Analytical Investigations of the Head-Neck Dynamic System Subjected to Repeated Head Impacts

Adeleye OA(1), Ugwuadu FT(2), Yinusa AA(3), Osuntoki AA(4),

(1) Department of Biomedical Engineering, University of Lagos, Akoka, Lagos, Nigeria
(2) Department of Biomedical Engineering, University of Lagos, Akoka, Lagos, Nigeria
(3) Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
(4) Department of Biochemistry, University of Lagos, Akoka, Lagos, Nigeria.
Corresponding Author


Background: The major cause of traumatic brain injury and neurodegenerative dementing diseases is the repeated head impact
from sporting activities such as boxing, American football, etc. The repeated head impacts with the control system is represented
with a rigid linkage and head-neck manipulator system, and governed by coupled nonlinear ordinary differential equations whose
exact solutions cannot be easily obtained with the common analytical methods.
Objective: The analytical investigation of the head neck dynamic system with repeated head impacts is presented in this study.
Methods: A special analytical technique known as differential transform method was applied to obtain solutions to the identified
challenge associated with common analytical methods.
Results: The obtained analytical results and experimental results from earlier studies were compared and then validated with the
fourth order Runge-Kutta numerical method. Good agreements are observed in the results. The effects of the systems’ parameters were investigated, and it is observed that the amplitude angular motion of the head becomes higher than that the neck region with time. Similarly, an increase in the eternal forcing function, head mass, lower and upper linkage lengths, head and neck moments of inertia resulted in increased amplitude of the system dynamic response whereas an increase in the neck mass resulted in decreased amplitude of the system.
Conclusion: This study shows that the developed model and its applied analytical method provide a better understanding of the
physical quantities in the head neck system and a platform for design adjustment and optimization of the physical quantities or
parameters for head protective devices.


Repeated head impact, head-neck dynamic system, biomechanical model, differential transform method, analytical solution.

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