Abstract
Tortuosity of the extracellular space describes hindrance posed to
the diffusion process by a geometrically complex medium in comparison
to an environment free of any obstacles. Calculating tortuosity in
biologically relevant geometries is difficult. Yet this parameter
has proved very important for many processes in the brain, ranging
from ischemia and osmotic stress to delivery of nutrients and drugs.
It is also significant for interpretation of the diffusion-weighted
magnetic resonance data. We use a volume-averaging procedure to obtain
a general expression for tortuosity in a complex environment. A simple
approximation then leads to tortuosity estimates in a number of two-dimensional
(2D) and three-dimensional (3D) geometries characterized by narrow
pathways between the cellular elements. It also explains the counterintuitive
fact of lower diffusion hindrance in a 3D environment. Comparison
with Monte Carlo numerical simulations shows that the model gives
reasonable tortuosity estimates for a number of regular and randomized
2D and 3D geometries. Importantly, it is shown that addition of dead-end
pores increases tortuosity in proportion to the square root of enlarged
total extracellular volume fraction. This conclusion is further supported
by the previously described tortuosity decrease in ischemic brain
slices where dead-end pores were partially occluded by large macromolecules
introduced into the extracellular space.
- 15345540
- animals,
- brain,
- carlo
- computer-assisted,
- diffusion,
- extracellular
- factors,
- gov't,
- humans,
- image
- imaging,
- ischemia,
- method,
- models,
- monte
- non-u.s.
- p.h.s.,
- processing,
- research
- space,
- statistical,
- support,
- theoretical,
- three-dimensional,
- time
- u.s.
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