Numerical Solutions of Maxwell Equations for a Full medical Imaging System – MEDIMAX

?Developing a numerical tool for solving the forward problem to realize a realistic model of the data acquired by the microwave imaging system is novel and challenging. The modeling must have to take account accurately of the high heterogeneity and complexity of head tissues (skin, fat, skull, bone marrow, brain/white matter, brain/grey matter, cerebrospinal fluid, arteries,...) for normal cases and for different possible brain pathology cases (ischemic and hemorrhagic strokes, brain injuries,...). The tissues are dissipative dielectric media in the microwave domain, i.e. they exhibit a complex permittivity. They are moreover dispersive (the complex permittivity varies versus frequency). The wave/matter interaction must take also in account accurately of the incident field from the transmitting antennas. This interaction is quite complex, as it must be seen as a coupling problem between the antennas and the head rather than a simple scattering problem. In other words, the presence of the head disrupts the incident field created by the antennas. In addition, the electric field is measured by means of sensors (antennas). Therefore, we don't have access directly to the electric field but through antennas. Looking at the state-of-art of numerical modeling, the whole interaction has never been modeled. Only simple models (using plane waves, with simple antenna models and without taking into account the coupling) have been carried out in the literature.
Developing a new numerical method for solving the inverse problem able to reconstruct tomographic microwave images from experimental data (for different realistic phantoms models) acquired with the system constructed by the company EMTensor GmbH, (Vienna, Austria) is challenging.

- Modeling and simulation of the transmission / reception system of EMTensor with HFSS commercial software.
Development of a simulation code using high-level environment FreeFem ++, modeling the acquisition of measurements of the brain through an array of 160 (5 rings of 32 antennas) three-dimensional antennas. Very good agreement for the comparison between numerical results and HFSS commercial code is in .

Development of a new numerical method for solving the inverse problem able to reconstruct tomographic microwave images from experimental data (from different realistic phantoms models) acquired with the system constructed by the company EMTensor GmbH, (Vienna, Austria).

1. L. Conen, V. Dolean, R. Krause, F. Nataf, A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator, Journal of Computational and Applied Mathematics, Volume 271, December 2014, Pages 83-99.
2. V. Dolean, P. Jolivet and F. Nataf, An Introduction to Domain Decomposition Methods: algorithms, theory and parallel implementation, Lecture Notes in Computer Science, 2015.
3. El Kanfoud, V. Dolean, C. Migliaccio, J. Lanteri, I. Aliferis, Ch. Pichot, P.-H.Tournier, F. Nataf, F. Hecht, S. Semenov, M. Bonazzoli, F. Rapetti,, R. Pasquetti, M. De Buhan, M. Kray, M. Darbas “Whole-microwave system modeling for brain imaging”. ”. 2015 IEEE CAMA (International Conference on Antenna Measurements & Applications) (November 30-December 2, 2015, Chiang Mai, Thailand). Special Session «Recent Advances in Electromagnetic Imaging«.

The main goal is the methodological and numerical development of a new robust inversion tool (associated with the electromagnetic forward problem) that supposes also the benchmarking of different other existing approaches (Time Reverse Absorbing Condition, Method of Small-Volume Expansions, Level Set Method).
This implies the development of a general parallel open source simulation code of a direct problem, based on the high-level integrated development environment of FreeFEM++, which can be used for modeling the scattering of arbitrary electromagnetic waves in highly heterogeneous media, over a wide frequency range.
The first applications considered here will be medical applications: microwave tomographic images of brain stroke, brain injuries,… from both synthetic and experimental data in collaboration with EMTensor GmbH, Vienna (Austria), an Electromagnetic Medical Imaging company and with neurologists, stroke and brain injury surgeon specialists (Carolinas Medical Center, NC, USA; Hospital of North Straffordshire, UK; Medical University of Vienna, Austria).

There are two major challenges to solve justifying the originality and novelty of the project:
1) Developing a numerical tool for solving the forward problem to realize a realistic model of the data acquired by the microwave imaging system is novel and challenging. The modeling must have to take account accurately of the high heterogeneity and complexity of head tissues (skin, fat, skull, bone marrow, brain/white matter, brain/grey matter, cerebro-spinal fluid, arteries,...) for normal cases and for different possible brain pathology cases (ischemic and hemorrhagic strokes, brain injuries,...). The tissues are dissipative dielectric media in the microwave domain, i.e. they exhibit a complex permittivity. They are moreover dispersive (the complex permittivity varies versus frequency). The wave/matter interaction must take also in account accurately of the incident field from the transmitting antennas. This interaction is quite complex as it must be seen as a coupling problem between the antennas and the head rather than a simple scattering problem. In other words, the presence of the head disrupts the incident field created by the antennas. In addition, the electric field is measured by means of sensors (antennas). Therefore, we don't have access directly to the electric field but through antennas. Looking at the state-of-art of numerical modeling, the whole interaction has never been modeled. Only simple models (using plane waves, with simple antenna models and without taking into account the coupling) have been carried out in the literature.
2) Developing a new numerical method for solving the inverse problem able to reconstruct tomographic microwave images from experimental data (for different realistic phantoms models) acquired with the system constructed by the company EMTensor, (Vienna, Austria) is challenging.

As a general rule, biomedical applications have plenty of scientific challenges waiting to be tackled, all with potentially tremendous effects on our future society.