Álvaro A. Orozco

Roger Gomez Nieto, Andres Marino Alvarez Meza, Julian David Echeverry Correa et al.

Parkinson's disease (PD) is a degenerative condition of the nervous system, which manifests itself primarily as muscle stiffness, hypokinesia, bradykinesia, and tremor. In patients suffering from advanced stages of PD, Deep Brain Stimulation neurosurgery (DBS) is the best alternative to medical treatment, especially when they become tolerant to the drugs. This surgery produces a neuronal activity, a result from electrical stimulation, whose quantification is known as Volume of Tissue Activated (VTA). To locate correctly the VTA in the cerebral volume space, one should be aware exactly the location of the tip of the DBS electrodes, as well as their spatial projection. In this paper, we automatically locate DBS electrodes using a threshold-based medical imaging segmentation methodology, determining the optimal value of this threshold adaptively. The proposed methodology allows the localization of DBS electrodes in Computed Tomography (CT) images, with high noise tolerance, using automatic threshold detection methods.

Pablo A. Alvarado, Mauricio A. Álvarez, Álvaro A. Orozco

Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources, its application to rapid stimulation pulses, which contain more high-frequency power, may not be appropriate, as DBS therapeutic results depend on stimulus parameters such as frequency and pulse width, which are related to time variations of the electric field. We propose an alternative hybrid approach based on probabilistic models and differential equations, by using Gaussian processes and wave equation. Our model avoids quasi-static approximation, moreover, it is able to describe dynamic behavior of DBS. Therefore, the proposed model may be used to obtain a more realistic phenomenon description. The proposed model can also solve inverse problems, i.e. to recover the corresponding source of excitation, given electric potential distribution. The electric potential produced by a time-varying source was predicted using proposed model. For static sources, the electric potential produced by different electrode configurations were modeled. Four different sources of excitation were recovered by solving the inverse problem. We compare our outcomes with the electric potential obtained by solving Poisson's equation using the Finite Element Method (FEM). Our approach is able to take into account time variations of the source and the produced field. Also, inverse problem can be addressed using the proposed model. The electric potential calculated with the proposed model is close to the potential obtained by solving Poisson's equation using FEM.

Hernan Dario Vargas Cardona, Mauricio A. Alvarez, Alvaro A. Orozco

Diffusion magnetic resonance imaging (dMRI) is an emerging medical technique used for describing water diffusion in an organic tissue. Typically, rank-2 tensors quantify this diffusion. From this quantification, it is possible to calculate relevant scalar measures (i.e. fractional anisotropy and mean diffusivity) employed in clinical diagnosis of neurological diseases. Nonetheless, 2nd-order tensors fail to represent complex tissue structures like crossing fibers. To overcome this limitation, several researchers proposed a diffusion representation with higher order tensors (HOT), specifically 4th and 6th orders. However, the current acquisition protocols of dMRI data allow images with a spatial resolution between 1 $mm^3$ and 2 $mm^3$. This voxel size is much smaller than tissue structures. Therefore, several clinical procedures derived from dMRI may be inaccurate. Interpolation has been used to enhance resolution of dMRI in a tensorial space. Most interpolation methods are valid only for rank-2 tensors and a generalization for HOT data is missing. In this work, we propose a novel stochastic process called Tucker decomposition process (TDP) for performing HOT data interpolation. Our model is based on the Tucker decomposition and Gaussian processes as parameters of the TDP. We test the TDP in 2nd, 4th and 6th rank HOT fields. For rank-2 tensors, we compare against direct interpolation, log-Euclidean approach and Generalized Wishart processes. For rank-4 and rank-6 tensors we compare against direct interpolation. Results obtained show that TDP interpolates accurately the HOT fields and generalizes to any rank.