EQI's stand for eccentric quasi-isometrics. This concept was first made famous by Dr. Mel Siff in his classic book Super Training. The idea beind EQI's is that you hold an isometric (i.e. static) position (e.g. the bottom positon of a squat) for a given period of time (e.g. 20-60 sec). As you fatique, you start to sink a little lower. The cool thing with this is that you gradually increase not only your mobility, but you also build strength at that end range and help reduce your risk of injury.
Through the work of brilliant people such as Gray Cook, we have learned that in some cases lack of stability can shut off mobility. For example, some people demonstrate great range of motion at the hips, knees and ankles and yet cannot squat deep. This can be due to a lack of stability at the bottom of a squat. As a result, there body shuts down their mobility to prevent itself from being in a position that it sences it cannot stabilize. Again, EQI's can be very helpful for this as they build that stability in those end ranges of mobility.
Another problem athletes often have is staying low. Getting into a low position is often critical for not only optimal movement and quickness (especially accelerating, decelerating and cutting) but also injury prevention. For example, when you try to stop high, the stress is on your knee ligaments. When you stop in a low position, you can transfer that stress to your muscles. Lack of mobility, lack of strength or lack of endurance can result in athletes being higher than they should for optimal performance and injury reduction. EQI's are great for building this much strength and endurance in these bottom positions.
Short-duration EQI's can be used at the beginning of a training session to improved mobility, technique, stability and muscle activation. Just be sure not to add additional loads or get into hold times that produce lactic acid or fatigue. Longer-duration EQI's can be used at the end of a training session to not only get some fantastic active flexibility benefits and strength, but also as a great finisher (this is especially good for those interested in muscle building or fat loss) or just a good physical and mental challenge.
While this can be used with many exercises (e.g. squats, pull-ups, push-ups - be careful on the shoulder), one of my all-time favorites is the Bulgarian Split Squat EQI (note: this one can also be called rear-foot elevated split squat, but that is not as cool).