### INTRODUCTION

### MATERIALS AND METHODS

^{++}and MATLAB (MathWorks, Natick, MA, USA) based software tool called 'Phased Array Coil Evaluator' (PACE) with three main functions:

### 3D Model Building

### Protocol for MRI Acquisition and Simulations

_{1}field map of each coil element, placing a uniform phantom model having the same dimensions and electrical properties of the experimental phantom and located inside the simulated coil structure considering the same FOV sizes of the MRI acquisitions. In this work, a 3T MRI system was used to acquire the volumetric data set and the above mentioned conditions were followed for the experiment and the simulations.

### Coil sensitivity FDTD Simulation of the Phase Array Coil

_{1}field of the coil geometry. In this study, SEMCAD (SEMCAD X, SPEAG, Switzerland) (13) was used as FDTD tool. The simulation has been performed in a model having the same physical dimensions and electrical properties of the phantom used in the experimental work. Figure 5 shows the FDTD-computed B1 field distributions for a single-element coil after excitation.

### Data Visualization

### The Relative planes

*Coil element plane points*) from each coil element. This important points are used to generate the coil element plane which will be used later as a reference to form the relative planes used for the visualization of the coil sensitivity. Since the data of the FASTSCAN is given in units relative to its own reference, we need to co-register the measured points of each coil element with the respective spatial position of the image data obtained during the MRI experiment to create accurate coil element plane reference for each coil channel. The co-registration is a simple transformation of two or more set of data into one coordinate system. Following the protocol for MRI acquisition and simulations mentioned two sections before and having the acquired MRI data in millimeter units, a simple coordinate translation will be sufficient to achieve a good co-registration. At this point, the 3D MRI data is combined with the model obtained with the 3D scanner as shown in Figure 7. By computing the MRI data isocenter as well as the coil structure center, both the MRI data and the coil 3D model are matched to share the same spatial domain.

*coil element plane points*obtained by the FASTSCAN tool from each coil element after co-registration are used to create the normal vector of the coil's plane which is given by the cross-product:

*n*is the normal vector of the

_{i}*i*coil element plane and

^{th}*p*

_{0},

*p*

_{1}and

*p*

_{2}are the measured coil element plane points from each coil channel. In the following we exclusively refer to

*p*

_{0}as the point acquired at the center of the coil element while the other two are obtained at arbitrary points of its own periphery. We consider

*p*

_{0}= (

*a*,

*b*,

*c*) where

*a*,

*b*and

*c*represent the

*x*,

*y*and

*z*coordinates of

*p*

_{0}respectively, using the same terminology for

*p*

_{1}and

*p*

_{2}, we will have

*p*

_{1}= (

*d*,

*e*,

*f*) and

*p*

_{2}= (

*g*,

*h*,

*i*). The two arbitrary points (

*p*

_{1}and

*p*

_{2}) will determine the orientation of the coil plane so these are given to the free choice depending on how the user wants to create the relative planes. In this work we choose

*p*

_{1}and

*p*

_{2}to be orthogonal with respect to

*p*

_{0}to obtain a standard visualization of the relative planes. After the normal vector is obtained, the coil element plane equation from each channel can be driven by using the plane equation:

*n*,

_{i,x}*n*and

_{i,y}*n*are the components of the normal vector

_{i,z}*n*given by Eq. 1.

_{i}*r*, from the coil plane, then the plane equation will be similar to Eq. 2 but shifted by a distance r as given in Eq. 3.

*p*

_{0}and

*p*

_{1}will determine the axis rotation vector as <

*u*,

*v*,

*w*>=<

*d*-

*a*,

*e*-

*b*,

*f*-

*c*>while for the r-Coronal plane,

*p*

_{0}and

*p*

_{2}will form the axis rotation vector <

*u*,

*v*,

*w*>=<

*g*-

*a*,

*h*-

*b*,

*i*-

*c*>. The matrix rotation about an arbitrary axis that passes through a point (

*p*

_{0}), is presented in Eq. 4:

##### [4]

${\scriptscriptstyle \mathrm{R}=\frac{1}{L}\left[\begin{array}{cccc}{u}^{2}+VW\xb7\mathrm{cos}\xb7\theta & u\xb7v\xb7\zeta -w\xb7\delta & u\xb7w\xb7\zeta +v\xb7\delta & \left(a\xb7VW-u\xb7\left(b\xb7v+c\xb7w\right)\right)\xb7\zeta +\left(b\xb7w-c\xb7v\right)\xb7\delta \\ u\xb7v\xb7\zeta +w\xb7\delta & {v}^{2}+UW\xb7\mathrm{cos}\xb7\theta & u\xb7w\xb7\zeta -v\xb7\delta & \left(b\xb7UW-v\xb7\left(a\xb7u+c\xb7w\right)\right)\xb7\zeta +\left(c\xb7u-a\xb7w\right)\xb7\delta \\ u\xb7w\xb7\zeta -v\xb7\delta & u\xb7w\xb7\zeta +u\xb7\delta & {w}^{2}+UV\xb7\mathrm{cos}\xb7\theta & \left(c\xb7UW-w\xb7\left(a\xb7u+b\xb7v\right)\right)\xb7\zeta +\left(a\xb7v-b\xb7v\right)\xb7\delta \\ 0& 0& 0& L\end{array}\right]}$*L*=

*u*

^{2}+

*v*

^{2}+

*w*

^{2},

*VW*=

*v*

^{2}+

*w*

^{2},

*UW*=

*u*

^{2}+

*w*

^{2}, UV =

*u*

^{2}+

*v*

^{2}, θ is the rotation angle, ζ= 1 - cosθ and δ = √L sin θ. In our case, the rotation angle θ is 90° which will simplify Eq. 4 and the whole procedure of relative planes creation is depicted in Figure 8.

### RESULTS

^{++}for the phased array coil performance evaluation. A MATLAB version of the toolbox is shown in Figure 9. PACE (Fig. 9a) contains ARCS for the creation of the script to form the 3D structure, and a visualization environment (Fig. 9b and c) to observe the coil performance.

### Coil Model Generation by ARCS

### Data Visualization

_{1}field distributions, having a coupling-free reference to be compared with the real phased array coil. On the simulations, we set a uniform grid distribution in a FOV of 256×256×320 mm

^{3}with the step sizes of h

_{x}= 2.0 mm, h

_{y}=2.0 mm and h

_{z}=1.25 mm. The total matrix size for the FDTD computation was 128×128×256. We also perform an MRI experiment using a spoiled GE 3D sequence, with: FOV = 256×256×320 mm, image matrix size = 256×256×32, TE = 7 ms, TR = 50 ms, FA = 50° and NEX=1. A cylindrical phantom with 200 mm of diameter and 300 mm height was used with ε

_{r}= 76.7, µ

_{r}= 1 and σ = 0.6 S/m, where ε

_{r}, µ

_{r}and σ are the relative permittivity, relative permeability and conductivity, respectively. For the FDTD simulations, the same phantom was modeled. Both simulations and experiments were conducted with similar characteristics as the above mentioned protocol demand.

*coil element plane points*were imported into PACE toolbox in order to compare and visualize the coil sensitivities and detect coupling by visual inspection. Two independent windows should be opened for comparing both set of data, one for the simulation (Fig. 9c) and other for the experimental (Fig. 9b) data.