The moment that we obtain from inverse dynamics tells us which muscle (flexor or extensor) is active, and how much moment (torque) that muscle is exerting. A common standard method of representation of these moments in graphical form, a flexor moment (dorsiflexor at the ankle) is shown as positive, while an extensor (plantarflexor at the ankle) moment is negative.
For example, the ankle moment curve (fig. 2) indicates a negative (plantarflexor) moment throughout nearly all of stance, with a very brief and small dorsiflexor moment immediately after heel-strike. The curve tells us that the main muscle group active at the ankle throughout stance are the plantarflexors (tricpes surae), with steadily increasing activity through stance up to a maximum just before toe-off, shown in the video picture. Note that there is a range of values at each time interval - we don't all walk exactly the same! - the range shows the mean value ± 1 standard deviation of a selection of normal individuals..
Fig. 2: Ankle moment during normal gait
Joint moment thus tells us which muscle (flexor or extensor) is contracting. It does not tell us why that muscle is contracting. For that we must look at what is termed the mechanical power. This is the joint moment multiplied by the angular velocity of the joint. So, if the joint is not moving (an isometric
contraction), the angular velocity, and therefore the power, will be zero. If it is moving in the direction of the muscle contraction, the power will be positive, corresponding to concentric
contraction of the muscle. If the joint is rotating away from the direction in which the muscle is pulling, the power will be negative, denoting an eccentric
contraction. This is very useful, because it tells us the function of a muscle contraction: whether the muscle is being used to do external work
, or to absorb energy
, in effect to accelerate
Fig. 3: Mechanical power at the ankle
The moment and power curves together therefore tell us everything we need to determine the function of the musculature during a movement. It is sometimes a little difficult to look at two curves simultaneously, however. A somewhat easier method is to plot the data instead as a bar graph, with the sign indicating the moment and colour (or shading) of the bars indicating power (fig. 4):
Fig. 4: Ankle joint activity
This chart shows us everything we need to know about the activity of the ankle joint musculature, clearly indicating the two distinct roles of the plantarflexors during stance. It also nicely shows the small eccentric contraction of the dorsiflexors (tibialis anterior and the peronei) immediately after heel-strike to control the foot as it lands, and their concentric contraction to lift the foot during swing.
Figs. 5 & 6 show the same plot for the knee and hip joints.
Fig. 5: Activity of the knee-joint musculature (cursor and video shown in K4 phase).
The knee shows 4 phases of distinct activity. K1 is the first eccentric phase and relates to quadriceps function during the loading response. K2 represents the same muscle group now acting concentrically to pull the trunk over the stance leg (about 10-15% of the forward energy of gait). K3 is an eccentric contraction of the quads to brace the knee against the strong contraction of the triceps (especially gastrocnemius, which tends to flex the knee as it contracts) at push-off. K4 is hamstrings braking of the leg during late swing, which increases greatly in running, when the leg swings forwards much more vigorously (with higher angular velocity).
The hip shows three rather small contractions (though there is considerable variation in hip function in normal individuals). H1 is a so-called push-from-behind caused by the gluteus maximus and hamstrings. It may contribute a small amount of forward energy, but is mainly used to stabilise the trunk at heel-strike. H2 is an eccentric burst to retard the backwards rotation of the thigh during stance, and H3 is so-called pull-off, coinciding with ankle push-off. H3 is also very much increased in running.
Limitations of Inverse Dynamics
Inverse dynamics is a very powerful technique for understanding movement, but it does have some inherent limitations:
- it relies on assumptions that are not always valid - specifically:
- there may be friction at the joint (e.g. in arthritis)
- the distribution of mass in the segment is not uniform, and certainly not concentrated at one point
- estimating the joint center of rotation is prone to error (Holden & Stanhope, 1998)
- the typical models (e.g. Helen Hayes) used rely heavily on anthropometry to define the hip joint center (because it is deep and so can't be directly defined by a marker)
- the joint center of rotation may also (and often does) move during motion, especially at the knee
- some models (e.g. Cleveland model and six degree of freedom model used at NIH using marker triads) make less assumptions in this respect
- measurement error (Holden et al, 1997)
- the worst of these tends to be inaccuracies in co-alignment of the force platform and motion analysis system
- best checked by a "stick" or "poker" test (Baker et al, 1997)
- marker motion on the skin - especially "wand" type markers on sticks
- motion at the skin-bone interface
- marker tracking is sometimes contaminated by errors due to interpolation when markers go missing and data from some frames is lost
- body segment parameters (anthropometry) are approximations and generalizations
- very thin or overweight people, childrena and patients with wasted legs may have different proportions
- note that this will mainly affect the swing phase - during stance the ground reaction forces are dominant and accelerations are minimal
- special consideration must be given to amputees, in order to use values appropriate to the prosthesis components
- error propagation (the errors of the distal joint calculations affect those at more proximal calculations)
- it can only determine the NET moment and power
- co-contraction of antagonistic muscles will cancel out - important in spastic conditions such as cerebral palsy and stroke
- it cannot differentiate between different muscles
- e.g. we can determine that the joint moment is flexor, but not the relative activity of each flexor muscle
- for this we need electromyography (but note that this is not without its problems too!)
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