This paper addresses the problem of quantifying the facial asymmetry from dynamic 3D data. We investigate here the role of 4D (i.e. 3D+time) data to reveal the amount of both static and dynamic asymmetry, in a clinical use-case of facial paralysis. The final goal is to provide tools and solutions to clinicians for facial paralysis assessment and monitoring, which can provide qualitative and quantitative evaluations. To this end, the approach proposed here consider 3D facial sequences and adopt a recently-developed Riemannian approach for facial deformation analysis. After a preprocessing step, each frame of a given 3D sequence is approximated by an indexed collection of elastic radial curves. Riemannian shape analysis of obtained curves and their symmetrical counterparts, both elements of the same shape space, give rise to a feature vector, called Dense Scalar Fields (DSFs). The use of these DSFs reveals the amount of bilateral asymmetry of the face, when conveying expressions. That is, given a 3D frame, it is first reflected with respect to the YZ-plane, then compared to the obtained reflection using the DSFs. To exemplify the use of the proposed approach, a new dataset have been collected (of patients) before and after injecting Botulinum Toxin (BT) in related facial muscles. Experimental results obtained on this dataset show that the proposed approach allows clinicians to evaluate the facial asymmetry before and after the medical treatment.