The spherical head model has been widely used in magnetoencephalography (MEG) as a simple forward model for calculating the external magnetic field producing by neural currents in a human brain. But this model may lea...The spherical head model has been widely used in magnetoencephalography (MEG) as a simple forward model for calculating the external magnetic field producing by neural currents in a human brain. But this model may lead to an inaccurate result, even if the computation speed is fast. For more precise computation, realistic brain-shaped head model is used with the boundary element method (BME), but at greatly increased computational cost. When solving MEG inverse problem by using optimization methods, the forward problem must often be solved for thousands of possible source configurations. So if the brain-shaped head model is used in all iterative steps of optimization, it may be computationally infeasible for practical application. In this paper, we present a method about using compound head model in MEG inverse solution. In this method, first spherical head model is used for a rough estimation, then brain-shaped head model is adopted for more precise solution. Numerical simulation indicates that under the condition of same accuracy, the computation speed for the present method is about three times faster than a method using the brain-shaped head model at all iterations.展开更多
The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravi...The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degen- erated into the classic ones.展开更多
A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the pot...A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.展开更多
基金This work is supported by the National Natural Science Foundation of China(No.30 0 0 0 0 34 )
文摘The spherical head model has been widely used in magnetoencephalography (MEG) as a simple forward model for calculating the external magnetic field producing by neural currents in a human brain. But this model may lead to an inaccurate result, even if the computation speed is fast. For more precise computation, realistic brain-shaped head model is used with the boundary element method (BME), but at greatly increased computational cost. When solving MEG inverse problem by using optimization methods, the forward problem must often be solved for thousands of possible source configurations. So if the brain-shaped head model is used in all iterative steps of optimization, it may be computationally infeasible for practical application. In this paper, we present a method about using compound head model in MEG inverse solution. In this method, first spherical head model is used for a rough estimation, then brain-shaped head model is adopted for more precise solution. Numerical simulation indicates that under the condition of same accuracy, the computation speed for the present method is about three times faster than a method using the brain-shaped head model at all iterations.
基金supported by the National Natural Science Foundation of China(Grant No.40374007).
文摘The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degen- erated into the classic ones.
基金Supported by the National Natural Science Foundation of China(No. 10102019) the Special Fund for Returning Scholars in the Chinese Academy of Sciences (No. 20010826214905) and the Ministry of Education of China
文摘A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.
