Modelling of FCU to EDC Tendon Transfer Using Mathematica

Using a combination of measured physiological parameters, approximations and a geometric muscle model, we are able to predict the biomechanical properties of a joint immediately following tendon transfer.

Physiological Parameters

Previous work in this lab has given us detailed knowlege of the flexor carpi ulnaris (FCU) muscle and tendon properties. Work done by Kai An's group gives us an estimate of the moment arm of the extensor digitorum communis (EDC). Finally, some in vivo sarcomere length measurements give us a good idea of the sarcomere lengths truly found before and after the tendon transfer.

Mathematical Modelling

We constructed a model, similar to Zuurbier and Huijing's (J Biomech 25:1017-1026), to estimate muscle forces and joint torques from these parameters. The model is, basically, a two dimensional cartoon of a real muscle: as the muscle shortens, it gets "fatter"...the constituent fibers shorten and rotate. The animation is a good representation of how our cartoon muscles behave. The model is implemented in Mathematica and the source notebooks (muscles.m and tendonforce.m) are available.

Forces After Transfer

We found that hand surgeons tend to attach the FCU under a great deal of passive tension (i.e. at long sarcomere lengths). The characteristics of force production following transfer are strongly dependent (as you would expect) on the sarcomere length of transfer. The animation illustrates this. As transfer length increases (decreasing overlap of the inset sarcomere), the force plateau shifts to greater wrist flexion (left along the x-axis) and finger extension (out of the page). If the surgical goal to to provide some extension strength everywhere in the range of motion, then shorter transfer sarcomere lengths are indicated. However strength is maximized in the position of normal use (slight wrist flexion and moderate finger flexion) by somewhat longer transfer lengths.



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