title: The thumb carpometacarpal joint: curvature morphology of the articulating surfaces, mathematical description and mechanical functioning.
abstract: OBJECTIVE
  The purpose is to present a mathematical model of the function of the thumb carpometacarpal joint (TCMCJ) based on measurements of human joints. In the TCMCJ both articulating surfaces are saddle-shaped. The aim was to geometrically survey the shapes of the articulating surfaces using precise replicas of 28 TCMCJs.
  
  
  METHODS
  None of these 56 articulating surfaces did mathematically extend the differential geometrical neighbourhood around the main saddle point so that each surface could be characterised by three main parameters: the two extreme radii of curvature in the main saddle point and the angle between the saddles' asymptotics (straight lines).
  
  
  RESULTS
  The articulating surfaces, when contacting at the respective main saddle points, are incongruent. Hence, the TCMCJ has functionally five kinematical degrees of freedom (DOF); two DOF belong to flexion/extension, two to ab-/adduction. These four DOF are controlled by the muscular apparatus. The fifth DOF, axial rotation, cannot be adjusted but stabilized by the muscular apparatus so that physiologically under compressive load axial rotation does not exceed an angle of approximately ±3°.
  
  
  CONCLUSIONS
  The TCMCJ can be stimulated by the muscular apparatus to circumduct. The mechanisms are traced back to the curvature incongruity of the saddle surfaces. Hence we mathematically proved that none of the individual saddle surfaces can be described by a quadratic saddle surface as is often assumed in literature. We derived an algebraic formula with which the articulating surfaces in the TCMCJ can be quantitatively described. This formula can be used to shape the articulating surfaces in physiologically equivalent TCMCJ-prostheses.
authors.affiliation: Biomechanical Working Group, Department of Orthodontics, University of Göttingen, Germany.
authors.forename: Henning
authors.initials: H
authors.lastname: Dathe
authors.affiliation: Department of Trauma and Orthopaedic Surgery, Klinikum Kassel, Germany.
authors.forename: Clemens
authors.initials: C
authors.lastname: Dumont
authors.affiliation: Biomechanical Working Group, Department of Orthodontics, University of Göttingen, Germany.
authors.forename: Rainer
authors.initials: R
authors.lastname: Perplies
authors.affiliation: Polyclinic of Orthodontics, University of Regensburg, Germany.
authors.forename: Jochen
authors.initials: J
authors.lastname: Fanghänel
authors.affiliation: Biomechanical Working Group, Department of Orthodontics, University of Göttingen, Germany.
authors.forename: Dietmar
authors.initials: D
authors.lastname: Kubein-Meesenburg
authors.affiliation: Biomechanical Working Group, Department of Orthodontics, University of Göttingen, Germany.
authors.forename: Hans
authors.initials: H
authors.lastname: Nägerl
authors.affiliation: Biomechanical Working Group, Department of Orthodontics, University of Göttingen, Germany.|Department of Trauma, Orthopaedics and Plastic Surgery, University of Göttingen.
authors.forename: Martin M
authors.initials: MM
authors.lastname: Wachowski
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D001696:Biomechanical Phenomena; D052737:Carpometacarpal Joints / Q000033:anatomy & histology* / Q000502:physiology*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008962:Models, Theoretical; D016059:Range of Motion, Articular; D012399:Rotation; D013933:Thumb / Q000033:anatomy & histology* / Q000502:physiology*