The sensitivity of surface coil arrays can be maximized by conforming them closely to the human body, maximizing coil loading. There is, however, great diversity in body shape and size. Rigid coils must adopt a compromise, allowing for the largest cases while not giving up too much sensitivity when imaging smaller examples. Flexible arrays can be wrapped tightly around the body, but if array dimensions are fixed there will always be gaps or undesired overlaps depending on body habitus.

A surface coil array which could stretch would allow optimal conformation to the human body. Other authors have demonstrated a flexible knee coil in which the surface coil conductors were constructed of braided copper and changed size as the array was elongated [1]. This caused shifts in resonant frequency and loading such that it was not possible to present the optimal noise-matched impedance to the preamp in all configurations. We present here a geometrical approach based on a trellis-like lattice of interlinked slats which allows a surface coil array to be re-shaped while maintaining coil tuning, coil loading and decoupling of neighboring coils.

The Trellis Coil design principle is shown in Fig. 1. Two sets of parallel lines at different angles to each other are overlaid. The lines are linked at each crossing point and the distance d between linking points along each line is a constant regardless of the angle between the lines. Paths for surface coil conductors are defined which pass through these crossing points. To create a 10% overlap between neighboring coils to minimize inductive coupling, it is necessary to have 10 crossing points per coil, determining the density of the underlying lattice. As the angle between the two sets of parallel lines in the underlying lattice is changed the shape of the surface coil changes while always maintaining a 10% overlap between neighboring coils. The coil perimeter and surface area enclosed by each coil change only slightly over this range.

As a practical example, consider a cylindrical coil array for knee imaging with 8 overlapped elements. If the size of the coil is to be adjustable from a diameter of 15 cm to 22 cm, the coil element must stretch from 6.5 cm to 9.5 cm in width. To examine the behavior and practical implementation of this concept, a two-coil example was constructed. The underlying lattice was designed in Solidworks (Waltham, MA, USA). Rods from one layer protruded through holes in the other layer of struts and were each capped to produce hinge points linking the structure together (Figure 2). Holes for mounting pins and wire guides were incorporated in the design. It was 3D printed in ABS material on a Stratasys Fortus 360 printer (Eden Prairie, MN, USA). Coil elements were constructed out of circuit board segments and Teflon-coated multistrand wire (Fig. 3), with appropriate capacitors to bring the coils to resonance at 123.2 MHz. Circuit boards are secured to the trellis with pins which slide in slots to maintain the orientation of the boards. The coils were tuned and matched when placed 1 cm above a body-sized tissue equivalent phantom (ε_r=40.5, σ=0.58 S/m).

Over the range of extensions studied here the coil tuning, match and decoupling all remained very stable as the array was stretched (Fig 3). S₁₁ and S₂₁ values were always less than -13 dB. The wires slide easily around the guides and have not succumbed to metal fatigue after several hundred extension and contraction cycles. The unloaded to loaded Q ratio for the surface coils was 242 / 33 = 7.3 in all configurations. This compares to 337 / 36 = 9.4 for a standard circuit board coil element of the same size. The coil circumference defined by the trellis does not stay constant as the array is flexed (Figure 4), which causes the wires to fall slack for some extensions. This did not compromise decoupling over this range of extensions.The use of thin wires reduced the unloaded Q of the trellis coil elements, but as they are designed to always be in close proximity a sufficiently high Q ratio of 7.3 is achieved. The unloaded Q may be increased by using thicker multistrand wire, finding the optimum trade-off between conductivity and flexibility. The concept can be extended to cylindrical structures [2] (Fig. 5) and multi-row arrays. Possible applications include knee and extremity coils, body arrays and pediatric coils. It can also be used to maintain the optimal distribution of electric dipole antennas around the torso for 7T body arrays [3].