Relaxation measurements of an MRI system phantom at low magnetic field strengths

Objective Temperature controlled T1 and T2 relaxation times are measured on NiCl2 and MnCl2 solutions from the ISMRM/NIST system phantom at low magnetic field strengths of 6.5 mT, 64 mT and 550 mT. Materials and methods The T1 and T2 were measured of five samples with increasing concentrations of NiCl2 and five samples with increasing concentrations of MnCl2. All samples were scanned at 6.5 mT, 64 mT and 550 mT, at sample temperatures ranging from 10 °C to 37 °C. Results The NiCl2 solutions showed little change in T1 and T2 with magnetic field strength, and both relaxation times decreased with increasing temperature. The MnCl2 solutions showed an increase in T1 and a decrease in T2 with increasing magnetic field strength, and both T1 and T2 increased with increasing temperature. Discussion The low field relaxation rates of the NiCl2 and MnCl2 arrays in the ISMRM/NIST system phantom are investigated and compared to results from clinical field strengths of 1.5 T and 3.0 T. The measurements can be used as a benchmark for MRI system functionality and stability, especially when MRI systems are taken out of the radiology suite or laboratory and into less traditional environments. Supplementary Information The online version contains supplementary material available at 10.1007/s10334-023-01086-y.


Introduction
Increasing efforts are being put towards the development of low field (< 1 T) magnetic resonance (MR) systems. Without the siting limitations of high field MR systems, low field systems allow magnetic resonance to be taken outside of a controlled laboratory or radiology suite and used for a broader range of applications. Low field MR can be used to image the roots of plants in soil [1,2], detect spoilage of food products [3][4][5], identify explosives [6] or for emergency room use and bedside patient diagnosis [7][8][9]. Taking an MR system out of the laboratory or radiology suite removes many environmental controls, such as temperature and noise levels, which can result in measurement variation [1,4,5]. To ensure a system is functioning properly and that accurate measurements are being recorded, there is a need for reference materials that are characterized over a wide range of magnetic fields and temperatures.
In the work presented here, precise T 1 and T 2 values are measured at 6.5 mT, 64 mT, and 550 mT on NiCl 2 and MnCl 2 solutions in the International Society for Magnetic Resonance in Medicine/National Institute of Standards and Technology (ISMRM/NIST) system phantom. Previously, quantitative measurements on the system phantom only included the clinical field strengths of 1.5 T and 3.0 T [10]. Here, we expand this range to include 6.5 mT, 64 mT, and 550 mT, which span the range of current low field research [7,[11][12][13] and clinical systems such as the Hyperfine Swoop (Guilford, Connecticut, USA), the Promaxo System (Oakland, California, USA), the ViewRay MRIdian (Denver, Colorado, USA), the Synaptive MRI (Toronto, Ontario, Canada) and the Siemens Magnetom Free.Max (Malvern, Pennsylvania, USA). In this study, the T 1 and T 2 values of five samples from the NiCl 2 array and five samples from the MnCl 2 array of the ISMRM/NIST system phantom are measured at temperatures ranging from 10 °C to 37 °C. These measurements 1 3 can serve as a benchmark to investigate changes over time and across systems in low field MR experiments, particularly for systems that are operating outside of a controlled laboratory or radiology suite.

Hardware
A Redstone spectrometer (Tecmag, Houston, Texas, USA) and Tecmag TNMR software along with a 1 kW RF amplifier (Tomco, Stepney, South Australia, Australia) were used with two variable field electromagnets. The first magnet, an air core magnet (model BFM-0C, Resonance Research Inc., Billerica, Massachusetts, USA), allows for field strengths between 1 and 40 mT. In this study, this magnet, shown in Fig. 1b, was used for relaxation measurements at 6.5 mT (276.5 kHz for 1 H). The magnet was powered using a magnet power supply (R63C-25265, PowerTen, Kirkland, Washington, USA), cooled by a liquid/liquid heat exchanger (WW2, Haskris, Elmhurst, Illinois, USA) and controlled and monitored using a custom safety system. The second magnet was a 2.9 Ω electromagnet (Bruker, Billerica, Massachusetts, USA) with a pole diameter and spacing of 150 mm and 63 mm, respectively. Operational between 50 mT and 1 T, the electromagnet was used to collect relaxation data at 64 mT and 550 mT (2.73 MHz and 23.4 MHz, respectively for 1 H). This magnet was powered by a power supply (PSC-4, Walker Scientific Inc., Joondalup, West Australia, Australia) with control voltage inputs with better than 1 ppm stability and was cooled by a Neslab liquid/liquid heat exchanger (System III, Thermo Scientific, Waltham, Massachusetts, USA). A schematic of the experimental set up is shown in Fig. 1a.

RF Probe
A custom probe containing the RF coil form was designed and 3D printed on a Form 3 printer (Formlabs, Somerville, Massachusetts, USA) using Formlabs clear resin (Fig. 1). The probe was designed to allow Fluorinert (Fluorinert Electronic liquid FC-40, 3M, Saint Paul, Minnesota, USA) [14] to flow around the sample for temperature control. This specific Fluorinert thermal fluid, FC-40, remains a liquid over a wide range of temperatures and is used in many heat transfer applications [15][16][17][18]. Importantly, Fluorinert FC-40 does not produce a 1 H NMR signal as it contains no hydrogen, making it ideal for controlling temperature during MR studies without introducing artifacts. Shown in Fig. 1c, the probe is made up of a 62 mm outer diameter, 54.8 mm inner diameter cup that allows temperature controlled Fluorinert FC-40 to continuously flow around the sample. The outer cup has two ports that connect hoses to the probe. The hoses connect the probe to a refrigerated circulator (PolyScience, Niles, Illinois, USA), used to heat and/or cool the Fluorinert FC-40 and keep the sample at a constant and desired temperature. A lid is clamped down using ¼"− 20 nylon threaded rod, nylon nuts, and O-rings (Oil-resistant Buna-N with 0.18 cm width and 3.15 cm inner diameter and an X-profile oil-resistant Buna-N with 0.18 cm width and 5.69 cm inner diameter) to seal the Fluorinert FC-40 compartment while allowing access for the sample (contained in a 30 mL plastic bottle) to be changed. A hole in the lid allows for an AccuSens fiber optic thermometer (OpSens, Quebec QC, Quebec, Canada) to be inserted into the Fluorinert FC-40, that is flowing in the outer cup, to monitor the temperature throughout experiments. The fiber optic thermometer used in this study has an uncertainty of 0.11 °C, based on the maximum deviation from NIST calibrated Resistance Temperature Detectors (RTDs).
Inside the outer cup is an inner insert that serves as the RF coil former. The removable insert allows for a 36 mm inner diameter, 45 mm long solenoid coil to be wrapped around it. Holes in the outer cup allow for the RF coil to be connected to a tune board via a rigid coaxial cable connected to a SMB connector. To tune the coils to the desired 1 H Larmor frequencies of 276.5 kHz (6.5 mT), 2.73 MHz (64 mT) and 23.4 MHz (550 mT), two solenoid coils were wound. The coil used for 6.5 mT and 64 mT is a 32-turn solenoid wound using insulated 20 AWG Litz wire (New England Wire Technologies, Lisbon, New Hampshire, USA). An SMB connection allowed for easy exchange of tune boards so that the same RF coil could be tuned to the different resonant frequencies. Due to the low capacitance values required to tune the coil to 550 mT (23.4 MHz for 1 H), a second coil was made of six turns of 15-gauge solid copper wire separated by 5 mm.
While the temperature of the Fluorinert FC-40 in the outer cup was measured throughout the experiment, the set point of the chiller was determined based on the temperature of the sample. A PT-104 Data Logger thermometer (Pico Technology, St. Neots, Cambridgeshire, UK) was placed in water contained in a 30 mL plastic bottle and the chiller settings needed to achieve sample temperatures of 10 °C, 17 °C, 20 °C, 23 °C, 26 °C, 30 °C, and 37 °C were determined. The maximum difference between the measured temperature of the Fluorinert FC-40 and the water sample was 0.44 °C.

Samples
The sample set included a subset of the NiCl 2 and MnCl 2 arrays from the ISMRM/NIST system phantom [10]. Due to the amount of signal averaging required at low fields and therefore the time required for each experiment, only a subset of the fourteen total components that make up each array in the standard system phantom were analyzed in this work. Samples were chosen to include a broad range of concentrations present in the system phantom. The two extreme concentrations were not included due to difficulty in measuring the short T 1 of the highest concentration sample and due to the time required to measure the longest

NMR experiments-inversion recovery and CPMG
T 1 was measured using a 20-step inversion recovery pulse sequence with a composite 180-degree pulse [19] and delay times between the composite 180-degree and 90-degree pulse ranging from 6 ms to 6 s. Between each scan, a recovery time greater than 5*T 1 was required to allow for a return to thermal equilibrium. The composite pulses are used to mitigate the effects of field inhomogeneities and off resonance effects [20]. A custom Python program comprised of Anaconda 3 data science processing packages including scipy, numpy, lmfit, and PyOpenGL was used to fit the data using an unweighted, nonlinear least-squares fitting algorithm. The values of T 1 were calculated by fitting the phased, integrated real signal (S) to 1 3 where τ is the delay time between the composite 180-degree and 90-degree pulse, A is a parameter that refers to the signal intensity at long τ times and δ is the inversion efficiency. For all experiments, δ was kept over 0.90 by adding resistance to the tuning circuit which reduces the Q factor and ensures properly shaped square pulses. T 2 values were measured using a 20 step Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. Fitting the CPMG data to the equation where S 0 is a fit parameter and τ is the delay time between 180-degree pulses, allowed for the calculation of the T 2 value for each sample.
Forty-eight signal averages were acquired for each scan at 6.5 mT to give a signal to noise ratio (SNR) of 50. Higher SNR at the higher fields allowed for 8 signal averages to be acquired at 64 mT (SNR = 50) and 550 mT (SNR = 250). T 1 and T 2 values were measured for all ten samples at field strengths of 6.5 mT, 64 mT, and 550 mT. At each field strength, relaxation measurements were measured at temperatures of 17, 20, 23, and 26 °C. The temperature range was increased for the 2.52 mM and 23.30 mM NiCl 2 samples as well as the 0.07 mM and 0.56 mM MnCl 2 samples to include 10, 30 and 37 °C. Due to the time required for each experiment, only two samples from both the NiCl 2 array and the MnCl 2 array were chosen for the expanded temperature survey. A high concentration sample and a low concentration sample were chosen from each array to represent the T 1 and T 2 behavior at these expanded temperatures. The upper limit of 37 °C was chosen based on the limitations of the 3D printed probe. Each measurement was performed in triplicate, and the mean and standard deviation were calculated. To ensure precise measurements, the number of signal averages was chosen so that the standard deviation was kept under 5%.

Results
The T 1 and T 2 values measured for the five NiCl 2 solutions, at temperatures ranging from 10 °C to 37 °C, are shown in Table S1 of the Supplemental Information. Similarly, Table S2 in the Supplemental Information shows the measured T 1 and T 2 values for the MnCl 2 array for the same temperature range. In addition to the T 1 and T 2 values, standard deviations showing the variation in three trials are given in both Table S1 and Table S2. The relaxation values are dependent on both the magnetic field strength and the sample temperature.
In Fig. 2, the relaxation rates (R 1 and R 2 ) are plotted as a function of concentration for both the NiCl 2 and MnCl 2 arrays at 20 °C. The temperature of 20 °C was chosen as it is a common room temperature and typical operating bore temperature of many systems. As expected, the relaxation rates increase linearly as the concentration of paramagnetic ions (Ni 2+ and Mn 2+ ) increase, resulting in shorter T 1 and T 2 values. The 1.5 T-P and 3.0 T-P data is from [10], which are prototype samples that have slightly different concentrations from the ones studied in this work. A second measurement at 3.0 T-C is shown for NIST measurements of the commercial system phantom solutions for the NIST Phantom Lending Library which includes samples with the same concentrations as those used in this low field study. The dispersion of the R 1 and R 2 versus concentration lines shows the dependence of the relaxation rates on field for the NiCl 2 and MnCl 2 containing solutions.
Based on the data in Fig. 2, the T 1 relaxivity (r 1 ) and the T 2 relaxivity (r 2 ) of the NiCl 2 and MnCl 2 arrays were calculated and are shown, along with the ratio of r 1 /r 2 , in Table 1. Relaxivity is a characteristic commonly used in magnetic resonance imaging (MRI) to evaluate contrast agents. The relaxivity indicates the degree to which the relaxation rate of a solution is affected by a paramagnetic species of a given concentration [21]. The r 1 and r 2 of the NiCl 2 solutions shows a small increase of 0.12 and 0.41, respectively, as the field is increased from 6.5 mT to 3.0 T. However, the r 1 of the MnCl 2 array decreases by 22.04 as the field is increased, while the r 2 increases by 80.67 as the field is increased. While both the ratios of r 1 / r 2 decrease with increasing field, the MnCl 2 array shows a much more drastic decrease at higher fields. The r 1 /r 2 of NiCl 2 decreased ~ 28% from 6.5 mT to 3 T while the r 1 /r 2 of the MnCl 2 array decreased by ~ 92%. Figure 3 shows the T 1 and T 2 measurements at 20 °C for each sample from both the NiCl 2 and MnCl 2 array as a function of magnetic field strength. The plots allow for the visualization of the behavior of T 1 and T 2 as the field strength increases from 6.5 mT to 3.0 T. High field data (1.5 and 3.0 T) for the prototype solutions of the system phantom (gray ♦) [10] as well as the values for the commercial system phantom at 3.0 T are added for comparison to the low field data collected in this study. Vertical error bars are included to show the standard deviation of three repeat measurements; for most experiments the error bars are within the width of the plotted data point. While the T 1 and T 2 for NiCl 2 remain relatively constant over the range of field strengths studied here, MnCl 2 shows a noticeable increase for T 1 and decrease for T 2 as the field is increased.
The T 1 results for the 23.30 mM and the 2.52 mM NiCl 2 samples and the 0.56 mM and 0.07 mM MnCl 2 samples for the expanded temperature range of 10 °C to 37 °C are shown in Fig. 4. The error bars show the standard deviation 1 3 from three repeat measurements. The NiCl 2 samples show an exponential decrease in T 1 as the temperature is increased, which is characteristic of the NiCl 2 at all concentrations. The MnCl 2 samples show a linear increase in T 1 with increasing temperature, again, this behavior is characteristic of all concentrations of MnCl 2 . Table S3 in the supplemental information shows literature T 1 and T 2 values for in vivo human tissue measured at magnetic field strengths at or near 6.5 mT, 64 mT, and 550 mT [22][23][24][25][26][27].

Discussion
The enhancement of proton relaxation due to the presence of electron paramagnetic spins has been extensively studied [28]. The increase in the R 1 and R 2 (Fig. 2) is linearly proportional to the concentration of paramagnetic compounds in solution and depends on the electron spin-nuclear spin interactions [28]. Ni 2+ ions cause relaxation in liquid solutions due to small deviations in the octahedral geometry. The small deviations break the symmetry and allow for relaxation rate to be affected [28]. Mn 2+ ions, on the other hand, have long electronic relaxation times and correlation times which are dependent on molecular tumbling [29]. Comparison of the NMR data presented here to the NMRD relaxometry data in [30] shows a similar trend for both the Ni 2+ and Mn 2+ containing solutions. Consistent with the NMRD results for solutions containing Ni 2+ ions, the small change in the value of r 1 and r 2 ( Table 1) for NiCl 2 suggests weak dependence of the relaxation rates on field strength. For solutions containing Mn 2+ , both the NMR data presented here and the NMRD data in [30] show an overall decrease in r 1 as the field is increased up to 100 MHz [30]. In [30], the r 2 decreases up to about 10 MHz after which it increases for fields up to 100 MHz. For the field strengths studied here, there is only a slight increase in r 2 at the lower field strengths of 6.5 mT (276.5 kHz), 64 mT (2.73 MHz), and 550 mT (23.4 MHz) before a steep increase at the higher fields of 1.5 T (64 MHz) and 3.0 T (128 MHz). It should be noted that the pH of the sample can alter the measured T 1 and T 2 [31]; therefore, in order to compare to literature values, attention should be given to the pH of the sample. The solutions in this study have a neutral pH of 7 to ensure safety when handling or transporting.
Previous studies have shown no field dependence of the T 1 of NiCl 2 solutions at the low fields (< 0.55 T) investigated in this study [29,31,32]. The short correlation time, τ c , of Ni 2+ ions that results from fast electron spin relaxation results in no change in the measured relaxation rates as the field is increased up to 2.35 T (100 MHz for 1 H) [29]. For each of the five components in the NiCl 2 Fig. 3 T 1 (left) and T 2 (right) as a function of magnetic field strength for the components of the NiCl 2 (top) and MnCl 2 (bottom) arrays. Gray ♦ show the measurements of the prototype samples from [10] at 1.5 T and 3 T. All measurements are taken at 20 °C array, the T 1 remained constant as the field was increased at low field strengths. As shown in Fig. 3 there is a slight downward trend as the field approaches 3.0 T. The independence of the NiCl 2 relaxation rates on magnet field strength make the system phantom useful for comparing methods across different MR systems.
On the other hand, the MnCl 2 shows a marked increase in T 1 with increasing field (Fig. 3). This change in relaxation rate with magnetic field is explained by the longer electron relaxation times and slower τ c . For Mn 2+ solutions, τ c is determined by the tumbling rate of the ions in solution [29]. Because of the dependence on the ion tumbling rate, the T 1 of the Mn 2+ array becomes more dependent on temperature [29]. As shown in Fig. 4, the T 1 of all components of the MnCl 2 array increase with increasing temperature. The concentration of Mn 2+ in the solution affects the degree to which the T 1 changes because of temperature. At higher concentrations the T 1 has a more drastic change with temperature. This behavior is seen at all fields. The T 2 for the MnCl 2 array shows a smaller change over the temperature range analyzed in this study.
The τ c for Ni 2+ is more dependent on electron spin relaxation time than ion tumbling causing a decreased dependence of the T 1 on temperature [29]. As shown in Fig. 4 the NiCl 2 array shows a decrease in T 1 values with increasing temperature. The slow decrease as a function of temperature is expected for solutions containing Ni 2+ ions [32]. In the high field characterization of these phantom components, a benefit of the NiCl 2 array is that it showed little change in T 1 and T 2 at typical bore temperatures (17 °C to 26 °C) at 1.5 T and 3.0 T [10]. However, at the lower fields of 6.5 mT, 64 mT, and 550 mT, the T 1 and T 2 values measured between 17 °C and 26 °C showed a constant decrease. This, as well as the MnCl 2 dependence on temperature, suggests that when the phantom is used on low field systems, accurate sample temperatures should be measured and known.
The ISMRM/NIST system phantom is a stable reference object that can be used to track system stability over time and validate experimental methods. Both the NiCl 2 and MnCl 2 arrays span the wide range of in vivo T 1 and T 2 values reported in literature for human tissues at low fields (Table S3). While more complex phantoms have been developed that better mimic human tissues [33][34][35][36][37][38], further study is needed to understand the behavior of those phantoms at low magnetic fields.
The uncertainty in the measurements presented here can be reduced by increasing the homogeneity of both the static and RF fields over the entire RF coil volume. The homogeneity of the static field can be greatly improved by the addition of shims on both low field systems used in this study. Furthermore, the probe, including the RF coil, was designed to be leak-proof so that Fluorinert FC-40 can continuously flow around the sample for temperature control. However, the probe design resulted in the 30 mL bottle samples being large compared to the RF coil volume. Better RF homogeneity can be achieved by redesigning the probe so that the sample is small compared to the RF coil. Finally, the 30 mL bottles containing the samples were not completely full and had empty space at the top. While this portion of the bottle was not in the RF coil volume, it is possible that evaporation during heating may cause the sample in the coil volume to appear more concentrated. In Fig. 4, there is a noticeable drop in the measured T 1 at higher temperatures at 6.5 mT, this may be explained by a higher than expected sample concentration due to evaporation in the empty space of the bottle. At 6.5 mT, more evaporation may have occurred due to longer experiments required by the necessary, additional signal averaging.
The temperature-controlled, low field relaxation data presented here can serve as a benchmark test to ensure system function and stability. As low field MR systems continue to be developed for industrial and medical systems, which may require use in uncontrolled environments, measurements of standard materials at low magnetic field strengths are important. Further work may be needed to develop a reference object that better mimics the human brain tissue relaxation values at low magnetic field strengths.

Supplementary Information
The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s10334-023-01086-y. Acknowledgements This research was funded by NIST (https:// ror. org/ 05xpv k416). The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (https:// ror. org/ 03q1r gc19), U.S. Department of Energy, under Award Number DE-AR0000823. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Disclosures Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States. Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
Author contribution Martin (0000-0002-4257-9589) contributed to the study conception and design, acquisition of data, analysis and interpretation of data, drafting of manuscript and critical revision. Jordanova (0000-0002-9097-3863) contributed to the analysis and interpretation of data and critical revision. Kos (000-0002-1780-860X) contributed to the acquisition of data and critical revision. Russek (0000-0002-8788-2442) contributed to the study conception and design, analysis and interpretation of data and critical revision. Keenan (0000-0001-9070-5255) contributed to the study conception and design, analysis and interpretation of data and critical revision. Stupic (0000-0001-8356-1160) contributed to the study conception and design, acquisition of data, analysis and interpretation of data, drafting of manuscript and critical revision.
Data availability Data will be made available upon request.

Conflict of interest
The authors declare that they have no known conflicts of interest.
Ethical approval This study does not contain any studies with human participants performed by any of the authors.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.