Fig 1.
Illustrative representation of the three test cases.
Red arrows indicate the movement of fluids through the compartments and blue arrows the diffusive movement of 14C-inulin. Double arrows indicate that the movement could be directed in both directions and is, a priori, not known. With exception of the blood compartments, the arrows pointing to the outside of any compartment denotes a connection of this compartment with the subarachnoid space. AEF denotes the astrocyte endfeet barrier and BBB the blood-brain barrier.
Fig 2.
a): The computational mesh of the rat brain used for most of the simulations within this article. The meshing procedure is described in section 2.6. For the given mesh, the maximum cell size is ≈1/32 times the diameter of the mesh. b): The initial 14C-inulin concentration within the ECS, simulating an injection directly into the brain tissue.
Table 1.
Baseline fluids (Blood and CSF) viscosity, permeability, porosity and diffusion parameters.
Table 2.
Baseline diffusive and convective exchange parameters.
Table 3.
Factors of variation for each of the tested parameters.
Fig 3.
Pressure fields in the 4 compartments (left: coronal cut, right: sagittal cut).
Table 4.
Velocities of CSF in the different compartments for baseline parameter values.
Fig 4.
a) Relative 14C-inulin mass located within regions of varying size surrounding the injection point. Solid lines result from the multi-compartment model simulations, while dashed lines result from diffusion only in the ECS. b) Relative 14C-inulin mass located in the totality of the brain for the different boundary conditions. Solid lines result from the multi-compartment model simulations, while dashed lines result from diffusion only in the ECS. c) Evolution in space and time of 14C-inulin relative concentration in the ECS for test case 1 (single diffusion). The colour scale is chosen for a visual comparison between all time points.
Fig 5.
Evolution in time and space of the relative 14C-inulin amount in the rat brain (frontal cut at the injection point) within the 4 compartments of test case 2.
Fig 6.
Comparison of 14C-inulin clearance for different variations of porosity and permeability coefficients.
“MC Baseline” denotes the clearance curve given by the multi-compartment model with baseline parameter values and is hidden by the dashed curve “Diffusion”, representing the clearance given by the application of the Diffusion model in the ECS compartment only. The enhancement of ECS porosity leads to the curve denoted “MC enhancement ECS” and the increase of the porosities in all the compartments gives the clearance curve denoted “MC enhancement ECS+PVS”
Table 5.
Velocities of CSF in the different compartments for an increase of porosity and permeability in all the 4 compartments.
Fig 7.
a-b) Comparison of pressure in ECS for the test cases 3 a) and 2 b). The velocity field is directed opposite of the gradient of pressure. Thus the velocity is mostly oriented to the outside of the brain, and the magnitude is larger when blood is considered in the model. c) Comparison of 14C-inulin clearance for test case 2 with baseline parameter values and increase of ECS and PVSs porosities with test case 3. “MC Baseline” denotes the clearance curve given by the multi-compartment model with baseline parameter values. The enhancements of ECS and PVSs porosities lead to the curve denoted “MC enhancement ECS+PVS”, and the result of test case 3 is denoted “MC 7-compartments”
Table 6.
Velocities of CSF and blood in the different compartments for baseline values coefficients for test case 3.