# Probability of a sphere travelling through a hoop (lipid nanoparticle delivery vehicles for mRNA delivery)

Homework Statement:: Not homework, but I want to calculate the probability of different size spheres travelling through different size pores.
Relevant Equations:: V=4/3πr^3 volume of sphere. Volume of 60nm diameter particle = 1.13x10^5 nm^3. Volume of 70nm particle = 1.8x10^5 nm^3

Hi all, this is in relation to biotech. I develop lipid nanoparticle delivery vehicles for mRNA delivery. There is a biological barrier for delivery to the liver known as sinusoidal fenestrae. Pores that vary in size from 80-120nm. We know that smaller particles are more likely to go through these pores. But I want to know how much more likely for example, a 60nm particle will fit through a 80nm pore vs a 70nm particle. Basically shooting a basketball through the hoop compared to a baseball.

The problem is probably complex, as there are many variables, such as direction of travel, media current, positive pressure gradients etc.

You can see that the volume of a 60nm particle is 61% of the volume of a 70nm particle. I'm unsure if we need to use momentum, as mass is obviously a lot greater for a 70nm particle, momentum means its less likely to be moved by outward forces towards the pore.

Or if we only need diameter? I should probably note, the pores are less of a hoop, but a slight tunnel, around 5nm long. Appreciate any help. Thanks

jrmichler
Mentor
Filter theory might provide some useful insights. Some good search terms include filter efficiency curves and hepa filter efficiency graph. The second search came up with this document: https://donaldsonaerospace-defense.com/library/files/documents/pdfs/042665.pdf. That document includes this graph, along with an excellent explanation of the four filter mechanisms:

The document discusses particle sizes down to 10 nm. Note that inertial impaction is insignificant with particles smaller than 200 nm. This implies that your 60 to 70 nm particles will follow the fluid through the pores, assuming that the particles have zero tendency to stick to the walls of the pores. Note that three of the four filter mechanisms depend on particles sticking to the filter media, with the fourth mechanism (sieving) trapping the particle with pores smaller than the particle.

All of this suggests that the key variable is not particle size vs pore size, but whether the particles have the slightest tendency to adhere to the pore walls. What happens to forces between particles and pores at distances less than 10 nm or so?

jim mcnamara and berkeman