Theo Arts

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Modeling of heart mechanics with adaptation of
tissue to load

• Theo Arts
• t.arts_at_bf.unimaas.nl
• 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

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Models

• Modeling- Finite Element Model
  Electro-Mechanics of the heart- CircAdapt
  whole circulation model- Incorporation of
  adaptation with Self-structuring

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leftright ventricle moviesarcomere length pV
FEM of LVRV- paced, depolarization wave with
pacing- full cardiac cycle(R. Kerckhoffs, 2003)
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CircAdapt model of heart and circulation
Dynamic(t)CompliancesInertiasNon-linear
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Parameter reduction Self-structuring by
simulation of adaptation

• Modeling structure of myocardial wall with
  adaptation- mechanical load determines wall
  mass fiber orientation sheet 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.

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Cardiovascular adaptation to mechanical load
Whole organ function
tissue stress strain
(pump) function
pressure flow load
gene expression protein formation adaptation
tissue properties structure geometry
Local tissue adaptation
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
apical view, upper layers peeled off(randomly?)
LV
RV
F. Torrent-Guasp
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What signals to the cells can be used for
adaptation?
Filling/Rest
Activation
Force/Stretch Synchrony
Shortening
Relaxation
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Used adaptation rules of cardiac tissue
extra-cellular matrix
myocyte orientation
(fiber structure)
in myocyte optimum - principal stress
alingment - sarcomere shortening
fibroblast
myocyte
stretch contractility
deformation
extra-cellular matrix strain softening
tissue mass
(wall mass)
(filling)
Arts, 1994, Biophys J. 66953-961.
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(No Transcript)
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Diffusion Tensor Imaging
1/2
Myofiber orientation components in cross-section
of the goat heart.
perpendicular
posterior
anterior
in plane
Base to apex In plane
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Transmural course of helix angle (goat)
L. GeertsAJP 2002
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Transverse angle, model ?experiment (pig)
midwall
radius
(


)
1
5
m
m
o
1
0
10
equator
5
0
o
0
-20
20
(mm)
0
ap
ex
ba
se
model prediction
o
-10
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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Hypothesis
Sheets split on plane of maximum shear
45o directions of maximum shear,
Fiber direction not in one of those planes
2 planes
Find plane with maximum shear
Constraint Sheet planes also contain the fiber
direction
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Sheet Angles
6 pooledexperiments
BASE
APEX
180o
135o
90o
45o
0o
rz
rz
rc
rc
model predicted 2 solutions with different
likelyhood
180o
135o
90o
45o
0o
epi endo
Arts, T, Am J Physiol. 280H2222-H2229 (2001).
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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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2 solutions for sheat orientation
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.
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Cross-sheet slice
Courtesy A. Young
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Sheet structure
- Sheet plane contains myofiber direction -
Designed to facilitate crossfiber 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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Aortic stenosis
Subendocardial dysfunction
region with high intramyocardial
pressure, causing coronary flow obstruction
aortic stenosis
high left ventricular pressure
endo
epi
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Wall segment model (cylindrical)
Determination of transmural differences
inner
outer
Shortening only inner - - - outer -
Torsion only inner outer -

• Torsion tuned to Shortening
• IF Subendocardial ?
• TSR( Torsion? / Shortening? ) ? ?

Shortening Torsion inner - - outer - -
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Magnetic Resonance Tagging (MRT)
ribs
RV
cavity
lung
Rotation and deformation of the heart can be
quantified
LV wall
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Torsion/Shortening measurement
shortening
MRT
Definitions
shortening D ln(Cavity Area)
torsion
torsion
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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
TSRslope 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
Inner wall strain ln(L/LVcVw)
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From TSR to TransDif
Model Torsion/Shortening (TSR)? normalized
transmural difference in myofiber shortening
(TransDif) TransDifDifference/Mean
Stunned subendocardial myocardium regains function
Van der Toorn A et al. Am J Physiol.
2002283H1609-1615
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CircAdapt model
a. Modeling of circulation - Lumped model in
modules chambers, tubes, valvesb. Adaptation
of modules to load
Search Google keyword CircAdapt hit AJP
Arts T et al. Am J Physiol. 2005288H1943-H1954h
it 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)
ventricle (LV)
wrapped in 1 myofiber
Vlvplv
?f myofiber stress??f myofiber strainplv LV
pressureVlv LV volumeVw wall volume
Vw
FEM model confirms Shape is practically
irrelevant
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Laws of adaptation
Adaptation of Cavity

• Contractilitydiastolic stretch ? Hypertrophy
• Deformation ? Dilatation

Adaptation of Blood vessel

• Shear stress ? Diameter ?
• Wall stress ? Wall thickness ?

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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 inertia doppler
velocity and acceleration mass 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 withdeformation intervention
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Situs Solitus (normal)
Situs Inversus Totalis (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
fiber direction
fiber direction
torsion
torsion
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Situs Inversus Totalis Normal
(pig SIT heart)
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Expected torsion in SIT
-0.20
-0.10
0
0.10
0.20
?? Situs Inversus Totalis ??
Situs Solitus (normal)
Torsion (rad)
NOT TRUE !
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Human torsion
Situs Solitus (normal)
Situs Inversus Totalis (n14)
Rotation
0.20
5 base
rad
4
0.10
3
2
0.00
1 apex
-0.10
Torsion
0.10
d base
0.00
c
b
-0.10
a apex
-0.20
0.5 s
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Torsion in SIT
Situs Solitus (normal)
Situs Inversus Totalis
-0.20
-0.10
0
0.10
0.20
Torsion (rad)
Delhaas, T. et al. Ann N Y Acad Sci 1015 190-201.
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Myofiber structure in SIT
Normal adaptation rules Start conditions for
fiber structure - normal apex - inverse
base Development to SIT structure
? RESULT
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Situs Inversus Totalis
boundary conditions
A natural in vivo experiment to investigate
cells long term response to a variety of
deformations
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Dualistic myofiber structure SIT
Helix angle endo - epi
inverse
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
The only escape of work pump work (p-V)
stress-strain work
stress-strain work
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General conclusion Self-structuring by adaptation

• 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