Understanding patterns of interhemispheric asymmetry is crucial for monitoring neuroplastic changes during post-stroke motor rehabilitation. However, conventional laterality indices often pose computational challenges when applied to functional near-infrared spectroscopy (fNIRS) data due to the bidirectional hemodynamic responses. In this study, we analyze fNIRS recordings from 15 post-stroke patients undergoing motor imagery brain-computer interface training across multiple sessions. We compare traditional laterality coefficients with a novel task response asymmetry coefficient (TRAC), which quantifies differential hemispheric involvement during motor imagery tasks. Both indices are calculated for oxygenated and deoxygenated hemoglobin responses using general linear model coefficients, and their day-to-day dynamics are assessed with linear regression. The proposed TRAC demonstrates greater sensitivity than conventional measures, revealing significantly higher oxygenated hemoglobin TRAC values (0.18 ± 0.19 vs. -0.05 ± 0.20, < 0.05) and lower deoxygenated hemoglobin TRAC values (-0.15 ± 0.27 vs. 0.04 ± 0.23, < 0.05) in lesioned compared to intact hemispheres. Among patients who exhibit substantial motor recovery, distinct daily TRAC dynamics were observed, with statistically significant temporal trends. Overall, the novel TRAC metric offers enhanced discrimination of interhemispheric asymmetry patterns and captures temporal neuroplastic changes not detected by conventional indices, providing a more sensitive biomarker for tracking rehabilitation progress in post-stroke brain-computer interface applications.