Modeling and behavior of the simulation of electric propagation during deep brain stimulation

Deep brain stimulation (DBS) is an effective treatment for Parkinson's disease. In the literature, there are a wide variety of mathematical and computational models to describe electric propagation during DBS; however unfortunately, there is no clarity about the reasons that justify the use of a specific model. In this work, we present a detailed mathematical formulation of the DBS electric propagation that supports the use of a model based on the Laplace Equation. Moreover, we performed DBS simulations for several geometrical models of the brain in order to determine whether geometry size, shape and ground location influence electric stimulation prediction by using the Finite Element Method (FEM). Theoretical and experimental analysis show, firstly, that under the correct assumptions, the Laplace equation is a suitable alternative to describe the electric propagation, and secondly, that geometrical structure, size and grounding of the head volume affect the magnitude of the electric potential, particularly for monopolar stimulation. Results show that, for monopolar stimulation, basic and more realistic models can differ more than 2900%

Basic mechanisms of DBS for Parkinson’s disease: computational and experimental studies on neural dynamics

Deep Brain Stimulation (DBS) has become an accepted therapy of last resort for Parkinson’s disease (PD). The acceptance of DBS for the management of PD motor symptoms is based on its success rate and contrasts sharply with ones understanding of the pathophysiology underlying the disease state and mechanism of DBS. Theoretical and experimental studies at a neuronal and population level continue to shed light on the mechanism of DBS. In this thesis, we employ computational models in order to test certain hypothesis put forward in the field regarding the mechanism of DBS and efficacy of high frequency stimulation. Moreover, we make use of cellular recordings in order to test the validity of observations made using computational models. We incorporate population level recordings, obtained from PD patients, into a theoretical population level model in order to infer possible neuronal mechanisms underlying the differences observed in the recordings, arising from different experimental conditions. Last but not least, we analyze experimental recordings obtained from PD patients and assess which signal properties are selective to certain brain regions of interest

Impact of brain tissue filtering on neurostimulation fields: A modeling study

Electrical neurostimulation techniques, such as deep brain stimulation (DBS) and transcranial magnetic stimulation (TMS), are increasingly used in the neurosciences, e.g., for studying brain function, and for neurotherapeutics, e.g., for treating depression, epilepsy, and Parkinson's disease. The characterization of electrical properties of brain tissue has guided our fundamental understanding and application of these methods, from electrophysiologic theory to clinical dosing-metrics. Nonetheless, prior computational models have primarily relied on ex-vivo impedance measurements. We recorded the in-vivo impedances of brain tissues during neurosurgical procedures and used these results to construct MRI guided computational models of TMS and DBS neurostimulatory fields and conductance-based models of neurons exposed to stimulation. We demonstrated that tissues carry neurostimulation currents through frequency dependent resistive and capacitive properties not typically accounted for by past neurostimulation modeling work. We show that these fundamental brain tissue properties can have significant effects on the neurostimulatory-fields (capacitive and resistive current composition and spatial/temporal dynamics) and neural responses (stimulation threshold, ionic currents, and membrane dynamics). These findings highlight the importance of tissue impedance properties on neurostimulation and impact our understanding of the biological mechanisms and technological potential of neurostimulatory methods.United States. Defense Advanced Research Projects Agency (Contract W31P4Q-09-C-0117)National Institute of Neurological Disorders and Stroke (U.S.) (Award R43NS062530)National Institute of Neurological Disorders and Stroke (U.S.) (Award 1R44NS080632

Numerical characterization of intraoperative and chronic electrodes in deep brain stimulation

An intraoperative electrode (microelectrode) is used in the deep bra In stImulation (DBS) technique to pinpoint the brain target and to choose the best parameters for the electrical stimulus. However, when the intraoperative electrode is replaced with the chronic one (macroelectrode), the observed effects do not always coincide with predictions. To investigate the causes of such discrepancies, a 3D model of the basal ganglia has been considered and realistic models of both intraoperative and chronic electrodes have been developed and numerically solved. Results of simulations of the electric potential (V) and the activating function (AF) along neuronal fibers show that the different geometries and sizes of the two electrodes do not change the distributions and polarities of these functions, but rather the amplitudes. This effect is similar to the one produced by the presence of different tissue layers (edema or glial tissue) in the pen-electrode space. Conversely, an inaccurate positioning of the chronic electrode with respect to the intraoperative one (electric centers not coincident) may induce a completely different electric stimulation in some groups of fibers

Neural network dynamics in Parkinson's disease

Parkinson's disease (PD) is characterized by the cell death of neuronal brain cells producing the signaling molecule dopamine. Due to resulting shortage of dopamine, the dynamics of neuronal cells changes, most notably abnormal synchronization of neuronal activity. Such changes complicate the information processing in the brain, resulting in symptoms such as tremor, rigidity and slowness of movement.\ud Deep brain stimulation (DBS) is a surgical treatment where an electrode is implanted to stimulate a specific brain region. DBS is a well-established treatment when medication is no longer effective for PD. DBS is meant to desynchronize pathological oscillations, as they are thought to be the main cause of the symptoms. Despite the high clinical success rate, the way how the pathological activity originates in the brain and how DBS can compensate it are still unresolved questions. Computational modeling is a valuable tool for finding answers to these questions.\ud In the first part of the thesis, computational models are employed in order to get insight in new proposed stimulation therapies for PD. It is demonstrated that stimulation of the pedunculopontine nucleus can eliminate the pathological activity from the entire network model. It is suggested that short-duration desynchronizing stimulation protocols may also disrupt pathological synchronous activity. The results of simulation show that plasticity within the globus pallidus pars externa might be an explanation for this claim.\ud The second half of this thesis focuses on the analysis of single-unit recordings of subthalamic nucleus (STN) cells obtained from PD patients and the acquisition of local field potentials (LFP) in parkinsonian rats. Although it was possible to record clean LFP data, using these data in combination with spiking neuron models is not straightforward. It has been shown that the firing behavior of single units is different in the sensorimotor part of the STN than in other parts of the STN. Postoperative evaluation of target stimulation areas in the investigated PD patients with DBS shows a significant preference for the sensorimotor part of the STN. Therefore, analysis of the firing behavior may help to discriminate the STN sensorimotor part for the optimal placement of the DBS electrode

Mathematical Model Investigating the Effects of Neurostimulation Therapies on Neural Functioning: Comparing the Effects of Neuromodulation Techniques on Ion Channel Gating and Ionic Flux Using Finite Element Analysis

Neurostimulation therapies demonstrate success as a medical intervention for individuals with neurodegenerative diseases, such as Parkinson’s and Alzheimer’s disease. Despite promising results from these treatments, the influence of an electric current on ion concentrations and subsequent transmembrane voltage is unclear. This project focuses on developing a unique cellular-level mathematical model of neurostimulation to better understand its e↵ects on neuronal electrodynamics. The mathematical model presented here integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the e↵ects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. This system is decoupled using the Gauss-Seidel method and then the equations are solved using the finite element method on a biologically-inspired discretized domain. Results demonstrate the influence of transcranial electrical stimulation on membrane voltage, ion channel gating, and transmembrane flux. Simulations also compare the e↵ects of two di↵erent types of neurostimulation (transcranial electrical stimulation and deep brain stimulation) showcasing cellular-level di↵erences resulting from these distinct forms of electrical therapy. Hopefully this work will ultimately help elucidate the principles by which neurostimulation alleviates disease symptoms