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PREDICTING CARPAL KINEMATICS USING THE MINIMUM ENERGY PRINCIPLE

Centre for Orthopaedic Biomechanics, Department. of Mechanical Engineering, University of Bath, BA2 7AY. Royal United Hospital, Combe Park, Bath, BA1 3NG

Background and Purpose: There is a high incidence of arthritis in the hand, but joint replacement technology in the wrist and other small joints is still in its infancy compared with the larger joints. The wrist is the most complex small joint and so there is a need for fundamental research into the way in which it works. At present there is no generally agreed upon satisfactory explanation for the complex movement patterns of the carpal bones. The purpose of the work was to test a new hypothesis on wrist kinematics. The basis of the hypothesis was that the bones of the wrist move in such a manner as to maximise total contact area in the joint, thereby minimising contact stress. Such a strategy would minimise the bone mass requirements, thereby minimising the biological "cost" of creating and maintaining the joint. This agrees with the minimum energy principle, which governs many natural processes.

Methods: A computer model was created to test the hypothesis. A cadaveric wrist was dissected and 3D faceted models of the carpal bones were created using laser digitisation. The model contained a program to evaluate the closeness of packing of the carpal bones and an optimisation algorithm [1] to maximise this quantity by adjusting the positions of the bones. The evaluation program computed the contact area and level of intersection between nine pairs of interacting bones. Rotation in the radial-ulnar deviation plane was applied in 1.0° increments to four rigidly connected bones defining the overall posture of the wrist, and an optimisation algorithm was used to maximise the contact area by adjusting the positions and orientations of the remaining bones.

Results: The results of the work are encouraging because certain known characteristics of carpal behaviour were clearly predicted by the model. The results for the scaphoid in particular were similar to the characteristic movements of this bone in both radial and ulnar deviation. During 20° of unlar deviation, the bone demonstrated 14.3° of extension, which is near to the 20.4° reported by an experimental study [2]. In 10° of radial deviation, the bone underwent 6.4° of flexion, which again is close to the 8.1° experimental result.

Conclusion: Although the computer model predicted certain aspects of carpal behaviour, the initial hypothesis was not conclusively proved. This is due in part to the computational complexity of the task. Despite some simplifying assumptions, there were still a large number of degrees of freedom, and it is almost certain that the optimisation process was afflicted with local minima problems. If the technical hurdles can be overcome and the hypothesis is proved correct, then we will gain a new explanation of the laws governing the kinematics of the wrist joint, which are not fully understood at present. This will provide invaluable information for surgical applications, where a thorough understanding of normal kinematics is essential for the treatment of joint injury and instability.

Correspondence should be addressed to Dr Carlos Wigderowitz, Honorary Secretary of BORS, Division of Surgery & Oncology, Section of Orthopaedic & Trauma Surgery, Ninewells Hospital & Medical School Tort Centre, Dundee, DD1 9SY.