Transport Mechanisms within Living Brain Tissue

The physical and chemical phenomena which can affect the transport of a drug (once it is released from its dosage form) within the living brain tissue are very complex and yet not fully understood. Excellent overviews on the importance of diffusion and related processes have been given by Tao and Nicholson (33,34). Nicholson and his co-workers as well as the group of Saltzman made major contributions towards a better understanding of these phenomena (35-41). A large variety of processes can be involved in the transport of a drug in the brain, including: (1) diffusion within the extracellular space; (2) reversible and irreversible binding to the extracellular matrix (which is built of long-chain macromolecules); (3) degradation/ metabolism (e.g. by enzymes or hydrolysis); (4) different types of passive and active uptake into CNS cells (e.g. by "simple" diffusion or receptor-mediated internalization); (5) release from endolysosomes into the cytosol; (6) diffusion and convection within the cytosol of the cells; (7) uptake into the cell nuclei; (8) elimination into the blood stream; (9) bulk flow within the extracellular space; (10) direction-dependent drug transport (anisotropy), because the brain is not one homogeneous mass. Figure 4 shows a schematic presentation of some of these processes.

The extracellular space represents approximately 20% of the total human brain volume. Its geometry can be compared to that of the water phase in an aqueous foam. Drug transport in this region can often (surprisingly well) be described based on Fick's second law of diffusion. Important aspects to be taken into account include the volume fraction in which diffusion can take place and the tortuosity of the diffusion pathways. Recently, the group of Charles Nicholson studied the effects of the geometry of CNS cells on the tortuosity of the extracellular space (42-44). Considering uniformly spaced convex cells, they found that the presence of dead-space micro-domains can help to better understand the difference between the experimentally measured tortuosity and the theoretically calculated one. It has to be pointed out that many brain diseases can significantly affect the conditions for drug transport within the CNS (45,46). For example, cellular swelling can lead to a significant shrinkage of the extracellular space, because the total brain volume is

Figure 4 Schematic presentation of some of the processes that can be involved in drug transport through the living brain tissue (indicated in the figure). The black circles represent drug molecules in the interstitial space. Source: From Ref. 40.

restricted by the rigid crane. Also the tortuosity can strongly be altered. In some cases, the non-physiological mass transport conditions are not the consequence of the disease, but its cause: The appropriate transport of oxygen, glucose, neurotransmitters, and many other substances is vital for a normal functioning of the brain. In addition, the conditions for drug transport within the brain can be significantly age-dependent: Lehmenkuhler et al. (47) showed that the volume fraction of the extracellular space of rats decrease from about 0.4 inches for 2-3 day old animals to only 0.2 inches 21 day old animals. Obviously, these changes can strongly affect the transport of intracranially administered drugs.

Interestingly, so far only a very few mechanistic mathematical models have been reported in the literature that quantitatively describe drug transport in living brain tissue (Fig. 5). In particular, Nicholson and coworkers as well as the group of Saltzman made major contributions to this field. For example, Saltzman and Radomsky (36) proposed an interesting theory, considering drug diffusion from intracranially administered cylindrical delivery systems. The model is based on the following assumptions: (1) The drug concentration at the surface of the dosage forms is constant. (2) The elimination of the drug from the brain tissue follows first order kinetics (the elimination rate of the drug is proportional to its concentration). (3) Diffusion is isotropic (does not dependent on a spatial direction). (4) Convectional processes are negligible. The model is based on Fick's second law of diffusion (considering one dimension), which is coupled with a first order elimination term (Eq. 8):

d 2c dx2

where c is the concentration of the drug within the brain tissue; t is time (t = 0 at the time of device administration); D represents the apparent diffusion coefficient of the drug within the brain; x is the spatial coordinate; and k is the first order elimination rate constant of the drug. The initial and boundary conditions were considered as shown in Equations 9, 10, and 11:

where, a is the half-thickness of the cylindrical dosage form and c0 the (constant) drug concentration at the surface of the device. Equation (9) indicates that the brain tissue is free of drug prior to the administration of the dosage form. Equation (10) states that the constant drug concentration at the interface "dosage form - brain tissue" (c0) is time-independent, and

Figure 5 Monitoring of the drug distribution within: (A) healthy, and (B) tumor-bearing rat brain using autoradiography: Relative radioactivity measured as a function of the distance from the bregma; 168 hours after intracranial administration of [3H]5-fluorouracil-loaded microspheres. The black bars indicate the administration site (7 mm under the bregma). Source: From Ref. 87.

Figure 5 Monitoring of the drug distribution within: (A) healthy, and (B) tumor-bearing rat brain using autoradiography: Relative radioactivity measured as a function of the distance from the bregma; 168 hours after intracranial administration of [3H]5-fluorouracil-loaded microspheres. The black bars indicate the administration site (7 mm under the bregma). Source: From Ref. 87.

Equation 11 expresses the fact that the drug concentration vanishes to zero at large distances from the cylinder. Assuming steady state conditions (the concentration of the drug within the brain tissue does not vary with time, only with position), this set of equations can be solved to give Equation 12:

On the other hand, considering non-steady state conditions (the drug concentration varies with time and position), the following solution can be derived (Eq. 13) (47):

■ efro

x\l D

where, x is the distance from the interface "delivery system-brain tissue." Both Equations (12) and (13) allow us to calculate the drug concentration at any distance from the axial surface of the cylindrical dosage form. Figure 6 shows examples of fittings of these models to sets of experimentally

0 0.5 1 1.5 2 0 0.5 t 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0 5 1 1.5 2 Distance from polymer, mm

Figure 6 Experiment (symbols) and theory (curve): Concentration profiles of radioactively labeled NGF within rat brain upon intracranial administration of a cylindrical controlled drug delivery system. The distance from the surface of the device is plotted on the x-axis; the times elapsed after implantation are indicated in the diagrams. The non-steady state and steady state model of Saltzman and coworkers [Equations (12) and (13)] were fitted to the experimental results obtained after 2, 4 days and 1, 2, 4 weeks, respectively. Source: From Ref. 48.

0 0.5 1 1.5 2 0 0.5 t 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0 5 1 1.5 2 Distance from polymer, mm

Figure 6 Experiment (symbols) and theory (curve): Concentration profiles of radioactively labeled NGF within rat brain upon intracranial administration of a cylindrical controlled drug delivery system. The distance from the surface of the device is plotted on the x-axis; the times elapsed after implantation are indicated in the diagrams. The non-steady state and steady state model of Saltzman and coworkers [Equations (12) and (13)] were fitted to the experimental results obtained after 2, 4 days and 1, 2, 4 weeks, respectively. Source: From Ref. 48.

measured concentration profiles of radioactively labeled nerve growth factor (NGF). The drug was incorporated within cylindrical poly(ethylene-co-vinyl acetate) (EVAc)-based discs and intracranially administered into rats. After pre-determined time intervals (indicated in the figures), the animals were sacrificed, the brains sliced and the radioactivity measured. The non-steady state model [Equation (13)] was fitted to the experimentally determined NGF concentration profiles at days 2 and 4, the steady state model [Equation (12)] was fitted to the concentration profiles measured after 1, 2, and 4 weeks. Clearly, good agreement between theory and experiment was obtained in all cases. Thus, NGF transport through the living brain tissue seems to be dominated by diffusion and first order elimination. The partially observed deviations between theory and experiment might be attributable to experimental errors or violation of model assumptions (e.g. time-dependent drug concentrations at the surface of the delivery systems). Importantly, the distance that NGF can penetrate into the brain tissue is rather limited: After 2-3 mm its concentration decreases to only 10% of the maximal value (at the interface "dosage form-brain tissue"). Furthermore, Saltzman and coworkers compared the transport of NGF in rat brain upon its release from three different types of intracranial, controlled drug delivery systems: (1) slowly releasing EVAc discs; (2) fast releasing PLGA-based micro-particles; and (3) PLGA-based microparticles with an intermediate release rate (48). In all cases, good agreement between theory and experiment was obtained. An apparent diffusion coefficient of about 8 x 10-7 cm2/s could be determined for NGF in rat brain.

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