An accurate in vivo imaging modality for mapping electrical conductivity with high spatial resolution can have a significant impact on the detection and diagnosis of cancer^1,2. Electrical properties tomography (EPT) holds promises for in vivo imaging of electrical conductivity and permittivity with high spatial resolution^3-6. In this study, a new EPT platform exploiting a microstrip array coil was developed for imaging small animals in vivo. Significant difference of conductivity between tumor and healthy tissue was found in a xenograft rat tumor model. Preclinical animal tumor models can be valuable for understanding electrical properties of tumor across tissue and cellular scales.

Animal model

Tumor-bearing Copenhagen rats (350-400 g, Charles River Laboratories) were used as the animal tumor model. AT-1 rat prostate cancer cells⁷ 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 B₁ 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 calculated⁶, 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 B₀₎ as shown in Fig. 1(b), and MRI scans were repeated to acquire another set of transmit B₁ 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 tumor⁹.

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.

Figure 2 shows the reconstructed conductivity in two animals. Tumors had been implanted on the right side of animals. The darker areas on the right side of the normalized T1-W images indicate the tumor region because of increased T1 in cancerous tissue. The dark area in T1-W image on the left side of animal #2 is artifact due to weak B1 coverage. For each animal, an ROI containing tumor tissue and healthy muscle tissue was chosen for reconstruction of electrical properties. It can be observed that in the reconstructed color maps of conductivity, the boundaries between high and low conductivity areas align well with the boundaries extracted from the T1-W images (red solid lines). The reconstructed average conductivities in tumor and muscle regions are 1.05±0.02 and 0.92±0.03 S/m, respectively, for animal #1 and 1.05±0.03 and 0.94±0.04 S/m for animal #2. The corresponding probe-measured values are 1.08 and 0.9 S/m for animal #1, and 1.09 and 0.95 S/m for animal #2.In this study, an EPT system with multichannel transmit B₁ mapping was developed for imaging tumor tissue in a rat model. It is shown capable of differentiating tumor and healthy tissue based on the reconstructed conductivity. The accuracy of the method was confirmed by probe measurement. The results suggest the clinical value of conductivity imaging for diagnosing tumor. The method is promising for investigating electrical properties and associated biophysics utilizing small animal models.