... why use Li?
 ... Can the bluetooth be turned off and only used to transmit data say every half hour rather than leaving it on?
 ... why the need for high current batteries?
(1) Light weight. Lots of power through 10-hour night. Rechargeable 1200 times.
(2) The Bluetooth sends 4 bytes of data, once every second. Response needs to be in real-time.
(3) Current appears to continuously vary from about 35ma to 80ma through the 10-hour night.
....It is my understanding that discharging a LIon below 3V/cell will cause damage to the cell....
Very good to know, Chuck. Thank you for the education.
Discharging an Li cell below about 3v ... may give problems with overheating on the next charge cycle.
Yikes! ...also very good to know.
Use batteries that have a built in circuitry protecting against overcharge and overdischarge....
I didn't know any battery came with protection circuitry, but now I know to look for it. Thank you.
Care to enlighten on the actual .... I am still trying to weight the advantage and disadvantages....
My headband uses only 3D-motion detection and an infra-red source and sensor. It does not make any electrical connection to the subject at all; there are no "electrodes".
The best description I've found of a "protected" 9v lithium ion battery is here, where it states that even 500ma continuous discharge is no problem. And that it has automatic cut-off to prevent (1) overcharge (2) over discharge (3) short circuit.
I've been unable to find such a full description for the battery I'm using described here. But it is evidently the same, as I did find mention of it containing a "protection ic", being widely used in medical equipment, officially certified by CE and ROHS, and able to be fully discharged without a problem (evidently due to a discharge limiter, explaining why mine stay nearly level around 7 volts for 10 hours and then fall to nothing rather suddenly).
So I'm assuming I don't need to add a fuse or other protection circuitry, as it's already built in. (...although if such protection is already in place, I'm left wondering why the side of the battery says not to "short circuit".)