Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results.

A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.

[1]  M. Freidlin.  Functional Integration And Partial Differential Equations , 1985 .

[2]  S. Perry,et al.  "Alveolar septal structure in different species". , 1994, Journal of applied physiology.

[3]  P W Kuchel,et al.  NMR “diffusion‐diffraction” of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics , 1997, Magnetic resonance in medicine.

[4]  Karl G. Helmer,et al.  Spin Echoes in a Constant Gradient and in the Presence of Simple Restriction , 1995 .

[5]  Baldwin Robertson,et al.  Spin-Echo Decay of Spins Diffusing in a Bounded Region , 1966 .

[6]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[7]  W. Happer,et al.  Biological magnetic resonance imaging using laser-polarized 129Xe , 1994, Nature.

[8]  Sean B Fain,et al.  Early emphysematous changes in asymptomatic smokers: detection with 3He MR imaging. , 2006, Radiology.

[9]  M Filoche,et al.  Renormalized random walk study of oxygen absorption in the human lung. , 2004, Physical review letters.

[10]  Karl G. Helmer,et al.  Restricted Diffusion in Sedimentary Rocks. Determination of Surface-Area-to-Volume Ratio and Surface Relaxivity , 1994 .

[11]  G. Miller,et al.  q‐space analysis of lung morphometry in vivo with hyperpolarized 3He spectroscopy , 2006, Journal of magnetic resonance imaging : JMRI.

[12]  Denis S. Grebenkov,et al.  NMR survey of reflected brownian motion , 2007 .

[13]  C. Butler.  Lung surface area in various morphologic forms of human emphysema. , 2015, The American review of respiratory disease.

[14]  B. Sapoval,et al.  Diffusional screening in the human pulmonary acinus. , 2003, Journal of applied physiology.

[15]  A. Barzykin,et al.  Theory of spin echo in restricted geometries under a step-wise gradient pulse sequence. , 1999, Journal of magnetic resonance.

[16]  Dyson,et al.  Transverse spin relaxation in inhomogeneous magnetic fields. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[17]  B. Sapoval,et al.  Diffusion-reaction in branched structures: theory and application to the lung acinus. , 2005, Physical review letters.

[18]  Eduard E de Lange,et al.  MRI of the lungs using hyperpolarized noble gases , 2002, Magnetic resonance in medicine.

[19]  Christopher P Bidinosti,et al.  In vivo NMR of hyperpolarized 3He in the human lung at very low magnetic fields. , 2002, Journal of magnetic resonance.

[20]  K. K. Hunt.  Synopsis of Diseases of the Chest , 1984 .

[21]  K. Brownstein,et al.  Importance of classical diffusion in NMR studies of water in biological cells , 1979 .

[22]  B. Make,et al.  Standards for the diagnosis and care of patients with chronic obstructive pulmonary disease. American Thoracic Society. , 1995, American journal of respiratory and critical care medicine.

[23]  Seungoh Ryu,et al.  Determining multiple length scales in rocks , 2000, Nature.

[24]  Callaghan,et al.  A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms , 1997, Journal of magnetic resonance.

[25]  Bernard Sapoval,et al.  Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Frank R. Korosec,et al.  Early Emphysematous Changes in Asymptomatic Smokers: Detection with 3He MR Imaging , 2006 .

[27]  S. Wassall.  Pulsed field gradient-spin echo NMR studies of water diffusion in a phospholipid model membrane. , 1996, Biophysical journal.

[28]  Dmitriy A Yablonskiy,et al.  Effects of restricted diffusion on MR signal formation. , 2002, Journal of magnetic resonance.

[29]  H. Laursen,et al.  Lung morphometry by unbiased methods in emphysema: bronchial and blood vessel volume, alveolar surface area and capillary length , 1998, APMIS : acta pathologica, microbiologica, et immunologica Scandinavica.

[30]  Edwin J R van Beek,et al.  Investigating 3He diffusion NMR in the lungs using finite difference simulations and in vivo PGSE experiments. , 2004, Journal of magnetic resonance.

[31]  P. Callaghan,et al.  Diffraction-like effects in NMR diffusion studies of fluids in porous solids , 1991, Nature.

[32]  Schwartz,et al.  Diffusion propagator as a probe of the structure of porous media. , 1992, Physical review letters.

[33]  Dunn,et al.  Theory of diffusion in a porous medium with applications to pulsed-field-gradient NMR. , 1994, Physical review. B, Condensed matter.

[34]  H. Pfeifer.  Principles of Nuclear Magnetic Resonance Microscopy , 1992 .

[35]  P. Linse,et al.  Diffusion of the Dispersed Phase in a Highly Concentrated Emulsion: Emulsion Structure and Film Permeation , 1996 .

[36]  B. Sapoval,et al.  Diffusional screening in real 3D human acini—a theoretical study , 2005, Respiratory Physiology & Neurobiology.

[37]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[38]  C. H. Neuman.  Spin echo of spins diffusing in a bounded medium , 1974 .

[39]  John P Mugler,et al.  Functional MRI of the lung using hyperpolarized 3‐helium gas , 2004, Journal of magnetic resonance imaging : JMRI.

[40]  Albert Gjedde,et al.  The pathway for oxygen in brain. , 2003, APMIS. Supplementum.

[41]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[42]  Dmitriy A Yablonskiy,et al.  Magnetization tagging decay to measure long‐range 3He diffusion in healthy and emphysematous canine lungs , 2004, Magnetic resonance in medicine.

[43]  Neil Woodhouse,et al.  Emphysematous changes and normal variation in smokers and COPD patients using diffusion 3He MRI. , 2005, European journal of radiology.

[44]  P. Kuchel,et al.  Restricted diffusion of bicarbonate and hypophosphite ions modulated by transport in suspensions of red blood cells , 1990 .

[45]  R Takaki,et al.  A three-dimensional model of the human pulmonary acinus. , 2000, Journal of applied physiology.

[46]  D. Yablonskiy,et al.  MR imaging of diffusion of 3He gas in healthy and diseased lungs , 2000, Magnetic resonance in medicine.

[47]  E. Weibel.  Morphometry of the Human Lung , 1965, Springer Berlin Heidelberg.

[48]  Ewald R. Weibel,et al.  The pathway for oxygen : structure and function in the mammalian respiratory system , 1984 .

[49]  Dmitriy A Yablonskiy,et al.  Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[50]  G. Miller,et al.  Time dependence of 3He diffusion in the human lung: Measurement in the long‐time regime using stimulated echoes , 2006, Magnetic resonance in medicine.

[51]  Neil Woodhouse,et al.  Finite‐difference simulations of 3He diffusion in 3D alveolar ducts: Comparison with the “cylinder model” , 2004, Magnetic resonance in medicine.

[52]  P. Sen,et al.  Decay of nuclear magnetization by bounded diffusion in a constant field gradient , 1994 .