Automatic Parameter-Range Estimation for Cardiac Cells Radu Grosu - PowerPoint PPT Presentation

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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    

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

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

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

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

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

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

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 )

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 )

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 )

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 )

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

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

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

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

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

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