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The Dynamic Response Index is a measure of the likelihood of spinal damage arising from a vertical shock load such as might be encountered in a military environment. The DRI is a dimensionless number which is proportional to the maximum spinal compression suffered during the event.
The DRI is derived as the solution to an equation which models the human spine as a lumped single-degree-of-freedom spring-shock absorber system. The model uses an ordinary linear second-order differential equation with constant coefficients with spinal compression as the variable. The forcing function in the equation is the accelerative shock load delivered to the pelvis by the event. The equation is given below:
d 2 X d t 2 + 2 ⋅ ζ ⋅ ω ⋅ d X d t + ω 2 ⋅ X = d 2 z d t 2 {\displaystyle {d^{2}X \over dt^{2}}+2\cdot \zeta \cdot \omega \cdot {dX \over dt}+\omega ^{2}\cdot X={d^{2}z \over dt^{2}}}
In this equation, X denotes the spinal compression, and dz/dt denotes the time-dependent shock acceleration. The coefficients ω and ζ are the lumped spinal frequency and damping, ω = 52.90 radians/second, ζ = 0.224.