Disclosed are systems and methods for accurately measuring T1 in magnetic resonance imaging (MRI) for short T2 tissues by an integrative three-dimensional Ultrashort Echo Time Actual Flip Angle Imaging Variable TR (3D UTE-AFI-VTR) technique. Also, disclosed are systems and methods for accurately measuring T1 for T2 tissues by an integrative three-dimensional Ultrashort Echo Time Actual Flip Angle Imaging Variable Flip Angle (3D UTE-AFI-VFA) technique. The disclosed methods and systems can be implemented to allow accurate T1 mapping for T2 tissues, including menisci, ligaments, tendons, myelin in gray and white matter, cortical bone, and soft tissue in whole joints.