Is there a relation between porosity and PPI density in porous media?

I've seen two methods to describe porosity of porous media (specifically metal foams):

1. Porosity $\epsilon$ which is a ratio between volume of voids and total volume of the medium.
2. PPI (Pores Per Inch) which is the number of pores in one linear inch.

Unfortunately while reading some papers about the relationship between volumetric heat transfer coefficient and porosity in metal foams, some authors describe the range of porosity they used with $\epsilon$ while the others use PPI density, so is there any relation to connect both terms?

There is a similar question on cfd-online and someone answered with this formula but I am not sure where it came from or if it's even correct:

$$\text{Pore density (ppcm)}=\frac{300}{D_{particle}}\sqrt{\frac{(1-\epsilon)^2}{\pi\epsilon}}$$

I have confirmed this through a quick search of literature on foams like the one you describe. This one (behind a paywall) for example has a table where they list their samples and some of them have the same ppi but different porosities. In their works they describe their porous material as being made of pores with diameters $d_p$ and fibers of diameter $d_f$. Given that additional information, I guess someone could develop a relationship between pore density and pore size.