The anthropometric generalization of the Body Mass Index

The Body Mass Index, is an important indicator of the risk of death, of obesity, of negative health consequences, body fat percentage and of the shape of the body. The main limitation of the BMI is that it does not account for body composition including non fat body mass such as muscles, joints, body frame and makes no difference between fat and non fat components of the body weight. The body composition and the proportion of fat and muscles make a difference in health outcomes. Body composition makes a difference also in the level of sport performance for athletes of every level.  In nearly two centuries since the Body Mass Index was developed, no formula had been successfully developed to account for body composition and make the difference between muscle and fat in a consistent way. I develop a direct generalization of BMI, in the mathematical and physiological sense to account for fat and fat free mass and muscles, small and large body frames.   The formulae I developed explain and generalize the conclusions of a large number of highly cited empirical experiments cited in the reference section.