Assessing the Permeability of Two Barriers in the Post-capillary Neurovascular Unit Part 1: The Problem Statement

The two barrier anatomy of the post-capillary NVU and why it matters

At the post-capilliary venule, the blood-brain barrier (BBB) is actually two barriers in series: 1) one created by the pericyte/BMEC layer at the blood interface and 2) one created by astrocytes and the astrocyte-produced glia limitans at the interface with the brain. We’ll name these the ‘blood barrier’ (BLB) and ‘brain barrier’ (BRB) for now, although the literature has alternative names. The gap between the BLB and the BRB is an interstitial space termed the ‘perivascular space’ (PVS). The perivascular space can become an important way station for leukocytes during inflammation. The cellular and molecular content of this space very likely determines if the inflammation resolves, or the leukocytes can make their way into the parenchyma. Our task is to develop models and methods to understand how the BLB and BRB work in tandem to create the overall BBB. Questions we can address include: 1) How does cross-talk between the various cells reinforce the overall BBB? and 2) How might inflammatory molecules originating from one barrier, or passing through it from a source in the blood or brain, impact the second barrier?

Conceptualizing the Measurement of Tandem Barriers

Conceptually, the task is straighforward: The rate at which a small molecule that originates in the blood will reach the brain will depend on its permeability through the BLB, the BRB and the perivascular space. To set up the problem its best to think of diffusive resistance, which is the inverse of diffusive permeability. The problem can then be described by analogy to electrical circuits assuming each stage of transport can be described as a resistor:

where concentrations, C_o, C_PVS, and C_BR are designated for each compartment, along with the three resistors.

The electrical analogy holds so long as we can assume the flux is constant. Under constant flux conditions the rate of material found in each compartment will increase linearly with the amount of time we let the experiment run. Knowing the concentrations in each compartment can then allow us to reliably determine the resistances/permeabilities. Unfortunately, the physics of diffusion makes it a challenge to set up conditions under which the constant flux assumption is true. Diffusion is inherently non-linear and if the concentrations are not actively managed, the system marches toward equilibrium (uniform concentrations everywhere) but at an ever slowing rate. The best way to establish constant flux is to have an inexhaustible source of the molecule of interest on the input end of the system and a perfect sink on the other. This is a task for a microfluidic system that we don’t currently have, and would be a significant challenge to build. The more approximate but also more accessible approach is to make measurements soon after adding the dye. During this time the concentration jumps across the barriers remain roughly constant and so does the flux. This is effectively what we’ve done with the sampling permeability strategy that has served us well for measuring BMEC and BMEC/pericyte barriers in the µSiM. So in those experiments, 1 hour is ‘early.’ Now we need to devise a similar strategy to measure the BLB and BRB individually and as a composite.

Mapping the Electrical Analogy to the µSiM and the µSiM-PCV

Using the conventional µSiM with a two slot membrane and a cell culture barrier insert in the well to ensure that the only communication between the two barriers occurs through the perivascular space, the resistance picture becomes …

Here I’m renaming R_PVS, R2.  We are not trying to model the PVS with sufficient accuracy that we should call our chip resistance an equivalent to the actual perivascular space. R2 is only important to a composite resistance R_BBB = R_BLB + R2 + R_BRB if its magnitude is comparable to (or much larger than) R_BLB and or R_BRB. So to begin we need independent measures of the three resistances and compare them. Importantly, Pelin and Michelle have modified the µSiM to make it possible to direct pericytes so that they seed under only under the BMEC side of the device, the µSiM-PCV. They did this by creating two basal side channels that can be feed independently. The details are worthy of a separate blog post, but the µSiM-PCV surely has a different R2 than the conventional µSiM. Minimally, we can represent it with the following cartoon which illustrates that the two channels are connected, but through a narrow passage between the membrane windows.

Measuring the Three Resistors

We already know R_BLB, which in the worse case of a highly leaky barrier, is R_BLB = 1 / (Pe_{max_leaky})  = 1 / (1.5 x 10^-3 cm/min) = 660 min/cm. See the attached figure from the submitted paper from Molly and Dan …
to measure R2 we can take advantage of the fact that the membranes do not pose any measurable resistance to small molecule diffusion and make measurements with LY but no cells, no coatings, like so …

Where I’ve used the µSiM figure. This is a simple enough measurement that we should try to get it for both device configurations. For R_BRB we can make the measurement in a conventional single slot µSiM as we did for the BRB but possibly backwards, so that the dye is coming from the basal lateral side?

There is a concern here about the small basal volumes depleting the dye significantly. Maybe. This could be avoided by using the hToC bottom component (100 µL) and/or the hToC reservoir (50 µL) as the bottom component. Another possibility is to plate the astrocytes on the backside of the membrane like so …

But this is for Pelin Kasap to solve … So onto the measurements.