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

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