Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.

References

References
1.
Dorfmann
,
A.
,
Trimmer
,
B. A.
, and
Woods
W. A.
, 2007,
“A Constitutive Model for Muscle Properties in a Soft-Bodied Arthropod,”
J. R. Soc., Interface
,
4
(
13
), pp.
257
269
.
2.
Holzapfel
,
G.
,
Gasser
,
T.
, and
Ogden
,
R.
, 2000,
“A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models,”
J. Elast.
,
61
(
1
), pp.
1
48
.
3.
Taber
,
L. A.
, 2004,
Nonlinear Theory of Elasticity: Applications in Biomechanics
,
World Scientific Publishing Co.
,
Singapore
.
4.
Fung
,
Y.
, 1967,
“Elasticity of soft tissues in simple elongation,”
Am. J. Physiol.
,
213
(
6
), pp.
1532
1544
.
5.
Tanaka
,
M. L.
,
Weisenbach
,
C. A.
,
Miller
,
M. C.
, and
Kuxhaus
,
L.
, 2011,
“A Continuous Method to Compute Model Parameters for Soft Biological Materials,”
J. Biomech. Eng.
,
133
(
7
), pp.
074502
.
6.
Jewell
,
B. R.
, and
Wilkie
,
D. R.
, 1958,
“An Analysis of the Mechanical Components in Frog’s Striated Muscle,”
J. Physiol.
,
143
(
3
), pp.
515
540
.
7.
Coburn
,
J.
, and
Crisco
,
J. J.
, 2005,
“Interpolating Three-Dimensional Kinematic Data Using Quaternion Splines and Hermite Curves,”
J. Biomech. Eng.
,
127
(
2
), pp.
311
317
.
8.
D’Errico
,
J.
, 2009,
“SLM-Shape Language Modeling,”
Matlab Central.
9.
Dierckx
,
P.
, 1980,
“Algorithm/Algorithmus 42 an Algorithm for Cubic Spline Fitting with Convexity Constraints,”
Computing
,
24
(
4
), pp.
349
371
.
10.
Mathews
,
J. H.
, and
Fink
,
K. D.
, 2004,
Numerical Methods Using MATLAB
,
Pearson Prentice Hall
,
New Jersey
.
You do not currently have access to this content.