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Over 22 million people worldwide are affected by Parkinson's disease, stroke, and Bell's palsy (BP), which can cause facial paralysis (FP). People with FP have trouble having their expressions understood: both laypersons and clinicians have difficulty understanding them and often misinterpret them, which can result in poor social interactions and poor care delivery. One way to address this problem is through better education and training, of which computational tools may prove invaluable. Thus, in this paper, we explore how to build systems that can recognize and synthesize asymmetrical facial expressions. We introduce a novel computational model of asymmetric facial expressions for BP, which we can synthesize on either virtual and robotic patient simulators. We explore this within the context of clinical education, and built a patient simulator with synthesized FP in order to help clinicians perceive facial paralysis in patients. We conducted both computational and human-focused evaluations of the model, including the feedback from clinical experts. Our results suggest that our BP model is realistic, and comparable to the expressions of people with BP. Thus, this work has the potential to provide a practical training tool for clinical learners to better understand the expressions of people with BP. Our work can also help researchers in the facial recognition community to explore new methods for asymmetric facial expression analysis and synthesis.