Skip to main content

Table 2 Assumed and estimated parameters and their variations for the models using a sphere.

From: Data-guide for brain deformation in surgery: comparison of linear and nonlinear models

Mechanical model Young modulus Poisson's ratio Force
Assumed 0.45 3000 Fx = 1500
      Fy = 1500
      Fz = 1500
Estimated 0.45 ± 0.0056 3000 ± 175.6 Fx = 1500 ± 90.8
      Fy = 1500 ± 87.9
      Fz = 1500 ± 93.2
Nonlinear model C100 C010 C200 C020 g 1 +g 2 Force
Assumed 263 263 491 491 0.815 Fx = -300
       Fy = 300
       Fz = 300
Estimated 263
±4.0401
263
±7.8404
491
±14.4139
491
±13.4578
0.815
±0.0083
Fx = -300 ± 9.1726
       Fy = 300 ± 10.0278
       Fz = 300 ± 8.7998
  1. We use sphere as a simple model of the brain. Specific parameters are assumed and the resulting deformations of specific points are used in the optimization process. Other points are used for testing of the optimization process. Then, the parameters are changed and the optimization process is repeated to estimate the model parameters again. The results illustrate that the brain deformation can be modeled by the proposed models and the proposed optimization method can accurately estimate the model parameters. For each model, we have done this process and have compared the accuracy of models using the matching errors of the points used in the optimization process and those that are not used. Note that the optimization process estimates the parameters of the nonlinear model more accurately (with less bias and variance) compared with the mechanical model.