Dynamic optimisation is another method for gait simulation. This often involves forward dynamic techniques and is used to predict the motion of the model over a given time. Thus, in contrast to static optimising, the predictions made for late stance are dependent upon what has happened earlier in the cycle.
Since this method uses forward, rather than inverse dynamics, simulations require much more computational effort to achieve a solution and so large numbers of muscles would slow the process down considerably, making it impractical. These types of studies tend to use single actuations to represent the effort of muscle groups (e.g. iliopsoas, vasti, hamstrings, dorsiflexors etc.), which can still pinpoint a problem area for a participant, albeit not with the same precision. Typically these models will model ten or fewer muscle groups (Davy & Audu, 1987; Yamaguchi & Zajac, 1990) but more recent models have been able to utilise more powerful computers to consider over 20 individual muscles (Anderson & Pandy, 2001a; Jonkers et al., 2003).
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They are predictive and have time-dependent objective functions. This means that novel movements can result and it is also possible to investigate the overall goal of a particular motor task (Ren et al., 2007; Thelen & Anderson, 2006). This can be particularly useful for those investigating motions other than walking (Hatze, 1981), where there is a more obvious measure of performance i.e. jumping higher, farther, etc.
This ability to produce novel motion can lead to physically impossible solutions being produced so it is often necessary to apply constraints to the joints of the model to avoid things like hyperextensions (Anderson & Pandy, 2001a, 2001b; Anderson & Pandy, 2003; Ren et al., 2007).
As mentioned, the types of objective functions differ between static and dynamic optimisations. Previous static optimisation works have used functions such as muscular endurance (Crowninshield & Brand, 1981), a fatigue criterion accounting for stride time, kinematics and joint forces and moments (Koopman et al., 1995), the sum of the squared muscle stresses (Glitsch & Baumann, 1997) or the sum of the cubed muscle stresses (Pedersen et al., 1997). Opinion seems to largely be in favour of the main goal of walking being to reduce the effort required from the muscles. A similar trend is apparent when the cost functions of dynamic optimisation studies are observed; metabolic expenditure per distance travelled (Anderson & Pandy, 2001a, 2001b; Anderson & Pandy, 2003), the sum of total work done by the muscles and enthalpy change during contraction (Davy & Audu, 1987), the mechanical energy cost (Channon et al., 1992; Marshall et al., 1989; Ren et al., 2007; Yen & Nagurka, 1987).
Other optimisations will be defined so that they track a data set gathered from laboratory testing and the judgement of performance will come from how well other predictions match another data set. For example, the muscle forces are controlled so that the kinematics of the joint angles correlate which their empirical counterparts. Then a comparison can be made between these predicted muscle forces and experiment EMG recordings (Thelen & Anderson, 2006). Equally, the EMG readings could be tracked to observe whether the correct kinematics result (Jonkers et al., 2003). There are many ways of comparing the tracking errors and quantifying the error for the performance criterion. Such examples include incorporating static optimisation within a dynamic one (Thelen & Anderson, 2006) or a simple least squares method (Cappozzo et al., 1975).
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2.3
Validation
With any simulation it is important to provide validation so that the results can be considered accurate. The most common way to do this is by means of experimental data captured in a gait laboratory. In the world of gait modelling, a low number of participants is quite common, perhaps only five or six (Anderson & Pandy, 2001a, 2001b; Anderson & Pandy, 2003; Crowninshield et al., 1978; Patriarco et al., 1981). Some studies have only used a single participant (Glitsch & Baumann, 1997; Pedersen et al., 1997). The justification for these low numbers is that often it is the performance of the model that is being examined, as opposed to some hypothesis regarding a particular group of participants. In fact, it could be argued that a large number of participants could be detrimental to the simulations. Gait data is often captured and presented in terms of
‘percentage of the gait cycle’ rather than in terms of absolute time. The instances at which certain gait events occur varies between participants so taking a data curve averaged across multiple participants could potentially be less representative than using a single person’s data. In clinical applications, the model would only be used for an individual participant anyway.
Gait analysts used to capture the motion of the participant by attaching LEDs to specified anatomical landmarks and, from the path of these LEDs captured by cameras, the segment positions and joint angles could be calculated (Crowninshield et al., 1978; Röhrle et al., 1984). More recently, researchers have been able to use reflective markers that are tracked by infra-red cameras to perform this same task (Anderson & Pandy, 2001a; Anderson & Pandy, 2003; Glitsch & Baumann, 1997; Pedersen et al., 1997). For the kinetics, almost all studies will use a walkway instrumented with force plates to record the GRF and perform multiple trials per participant, although it is possible that even intra- participant averaging could lessen accuracy. Many will also record electromyographic (EMG) data to provide knowledge of the temporal changes in the activation of different muscles (Anderson & Pandy, 2001a; Anderson & Pandy, 2003; Crowninshield et al., 1978; Davy & Audu, 1987; Glitsch & Baumann, 1997; Patriarco et al., 1981; Pedotti, 1977;
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Yamaguchi & Zajac, 1990). Information detailing the best ways to perform such experiments is readily available (Delagi & Perotto, 1980).
The anatomical parameters, such as segment lengths and the participant’s height and weight can be measured in the gait lab, thus making the model participant specific. Generic values, as well as information gathered from cadaver studies regarding the inertial properties of different body segments, can be found in previous works (Crowninshield et al., 1978; Winter, 1979). These data sources are widely accepted and used in other works (Yamaguchi & Zajac, 1990) due to the difficulties and administrative processes involved in obtaining permission for cadaver studies.