Table 1 Model parameters

Barrier permeability for albumin P _b [μg/min]

In the cortical subarachnoid space

29.4

[27]

In the ventricular space

7.6

[27]

In the spinal space

4.8

[27]

CSF compartments volume [ml]

Ventricular space

30

Cortical subarachnoid space

90

Spinal subarachnoid space

30

Protein and pore size used in the membrane pore model for barrier permeability [nm]

Pore radius, r

19.4

[6]

Albumin hydrodynamic radius, \(a_{Al}\)

3.58

[6]

Immunoglobulin G hydrodynamic radius, \(a_{IgG}\)

5.34

[6]

CSF production and drainage rate

CSF total production and drainage rate, F [ml/day]

500

[30]

CSF pulsation

CSF pulsation amplitude in the cervical region [mm/s]

10

[25]

CSF pulsation amplitude in the lumbar region [mm/s]

0

[24]

CSF pulsation time period [s]

0.8

[25]

CSF physical properties

Density, \(\rho\) [kg/m³]

1000

Viscosity, \(\mu\) [Pa s]

0.001

Spinal canal porosity and permeability

Porosity, \(\varepsilon\)

0.99

[21]

Permeability in the longitudinal direction, K_longitudinal [m²]

1.45 · 10⁻⁷

[21]

Permeability in the radial direction, K_radial [m²]

2.36 · 10⁻⁸

[21]

CSF albumin concentrations

Albumin concentration in the lumbar CSF [mg/ml]

0.363

[27]

Albumin CSF/blood quotient in the lumbar space

0.002

[31]

Albumin quotient ratio (lumbar to cisternal)

2

[27]

Albumin quotient ratio (cortical subarachnoid space to cisternal)

3

[27]

Dimensions [mm]

Spinal cord diameter

10

[16, 17]

Spinal subarachnoid space thickness, w

4

[16, 17]

Spinal segment length

100

Spine length between cistern and lumbar space

700

Protein properties [m²/s]

Albumin diffusion coefficient, D_Al

6 · 10⁻¹¹

Immunoglobulin G diffusion coefficient, D_IgG

2.4 · 10⁻¹¹