MRI Biomarker NMR Water Diffusion Coefficient

1 Page 1 NIST Special Publication 250 NIST SP 250-100 Magnetic Resonance Imaging Biomarker Calibration Service: NMR Measurement of Isotropic Water Diffusion Coefficient Michael A. Boss Kathryn E. Keenan Karl F. Stupic Nikki S. Re... Open at page → 2 Page 2 NIST Special Publication 250 NIST SP 250-100 Magnetic Resonance Imaging Biomarker Calibration Service: NMR Measurement of Isotropic Water Diffusion Coefficient Michael A. Boss* Kathryn E. Keenan Karl F. Stupic Cassandra... Open at page → 3 Page 3 NIST SP 250-100 March 2023 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended... Open at page → 4 Page 4 NIST SP 250-100 March 2023 i Abstract This document describes a calibration service to measure the water diffusion coefficient, or diffusivity, in reference materials and tissue mimics using nuclear magnetic resonance (N... Open at page → 5 Page 5 NIST SP 250-100 March 2023 ii Table of Contents 1. Introduction ..................................................................................................................... 1 2. Calibration Service Summary ........ Open at page → 6 Page 6 NIST SP 250-100 March 2023 iii 7. Monte Carlo Uncertainty Calculation ......................................................................... 51 8. Quality Control ......................................................... Open at page → 7 Page 7 NIST SP 250-100 March 2023 iv Fig. 4. Normalized signal derived from the integrated spectra and maxima of spectra verses b-value. The diffusion coefficients derived from the fit (black lines) are ???????????? = 2.060 x10... Open at page → 8 Page 8 NIST SP 250-100 March 2023 v Fig. 21. (a) 1D images of the sample cell. (b) measured gradient versus gradient current. . 28 Fig. 22. 1D image of cylindrical sample cell filled with a 30 % PVP solution taken with 1.451 A... Open at page → 9 Page 9 NIST SP 250-100 March 2023 vi Fig. 40. The combined expanded ????????????=2???????????? uncertainty (a), combined expanded relative uncertainty(b), and estimated bias in diffusivity (c) for a water sample with 50 % by we... Open at page → 10 Page 10 NIST SP 250-100 March 2023 1 1. Introduction This calibration service provides traceable measurements of the isotropic water diffusion coefficient D , in materials used in magnetic resonance imaging (MRI) phantoms (calib... Open at page → 11 Page 11 NIST SP 250-100 March 2023 2 different environments with membranes and barriers. Tissues may show multiple water diffusion coefficients, non-Gaussian diffusion, as well as strong dependence of diffusion on the measuremen... Open at page → 12 Page 12 NIST SP 250-100 March 2023 3 line broadening. The inhomogeneous broadening for diffusion measurements is required to be less than 10 Hz and is typically between 2 Hz and 7 Hz. The most important calibrations are the grad... Open at page → 13 Page 13 NIST SP 250-100 March 2023 4 have the form ????????????̄̄ (????????????⃗)=????????????????????????̿, with ????????????̿ being the identity matrix. Note, an additional term, ???????????? ???????????? ̄ ̄ (????????????⃗),... Open at page → 14 Page 14 NIST SP 250-100 March 2023 5 Note, the gradient field term is approximate and does not satisfy the Maxwell equation ????????????�⃗⋅ ????????????�⃗=0. The additional field terms, transverse to the applied field axis, requ... Open at page → 15 Page 15 NIST SP 250-100 March 2023 6 where ????????????(????????????⃗ ???????????? ) is the coil sensitivity function, the field per unit current produced by the RF coil at ????????????⃗ ????????????, the position of the spin pa... Open at page → 16 Page 16 NIST SP 250-100 March 2023 7 For an ideal PGSE sequence, q returns to zero after the end of the second gradient pulse. For the case of rectangular pulses, the b-value after the completion of the gradient pulses can be ca... Open at page → 17 Page 17 NIST SP 250-100 March 2023 8 shapes and pulse sequences can vary since nonidealities, such as output current unfaithfulness and eddy currents can depend on gradient pulse shape. The b-value can also be determined by a nu... Open at page → 18 Page 18 NIST SP 250-100 March 2023 9 The measured FID signal is proportional to the magnetic moment ???????????? ∝ ???????????? ???????????? ???????????? 0 . The full FIDs, both real and imaginary components, are recorded during... Open at page → 19 Page 19 NIST SP 250-100 March 2023 10 of the strength of the signal, which are also proportional to ???????????? ????????????, including the maximum of the amplitude of the FID and the maxima of the spectra. For a system with a... Open at page → 20 Page 20 NIST SP 250-100 March 2023 11 Fig. 5. Schematic diagram of the NIST NMR measurement system. 4.1 NMR system The NMR system, shown in Fig. 5, was assembled by NIST using commercially available parts. The NMR magnet is Oxfo... Open at page → 21 Page 21 NIST SP 250-100 March 2023 12 4.1.1 Magnetic Field Ramp and Shimming The magnet is ramped by insertion of a set of down leads and energized using a superconducting magnet power supply following the manufacturer’s operati... Open at page → 22 Page 22 NIST SP 250-100 March 2023 13 capacitor. The resonance impedance is adjusted by a variable “Match” capacitor to approximately 50 ohm, which is identified by maximizing the absorption of RF power in the |S 11| measurement... Open at page → 23 Page 23 NIST SP 250-100 March 2023 14 Fig. 7. The magnitude of the reflection coefficient |S 11|, on a linear (A) and a log scale (B), for the RF coil when the magnetic field is at 3.015 T and the sample temperatures is at 0 °C,... Open at page → 24 Page 24 NIST SP 250-100 March 2023 15 The exponential decay time ???????????? is also determined and is required to satisfy ????????????(???????????? 810 ) ????????????(???????????? 90) > 0.7 and ????????????>22.4???????????? 90... Open at page → 25 Page 25 NIST SP 250-100 March 2023 16 Fig. 8. Nutation data for a 3 mM CuSO 4 solution at 20 °C in the diffusion sample cell. The black line is a fit using a damped sinusoid model, which results in t 90 = 14.2 μs. -6 -4 -2 0 2 4... Open at page → 26 Page 26 NIST SP 250-100 March 2023 17 4.1.5 NMR instrument linewidth and peak integration: After equilibration, a single spectrum of American Chemical Society (ACS) reagent-grade water is acquired with eight free- induction deca... Open at page → 27 Page 27 NIST SP 250-100 March 2023 18 over a region of ±10 x FWHM, as shown in the figure. This range is sufficient to capture all the water signal and exclude CH 2, CH3, protons. Fig. 11. Spectra from water protons in a 40 % by... Open at page → 28 Page 28 NIST SP 250-100 March 2023 19 ???????????? ???????????? (????????????)=????????????????????????????????????��????????????(????????????)−????????????(????????????−1)�+???????????? − ????????????Δ???????????? ????????????... Open at page → 29 Page 29 NIST SP 250-100 March 2023 20 This model is used in the Monte Carlo Bloch simulations to determine uncertainty in diffusivity due to uncertainty in the sample position and the lack of a well-defined gradient value. The s... Open at page → 30 Page 30 NIST SP 250-100 March 2023 21 Fig. 13. Diffusion coefficient of water at 20 °C with 3 mM CuSO 4 as a function of sample position, using both a single gradient calibration at z = 0, and point by point gradient calibration... Open at page → 31 Page 31 NIST SP 250-100 March 2023 22 The dimensions of the sample cell are calibrated with microCT at room temperature, as shown in Fig. 14(b), which in turn is calibrated by using a 3.000 mm ± 0.0025 mm alumina sphere. The unc... Open at page → 32 Page 32 NIST SP 250-100 March 2023 23 evaporation. Any loss of sample due to evaporation readily shows up as an increase in the NMR line width and the presence of a bubble or inhomogeneity is seen in the 1D MR images (Fig. 15).... Open at page → 33 Page 33 NIST SP 250-100 March 2023 24 4.3 Fiber optic temperature probe and temperature control system The temperature control system, shown in Fig. 17, consists of six computer- controlled components: 1) a fiber optic thermomet... Open at page → 34 Page 34 NIST SP 250-100 March 2023 25 Temperature scans are taken from low to high temperature, with the shimming recommended at each temperature. Measurements begin at low temperatures to minimize effects due to evaporation and... Open at page → 35 Page 35 NIST SP 250-100 March 2023 26 Fig. 18. Water diffusion coefficient (red) in a 40 % by weight polyvinyl pyrrolidone solution as a function of temperature along with its derivative (blue) which gives the diffusion temperat... Open at page → 36 Page 36 NIST SP 250-100 March 2023 27 Fig. 19. Gradient calibration traceability chain. A set of 20 1D spin echo images are obtained by varying the gradient output current, ranging from approximately -5 A to 5 A. Voltage traces... Open at page → 37 Page 37 NIST SP 250-100 March 2023 28 count. Measuring the precise current is not needed, it is just a convenient and intuitive method of reporting the calibration. All that is required is that the monitor output is consistently... Open at page → 38 Page 38 NIST SP 250-100 March 2023 29 Fig. 22. 1D image of cylindrical sample cell filled with a 30 % PVP solution taken with 1.451 A maximum current applied to the y-gradient coil along with the fit to an ideal cylinder (equati... Open at page → 39 Page 39 NIST SP 250-100 March 2023 30 4.5.1 Gradient recovery and eddy current compensation After application of a gradient pulse there can be ringing or overshoot that has not been eliminated by the gradient pre-emphasis settin... Open at page → 40 Page 40 NIST SP 250-100 March 2023 31 4.5.2 Gradient pulse shape and spacing There is a lot of latitude in choosing the gradient pulse shape, polarity, and spacing. The current measurement service uses trapezoidal positive-polar... Open at page → 41 Page 41 NIST SP 250-100 March 2023 32 Fig. 25. NMR signal of 50 % polyvinyl pyrrolidone/water solution doped with paramagnetic salts at 3 T, 20 °C versus b -value for the standard scans (StandardScan bmax = 5000 s/mm 2 and Stand... Open at page → 42 Page 42 NIST SP 250-100 March 2023 33 Fig. 26. Signal from a set of PGSE pulse sequences similar to those listed in Table 4 for a liposomal tissue mimic. 4.5.3 Computed vs. measured b-values The accuracy of the computed b-values... Open at page → 43 Page 43 NIST SP 250-100 March 2023 34 Fig. 27. Measured PGSE gradient pulses and associated spin modulation wavevectors. Fig. 28. Lower plot: b-values determine from analytical formula for trapezoidal pulses and numerically inte... Open at page → 44 Page 44 NIST SP 250-100 March 2023 35 inversion pulse width is varied about the ideal value with a distribution given by the ???????????? 180 calibration uncertainty. Fig. 29. Measured water diffusion coefficient as a function o... Open at page → 45 Page 45 NIST SP 250-100 March 2023 36 given by Eq. 26 and the deviations of our water diffusion measurements from the literature consensus over a range of temperature from 0 °C to 26 °C are shown in Fig. 30. At present, our aver... Open at page → 46 Page 46 NIST SP 250-100 March 2023 37 5. Standard Operating Procedures 5.1 Diffusion Measurement Protocol The measurement protocol, shown in Fig. 31, has 5 main components: 1) system startup and calibration, 2) sample preparatio... Open at page → 47 Page 47 NIST SP 250-100 March 2023 38 thermometer is inserted into the sample rod and spinner, using a gauge to ensure the correct insertion depth shown in Fig. 14. The sample is inserted into the NMR and the fiber optic connect... Open at page → 48 Page 48 NIST SP 250-100 March 2023 39 Table 5. Phase cycling scheme for the PGSE sequence showing the eight measurements that are averaged to get the FID that is analyzed to obtain a diffusion weighted signal. The table entries... Open at page → 49 Page 49 NIST SP 250-100 March 2023 40 The gradient strength, maximum q value, and the b-value are also calculated using the stored reference gradient calibration value. The script then opens the raw time- domain 1D gradient -ech... Open at page → 50 Page 50 NIST SP 250-100 March 2023 41 squares fit to an exponential decay to extract the apparent diffusion coefficient ???????????? ????????????. The eddy current correction is subtracted to get corrected diffusion coefficients... Open at page → 51 Page 51 NIST SP 250-100 March 2023 42 Note that for our Monte Carlo replicates described in the next section, the normality assumption may well approximate some cases but not all cases. Additionally, the standard uncertainty det... Open at page → 52 Page 52 NIST SP 250-100 March 2023 43 ???????????? ???????????????????????????????????????????????? ????????????=� 1 ????????????−1 �(???????????? ℎ−????????????̅) 2 ???????????? ℎ=1 , (27) where ???????????? ℎ represents the in... Open at page → 53 Page 53 NIST SP 250-100 March 2023 44 measurement system and measured data. For example, the B 0 uncertainty is taken from the measured inhomogeneous linewidth, described in Sec 6.4, and a worst-case distribution is defined as a... Open at page → 54 Page 54 NIST SP 250-100 March 2023 45 where R is a random variable taken from a contin uous uniform distribution from − 1 to 1, ????????????????????????????????????????????????????????????????????????????????????????????????????... Open at page → 55 Page 55 NIST SP 250-100 March 2023 46 Gradient calibrations (TC4) The gradient calibrations are described in Sec. 4.4. The uncertainties in the calibration are primarily derived from the uncertainty in the cell diameter d, which... Open at page → 56 Page 56 NIST SP 250-100 March 2023 47 standard deviation in the range of 0.125 µT to 0.50 µ T depending on the obtainable quality of the shimming for a particular set of samples. Nonuniformity of the RF field amplitude (LE2): Fo... Open at page → 57 Page 57 NIST SP 250-100 March 2023 48 Nonuniform gradients and gradient offsets (LE7) As shown in Fig. 9b, the gradient strength will vary slightly over the 3 mm sample volume. The spatial variation of the magnetization, describ... Open at page → 58 Page 58 NIST SP 250-100 March 2023 49 as uniform as possible by using a multi-pass N 2 flow sample cell and maintaining the probe temperature close to the sample temperature. Convective flow will be worse in low viscosity sample... Open at page → 59 Page 59 NIST SP 250-100 March 2023 50 dissolved gases, such as oxygen, which can modify proton spin relaxation, can change over time or during sample handling and measurement, particularly during temperature cycling. Samples can... Open at page → 60 Page 60 NIST SP 250-100 March 2023 51 resulting in a similar change in signal for all spectra. Uncertainty occurs due to errors in determining the phase shift to be applied. The magnitude of the error in the phase shift was less... Open at page → 61 Page 61 NIST SP 250-100 March 2023 52 Figure 34 shows typical spin packet distributions for the 3 mm cylindrical sample, color coded for local field and gradient nonuniformity. The second loop (parameter loop) is over the desire... Open at page → 62 Page 62 NIST SP 250-100 March 2023 53 polynomial. The uncertainty for the full set of measurements, 12 temperatures in this case, can be taken from the fit. This allows us to leverage all of the Monte Carlo repeats taken for a p... Open at page → 63 Page 63 NIST SP 250-100 March 2023 54 Table 6. Input uncertainties used in the Monte Carlo Bloch simulations shown in Figs. 35, 36. Type A evaluations of uncertainty are based on the statistical analysis of repeated measurements... Open at page → 64 Page 64 NIST SP 250-100 March 2023 55 Fig. 33. Schematic of Monte Carlo calculation showing conversion of uncertainties in input parameters into uncertainty in diffusion coefficients. Fig. 34. Point clouds showing typical spin p... Open at page → 65 Page 65 NIST SP 250-100 March 2023 56 Fig. 35. Signal versus b -values for a 20 % PVP solution at 3 T, 20 °C including data and simulated data along with diffusion fits. The inset shows a set of simulated spectra from which the... Open at page → 66 Page 66 NIST SP 250-100 March 2023 57 Fig. 37. Empirical distributions from a Monte Carlo simulation of a 20 % PVP sample at 20 °C, 3 T. Distribution of important input values are shown in orange, while the output distribution f... Open at page → 67 Page 67 NIST SP 250-100 March 2023 58 Fig. 38. Two sets of simulated measurements of diffusivity on the identical sample of pure water at 20 °C with coverage intervals determined using ????????????=2????????????�, where ????????... Open at page → 68 Page 68 NIST SP 250-100 March 2023 59 Fig. 40. The combined expanded ????????????=2????????????� uncertainty (a), combined expanded relative uncertainty(b), and estimated bias in diffusivity (c) for a water sample with 50 % by w... Open at page → 69 Page 69 NIST SP 250-100 March 2023 60 measurement series at 0 °C (ice-point) and with traceable platinum resistance thermometers at several temperatures. The quality control plan for NMR measurements, software version control, a... Open at page → 70 Page 70 NIST SP 250-100 March 2023 61 References 1. Kessler LG, Barnhart HX, Buckler AJ, Choudhury KR, Kondratovich MV, Toledano A, Guimaraes AR, Filice R, Zhang Z, Sullivan DC, Group QTW. The emerging science of quantitative im... Open at page → 71 Page 71 NIST SP 250-100 March 2023 62 16. Malyarenko DI, Swanson SD, Konar AS, LoCastro E, Paudyal R, Liu MZ, Jambawalikar SR, Schwartz LH, Shukla-Dave A, Chenevert TL. Multicenter Repeatability Study of a Novel Quantitative Dif... Open at page → 72 Page 72 NIST SP 250-100 March 2023 63 corresponds to the upper tail of the F distribution: p-value = 1- F.cdf(F-statistic, M-d, N-M ) , where F.cdf is the F-cumulative distribution h calculated using the Python SciPy library sci... Open at page → 73 Page 73 NIST SP 250-100 March 2023 64 Fig. A2. Diffusivity measurement which cannot be well fit with a single exponential model but can be well fit with a bi- exponential model. The text at the top of the figure, in red and gree... Open at page → 74 Page 74 NIST SP 250-100 March 2023 65 -3.182 -156.09 -68.72 4468.24 -2.828 -138.72 -61.07 3529.60 -2.474 -121.36 -53.42 2701.73 -2.121 -104.05 -45.81 1984.86 -1.769 -86.75 -38.20 1380.68 -1.414 -69.37 -30.54 881.92 -1.061 -52.03... Open at page → 75 Page 75 NIST SP 250-100 March 2023 66 Calculate Image Widths: X-direction Open 1D Image for Gradient Calibration X-direction **************************************************************************************************** Fi... Open at page → 76 Page 76 NIST SP 250-100 March 2023 67 -3.182 2.5e+07 2270.5 19823.8 415764.1 - 155.20 0.08 5.00 - 225000 -2.828 3.6e+07 2027.7 17578.8 420194.1 - 137.63 0.06 3.86 - 200000 -2.474 5.3e+07 1790.2 15404.1 425926.6 - 120.60 0.04 2.2... Open at page → 77 Page 77 NIST SP 250-100 March 2023 68 Open Eddy Current Correction PGSE File, Gradient direction= X **************************************************************************************************** File= EddyTests\eddytest_PG... Open at page → 78 Page 78 NIST SP 250-100 March 2023 69 Integrate n linewidths, Integration width (Hz) =34.17969 Fine phase adjust 0: Phase angles=[-20.933 -15.227 -11.96 -9.541 -7.964 -5.629 -3.757 -2.808 -1.965 -0.801 0.978 1.562 2.187 3.611 3.... Open at page → 79 Page 79 NIST SP 250-100 March 2023 70 Open Diffusion PGSE File, Gradient direction= X **************************************************************************************************** File= DifMeasure\e_PGSE_trap_Gx_delta=14m... Open at page → 80 Page 80 NIST SP 250-100 March 2023 71 Integrate n linewidths, Integration width (Hz) =29.29688 Fine phase adjust 0: Phase angles=[ 109.503 107.479 107.533 107.156 108.363 108.126 107.299 107.329 106.646 108.673 107.641 107.308 1... Open at page → 81 Page 81 NIST SP 250-100 March 2023 72 Input Gradient Current Traces: X-direction Input current traces: //68608nmr/data/BreastPhantomCal/PVP25_07- 20-2021/PVP25p_20C/DifSetup/GyCal_tflip= 10.6ms_DACmax=50_20C/GyCal_tflip=10.6ms_D... Open at page → 82 Page 82 NIST SP 250-100 March 2023 73 Reset Gy Imax=7.214A Calculate Image Widths: Y -direction Open 1D Image for Gradient Calibration Y-direction *********************************************************************************... Open at page → 83 Page 83 NIST SP 250-100 March 2023 74 Igrad(A), Smax, f0(Hz), df(Hz), bg, G(mT/m), Gerr(mT/m), ferr (Hz), DAC -3.607 1.9e+07 317.7 21786.3 400148.8 -170.57 0.08 5.17 - 250000 -3.247 2.7e+07 307.4 19630.7 408786.6 -153.69 0.05 3.... Open at page → 84 Page 84 NIST SP 250-100 March 2023 75 Open Eddy Current Correction PGSE File, Gradient direction= Y **************************************************************************************************** File= EddyTests\eddytest_PG... Open at page → 85 Page 85 NIST SP 250-100 March 2023 76 Integrate n linewidths, Integration width (Hz) =43.94531 Fine phase adjust 0: Phase angles=[-3.796 -2.41 -2.198 -1.399 -0.899 -2.231 -1.651 -0.738 -1.345 -0.846 -0.055 -1.08 -0.208 -0.022 -0... Open at page → 86 Page 86 NIST SP 250-100 March 2023 77 Open Diffusion PGSE File, Gradient direction= Y **************************************************************************************************** File= DifMeasure\f_PGSE_trap_Gy_delta=14m... Open at page → 87 Page 87 NIST SP 250-100 March 2023 78 Integrate n linewidths, Integration width (Hz) =29.29688 Fine phase adjust 0: Phase angles=[ 127.002 126.355 128.956 127.521 126.834 127.849 128.35 128.777 128.369 128.537 128.298 127.61 128... Open at page → 88 Page 88 NIST SP 250-100 March 2023 79 Diffusion Summary ***Recovery time(s)= 9.096 ?adequate? *** ImaxGx, ImaxGy(A)=7.069 7.214, Gradient Cal: Gxcal, Gycal(mT/m/A)=48.606 47.116 Eddy Current Corrections (ECC): GxECC,GyECC(10^-3... Open at page → 89 Page 89 NIST SP 250-100 March 2023 80 SpinPacketDistribution=RandomCylinder nIterations=4 SampleLength(mm)=3.0 SampleWidth(mm)=3.0 SampleOffsetMax=1 SampleOffsetType=Random B1AmpError=0.05 B1NonUniformity=TecMagQuartic RandomLoc... Open at page → 90 Page 90 NIST SP 250-100 March 2023 81 Fig. A3.1 Screen shot from Monte Carlo simulation showing a PGSE pulse sequence and simulated free induction decay Open at page →