Modeling of heart mechanics with
adaptation of tissue to load
Theo Arts
t.arts@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
1
Models
Modeling:
- Finite Element Model Electro-Mechanics of
the heart
- CircAdapt = whole circulation model
- Incorporation of adaptation with Selfstructuring
2
FEM of LV+RV
- paced, depolarization
wave with pacing
- full cardiac cycle
(R. Kerckhoffs, 2003)
left+right
ventricle
movie:
sarcomere
length & pV
3
CircAdapt model of heart and circulation
lungs
aorta
RA
Dynamic(t)
Compliances
Inertias
Non-linear
LA
RV
LV
system
4
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.
5
Cardiovascular adaptation to mechanical load
Whole organ function
tissue
stress & strain
gene expression
protein formation
adaptation
Local tissue
adaptation
(pump)
function
pressure
flow load
tissue properties
structure
geometry
Implication: Cell adaptation determines organ structure6
Myofiber structure
and hypertrophy
Result of local adaptation?
7
Cardiac fiber structure
apical view, upper layers peeled off
(randomly?)
RV
LV
F. Torrent-Guasp
8
What signals to the cells can be used for adaptation?
Filling/Rest
Activation
Force/Stretch
Synchrony
Shortening
Relaxation
9
Used adaptation rules of cardiac tissue
extra-cellular
matrix
myocyte orientation
(fiber structure)
fibroblast
myocyte
in myocyte optimum:
- principal stress alingment
- sarcomere shortening
deformation
stretch
contractility
extra-cellular
matrix strain
softening
tissue mass
(wall mass)
(filling)
10
Arts, 1994, Biophys J. 66:953-961.
11
1/2
Diffusion Tensor Imaging
Myofiber orientation components in cross-section
of the goat heart.
perpendicular
posterior
anterior
in plane
Base to apex
In plane
12
Transmural course of helix angle (goat)
model predicted
L. Geerts
AJP 2002
13
Transverse angle, model experiment (pig)
midwall radius ( )
15
mm
10o
10
left
ventricle
equator
5
0
-20
apex
0 (mm) 20
base
model prediction
0o
transverse
angle ( )
-10o
L. Geerts, AJP 2002
14
Myofiber structure
Proposed adaptation
rules for local tissue →
Realistic helical and
transverse fiber structure
15
Sheet structure
16
Fiber-Sheet Structure
endocardium
midwall
epicardium
17
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
18
Sheet Angles
6 pooled
experiments
APEX
BASE
180o
135o
90o
45o
0o
rz
rc
rz
rc
model predicted: 2 solutions with different likelyhood
180o
135o
90o
45o
0o
epi
endo
19
Arts, T, Am J Physiol. 280:H2222-H2229 (2001).
Simulation of short axis sheet
cross-sections
seems
realistic
20
Sheets facilitate wall thickening and
shortening by shear
(and rotation)
(J. Covell)
21
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.
22
Cross-sheet slice
Courtesy A. Young
23
Sheet structure
- Sheet plane contains
myofiber direction
- Designed to facilitate crossfiber deformation, thus
minimizing chamber stiffness
24
Application of predicted
structure in analysis
Non-invasive determination of
transmural difference in myofiber
shortening with aortic stenosis
25
Aortic
stenosis
Subendocardial
dysfunction
region with high
intramyocardial
pressure,
causing coronary
flow obstruction
aortic stenosis
high left
ventricular
pressure
endo
epi
26
Wall segment model (cylindrical)
Determination of
transmural
differences
inner
outer
Shortening only
inner - - outer Shortening & Torsion
inner - - outer - -
Torsion only
inner +
outer - Torsion tuned to Shortening
- IF Subendocardial 
TSR=( Torsion / Shortening )  
27
Magnetic Resonance Tagging (MRT)
ribs
RV
cavity
lung
Rotation and
deformation
of the heart
can be
quantified
LV wall
28
Torsion/Shortening measurement
shortening
MRT
Definitions
torsion
shortening =
D ln(Cavity Area)
torsion
29
Mri-Software: Midwall motion and circumferential strain
Normal
human
left
ventricle
30
TSR in Control and AVS patients
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
Inner wall strain ln(L/LVc=Vw)
31
From TSR
to TransDif
Model:
Torsion/Shortening (TSR)
↓
normalized transmural
difference in myofiber
shortening (TransDif)
Stunned
subendocardial
myocardium
regains
function
TransDif=Difference/Mean
32
Van der Toorn A et al. Am J Physiol. 2002;283:H1609-1615
CircAdapt model
a. 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-H1954
hit ‘Biophysics’: MatLab source code
33
Circulation in modules
34
1-fiber model of a thick-walled
cavity (chamber or blood vessel)
ventricle
(LV)
Vlv
plv
Vw
wrapped in
1 myofiber
f  plv 1  3 Vlv Vw 
Df  31 D ln1  3 Vlv Vw 
f= myofiber stress
Df= myofiber strain
plv= LV pressure
Vlv= LV volume
Vw= wall volume
FEM model confirms: Shape is practically irrelevant
35
Laws of adaptation
Adaptation of Cavity
• Contractility+diastolic stretch → Hypertrophy
• Deformation → Dilatation
Adaptation of Blood vessel
• Shear stress → Diameter ↑
• Wall stress → Wall thickness ↑
36
Input to CircAdapt
value
SI-unit
description
37
Simulations after adaptation
38
Pressure-Volume & Stress-Strain Loops
39
Calculated parameters= Result
40
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
41
Hypertrophy
in12 wks
myofiber
mechanics
in AV-block
Systolic fiber stress
is not the stimulus to
hypertrophy.
More likely: enddiastolic stress
(Donker et al, Basic Res
Cardiol, 2005).
42
Adaptation rules with
‘deformation intervention’
43
Situs Solitus
(normal)
Situs Inversus
Totalis (SIT)
Hypothesis
SIT heart with
mirrored fiber
structure is an
alternative
solution satisfying
adaptation rules
of cardiac cells.
occurrence
8000 : 1
Test
fiber direction
torsion
fiber direction
SIT heart should
have equal
torsion but in
opposite direction.
torsion
44
Situs Inversus Totalis
(pig SIT heart)
Normal
45
Expected torsion in SIT
-0.20 -0.10
Situs Solitus (normal)
0
0.10 0.20
Torsion (rad)
?? Situs Inversus Totalis ??
NOT TRUE !
46
Human
torsion
Situs Solitus
(normal)
Rotation
0.20
[rad]
0.10
0.00
Situs Inversus
Totalis (n=14)
5 base
4
3
2
1 apex
-0.10
Torsion
0.10
0.00
-0.10
d base
c
b
a apex
-0.20
0.5 s
47
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.
48
Myofiber structure in SIT
Normal adaptation rules
Start conditions for fiber structure:
- normal apex
- inverse base
Development to SIT structure
→ RESULT
49
Situs
Inversus
Totalis
boundary
conditions
A natural in vivo
‘experiment’ to
investigate cell’s
long term
response to a
variety of
deformations
50
Dualistic myofiber structure SIT
Helix angle
endo - epi
inverse
inverse
normal
normal
51
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.
stressstrain work
stressstrain work
stressstrain work
The only escape
of work:
pump work (p-V)
52
General conclusion: Self-structuring by adaptation
“morphogenetic
draft”
result
growing
brick
Self-adaptation
until load is proper
- works for cardiovascular modeling on all levels
- adaptation can be modeled
- should be used as prior knowledge in heart modeling
53
That
’SIT
54