Modeling of Electrical Conduction in Cardiac Tissue III

Transcription

1 Bioeng 6460 Electrophysiology and Bioelectricity Modeling of Electrical Conduction in Cardiac Tissue III Frank B. Sachse

2 Overview Cellular Automata History Introduction Implementation Examples EKG Calculation Summary Group work Group work BIOEN Page 2

3 Cellular Automatons of Cardiac Excitation Propagation 1946 today Wiener, Rosenblueth 2D sheets Moe, Rheinboldt, Abildskov Atria (2D sheet) Eiffler, Plonsey Ventricular myocardium (2D sheet) Adam Human ventricles (ellipsoids) Killmann, Wach, Dienstl Human heart (from drawings) Saxberg, Cohen Myocardium Wei, Okoazaki, Harumi, Harasawa, Human ventricles (Anisotropic) Hosaka Siregar, Sinteff, Chadine, Le Beux Human heart (2D) Werner, Sachse, Dössel Human heart (Anisotropic) Siregar, Sinteff, Julen, Le Beux Human heart (CAD) BIOEN Page 3

4 Cellular Automaton: Basics Anatomical Model Physiological Parameters Cellular Automaton Autorhythmicity Transmembrane voltage Conduction velocity Refractory period BIOEN Page 4

5 Cellular Automaton: Modeling of Propagation 1 2 Passive element Active element 3 4 Initial excitation 5 6 Excitation BIOEN Page 5

6 Anatomical Model of Heart: Requirements Necessary: Anatomical model of all excitation triggering and conductive components Example: Components in model of Werner et al.: Image segmentation left atrial myocardium right atrial myocardium left ventricular myocardium right ventricular myocardium Manual/rule-based definition Sinus node AV node His bundle Tawara bundle branches Purkinje fibers Fiber orientation BIOEN Page 6

7 Parameters for Simulation: Lookup Tables Known per volume element dv and for time t dv Time since activation t S Stimulus frequency f Tissue type Fiber orientation Transmembrane voltage (t S ) Refractory period (t S ) Autorhythmicity (t S ) Conduction velocity (f) Excitable neighborhood (constant) BIOEN Page 7

8 Cellular Automaton: Parameter - Transmembrane Voltage Course of transmembrane voltage is dependent on tissue type and stimulus frequency. Activation is only possible outside of absolute refractory time. V m [mv] t [ms] V m [mv] t [ms] V m [mv] t [ms] Sinus node AV node Atrial myocardium Most cellular electrophysiological properties, e.g. ion and transmitter concentrations, nervous influences, extracellular potentials etc. are neglected! BIOEN Page 8

9 Cellular Automaton: Parameterization Course of transmembrane voltage Longitudinal/transversal propagation velocity } { Measurements Numerical experiments Ventricle: Noble-Varghese-Kohl-Noble 98 Atrium: Earm-Hilgemann-Noble 90 BIOEN Page 9

10 Group Work Example * *: Stimulus site : Obstacle Connection: 4-neighborhood Δt in x-direction: 1 Δt in y-direction: 3 * * BIOEN Page 10

11 Unidirectional Block/Rotation Around Obstacles (2D) BIOEN Page 11

12 Unidirectional Block/Rotation Around Obstacles (2D) BIOEN Page 12

13 Unidirectional Block in Homogeneous Slice (2D) BIOEN Page 13

14 Results of Whole Heart Simulations Transmembrane voltage color-coded at heart surface for physiological excitation propagation 8 time steps atrial activation starting at sinus node... atrial repolarisation ventricular activation starting at subendocardium... ventricular repolarisation BIOEN Page 14

15 Simulation of 3rd Degree AV Block BIOEN Page 15

16 Simulation of Infarction BIOEN Page 16

17 Cellular Automaton: Application in ECG/BSPM Simulation Anatomie Cellular Automaton Transmembrane voltages Membrane current densities U m / mv T / ms 0-80 Electrophysiology EKG Numerical Field Calculation Volume and surface voltages Current densities BSPM Body Surface Potential Map BIOEN Page 17

18 Simulation System: Overview Source model Bidomain approximation Current source density Electrical Model Body/Thorax Transmembrane voltage Visualization Images/Movies Electrical Voltages Electrophysiological Model Macro-/microscopic, rule-based/analytical Lead Model e.g. standard leads of Einthoven and Goldberger BIOEN Page 18

19 Example: ECG Simulation V m Transmembrane voltage f e Current source densities ECG BSPM Cellular automaton of excitation propagation Bidomain model BIOEN Page 19

20 BIOEN Page 20

21 Group Work Compare cellular automata with mono-/bidomain models of cardiac conduction! Apply ~5 criteria for comparison. BIOEN Page 21

22 Summary Cellular Automata History Introduction Implementation Examples EKG Calculation BIOEN Page 22