HEAD INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 236

where t 1 and t 2 are the beginning and end instants of the impact pulse,
respectively, and a is the magnitude of the acceleration of the brain's center
of mass.
Versace's measure is defined by the expression

a(t) dt

2 . 5

t 2

1

V = (t 2 − t 1 ). (7.5)

t 2 − t 1

t 1

This measure coincides with the left-hand side of relation (7.3) since the
duration of the impact pulse, t , is defined by the difference t 2 − t 1 ,and
the expression in the square brackets is the mean acceleration over this time
interval. On the other hand, the functional V coincides in form with the
expression to be maximized in the HIC functional of Eq. (7.1). For measures
of both Eqs. (7.4) and (7.5), the value 1000 is regarded as critical; exceeding
this value means that severe head injuries are possible.
Unlike the criteria of Eqs. (7.4) and (7.5), in the criterion of Eq. (7.1), the
time instants t 1 and t 2 are chosen to provide a maximum for the expression
in curly brackets, rather than being fixed. This is done to avoid underesti-
mating the value if the impact pulse involves time intervals on which the
acceleration magnitude is substantially less than its maximum value.
Although the HIC is utilized in a number of countries as a standard
safety criterion for transport vehicles and some structures (e.g., sporting
playgrounds; Shorten and Himmelsbach, 2002) for head injuries and as the
basic performance index for impact protection helmets, the biomechanical
adequacy of this measure is still being disputed and has been criticized in
a number of papers (see, e.g., Lockett, 1985; Newman, 1980).
The HIC will be used here as a tolerance criterion to be taken into
account when designing systems for which impacts of the head against
various surfaces can occur. These surfaces should be covered with impact
isolation materials. The mechanical properties of these materials and the
thickness of the coating should be chosen so as to provide HIC values
that lie below the major injury threshold for impacts with typical veloci-
ties. (The range of these velocities is usually defined by appropriate stan-
dards.)
One of the basic problems associated with the creation of impact isolation
coatings is that of determining the minimal thickness of the coating that
guarantees a prescribed degree of head injury prevention (in terms of the
HIC). It is also of interest to know the specific features of the deceleration
of the head by this coating. Furthermore, the inverse problem, in which the
HIC value is to be minimized, provided that the thickness of the coating
is constrained, is important. From the mathematics point of view, such