Modelado y comportamiento de la simulación de propagación eléctrica durante la estimulación cerebral profunda

Publicado

2016-09-01

Modelado y comportamiento de la simulación de propagación eléctrica durante la estimulación cerebral profunda

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

Palabras clave:

Estimulación Cerebral Profunda, Ecuación de Laplace, Enfermedad de Parkinson, FEM (es)
DBS, Parkinson disease, electric brain propagation, Laplace equation, FEM (en)

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Autores/as

Pablo Alejandro Alvarado Universidad Tecnológica de Pereira https://orcid.org/0000-0002-9347-5093
Cristian Alejandro Torres Valencia Universidad Tecnológica de Pereira https://orcid.org/0000-0001-7568-6148
Álvaro Ángel Orozco Gutiérrez Universidad Tecnológica de Pereira https://orcid.org/0000-0002-1167-1446
Mauricio Alexander Álvarez López Universidad Tecnológica de Pereira https://orcid.org/0000-0002-8980-4472
Genaro Daza Santacoloma Instituto de Epilepsia y Parkinson del Eje Cafetero - Neurocentro https://orcid.org/0000-0002-1429-5925
Hans Carmona Vilada Instituto de Epilepsia y Parkinson del Eje Cafetero https://orcid.org/0000-0002-8099-9461

Resumen (es)
Resumen (en)

La Estimulación Cerebral Profunda (DBS) es un tratamiento efectivo para la enfermedad de Parkinson. Gran variedad de modelos matemáticos y computacionales para describir la propagación eléctrica debido a la DBS han sido propuestos, desafortunadamente, no existe claridad sobre las razones que justifican el uso de un modelo específico. En el presente trabajo se presenta una formulación matemática detallada de la propagación eléctrica debido a DBS que soporta un modelo basado en la ecuación de Laplace. Se realizan simulaciones para diferentes modelos geométricos del cerebro para determinar si la geometría, el tamaño y la ubicación de la tierra del modelo afectan la predicción de la estimulación eléctrica mediante el uso del Método de Elementos Finitos (FEM). Los análisis teórico y experimental muestran en primera instancia que la ecuación de Laplace es adecuada para describir la propagación eléctrica en el cerebro, y en segunda instancia que la estructura geométrica, tamaño y ubicación de la tierra afectan la magnitud del potencial eléctrico, particularmente para modos de estimulación monopolar. Los resultados muestran que para modelos básicos y más realistas pueden existir diferencias en la propagación de hasta un 2900%.

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%.

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Citas

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