Mechanics of Cardiac Tissuefs/lessons/bioeng6000/lesson3.pdfMechanics of Cardiac Tissue - Page 4...

Bioengineering 6000: System Physiology I

Mechanics ofCardiac Tissue

CVRTIPD Dr.-Ing. Frank B. Sachse

Mechanics of Cardiac Tissue -

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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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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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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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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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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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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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Force Development: Sliding Filament TheoryForce Development: Sliding Filament Theory

http://www.sci.sdsu.edu/movies/actin_myosin.html


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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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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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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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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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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

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