A Tabletop Persistent-Mode, Liquid-Helium-Free, 1.5-T/90-mm MgB₂ “Finger” MRI Magnet for Osteoporosis Screening: Two Design Options

Abstract

In this paper we present two design options for a tabletop liquid-helium-free, persistent-mode 1.5-T/90-mm MgB₂ “finger” MRI magnet for osteoporosis screening. Both designs, one with and the other without an iron yoke, satisfy the following criteria: 1) 1.5-T center field with a 90-mm room-temperature bore for a finger to be placed at the magnet center; 2) spatial field homogeneity of <5 ppm over a 20-mm diameter of spherical volume (DSV); 3) persistent-mode operation with temporal stability of <0.1 ppm/hr; 4) liquid-helium-free operation; 5) 5-gauss fringe field radius of <50 cm from the magnet center; and 6) small and light enough for placement on an exam table. Although the magnet is designed to operate nominally at 10 K, maintained by a cryocooler, it has a 5-K temperature margin to keep its 1.5-T persistent field up to 15 K. The magnet will be immersed in a volume of solid nitrogen (SN₂) that provides additional thermal mass when the cryocooler is switched off to provide a vibration-free measurement environment. The SN₂ enables the magnet to maintain its persistent field over a period of time sufficient for quiescent measurement, while still limiting the magnet operating temperature to ≤15 K. We discuss first pros and cons of each design, and then further studies of our proposed MgB₂ finger MRI magnet.

I. Introduction

Bone densitometry screening is a critically important and effective tool for detecting the risk of osteoporotic fracture. There are over 44 million people at risk and about 10 million people currently suffering from osteoporosis in the United States alone, yet less than half of those at risk receive screening [1]. Having a low-cost screening device that could be widely deployed for metabolic bone disease would assist in identifying the individuals who need further diagnostic assessment and possible treatment.

A solid-state MRI can separately measure both bone mineral and matrix densities, and can image the bone micro-architecture, thus yielding comprehensive characterization of metabolic bone disease, including osteoporosis and osteomalacia, noninvasively [2]. However, the conventional MRI is too expensive to be practical or cost effective for widespread screening exclusively for metabolic bone disease.

At the Magnet Technology Division of the MIT Francis Bitter Magnet Laboratory, we have proposed a tabletop 1.5-T MgB₂ “finger” MRI magnet targeted exclusively for osteoporosis screening [3]. Because metabolic bone disease is generally systemic, all skeletal sites, including fingers, are affected and there is a significant correlation among the bone mineral density (BMD) scores of various sites.

This paper describes, first the liquid-helium-free and persistent-mode MgB₂ magnet operation and then, two magnet design options, one actively-shielded and the other passively-shielded, to meet all the required specifications for our proposed tabletop MRI magnet. Finally, pros and cons of different magnetic shielding options, further studies are described and discussed.

II. MgB₂ for MRI Magnets: Liquid-Helium-Free and Persistent-Mode Operation

A. Solid Nitrogen Cooling

Recently, the global helium shortage has become a challenge for both manufacturer and users of superconducting NMR/MRI magnets mostly cooled and operated in a bath of liquid helium (LHe) [4, 5]. A cryogen-free magnet relying on a cryocooler is one obvious option to resolve the issue but such a magnet has practically no thermal mass at cryogenic temperatures. Solid nitrogen (SN₂) is an excellent thermal mass enhancing substance to LHe-free magnets [3]. The operating temperature of the persistent-mode tabletop MgB₂ MRI magnet is designed to be ≤15 K and we adopt SN₂ cooling method with following objectives:

1. Due to its heat capacity of 0.2–0.5 J·cm⁻³·K⁻¹ in the range 10–15 K, ~20 times higher than that of copper, SN₂ is a great thermal mass enhancer [6]. If the total heat input to the cold chamber is 0.5 W when the cryocooler is off and for an SN₂ volume of ~10 liter in the cold chamber, the magnet can remain in its operating temperature range 10–15 K for ~10 hours—the cryocooler can be off either by power outage or intentionally to provide a noise-free environment for MRI imaging;

2. Thermal conductivity of SN₂ in the range 10–15 K is quite good to keep a temperature difference of <1 K within a “large” cold mass [7], making it unnecessary to provide additional conductive thermal passages such as by aluminum foil or to impregnate the winding with epoxy that requires an additional process.

B. Superconducting Joint Technique with MgB₂ wire

For temporal stability, operation in persistent mode is much more desirable than driven mode. To achieve a stability of 0.1 ppm/hr, required for most commercial MRI magnets, each joint resistance must be ≤10⁻¹¹ Ω and in a small magnet with lower inductance like this tabletop MRI magnet, joint resistance should be less than 10⁻¹² Ω. The field can also decay due to the conductor’s relatively low index, n, ~30 for the in situ MgB₂ [8].

We have developed a technique to make a superconducting joint with unreacted MgB₂ wires, first with multifilament and later with monofilament to improve the technique’s success repeatability [9–11]. The results have shown that good joints have critical currents, I_c, of >200 A in self-field at 15 K. To date Patel et al. also reported improved joint results using the unreacted in situ C-doped MgB₂ monofilament wires with I_c of >200 A and 140 A in self-field and 0.5 T, respectively, at 20 K [12]. Fig. 1 shows I_c (B, T) data of MgB₂ conductor manufactured by Hyper Tech Research, Inc. [13]. At an operating current, I_op, of 108 A, the wire I_c is sufficient to keep a magnet in current-persistent mode in the range 10–15 K for n ≥30. Also the data indicate that the joint at <0.5 T has sufficiently high I_c, >140 A, and low resistance, ~10⁻¹³ Ω.

Fig. 1.

I_C(B) and J_C(B) plots at selected temperatures for 0.84-mm diameter MgB₂ conductor by Hyper Tech Research, Inc. [13].

C. Tabletop 1.5-T/90-mm MRI Magnet Design

Table I lists the design specifications for our LHe-free, persistent-mode tabletop 1.5 T MgB₂ finger MRI magnet. We adopt a 2-step RT bore idea to minimize total conductor length. A large bore diameter (>100 mm) is required for hand penetrating through. Of the second Ø90-mm small bore, the center Ø25-mm space is for a finger, leaving an annular space, between ≥25-mm and ≤89-mm, for gradient/shim coils. The distance from the gradient coil top end to the magnet center for a finger needs to be <50 mm.

TABLE I.

A Tabletop LHe-Free, Persistent-Mode 1.5 T Osteoporosis MRI Magnet Design Requirement

Parameter		Specification
Field strength	[T]	1.5
Patient bore; small bore; large bore size	[mm]	25; 90; 100
Distance to magnet center for a finger	[mm]	<50
Magnet outer diameter / overall height	[mm]	<380 / <1000
Region of interest (ROI) in DSV	[mm]	20
Homogeneity (Peak-to-Peak) in ROI	[ppm]	<5
Temporal Stability	[ppm/hr]	<0.1
5-gauss fringe field radius (radial)	[m]	<0.5
Magnet Overall Weight	[kg]	<100
Cooling Method	Cryocooler, Solid Nitrogen

For flexible site planning of this tabletop MRI magnet, its fringe field radius should be minimized. To limit the fringe field to ≤0.5 m in the radial direction, we need a magnetic field shielding technique. In this section, we introduce two MRI magnet designs both satisfying all the requirements but with different magnetic shielding methods: active and passive. Because of dimensional tolerances in manufacturing processes (parts and assembly), we expect the as-assembled magnet to have field a homogeneity of <500 ppm/mm.

D. Actively Shielded (AS) Magnet

An actively shielded (AS) magnet design includes shielding coils, placed radially outside the main coils. The shielding coils generate an axial center field opposite from that of the main coils, thus reducing the field everywhere, most effectively outside the main coils. Although this active shielding technique enables the overall magnet more compact and lightweight than the passive shielded counterpart that generally use a massive iron shield, it subtracts the main field and generate undesirable interaction forces.

The positions and boundaries of the superconducting coil windings are constrained by the design specifications listed in Table I. To operate this MgB₂ magnet persistently over the range 10–15 K, at 108 A, the coils are wound with insulated rectangular cross section MgB₂ wire, 1-mm wide by 0.87-mm thick. The cost function implemented during optimization includes designing field error of ≤5 ppm within 20-mm DSV at the center, while meeting the center field and fringe field requirements. We have performed optimization to minimize the total MgB₂ conductor requirement and compared two magnet options prior to further detailed magnet design.

Generally, two coils are incorporated for an active shield. Fig. 1(a) and Table II illustrate the configuration, position, and dimension of our AS magnet. The AS magnet consists of 5 main coils (C1–C5) and 2 shield coils (C6, C7). A total of 3.53-km long conductor is required. The key parameters of each coil at 108 A are summarized in the Table III. At 15 K, the maximum operating temperature, I_op/I_c(B_Max)=0.54 is sufficient for persistent-current operation. Note that the magnet still can be operated in superconducting state even at 20 K because I_c(B_Max, 20 K) is 121 A and I_op/I_c(B_Max) is still <100%. So technically, the magnet has a sufficient margin well above 15 K.

TABLE II.

Coil Positions of the Tabletop 1.5 T MRI Magnet with Insulated MgB₂ Wire of overall dimensions, 1 mm × 0.87 mm, Operating at I_op = 108 A and T_op = 10 K

Coil #	r1 [mm]	r2 [mm]	z1 [mm]	z2[mm]	NTurns	NLayers	Length [km]
AS Magnet Coil (note: C4, C5, C7 are mid-plane symmetric)
C1	58.60	69.04	−13.00	13.00	26	12	0.13
C2	70.00	94.36	26.75	49.75	23	28	0.34
C3	70.00	94.36	51.00	100.00	49	28	0.71
C6	126.00	139.92	46.00	94.00	48	16	0.65
PS Magnet Coil (note: C4, C5 are mid-plane symmetric)
C1	57.62	68.06	−10.00	10.00	20	12	0.1
C2	70.00	87.40	29.20	57.20	28	20	0.28
C3	70.00	87.40	59.00	90.00	31	20	0.31
Iron Yoke	r1f [mm]		r2f [mm]	r3f [mm]	z1f [mm]		z2f [mm]
	100		70	125	104		120

TABLE III.

Operating Parameters of Each Coil for Two Magnet Options

Coil #	BMax [T]	IOP/IC(B), 10 K [%]	IOP/IC(B), 15 K [%]	Axial Force [kN]	Max. Hoop Stress (Energization only) [MPa]
AS Magnet Coil (note: C4, C5, C7 are mid-plane symmetric)
C1	1.61	36.7	47.6	0.0	11.9
C2	1.81	39.9	52.1	14.0	16.0
C3	1.88	41.1	53.8	−33.1	16.6
C6	1.45	34.3	44.2	6.2	22.6
PS Magnet Coil (note: C4, C5 are mid-plane symmetric)
C1	1.69	37.9	49.3	0.0	12.0
C2	1.96	42.5	55.8	9.1	17.0
C3	2.00	43.2	56.8	−14.4	17.2

E. Passively Shielded (PS) Magnet

A passive shielding technique for conventional MRI magnets relies on a ferromagnetic structure, here an iron yoke. Two negatives with the PS magnet are: 1) the structure adds a significant weight; and 2) the material poses challenges because of its nonlinear magnetic properties that also varies with ambient temperature. Here, we are proposing an iron yoke that surrounds the main coils inside the cold chamber. The iron yoke: 1) limits a 5-gauss fringe field in the radial-axis to <0.5 m; 2) contributes an extra field to the center; and 3) shields the magnet from an external interference field such as of moving elevators, passing cars. We first used the same optimization method to design an AS magnet composed of 5 primary coils. This time not aiming to find an optima solution to minimize all the harmonic errors, we decided Z2 harmonic error to be compensated by the iron yoke, and then, we used finite element method (FEM) to meet the design requirements. We will use low-carbon steel 1002 for iron yoke. The gray shades in Fig. 2(b) shows a cross-section view and Table II lists key parameters of the PS magnet. Note that a total conductor length is 1.26 km, less than 40% of the length of an AS magnet. The maximum field in the coils is slightly larger than AS magnet because the iron yoke adds a field as shown in Table III. Calculated axial force and a maximum hoop stress induced only by energization in each coil of both AS and PS magnets are in the reasonable range, not requiring additional reinforcement. Fig. 3 shows plots of homogeneity in ROI and 5-gauss fringe field lines of (a) AS magnet, and (b) PS magnet. Peak-to-peak homogeneities in 20-mm DSV of the AS and PS magnets are 4.2 ppm and 4.7 ppm, respectively, and both design satisfy a 5-gauss fringe field radius of <0.5 m. The dimensional uncertainties of the AS coils and the iron yoke must be kept within ±1 mm, not a formidable requirement, to be shimmed.

Fig. 2.

The tabletop MRI magnet cross-section profile. (a) AS magnet; (b) PS magnet.

Fig. 3.

Field homogeneity in ppm in ROI (upper) and calculated fringe field lines in gauss (lower). (a) AS magnet and (b) PS magnet. (Axes unit: meter)

Since MgB₂ has much higher stability margin than that of LTS [7], the AS and PS magnets wound with MgB₂ wire are not susceptible to quench caused by disturbances. However, in case of a quench, we will employ the same protection technique, using a resistive-state mass of the PCS as a protection resistor, developed in our previous MgB₂ magnet project [14].

III. Discussion

A. Design Options

We have designed two magnets adopting different types of magnetic shielding methods in Section III. Key design parameters of both AS and PS magnet for tabletop 1.5 T MRI are listed in Table IV. Most of recent commercially produced LTS MRI magnets have designed and manufactured with an active shielding technique because of its lightweight and compactness compared with a passive shielding technique that requires massive ferromagnetic material. With NbTi, the space, site construction, and moving cost for these >tons of massive iron wall can be greater than >2 times the cost of the conductor required for active shielding magnet. But with a tabletop, i.e., compact, MgB₂ magnet, in which MgB₂ may be several times more expensive than NbTi, a passive shielding option seems more viable at this time. Total conductor length difference between two shielding options is ~2 km. Also an iron yoke shields ROI in the magnet from an external interference field. Whereas in the AS magnet, additional superconductive loops, placed on top of the main and shield coils, may be necessary to effectively shield the interference field from outside. Based on above discussions, we have decided to use the PS magnet design. Fig. 4 shows a schematic view of the overall system.

TABLE IV.

Key Parameters of the Tabletop 1.5 T MgB₂ MRI Magnet

Parameter		AS Magnet	PS Magnet
Center Field	[T]	1.5	1.5
Nominal Operating Current	[A]	108	108
Persistent-Mode Operating Temperature	[K]	10~15 K
Total Conductor Length	[km]	3.53	1.26
Homogeneity (Peak-to-Peak / VRMS) @ 2 cm-DSV	[ppm]	4.2 / 0.8	4.7 / 1
Inductance	[H]	1.15	0.66
5-Gauss Fringe Field (Radial)	[m]	0.4	0.49
Stored Energy	[kJ]	6.71	3.86
Mass of Conductor / Iron	[kg]	18 / 0	7 / 38

Fig. 4.

Overall magnet system view of the iron shielded tabletop MgB₂ “finger” MRI magnet.

B. Further Studies

Two further studies for successful development of the passively-shielded MgB₂ MRI magnet are discussed below.

1. Superconducting joint with pre-reacted MgB₂ wire will be investigated. We will adopt the wind-and-react procedure, because unreacted wire would make it much easier than reacted wire to wind a magnet and make superconducting joints. But generally the react-and-wind procedure is preferable because it eliminates the need to heat treat the magnet and makes it possible, if required, to repair defective joints even they have been heat treated.

2. Magnetic properties of an iron yoke in the cryogenic temperature will be investigated and may be measured in house. Homogeneity of the passively shielded MRI magnet is affected by the magnetic property of an iron yoke. Although we specified the material of an iron yoke in this design, the magnetic property varies with temperature and even with manufacturer. We will first investigate the nonlinear magnetic properties in the temperature range 10–15 K, of the iron selected for the yoke and then, we will refine the magnet design to achieve the best possible homogeneity.

IV. Conclusion

We have presented and discussed here two design options for a tabletop LHe-free, persistent-mode 1.5-T/90-mm MgB₂ “finger” MRI magnet for osteoporosis screening: 1) actively shielded (AS); and 2) passively shielded (PS). The magnet, wound-and-reacted with a monofilament MgB₂ wire, will operate in the temperature range 10–15 K immersed in a volume of SN₂ that provides extra thermal mass to the cold chamber. As discussed above, we have tentatively decided to adopt a PS option that requires a total length of <1.5 km MgB₂ wire.