In Vivo Conductivity Imaging of Rat Tumor Model Using MRI

Jiaen Liu^{1}, Qi Shao^{1}, Yicun Wang^{1}, Gregor Adriany^{2}, John Bischof^{3}, Pierre-Francois Van de Moortele^{2}, and Bin He^{1,4}

*Animal model*

Tumor-bearing Copenhagen rats (350-400 g, Charles River Laboratories) were
used as the animal tumor model. AT-1 rat prostate cancer cells^{7} were injected subcutaneously above the right hind
limb of the animal. Tumor was allowed to grow for three to four weeks to reach
a diameter of 2.5 cm before the imaging experiment.

*Experiment*

Animal experiment protocol was approved by IACUC, University of Minnesota. Animals were kept anesthetized during the experiment. An eight-channel microstrip array coil as shown in Fig. 1(a) was built for RF transmission and MRI signal detection. The coil has an inner diameter of 10 cm, outer diameter of 12.7 cm and length of 12 cm. The experiment was performed on a 7T MRI scanner (Siemens, Erlangen, Germany; Magnex Scientific, Oxford, UK) equipped with sixteen 1kW RF amplifiers (CPC, Hauppauge, NY, USA).

The magnitude and relative phase of the eight transmit B_{1}
fields were acquired with a resolution of 1.1x1.1x2 mm^{3} ^{6,8}. From the magnitude and relative phase, the gradient-related term $$$\frac{\partial{\ln\varepsilon_c}}{\partial{x}}+i\frac{\partial{\ln\varepsilon_c}}{\partial{y}}$$$ can be calculated^{6}, where $$$\varepsilon_c\equiv\varepsilon-i\frac{\sigma}{\omega}$$$ is the complex permittivity with $$$\varepsilon$$$ the permittivity, $$$\sigma$$$ the conductivity and $$$\omega$$$ the angular Larmor frequency. In order to obtain the full gradient $$$\left(\frac{\partial{\ln\varepsilon_c}}{\partial{x}},\frac{\partial{\ln\varepsilon_c}}{\partial{y}}\right)$$$, the setup including the RF coil and the animal was flipped 180 degrees relative to the z-direction
(the direction of B_{0)} as shown in Fig. 1(b), and MRI scans were
repeated to acquire another set of transmit B_{1} data. From the second dataset, the term $$$-\frac{\partial{\ln\varepsilon_c}}{\partial{x}}+i\frac{\partial{\ln\varepsilon_c}}{\partial{y}}$$$ can be calculated with the positive direction of the horizontal x-axis
relative to the animal defined identically to that in the first setup. T1-weighted
MRI images, normalized by proton density(PD)-weighted images, were acquired to
provide a reference for identifying tumor^{9}.

The animals were euthanized after the imaging experiments. Their electrical properties of tumor and nearby healthy muscle tissue were measured using a dielectric probe (85070E Agilent Technologies, Santa Clara, CA, USA) immediately after euthanasia.

*EPT Reconstruction*

Inside a region of interest (ROI), the discretized $$$\varepsilon_c$$$ and gradient $$$g_x\equiv\frac{\partial{\ln\varepsilon_c}}{\partial{x}}$$$ and $$$g_y\equiv\frac{\partial{\ln\varepsilon_c}}{\partial{y}}$$$ can be written as vectors $$$\vec{\varepsilon_c}$$$, $$$\vec{g_x}$$$ and $$$\vec{g_y}$$$, respectively. The final maps of $$$\varepsilon_c$$$ can be derived based on the optimizer $$$\varepsilon_c=\underset{\vec{\varepsilon_c}}{\mathop{\arg\min}}\,\left({{\left\|\frac{\partial\ln\vec{\varepsilon_c}}{\partial{x}}-\vec{g_{x0}}\right\|}^2}+{{\left\|\frac{\partial\ln\vec{\varepsilon_c}}{\partial{y}}-\vec{g_{y0}}\right\|}^2}+\lambda{{\left\|\ln\vec{\varepsilon_c}-\ln\vec{\varepsilon_{c0}}\right\|}^{2}}\right)$$$ where $$$\vec{g_{x0}}$$$ and $$$\vec{g_{y0}}$$$ are the calculated gradient, $$$\lambda$$$ a regularization constant and $$$\vec{\varepsilon_{c0}}$$$ an initial map of the complex permittivity. In this study, a constant $$$\vec{\varepsilon_{c0}}$$$ with $$$\sigma=1\:{\tt{S}}/{\tt{m}}$$$ and $$$\varepsilon=66\:\varepsilon_0$$$ was chosen to fit the range of measured $$$\varepsilon_c$$$ of tumor and healthy tissue using the dielectric probe. Here, $$$\varepsilon_0$$$ is the absolute permittivity of free space.

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(a) A cross-sectional schematic of the eight-channel microstrip RF coil.
(b) A diagram showing flipping the direction of the experiment setup to acquire
two sets of B1 data.

Results from two animals (top and bottom rows). Left: Axial T1-weighted
images normalized by PD-weighted images of the animals. Middle:
PD-weighted images. Red solid lines outline the tumor region based on the T1-W
images. Right: reconstructed conductivity in an ROI (surrounded by red dashed
lines) overlaid on the PD-W images.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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