A 3D brain unit model to further improve prediction of local drug distribution within the brain
Summary (3 min read)
1 Introduction
- The brain capillary bed is the major site of drug exchange between the blood and the brain.
- The brain ECF bulk flow results from the generation of brain ECF by the BBB and drainage into the cerebrospinal fluid (CSF).
- Here, the authors developed a 3D brain unit model, in which local brain drug distribution is explicitly taken into account.
- Thereafter, drug distribution within the brain ECF is affected by diffusion, bulk flow and binding.
2 The 3D brain unit
- The 3D brain unit represents the smallest piece of brain tissue that contains all physiological elements of the brain.
- The segments of red rectangular boxes protruding from the vertices from the 3D brain unit are parts of brain capillaries from neigh- bouring units.
- (vii) Drug within the blood plasma does not bind to blood plasma proteins.
- Within the brain ECF, the authors formulate: Assumptions 2. (i) Drug within the brain ECF is transported by diffusion and brain ECF bulk flow.
2.1 Formulation of the 3D brain unit
- There, xr, yr and zr are constants that represent the length of one unit and are defined as dcap+2r, with dcap the distance between the brain capillaries and r the brain capillary radius.
- In one brain unit, the brain capillaries, the BBB and the brain ECF are represented by the subsets Upl�U, UBBB�U and UECF�U, respectively, such that U = Upl [ UBBB [ UECF.
- Within Upl, the authors define Uin as the domain where the blood plasma, containing drug, enters the 3D brain unit from a feeding arteriole.
- The authors focus on single oral administration but can also study other choices.
2.4 Boundary conditions
- The authors formulate boundary conditions that describe the change in concentration of drug at the boundary between the blood-plasma-domain (Uok) and the brain-ECF-domain (UECF), hence at UBB as well as at the boundaries of the 3D brain unit (Upl\@ U, UECF\@U).
- 4.1 Drug exchange between Upl and UECF.
- The authors describe diffusive transport by the difference in drug concentrations in CECF and Cpl, multiplied by the BBB permeability, P. In PLOS ONE | https://doi.org/10.1371/journal.pone.0238397.
- September 23, 2020 7 / 24 addition, the authors model active transport into and out of the brain ECF with Michaelis-Menten kinetics, as they are well established and match with most available data on parameters related to BBB active transport, similar to the approach of [6].
- The authors use additional boundary con- ditions to describe the drug concentrations at the sides of the domain.
2.5 Model parameter values and units
- The dimensions of the 3D brain unit are based on the properties of the rat brain.
- The model is suitable for data from human or other species as well, but the authors have chosen for the rat as for this species most data is available.
- In their model, the authors use Eqs (1)–(5) to describe drug concentration within the blood plasma, with boundary conditions described in Eqs (11)–(15).
- The range of values the authors use for the parameters in the model as well as their units are given in Table 1 below.
- The literature does not provide values on the kinetic parameters related to non-specific binding kinetics (B2max, k2on and k2off).
3 Model results
- The authors study the distribution of a drug within the 3D brain unit by plotting its concentration- time profiles within the brain ECF (brain ECF PK).
- In addition, the authors study the distribution of the drug within the 3D brain unit.
- The authors first nondimensionalise the system of equations and boundary conditions by scaling all variables by a characteristic scale.
- The model can easily be used to study a specific drug by choosing the parameter values that are specific for this drug, provided that parameter values for this drug are known.
3.1 The effect of the brain capillary blood flow velocity on brain ECF PK within the 3D brain unit
- The impact of the brain capillary blood flow velocity, vblood, on brain ECF PK within the 3D brain unit is evaluated.
- The total passive permeability, P, includes both transcellular and paracellular permeability.
- When vblood = 0.5 (left), there are clear differences between Cpl in Uin (Distance = 0) and Cpl in the opposite corner (Distance = 150) at the time-points shown.
3.2 The effect of active transport on the drug concentrations within the brain ECF
- Active transport kinetics are regulated by the maximal transport rate (Tm) and the concentration of drug needed to reach half of the maximal transport rate (Km), see section 2.4.1.
- Fig 5 (top) reveals that an increased value of Tm-in correlates with increased concentrations of CECF.
- The non-specific binding sites within the brain ECF become saturated with drug when Tm-in is sufficiently high (Tm-in = 100�10-7 μmol s-1).
- Fig 6 reveals that Tm-out affects the time during which specific binding sites are saturated: the time at which B1 attains 90% max(B1) is smaller for a high value of Tm-out.
3.3 The effect of the brain capillary blood flow velocity in the presence of active transport
- In section 3.1 the authors have shown that both the passive BBB permeability, P, and the brain capillary blood flow velocity, vblood, affect dug brain ECF PK in the absence of active transport.
- If P is high, drug can easily flow across the BBB back into the brain ECF, following the concentration gradient between the blood plasma and the brain ECF, thereby countering the effect of Tm-out.
- Values of CECF are given in the table in Fig 10c in order to show the differences within the 3D brain unit more clearly.
- The table again (as in Figs 7, 8 and 9) shows that vblood and P affect the impact of Tm-in and Tm-out on CECF.
4 Discussion
- This new model provides an important step towards more realis- tic features of the brain.
- This enables us to more realistically predict the impact of the interplay of cerebral blood flow, BBB characteristics, brain ECF diffusion, brain ECF bulk flow and brain binding on drug distribution within the brain.
- Assumption 1(vii) is not violated for drugs that do not bind plasma pro- teins.
- To ensure the quality of a mathematical model, the model predictions are ideally compared to experimental data.
Did you find this useful? Give us your feedback
Citations
5 citations
4 citations
1 citations
References
570 citations
"A 3D brain unit model to further im..." refers background in this paper
...Unbound drug 12 may cross the BBB by passive and/or active transport [2–10]....
[...]
544 citations
Additional excerpts
...2 [47–50] 3 [51–56] http://www....
[...]
539 citations
"A 3D brain unit model to further im..." refers background in this paper
...within the brain, and, as anticipated [68,69] that a low brain capillary blood flow 437 velocity affects the short-term, but not the long-term concentration-time profiles of C pl 438 and CECF, (Fig 3 and 4)....
[...]
526 citations
Additional excerpts
...2 [47–50] 3 [51–56] http://www....
[...]
526 citations
Additional excerpts
...2 [47–50] 3 [51–56] http://www....
[...]
Related Papers (5)
Frequently Asked Questions (2)
Q2. What are the future works mentioned in the paper "A 3d brain unit model to further improve prediction of local drug distribution within the brain" ?
However, for drugs that do bind plasma proteins, the assumption is likely violated with an impact to be investigated in future work. In similar fashion, assumptions 2 ( ii ), 2 ( iv ) and 2 ( vii ) are not violated for drugs that do not cross cells, but it is likely that for drugs that do, they are violated with an impact to be investigated in future work. With the establishment of the current 3D brain unit model, the authors are now ready to incorporate intra-extracellular exchange and drug binding to intracellular binding sites in future modelling work. It is anticipated that in certain cases, like those of high drug-target binding or active transport, these differences may also exist on a larger time-scale, but this requires further investigation.