Yaohui Wang^{1}, Xuegang Xin^{1}, Lei Guo^{2}, Zhifeng Chen^{1}, and Feng Liu^{2}

A novel gradient coil design scheme was proposed for use in planar MRI systems. Unlike conventional scheme in a limited magnet pole-pole space which usually applies unshielded design, the novel strategy integrated a set of actively-shielded gradient coils in only four layers in the pole-pole space with the utilization of the system peripheral sections. The design largely improved the shielding effect of the gradient coils and meanwhile left adequate space for the patients and installation of cooling device. The design scheme did not significantly increase the system manufacturing complexity either.

In
a BEM-based gradient coil design procedure, the following optimization problem
can be formed$$ ({\bf{A^TA}}+{\it{w}}_1{\bf{B^TB}}+{\it{w}}_2{\bf{L}}+{\it{w}}_3{\bf{R}}){\bf{X}}={\bf{A^TT_{Bz}}}\qquad\qquad(1)$$where
**A** is the system matrix relates the coil
current density and magnetic fields over the diameter of spherical volume (DSV),
**B** is the matrix relates to the coil current
density and magnetic fields over the shielding region, **L** is the inductance matrix, **R**
is the resistance matrix, **X** is
stream function vector, **T _{Bz}**
is the target gradient magnetic field,

Fig. 1(a) illustrates a planar MRI system, with a profile of the gradient assembly and main magnet. The coil layers and dimensions of the proposed actively-shielded planar gradient coil design concept are given in Fig. 1(b). In the limited magnet-pole space, there are only four coil layers placed, and the rest of the coils are placed in the peripheral section of the system, as shown in the 3D configuration (see Fig.1(c)~(e)) for the x, y and z coils, respectively.

In the design process, the maximum target field error was set
as 5% for all the coils, the weighting factor *w*_{1}, *w*_{2} and *w*_{3} are 1, 0.2 and 0.5,
and the maximum stray field intensity was set as 5 Gauss, 5 Gauss and 12 Gauss
(the achievable mimimum stray field constraint based on many trials) for the x,
y and z coil respectively. The DSV is 40 cm.

Fig.1 A
diagram of the novel gradient coil design scheme: (a) is the diagram of a
planar MRI system, (b) shows the dimensions of the x, y and z coils, (c) is the
current density layers for the x coil design, (d) is the current density layers
for the y coil design and (e) is the current density layers for the z coil
design. There is only 21-mm space available for the gradient assembly
placement.

Fig.2 Novel
shielded planar gradient coil design: (a), (c) and (e) are the wire patterns of
the x, y and z coils, respectively, and (b), (d) and (f) are the stray field
distributions on the sampling region of shielding of the x, y and z coils,
respectively.

Table.I Coil
performance parameters of the novel three-axis planar gradient coils