I've tested filters that were 9k old ..in cold starting temps with heavy oil. The whole thing is way over blown ...REALLY. Now one engine or another can surely react differently. If you've got larger oil galleries that empty upon shutdown, then, until they're fully enveloped, you can see your elevated PSID ..and, as I mentioned, when the oil pump is in relief ..but these are transitional states and not long lasting.
I'll have to fill in the blanks for you ..the images are missing. I had thought that I had copied them ..but apparently I did not.
read this
The temp was sub-freezing - the oil was a 15w-40 (it was supposed to be 20w-50) and the max PSID was near 10 PSID. I used a differential pressure gauge in a remote dual mount where I used the second filter boss as a place to tap in the pressure tubing. I used the other ports for temp senders.
From loading, imo, it would take a very long time or a very dirty engine to wear out a filter. Otherwise, it's mainly how "much" you're in relief at startup (and beyond). The pressure differential is some relationship between the pump output and the flow realized to the engine. I can't mathematically model it ..except in reverse. That is, when the flow is 100% to the engine, the differential evaporates ..hence one would reason that the differential is an expression of flow divergence. One can also reason (but I cannot prove) that the lost flow can be some +/- of 100% vs. realized pressure.
For example: 80 PSI relief setting.
Upstream pressure/downstream pressure/PSID/ assumed diverted flow
80/70/10PSID/12.5%
50/40/10PSID/20%
Now these are always transitional states. The oil can't move from a standstill to pump speed on a dime, so you've got some tire spinning initially if the stuff is too heavy. As the fluid gets in motion, the differential retreats, even if the viscosity hasn't changed much.