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.