Computational Modeling of the Cardiovascular System

Transcription

1 ibiomep - International Doctoral Programme in Biomedical Engineering and Medical Physics Computational Modeling of the Cardiovascular System Microstructural Basis of Conduction Introduction to Functional Studies Frank B. Sachse, University of Utah

2 Overview Basics and Concepts Imaging Approaches Microscopic Anatomy of Tissue Tissue Cells Gap Junctions in Tissue Fibroblasts Introduction to Experimental Studies Whole Heart Tissue Preparations Cell Culture Summary Group work Group work Group work Computational Modeling of the Cardiovascular System - Page 2

3 Basics Electrical signaling in cardiac tissue is a multiscale process Microscopic conduction is a function of arrangement of cells and proteins Microscopic scale: from ~1 to ~100 µm Major cell types in cardiac tissue: myocytes and fibroblast Electrical coupling through gap junctions channels Objective of this lecture Insights into microstructure of cardiac tissue with perspective on electrical signaling Introduction of research tools for studying microstructure of tissue Computational Modeling of the Cardiovascular System - Page 3

4 Conductive Tissue: Concepts Syncytium: Large cell-like structure Structural/functional Coupling: continuous/discrete Network Topology: mesh, tree, ring, Coupling: gap junctions, synapses Computational Modeling of the Cardiovascular System - Page 4

5 Approaches for Imaging of Tissue Microstructure Light Microscopy Transmission / Reflection Confocal Microscopy Electron Microscopy Thin Sectioning Microtome / Ultramicrotome Vibrotome Cryosectioning Labeling Antibody-antibody conjugated label Reactive label Computational Modeling of the Cardiovascular System - Page 5

6 Principles of Confocal Microscopy Detector Beamsplitter Confocal pinholes Laser Mathematical description of imaging system: g = h * f g : Response of imaging system h : Point spread function f : Source image not in focal plane in focal plane not in focal plane Objective f g h ( ( Computational Modeling of the Cardiovascular System - Page 6

7 Point Spread Functions: BioRad, 60x Oil, NA 1.4 YZ XZ XY Resolution: 130nm x 130nm x 130nm Full width at half maximum Z: 1.04µm XY: 0.260µm Computational Modeling of the Cardiovascular System - Page 7

8 Point Spread Functions: Zeiss LSM5, 60x Oil, NA 1.4 YZ XZ XY Resolution: 100nm x 100nm x 100nm Full width at half maximum Z: 0.8µm XY: 0.2µm Computational Modeling of the Cardiovascular System - Page 8

9 Image Deconvolution Assumptions Deconvolution Imaging system can be described by ( ) = f h( x) = f( x) g x ( ) d x & h x x & g : Response of imaging system h : Point spread function f : Source image Linearity Translation independence Richardson-Lucy Algorithm $ g g n +1 = g 0 n & % g n h h ' ) ( g n : Solution for step n with g 0 = g : Cross - correlation operator Sensitive to noise and imaging artefacts! Regularization Computational Modeling of the Cardiovascular System - Page 9

10 Group Work Imagine a horizontally and vertically oriented structure with a thickness of 1 voxel and length of 10 voxel. Assume that the point spread function of an imaging system can be described with a Gaussian having the following properties: full width at half maximum XY: 1 voxel full width at half maximum Z: 3 voxel Estimate the blurring of the vertical and horizontal structure by the point spread function. Computational Modeling of the Cardiovascular System - Page 10

11 Microscopic Anatomy of Cardiac Tissue Myocytes connected at intercalated discs Interstitial space primarily laterally of myocytes intracellular space via gap junctions mechanical coupling (Saffitz et al. 99) Computational Modeling of the Cardiovascular System - Page 11

12 Microstructure of Living Tissue Polycarbonate Tube Hydrogel Glass Slide Objective Lens 40x Tyrode s Solution Cardiac Tissue Oil 50 µm Epicardial surface Depth: 5 µm Depth: 15 µm (Lasher et al, IEEE Trans Med Imaging, 2009) Computational Modeling of the Cardiovascular System - Page 12

13 Imaging-Based 3D Model of Cardiac Tissue (Lasher et al, IEEE Trans Med Computational Imaging, Modeling 2009) of the Cardiovascular System - Page 13

14 Microstructure of Fixed Rabbit Myocardium Ventricular myocardium Atrial myocardium Sinoatrial nodal tissue 50 µm 50 µm Computational Modeling of the Cardiovascular System - Page 14

15 Conduction System in Cow Heart (Lewis 1925) Computational Modeling of the Cardiovascular System - Page 15

16 Microstructure of Rabbit Conduction System P: Purkinje cell V: Ventricular myocyte (Romero et al. 11) Computational Modeling of the Cardiovascular System - Page 16

17 Gap Junctions in Mammalian Cardiac Tissue (Severs et al. 08) Computational Modeling of the Cardiovascular System - Page 17

18 Imaging of Cx43 Distribution Base 0.1 mm Right Ventricle Left Ventricle Endocardium Epicardium 5 mm Apex Mid-myocardial Tissue Section Thin Section of Tissue Coverslip Glass slide Glycerol Oil Objective (Lackey et al. 11) Computational Modeling of the Cardiovascular System - Page 18

19 3D Distribution of Cx43 in Rat Left Ventricular Myocardium y x z y 50 µm z x Wheat Germ Agglutinin - Extracellular Space Cx43 - Gap Junctions (Lackey et al. 11) Computational Modeling of the Cardiovascular System - Page 19

20 Analysis of Cx43 Distributions: Polarization z x Measure Value Polarization Pol 10% 59.2% Polarization Pol 25% 81.0% (Lackey et al. 11) Computational Modeling of the Cardiovascular System - Page 20

21 Analysis of Cx43 Distributions: Examples Measure Value Polarization Pol 10% 40.1% Polarization Pol 25% 77.6% Value 24.2% 53.5% (Lackey et al. 11) Computational Modeling of the Cardiovascular System - Page 21

22 Cx40/45 Distribution in Mouse Conduction System P Purkinje cell T Transitional cell WM Working myocardium * Most superficial myocyte of WM (Severs et al. 08) Computational Modeling of the Cardiovascular System - Page 22

23 Cx43 Lateralization in Pacing Induced Heart Failure (Akar et al. 07) Computational Modeling of the Cardiovascular System - Page 23

24 Group Work Discuss the effects of the spatial arrangement of gap junction channels on cardiac conduction! Speculate about effects on anisotropy and velocity of conduction! Computational Modeling of the Cardiovascular System - Page 24

25 Fibroblast Organization in Rat Neonatal Myocardium Discoidin domain receptor (DDR) - Fibroblasts Actin - Myocytes Cx43 - Gap Junctions Arrows indicate gap junctions of fibroblasts (E. C. Goldsmith et al, Develop Dyn 2004) Computational Modeling of the Cardiovascular System - Page 25

26 Fibroblasts in Mouse Ventricular Myocardium Fluorescent microsphere in blood vessels DAPI Nuclei DDR - Fibroblasts (Sounders et al, Circ Res, 2009) Computational Modeling of the Cardiovascular System - Page 26

27 Fibroblasts in Normal Rat Ventricular Tissue 50 µm WGA Extracellular space DAPI Nuclei Cx43 Vimentin - Fibroblasts (M. Arp et al, Biomed Tech, 2011) Computational Modeling of the Cardiovascular System - Page 27

28 Fibroblasts in Rat Ventricular Tissue (Zoom) WGA Extracellular space DAPI Nuclei Cx43 Vimentin - Fibroblasts (M. Arp et al, Biomed Tech, 2011) Computational Modeling of the Cardiovascular System - Page 28

29 Fibroblast Differentiation (Tomasek et al, Nat Rev, 2002) Computational Modeling of the Cardiovascular System - Page 29

30 Role of Fibroblasts in Electrophysiology electrically inexcitable passive role septa due to fibrosis reduced volume fraction of myocytes reduced lateral coupling active role electrical myocyte-fibroblast coupling via gap junction channels electrical bridging of myocytes in culture: over distances up to 300µm (G. Gaudesius et al, Circ Res 2003) additional sink or source for activation of myocytes (Jong et al, J Cardiovasc Pharm, 2011) role dependent on phenotype of fibroblast (Rook et al, Am J Physiol, 1992) Computational Modeling of the Cardiovascular System - Page 30

31 Electrical Signaling in the Heart (from Malmivuo and Plonsey) Computational Modeling of the Cardiovascular System - Page 31

32 Experimental Studies of Cardiac Electrical Conduction Measurement methods Electrode arrays: Extracellular voltages (similar ECG measurements on body surface) Sampling rate up to several khz Channels up to 2000 Optical: Transmembrane voltages CCD-camera Photodiode array Preparations Cell strands - Purkinje fibers Small muscles - papillary muscle, trabeculae Sections - wedge preparations from ventricles Atria/ventricle Whole heart Color-coded visualization of extracellular voltages measured on surface of canine ventricles in vivo/in vitro Computational Modeling of the Cardiovascular System - Page 32

33 Epicardial Electrical Mapping System for Mouse Heart Sohn et al, IEEE TBME,! 2011 Computational Modeling of the Cardiovascular System - Page 33

34 Electrical Mapping of Canine Ventricles Computational Modeling of the Cardiovascular System - Page 34

35 Optical Mapping System Eloff et al, Cardiovasc Res, 2001 Computational Modeling of the Cardiovascular System - Page 35

36 Optical Mapping of Canine Ventricular Area Computational Modeling of the Cardiovascular System - Page 36

37 Isotropic/Anisotropic Propagation of Excitation (2D) Long axis of myocytes parallel to y-axis Stimulus at point (0,0) Isotropic x/y - 1/1 Velocity v: 1 / s x Anisotropic x/y - 1/3 Velocity v x : 1 / s, v y : 3 / s x t=2 3 4 y t=2 3 4 y Simplifications Homogeneous tissue Neglect of microstructure Computational Modeling of the Cardiovascular System - Page 37

38 In-/Outflow of Currents during Excitation 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms Computational Modeling of the Cardiovascular System - Page 38

39 In-/Outflow of Currents during Repolarization 110 ms 130 ms 150 ms 170 ms 190 ms 210 ms Computational Modeling of the Cardiovascular System - Page 39

40 Dipole Approximation and Surface ECG RA (-) RA (-) RA (-) II II R II P P P LF(+) Q LF(+) Q LF(+) RA (-) RA (-) P R II P R T II Q S LF(+) Q S LF(+) Computational Modeling of the Cardiovascular System - Page 40

41 One-Dimensional Cardiac Electrical Conduction Species: Adult New Zealand White rabbits ( kg) 1. Anti-coagulated with heparin and anesthetized with pentobarbital 2. Hearts are rapidly excised and moved to dissection tray 3. Retrograde perfusion via aorta with modified Tyrode solution 4. Opening of right ventricle 5. Selection and excision of papillary muscle including onset of chordae tendinae Criteria: Small diameter, large length, unramified 6. Transfer to horizontal flow-through chamber 7. Fixation of muscle 8. Measurement Fix Stimulus position Tendon Rabbit papillary muscle EG measurement Oxygenated HEPES solution, 37 C Computational Modeling of the Cardiovascular System - Page 41

42 Measurement Results: Electrograms Distance to stimulus site Stimulus artifact Computational Modeling of the Cardiovascular System - Page 42

43 Experimental Studies of Conduction in Cell Culture Myocyte strand with fibroblast insert Optical mapping using voltage sensitive dyes (Gaudesius et al, Circ Res, 2005) Computational Modeling of the Cardiovascular System - Page 43

44 Optical Mapping of Co-Culture of Rat Myocyte/Myofibroblast 100µm DAPI - nuclei Actin - myocytes α-smooth muscle actin - myofibroblast (Zlochiver et al, Biophys J, 2008) Computational Modeling of the Cardiovascular System - Page 44

45 Optical Mapping of Reentrant Arrhythmia (Zlochiver et al, Biophys J, 2008) Computational Modeling of the Cardiovascular System - Page 45

46 Group Work Identify the major mechanisms of cardiac conduction! What would be an electrical engineering description of those? Which other systems exhibit similar phenomena? List at least 10. Computational Modeling of the Cardiovascular System - Page 46

47 Summary Basics and Concepts Imaging Approaches Microscopic Anatomy of Tissue Tissue Cells Gap Junctions in Tissue Fibroblasts Introduction to Experimental Studies Whole Heart Tissue Preparations Cell Culture Computational Modeling of the Cardiovascular System - Page 47