Dear Biomch-L readers,

Now that Herman Woltring has shown us the mathematical

relationships between various definitions of joint

moments/forces, as well as the 3-dimensional generalization, I

want to point out a difference between two views on dynamic

analysis. In my view this is important to clarify the discussion.

Herman is deliberately limiting the discussion to *net* joint

kinetics, i.e. the model consists of rigid links with one force

and one moment transmitted by each joint. These variables are

calculated, plus sometimes the joint powers (moment x angular velocity).

The analysis essentially stops there, and individual muscles are

not part of the model. This is probably a good method for clinical

gait analysis, because no detailed information on muscle lines of

action is needed, and no assumptions on load sharing of muscles have to

be made. However, these joint forces and moments are not physical

quantities but mathematical abstractions: they do not exist at all

anywhere in the system. When I say 'not exist', I mean that there

is no anatomical structure loaded by (= deformed as a function of)

either the force or the moment. Is that not a good definition of

'physical existence' of a force: that it produces a deformation

somewhere that has a one-to-one relationship to the force? Hmm,

you could even say that force is then also a mathematical

abstraction, and that only stresses 'exist'. But let's accept the

concept of force (muscle force, ligament force, contact force...)

for now.

Another way to look at 'net kinetics' analysis is as a

transformation of the original kinematic, kinetic and

anthropomorphic measurements, intended to facilitate the

(clinical) quantification of 'gait quality' or the recognition of

certain abnormalities. A mechanical interpretation of the

resulting 'net kinetics' variables is not the real purpose of the

analysis (apart from the fact that, strictly speaking, it is not

even allowed - see above). Looking at it this way, I must agree

with Ian Stokes that it does not really matter which reference

point is used to calculate the joint moment. Just as long as you

use the same reference point when comparing results, and the

variables obtained still contain useful information. In fact,

using a fixed point is to preferred above the elusive ICR. The

ICR can only be estimated when the kinematic data are of

sufficient quality, and even then requires sophisticated filtering

and analysis methods. For such a 'net kinetic' analysis it might

be more reliable to use the lateral epicondyle as reference at the

knee, rather than the ICR, because it can be marked directly and

measured by the measuring system. The choice of reference point

does require standardization however, to avoid problems when

comparing published results.

Many biomechanicians however, *are* interested in real muscle

forces and real joint forces, and try to estimate them as well as

possible. These forces are not mathematical but physical

quantities. There are of course the well-known indeterminacy

problems because the equilibrium equations for moment and force

often have too many unknowns. For some situations however, such an

analysis is the right tool for the job. In that case, the reasoning

of my previous posting applies: the ICR is the only point about which the

moment arms of muscle forces (dL/dA) and joint forces (zero) are easy to

obtain. (For simplicity I limit the discussion to 2D). Note that the

'net joint force' resulting from this type of analysis is not the same

as in the 'net kinetics' analysis, but is much larger (and more

realistic). This force may also be only a resultant of several physical

(contact & ligaments) forces, but the muscle forces that have been

obtained are real physical quantities.

So my revised opinion is: use the ICR as reference point when

estimating muscle and joint forces. For a 'net kinetic' analysis,

only standardization is required; there is no preferred reference

point. Clinical usefulness seems to be more important than mechanical

interpretation in that case.

Finally, this is probably a very academic discussion without

practical implications; the various definitions reviewed by Ian

Stokes produce very similar results. But sometimes it is

enlightening to think about why you do things one way, and not the

other way.

-- Ton van den Bogert

University of Utrecht, Netherlands

Now that Herman Woltring has shown us the mathematical

relationships between various definitions of joint

moments/forces, as well as the 3-dimensional generalization, I

want to point out a difference between two views on dynamic

analysis. In my view this is important to clarify the discussion.

Herman is deliberately limiting the discussion to *net* joint

kinetics, i.e. the model consists of rigid links with one force

and one moment transmitted by each joint. These variables are

calculated, plus sometimes the joint powers (moment x angular velocity).

The analysis essentially stops there, and individual muscles are

not part of the model. This is probably a good method for clinical

gait analysis, because no detailed information on muscle lines of

action is needed, and no assumptions on load sharing of muscles have to

be made. However, these joint forces and moments are not physical

quantities but mathematical abstractions: they do not exist at all

anywhere in the system. When I say 'not exist', I mean that there

is no anatomical structure loaded by (= deformed as a function of)

either the force or the moment. Is that not a good definition of

'physical existence' of a force: that it produces a deformation

somewhere that has a one-to-one relationship to the force? Hmm,

you could even say that force is then also a mathematical

abstraction, and that only stresses 'exist'. But let's accept the

concept of force (muscle force, ligament force, contact force...)

for now.

Another way to look at 'net kinetics' analysis is as a

transformation of the original kinematic, kinetic and

anthropomorphic measurements, intended to facilitate the

(clinical) quantification of 'gait quality' or the recognition of

certain abnormalities. A mechanical interpretation of the

resulting 'net kinetics' variables is not the real purpose of the

analysis (apart from the fact that, strictly speaking, it is not

even allowed - see above). Looking at it this way, I must agree

with Ian Stokes that it does not really matter which reference

point is used to calculate the joint moment. Just as long as you

use the same reference point when comparing results, and the

variables obtained still contain useful information. In fact,

using a fixed point is to preferred above the elusive ICR. The

ICR can only be estimated when the kinematic data are of

sufficient quality, and even then requires sophisticated filtering

and analysis methods. For such a 'net kinetic' analysis it might

be more reliable to use the lateral epicondyle as reference at the

knee, rather than the ICR, because it can be marked directly and

measured by the measuring system. The choice of reference point

does require standardization however, to avoid problems when

comparing published results.

Many biomechanicians however, *are* interested in real muscle

forces and real joint forces, and try to estimate them as well as

possible. These forces are not mathematical but physical

quantities. There are of course the well-known indeterminacy

problems because the equilibrium equations for moment and force

often have too many unknowns. For some situations however, such an

analysis is the right tool for the job. In that case, the reasoning

of my previous posting applies: the ICR is the only point about which the

moment arms of muscle forces (dL/dA) and joint forces (zero) are easy to

obtain. (For simplicity I limit the discussion to 2D). Note that the

'net joint force' resulting from this type of analysis is not the same

as in the 'net kinetics' analysis, but is much larger (and more

realistic). This force may also be only a resultant of several physical

(contact & ligaments) forces, but the muscle forces that have been

obtained are real physical quantities.

So my revised opinion is: use the ICR as reference point when

estimating muscle and joint forces. For a 'net kinetic' analysis,

only standardization is required; there is no preferred reference

point. Clinical usefulness seems to be more important than mechanical

interpretation in that case.

Finally, this is probably a very academic discussion without

practical implications; the various definitions reviewed by Ian

Stokes produce very similar results. But sometimes it is

enlightening to think about why you do things one way, and not the

other way.

-- Ton van den Bogert

University of Utrecht, Netherlands