A pre-computed brain response atlas (pcBRA) may have the potential to accelerate the investigation of the biomechanical mechanisms of traumatic brain injury on a large-scale. In this study, we further enhance the technique and evaluate its performance using angular velocity profiles from dummy head impacts. Using the pcBRA to simplify profiles into acceleration-only shapes, sufficiently accurate strain estimates were obtained for impacts with a major dominating velocity peak. However, they were largely under-estimated when substantial deceleration occurred that reversed the direction of angular velocity. For these impacts, estimation accuracy was substantially improved with a biphasic profile simplification (average correlation coefficient and linear regression slope of 0.92±0.03 and 0.95±0.07 for biphasic shapes, respectively, vs. 0.80±0.06 and 0.80±0.08 for acceleration-only shapes). Peak maximum principal strain (εp) and cumulative strain damage measure (CSDM) from the estimated strains consistently correlated stronger than kinematic metrics with respect to the baseline εp and CSDM from the directly simulated responses, regardless of the brain region (e.g., correlation of 0.93 vs. 0.75 compared to Brain Injury Criterion (BrIC) for εp in the whole-brain, and 0.91 vs. 0.47 compared to BrIC for CSDM in the corpus callosum). These findings further support the pre-computation technique for accurate, real-time strain estimation, which could be important to accelerate the pace of model-based brain injury studies in the future.