title: The distributed lambda (λ) model (DLM): a 3-D, finite-element muscle model based on Feldman's λ model; assessment of orofacial gestures.
abstract: OBJECTIVE
  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.
  
  
  METHODS
  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.
  
  
  CONCLUSIONS
  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.
authors.forename: Mohammad Ali
authors.initials: MA
authors.lastname: Nazari
authors.forename: Pascal
authors.initials: P
authors.lastname: Perrier
authors.forename: Yohan
authors.initials: Y
authors.lastname: Payan
mesh_terms: D001696:Biomechanical Phenomena / Q000502:physiology; D005152:Facial Muscles / Q000502:physiology*; D020342:Finite Element Analysis; D005868:Gestures; D006801:Humans; D008046:Lip / Q000502:physiology; D008954:Models, Biological; D009055:Mouth / Q000502:physiology*; D009119:Muscle Contraction / Q000502:physiology; D009129:Muscle Tonus / Q000502:physiology; D010160:Palate, Soft / Q000502:physiology; D010609:Pharyngeal Muscles / Q000502:physiology; D013060:Speech / Q000502:physiology*; D014059:Tongue / Q000502:physiology