Biomedical Engineering and Bioengineering Commons^™

A Fractal Art Approach To The Three-Body Problem, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This preliminary study explores a new search strategy for identifying relatively stable vs. unstable solutions to the planar three-body problem in astrophysics, starting from the perspective of computer-generated art. Here classical Newtonian accelerations, speeds, and positions of all three bodies in a fixed plane are calculated. All three bodies are stationary at time zero, and the fate of the system is classified as reflecting either a bound stable orbit, a likely collision, or the ejection of one body. The initial position of one of the three bodies is varied in the image plane, and the outcome coded as one of …

Brain Motion, Deformation, And Potential Injury During Soccer Heading, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This paper addresses the problem of what is happening physically inside the skull during head-ball contact. Mathematical models based upon Newton’s laws of motion and numerical methods are used to create animations of brain motion and deformation inside the skull.

Initially a 1 cm gap filled with cerebrospinal fluid (CSF) separates the brain from the rigid skull in adults and older children. Whole head acceleration induces a pulse of artificial gravity within the skull. Because brain density differs slightly from that of CSF, the brain accelerates and strikes the inner aspect of the skull, undergoing viscoelastic deformation, ranging from 1 …

A New Biomechanical Head Injury Criterion, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Publications

This paper presents a new analysis of the physics of closed head injury caused by intense acceleration of the head. At rest a 1 cm gap filled with cerebrospinal fluid (CSF) separates the human brain from the skull. During impact whole head acceleration induces artificial gravity within the skull. Because its density differs slightly from that of CSF, the brain accelerates, strikes the inner aspect of the rigid skull, and undergoes viscoelastic deformation. Analytical methods for a lumped parameter model of the brain predict internal brain motions that correlate well with published high-speed photographic studies. The same methods predict a …

Biomechanics Of Heading A Soccer Ball: Implications For Player Safety, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Publications

To better understand the risk and safety of heading a soccer ball, the author created a set of simple mathematical models based upon Newton’s second law of motion to describe the physics of heading. These models describe the player, the ball, the flight of the ball before impact, the motion of the head and ball during impact, and the effects of all of these upon the intensity and the duration of acceleration of the head. The calculated head accelerations were compared to those during presumably safe daily activities of jumping, dancing, and head nodding and also were related to established …