Skip to main content

Advertisement

SpringerLink
Log in

Assessing the accuracy of using oscillating gradient spin echo sequences with AxCaliber to infer micron-sized axon diameters

  • Research Article
  • Published:
Magnetic Resonance Materials in Physics, Biology and Medicine Aims and scope Submit manuscript

Abstract

Objective

Current magnetic resonance imaging (MRI) axon diameter measurements rely on the pulsed gradient spin-echo sequence, which is unable to provide diffusion times short enough to measure small axon diameters. This study combines the AxCaliber axon diameter fitting method with data generated from Monte Carlo simulations of oscillating gradient spin-echo sequences (OGSE) to infer micron-sized axon diameters, in order to determine the feasibility of using MRI to infer smaller axon diameters in brain tissue.

Materials and methods

Monte Carlo computer simulation data were synthesized from tissue geometries of cylinders of different diameters using a range of gradient frequencies in the cosine OGSE sequence . Data were fitted to the AxCaliber method modified to allow the new pulse sequence. Intra- and extra-axonal water were studied separately and together.

Results

The simulations revealed the extra-axonal model to be problematic. Rather than change the model, we found that restricting the range of gradient frequencies such that the measured apparent diffusion coefficient was constant over that range resulted in more accurate fitted diameters. Thus a careful selection of frequency ranges is needed for the AxCaliber method to correctly model extra-axonal water, or adaptations to the method are needed. This restriction helped reduce the necessary gradient strengths for measurements that could be performed with parameters feasible for a Bruker BG6 gradient set. For these experiments, the simulations inferred diameters as small as 0.5 μm on square-packed and randomly packed cylinders. The accuracy of the inferred diameters was found to be dependent on the signal-to-noise ratio (SNR), with smaller diameters more affected by noise, although all diameter distributions were distinguishable from one another for all SNRs tested.

Conclusion

The results of this study indicate the feasibility of using MRI with OGSE on preclinical scanners to infer small axon diameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Hursh JB (1939) The properties of growing nerve fibers. Am J Physiol 127:140–153

    Google Scholar 

  2. Ritchie JM (1982) On the relation between fibre diameter and conduction velocity in myelinated nerve fibres. Proc R Soc Lond B Biol Sci 217:29–35

    Article  CAS  PubMed  Google Scholar 

  3. Waxman SG (1980) Determinants of conduction velocity in myelinated nerve fibers. Muscle Nerve 3:141–150

    Article  CAS  PubMed  Google Scholar 

  4. Tasaki I, Ishii K, Ito H (1943) On the relation between the conduction-rate, the fiber-diameter and the internodal distance of the medullated nerve fiber. Jpn J Med Sci III Biophy 9:189–199

    Google Scholar 

  5. 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

    Article  PubMed  PubMed Central  Google Scholar 

  6. Malysz T, Ilha J, do Nascimento PS, Angelis KD, Schaan BD, Achaval M (2010) Beneficial effects of treadmill training in experimental diabetic nerve regeneration. Clinics (Sao Paulo) 65:1329–1337

    Article  Google Scholar 

  7. Armstrong RA (2009) Alzheimer’s disease and the eye. J Optom 2:103–111

    Article  Google Scholar 

  8. Piven J, Bailey J, Ranson BJ, Arndt S (1997) An MRI study of the corpus callosum in autism. Am J Psychiatry 154:1051–1056

    Article  CAS  PubMed  Google Scholar 

  9. Hughes JR (2007) Autism: the first firm finding = underconnectivity? Epilepsy Behav 11:20–24

    Article  PubMed  Google Scholar 

  10. Njiokiktjien C, de Sonneville L, Vaal J (1994) Callosal size in children with learning disabilities. Behav Brain Res 64:213–218

    Article  CAS  PubMed  Google Scholar 

  11. Randall PL (1983) Schizophrenia, abnormal connection, and brain evolution. Med Hypotheses 10:247–280

    Article  CAS  PubMed  Google Scholar 

  12. Rice D, Barone S Jr (2000) Critical periods of vulnerability for the developing nervous system: evidence from humans and animal models. Environ Health Perspect 108(Suppl 3):511–533

    Article  PubMed  PubMed Central  Google Scholar 

  13. Virtanen J, Uusitalo H, Palkama A, Kaufman H (1984) The effect of fixation on corneal endothelial cell dimensions and morphology in scanning electron microscopy. Acta Ophthalmol (Cph) 62:577–585

    Article  CAS  Google Scholar 

  14. Barazany D, Basser PJ, Assaf Y (2009) In vivo measurement of axon diameter distribution in the corpus callosum of rat brain. Brain 132(Pt 5):1210–1220

    Article  PubMed  PubMed Central  Google Scholar 

  15. Horowitz A, Barazany D, Tavor I, Bernstein M, Yovel G, Assaf Y (2015) In vivo correlation between axon diameter and conduction velocity in the human brain. Brain Struct Funct 220(3):1777–1788

    Article  PubMed  Google Scholar 

  16. 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

    Article  PubMed  Google Scholar 

  17. Assaf Y, Freidlin RZ, Rohde GK, Basser PJ (2004) New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn Reson Med 52:965–978

    Article  PubMed  Google Scholar 

  18. Zhang H, Hubbard PL, Parker GJ, Alexander DC (2011) Axon diameter mapping in the presence of orientation dispersion with diffusion MRI. Neuroimage 56(3):1301–1315

    Article  PubMed  Google Scholar 

  19. Nilsson M, Lätt J, Ståhlberg F, van Westen D, Hagslätt H (2012) The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study. NMR Biomed 25:795–805

    Article  PubMed  Google Scholar 

  20. Ronen I, Budde M, Ercan E, Annese J, Techawiboonwong A, Webb A (2014) Microstructural organization of axons in the human corpus callosum quantified by diffusion-weighted magnetic resonance spectroscopy of N-acetylaspartate and post-mortem histology. Brain Struct Funct 219(5):1773–1785

    Article  CAS  PubMed  Google Scholar 

  21. Innocenti GM, Caminiti R, Aboitiz F (2015) Comments on the paper by Horowitz et al. (2014). Brain Struct Funct 220:1789–1790

    Article  Google Scholar 

  22. Shemesh N, Jespersen SN, Alexander DC, Cohen Y, Drobnjak I, Dyrby TB, Finsterbusch J, Koch MA, Kuder T, Laun F, Lawrenz M, Lundell H, Mitra PP, Nilsson M, Özarslan E, Topgaard D, Westin CF (2016) Conventions and nomenclature for double diffusion encoding NMR and MRI. Magn Reson Med 75:82–87

    Article  CAS  PubMed  Google Scholar 

  23. Drobnjak I, Zhang H, Ianuş A, Kaden E, Alexander DC (2015) PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: insight from a simulation study. Magn Reson Med. doi:10.1002/mrm.25631

    PubMed Central  Google Scholar 

  24. 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

  25. 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

    Article  PubMed  PubMed Central  Google Scholar 

  26. Drobnjack I, Siow B, Alexander DC (2010) Optimizing gradient waveforms for microstructure sensitivity in diffusion-weighted MR. J Magn Reson 206(1):41–51

    Article  Google Scholar 

  27. Thiessen JD, Zhang Y, Zhang H, Wang L, Buist R, Del Bigio MR, Kong J, Li X-M, Martin M (2013) Quantitative MRI and ultrastructural examination of the cuprizone mouse model of demyelination. NMR Biomed 26:1562–1581

    Article  CAS  PubMed  Google Scholar 

  28. Martin M (2013) Measuring restriction sizes using diffusion weighted magnetic resonance imaging: a review. Magn Reson Insights 6:59–64

    Article  PubMed  PubMed Central  Google Scholar 

  29. Schachter M (2000) Development of methods to assess water diffusion using oscillating gradient nuclear magnet resonance. In: Doctoral thesis, Yale University, USA

  30. Gross B, Kosfeld R (1969) Anwendung der spin-echo-methode der messung der selbstdiffusion. Messtechnik 77:171–177

    Google Scholar 

  31. 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

    Article  Google Scholar 

  32. Gore JC, Anderson AW, Does MD, Gochberg DF, Joers JM, Kennan RP, Parsons EC, Schachter M (2001) The relationship of problems in biomedical MRI to the study of porous media. Magn Reson Imaging 19:295–300

    Article  CAS  PubMed  Google Scholar 

  33. Stepisnik J (1981) Analysis of self-diffusion measurements by density matrix calculation. Physica 104B:350–364

    Google Scholar 

  34. Stepisnik J (1985) Measuring and imaging of flow by NMR. Prog NMR Spec 17:187–209

    Article  Google Scholar 

  35. Callaghan PT, Stepisnik J (1995) Frequency-domain analysis of spin motion using modulated-gradient NMR. J Magn Reson A 117:232–237

    Article  Google Scholar 

  36. 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

    Article  PubMed  Google Scholar 

  37. Van AT, Holdsworth SJ, Bammer R (2014) In vivo investigation of restricted diffusion in the human brain with optimized oscillating diffusion gradient encoding. Magn Reson Med 71(1):83–94

    Article  PubMed  Google Scholar 

  38. 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

  39. 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

    Article  CAS  PubMed  Google Scholar 

  40. Jiang X, Li H, Xie J, Zhao P, Gore JC, Xu J (2016) Quantification of cell size using temporal diffusion spectroscopy. Magn Reson Med 75:1076–1085

    Article  PubMed  Google Scholar 

  41. Reynaud O, Winters KV, Hoang DM, Wadghiri YZ, Novikov DS, Kim SG (2015) In vivo and ex vivo characterization of extracellular space (ECS) in mouse GBM using PGSE and OGSE. In: Proceedings of the 23rd scientific meeting, international society for magnetic resonance in medicine, Toronto, p 0344

  42. 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

    Article  PubMed  Google Scholar 

  43. Stepisnik J (1993) Time-dependent self-diffusion by NMR spin-echo. Physica B 183:343–350

    Article  CAS  Google Scholar 

  44. Xu J, Does MD, Gore JC (2009) Quantitative characterization of tissue microstructure with temporal diffusion spectroscopy. J Magn Reson 200(2):189–197

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Gore JC, Xu J, Colvin DC, Yankeelov TE, Parsons EC, Does MD (2010) Characterization of tissue structure at varying length scales using temporal diffusion spectroscopy. NMR Biomed 23:745–756

    Article  PubMed  PubMed Central  Google Scholar 

  46. Hall MG, Alexander DC (2009) Convergence and parameter choice for Monte-Carlo simulations of diffusion MRI. IEEE Trans Med Imaging 28:1354–1364

    Article  PubMed  Google Scholar 

  47. Szafer A, Zhong J, Gore JC (1995) Theoretical model for water diffusion in tissues. Magn Reson Med 33:697–712

    Article  CAS  PubMed  Google Scholar 

  48. Vincent, TJ (2013) Monte Carlo Diffusion MRI Simulations on the GPU. Honours thesis, University of Winnipeg, Winnipeg

  49. Stanisz GJ, Szafer A, Wright GA, Henkelman RM (1997) An analytical model of restricted diffusion bovine optic nerve. Magn Reson Med 37(1):103–111

    Article  CAS  PubMed  Google Scholar 

  50. Nilsson M, Lätt J, Nordh E, Wirestam R, Ståhlberg F, Brockstedt S (2009) On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted? Magn Reson Imaging 27:176–187

    Article  PubMed  Google Scholar 

  51. Aster RC, Borchers B, Thurber CH (2012) Parameter estimation and inverse problems. Academic Press, Cambridge

    Google Scholar 

  52. Lam WW, Jbabdi S, Miller KL (2015) A model for extra-axonal diffusion spectra with frequency-dependent restriction. Magn Reson Med 73:2306–2320

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

Funding was provided by the Natural Sciences and Engineering Research Council of Canada, Canadian Institutes of Health Research, Canadian Foundation for Innovation, and the Manitoba Research and Innovation Fund.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada

    Morgan Mercredi, Christopher P. Bidinosti & Melanie Martin

  2. Department of Physics, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9, Canada

    Trevor J. Vincent, Christopher P. Bidinosti & Melanie Martin

  3. Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, M5S 3H8, Canada

    Trevor J. Vincent

  4. Department of Radiology, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada

    Melanie Martin

Authors
  1. Morgan Mercredi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Trevor J. Vincent
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christopher P. Bidinosti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Melanie Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Morgan Mercredi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mercredi, M., Vincent, T.J., Bidinosti, C.P. et al. Assessing the accuracy of using oscillating gradient spin echo sequences with AxCaliber to infer micron-sized axon diameters. Magn Reson Mater Phy 30, 1–14 (2017). https://doi.org/10.1007/s10334-016-0575-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10334-016-0575-y

Keywords

Search

Navigation