Karol Miller
Department
of Mechanical and Materials Engineering, The University of Western Australia “Non-linear Computer Simulation of Brain Deformation In-Vivo” The
presentation describes realistic computer simulation of deformation
of the brain subject to in-vivo indentation. This work provides
a step towards neurosurgical simulation, with applications to non-rigid
registration, virtual reality training and operation planning systems
and robotic devices to perform minimally invasive brain surgery. An
in-vivo indentation experiment is described. The force-displacement
curve for the loading speed typical for surgical procedures (10 mm/s)
is concave upward containing no linear portion, from which a meaningful
elastic modulus might be determined. To properly analyze experimental
data, a three-dimensional, non-linear mathematical model of the brain
was developed. The model included large deformation, non-linear (hyper-viscoelastic)
material properties and non-linear (finite sliding) boundary conditions.
The model was solved using the finite element method. Magnetic resonance
imaging techniques were used to obtain geometric information needed
to create the finite element mesh. The shape of the force-displacement curve obtained using
the numerical solution was very similar to the experimental one. The
predicted forces were about 31% lower than those recorded during the
experiment. Having in mind that the coefficients in the model had been
identified based on experimental data obtained in-vitro, and
large variability of mechanical properties of biological tissues, such
agreement can be considered as very good. By appropriately increasing
material parameters describing instantaneous stiffness of the tissue
one is able, without changing the structure of the model, to reproduce
the experimental curve almost perfectly. Results obtained using the implicit time integration
may serve for calibration of simpler, real-time models. The explicit
time integration may allow simulating soft organ deformation in real-time.
Numerical studies showed also, that the linear, viscoelastic model of
brain tissue is not appropriate for the modeling brain tissue deformation
even for moderate strains. More information about soft organ mechanical properties
and computer simulation of brain deformation can be found in the following
references, available in .pdf format from www.sciencedirect.com :
Miller, K., "How to test very soft biological tissues
in extension?", J. Biomechanics,Vol 34/5, pp. 651-657, 2001
Miller K., Chinzei K., Orssengo G. and Bednarz
P. , "Mechanical properties of brain tissue in-vivo: experiment
and computer simulation", J. Biomechanics, Vol. 33, pp.
1369-1376, 2000
Miller, K. "Constitutive Model of Abdominal
Organs", J. Biomechanics., Vol. 33/3, pp. 367-373, 2000.
Miller, K. "Constitutive Model of Brain Tissue
Suitable for Finite Element Analysis of Surgical Procedures", J.
Biomechanics, Vol. 32, pp. 531-537, 1999.
Miller, K., "Modelling Soft Tissue Using Biphasic
Theory - A Word of Caution". Comp. Meth. Biomech. Biomed. Eng.,
Vol.1, pp.261-263, 1998.
Miller, K., Chinzei K., "Constitutive Modelling
of Brain Tissue; Experiment and Theory", J. Biomech., Vol.
30, No. 11/12, pp. 1115-1121, 1997. |