Hrabetova, Sabina

Nicholson, Charles

Tao, Lian

Thorne, Robert G.

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Measurement of Local Diffusion Properties in Brain Tissue Charles Nicholson, Lian Tao, Sabina Hrabetova, Robert G. Thorne New York University School of Medicine, Department of Physiology and Neuroscience, 550 First Avenue, New York, NY 10016, E-Mail: nichoc01@nyu.edu 1. Introduction The extracellular space (ECS) of the brain comprises the narrow connected regions between cells and resembles the water phase of foam.  The diffusion of an idealized point molecule within the ECS [1] is described by three parameters. 1) Volume fraction defines the tissue volume accessible to the diffusing molecule (α = VECS/Vtissue). 2) Tortuosity measures the average hindrance of the ECS relative to an obstacle-free medium (λ = (D/D*)0.5, where D is the free diffusion coefficient and D* the effective diffusion coefficient in tissue). 3) Irreversible loss of the molecules from the ECS, with kinetic constant k′ (s-1).  Then if S is a source function, the appropriate diffusion equation is:  22C D SC kt λ α∂C′= ∇ + −∂  (1) Our laboratory has devised two methods to measure these parameters in small brain regions, both based on a ‘point-source paradigm’.  The first uses tetramethylammonium (TMA, 74 MW) cations to approximate the ideal small marker molecule and measures α, λ and k′.  The second method uses integrated optical imaging (IOI) to measure λ for a wide range of macro-molecules.  Experiments are made in brain slices or in anesthetized animal models.   Fig. 1. Setup for combined TMA and IOI methods. Asource micropipette releases molecules and these areeither detected with an ISM (TMA) or imaged with acamera using an epi-fluorescent microscope (IOI). 2. TMA+ real-time iontophoretic method (Fig. 1) A micropipette releases TMA+ by iontophoresis with source-strength Q for duration tp.  An ion-selective microelectrode (ISM) at a distance r (~ 100 μm) from the release point measures the concentration of TMA+, C, described by the appropriate solution to Eq (1) [1, 2, 3]: © 2005, C. Nicholson The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationDiffusion Fundamentals 2 (2005) 126.1 - 126.2 1( ) ( ) ( ) ( ) ( )2p p p, ;  , ;  8erfc exp erfc exp2 2GC G t t t C G t G t t t t Q D rr k rk u r k u rD DDu Duu λ π αλ λλ λ= ≤ = − − > = ×k′ ′′ ′+ + − −⎡ ⎛ ⎞ ⎛⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎝ ⎠ ⎝⎞⎤⎟⎠⎦. (2) Experimental data are fitted to Eq (2) using non-linear algorithms written in MATLAB. 3. Integrated optical imaging (IOI) method for fluorescent macromolecules (Fig. 1) A volume U of macromolecules at concentration Cf  with a fluorescent label are released from a micropipette by a very brief pulse of nitrogen. Then C is described by the appropriate solution to Eq (1): [1, 4, 5]:  ( )3 2 2f03 2exp ;  44UC rCDTDTλ λα π′= − −⎛ ⎞⎜ ⎟⎝ ⎠k T T t t= + . (3) The variable t0 represents a virtual source time-origin (see [5]).  For IOI, k' = 0. The theory of how the image of the diffusing cloud of molecules maps onto the plane of the CCD (Fig. 1) [4, 6] shows it is legitimate to fit Eq (3) to the image intensity profile to estimate D* and λ. 4. Conclusions Measurements with the TMA method show typically α = 0.2, λ = 1.6, k′ = 0.005 s-1[1]. Measurements with the IOI method show that for globular macromolecules, λ increases with MW, e.g. for epidermal growth factor (MW 6,600) λ = 1.8 [7], for bovine serum albumin (MW 66,000) [8] and dextran (MW 70,000) [4] λ = 2.3.  In contrast, the linear flexible polymer PHPMA [5] has λ = 1.5.  These data show that we can accurately characterize the diffusion properties of the ECS in living brain tissue using a wide variety of molecules. References [1] C. Nicholson, Rep. Prog. Phys. 64 (2001) 815-884. [2] C. Nicholson, J. M. Phillips, J. Physiol. 321 (1981) 225-257. [3] C. Nicholson, J. Neurosci. Meth. 48 (1993) 199-213. [4] C. Nicholson, L. Tao, Biophys. J. 65 (1993) 2277-2290. [5] S. Prokopova-Kubinova et al., Biophys J. 80 (2001) 542-548. [6] L. Tao, C. Nicholson, J. Micros. 178 (1995) 267-271. [7] R. G. Thorne, S. Hrabetova, C. Nicholson, J. Neurophysiol. 92 (2004) 3471-3481. [8] L. Tao, C. Nicholson, Neuroscience 75 (1996) 839-847. Diffusion Fundamentals 2 (2005) 126.1 - 126.2 2

Measurement of local diffusion properties in brain tissue

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Measurement of local diffusion properties in brain tissue

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