The Distributed Lambda (λ) Model (DLM): A 3-D, Finite-Element Muscle Model Based on Feldman's λ Model; Assessment of Orofacial Gestures

Abstract

Purpose The authors aimed to design a distributed lambda model (DLM), which is well adapted to implement three-dimensional (3-D), finite-element descriptions of muscles. Method A muscle element model was designed. Its stress–strain relationships included the active force–length characteristics of the λ model along the muscle fibers, together with the passive properties of muscle tissues in the 3-D space. The muscle element was first assessed using simple geometrical representations of muscles in the form of rectangular bars. It was then included in a 3-D face model, and its impact on lip protrusion was compared with the impact of a Hill-type muscle model. Results The force–length characteristic associated with the muscle elements matched well with the invariant characteristics of the λ model. The impact of the passive properties was assessed. Isometric force variation and isotonic displacements were modeled. The comparison with a Hill-type model revealed strong similarities in terms of global stress and strain. Conclusion The DLM accounted for the characteristics of the λ model. Biomechanically, no clear differences were found between the DLM and a Hill-type model. Accurate evaluations of the λ model, based on the comparison between data and simulations, are now possible with 3-D biomechanical descriptions of the speech articulators because of the DLM.