Abstract
Object
Recent advances have allowed oscillating gradient (OG) diffusion MRI to infer the sizes of micron-scale axon diameters. Here the effects on the precision of the inferred diameters are studied when reducing the number of images collected to reduce imaging time for clinical feasibility.
Materials and methods
Monte Carlo simulations of cosine OG sequences (50–1000 Hz) using a two-compartment model on a parallel cylinder (diameters 1–5 μm) geometry were conducted. Temporal diffusion spectroscopy was used to infer axon diameters. Three different gradient sets were simulated with different combinations of gradient strengths.
Results
Five frequencies were adequate for d = 3–5 μm with single-sized cylinders and for effective mean axon diameters greater than 2 μm for cylinders with a distributions of diameters. There was some improvement in precision for d = 1–2 μm with 10 frequencies. It is better to repeat measurements at higher gradient strengths than to use a range of gradient strengths. The improvement tended to be greatest when using fewer frequencies and was especially noticeable at very high gradient strengths.
Conclusion
Images can be collected with fewer gradient strengths and frequencies without sacrificing the precision of the measurements. This could be useful in reducing imaging time so that OG techniques can be used in clinical settings.
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References
Schachter M, Does MD, Anderson AW, Gore JC (2000) Measurements of restricted diffusion using an oscillating gradient spin echo sequence. J Magn Reson 147(2):233–237
Parsons EC, Does MD, Gore JC (2006) Temporal diffusion spectroscopy: theory and implementation in restricted systems using oscillating gradients. Magn Reson Med 55:75–84
Xu J, Li H, Harkins KD, Jiang X, Xie J, Kang H, Does MD, Gore JC (2014) Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. Neuroimage 103:10–19
Mercredi M, Vincent TJ, Bidinosti CP, Martin M (2017) Assessing the accuracy of using oscillating gradient spin echo sequences with AxCaliber to infer micron-sized axon diameters. Magn Reson Mater Phy 30(1):1–14
Drobnjak I, Zhang H, Ianuş A, Kaden E, Alexander DC (2016) PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: insight from a simulation study. Magn Reson Med 75(2):688–700
Kakkar LS, Bennett OF, Siow B, Richardson S, Ianuş A, Quick T, Atkinson D, Phillips JB, Drobnjak I (2017) Low frequency oscillating gradient spin-echo sequences improve sensitivity to axon diameter: an experimental study in viable nerve tissue. Neuroimage. https://doi.org/10.1016/j.neuroimage.2017.07.060
Alexander DC (2008) A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magn Reson Med 60(2):439–448
Drobnjack I, Siow B, Alexander DC (2010) Optimizing gradient waveforms for microstructure sensitivity in diffusion-weighted MR. J Magn Reson 206(1):41–51
Drobnjak I, Alexander DC (2011) Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR. J Magn Reson 212(2):344–354
Siow B, Drobnjak I, Chatterjee A, Lythgoe MF, Alexander DC (2012) Estimation of pore size in a microstructure phantom using the optimised gradient waveform diffusion weighted NMR sequence. J Magn Reson 214(1):51–60
Callagan PT (1997) A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms. J Magn Reson 129(1):74–84
Perrault W, Duval T, Cohen-Adad J (2015) Comparison of NOGSE and PGSE sequences for axon diameter estimation. In: Proceedings of the 23th scientific meeting, International Society for Magnetic Resonance in Medicine, Toronto, p 2884
Li H, Gore JC, Xu J (2014) Fast and robust measurement of microstructural dimensions using temporal diffusion spectroscopy. J Magn Reson 242:4–9
Gross B, Kosfeld R (1969) Anwendung der spin-echo-methode der messung der selbstdiffusion. Messtechnik 77:171–177
Stepisnik J (1985) Measuring and imaging of flow by NMR. Prog NMR Spec 17:187–209
Stepisnik J (1993) Time-dependent self-diffusion by NMR spin-echo. Physica B 183:343–350
Does MD, Parsons EC, Gore JC (2003) Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain. Magn Reson Med 49:206–215
Xu J, Does MD, Gore JC (2009) Quantitative characterization of tissue microstructure with temporal diffusion spectroscopy. J Magn Reson 200(2):189–197
Assaf Y, Blumenfeld-Katzir T, Yovel Y, Basser PJ (2008) AxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magn Reson Med 59:1347–1354
Li H, Jiang X, Xie J, McIntyre JO, Gore JC, Xu J (2016) Time-dependent influence of cell membrane permeability on MR diffusion measurements. Magn Reson Med 75(5):1927–1934
Hall MG, Alexander DC (2009) Convergence and parameter choice for monte-carlo simulations of diffusion MRI. IEEE Trans Med Imaging 28:1354–1364
Herrera SL, Mercredi ME, Vincent TJ, Buist R, Martin M (2015) Using oscillating gradient spin-echo sequences to infer micron-sized bead and pore radii. In: Proceedings of the 23rd scientific meeting, International Society for Magnetic Resonance in Medicine, Toronto, p 3027
Eis M, Hoehn-Berlage M (1995) Correction of gradient crosstalk and optimization of measurement parameters in diffusion MR imaging. J Magn Reson B 107:222–234
Alexander DC, Hubbard PL, Hall MG, Moore EA, Ptito M, Parker GJ, Dyrby TB (2010) Orientationally invariant indices of axon diameter and density from diffusion MRI. Neuroimage 52:1374–1389
Clayden JD, Nagy Z, Weiskopf N, Alexander DC, Clark CA (2016) Microstructural parameter estimation in vivo using diffusion MRI and structured prior information. Magn Reson Med 75:1787–1796
Lam WW, Jbabdi S, Miller KL (2015) A model for extra-axonal diffusion spectra with frequency-dependent restriction. Magn Reson Med 73:2306–2320
Nilsson M, van Westen D, Stahlberg F, Sundgren PC, Latt J (2013) The role of tissue microstructure and water exchange in biophysical modelling of diffusion. Magn Reson Mater Phy 26:345–370
Zhang H, Hubbard PL, Parker GJM, Alexander DC (2011) Axon diameter mapping in the presence of orientation dispersion with diffusion MRI. Neuroimage 56(3):1301–1315
Avram L, Assaf Y, Cohen Y (2004) The effect of rotational angle and experimental parameters on the diffraction patterns and micro-structural information obtained from q-space diffusion NMR: implication for diffusion in white matter fibers. J Magn Reson 169(1):30–38
Nilsson M, Latt J, Stahlberg F, van Westen D, Hagslatt H (2012) The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study. NMR Biomed 25(5):795–805
Nilsson M, Latt J, Nordh E, Wirestam R, Stahlberg F, Brockstedt S (2009) On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted? Magn Reson Imaging 27(2):176–187
Nilsson M, Alerstam E, Wirestam R, Stahlberg F, Brockstedt S, Latt J (2010) Evaluating the accuracy and precision of a two-compartment Karger model using Monte Carlo simulations. J Magn Reson 206(1):59–67
Kakkar LS, Atkinson D, Chan RW, Siow B, Ianus A, Drobnjak I (2017) Sensitivity of OGSE ActiveAx to Microstructural Dimensions on a Clinical Scanner. In: Fuster A, Ghosh A, Kaden E, Rathi Y, Reisert M (eds) Computational diffusion MRI. MICCAI 2016. Mathematics and visualization. Springer, Cham, pp 85–97
Sepehrband F, Alexander DC, Kurniawan ND, Reutens DC, Yang Z (2016) Towards higher sensitivity and stability of axon diameter estimation with diffusion-weighted MRI. NMR Biomed 29(3):293–308
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Mercredi, M., Martin, M. Toward faster inference of micron-scale axon diameters using Monte Carlo simulations. Magn Reson Mater Phy 31, 511–530 (2018). https://doi.org/10.1007/s10334-018-0680-1
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DOI: https://doi.org/10.1007/s10334-018-0680-1