Current measurement using NI 9219

Hello, I am trying to do low-current measurement using NI-9219.

Basically, the current will be carried by the jet produced by a process called electrospinning (Please, look at figure).

The current will be from micro to nanoampere, so I think I measure the voltage drop across the resistor and then calculate the current using Ohm's law.

My concern is the setup design (Figure). If I follow this diagram, I am worried that the conductive collector causes serious measurement flaws as itself is a huge resistor since the current is very low (micro-nano). 

I am new to electric stuff, so please be generous.

Thanks.