ONE YEAR OLD BABY BOUNCING OFF BED
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Low-level Fall Simulation: 1-year old baby bouncing off bed
R. J. Reimann, Professor Emeritus of Physics, Boise State University, 22 October 2012 (rev. 7/9/2013)
This simulation was generated using Working Model® software licensed at Boise State University for educational use only.
A mother reported that her large 11-month old son was bouncing on his knees on a 0.76 m high bed while clutching a cell phone near his neck.
He fell off striking the back of his head on a hardwood floor resulting in a concussion, a subdural hematoma (SDH), and retinal hemorrhages (RH).
Medical intervention was successful and the boy is now doing well.
However, Child Protective Services took over custody pending a full
Working Model® Simulation
The simulation performed with Working model 2D allows flexible joints and other variable parameters to demonstrate one of countless possible scenarios between that described by a witness and other situations where the head does not even hit the floor.
It is intended as a
demonstration aid that is more realistic than an artist's conception.
Although the arms slow the descent, the head is still predicted to hit at vy = 4m/s
Derived results such as accelerations and forces depend on contact time as explained in Appendix A.
Prediction reliability is limited by the choice of model parameters given in Appendix B (mass distribution, joint approximations, elasticity and friction). Any changes to these parameters, initial posture, or rigidity of linked segments may change the outcome significantly.
The simulation is based on average dimensions for a 12-month old child crash-test dummy  with a stature of 0.74 m and mass of 10.0 kg, including a 2.6 kg head. More details are given in Appendix B.
Scale dimensions are in meters. Velocities are displayed for the initial cranial impact point.
The integrity of the software was checked by generating accurate predictions for cases with known analytical solutions. These were free-fall for a ball and toppling a long thin vertical rod about an ideal axis fixed at the bottom.
Other computer simulations, physical models and video analysis are invited for comparison to help evaluate this simulation.
This simulation clearly shows the potential for severe head injuries from low-level falls.
The resulting accelerations and forces for the first impact are more than 10 times greater than those that can usually be produced by manually shaking a realistic dummy ,.
Even the second bounce exceeds that due to shaking.
Appendix A. Physics Relationships
By definition, the average acceleration in the vertical dimension ay = delta vy / Delta t
where delta vy is the change in velocity and Delta t is the interaction time with the floor.
A toddler head colliding with a rigid surface has Delta t aprox. 0.005 s ,. Moderate padding extends this to Delta t aprox 0.020 s. Delta t = 0.006 s was chosen as a reasonable value for a hardwood floor.
As illustrated, a linear approximation of the acceleration or force between the floor and the head shows that the maximum or peak value is about twice the average ,.
Divide accelerations in m/s² by g = 9.8 m/s² to convert into g’s. Multiply accelerations by mass to convert into forces.
Appendix B. Model specifications for a typical 12 month old baby 
By definition, elasticity or coefficient of restitution is modulus of rebound velocity / impact velocity. The bed and floor are assigned values of 0.5 and the body segments are given here below.
The torso was also given an initial downwards velocity of 0.5 m/s.
Rotational joint values were chosen for realistic response since standards are impossible for a variable organism.
Kutta-Merson with 0.0001 second integration step provides accuracy and model stability. Only one step out of every thousand is illustrated.
 Baker, Susan P., O'Neill, Brian, Ginsburg, Marvin J., and Li, Guohua. The Injury Fact Book (Oxford University Press 1992), 2nd ed., p.140
 Ommaya A K, Goldsmith W and Thibault L. Biomechanics and neuropathology of adult and paediatric head injury. British Journal of Neurosurgery 2002; 16(3): 220-242
 Goldsmith W and Plunkett J. A biomechanical analysis of the causes of traumatic brain injury in infants and children. The American Journal of Forensic Medicine and Pathology June 2004; 25(2): 89-100
 Cross, Rod. The Bounce of a Ball. American Journal of Physics March 1999; 67 (3): 222-227
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