An accelerometer-only algorithm for determining the acceleration field of a rigid body, with application in studying the mechanics of mild traumatic brain injury

Head concussions can cause a hazardous situation and result in mild traumatic brain injury (mTBI), a medical condition that alters an individual’s mental status. It causes serious health problems, manifested by permanent damage to neural tissues and progressive neurodegenerative disease due to repetitive head injuries. The study of mTBI is one of the bio-mechanics problems that has attracted research attention. Research shows that brain injuries due to blunt trauma are potentially caused by large strains and strain-rates created in the tissues. Whereas these strains and strain-rates have been successfully estimated in the laboratory settings, their estimation outside the laboratory environment has remained a great challenge due to the lack of effective indirect estimation strategies.

Typically, blunt impact events leading to mTBI involve small and elastic strains in the skull. And one promising indirect strategy for estimating the brain strains involves modeling the skull as a rigid body, calculating the accelerations via induced blunt impact events, and using the results to develop continuum mechanics to determine the brain deformation. The acceleration of any finite points on the head can be measured using accelerometers attached to headgears, such as helmets, placed in close contact with the points, and are useful in determining the acceleration fields of the rigid bodies. Despite the numerous techniques for determining the acceleration fields, most assume small rotation of the rigid body’s motion leading to inaccurate results. Moreover, the existing frameworks provide limited information about the orientation of the rigid body frame with respect to the fixed frame.

To address these challenges, researchers at Brown University: Dr. Mohammad Masiur Rahaman, Dr. Wenqiang Fang, Dr. Alice Lux Fawzi, Dr. Yang Wan and led by Professor Haneesh Kesari developed an accelerometer-only algorithm for determining the acceleration field of a rigid body to study mTBI. The mathematical formulation of the algorithm involved the theory of rigid body motion, combined with new features like modeling the body as a topological space, measuring the modeling forces, and using positions and velocities in different vector planes. The acceleration measurements were obtained from four tri-axial accelerometers without assuming small rotations and were used to determine the in vivo brain strains. The feasibility of the algorithm was validated through numerical simulations. Their work is currently published in the journal, Journal of the Mechanical and Physics of Solids.

The authors reported that the accelerometer-only algorithm was straightforward, efficient, and more suitable for studying the mechanics of mTBI. Unlike other techniques that use a combination of gyroscopes and accelerometers, this algorithm only uses data from accelerometers and did not involve numerical data differentiation. Additionally, the algorithm could be used in applications that only required the magnitude of the acceleration vectors as well as those that required both the magnitude and the direction. The latter, however, involved the calculation of the vector orientation and angular velocity.

In summary, the study proposed a fairly general accelerometer-only algorithm, using only the exclusive data from the accelerometers, to determine the acceleration field of rigid bodies. It demonstrated potentially high sensitivity to bias errors than inertial measurements units (IMUs)-based algorithms since it did not involve data differentiation. Other advantages included application to three-dimensional (3D) motions and different rigid body motions involving finite rotations and the ability to provide in-depth information of the acceleration field of rigid bodies. In a statement to Advances in Engineering, the authors explained their new algorithm simplified the understanding of mechanics of mTBI and could be modified to expand its applications in other areas like platform guidance and control.