Anar Rahimov was on a scientific visit at the Institute of Fresnel in Marseille, France
Associate Professor, PhD from the Institute of Control Systems of Azerbaijan National Academy of Sciences Anar Rahimov was on a scientific visit at the Institute of Fresnel under the Aix-Marseille University and French National Centre for Scientific Research (CNRS) in Marseille, France for two years to conduct research on the topic "Development of novel numerical solution methods of inverse problems for accurate microwave imaging of human brain".
Research was conducted under the supervision of Professor Amelie Litman, the head of HIPE team of Fresnel Institute.Research was supported by Azerbaijan National Academy of Sciences (ANAS) and fellowship of the President of the Republic of Azerbaijan.
The goal and the results of the research: This problem was raised for consideration at Fresnel Institute by the French Alternative Energies and Atomic Energy Commission (CEA, Paris, France).Magnetic resonance electric properties tomography (MREPT) method is a highly promising technique as it can be applied to obtain not only the anatomical and functional features of the human body but as well quantitative high-resolution images of its electromagnetic properties (dielectric permittivity and conductivity). Anar Rahimov worked on an inverse problem described by the electric Helmholtz equation and by recasting this inverse problem into a constrained optimization algorithm, he investigated a MREPT gradient-based inversion algorithm to quantitatively recover the complex permittivity values of human brain tissues based on magnetic field mapping, which can be acquired in magnetic resonance imaging (MRI) setups. He has solved the direct problem using finite element method. He has derived the associated adjoint field equation, obtained the formulas of gradient and employed a Quasi-Newton minimization scheme. He has developed a simulation tool which adequately combines the specificities of microwave imaging (MI) algorithms with the problematic of MRI for the direct and inverse problems.Furthermore, he has also worked on investigation and development of methods of numerical solution to non-local inverse problems for parabolic and hyperbolic type equations during scientific probation period.
Application possibilities and significance of research results: These problems are of practical importance for medical applications, as for example brain imaging. MRI scans are nowadays routinely ordered to visualize the anatomy of the inside of the human body. In addition, MRI systems can also provide quantitative mapping of the dielectric permittivity and conductivity properties inside the human body. Such technique could help in the diagnostic of pathologies which induce an important variation of the dielectric permittivity. For example, it has been shown that cancerous tissues may have different electromagnetic values than normal tissues over a wide electromagnetic frequency spectrum and most of them exhibit increased conductivity values. Numerous diseases such as stroke, hemorrhage, edema, inflammation and others are known to alter tissue electromagnetic properties. MRI could also provide a more accurate and personalized prediction of the Specific Absorption Rate (SAR) that is encountered in high-field and ultra high-field MRI, typically above 3 Tesla. Thus, development of the methods of accurate reconstruction of the complex permittivity is of vital importance in medical diagnostics. Five papers on the results of the research work were published in high impact factor journals (Inverse Problems, Inverse Problems in Science and Engineering, Differential Equations, Automation and Remote Control, etc.). During his scientific visit A. Rahimov attended several international summer schools, conferences and symposiums.