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Barker, Dan
12-02-1997, 05:03 AM
My initial posting,

Dear Colleagues

As part of the design process of a new MCP joint we are reviewing
biomechanical models of the finger which provide a solution for the joint
reaction force at the MCP joint.

Many papers have tackled this problem, notably An, Chao and colleagues. The
methodology in all these papers was to solve equilibrium equations at the
MCP and IP joints of the fingers considering the application of an external
load.

To create the moment equilibrium equations, the moment arms of the tendons
were required. Moment arms, defined as the perpendicular distance from the
centre of joint rotation to the line of the tendon, were determined at each
joint based on techniques such as biplanar xray. These moment arms at each
joint were then used in the equilibrium equations. This implies that the
tendon has a line of action, at the joint under consideration, originating
from the bone distal to the joint under consideration. This to my mind does
not seem to be the case. For example the flexor profundus tendon does not
attach to the proximal phalanx, however in the models a moment arm is
assumed at the MCP joint. Surely the only action on the proximal phalanx is
via the digital sheath, completely altering the assumed line of action.

This has been noted by Delattre and colleagues "The mechanical role of the
digital fibrous sheath: Application to reconstructive surgery of the flexor
tendons. JF Delattre et al. Anat Clin (1983) 5: 187-197." These workers
pointed out the dual mechanical function of the extrinsic flexor tendons ie
the phalanges are stabilised both by direct insertion AND action of the
tendon on the tendon sheath.

Is anyone aware of force analyses which have considered this arrangement.
Have I missed some assumptions used in the previous models. My feeling is
that indirect load transfer via the pulleys of the finger must alter the
joint reaction force at the MCP joint.

As customary I will post all replies

Regards

Dan Barker (sbarkds@rgh.sa.gov.au)
Research Engineer
Repatriation General Hospital
Division of Orthopaedic Surgery
Daws Rd. Daw Park 5041 S.A.
Australia
Fax: 61 8 8374 0712
Tel: 61 8 8275 1107

Many thanks to Ton van den Bogert, Peter Sinclair and David Giurintano for
excellent replies and some lively discussion.

The extrinsic flexor tendons of the fingers attach only at the distal and
middle phalanx. As the tendons contract, a force is exerted onto the middle
and distal phalanges. This force may be resolved into a component parallel
to the phalanx which acts to compress the phalanx onto the next proximal
phalanx, and a perpendicular component which acts to flex the phalanx about
the MCP joint. The assumption is that the distal phalanges are prevented
from flexing, hence the distal phalanges may be considered as a continuous
rigid body.

Load is also transferred via the digital sheath to the phalanges which acts
to flex the MCP joint.

The objective is to determine the moment at the MCP joint produced by the
action of the extrinsic flexors. This moment can be determined by
considering the principle of virtual work. This was explained by Ton van
den Bogert

"The mechanical principle that can be used to prove this, is the
principle of virtual work. The transverse forces produced by the
tendon do no work, so they don't go into the equations of motion.
The only work produced by the tendon is F*dL (force times amount
of shortening). Based on geometry the amount of shortening can
be shown to be proportional to the change in joint angles:

dL = d1*dA1 + d2*dA2 + d3*dA3

where dAi is the change in joint angle (in radians) of joint i,
and di is the moment arm at that joint. In fact, this can be
used as definition of moment arm (see An et al.).

The moment Mi at joint i due to the muscle force is defined using
the principle of virtual work:

F*dL = Mi*dAi

(remember work due to a moment is moment times angular
displacement in radians)

This will give:

Mi = F*dL/dAi = F*di

(dL/dAi is the partial derivative of Dl with respect to angle
Ai). "

Therefore, the moment arm of the tendon at the joint under consideration
will enable the moment at the joint to be determined, provided the tendon
force is known (a significant problem in itself!!)

This argument assumes the following;

The tendon-sheath interaction is frictionless,

The digital sheath is inextensible,

These assumptions may affect the results but by how much is unclear.

A couple of references:

Brook, N., Mizrahi, J., Shoham, M. and Dayan, J.
A Biomechanical Model of Index Finger Dynamics.
Med. Eng. Phys., Vol. 17, pp. 54-63. 1995.

Andrews, J.G. (1985) A general method for determining the func-
tional role of a muscle. J. Biomechanical Eng. 107,348-353.

Zajac, F.E. and M.E. Gordon (1989) Determining muscle's force and
action in multi-articular movement. Exerc. Sport Sci. Rev.
17,187-230.

Giurintano Medical Engineering and Physics Vol 17(4) p.297-303

As part of this discussion, the need for drawings became quite obvious. This
resulted in the need for faxes being sent as part of the discussion. Dave
Giurintano made a suggestion which I believe is an excellent idea

"Maybe we need to create a www sketchpad so we can
interactively sketch figures to communicate our ideas - a digital chalk
board."

Dan Barker (sbarkds@rgh.sa.gov.au)
Research Engineer
Repatriation General Hospital
Division of Orthopaedic Surgery
Daws Rd. Daw Park 5041 S.A.
Australia
Fax: 61 8 8374 0712
Tel: 61 8 8275 1107