The bovine knee is similar to the human knee except for the fact that the femur and tibia are not in a straight vertical alignment when standing or walking. From my observations the femur makes an angle of about 35 degrees with the ground at the beginning of a stride.
Currently I am measuring the distance from the centre of the femoral head to the point of contact between the tibia and femur then using Pythagoras theorem to account for the angle and subsequent change in distance. On the front of the knee I also measure the distance from the point of contact between the tibia and femur and the front face of the patella. With these two distances I then use simple mechanics principles (sum of anti-clockwise moments = sum of clockwise moments) to calculate the force required on the patella side of the knee to balance the force being applied through the femur (1/4 body weight multiplied by corrected length of the femur) and then add the two forces together to estimate the total force applied at the joint. Is this an acceptable method or am I simplifying this calculation too much?
Michael,
I am not sure I understand how you are deriving your calculations. In particular, I'm not sure that 1/4 of body weight is a good assumption of the force acting on the femur during walking. Typically, peak active forces in the joints of animals will be many times higher than body weight during locomotion.
Inverse dynamics is a suitable approach for estimating resultant forces, and in order to do this, you would need to know something about the intertial properties of the animal as well as some external forces that are measurable (i.e. ground reaction forces). Actual physiological forces are trickier, and you would likely need a powerful musculoskeletal model of the animal to estimate these as well as some data regarding muscle activations.
Hi Sean,
Thanks for your response. I'll look into your suggestion immediately. Just to clarify my method I'll explain it in a little more detail.
From the literature, 45% of a cows mass is carried by the back legs. So I divide this mass by 2 for 1 leg (although I know at times one leg will be carrying this total mass but I'm not interested in this phase of the stride). Using this mass figure, I then have to resolve for the angulations of the bones relative to a plumb line dropped vertically down through the tibia. The contact point between the tibia and the femur acts as a pivot point, so the mass I calculated for one leg previously, is multiplied by the horizontal distance from this pivot point to where the mass is applied to the leg (at the femoral head). This makes up one side of a balancing beam, and in order for it to balance I then calculate the distance from the contact point between the tibia and femur, to the patella. The muscles acting through the patella I'm assuming counter act the mass acting at the femoral head. However the distance between the patella and the contact point is much shorter and hence requires a much larger force. I calculate this using beam theory clockwise moments = anticlockwise moments. The addition of these two forces then gives me the total force applied to the joint, and it generally is about 3 times bigger than the force calculated directly using 45% mass of the cow. Hope this makes more sense.
You might want to try structuring your equations based on a dynamic situation. Your description sounds like you are using assumptions typically reserved for static situations. For example, it doesn't appear that you are taking into account the inertial effects of the segment masses (thigh, shank, hoof). These aren't negligible, especially for a large animal.
A standard inverse dynamics procedure takes all of this into account, and should provide a good starting point for your calculations. Keep in mind, it will only give you resultant forces. These don't necessarily reflect the actual forces in the joint.
Thanks Sean, you've been a great help. I'll look into using an inverse dynamics procedure from now on.
To get an estimate for ground reaction forces in cows, the work of Rick vd Tol may be helpful:
P.P.J. van der Tol, J.H.M. Metz, E.N. Noordhuizen-Stassen, W. Back, C.R. Braam, W.A. Weijs, The Vertical Ground Reaction Force and the Pressure Distribution on the Claws of Dairy Cows While Walking on a Flat Substrate, Journal of Dairy Science, Volume 86, Issue 9, September 2003, Pages 2875-2883, ISSN 0022-0302, http://dx.doi.org/10.3168/jds.S0022-0302(03)73884-3.
Keywords: dairy cattle; lameness; horn; biomechanics
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