mechanics of cardiac tissuefs/lessons/bioeng6000/lesson3.pdfmechanics of cardiac tissue - page 4...
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Bioengineering 6000: System Physiology I
Mechanics ofCardiac Tissue
CVRTIPD Dr.-Ing. Frank B. Sachse
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Mechanics of Cardiac Tissue - Page 2
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OverviewOverview
• Recapitulation Excitation Propagation II
• Force Development• Experimental Studies • Anatomy• Cross Bridge Binding• Modeling
• Passive Mechanics
• Coupled Electro-Mechanics
• Summary
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Mechanics of Cardiac Tissue - Page 3
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Contraction of Myocyte by Electrical StimulationContraction of Myocyte by Electrical Stimulation
Microscopic imaging of isolated ventricular cell from guinea pighttp://www-ang.kfunigraz.ac.at/˜schaffer
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Mechanics of Cardiac Tissue - Page 4
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Measurement of Force Development in Single CellMeasurement of Force Development in Single Cell
Myocyte clued betweenglass plates
Glass plates
Force transmission to measurement system
Fluid at bodytemperature
Mechanical Fixation(variable strain)
Stimulator
Measured forceper myocyte: 0.15-6.0 µN
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Mechanics of Cardiac Tissue - Page 5
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Sarcomeres in Cardiac Muscle (Fawcett & McNutt 69)Sarcomeres in Cardiac Muscle (Fawcett & McNutt 69)
Sarcoplasmic reticulumTerminal cisternae Mitochondrion Transversal tubuli
Sarcoplasmic reticulum
DyadZ-Disc
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Mechanics of Cardiac Tissue - Page 6
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Force Development: Involved ProteinsForce Development: Involved Proteins
Actin
Actin
(adapted from Gordon et al. 2001)
TnCTnTTnI
Tm ActinHead-to-tail
overlap
Tn: Troponin Tm: Tropomyosin A: Actin Z: Z-Disk
Myosin
2 µm
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Mechanics of Cardiac Tissue - Page 7
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Force Development: Sliding Filament TheoryForce Development: Sliding Filament Theory
Filament sliding
Detachment Spanning of myosin heads
Cellular force development by sliding myofilaments (Huxley 1957), i.e. actin andmyosin, located in sarcomere
Attachment of myosin heads to actin
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Mechanics of Cardiac Tissue - Page 8
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Force Development: Sliding Filament TheoryForce Development: Sliding Filament Theory
http://www.sci.sdsu.edu/movies/actin_myosin.html
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Mechanics of Cardiac Tissue - Page 9
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High concentration ofintracellular Ca2+
Force developmentContraction ofsarcomere/cell
Coupling of Electrophysiology and Force DevelopmentCoupling of Electrophysiology and Force Development
ContractionStimulus
Rest small Ca2+
Ca2+ release from SR high Ca2+
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• 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
• Glänzel, Sachse, Seemann Ventricular myocytes Human
…
1938
today
Models of Force DevelopmentModels of Force Development
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Mechanics of Cardiac Tissue - Page 11
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Modeling of Cellular Force DevelopmentModeling of Cellular Force Development
t [s] t [s]
[Ca]
i/µM
Intracellular concentration of calcium
Calculated withelectrophysiological
cell models
System of coupled ordinary differential
equations
Processes inmyofilaments
State of troponins,tropomyosins and
cross bridges
System of coupled ordinary differential
equations
Force Development
t [s]
F/F m
axi
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1st Model of Rice 1999 et al./ Landesberg et al.19941st Model of Rice 1999 et al./ Landesberg et al.1994
€
∂∂ t
N0
T0
T1N1
=
−Kl kl 0 g 0 + g1VKl − f − kl g0 + g1V 00 f −g 0 −g1V − k
−l Kl
0 0 k−l −g 0 −g1V −Kl
N0
T0
T1N1
Transfer coefficients: Kl ,kl, f, g 0, g1,k− l und V
States of Troponin Calcium Cross bridgesN0 unbound weakT0 bound weakT1 bound strongN1 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]
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Mechanics of Cardiac Tissue - Page 13
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State Diagram of 3rd Model of Rice 1999 et al.State Diagram of 3rd Model of Rice 1999 et al.
Tunbound
TCabound
P0Permissive
0 XB
N00 XB
P1Permissive
1 XB
N11 XB
f
koffkon k1(TCa,SL) k1(TCa,SL)
g
g
k-1 k-1
States of Troponin States of Tropomyosin andcross bridges
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Mechanics of Cardiac Tissue - Page 14
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Dokos et al.J. Biomed. Eng.2000
Triaxial Measurement System for Soft Biological Tissue
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Inhomogeneous, Anistropic Strain-Stress RelationshipInhomogeneous, Anistropic Strain-Stress Relationship
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
Strain[m/m]
Strain[m/m]
Stress[N/m2]
Stress[N/m2]
Epicardial Myocardium Midwall Myocardium
f s t f s t
f: Fiber direction s: Sheet direction t: Sheet normal
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Example: Passive Cardiac MechanicsExample: 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
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Example: Versions of Fiber OrientationExample: Versions of Fiber Orientation
-45°, -45°, -45° -45°, 0°, 45° 0°, 0°, 0°
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Example: -45°, -45°, -45°Example: -45°, -45°, -45°
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Mechanics of Cardiac Tissue - Page 19
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Example: -45°, 0°, 45°Example: -45°, 0°, 45°
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Example: 0°, 0°, 0°Example: 0°, 0°, 0°
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Coupled Electro-MechanicsCoupled Electro-Mechanics
AnatomyElectro-physiology
Force development
Structure mechanics
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Example: Electro-Mechanics of MyocardiumExample: Electro-Mechanics of Myocardium
Array of myocytes
Volume:23 mm3 Elements: 203
with fiber orientation and lamination
Electrophysiology
Noble et al. 98Bidomain model
Force Development
Six-state model ofRice et al. 99
Structure Mechanics
Constitutive law ofHunter et al. 95
(Sachse, Seemann, Werner, Riedel, and Dössel, CinC, 2001)
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AnatomyLattice of elementsVolume: 273.6 mm3 Fiber orientation:-70°, 0°,70°
ElectrophysiologyNoble et al. 98Monodomain modelElements: 46x46x58Step-length: 20 µs
TensionGlänzel et al. 02Elements: 46x46x58 Step-length: 20 µs
Structure MechanicsConstitutive law ofGuccione et al. 91Elements: 23x23x29Step-length: 5 ms
(Sachse, Seemann, and Werner, CinC, 2002)
Example: Electro-Mechanics in Ventricular ModelExample: Electro-Mechanics in Ventricular Model
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SummarySummary
• Force Development• Experimental Studies • Anatomy• Cross Bridge Binding• Modeling
• Passive Mechanics
• Coupled Electro-Mechanics