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Given the complex nature of traumatic brain injury (TBI), assessment of injury risk directly from kinematic measures of head motion remains a challenge. Despite this challenge, kinematic-based measures of injury continue to be widely used to guide the design of protective equipment. In an effort to provide more insight into the relationship between rotational head kinematics and injury risk, we have conducted a large scale parametric finite element analysis (FEA) to investigate the role of angular acceleration, angular velocity, and angular jerk on the brain tissue strains and strain rates. The peak strains and strain rates resulting from rotational head accelerations were obtained for peak angular accelerations ranging from 0.5 - 25 krad/s2 and peak angular velocities ranging from 10 - 100 rad/s. The results of this study show that both angular acceleration and angular velocity have a significant effect on the peak tissue strains and strain rates, reinforcing the importance of accounting for both of these kinematic measures when evaluating injury risk. For a given magnitude of peak angular acceleration and angular velocity, increases in angular jerk are shown to have minimal effect on the peak tissue strains but can lead to an increase in the peak tissue strain rates. This advancement in our understanding of the relationship between angular head kinematics, tissue strain, and tissue strain rate is an important step toward developing improved kinematic-based measures of injury. To reduce the risk of traumatic brain injury, we must first fully understand the relationship between impact-induced head motions and the brain deformation response. Large deformations of the brain have been shown to cause damage to neural cells and can result in long-term neurocognitive deficits. This study investigates the role of angular acceleration, angular velocity, and angular jerk on the tissue strains and strain rates that develop in the brain. By providing further insight into how each of these kinematic parameters affect the brain deformation response, we can begin to identify the types of head motions that are the most injurious and develop new targeted approaches to reduce the risk of injury.