Diffusion in Brain Extracellular Space

Abstract

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 molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is ∼20% and the tortuosity is ∼1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.

Impact of Drug Size on Brain Tumor and Brain Parenchyma Delivery after a Blood–Brain Barrier Disruption

“…This is consistent with prior reports linking diffusion and molecular weight. 35,36 The second set of experiments consisted in assessing the exposure of the brain of F98 implanted Fischer rats to the two CAs without any manipulation of the BBB. This provided an estimate of the baseline BTB and BBB permeability to these two compounds.…”

A model for simulation and patient-specific visualization of the tissue volume of influence during brain microdialysis

“…By using volume averaging and assuming that the molecules are restricted to the extracellular space of the tissue, the migration of molecules in brain tissue can be described using a volume averaged form of Fick´s diffusion equation [9,10]:…”

“…Mathematical formulas and models have been developed in order to describe the movement of analytes in brain tissue [9][10][11]. Diffusion, as described by Fick's law, is considered the dominating process for analyte transport in tissue [11,12].…”

“…If analyte movement is assumed to occur in the extracellular space, a process known as volume transmission [13], diffusion in vivo can be satisfactorily described by using a volume averaged formulation of Fick´s diffusion equation [9,11]. The input parameters of this equation have been extensively evaluated for different parts of the brain [10]. Furthermore, the equation has been implemented using the finite element method (FEM) and finite volume discretization methods, in order to simulate and visualize movement of analytes in the brain [14,15].…”

Windows to cell function and dysfunction: Signatures written in the boundary layers

“…However, in non-synaptic areas within tissues, such as the brain, cells frequently lie within tens of nanometers of each other, giving rise to both an integral association and profound tortuosity. (7,8) Elements of the structural boundary layer, the glycocalyx, will overlap in these constrained spaces, blurring the boundaries of one cell to another. When considering cellular physiology, the 50 impact of extracellular functional nanodomains is given short shrift.…”