Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. symptoms it is best for DBS to target the Subthalamic Nucleus It is unusual to find academic discussions about the physical. STN 4 the brain structure related to sensorimotor cognitive laws that support the behavior of the deep brain electric fields. and limbic functions 5 The fundamental purpose of DBS is to induced by an external source In fact there is no interpretation. modulate neural activity with applied electric fields 6 However or explanation about the consequences of most of the. the mechanisms by which DBS works are not yet well mathematical simplifications carried out by the basic equations. understood 7 In this sense DBS s therapeutic action seems to that describe the phenomenon Moreover in order to establish. depend on the electrical excitation of neural elements 8 which kind of representations are appropriate to describe the. Moreover there are also studies that support neuronal inhibition electric propagation inside the human brain s behavior it is. 9 Other studies suggest that DBS reduces the PD symptoms convenient to make a quantitative comparison of several. through the excitation of axons and the inhibition of the dendritic geometrical head models taking into account the ground. activity 10 11 positioning that is assumed by the computational algorithms. To achieve successful stimulation it is necessary to excite In this work we present a mathematical formulation of the. the intended brain areas while preventing the unintended electric propagation during DBS Indeed we offer an argument. excitation of other zones the spread of current to non motor that sustains the use of an electrostatic propagation model based on. areas of the STN or adjacent structures is implicated in the Laplace equation The theoretical framework is corroborated. cognitive and cognitive motor declines 12 14 The by a set of computer simulations of the electric potential generated. stimulation of the dorsolateral STN and the bottom ventral by DBS Furthermore the simulation analysis indicates that for. part of the thalamus could reduce parkinsonian tremor and monopolar stimulation the geometrical structure size and. trigger dyskinesias whereas stimulation outside the STN grounding of the conducting head volume alter the magnitude of. could induce adverse effects 15 the electric field In fact a voltage comparison between basic and. A suitable stimulation protocol involves not only the more realistic models can differ by more than 2900. accurate placement of the electrode inside the brain but also. the proper configuration of some electrical and geometrical 2 Deep brain stimulation considerations. parameters for the DBS device 4 The electrical parameters. for DBS are pulse width frequency and the voltage An accurate treatment of Parkinson s disease using DBS. amplitude Additionally each of the lead s electrodes can be should analyze the different effects of potential propagation around. designated as anode or cathode 4 To facilitate the the objective structure that is the STN 15 Adverse effects could. configuration of the DBS device it is propitious to employ be produced from undesired potential propagation to non motor. computational models this allows the electric propagation of regions of the brain as is presented in Fig 1 In order to improve. the stimulation to be predicted as a function of the previously the Parkinsonian motor symptoms the electrode must be placed at. mentioned electrical and geometrical parameters the motor section of the STN as presented in Fig 2 15. These computational simulations help to visualize the Given a specific electrode e g the Medtronic DBS lead. electric behavior of the stimulus in the brain In this sense model 3389 that has four configurable electrodes there are. several works 16 18 have developed simulators of the several geometrical possible arrangements to configure the. electric activity for DBS stimulation parameters In clinical practice usually one or. The mathematical and computational models found in the two stimulation contacts are used at most Fig 3 shows three. literature 18 21 require information such as the conductivity different monopolar Fig 3 a and bipolar Fig 3 b c. and permittivity of brain tissue geometrical description of the configurations and their corresponding electric potential 8. head volume the physical laws that govern the system and the. associated equation constraints Most of the simulation. approaches are specifically based on electrostatic models The. electric potential is often computed using the Laplace 17 22 or. Poisson s 23 24 equation Unfortunately there are no major. justifications about the use of this mathematical background. which is essential to define the scope realism and accuracy of the. simulation The core of these simulations is the Finite Element. Method FEM that has been widely used in DBS problems and. other engineering fields see 25 and 26, Previous research undertaken by authors such as 27 and. 28 address some of the effects of the DBS that show some. simulations from schemes different to the one proposed in this. work In 27 a latent force model was developed in order to. include the dynamics of the electric propagation in the brain. unlike several state of the art works that only focus on the quasi. static or static approach In 28 some propagation models. following the quasi static approach were developed using an. open source library of finite element methods with no deep. analysis of the physical laws that govern the DBS problem. Additionally the results are difficult to compare against the state Figure 1 Sites of stimulation induced effects in the STN region a Sagittal. view b Coronal view, of the art works due to the difference in the simulation tool used Source 15. Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. Maxwell s equation 34 Some particular forms of these. equations have been used by other authors to model the electric. propagation produced by DBS 17 22 24 These equations. can be simplified when slow electromagnetic fields are analyzed. i e fields in the so called low frequency range up to 30kHz. when wave propagation does not play a fundamental role. 31 34 Before defining the situations in which wave. propagation effects can be neglected it is important to clarify. some electromagnetic waves properties, Generally electromagnetic fields propagate with a finite. velocity c 34 defined as where denotes, the permittivity and represents the permeability of the brain. tissue 31 In addition to this represents the time, required for the electromagnetic field to propagate at a. distance l from one region to another in a volume brain tissue. The wave propagation equation for the, Figure 2 Positioning of the electrode at STN coronal view Medtronic DBS electrodynamic scalar potential is defined as. lead model 3389,Source 15 2, Where is the electric potential function and denotes. the charge density 35 If the field problem is considered. with a characteristic spatial dimension l and a characteristic. time constant spatial and temporal differentiations can be. approximated by 1 l and 1 respectively In this case l. is related to the brain tissue volume considered i e the STN. and its surroundings whereas is considered as the time. interval for which significant changes in the field quantities. arise For time varying electric stimulation would be the. Figure 3 Examples of commonly used electrode configurations a reciprocal of the excitation s angular frequency. Monopolar b c Bipolar 31 34 If these previous considerations are applied. Source 8 equation 1 can be approximated by,3 Electric stimulation modeling 2 1. Electromagnetic fields generated by DBS are dynamic. since the source field or electric stimulation is time varying For slow time varying fields the characteristic time. and has a fundamental frequency range from 130Hz to 185Hz constant is supposed to be much greater than the transit. 7 20 29 30 the frequency commonly used is around time i e 1 If this expression holds then. 140Hz Moreover the electric potential induced throughout 0 and the propagation effects can be neglected. the brain tissue close to the stimulating electrode is. commonly modeled using the Laplace equation which 3 2 Static and quasi static models. assumes a quasi static or static field 17 21, It is worthwhile mentioning that the quasi static When wave propagation does not play a fundamental. approximation is only valid when the electrodynamic system role the electromagnetic field simulations of slow processes. analyzed is a low frequency time varying field 31 33 In are carried out by using 36. this section we provide a detailed explanation of how to a static model i e electrostatics or magnetostatics if all. derive the quasi static model in order to support a DBS variations in time can be neglected. propagation model based on the Laplace equation This a quasi static model i e electro quasistatics or magneto. explanation involves the use of generalized Maxwell s quasistationary. equations and some physical assumptions We then present The static models are just special cases of the full. the conditions which allow us to make a decision as to Maxwell s equations whereas the quasi static models are. whether the approximation is valid for DBS approximations that are not always valid 31 32 The quasi. static models are obtained from Maxwell s equations by. 3 1 Low frequency range time varying fields neglecting either the magnetic induction or the electric. displacement current as well as the electromagnetic waves. The large variety of electromagnetic phenomena can all be that result from their coupling 32. described by a unique system of field equations known as. Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. 3 2 1 Electro quasistatic model, The electro quasistatic assumption establishes that the. electric field E is essentially irrotational In general the field. of gradient V for any scalar V is purely irrotational. since 0 thus the irrotational field E can always,be expressed in terms of a scalar field V that is. The negative sign shows that the direction of E is opposite. to the direction in which V increases The electric field E. looks like an electrostatic field at any tissue point Changes. in the electric stimulation will immediately take effect in the. whole brain tissue volume under consideration,3 2 Magneto quasistationary model. Figure 4 Electric field distribution within a specific geometry and different. Analogously the magneto quasistationary models are boundary conditions when DBS is performed a Cubic geometry ground. on base side b Cubic geometry ground on whole boundary c Spherical. characterized by setting the magnetic field H as solenoidal geometry ground on base side d Spherical geometry ground on whole. This implies that the divergence of current density J is zero boundary. i e Source authors,3 2 3 Laplace equation, If electro quasistatic and magneto quasistationary. approximations are simultaneously applied then all temporal. variations in Maxwell s equations are neglected This does. not mean however that the sources and hence the fields are. not functions of time But given the sources at a certain. instant the fields at that same instant are determined without. regard for what the sources of fields were an instant earlier. Using Maxwell s equations and Ohm s law the Laplace. equation used to model the electric potential in DBS can be Figure 5 a Electro quasistatic approximation errors for different. derived The current density J is related to the electric field frequencies and radius sizes b Magneto quasistationary approximation. E by Ohm s law as follows 31 32 errors for different frequencies and radius sizes all curves are almost. J 3 Source authors, Where is the tissue conductivity It is measured in. Siemens per meter S m If the divergence is applied on both The electric potential calculation is based on a model with. sides of 3 we have 0 and using 2 we get the a homogeneous tissue medium to reduce model complexity. Laplace equation Several authors have developed their experiments using this. assumption 6 17 21 24 Furthermore the STN is, V 0 4 cytologically homogeneous i e neurons are identical in. every part of the nucleus 37 We will now present four. examples of the electric field E propagation obtained. Equation 4 corresponds to an inhomogeneous tissue, solving the Laplace equation 5 for a finite homogeneous. For a homogeneous tissue equation 4 becomes, and isotropic volume tissue using different geometries and. boundary conditions The red arrows in Fig 4 correspond to. the electric field Fig 4 a and 4 b show a cubic geometry. in Fig 4 a just one side of the cube is grounded in Fig 4 b. In order to obtain Equation 5 the conductivity is, all sides of the cube are grounded Likewise Fig 4 c and. assumed constant throughout the tissue region in which is 4 d show the electric field distribution see Equation 2. defined The Laplacian operator can be defined in, obtained for a spherical geometry In Fig 4 c a small base is. Cartesian coordinates in the following way, grounded whereas in Fig 4 d all the external surface of the. sphere is grounded, Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. 3 3 Conditions for the quasistatic approximation and l 500mm and a frequency band from 100Hz to 1kHz. Works such as 19 and 21 use several sizes of, The validity of an approximation for a given slow time geometrical models in 2D and 3D These include. varying field problem is determined by an analysis based on specifications of the DBS lead shape that go into a monopolar. significant time constants 31 In this sense two constants configuration and the specification for the tissue conductivity. are defined the time constant of dielectric relaxation properties of the region analyzed Usually two different. and the constant of magnetic diffusion In ground configurations of the electrical models are used one. addition the transit time is the geometric average of to define all the boundaries of the geometrical model such as. and the ground and the other to configure a specific area of the. 2 model such as the ground 21 In 40 one model is, 2 developed assuming an infinite homogeneous and isotropic. medium to compute the electric propagation in different large. frequencies In 41 a detailed model of the tissue, The electro quasistatic and magneto quasistationary surrounding the DBS lead is built using information from. approximations can be used if the relative error of the electric magnetic resonance imaging MRI The model is used to. field and magnetic field calculated under these assess the influence of the tissue information when the. approximations are much smaller than one In order to electric field surrounding the electrode is computed It should. estimate this error time derivatives in Maxwell s equations be noted that for future work the patient real head shape. are substituted by 1 Furthermore only the scalar could be included and studied in order to increase the model s. magnitudes of the fields are considered All properties of the realism Research such as 42 where a reconstruction of the. brain tissue are assumed to be homogeneous linear and head from MRI is performed could be useful. isotropic The relative error of the electric field within the. electro quasistatic approximation is defined as 5 Results. 1 1 6 The propagation of the electric potential in the simulated. models is obtained by solving the Laplace equation from the. finite element method FEM using Comsol Multiphysics. If this condition holds electric fields can be calculated COMSOL Inc Burlington MA As the. accurately by using the electro quasistatic theoretical analysis in section 2 demonstrated how the electric. approximation 17 Likewise the relative error of the potential propagation is conductivity independent when a. magnetic field within the magneto quasistationary homogeneous medium is considered the results obtained from. approximation is these models allows for the geometry to be analyzed and for. building effects to be modeled in the Laplace equation. solution The main objective of this work is to present a. detailed analysis of the electrostatic process that governs the. electric propagation during DBS Several DBS simulations. Magnetic fields can be calculated by using the magneto based on the development of geometrical models of the brain. quasistationary approximation if this condition holds that confirm the theoretical analysis of the electric. propagation were built The presented models include more. 4 Experimental background realistic geometries that allow better analysis of the. stimulation results Different ground configurations and. To be allowed to use the electro quasistatic and magneto boundary constraints are proposed to determine the influence. quasistationary approximations to model the electric of the ground in terms of the electric propagation results The. potential produced by DBS the approximation errors 6 electrical conductivity of a homogeneous medium is not. and 7 have to be much less than one To verify this the taken into account because it has no influence over the. approximation errors were calculated for different l radius solution obtained through the Laplace equation. and stimulation frequencies The dielectric properties of the. tissue are frequency dependent 38 and the electric field. propagation time is a function of the spatial quantity. l 34 Therefore the errors 6 and 7 depend on the, stimulation frequency and the size of the brain tissue region. considered The errors obtained for different frequencies. 100Hz up to 1 kHz assuming a radius of l 50mm l,80mm l 150mm and l 500mm are shown in Fig 5. According to the Andreuccetti online dataset 39 white. matter dielectric property values where considered Based on. Fig 5 and assuming that all properties of the brain tissue. Figure 6 Geometrical forms considered to represent the volume of an adult. arehomogeneous linear and isotropic we can conclude that human head a Cube 50mm 150mm and 500mm edge length b Sphere. the electro quasistatic and magneto quasistationary 80mm radius c Ellipsoid semi axes x 70mm y 82 5mm and z 65mm. approximations are valid for a radius of between l 50mm Source authors. Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. Three geometrical forms are considered to represent the cylinder configuration is used can be noticed and it has. volume of an adult human head The first form is a cubic model higher potential levels in farther regions from the electrode. Fig 6 a where the edge length is fixed to 50mm 150mm and In order to better understand the results a quantitative. 500mm in order to study the changes in the electric propagation assessment was developed to measure the electric potential in. when the head volume is small normal and large The second the regions that surround the electrode in order to determine the. geometry corresponds to a spherical model with a radius 80mm change in the electric propagation pattern according to different. see Fig 6 b Finally as in 17 we created an ellipsoidal geometries According to the solution of the models the. model with semi axes measuring 70mm 82 5mm and 65mm in distances from the center of the electrode to each point of a. the x y and z directions respectively Fig 6 c The last two single potential curve were computed In order to measure the. geometrical forms and sizes are more realistic representations of distance of different potential levels in the analyzed region the. the head facilitating the interpretation of simulated electric. Euclidean distance from the electrode to every point within a. potential propagation during DBS Moreover a Medtronic 3389. potential curve is calculated using, DBS lead in monopolar configuration with a stimulus voltage of. 1V was used other material properties were discarded in the. idealized FEM representation by using the Laplace equation in 8. a homogeneous medium, All the cubic models were analyzed with two different. ground configurations following the Dirichlet boundary where q is the origin and p is one point placed on a. conditions one uses the base of the cube as ground and the potential level curve from the coronal view and. second uses all the sides of the cube as ground For the are the components on the plane This Euclidean. spherical and ellipsoidal models two ground configurations distance is calculated for every model and 100 different. were used The first configuration has all the surface settled potential levels of propagation are analyzed After the. at 0 For the second configuration a cylinder 28 mm in distance from the center of the electrode to each point of the. diameter and 20mm in height on the base of the model was equipotential curve has been computed the minimum. included The cylinder represents the path that the return distance for each potential curve is selected Fig 8 describes. current should follow to the reference electrode placed in the the methodology using. chest cavity then the base of the cylinder is considered as Fig 9 d shows the results from the spherical and. ground The models use an adaptive mesh refinement for the ellipsoidal forms In the cylinder base grounded models the. FEM in order to improve the precision of particular small electric potential reaches higher values at distances far from. regions of the model the region closer to the electrode the electrode until an inflexion point is reached After the. Results obtained from the solution of the Laplace inflection point the potential starts to decrease linearly. equation using FEM are presented as curves around the active alongside the cylinder region The analysis of the electric. contact of the electrode These represent ten different levels potential before the inflection point shows that it is. of potential as the distance from the electrode increases in the represented by a monotonically increasing function that. y z plane coronal view These potential curves are obtained behaves similarly to the potential for the models without the. for all the models following the above mentioned ground cylinder ground configuration. configurations Fig 7 a and 7 b show the results for the. 50mm edge length cube A large difference in the potential. levels between ground configuration models as function of. the distance is observed When the base side of the cube is. set to 0 higher electric potential levels can be found at. larger distances from the electrode in comparison with the. case in which all the sides of the cube are set to 0 Also the. shape of the potential curves is influenced by the position of. the ground It becomes a uniform circle when all the. boundaries are used The same calculations are undertaken. for the 150mm and 500mm edge length cubes Similar, behavior to the electric potential levels is shown in Fig 7 c. and 7 d which compares to the results for the 50mm edge. length cube,Moreover when the size of the cube increases the. influence of the ground configuration becomes less. determinant in the shape and level of the potential Fig 7 f. and 7 e show the results of ten potential curves for the two. different ground configurations of the spherical models The Figure 8 Black solid lines representing the minimum distance from the. same results are presented in Fig 7 h and 7 g for the center of the electrode to the first 4 electric potential levels in the 50mm. ellipsoidal model The influence of the ground when the cubic model. Source authors, Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. Figure 7 Electric potential propagation Potential level curves computed on three sizes of cubical forms one spherical form and one ellipsoidal form. varying the ground configuration of the models a Cube 50mm Ground on base side b Cube 50mm Ground on whole boundary c Cube 500mm. Ground on base side d Cube 500mm Ground on whole boundary e Sphere Ground on base of the cylinder f Sphere Ground on whole boundary. g Ellipse Ground on base of the cylinder h Ellipse Ground on whole boundary. Source authors, Furthermore Table 1 presents the information regarding a lack of real metrics that allowed a better understanding of. the percentile difference of electric potential between each the simulation results such as the ones presented in this work. model s two boundary conditions at specific distances 1 2 Additionally simulations for different ground configurations. 3 4 5 10 15 20 and 30mm from the center of the were not presented in the previously mentioned state of the. electrode This is computed as in Equation 10 art studies but they were in this present work. Based on results the size of the model and the ground. 100 10 configuration are important parameters when modeling a. 1 specific DBS simulation The boundary conditions specified. for the ground configuration and the size of the different. models directly affect the shape and the magnitude of the. where and represent the value of the potential at a electric potential in the region surrounding the electrode This. specific distance of the two different ground configurations can be seen in all the results for the different models in Fig. of the same model for the model with all the boundaries 7 For the smaller models the pattern of propagation of the. and for the model with the ground placed on the base side potential is more influenced by the ground more negative. The value of the electric potential at the fixed distances. potential levels are reached far from the electrode in. from the electrode is obtained from linear interpolation of the. comparison to bigger sized models The shape of the. curves from the minimum distances The size of the model. influences the propagation of the electric potential lower potential levels around the electrode also changes for the two. levels of potential are reached for the smaller models in different ground configurations When all the model s. comparison with the larger models as the distance from the surfaces are grounded Figs 7 b 7 d 7 e and 7 h a. electrode increases This result confirms that building a uniform potential distribution can be observed around the. realistic model of DBS should consider size and boundary electrode and a non uniform shape of the potential levels can. conditions due to the direct influence of these parameters on be found when the base side of the models is grounded Figs. the final solution of the electric potential propagation 7 a 7 c 7 f and 7 g. For the quantification analysis presented in Fig 9 it can. 6 Discussion be noticed that for the models with the ground configured. in the whole surface the higher potential levels reach. The results obtained in this work could be compared to shorter distances from the electrode than they do for the. studies such as 17 18 and 19 in which simulation models. were built for the same DBS electrode however there were models in which only the base side is settled to 0. Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. Results for the percentile difference between ground configurations in all the. for different models,From Cubic models,50mm 150mm 500mm Sphere Ellipse. 1 mm 3 73 1 09 0 14 24 59 32 84,2 mm 12 9 3 92 0 64 87 36 92 42. 3 mm 23 43 6 97 1 66 153 67 155 51,4 mm 34 24 10 13 2 55 221 28 220 38. 5 mm 43 63 13 31 3 31 290 25 287 27,10 mm 79 29 28 98 7 79 668 37 653 64. 15 mm 113 22 41 66 12 84 1092 10 1068 41,20 mm 137 12 51 12 19 26 1590 39 1558 30. 30 mm N A 79 36 25 43 2965 71,Source authors, From Table 1 it is possible to determine that for the cubic. models the larger the size of the cube the less the influence. of the ground configuration In the case of the spherical and. ellipsoidal models since the results of the potential level. propagation changes considerably when the base of the. cylinder corresponds to the ground the percentile difference. between the two configurations for these models is larger. than for the cubic models Differences are reached of up to. 2900 between the two different ground configurations for. some distances from the electrode Even the comparative. result shows a clear difference between the ground. configurations applied to the models The development of a. DBS realistic model should include tissue electrical. properties and other boundary conditions From all of these. assumptions a DBS model could give more realistic results. From the DBS modeling presented several applications. could be derived for example a work presented by, Michmizos et al in 43 details the process of predicting the. Parkinsonian STN spikes using the local field potentials that. could be obtained using this approach,7 Conclusion. We have described the electromagnetic phenomena that. take place during DBS using classical electromagnetic. theory Moreover we have shown that under the correct. assumptions the Laplace equation is a suitable alternative to. represent the electrostatic field propagation generated. after the stimulation We have also shown through different. computer simulations how factors such as the geometrical. Figure 9 Curves representing the Electric Potential vs Minimum Distance. for 100 different potential levels using the cubic spherical and ellipsoidal structure size and the grounding of the conducting head. models and the two ground configurations a 50mm edge length cube volume have dramatic effects over the magnitude of the. b 150mm edge length cube c 500mm edge length cube d Sphere and electric field particularly for monopolar stimulation. Source authors,Acknowledgments, Author P A A was funded by the program 617 J venes. 9 Investigadores e Innovadores funded by Colciencias. Author C A T thanks the program Formaci n de alto nivel. para la ciencia la tecnolog a la innovaci n Doctorado. Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. Nacional Convoctoria 647 de 2014 and the research project Conference of the IEEE EMBS New York NY USA pp 893 895. 111045426008 funded by Colciencias and UTP Author GDS 2006. 17 Grant P F and Lowery M M Electric field distribution in a finite. was partially supported by Patrimonio Aut nomo Fondo volume head model of deep brain stimulation Medical Engineering. Nacional de Financiamiento para la Ciencia la Tecnolog a y Physics 31 pp 1095 1103 2009. la Innovaci n Francisco Jos de Caldas by project number 18 Schmidt C and van Rienen U Modeling the field distribution in. 499153 530997 This work was also supported by the deep brain stimulation The influence of anisotropy of brain tissue. projects 111045426008 and 111056934461 both funded by IEEE Transactions on Biomedical Engineering 59 6 pp 1583 1592. Colciencias 19 McIntyre C C Morib S Shermanc D L Thakorc N V and Vitek. J L Electric field and stimulating influence generated by deep brain. 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Alvarado et al DYNA 83 198 pp 49 58 Septiembre 2016. 37 Carpenter M Anatomy of the corpus striatum and brain stem training pattern recognition systems arti cial vision and machine learning. integrating systems John Wiley Sons Inc 1981 ORCID 0000 0002 1429 5925. 38 Bossetti C A Birdno M J and Grill W M Analysis of the quasi. static approximation for calculating potentials generated by neural H Carmona Villada received a Medical degree in 1995 from the. stimulation Journal of Neural Engineering 59 5 pp 44 53 2008 Universidad Tecnologica de Pereria an MSc in Neurosurgery in 1999 from. 39 Andreuccetti D Fossi R and Petrucci C An internet resource for the Universidad Catolica de Chile and a Subspecialist degree in functional. the calculation of the dielectric properties of body tissues in the neurosurgery in 2002 from the Albert Ludwig University from Freiburg. frequency range 10 hz 100 ghz IFAC CNR Florence Italy 1997 Germany Currently he is the Scientific Manager at Neurocentro Pereira. pp 87 95 Colombia and the head of the functional neurosurgery program in. 40 Hofmanis J Louis Dorr V Cecchin T Caspary O and Koessler Neurocentro and Colombia s Neurological Institute where he undertakes. L Propagation of electrical field in the brain using electrical intra movement disorder surgery epilepsy surgery and pain surgery His research. cerebral stimulations In Engineering in Medicine and Biology interests include neuromodulation neuroengineering brain mapping. Society EMBC 2011 Annual International Conference of the IEEE intraoperative monitoring. pp 3888 3891 2011 DOI 10 1109 IEMBS 2011 6090966 ORCID 0000 0002 8099 9461. 41 Iacono M I Makris N Mainardi L T Angelone L M and. Bonmassar G Mri based multiscale model for electromagnetic. analysis in the human head with implanted dbs Comp Math Methods. in Medicine Online 2013 Available at http dblp uni. trier de db journals cmmm cmmm2013 html IaconoMMAB13. 42 Forero M and Zulanga D Medical station for image processing and. visualization of the brain electrical activity on a three dimensional. reconstruction of the patient s head Ingenier a e Investigaci n 23 3. pp 31 38 2010, 43 Michmizos K Sakas D and Nikita K Prediction of the timing and. the rhythm of the parkinsonian subthalamic nucleus neural spikes. using the local field potentials Information Technology in. Biomedicine IEEE Transactions on 16 2 pp 190 197 2012 DOI. 10 1109 TITB 2011 2158549, P A Alvarado is interested in probabilistic approaches for modeling music. signals with a focus on Gaussian processes and kernel methods Alvarado rea Curricular de Ingenier a. holds an Electronic Engineering degree from Universidad Tecnol gica de. Pereira Colombia and a MSc in Electric Engineering from the UTP El ctrica e Ingenier a de Control. Alvarado is currently a member of Centre for Digital Music pursuing a PhD. at Queen Mary University of London,ORCID 0000 0002 9347 5093 Oferta de Posgrados. C A Torres Valencia received his BSc in Electronic Engineering in 2010. from the Universidad del Quind o his MSc in Electric Engineering in 2013 Maestr a en Ingenier a Ingenier a El ctrica. from the Universidad Tecnol gica de Pereira Colombia From 2011 to date. he has been working in the Automatics research group at the Universidad. Tecnol gica de Pereira Currently he is a Doctoral student at the Universidad. Tecnol gica de Pereira and funded by Colciencias Doctorado Nacional Mayor informaci n. 647 program His research interests include image processing biosignal. processing neuroengineering and machine learning E mail ingelcontro med unal edu co. ORCID 0000 0001 7568 6148 Tel fono 57 4 425 52 64, A A Orozco Gutierrez received a degree Electric Engineering in 1985 a. MSc degree in Electric Engineering in 2004 both from the Universidad. Tecnol gica de Pereira and a PhD in Bioengineering from the Universidad. Polit cnica de Valencia in 2009 He is currently an Associate Professor at. the Universidad Tecnol gica de Pereira His research interests include. instrumentation and control bioengineering and biosignal processing. ORCID 0000 0002 1167 1446, M A lvarez L pez received a degree BSc in Electronic Engineering. from the Universidad Nacional de Colombia in 2004 a MSc degree in. Electrical Engineering from the Universidad Tecnol gica de Pereira. Colombia and a PhD in Computer Science from the University of. Manchester UK in 2011 He is currently an associate professor at the. Universidad Tecnol gica de Pereira Colombia His research interests. include probabilistic models kernel methods and stochastic processes. ORCID 0000 0002 8980 4472, G Daza Santacoloma received a BSc in Electronic Engineering in 2005 a. MSc in Engineering Industrial Automation with honors in 2007 and a PhD. in Engineering Automatics with honors in 2010 from the Universidad. Nacional de Colombia Currently he is the R D Manager at Neurocentro. Pereira Colombia where he is researching Neuroengineering His. research interests include neuroscience feature extraction selection for.

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