Are your arms/legs elevated when you're bound? That can reduce blood flow. Perhaps try a position where your arms and legs are lower than your abdomen (tied face-down on a bench with your hands and legs bound to the legs, for example). The gravity might be enough to increase blood flow so you don't get as much tingling sensation.

I would be really careful about this; tingling and numbness every time you're tied won't be good over the long run. Perhaps you can talk to your doctor about ways to improve your circulation.