Yzeeir gave a good alternative, but as far as your basic question about differential (milli volt) signals and 4051 is concerned, here is my experience.

Few months ago, i finished a PC based ECG recorder. It was a 12 lead type, where you can select the desired lead set through PC software.

Remember, ECG signal from human body is of the order of 1 mV, and should be amplified with a very high CMRR amplifier.

I had no problem, using one amplifier for all 12 leads. Thanks to 4051

PS the results of this ECG recorder are comparable to professional quality recorders.

IA