modeling of heart mechanics with adaptation of tissue to load
DESCRIPTION
Modeling of heart mechanics with adaptation of tissue to load. Theo Arts [email protected] Frits Prinzen, Tammo Delhaas*, Peter Bovendeerd**, J. Lumens, W. Kroon (Biophysics, Physiology, Pediatric Cardiology, Engineering) Maastricht University, *Maastricht University Hospital - PowerPoint PPT PresentationTRANSCRIPT
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Theo [email protected]
Frits Prinzen, Tammo Delhaas*, Peter Bovendeerd**, J. Lumens, W. Kroon (Biophysics, Physiology, Pediatric Cardiology, Engineering)
Maastricht University, *Maastricht University Hospital**University of Technology, Eindhoven
The Netherlands
IPAM Feb 06
Modeling of heart mechanics with adaptation of tissue to load
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Modeling:- Finite Element Model Electro-Mechanics of the heart- CircAdapt = whole circulation model- Incorporation of adaptation with Self-structuring
Models
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left+right ventricle movie:
sarcomere length & pV
FEM of LV+RV- paced, depolarization wave with pacing- full cardiac cycle(R. Kerckhoffs, 2003)
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CircAdapt model of heart and circulation
lungs
RA
RV
LA
LV
aorta
system
Dynamic(t)CompliancesInertiasNon-linear
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Modeling structure of myocardial wall with adaptation:- mechanical load determines
wall massfiber orientationsheet orientation
- size and shape of blood vessels
Enormous reduction of number of parameters
Especially in pathology: Generally 1 basic cause of pathology, followed by physiological adaptation processes.
Parameter reduction: Self-structuring by simulation of adaptation
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gene expressionprotein formation
adaptation
Local tissue adaptation
(pump) function
pressure flow load
tissue propertiesstructuregeometry
tissuestress & strain
Whole organ function
Cardiovascular adaptation to mechanical load
Implication: Cell adaptation determines organ structure
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Myofiber structure and hypertrophy
Result of local adaptation?
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Cardiac fiber structure
F. Torrent-Guasp
LVRV
apical view, upper layers peeled off(randomly?)
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Filling/Rest
Activation
Relaxation
Force/StretchSynchrony
Shortening
What signals to the cells can be used for adaptation?
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fibroblast
extra-cellularmatrix
myocyte
deformation
(filling)
myocyte orientation
in myocyte optimum: - principal stress alingment - sarcomere shortening
(fiber structure)
tissue mass (wall mass)
stretch contractility
extra-cellular matrix strain
softening
Used adaptation rules of cardiac tissue
Arts, 1994, Biophys J. 66:953-961.
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Diffusion Tensor ImagingMyofiber orientation components in cross-section
of the goat heart.
posterior
anterior
perpendicular
in plane Base to apex In plane
1/2
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Transmural course of helix angle (goat)
L. GeertsAJP 2002
model predicted
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10
5
0
midwall radius ( )
mm
baseapex-20 20(mm)
equator
0
model prediction
10o
0o
-10o
transverseangle ( )
Transverse angle, model experiment (pig)
leftventricle
L. Geerts, AJP 2002
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Myofiber structure
Proposed adaptation rules for local tissue →
Realistic helical and transverse fiber structure
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Sheet structure
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Fiber-Sheet Structure
endocardium
midwall
epicardium
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Sheets split on plane of maximum shear
Hypothesis
Find plane with maximum shear
45o directions of maximum shear,
2 planes
Fiber direction not in one of those planes
Constraint: Sheet planes also contain the fiber direction
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Sheet Angles6 pooledexperiments BASE
rz rzrc rc
APEX
0o
45o
90o
135o
180o
0o
45o
90o
135o
180o
epi endo Arts, T, Am J Physiol. 280:H2222-H2229 (2001).
model predicted: 2 solutions with different likelyhood
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Simulation of short axis sheet cross-sections
seems realistic
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Sheets facilitate wall thickening and shortening by shear
(and rotation)
(J. Covell)
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Unloading for shear by 90º sheet rotation has same macroscopic effect on mechanics, ab= ba ≈ 0
So, sheet orientation itself is quite irrelevant for modeling, as long as it unloads the major component of shear stress.
2 solutions for sheat orientation
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Cross-sheet slice
Courtesy A. Young
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Sheet structure
- Sheet plane contains myofiber direction
- Designed to facilitate cross fiber deformation, thus minimizing chamber stiffness
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Application of predicted structure in analysis
Non-invasive determination of transmural difference in myofiber shortening with aortic stenosis
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epi
Aortic stenosis
aortic stenosis
endo
region with high intramyocardial pressure,causing coronary flow obstruction
high left ventricular
pressure
Subendocardial dysfunction
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- Torsion tuned to Shortening- IF Subendocardial TSR=( Torsion / Shortening )
Shortening & Torsioninner - - outer - -
outer
inner
Shortening onlyinner - - -outer -
Torsion onlyinner +outer -
Wall segment model (cylindrical)
Determination of transmural differences
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Rotation and deformation of the heart can be quantified
ribs
LV wall
RV
cavity
lung
Magnetic Resonance Tagging (MRT)
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MRTshortening
torsion
torsion
shortening = ln(Cavity Area)
Definitions
Torsion/Shortening measurement
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Mri-Software: Midwall motion and circumferential strain
Normal human left ventricle
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TSR in Control and AVS patients
Inner wall strain ln(L/LVc=Vw)
TSR=slope of torsion versus inner wall strain in systole:
- Dimensionless- Species independent- Expresses transmural difference in contractile function
Control= healthy young
AVSten= Aortic Valve Stenosis
AVRepl= 3 mo after aortic valve replacement
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From TSR to TransDifModel:
Torsion/Shortening (TSR)↓
normalized transmural difference in myofiber shortening (TransDif)
TransDif=Difference/Mean
Van der Toorn A et al. Am J Physiol. 2002;283:H1609-1615
Stunned subendocardial
myocardium regains function
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CircAdapt modela. Modeling of circulation
- Lumped model in modules:chambers, tubes, valves
b. Adaptation of modules to load
Search:
Google + keyword ‘CircAdapt’
hit ‘AJP’: Arts T et al. Am J Physiol. 2005;288:H1943-H1954hit ‘Biophysics’: MatLab source code
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Circulation in modules
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1-fiber model of a thick-walled cavity (chamber or blood vessel)
Vlv
plv
Vw
ventricle (LV)
wrapped in 1 myofiber
wlv3
1f
wlvlvf
VV31ln
VV31p
f= myofiber stressf= myofiber strainplv= LV pressureVlv= LV volumeVw= wall volume
FEM model confirms: Shape is practically irrelevant
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Laws of adaptation
Adaptation of Blood vessel• Shear stress → Diameter ↑
• Wall stress → Wall thickness ↑
• Contractility+diastolic stretch → Hypertrophy
• Deformation → Dilatation
Adaptation of Cavity
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Input to CircAdapt value SI-unit description
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Simulations after adaptation
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Pressure-Volume & Stress-Strain Loops
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Calculated parameters= Result
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Promising applications
1. Boundary conditions for FEM of heart
2. Patient specific modeling
3. “Non-invasive catheterization”Pressure difference over:
- membrane → pressure transducer
- valve with inertiadoppler velocity and accelerationmass ~ dynamic membrane
→ pressure transducer
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Hypertrophy in12 wks myofiber
mechanics in AV-block
Systolic fiber stress is not the stimulus to hypertrophy.
More likely: end-diastolic stress
(Donker et al, Basic Res Cardiol, 2005).
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Adaptation rules with‘deformation intervention’
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fiber direction
torsion
fiber direction
torsion
Situs Solitus(normal)
Situs InversusTotalis (SIT) Hypothesis
SIT heart with mirrored fiber structure is an alternative solution satisfying adaptation rules of cardiac cells.
Test
SIT heart should have equal torsion but in opposite direction.
occurrence
8000 : 1
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Situs Inversus Totalis Normal
(pig SIT heart)
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Situs Solitus (normal) ?? Situs Inversus Totalis ??Torsion (rad)
-0.20 -0.10 0 0.10 0.20
Expected torsion in SIT
NOT TRUE !
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-0.10
0.00
0.10
0.20Rotation
[rad]
-0.20
-0.10
0.00
0.10Torsion
5 base43
2
1 apex
d basecba apex
Situs Solitus(normal)
Situs InversusTotalis (n=14)
0.5 s
Human torsion
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-0.20
Situs Solitus (normal) Situs Inversus Totalis
Torsion (rad)
Torsion in SIT
-0.10 0 0.10 0.20
Delhaas, T. et al. Ann N Y Acad Sci 1015: 190-201.
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Myofiber structure in SITNormal adaptation rules
Start conditions for fiber structure:- normal apex- inverse base
Development to SIT structure
→ RESULT
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Situs Inversus Totalis
A natural in vivo ‘experiment’ to investigate cell’s long term response to a variety of deformations
boundary conditions
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inverse
Dualistic myofiber structure SIT
Helix angleendo - epi
inverse
normal
normal
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Efficency
The structure of the SIT heart is different.
Because each cell optimizes generation of mechanical work (= adaptation rule), all cells work close to their optimum. Since the only escape of mechanical work is pump work, the SIT heart works about just as optimal as the normal heart.
stress-strain work
stress-strain work
stress-strain work
The only escape of work:
pump work (p-V)
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General conclusion: Self-structuring by adaptation
“morphogenetic draft”
result
Self-adaptation until load is proper
growing brick
- works for cardiovascular modeling on all levels- adaptation can be modeled- should be used as prior knowledge in heart modeling
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That ’SIT