Does the Minimum Energy Principle Govern Wrist Kinematics?

D.M. Sirkett, G. Mullineux, A.W. Miles, and G.E.B. Giddins (UK)


Kinematics and Kinematic Assessment, Comutational Biomechanics


While theoretical and computer models describing kinematics of the larger joints have been developed, there is still no generally agreed upon satisfactory explanation of how the wrist works. A new explanation of the underlying rules that may govern the motion of the carpal bones has been outlined. We propose that the carpal bones move in such as way as to maximise the total contact area between all pairs of articular surfaces. This would minimise contact stress, thereby minimising in biological terms the "construction cost" of the carpal bones. This agrees with the principle of minimum energy, which governs many natural processes. Carpal bones from a fresh frozen cadaveric forearm were dissected and their shapes converted into threedimensional computer models using non-contact laser digitisation. A computer program was developed to measure contact area between neighbouring articular surfaces and to maximise this quantity by adjusting the six degrees of freedom of the carpal bones. The program is able to avoid impingement of bones upon one another through the use of collision detection. The method has been applied to a pair of articulating surfaces that may be found in biaxial type wrist prostheses and correctly computed the kinematics of the joint. The purpose of the work is to test a new theory of wrist kinematics. The underlying premise is that the shape of the carpal bones and the manner in which they move are governed by the minimum energy principle. It is assumed that biological structures are formed using the minimum of materials necessary to provide adequate function. In the case of the carpal bones, this may suggest that their form is such that loading forces are evenly distributed throughout the joint surfaces, thereby minimising peak local loading. This is achieved by maximising contact area through the use of conforming joint surfaces. If peak loading is reduced in this way, then the material used to create the bones is minimised, which agrees with our initial assumption. To date, investigations into wrist kinematics have been primarily observational in nature. The movement patterns of the individual carpal bones have been recorded using cadaveric wrists [1,2,3] and with live subjects using imaging methods with three-dimensional computer reconstructions [4,5,6]. There is variation in the movement patterns of carpal bones between individuals [7,8,9] but there is no general rule that can be applied to explain the movement patterns of carpal bones, taking into account morphological variations. This hampers understanding of normal carpal mechanics. 2. Aims and Objectives The aim of the work is to develop a three-dimensional computer model of the wrist that will predict movement patterns of the carpal bones based upon maximisation of contact area. Specific objectives for the work are i) to develop the computer algorithm used to calculate contact area, ii) to find a suitable numerical optimisation scheme to maximise the contact area for increments of hand position, iii) to obtain a set of three-dimensional computer models of the carpal bones, including the articular surfaces and iv) to validate the method by comparing the results to those obtained from an experimental study of normal wrist kinematics. This paper covers objectives (i) to (iii).

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