Magnetic Field Tomography Based On Magneto Eencephalography - Case Study Example

Magnetic Field Tomography Based On Magneto Eencephalography Basics of Finite Element Method: Finite element method or FEM is basically a numerical technique that is used to solve different kinds of equations like a differential or integral equation. Since its introduction, FEM has been regularly applied to a wide range of physical problems like boundary value problems. It stands distinguished in respect that it first divides a problem into smaller parts. After dividing a big problem into simpler parts which are called finite elements, variational methods are used to address all elements by reducing associated error function. FEM also focuses on connecting many finite elements to form a complex equation. This method of solving equations instead of going for the larger solution directly offers solution for the problem at hand in a piecewise manner. This reduces the risk of error in solution. Some main advantages of dividing a bigger problem or a whole domain into simpler parts or finite elements relate to early and easy discovery of the total solution and inclusion of all material properties. When a domain is divided into elements, no property is missed and all local effects are effectively captured. Starting from the first step, a typical FEM method involves dividing the whole domain of a problem into subdomains or elements. A different set of element equations is then used to represent each subdomain or finite element. All sets of element equations which were earlier used to represent subdomains are subsequently recombined into a larger system of equations to represent the final solution calculations to the problem. This larger or global system of equations is then used to obtain a final numerical answer. FEM has amassed much popularity over the years for making it possible to reduce the error of approximation. In order to generate a global system of equations, a transformation of coordinates occurs from local nodes of subdomains to global nodes of the large domain. This transformation helps to produce a global system of equations. FEM software is used for this purpose. It helps to coordinate or adjust data that is obtained from subdomains. FEM’s practical application is called Finite element analysis or FEA. It is FEA which has proven to be highly useful in case of solving problems in complicated domains particularly when the domain is dynamic or there is variation in the desired precision like in case of magnetoencephalography (MEG). MEG is the name of a very important non-invasive diagnostic technique which is “based on measuring the electric and magnetic field on the scalp, linked to the neural activity” (Kybic et al. 2004). Neural activity is a complicated domain in which great variations are noticed in the desired precision. It is due to complex nature of such domains that better numerical techniques are required to retrieve spatial information from all MEG data acquired over time. Summing up, FEM is a model which is used specifically for FEA. FEA is a numerical method by which a complex problem or a large domain is broken down into smaller parts or subdomains from which a global system of equations is again generated. Introduction to Ansys: What Is It and How It Works? Ansys is one of the most valuable products offered by Ansys, Inc. which is headquatered in Pennsylvania, US. It is basically a too used for FEA analysis. It helps engineers in comprehensive FEA analysis which makes it easier to carry on structural analysis. This software is also used for linear, nonlinear, and dynamic studies. When a big complex problem is divided into finite elements, Ansys can be used because it helps to analyse behaviour of elements. In addition to enumerating elements behaviour, equation solvers for a wide variety of design problems are also provided. Any risk of errors is effectively avoided when Ansys is used because it makes error-free computation of bigger problems possible. Ansys is also very popular due to its highly efficient and powerful solver capabilities. This is because it is based on such structural analysis software which provides a large collection of interesting equation solvers. These equation solvers provided by Ansys program can be used to solve different kinds of complicated problems. Among the collection of solvers provided by Ansys software are “the sparse direct solver, preconditioned conjugate gradient (PCG) iterative solver, Jacobi conjugate gradient (JCG) solution and more” (ANSYS, Inc. 2015). These equation solvers can be easily used in large-scale computing. The solution time for big problems is remarkably reduced with the help of Ansys as is claimed by the company itself as well. It is suggested that in order to use equation solvers like JCG and PCG in large-scale computing, parallel algorithms should be combined with the power of GPUs. This “can further reduce the solution time required for large models” (ANSYS, Inc. 2015). Ansys program works by accelerating computation which otherwise takes up a large amount of time. There is a variety of technology offered by Ansys all of which concentrates on “accelerating computation of normal modes for cyclic structures” (ANSYS, Inc. 2015). Variational technology from Ansys proves to be really helpful when a large number of harmonic indexes are encountered. This is because frequency sweeps are very common in harmonic analyses and variational technology from Ansys helps to comprehend any such frequency sweeps. Research also claims that “frequency sweeps such as those found in harmonic analyses benefit from variational technology” (ANSYS, Inc. 2015). Also, many kinds of problems like nonlinear structural transient problems become able to be computed in a shorter time. Computation of these problems is made possible in a significantly shorter time using principles on which Ansys is based. It is recommended to use many GPUs to shorten computing time when solving problems. Another great advantage of Ansys worth mentioning here is related to its innovative numerical methods. Many advanced numerical methods are offered by Ansys to address nonlinear problems. The groundwork of Ansys software is formed by element and material technology. On basis of this groundwork or foundation, Ansys program “offers various advanced modeling methods for different kinds of applications” (ANSYS, Inc. 2015). FEA tools provided by Ansys are also highly effective as they are laced with myriad advanced capabilities needed to “enable simulation of a variety of physics phenomena” (ANSYS, Inc. 2015). Models of Neuronal Current: Single Current Dipole Model: MEG-based imaging is a new approach when it comes to imaging neuronal current sources. This approach offers a unique solution to many problems encountered in the past when other methods were used like weighted minimum norm inverse methods. Singly current dipole model is one such model which provides information relevant to the MEG inverse problem. It is also called a single equivalent current dipole model or simply ECD. In clinical scenarios, analysis of MEG data has been made immensely simple and a lot less complex by fitting an ECD to MEG data. Research has labelled this approach “a simple, practical and very robust method given the speed of modern computers” (Cover et al. 2007). This has already become a widely used method owing to its valuable nature and time-saving qualities. ECD model helps to analyse the spatial distribution of magnetic fields which pass through brain tissue and skull. ECD model makes it possible and also to assess the generator source’s intracranial localization. This is then superimposed on an MRI. ECD model also helps users to determine the spike location in brain tissue. This localization of the spike source is of extreme importance in MEG which is made possible by ECD. Multiple Dipole Model: Multiple dipole models can be used to analyse MEG responses. It can also be used to describe spatial resolution like ECD model. Unlike ECD, multiple dipoles are included by this model with each dipole representing a different anatomical region of a body part being imaged. So, the basic reason a multiple dipole model differs from a single current dipole model is because several dipoles are included by it. It helps to assess effects of these spreading multiple dipoles. Spatio-temporal patterns of MEG are investigated using effects of multiple dipoles. This helps to acquire important information regarding the peak source in the brain. So much complexity presides in electrical conductivities in the head that solving the inverse problem in MEG becomes a highly arduous task. Conventionally, these inverse problems have been tried to be solved using a small number of dipoles. However, given highly intricate nature of neuronal sources in the brain and the fact that their electrical activities change by the second, ECD model does not work in many cases. A single or two-current dipole model does not prove to be a solution in many cases. This is when a multiple dipole model proves to be highly valuable because it includes multiple spreading dipoles. Using this model makes it a lot easier to study spatio-temporal patterns of MEG. Novel Neuronal Current Source Modelling: This refers to a novel method for recording depolarization from neuronal sources in the brain tissue. It has widespread implications for imaging very fast neural activity and recording electrical activities of sources which change by the second without making it difficult to solve the inverse problem. It is actually such a highly efficient method that neuronal depolarization can be recorded “with recording at 125-825 Hz” (Gilad et al. 2011, p. 593). This fact speaks volumes about the efficacy and agility of novel neuronal current source model. This is a relatively new medical imaging method which is capable of creating images of “fast neuronal depolarization in the brain” (Gilad et al. 2011, p. 593). Previous models of neuronal current sources required applied current to be essentially below 100 Hz. Also, this novel method surpasses other models on grounds that the signal-to-noise ratio (SNR) recorded during responses is not too low to obstruct imaging. With previous models, SNR used to be too low to permit imaging appropriately. A novel neuronal current source method allows users to easily apply currents at 225 Hz to cerebral cortex during evoked responses. Results are improved owing to a better SNR which is made possible by a staggering reduction in the noise from the EEG. Research has it that “the principal noise from the EEG is reduced by about 10009, resulting in an improved SNR” (Gilad et al. 2011, p. 593). Blue Brain Project: The Blue Brain Project (BBP) was founded in 2005. It is an attempt to reverse engineer the human brain circuitry to create a synthetic brain at the cellular level. The core objective of BBP is to explore and study the brain from an architectural and functional perspective. Reverse-engineering of human brain activity can help scientists to study architectural and functional principles on a whole new level. When the brain is recreated inside a computer simulation, this simulation does not only show an artificial neural network, but also consists of a model of neurons that is biologically very realistic. Presently, this project also aspires to facilitate understanding of the nature of consciousness. Investigation into different tasks this project hoped to accomplish over passing years helps one to realize how far BBP has come in revolutionizing science. In the beginning, BBP’s core objective was to simulate neocortical column which got accomplished in 2006 and now efforts are being made to study the nature of consciousness. Simulation of a neocortical column was a very big achievement for everyone involved in BBP because it is considered by researchers to be the smallest unit of the neocortex which is responsible for higher functions. Human Brain Project: Like BBP, Human Brain Project or HBP is another ambitious scientific project which was founded in 2013. This project is even ahead of BBP in that it aims to provide whole human brain models within a 10 year period. The program hopes to amass milestone achievements in different areas from medical informatics to neurobotics to neuroinformatics to brain simulation to high-performance computing to neuromorphic computing. BBP focuses on developing technology platforms in the area of brain simulation, while HBP focuses on five additional areas. Previous brain research has not proven to be much helpful to advance this project because of its inconsistent and unsystematic nature. Big variations are found in previous neurological research evidence which has become a hurdle in the way of simulating the brain. This is because that data cannot be used owing to its unreliable nature to replicate the brain in a whole model as a single system. References: ANSYS, Inc. 2015, ANSYS Mechanical, viewed, 06 April 2015, Cover, KS et al. 2007, ‘Fitting a single equivalent current dipole model to MEG data with exhaustive search optimization is a simple, practical and very robust method given the speed of modern computers’, International Congress Series, vol. 1300, pp. 121-124, viewed, 06 April 2015, Gilad, O et al. 2011, ‘A novel method for recording neuronal depolarization with recording at 125–825 Hz: implications for imaging fast neural activity in the brain with electrical impedance tomography’, Med Biol Eng Comput, vol. 49, pp. 593–604. Kybic, J et al. 2004, Accurate Boundary Element Method for the Electro- and Magnetoencephalography Forward Problem, viewed 06 April 2015, Read More