ) Piecewise Sigmoidal Resistanc Resistanc e e

  31. MRM: Currents Equations u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u ) Piecewise Nonlinear

  32. MRM: Gates ODEs u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )  H  ( u ,  v ,0,1) ( v   v ) /  v  ( u )  H  ( u ,  v ,0,1) v /  v  v ( u , v ) w ( u , w )  H  ( u ,  w ,0,1)( w   w ) /  w  ( u )  H  ( u ,  w ,0,1) w /  w  &  ( S  ( u , u s , k s ,0,1)  s ) /  s ( u ) s ( u , s ) &   H ( u   v )( u   v )( u u  u ) v /  fi J fi

  33. MRM: Gates ODEs u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si Piecewise  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u ) Resistance  H  ( u ,  v ,0,1) ( v   v ) /  v  ( u )  H  ( u ,  v ,0,1) v /  v  v ( u , v ) w ( u , w )  H  ( u ,  w ,0,1)( w   w ) /  w  ( u )  H  ( u ,  w ,0,1) w /  w  &  ( S  ( u , u s , k s ,0,1)  s ) /  s ( u ) s ( u , s ) &   H ( u   v )( u   v )( u u  u ) v /  fi J fi Piecewise Resistance

  34. MRM: Gates ODEs u ( u , v , w , s )   ( D  u )  ( J fi ( u , v )  J si ( u , w , s )  J so ( u ))   H  ( u ,  v ,0,1) ( u   v )( u u  u ) v /  fi J fi ( u , v ) J si ( u , w , s )   H  ( u ,  w ,0,1) ws /  si  H  ( u ,  w ,0,1) u /  o ( u )  H  ( u ,  w ,0,1) /  so ( u ) J so ( u )  H  ( u ,  v ,0,1) ( v   v ) /  v  ( u )  H  ( u ,  v ,0,1) v /  v  v ( u , v ) w ( u , w )  H  ( u ,  w ,0,1)( w   w ) /  w  ( u )  H  ( u ,  w ,0,1) w /  w  &  ( S  ( u , u s , k s ,0,1)  s ) /  s ( u ) s ( u , s ) & Sigmoidal Resistance   H ( u   v )( u   v )( u u  u ) v /  fi J fi Sigmoid

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