Using LEDs in series with optocoupler for biosensor
The arrangement limits the current through the isolator LED by adding diode drops, thus lowering the voltage that the 220 ohm resistor sees.  Without them, you'd likely saturate your phototransistor, or damage the LED.  I see no reason why adding a bigger resistor wouldn't do the same thing, though the fixed diode drops to get rid of some voltage probably take out some of the guesswork.

Personally, I tend to use those types of isolators as digital devices.  For analog isolation, I'd point you to something more appropriate, like an HCNR200.  Yes, you need some support circuitry, but you've already got a full biopotential amp on the left side, so you probably have the resources you'll need in place.