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Water diffusion in rat brain in vivo as detected at very largeb values is multicompartmental

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Abstract

The diffusion-weighted signal attenuation of water in rat brain was measured with pulsed-field gradient nuclear magnetic resonance methods in a single voxel under in vivo and global ischemic conditions. The diffusion-attenuated water signal was observed in vivo atb values of 300 ms/μm2 (strength of diffusion weighting) and diffusion times up to 400 ms. A series of constant diffusion time (CT) experiments with varied gradient directions and diffusion times revealed a multiexponential decay with apparent diffusion coefficients (ADC) covering two orders of magnitude from 1 to 0.01 μm2/ms. In a four-exponential fit, the observed changes during global ischemia could be fully explained by changes in the relative volume fractions only with unchanged ADCs. An anisotropy of the ADC, detected at smallb values, was not observed for the ADC at largeb values, but for the concomitant volume fractions. An inverse Laplace Transform of the CT curves, performed with CONTIN, resulted in continuously distributed diffusion coefficients, for which the term ‘diffusogram’ is proposed. This approach was more appropriate than a discrete exponential model with four to six components, being related to the morphology of brain tissue and its cell size distribution. On the basis of an analytical, quantitative model, it is suggested that the measured ADC at smallb values reflects mainly properties of the restricting boundaries, i.e. the relative volume fractions and the extracellular tortuosity, while the intrinsic intracellular diffusion constant and the exchange time are predicted to have minor influence.

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References

  1. Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J Chem Phys 1965;42:288–92.

    Article  CAS  Google Scholar 

  2. Tanner JE, Stejskal EO. Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method. J Chem Phys 1968;49:1768–77.

    Article  CAS  Google Scholar 

  3. Moseley ME, Butts K, Yenari MA, Marks M, de Crespigny A. Clinical aspects of DWI. NMR Biomed 1995;8:387–96.

    Article  PubMed  CAS  Google Scholar 

  4. Anderson AW, Zhong J, Petroff OA, Szafer A, Ransom BR, Prichard JW, Gore JC. Effects of osmotically driven cell volume changes on diffusion-weighted imaging of the rat optic nerve. Magn Reson Med 1996;35:162–7.

    Article  PubMed  CAS  Google Scholar 

  5. Nicholson C, Phillips JM. Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum. J Physiol (Lond) 1981;321:225–57.

    CAS  Google Scholar 

  6. van der Toorn A, Sykova E, Dijkhuizen RM, Vorisek I, Vargova L, Skobisova E, van Lookeren C, Reese T, Nicolay K. Dynamic changes in water ADC, energy metabolism, extracellular space volume, and tortuosity in neonatal rat brain during global ischemia. Magn Reson Med 1996;36:52–60.

    Article  PubMed  Google Scholar 

  7. Nicholson C, Sykova E. Extracellular space structure revealed by diffusion analysis. Trends Neurosci 1998;21:207–15.

    Article  PubMed  CAS  Google Scholar 

  8. Helmer KG, Dardzinski BJ, Sotak CH. The application of porous-media theory to the investigation of time- dependent diffusion in in vivo system. NMR Biomed 1995;8:297–306.

    Article  PubMed  CAS  Google Scholar 

  9. Stanisz GJ, Szafer A, Wright GA, Henkelman RM. An analytical model of restricted diffusion in bovine optic nerve. Magn Reson Med 1997;37:103–11.

    Article  PubMed  CAS  Google Scholar 

  10. Helpern JA, Ordidge RJ, Knight RA. The effect of cell membrane water permeability on the apparent diffusion coefficient of water. Proceedings of the ISMRM 11th Annual Meeting, Berlin, 1992, p. 1201.

  11. Waldeck AR, Nouri-Sorkhabi MH, Sullivan DR, Kuchel PW. Effects of cholesterol on transmembrane water diffusion in human erythrocytes measured using pulsed field gradient NMR. Biophys Chem 1995;55:197–208.

    Article  PubMed  CAS  Google Scholar 

  12. Pfeuffer J, Dreher W, Sykova E, Leibfritz D. Water signal attenuation in diffusion-weighted1H NMR experiments during cerebral ischemia: influence of intracellular restrictions, extracellular tortuosity, and exchange. Magn Reson Imaging 1998;16:1023–32.

    Article  PubMed  CAS  Google Scholar 

  13. Stanisz GJ, Henkelman RM. Diffusional anisotropy ofT 2 components in bovine optic nerve. Magn Reson Med 1998;40:405–10.

    Article  PubMed  CAS  Google Scholar 

  14. Duong TQ, Ackerman JJ, Ying HS, Neil JJ. Evaluation of extra-and intracellular apparent diffusion in normal and globally ischemic rat brain via19F NMR. Magn Reson Med 1998;40:1–13.

    Article  PubMed  CAS  Google Scholar 

  15. Latour LL, Svoboda K, Mitra PP, Sotak CH. Time-dependent diffusion of water in a biological model system. Proc Natl Acad Sci USA 1994;91:1229–33.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  17. Pfeuffer J, Norris DG, Niendorf T, Leibfritz D. Monte Carlo modelling of pulsed gradient spin echo experiments in ischemic brain tissue. Proceedings of the ISMRM 3rd Scientific Meeting, Nice, 1995, p. 1382.

  18. Pfeuffer J, Flögel U, Dreher W, Leibfritz D. Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of1H NMR measurements on perfused glial cells. NMR Biomed 1998;11:19–31.

    Article  PubMed  CAS  Google Scholar 

  19. Price WS, Barzykin AV, Hayamizu K, Tachiya M. A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR. Biophys J 1988;74:2259–71.

    Article  Google Scholar 

  20. Horsfield MA, Barker GJ, McDonald WI. Self-diffusion in CNS tissue by volume-selective proton NMR. Magn Reson Med 1994;31:637–44.

    Article  PubMed  CAS  Google Scholar 

  21. Basser PJ, Pierpaoli C. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 1996;111:209–19.

    Article  PubMed  CAS  Google Scholar 

  22. Pierpaoli C, Basser PJ. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med 1996;36:893–906 [published erratum appears in Magn Reson Med 1997;37(6):972].

    Article  PubMed  CAS  Google Scholar 

  23. Niendorf T, Norris DG, Leibfritz D. Detection of apparent restricted diffusion in healthy rat brain at short diffusion times. Magn Reson Med 1994;32:672–7.

    Article  PubMed  CAS  Google Scholar 

  24. Assaf Y, Cohen Y. Non-mono-exponential attenuation of water andN-acetyl aspartate signals due to diffusion in brain tissue. J Magn Reson 1998;131:69–85.

    Article  PubMed  CAS  Google Scholar 

  25. Assaf Y, Cohen Y. Diffusion MRS and MRI of fibers in bovine optic nerve and in rat brain in vivo. Proceedings of the ISMRM 6th Scientific Meeting, Sydney, 1998, p. 1263.

  26. King MD, Houseman J, Roussel SA, van Bruggen N, Williams SR, Gadian DG. q-Space imaging of the brain Magn Reson Med 1994;32:707–13.

    Article  PubMed  CAS  Google Scholar 

  27. King MD, Houseman J, Gadian DG, Connelly A. Localized q-space imaging of the mouse brain. Magn Reson Med 1997;38:930–7.

    Article  PubMed  CAS  Google Scholar 

  28. Kuchel PW, Coy A, Stilbs P. NMR ‘diffusion-diffraction’ of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics. Magn Reson Med 1997;37:637–43.

    Article  PubMed  CAS  Google Scholar 

  29. Niendorf T, Dijkhuizen RM, Norris DG, van Lookeren C, Nicolay K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn Reson Med 1996;36:847–57.

    Article  PubMed  CAS  Google Scholar 

  30. Mitra PP, Sen PN. Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: simple pore geometries. Phys Rev B 1992;45:143–56.

    Article  Google Scholar 

  31. Mitra PP, Sen PN, Schwartz LM, Doussal PL. Diffusion propagator as a probe of the structure of porous media. Phys Rev Lett 1992;68:3555–8.

    Article  PubMed  CAS  Google Scholar 

  32. Callaghan PT, Coy A, MacGowan D, Packer KJ, Zelaya FO. Diffraction-like effects in NMR diffusion studies of fluids in porous solids. Nature 1991;351:467–9.

    Article  CAS  Google Scholar 

  33. Callaghan PT. NMR imaging, NMR diffraction and applications of pulsed gradient spin echoes in porous media. Magn Reson Imaging 1996;14:701–9.

    Article  PubMed  CAS  Google Scholar 

  34. Pfeuffer J. Beschränkte Diffusion und Austausch von Wasser in Zellkulturen und im Gehirn: Theoretische Modelle und1H-NMR-Messungen. Dissertation, Universität Bremen Shaker Verlag. Aachen, 1996.

    Google Scholar 

  35. Pfeuffer J, Flögel U, Leibfritz D. Monitoring of cell volume and water exchange time in perfused cells by diffusion-weighted1H NMR spectroscopy. NMR Biomed 1998;11:11–8.

    Article  PubMed  CAS  Google Scholar 

  36. Pfeuffer J, Flögel U, Leibfritz D. Influences of diffusion time and osmotic stress on intracellular metabolite signals in perfused glial cells as detected by diffusion-weighted1H NMR Spectroscopy. Proceedings of the ISMRM 6th Scientific Meeting, Sydney, 1998, p. 533.

  37. Tkac I, Starcuk Z, Choi I-Y, Gruetter R. In vivo1H NMR spectroscopy of rat brain at 1 ms echo time. Magn Reson Med 1999;41:649–56.

    Article  PubMed  CAS  Google Scholar 

  38. Merboldt KD, Hanicke W, Frahm J. Diffusion imaging using stimulated echoes. Magn Reson Med 1991;19:233–9.

    Article  PubMed  CAS  Google Scholar 

  39. Terpstra M, Andersen PM, Gruetter R. Localized eddy current compensation using quantitative field mapping. J Magn Reson 1998;131:139–43.

    Article  PubMed  CAS  Google Scholar 

  40. Gruetter R. Automatic, localized in vivo adjustment of all first-and second-order shim coils. Magn Reson Med 1993;29:804–11.

    Article  PubMed  CAS  Google Scholar 

  41. Provencher SW. An eigenfunction expansion method for the analysis of exponential decay curves. J Chem Phys 1976;64:2772–7.

    Article  CAS  Google Scholar 

  42. Provencher SW, Vogel RH. Information loss with transform methods in system identification: a new set of transforms with high information content. Math Biosci 1980;50:251–62.

    Article  Google Scholar 

  43. Provencher SW, Vogel RH. Regularization techniques for inverse problems in molecular biology. In: Deuflhard P, Hairer E, editors. Numerical treatment of inverse problems in differential and integral equations. Boston: Birkhäuser, 1983:304–19.

    Google Scholar 

  44. Provencher SW. A constrained regularization method for inverting data represented by linear algebraic or integral equations. Comput Phys Commun 1982;27:213–27.

    Article  Google Scholar 

  45. Provencher SW. CONTIN: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations. Comput Phys Commun 1982;27:229–42.

    Article  Google Scholar 

  46. Labadie C, Lee JH, Vetek G, Springer CS. Relaxographic imaging. J Magn Reson B 1994;105:99–112.

    Article  PubMed  CAS  Google Scholar 

  47. Weingartner H. Self diffusion in liquid water. a reassessment. Z. Phys Chem 1982;132:129–49.

    Google Scholar 

  48. van Zijl PC, Moonen CT, Faustino P, Pekar J, Kaplan O, Cohen JS. Complete separation of intracellular and extracellular information in NMR spectra of perfused cells by diffusion-weighted spectroscopy. Proc Natl Acad Sci USA 1991;88:3228–32.

    Article  PubMed  Google Scholar 

  49. Flögel U, Niendorf T, Serkowa N, Brand A, Henke J, Leibfritz D. Changes in organic solutes, volume, energy state, and metabolism associated with osmotic stress in a glial cell line: a multinuclear NMR study. Neurochem Res 1995;20:793–802.

    Article  PubMed  Google Scholar 

  50. Lehmenkuhler A, Sykova E, Svoboda J, Zilles K, Nicholson C. Extracellular space parameters in the rat neocortex and subcortical white matter during postnatal development determined by diffusion analysis. Neuroscience 1993;55:339–51.

    Article  PubMed  CAS  Google Scholar 

  51. van der Veen JW, Van Gelderen P, Creyghton JH, Bovee WM. Diffusion in red blood cell suspensions: separation of the intracellular and extracellular NMR sodium signal. Magn Reson Med 1993;29:571–4.

    Article  PubMed  Google Scholar 

  52. Pilatus U, Shim H, Artemov D, Davis D, van Zijl PC, Glickson JD. Intracellular volume and apparent diffusion constants of perfused cancer cell cultures, as measured by NMR. Magn Reson Med 1997;37:825–32.

    Article  PubMed  CAS  Google Scholar 

  53. Cory DG, Garroway AN. Measurement of translational displacement probabilities by NMR: an indicator of compartmentation. Magn Reson Med 1990;14:435–44.

    Article  PubMed  CAS  Google Scholar 

  54. Sen PN, Schwartz LM, Mitra PP, Halperin BI. Surface relaxation and the long-time diffusion coefficient in porous media: periodic geometries. Phys Rev B 1994;49:215–25.

    Article  Google Scholar 

  55. Assaf Y, Cohen Y. Detection of different water populations in brain tissue using 2H single- and double-quantum-filtered diffusion NMR spectroscopy. J Magn Reson B 1996;112:151–9.

    Article  PubMed  CAS  Google Scholar 

  56. Assaf Y, Navon G, Cohen Y. In vivo observation of anisotropic motion of brain water using 2H double quantum filtered NMR spectroscopy. Magn Reson Med 1997;37:197–203.

    Article  PubMed  CAS  Google Scholar 

  57. Latour LL, Hasegawa Y, Formato JE, Fisher M, Sotak CH. Spreading waves of decreased diffusion coefficient after cortical stimulation in the rat brain. Magn Reson Med 1994;32:189–98.

    Article  PubMed  CAS  Google Scholar 

  58. Pfeuffer J, Bröer S, Bröer A, Lechte M, Flögel U, Leibfritz D. Expression of aquaporins in Xenopus laevis oocytes and glial cells as detected by diffusion-weighted1H NMR spectroscopy and photometric swelling assay. Biochim Biophys Acta 1998;1448:27–36.

    Article  PubMed  CAS  Google Scholar 

  59. Han SS, Vetek G, Springer CS Sotak CH. Apparent diffusion coefficient of intra- and extracellular water in yeast suspension measured by combined diffusion and relaxography. Proceedings of the ISMRM 6th Scientific Meeting, Sydney, 1998, p. 535.

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Pfeuffer, J., Provencher, S.W. & Gruetter, R. Water diffusion in rat brain in vivo as detected at very largeb values is multicompartmental. MAGMA 8, 98–108 (1999). https://doi.org/10.1007/BF02590526

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  • DOI: https://doi.org/10.1007/BF02590526

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