Relationship between linear and rotational head acceleration in various activities.

Head injury is typically predicted using linear or rotational acceleration-based injury criteria. In many cases, the linear components of head acceleration can be determined more easily than the rotational components. Peak rotational head acceleration (apeak) can be calculated from the peak linear head acceleration (apeak) by assuming a value for the effective radius of rotation (r) of the head (apeak = apeak / r). Empirical values for the effective radius of rotation were calculated using linear and angular head acceleration data from 20 human volunteers subjected to a wide variety of test scenarios, including a soccer ball impact to the forehead, a voluntary hand strike to the forehead, voluntary shaking of the head, plopping down in a chair, and a vertical drop while seated supine in a chair. In addition, values for the effective radius of rotation of the head were calculated for American football, boxing, and frontal and rear end automotive impacts using data from the literature. The range of values for the effective radius of rotation of the head for each activity was characterized statistically by calculating median, middle 50%, and middle 95% values from the cumulative distribution. Median values for the effective radius of rotation of the head ranged from 84 mm for boxing to 376 mm for voluntary hand strikes to the forehead. It is important to note that the concept of an effective radius of rotation of the head is simply a convenient method for expressing an empirical relationship between peak linear and peak rotational head acceleration, and does not represent an accurate model of the kinematics of the head. In most of the activities studied, the head kinematics were complex, and the center of gravity of the head did not rotate at a constant radius about a fixed point.