Second order diffusion tensor (DT) fields are widely used in several clinical applications: brain fibers connections, diagnosis of neuro-degenerative diseases, image registration, brain conductivity models, etc. However, due to current acquisition protocols and hardware limitations in MRI machines, the diffusion magnetic resonance imaging (dMRI) data is obtained with low spatial resolution (1 or 2 mm3 for each voxel). This issue can be significant, because tissue fibers are much smaller than voxel size. Interpolation has become in a successful methodology for enhancing spatial resolution of DT fields. In this work, we present a feature-based interpolation approach through multi-output Gaussian processes (MOGP). First, we extract the logarithm of eigenvalues (direction) and the Euler angles (orientation) from diffusion tensors and we consider each feature as a separated but related output. Then, we interpolate the features along the whole DT field. In this case, the independent variables are the space coordinates (x, y, z). For this purpose, we assume that all features follow a multi-output Gaussian process with a common covariance matrix. Finally, we reconstruct new tensors from the interpolated eigenvalues and Euler angles. Accuracy of our methodology is better compared to approaches in the state of the art for performing DT interpolation, and it achieves a performance similar to the recently introduced method based on Generalized Wishart processes for interpolation of positive semidefinite matrices. We also show that MOGP preserves important properties of diffusion tensors such as fractional anisotropy.
The success of stereotactic surgery for Deep Brain Stimulation depends critically on the exact positioning of a microelectrode recording in a target area of the brain. This paper presents the software system NEUROZONE composed of two main applications: first, it allows online recognition of brain structures by the analysis of signals from microelectrode recordings (MER), and second, it processes and analyses off-line databases allowing the inclusion of new trained classifiers for automatic identification. The software serves as a support to the analysis done by a medical specialist during surgery, and seeks to reduce the adverse side effects that may occur because of inadequate identification of the target areas. The software also allows the specialists to label recordings obtained during surgery, in order to generate a new off-line database or increase the amount of records in an already existing off-line database. NEUROZONE has been tested for Deep Brain Stimulation performed at the Institute for Epilepsy and Parkinson of the Eje Cafetero (Colombia), achieving positive identifications of the Subthalamic Nucleus (STN) over to 85% using a naive Bayes classifier.
Deep brain stimulation (DBS) of Subthalamic nucleus (STN) is the most successful treatment for advanced Parkinson's disease. Localization of the STN through Microelectrode recordings (MER) is a key step during the surgery. However, it is a complex task even for a skilled neurosurgeon. Different researchers have developed methodologies for processing and classification of MER signals to locate the STN. Previous works employ the classical paradigm of supervised classification, assuming independence between patients. The aim of this paper is to introduce a patientdependent learning scenario, where the predictive ability for STN identification at the level of a particular patient, can be used to improve the accuracy for STN identification in other patients. Our inspiration is the multi-task learning framework, that has been receiving increasing interest within the machine learning community in the last few years. To this end, we employ the multi-task Gaussian processes framework that exhibits state of the art performance in multi-task learning problems. In our context, we assume that each patient undergoing DBS is a different task, and we refer to the method as multi-patient learning. We show that the multipatient learning framework improves the accuracy in the identification of STN in a range from 4.1% to 7.7%, compared to the usual patient-independent setup, for two different datasets. Given that MER are non stationary and noisy signals. Traditional approaches in machine learning fail to recognize accurately the STN during DBS. By contrast in our proposed method, we properly exploit correlations between patients with similar diseases, obtaining an additional information. This information allows to improve the accuracy not only for locating STN for DBS but also for other biomedical signal classification problems.
Multi-output learning has become in a strong field of research in machine learning community during the last years. This setup considers the occurrence of multiple and related tasks in real-world problems. Another approach called semi-supervised learning (SSL) is the middle point between the case where all training samples are labeled (supervised learning) and the case where all training samples are unlabeled (unsupervised learning). In many applications it is difficult or impossible to access to fully labeled data. At these scenarios, SSL becomes a very useful methodology to achieve successful results, either for regression or for classification. In this paper, we propose the use of kernels for vector-valued functions for Gaussian process multi-output regression in the context of semi-supervised learning. We combine a Gaussian process with process convolution (PC) type of covariance function with techniques commonly used in semi-supervised learning like the Expectation-Maximization (EM) algorithm, and Graph-based regularization. We test our proposed method in two widely used databases for multi-output regression. Results obtained by our method exhibit a better performance compared to supervised methods based on Gaussian processes in scenarios where there are not available a good amount of labeled data.
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