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

Surface Registration with Eigenvalues and Eigenvectors

This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. In our technique, the variation of the shape is expressed using a scale function defined at each vertex. Consequently, the total energy function to align the two given surfaces can be defined using the linear interpolation of the scale function derivatives. Through the optimization of the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid Iterative Closest Point (ICP) and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method.

Brain shift in neuronavigation of brain tumors: A review

PURPOSE

Neuronavigation based on preoperative imaging data is a ubiquitous tool for image guidance in neurosurgery. However, it is rendered unreliable when brain shift invalidates the patient-to-image registration. Many investigators have tried to explain, quantify, and compensate for this phenomenon to allow extended use of neuronavigation systems for the duration of surgery. The purpose of this paper is to present an overview of the work that has been done investigating brain shift.

METHODS

A review of the literature dealing with the explanation, quantification and compensation of brain shift is presented. The review is based on a systematic search using relevant keywords and phrases in PubMed. The review is organized based on a developed taxonomy that classifies brain shift as occurring due to physical, surgical or biological factors.

RESULTS

This paper gives an overview of the work investigating, quantifying, and compensating for brain shift in neuronavigation while describing the successes, setbacks, and additional needs in the field. An analysis of the literature demonstrates a high variability in the methods used to quantify brain shift as well as a wide range in the measured magnitude of the brain shift, depending on the specifics of the intervention. The analysis indicates the need for additional research to be done in quantifying independent effects of brain shift in order for some of the state of the art compensation methods to become useful.

CONCLUSION

This review allows for a thorough understanding of the work investigating brain shift and introduces the needs for future avenues of investigation of the phenomenon.

Estimation of intra-operative brain shift based on constrained Kalman filter

In this study, the problem of estimation of brain shift is addressed by which the accuracy of neuronavigation systems can be improved. To this end, the actual brain shift is considered as a Gaussian random vector with a known mean and an unknown covariance. Then, brain surface imaging is employed together with solutions of linear elastic model and the best estimation is found using constrained Kalman filter (CKF). Moreover, a recursive method (RCKF) is presented, the computational cost of which in the operating room is significantly lower than CKF, because it is not required to compute inverse of any large matrix. Finally, the theory is verified by the simulation results, which show the superiority of the proposed method as compared to one existing method.