Mechanics of Cardiac Tissue
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1 Bioengineering 6000: System Physiology I Mechanics of Cardiac Tissue PD Dr.-Ing. Frank B. Sachse
2 Overview Recapitulation Excitation Propagation II Force Development Experimental Studies Anatomy Cross Bridge Binding Modeling Passive Mechanics Coupled Electro-Mechanics Summary Mechanics of Cardiac Tissue - Page 2
3 Contraction of of Myocyte by by Electrical Stimulation Microscopic imaging of isolated ventricular cell from guinea pig schaffer Mechanics of Cardiac Tissue - Page 3
4 Measurement of of Force Development in in Single Cell Myocyte clued between glass plates Force transmission to measurement system Stimulator Fluid at body temperature Mechanical Fixation (variable strain) Glass plates Measured force per myocyte: µn Mechanics of Cardiac Tissue - Page 4
5 Sarcomeres Sarcomeres in incardiac CardiacMuscle Muscle(Fawcett (Fawcett&&McNutt McNutt69) 69) Sarcoplasmic reticulum Terminal cisternae Z-Disc Mitochondrion Transversal tubuli Sarcoplasmic reticulum Dyad Mechanics of Cardiac Tissue - Page 5
6 Force Development: Involved Proteins 2 µm Actin Myosin Actin TnC TnI TnT Actin Head-to-tail overlap Tm Tn: Troponin Tm: Tropomyosin A: Actin Z: Z-Disk (adapted from Gordon et al. 2001) Mechanics of Cardiac Tissue - Page 6
7 Force Development: Sliding Filament Theory Cellular force development by sliding myofilaments (Huxley 1957), i.e. actin and myosin, located in sarcomere Attachment of myosin heads to actin Filament sliding Detachment Spanning of myosin heads Mechanics of Cardiac Tissue - Page 7
8 Force Development: Sliding Filament Theory Mechanics of Cardiac Tissue - Page 8
9 Coupling of of Electrophysiology and Force Development Rest small Ca 2+ Stimulus Contraction Ca 2+ release from SR high Ca 2+ High concentration of intracellular Ca 2+ Force development Contraction of sarcomere/cell Mechanics of Cardiac Tissue - Page 9
10 Models of of Force Development 1938 Hill Skeletal muscle Frog Huxley Skeletal muscle - Wong Cardiac muscle - Panerai Papillary muscle Mammalian Peterson, Hunter, Berman Papillary muscle Rabbit Landesberg, Sideman Skinned cardiac - myocytes Hunter, Nash, Sands Cardiac Muscle Mammalian Noble, Varghese, Kohl, Noble Ventricular Muscle Guinea pig Rice, Winslow, Hunter Papillary muscle Guinea pig Rice, Jafri, Winslow Cardiac muscle Ferret today Glänzel, Sachse, Seemann Ventricular myocytes Human Mechanics of Cardiac Tissue - Page 10
11 Modeling of of Cellular Force Development [Ca] i /µm F/F maxi t [s] Intracellular concentration of calcium Calculated with electrophysiological cell models System of coupled ordinary differential equations t [s] Processes in myofilaments State of troponins, tropomyosins and cross bridges System of coupled ordinary differential equations t [s] Force Development Mechanics of Cardiac Tissue - Page 11
12 1st Model of of Rice 1999 et et al./ Landesberg et et al.1994 t N 0 T 0 T 1 N 1 = K l k l 0 g 0 + g 1 V K l f k l g 0 + g 1 V 0 0 f g 0 g 1 V k l K l 0 0 k l g 0 g 1 V K l N 0 T 0 T 1 N 1 Transfer coefficients: K l,k l, f, g 0, g 1,k l und V States of Troponin Calcium Cross bridges N 0 unbound weak T 0 bound weak T 1 bound strong N 1 unbound strong Description by set of coupled differential equations Transfer of states are dependent of transfer coefficients Transfer coefficients are parameterized Numerical solution e.g. with Euler- and Runge-Kutta-methods t [s] Mechanics of Cardiac Tissue - Page 12
13 State Diagram of of 3rd Model of of Rice 1999 et et al. al. States of Troponin States of Tropomyosin and cross bridges T unbound N0 0 XB g N1 1 XB k on k off k 1 (TCa,SL) k -1 k -1 k 1 (TCa,SL) TCa bound P0 Permissive 0 XB f g P1 Permissive 1 XB Mechanics of Cardiac Tissue - Page 13
14 Triaxial Measurement System for Soft Biological Tissue Dokos et al. J. Biomed. Eng Mechanics of Cardiac Tissue - Page 14
15 Inhomogeneous, Anistropic Strain-Stress Relationship Stress [N/m 2 ] Epicardial Myocardium Midwall Myocardium f s t Stress [N/m 2 ] f s t Strain [m/m] f: Fiber direction s: Sheet direction t: Sheet normal Strain [m/m] Hunter et. al., Computational Electromechanics of the Heart, in Computational Biology of the Heart, Editors: A. V. Panfilov et A. V. Holden, S. 368, 1995 Mechanics of Cardiac Tissue - Page 15
16 Example: Passive Cardiac Mechanics Left ventricle model approximated with 3752 cubic elements trilinear shape functions 3 versions of fiber orientation hyperelastic material (Guccione et al. 1991) incompressible Boundary condition tension 1 kpa in fiber direction homogeneous Mechanics of Cardiac Tissue - Page 16
17 Example: Versions of of Fiber Orientation -45, -45, , 0, 45 0, 0, 0 Mechanics of Cardiac Tissue - Page 17
18 Example: -45, -45, -45 Mechanics of Cardiac Tissue - Page 18
19 Example: -45, 0, 0, 45 Mechanics of Cardiac Tissue - Page 19
20 Example: 0, 0, 0, 0, 0 0 Mechanics of Cardiac Tissue - Page 20
21 Coupled Electro-Mechanics Force development Electrophysiology Anatomy Structure mechanics Mechanics of Cardiac Tissue - Page 21
22 Example: Electro-Mechanics of of Myocardium Array of myocytes Volume:2 3 mm 3 Elements: 20 3 with fiber orientation and lamination Electrophysiology Noble et al. 98 Bidomain model Force Development Six-state model of Rice et al. 99 Structure Mechanics Constitutive law of Hunter et al. 95 (Sachse, Seemann, Werner, Riedel, and Dössel, CinC, 2001) Mechanics of Cardiac Tissue - Page 22
23 Example: Electro-Mechanics in in Ventricular Model Anatomy Lattice of elements Volume: mm 3 Fiber orientation: -70, 0,70 Electrophysiology Noble et al. 98 Monodomain model Elements: 46x46x58 Step-length: 20 µs Tension Glänzel et al. 02 Elements: 46x46x58 Step-length: 20 µs Structure Mechanics Constitutive law of Guccione et al. 91 Elements: 23x23x29 Step-length: 5 ms (Sachse, Seemann, and Werner, CinC, 2002) Mechanics of Cardiac Tissue - Page 23
24 Summary Force Development Experimental Studies Anatomy Cross Bridge Binding Modeling Passive Mechanics Coupled Electro-Mechanics Mechanics of Cardiac Tissue - Page 24
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