Table 1.

Summary of requirements and recommendations for brain biomechanics modeling depending on application, based on the Intelligent Systems for Medicine Laboratory’s (ISML) 23 years of experience.

	Type of Application
	Intraoperative neuroimage registration	Neurosurgical simulation for training and/or skill assessment	Neurosurgical simulation for operation planning
Patient specific?	Yes	No	Yes
Model components	Brain parenchyma (separate treatment of gray and white matter not necessary), CSF (especially in ventricles), tumor. Explicit modeling of the brain vasculature — not needed	Depends on specific application
Real time?	Yes, ca. between 40 s and 90 s to compute deformations and warp image. Practical limit can be defined as the time a neuro-surgeon is willing/can wait for the modeling results.	Yes, haptic rate 500 Hz or better
Source of geometric information	Anatomical MRI	Electronic brain atlas	Anatomical MRI
Rapid generation of computational grid	Needed	Not needed	Needed
Spatial discretization method	Meshless	Finite elements	Meshless
Reliable computation of displacements	Needed	Needed
Reliable computation of internal stresses	Not needed	Not needed
Reliable computation of reaction forces (e.g. acting on surgical tools)	Not needed	Needed
Loading	Enforced motion of the exposed brain surface (measured intraoperatively)	Enforced motion of the boundary (at the contact with the virtual tool)
Constitutive model of intracranial constituents	The simplest model compatible with finite deformation solution procedure: Neo-Hookean	Deformation gradients computed using the simplest model (Neo-Hookean) compatible with the finite deformation procedure are resubstituted to realistic constintutive model (we recommend Ogden-type) in the vicinity of the surgical tool where the reactions acting on surgical tool need to be computed.
Brain-skull interaction model	Frictionless finite sliding with separation
Solution procedure	Fully geometrically and materially nonlinear
Time stepping	Explicit with dynamic relaxation, the simplest central differences	Explicit, time-accurate, the simplest central differences
Practical model size	40–100 × 103 degrees of freedom	40–100 × 103 degrees of freedom for computational grid, more can be used for visualization.
Solution algorithm verification	Against a converged finite element solution using hybrid (i.e. displacement-pressure formulation) finite elements
Model validation	Against intraoperative imaging, preferable intraoperative MRI	N/A. However, expert user feedback may be useful