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Stratied spherical model for microwave imaging of the
brain Analysis and experimental validation of
transmitted power
M. Bjelogrlic, M. Volery, Benjamin Fuchs, J.-P. Thiran, J.R. Mosig, M. Mattes
To cite this version:
M. Bjelogrlic, M. Volery, Benjamin Fuchs, J.-P. Thiran, J.R. Mosig, et al.. Stratied spherical model
for microwave imaging of the brain Analysis and experimental validation of transmitted power. Mi-
crowave and Optical Technology Letters, Wiley, 2018, 60 (4), pp.1042-1048. �10.1002/mop.31101�.
�hal-01739926�
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Stratified Spherical Model for Microwave Imaging of the Brain: Analysis and
Experimental Validation of Transmitted Power
Mina Bjelogrlic, Maxime Volery, Benjamin Fuchs, Jean-Philippe Thiran, Juan R. Mosig, and Michael
Mattes
Abstract—This work presents the analysis of power transmission of a radiating field inside the human
head for microwave imaging applications. For this purpose, a spherical layered model composed of
dispersive biological tissues is investigated in the range of [0.5-4] GHz and is confronted to
experimental verification.
Index Terms—Microwave Imaging, bio-medical applications, spherical wave expansion, 3D printed head
phantom.
I. INTRODUCTION
Microwave Imaging (MWI) [1] for bio-medical applications aims at localizing and reconstructing a
pathological tissue region from scattered microwaves. In the framework of head MWI this non-invasive,
non-ionizing technique is suitable to monitor brain anomalies such as brain stroke [2], internal bleeding, etc.
Several main factors influence the quality of the MWI: the scattered power, the frequency and the medium
in which the test object is immersed, called the matching or the background medium. The frequency is an
essential parameter since all biological tissues are dispersive and the losses increase exponentially according
to it.
Another important parameter is the spatial resolution of MWI which has a lower bound defined by the far
field and only depends on the wavelength in the background medium. Devaney [3] first suggested that this
limit of resolution was about
, then Bolomey and Pichot [4] estimated it to
. Chen and Chew [5]
experimentally observed a resolution up to
, for high contrast, but non-dispersive and lossy objects,
2
which is a so-called super-resolution behavior, exploiting the near field and non-linear reconstruction
algorithms. Meaney et al. [6] have suggested that image reconstruction “is fundamentally unlimited by
wavelength” and “is restricted by signal-to-noise” ratio. The latter papers have been experimentally
discussed by Semenov [7] and tested for the detection of myocardial ischemia and infarction. They
concluded that the resolution lies between a quarter and a half of a wavelength in the background medium.
Several groups have developed complex imaging setups and algorithms for imaging brain anomalies [8] [9]
[10] [11]. Experimental phantoms for the head have been developed, the most complex one using molded
semi-rigid parts assembled inside an outer solid cavity [12]. The complex molding procedure and the high
number of used ingredients makes this approach precise, however not easily repeatable. Moreover, the skin
is not represented realistically as it is included in the fat/bone layer printed in a plastic material with
dielectric constant of 6 at 2 GHz [13]. These models are very useful to realistically simulate the dielectric
properties inside the brain itself and are used for imaging [9]. To validate numerical models, interesting
works have been done in the microwave imaging community with a 3D printed breast phantoms [17] [18]
with Triton X-100 based mixtures to mimic biological tissues. In the 7T MRI community 3D printed liquid
phantoms [19] are also used as they are easy to handle and transportable. A similar approach is followed
here, to our best knowledge, for the first time in the framework of MWI of the brain, and a first attempt of
using this simple, repeatable and over time stable procedure was published recently in [20].
In [14] guidelines to design an optimal MWI setup and to properly set the working frequency and the
matching medium, needed to facilitate the penetration of the probing wave into the head, are determined
using a plane wave Transmission Line (TL) model since it allows a simple analysis. On the other hand, a
multilayered spherical model better approximates the head geometry while still allowing an analytical
solution to the electromagnetic scattering problem [15] [16].
This paper focuses on the analysis of the power transmission through the four main layers between the brain
and the background medium, namely the Cerebrospinal Fluid (CSF), the bone, the fat and the skin. These
four layers have very different influence on the propagation of the wave from and into the brain, according
3
to the frequency. For this, a spherically stratified head phantom has been built to experimentally estimate
the power transmitted into the brain and to analyze the influence of these layers on the propagation of the
EM wave.
II. MODEL AND ELECTROMAGNETIC ANALYSIS
Figure 1: Spherical multilayered model to analyze the power transmitted into the human head.
The spherically stratified model, sketched in Fig. 1 (right), is a more realistic model of the human head than
the planar model in [14] while still allowing an analytic solution for the electric field distribution. The core
of the sphere is the brain with a radius of
mm, the
layer (the core is the
layer) is given by
, , and represents, respectively, the CSF (3mm), the cortical bone (7mm) (denoted
here bone), the fat (4mm), the skin (4mm) and the matching medium (see Fig. 1). In [19] for 7T MRI the
Larmor frequency is around 300MHz and the brain region is modeled as a combination of CSF, grey matter,
and white matter. Since we deal with higher frequencies and, thus, shorter wavelengths, we model the CSF
separately and the dielectric characteristics of the brain are set with a grey over white matter ratio (GM/WM
4
ratio) of 1.5 as shown in [21]. A similar ratio was used in [20], as the dielectric properties of the latter two
are similar in the frequency range of interest.
Due to the spherical geometry of the boundary conditions, the electric field can be expanded as an infinite
sum of vector spherical harmonics and be expressed analytically. Reference [22] provides a review on the
governing equations of the spherical wave expansion used to solve this problem, and gives a detailed
analysis and validations of the implementation. These results are valid for a plane wave impinging on the
head phantom. This needs to be taken into account when comparing theoretical and experimental results.
However, because we are only interested in the transmission inside the head, this is not a real restriction and
the results using a plane wave should be also valid for an antenna directly placed on the head since the
propagation of an electromagnetic wave depends only on the properties of the medium and not on the
characteristics of the wave, that is plane wave, spherical wave, etc. Finally, we define the normalized
transmitted power,
, as the ratio between the transmitted power into a bounded domain in the center of
the brain and the power available in the lossless background in the very same bounded domain.
C. Simulation Results and Discussion
Figure 2: Normalized transmitted power according to the frequency GHz, for a matching medium of
(left). Cuts for
of the
(right).
The normalized transmitted power represents the incoming power that can excite any anomaly in the center
of the head (worst case scenario) and therefore produce a scattered field. Fig. 2 represents a map of the
![Figure 4: Theoretical (solid line) [12] and measured (dashed line) dielectric properties of the measurements of brain (black), CSF (dark blue), bone (green), fat (light blue) and skin (magenta).](/figures/figure-4-theoretical-solid-line-12-and-measured-dashed-line-20qz53ia.webp)
