Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecule...

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Diffusion in brain extracellular space.

Extracellular space structure revealed by diffusion analysis

We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L(infinity) constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.

Gaussian approximations of fluorescence microscope point-spread function models.

Diffusion plays a crucial role in brain function The spaces between cells can be likened to the water phase of a foam and many substances move within this complicated region Diffusion in this interstitial space can be accurately modelled with appropriate modifications of classical equations and quantified from measurements based on novel micro-techniques Besides delivering glucose and oxygen from the vascular system to brain cells, diffusion also moves informational substances between cells, a process known as volume transmission Deviations from expected results reveal how local uptake, degradation or bulk flow may modify the transport of molecules Diffusion is also essential to many therapies that deliver drugs to the brain The diffusion-generated concentration distributions of well-chosen molecules also reveal the structure of brain tissue This structure is represented by the volume fraction (void space) and the tortuosity (hindrance to diffusion imposed by local boundaries or local viscosity) Analysis of these parameters also reveals how the local geometry of the brain changes with time or under pathological conditions Theoretical and experimental approaches borrow from classical diffusion theory and from porous media concepts Earlier studies were based on radiotracers but the recent methods use a point-source paradigm coupled with micro-sensors or optical imaging of macromolecules labelled with fluorescent tags These concepts and methods are likely to be applicable elsewhere to measure diffusion properties in very small volumes of highly structured but delicate material

https://iopscience.iop.org/article/10.1088/0034-4885/64/7/202/pdf

Diffusion and related transport mechanisms in brain tissue

Therapeutics must diffuse through the brain extracellular space (ECS) in order to distribute within the central nervous system (CNS) compartment; this requirement holds both for drugs that are directly placed within the CNS (i.e., central input) and for drugs that cross the barriers separating blood and brain following systemic administration. The diffusion of any substance within the CNS may be affected by a number of properties associated with the brain microenvironment, e.g., the volume fraction, geometry, width, and local viscosity of the ECS, as well as interactions with cell surfaces, the extracellular matrix, and components of the interstitial fluid. Here, we discuss ECS properties important in governing the distribution of macromolecules (e.g., antibodies and other protein therapeutics), nanoparticles and viral vectors within the CNS. We also provide an introduction to some of the methods commonly applied to measure diffusion of molecules in the brain ECS, with a particular emphasis on those used for determining the diffusion properties of macromolecules. Finally, we discuss how quantitative diffusion measurements can be used to better understand and potentially even improve upon CNS drug delivery by modeling delivery within and across species, screening drugs and drug conjugates, evaluating methods for altering drug distribution, and appreciating important changes in drug distribution that may occur with CNS disease or injury.

Diffusion of Macromolecules in the Brain: Implications for Drug Delivery

SUMMARY

The three-dimensional point spread function (3-D PSF) of an optical system in image space is distinguished from the 3-D PSF in object space and the relation between the two 3-D PSFs is derived. By using this relation one 3-D PSF can be easily obtained from the other. The 3-D PSFs are given in a single integral expression, which can be computed numerically. The results of this study can be used in 3-D image processing for microscopy and have been applied to the analysis of the diffusion of fluorescent molecules in a 3-D porous medium.

L. Tao

Papers

The three-dimensional point spread functions of a microscope objective in image and object space.