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Why is center of pressure calculated relative to the transverse plane only

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Simon Spooner, Feb 10, 2011.

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    All, why is center of pressure calculated using X and Y co-ordinates in the transverse plane? Great if we are walking on a flat surface; questionable when walking on the 3-dimensional curves of an orthosis- right? Can CoP be calculated in 3-dimensions?
  2. davidh

    davidh Podiatry Arena Veteran

    You asked two questions.
    The first is easy to answer - it is relatively simple and inexpensive to calculate and record COP in the transverse plane only. It's fairly relevant to normal walking - arguably as relevant as any gait lab studies are.

    The second question "can COP be calculated in 3-dimensions" is interesting (I don't have the answer). I have another question - would COP in 3-D show anything additional other than sinusoidal motion?
    I'm not sure how 3-D COP would be relevant to gait in normal life (as opposed to life in a gait lab).

    As an aside, and perhaps to illustrate the fact that research tools can be great fun but sometimes not much use clinically, I remember seeing a Vicon system in action some years ago. For those not familiar with this system it consists of a Kistler forceplate to collect vertical loading data (Wikipedia:rolleyes: suggests it collects 3-D data so perhaps thats the answer?), and sway.
    The forceplate is synchronised with five cameras lit by strobe. The subject has reflective markers taped to shoulders, elbows, wrists, hips, knees and ankles, and is videoed walking over the forceplate.

    This was a state-of-the-art NHS gait lab facility in Edinburgh. I seem to remember there were only two in the UK at the time. The system itself (not the lab) cost around £500,000.00.
    It was nothing to do with the Edinburgh School of Podiatry, just to avoid any confusion. I was invited in as a post-grad student - guest of Med Physics Dept at Dryburn Hospital in Durham..

    The data collection and analysis took around three hours per subject.

    I was hugely impressed, until I enquired of one researcher what the results were used for.
    "Oh, mostly to persuade surgeons not to operate on CP kids".
    Not, you will note, to present objective data so that surgeons can make an informed decision on whether or not to operate.
    In fact the data itself seems to have been rarely presented.

    In light of that it seemed about as much use as the much-vaunted optical pedobarograph at Dryburn which was used in the 80's to look at arch-height and justify dishing out sorbothane insoles to orthopaedic patients.
    Last edited: Feb 10, 2011
  3. efuller

    efuller MVP

    The ground is the transverse plane. If we want to look at ground reaction force we have to look where it is applied. If we were walking on walls then we would want to look at forces perpendicular to the plane of the wall.

    The vast majority of ground reaction force is vertical. So even if you stand on an irregularly shaped device, you will still want to know where the vertical force will be applied.


  4. Yes we walk on the transverse plane, but when walking upon an orthoses we are walking on a 3-dimensional surface, not a flat one. Yet we only use a 2-dimensional calculation of a 3-dimensional quantity? Indeed, very few of the pressures exerted at the foot-orthosis interface will be perpendicular to the transverse plane, since very little of the orthotic shell will be parallel to it.
  5. David Smith

    David Smith Well-Known Member


    If your talking strictly of Pressure as force applied to a surface area then I would say no. Pressure by definition is only one dimensional i.e. normal / perpendicular to that surface at the point of measurement. The CoP can only be calculated if you have information about the distribution of 2, and preferably 3, or more discreet normal forces applied in the plane of the pressure field of interest. The normal forces have only 2 rotational degrees of freedom, if they had 3 degrees of rotational freedom then they would also have 2 or 3 degrees of translational freedom and so the normal forces would be applied to planes outside or not normal to the plane of interest for the measured pressure and so not be relevant to any pressure calculation on that plane.

    For instance if you consider a sphere with an even force applied to the total outside surface area, then we would know that the centre of pressure could be calculated as at the centre of the sphere and without any determinable direction, which is useless as a determination or description of CoP on the surface of interest. So any curvilinear surface that contains or is a boundary for a space and has a force applied to it will most likely return a CoP within that space and not on the surface and even if the CoP was determined to be on the surface and in some direction then this would be meaningless in terms of any pressure plane not perpendicular to that pressure vector.

    If you were talking Centre of Force (CoF) calculated from many discreet force measurements over a surface of interest then it would be valid to calculate CoF if we knew the direction and magnitude of each force and their distance from a 3D point of reference This is similar to how a force plate works when it returns or determines a force vector from applied forces in all axes.

    E.G. So from each force cell you would have to define a 3D axis system common to all the cells (i.e. a reference frame) and determine the three component forces that make up the single applied force in both direction and magnitude relative to the reference frame. Then for each cell the you could calculate the moment about some predefined point in space applied by each component force. Then by summing all the moments from each cell you would arrive at a single moment in a given direction within a 3D reference frame. This could be expressed or characterised as a single force with a determined magnitude and direction that would equal a centre of force vector. The major problem here is how to determine the force direction of each cell's discreet applied force.

    The problem is exactly the same problem as in the 2D pressure measuring device except that you always know the reference frame i.e. direction of the applied discreet force because it is normal to the cell and the whole cell matrix, unless of course you decide to drape the matrix over a foot orthotic, as we have explained in our recent paper in JAPMA.

    Regards Dave Smith
    Last edited: Feb 13, 2011
  6. efuller

    efuller MVP

    Further thought. During single limb stance the vertical force on the foot has to oscillate around body weight. If it doesn't you would have sink through the floor. So, you can't reduce the total vertical force when stand or walk on an orthotic. The vertical vector will still be the biggest.

    Also the vectors in the transverse plane will have to cancel each other or there will be horizontal acceleration. Friction or "walls" (lateral heel cup with medial heel skive.)

  7. Dananberg

    Dananberg Active Member

    I have a bit of a different take on CoP intrepretation. First, I have found CoP of greatest value when the speed at which it advances is assessed. Advancement of CoP towards the forefoot occurs during single support. Gradual, heel to met head progression is ideal. What is visualized as pathologic are periods in which CoP stops or slows substantially. The longer the duration of this “delayed advancement” period, the greater the stress. On the force/time curves, this same period is represented by periods of flatness on the graph, ie constant force. Since the movement of the CoM is expressed as the forward advancement of the CoP, then lack of CoP motion at the time when CoM motion is greatest represents the difference between Power-In and Power-out during the gait cycle. When the CoM moves, but the CoP does not, the foot must accommodate the advancement of the body above it. Excess pronation at the foot level is the manifestation of this process.

    Now, instead of nitpicking the graphic effects between a curved foot orthotic vs. the flat state, it is far more important to recognize that the plantar foot surfaces are not flat, but ovoid. Perhaps, the couple between the inverse surfaces (foot and orthotic) make the combination “flat” and positively, rather than negatively, influences the fluidity of the step.


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