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View Full Version : Re: BioNet Controversial Topic #4: knee joint DoUF

Ton Van Den Bogert
02-27-2002, 02:48 AM
Dear Colleagues:

I very much enjoyed reading Alberto Leardini's introduction to this
topic. It is a question that we have wrestled with recently. I believe
some answers can be given from a practical point of view.

The question is:

> How many independent degrees of unresisted freedom has the human knee joint?

As Alberto already stated from the start: the easy answer is: 6, because there
is translation and rotation in all three directions. This is too easy. If
your measurements are sufficiently accurate, you will get this same answer
for any mechanism that you can test. In fact, you can get any answer,
dependent on how closely you look at joint motion. So obviously this answer
does not give any insight at all. Maybe the question can be rephrased to
apply to a specific situation.

Joint testing
-------------
One practical question could be: if you want to test a knee joint (or
a computational model of one), which variables should be inputs (controlled)
and which are outputs (measured)?

In my view there is only one correct way to set up such mechanical tests,
and this approach has been used by, among others, Leendert Blankevoort
(for specimens and computational models) and by the Prof. Woo's group in
Pittsburgh for robotic testing of cadaver joints.

Input variables:
3-D force across the joint
flexion angle
varus-valgus torque
internal-external rotation torque

Output variables:
3-D translational motion
varus-valgus angle
internal-external rotation angle

So there are six input variables and five output variables. But only one
of the input variables is a kinematic variable. The stiffness in the other
degrees of freedom is potentially very large, so it is better to use force
control than position control for those. So, in this sense, we have
assumed that there is only one kinematic degree of freedom. But note that
we measure the other five as output variables, so we do recognize the fact
that there is motion in the other five degrees of freedom.

This approach requires a sophisticated loading device where flexion angle
is controlled but all other motions are left free to move under the influence
of a controlled force. A robot arm with mixed force/position feedback is
the ideal device to do this.

In the absence of forces and torques, you will get an unloaded path of flexion
(I have heard Prof. Woo talk about this), where the other kinematic degrees of
freedom are dependent on flexion angle only, i.e. the knee behaves as a pure 1-DOF
mechanism. However, this path may be sensitive to perturbations, indicating
that the (partially) unloaded joint is perhaps better described as having more
than 1 DOF.

As mentioned by Alberto, Blankevoort also observed this sensitivity and then
decided to determine helical axes as a function of knee flexion while applying
3 Nm of internal or external rotation torque. This made the results
reproducible. I sometimes wonder if this sensitivity problem is worse in cadaver
joints than in vivo. Do they become more lax after dissection, and during
testing?

Forward dynamics
----------------
The extra DOFs that exist when close to the neutral position can be important. We
are doing some work where we try to predict landing movements with forward
dynamics. If the knee joint is modeled as a 1-DOF mechanism, there is no
possibility for an independent internal tibial rotation at impact. This then
means that there is a large effective inertia for internal tibial rotation,
since the thigh has to rotate internally too. This will lead to overestimating
the joint loading during impact. I have no numbers yet to illustrate this,
we are just about to do a comparison between a 1-DOF and 2-DOF knee model.

This would probably have relevance also to design of total knee replacements.
A joint with 1 DOF may perform well for slow movements but maybe not during
impacts.

Other than impact response, I see no reason to have more than 1 DOF in the
knee joint when the knee is only considered for its function within a larger system,
rather than studied for its own sake. The component of the 3-D kinematics that is
not coupled to flexion is so small that it can't possibly have an influence on
muscle function or whole body movement. The lower extremity model of SIMM
(http://www.musculographics.com) does it this way. Flexion is the only DOF and
the other five have a fixed relationship to flexion angle. So it has a built-in
unloaded path of flexion, with infinite stiffness for deviations from this path.
It is not a simple hinge, but it has one degree of freedom.

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation
9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA
Phone/Fax: (216) 444-5566/9198

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