An ICCG-SFDTD Algorithm For Bio-Electromagnetic Applications

Most domestic and international universities and research institutions only do the computational numerical simulation according to the actual biological models to get the data of the response signal from the human body. Then they research the imaging algorithm and signal processing method as well. The electromagnetic detection technique is also limited in the biomedical field, for monitoring an organ of the human body, such as early breast cancer detection and hyperthermia, colorectal cancer detection and cardiac monitoring. But few people do detailed electromagnetic simulation studies in the field of Biophotonics, for researching the plasma biological phatonic crystals. Also few people involve the fetal biological electromagnetic protection field.Because the electromagnetic numerical simulation is on the biological tissue, the results need to be very accurate and reliable. But they most use the traditional FDTD method or the mature electromagnetic computing software. As we know, the traditional FDTD method has two shortcomings. First, it cannot accurately model curved complex surfaces and material discontinuity by using the staircasing approach with structured grids. Second, it has the significant accumulated errors from numerical instability, dispersion and anisotropy with long time simulation. For these disadvantages can lead the accuracy of the electromagnetic simulation greatly reduced, they will greatly affect the final result. So, a modified FDTD algorithm, which is the SFDTD method, is proposed to solve the problem above.Compared with the traditional FDTD method, the high-order FDTD method can reduce the numerical dispersion effectively. But because these high-order FDTD approaches above have destroyed the symplectic structure of the Maxwell’s equations, the computed result is not satisfactory. And the most traditional algorithm is non-symplectic. Evolved with time, the total energy of the Hamiltonian system changes linearly and the result of the traditional algorithm is distorted seriously with error cumulation finally. So it is necessary to pull the symplectic integrator into the high-order FDTD algorithm. Since the Maxwell’s equations can be derived as an infinite dimensional Hamiltonian system, one stable and accurate solution, which called the Symplectic Finite-difference Tme-domain (SFDTD) method, can solve the problem above well. For the SFDTD method is based on the dynamic system expressed in Hamilton, it can maintain the energy of the Hamiltonian system constant. The right mathematical formulation for the evolution of the system state is the symplectic transformation.Although the SFDTD method has been used to solve the guided-wave, electromagnetic radiation, penetration and scattering problems, little research has been performed on bioelectromagnetic simulations.But the SFDTD method causes the computational time is relatively long and the memory is consumed more. To solve the problems, the advantage of the Incomplete Cholesky Conjugate Gradient (ICCG) method for solving large sparse matrix will be taken into the SFDTD differential equations solving. The ICCG method can accelerate the iteration of the numerical calculation and reduce memory overhead with fast and stable convergence speed. With the advantages of these algorithms combined, the new ICCG-SFDTD method is proposed.In chapter two, we have introduced the SFDTD algorithm theory, which is based on the Hamilton system, the symplectic propagator theory and the space high order difference equation.In chapter three, the difference scheme of SFDTD in Maxwell equation and the high-order PML absorbing boundary conditions are researched. Also, we have done some numerical dispersion analysis. Then, the Incomplete Cholesky Conjugate Gradient (ICCG) method for solving large sparse matrix is taken into the SFDTD differential equations solving. And the ICCG-SFDTD scheme’s benefits are demonstrated.In chapter four, the difference scheme of ICCG-SFDTD in one-dimensional Maxwell equation with the static and moving state are derived respectively. And we apply the ICCG-SFDTD method for numerical simulation of the one dimensional Plasma Biological Phatonic Crystals (PBPC). The plasma frequency, biological dielectric constant, and the thickness ratio of plasma and biological medium of PBPC can influence the band gap structure.Finally, in chapter five, the difference scheme of ICCG-SFDTD in two-dimensional and three-dimensional Maxwell equation with the static and moving state is derived respectively too. Also we apply the high-order ICCG-SFDTD scheme to a bioelectromagnetic simulation using a simple model of a pregnant woman and her fetus.Because the protection of a pregnant woman and her fetus is very important, the algorithm that is used in mother/fetus modeling and simulation must have a high precision and must be numerically stable.The ICCG-SFDTD algorithm just meets the requirement. Though the traditional FDTD method has been used to calculate SARs using the pregnant woman/fetus model, no one has used the ICCG-SFDTD algorithm to this end. In addition, many researchers model SARs in the human body, which are limited by safety guidelines to ensure the safety of the patient. However, few researchers are concerned with protective measures to reduce the risks posed by RF radiation. For lower SAR distributions at 64 MHz, we choose a plasma protective layer to reduce the mother’s/fetus’s SARs from a 1.5 T MRI system. By simulating the mother/fetus model, we find an optimal angle that not only best protects the patient, but it also significantly reduces the raw material costs. Also, with the thickness of the plasma protective layer becoming thicker and the plasma frequency of the plasma protective layer becoming higher, the protective effect is better and better linearly.