Dynamic<i>q</i>space microscopy of cellular tissue

Hills, B.P.; Snaar, J.E.M.

doi:10.1080/00268979200101791

Cited by 46 publications

(30 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Plant cells, which have cellulose membranes that provide an impermeable barrier to water transport, offer another example of biological media in which restricted diffusion within pores is observed (15). Restricted diffusion in blood cells (16) and cellular systems (17) has also been studied.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

et al. 2008

View full text Add to dashboard Cite

Characterizing diffusion of gases and liquids within pores is important in understanding numerous transport processes and affects a wide range of practical applications. Previous measurements of the pulsed gradient stimulated echo (PGSTE) signal attenuation, E(q), of water within nerves and impermeable cylindrical microcapillary tubes showed it to be exquisitely sensitive to the orientation of the applied wave vector, q, with respect to the tube axis in the high-q regime. Here, we provide a simple three-dimensional model to explain this angular dependence by decomposing the average propagator, which describes the net displacement of water molecules, into components parallel and perpendicular to the tube wall, in which axial diffusion is free and radial diffusion is restricted. The model faithfully predicts the experimental data, not only the observed diffraction peaks in E(q) when the diffusion gradients are approximately normal to the tube wall, but their sudden disappearance when the gradient orientation possesses a small axial component. The model also successfully predicts the dependence of E(q) on gradient pulse duration and on gradient strength as well as tube inner diameter. To account for the deviation from the narrow pulse approximation in the PGSTE sequence, we use Callaghan's matrix operator framework, which this study validates experimentally for the first time. We also show how to combine average propagators derived for classical one-dimensional and two-dimensional models of restricted diffusion (e.g. between plates, within cylinders) to construct composite three-dimensional models of diffusion in complex media containing pores (e.g. rectangular prisms and/or capped cylinders) having a distribution of orientations, sizes, and aspect ratios. This three-dimensional modeling framework should aid in describing diffusion in numerous biological systems and in a myriad of materials sciences applications.

show abstract

Section: Introductionmentioning

confidence: 99%

Three‐dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments

et al. 2008

View full text Add to dashboard Cite

show abstract

“…Such an interpretation of boundary conditions leads to the representation of each membrane as an additional compartment of length ⌬x with the diffusion coefficient ⌬x, similar to earlier reports (2,20). After some transformations Eq.…”

Section: Figmentioning

confidence: 67%

“…In recent years pfg NMR has gained considerable attention by several groups (1)(2)(3). This is caused by technical improvements of the (active shielded) gradient sets, which allow for much more accurate pfg NMR measurements, and by new theoretical developments started by Kärger and Heink (4) and later Cory and Garroway (5) and Callaghan (6).…”

Section: Introductionmentioning

confidence: 98%

“…However, analytical solutions of the partial differential equation can only be found for a certain combination of initial and boundary conditions, and become difficult in common situations. Probably the best way out of this problem is to solve this differential equation numerically (2,20). This way could be very fruitful from a practical point of view since numerical solutions let us explore a wide range of different systems and obtain results quickly.…”

Section: Introductionmentioning

confidence: 98%

“…For a given geometry this is a partial differential equation with respect to the local spin magnetization, which can be solved either analytically or numerically. This equation was used for the exploration of T 2 relaxation processes (2,18,19) and the influence of magnetic field gradient pulses on diffusing particles (2,11,12). Differential equation models allow for the investigation of a variety of systems with complicated configurations by changing the boundary conditions, or inserting functions, properly describing the shape of the magnetic field, etc.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations