Abstract

Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a L2-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.

1.
Leite-Moreira
,
A. F.
, 2006, “
Current Perspectives in Diastolic Dysfunction and Diastolic Heart Failure
,”
Heart
1355-6037,
92
, pp.
712
718
.
2.
Augenstein
,
K. F.
,
Cowan
,
B. R.
,
LeGrice
,
I. J.
,
Nielsen
,
P. M. F.
, and
Young
,
A. A.
, 2005, “
Method and Apparatus for Soft Tissue Material Parameter Estimation Using Tissue Tagged Magnetic Resonance Imaging
,”
ASME J. Biomech. Eng.
0148-0731,
127
(
1
), pp.
148
157
.
3.
Moulton
,
M. J.
,
Creswell
,
L. L.
,
Downing
,
S. W.
,
Actis
,
R. L.
,
Szabo
,
B. A.
, and
Pasque
,
M. K.
, 1996, “
Myocardial Material Property Determination in the in vivo Heart Using Magnetic Resonance Imaging
,”
Int. J. Card. Imaging
0167-9899,
12
(
3
), pp.
153
167
.
4.
Moulton
,
M. J.
,
Creswell
,
L. L.
,
Actis
,
R. L.
,
Myers
,
K. W.
,
Vannier
,
M. W.
,
Szabo
,
B. A.
, and
Pasque
,
M. K.
, 1995, “
An Inverse Approach to Determining Myocardial Material Properties
,”
J. Biomech.
0021-9290,
28
(
8
), pp.
935
948
.
5.
Sacks
,
M. S.
, and
Sun
,
W.
, 2003, “
Multiaxial Mechanical Behaviour of Biological Materials
,”
Annu. Rev. Biomed. Eng.
1523-9829,
5
, pp.
251
284
.
6.
Hunter
,
P. J.
,
Pullan
,
A. J.
, and
Smaill
,
B. H.
, 2003, “
Modelling Total Heart Function
,”
Annu. Rev. Biomed. Eng.
1523-9829,
5
, pp.
147
177
.
7.
Humphrey
,
J. D.
, 2002,
Cardiovascular Solid Mechanics—Cells, Tissues, and Organs
,
Springer
,
New York
.
8.
Dokos
,
S.
,
Smaill
,
B. H.
,
Young
,
A.
, and
LeGrice
,
I. J.
, 2002, “
Shear Properties of Passive Ventricular Myocardium
,”
Am. J. Physiol. Heart Circ. Physiol.
0363-6135,
283
, pp.
H2650
H2659
.
9.
Schmid
,
H.
,
Nash
,
M. P.
,
Young
,
A. A.
, and
Hunter
,
P. J.
, 2006, “
Myocardial Material Parameter Estimation—A Comparative Study for Simple Shear
,”
ASME J. Biomech. Eng.
0148-0731,
128
, pp.
742
750
.
10.
Schmid
,
H.
,
Nash
,
M. P.
,
Young
,
A. A.
, and
Hunter
,
P. J.
, 2006, “
Myocardial Material Parameter Estimation From Simple Shear Tests—A non-Homogeneous Finite Element Study
,” Biomechanics and Modelling in Mechanobiology, in review.
11.
Holzapfel
,
G. A.
, 2000,
Nonlinear Solid Mechanics
,
Wiley
,
Chichester
.
12.
Costa
,
K. D.
,
Holmes
,
J. W.
, and
McCulloch
,
A. D.
, 2001, “
Modeling Cardiac Mechanical Properties in Three Dimensions
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
359
(
1783
), pp.
1233
1250
.
13.
LeGrice
,
I. J.
,
Smaill
,
B. H.
,
Chai
,
L. Z.
,
Edgar
,
S. G.
,
Gavin
,
J. B.
, and
Hunter
,
P. J.
, 1995, “
Laminar Structure of the Heart: Ventricular Myocyte Arrangement and Connective Tissue Architecture in the Dog
,”
Am. J. Physiol. Heart Circ. Physiol.
0363-6135,
38
(
269
), pp.
H571
H582
.
14.
Bonet
,
J.
, and
Wood
,
R. D.
, 1997,
Nonlinear Continuum Mechanics for the Finite Element Analysis
,
Cambridge University Press
,
Cambridge
.
15.
Schmid
,
H.
, 2006, “
Passive Myocardial Mechanics—Constitutive Laws and Material Parameter Estimation
,” Ph.D. thesis, University of Auckland, New Zealand.
16.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
, 1989,
Numerical Recipes
,
Cambridge University Press
,
Cambridge
.
17.
Atkinson
,
K.
, 1989,
An Introduction to Numerical Analysis
, 2nd ed.,
Wiley
,
New York
.
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