Lumbar injection is an image-guided procedure performed manually for diagnosis and treatment of lower back pain and leg pain. Previously, we have developed and verified an MR-Conditional robotic solution to assisting the needle insertion process. Drawing on our clinical experiences, a virtual remote center of motion (RCM) constraint is implemented to enable our robot to mimic a clinician's hand motion to adjust the needle tip position in situ. Force and image data are collected to study the needle behavior in gel phantoms during this motion, and a mechanics-based needle-tissue interaction model is proposed and evaluated to further examine the underlying physics. This work extends the commonly-adopted notion of an RCM for flexible needles, and introduces new motion parameters to describe the needle behavior. The model parameters can be tuned to match the experimental result to sub-millimeter accuracy, and this proposed needle manipulation method presents a safer alternative to laterally translating the needle during in situ needle adjustments.