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.

Visualizing Shape Deformations with Variation of Geometric Spectrum.

This paper presents a novel approach based on spectral geometry to quantify and visualize non-isometric deformations of 3D surfaces by mapping two manifolds. The proposed method can determine multi-scale, non-isometric deformations through the variation of Laplace-Beltrami spectrum of two shapes. Given two triangle meshes, the spectra can be varied from one to another with a scale function defined on each vertex. The variation is expressed as a linear interpolation of eigenvalues of the two shapes. In each iteration step, a quadratic programming problem is constructed, based on our derived spectrum variation theorem and smoothness energy constraint, to compute the spectrum variation. The derivation of the scale function is the solution of such a problem. Therefore, the final scale function can be solved by integral of the derivation from each step, which, in turn, quantitatively describes non-isometric deformations between two shapes. To evaluate the method, we conduct extensive experiments on synthetic and real data. We employ real epilepsy patient imaging data to quantify the shape variation between the left and right hippocampi in epileptic brains. In addition, we use longitudinal Alzheimer data to compare the shape deformation of diseased and healthy hippocampus. In order to show the accuracy and effectiveness of the proposed method, we also compare it with spatial registration-based methods, e.g., non-rigid Iterative Closest Point (ICP) and voxel-based method. These experiments demonstrate the advantages of our method.

Degree of corticospinal tract damage correlates with motor function after stroke.

OBJECTIVES: Direct injury to the corticospinal tract (CST) is a major factor defining motor impairment after stroke. Diffusion tensor imaging (DTI) tractography allows definition of the CST. We sought to determine whether DTI-based assessment of the degree of CST damage correlates with motor impairment at each phase of ischemic stroke. METHODS: We evaluated patients at the acute (3-7 days), subacute (30 days), and chronic (90 days) phases of ischemic stroke with DTI and clinical motor scores (upper extremity Fugl-Myer test [UE-FM], motor items of the National Institutes of Health Stroke Scale [mNIHSS]). The CST was identified and virtual fiber numbers (FN) were calculated for the affected and contralateral CST. We used Spearman correlation to study the relationship of FN ratio (FNr) (affected/unaffected CST) with motor scores at each time point, and the regression model to study the association of the acute parameters with chronic motor scores. RESULTS: We studied 23 patients. Mean age was 66.7 (±12) years. FNr correlated with UE-FM score in the acute (r = 0.50, P = 0.032), subacute (r = 0.57, P = 0.007), and chronic (r = 0.67, P = 0.0008) phase, and with mNIHSS in the acute (r = -0.48, P = 0.043), subacute (r = -0.58, P = 0.006), and chronic (r = -0.75, P = 0.0001) phase. The combination of acute NIHSS and FNr significantly predicted chronic UE-FM score (r = 0.74, P = 0.0001). INTERPRETATION: DTI-defined degree of CST injury correlates with motor impairment at each phase of ischemic stroke. The combination of baseline FNr and NIHSS predicts motor outcome. DTI-derived CST assessment could become a surrogate marker of motor impairment in the design of neurorestorative clinical trials.

Lateralization of temporal lobe epilepsy using a novel uncertainty analysis of MR diffusion in hippocampus, cingulum, and fornix, and hippocampal volume and FLAIR intensity.

PURPOSE: To analyze the utility of a quantitative uncertainty analysis approach for evaluation and comparison of various MRI findings for the lateralization of epileptogenicity in mesial temporal lobe epilepsy (mTLE), including novel diffusion-based analyses. METHODS: We estimated the hemispheric variation uncertainty (HVU) of hippocampal T1 volumetry and FLAIR (Fluid Attenuated Inversion Recovery) intensity. Using diffusion tensor images of 23 nonepileptic subjects, we estimated the HVU levels of mean diffusivity (MD) in the hippocampus, and fractional anisotropy (FA) in the posteroinferior cingulum and crus of fornix. Imaging from a retrospective cohort of 20 TLE patients who had undergone surgical resection with Engel class I outcomes was analyzed to determine whether asymmetry of preoperative volumetrics, FLAIR intensities, and MD values in hippocampi, as well as FA values in posteroinferior cingula and fornix crura correctly predicted laterality of seizure onset. Ten of the cohort had pathologically proven mesial temporal sclerosis (MTS). Seven of these patients had undergone extraoperative electrocorticography (ECoG) for lateralization or to rule out extra-temporal foci. RESULTS: HVU was estimated to be 3.1×10(-5) for hippocampal MD, 0.027 for FA in posteroinferior cingulum, 0.018 for FA in crus of fornix, 0.069 for hippocampal normalized volume, and 0.099 for hippocampal normalized FLAIR intensity. Using HVU analysis, a higher hippocampal MD value, lower FA within the posteroinferior cingulum and crus of fornix, shrinkage in hippocampal volume, and higher hippocampal FLAIR intensity were observed beyond uncertainty on the side ipsilateral to seizure onset for 10, 10, 9, 9, and 10 out of 10 pathology-proven MTS patients, respectively. Considering all 20 TLE patients, these numbers were 18, 15, 14, 13, and 16, respectively. However, consolidating the lateralization results of HVU analysis on these quantities by majority voting has detected the epileptogenic side for 19 out of 20 cases with no wrong lateralization. CONCLUSION: The presence of MTS in TLE patients is associated with an elevated MD value in the ipsilateral hippocampus and a reduced FA value in the posteroinferior subregion of the ipsilateral cingulum and crus of ipsilateral fornix. When considering all TLE patients, among the mentioned biomarkers the hippocampal MD had the best performance with true detection rate of 90% without any wrong lateralization. The proposed uncertainty based analyses hold promise for improving decision-making for surgical resection.

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

BACKGROUND: Pre-operative imaging devices generate high-resolution images but intra-operative imaging devices generate low-resolution images. To use high-resolution pre-operative images during surgery, they must be deformed to reflect intra-operative geometry of brain. METHODS: We employ biomechanical models, guided by low resolution intra-operative images, to determine location of normal and abnormal regions of brain after craniotomy. We also employ finite element methods to discretize and solve the related differential equations. In the process, pre- and intra-operative images are utilized and corresponding points are determined and used to optimize parameters of the models. This paper develops a nonlinear model and compares it with linear models while our previous work developed and compared linear models (mechanical and elastic). RESULTS: Nonlinear model is evaluated and compared with linear models using simulated and real data. Partial validation using intra-operative images indicates that the proposed models reduce the localization error caused by brain deformation after craniotomy. CONCLUSIONS: The proposed nonlinear model generates more accurate results than the linear models. When guided by limited intra-operative surface data, it predicts deformation of entire brain. Its execution time is however considerably more than those of linear models.