Welcome back to Basics of Biomechanics, a series of blog posts covering foundational topics in the field using practical, data-driven examples. In this post we cover one of the fundamental approaches to analyzing biomechanical measurement data: extracting discrete outcomes.

In order to capture human movement in adequate detail, biomechanical equipment generates thousands, if not tens or hundreds of thousands, of data points per second. Usually, the only hope for finding something meaningful in this deluge of numbers is to extract summary metrics (outcomes) that we can more easily interpret. Part of the skillset of a biomechanist is being able to formulate biomechanically relevant questions, choosing the outcomes that will address these questions effectively and then interpreting them in a given context. In this post, however, we will focus only on the basic theoretical process of extracting outcomes from a single data recording.

*Challenge #1: if you were to open the text file containing the force data for the graph above and see that the sample rate was 1000 Hz, how many data points would you expect to see in the force signal column, at a minimum? Hint: assume that the entire recording was as at least as long as the time values on the horizontal axis (humanly speaking, it is an unmanageable amount!).*

Let us return to the jump analysis example and assume that we have already completed the phase segmentation for our countermovement test recording, calculated our signals and conditioned them. If you have not yet read these posts, please consider doing so before continuing here.

## Types of discrete outcomes

There are many different ways to categorise biomechanical outcomes. We could group outcomes in terms of sensor type (force plate, camera system, etc.), data type (kinematics, kinetics and EMG) or application (jump performance, strength outcomes, symmetry outcomes, etc.). Here we will take the approach of categorising outcomes in terms of how they are extracted:

1. **Points of interest **(signal values at a specific event in time)

2. **Phase statistics **(summary metrics for a signal over the duration of a phase)

3. **Application features **(specialised metrics that are usually activity-specific)

Point of interest outcomes are relatively trivial to extract. They are simply the value of a particular signal at a particular *point *in time (usually an event inserted into the timeline during phase segmentation). For our countermovement jump analysis, we may be interested in the force at the Turn event (1472 N) as an indicator of the amount of pre-tensioning that has built up in the stretch-shortening cycle. If we are performing a group analysis or comparing this outcome to group reference data, we may also normalise it relative to the jumper’s body weight or body mass (many discrete outcomes are normalised in this way so that we can compare people of different sizes where anthropometry influences the outcome measure). We may also be interested in analysing the take-off velocity (2.14 m/s).

Phase statistics are extracted using generic data reduction techniques and provide a summary of some portion of a measured or calculated signal. They are single values that typically quantify amplitude characteristics such as central tendency, extrema (max and min) and variability across all the samples in a signal during a particular phase. They may also reflect spectral characteristics such as the power in certain frequency ranges. Each summary metric has advantages and disadvantages which are important to understand in relation to our biomechanical interpretation. Range metrics, for example, are useful for things like range of motion in joint angle signals but are also highly sensitive to outlier values. This may not be desirable if you are actually interested in overall variability, in which case it may be better to consider another statistic such as the variance or standard deviation. Similarly, it is worth considering whether a mean or median statistic is more suitable for a given case.

In our jump analysis, depending on our question, we may want to extract phase statistics such as peak power during propulsion (2397 W) or the mean power during propulsion (1418 W). We may also be interested in the minimum force during the countermovement (177 N) or the range of force (1295 N). Considering these values together may give us deeper insight into the jumpers athletic abilities than interpreting them separately. For example, if peak power is high and mean power is low this may lead to a different conclusion than if mean power is high and peak power is low.

A simple yet very useful phase statistic is the duration of a phase. In the case of our countermovement jump example, we can determine that the time to take-off (from Initiate to Take-off) is 828 ms and that the flight time is 452 ms. A surprising number of outcomes can be derived from this basic information. The flight time can actually be used to calculate the jump height (more on this in the section on application feature outcomes below). We can also derive a well-known outcome called the Modified Reactive Strength Index (RSI_{mod}) from these two phase durations. RSI_{mod} is the ratio of flight time over ground contact time and is another measure of jump explosiveness. For this jump we get an RSI_{mod} value of 0.546 (the ratio is unitless).

*Challenge #4: We now have three discrete outcomes describing aspects of jump explosiveness (mean power, peak power and RSI _{mod} ). Which one of these outcomes would you use to assess explosive capability? Does it make sense to interpret them together? What if their interpretations are in conflict? *

Many discrete biomechanical outcomes are application feature outcomes. These are data reductions related to a specific type of test or analysis (or group of similar applications). For example in gait analysis, step length and cadence are popular feature outcomes. Similarly in postural sway analysis using pressure distribution measurements, a large number of features have been developed to describe aspects of balance performance such as the sway area or time-to-boundary. One common feature in countermovement jump analysis is the Rate of Force Development (RFD) during the eccentric loading phase (blue line in the graph below). This can be defined as the average slope of the curve from minimum eccentric force to the force at the Turn event as shown below (4191.6 N/s).

Another classical example of a countermovement jump application outcome is jump height calculated by flight time (see the green and red curves in the figure above). This outcome is determined by making the assumption that the jumper travelled the same distance up as they travelled down. In this case, since we know that the COM velocity is zero at the top of flight and we know that COM acceleration is equal to 9.81 m/s^{2}, we can calculate how far the jumper will fall down before running out of time (half the flight time) using Newton’s laws of motion:

*position change = v _{initial} t + 0.5at^{2} *

*i.e.*

*Jump Height*= (

*g/2) (flight time/2)*

^{2}Many outcomes have advantages and disadvantages to consider. If we think about it, we can actually determine jump height without a force plate if we have another way to measure flight time. We might use a video camera or a sensor that can detect take-off and landing such as a pressure mat or an inertial sensor (all of which are much more affordable). However, the flight time calculation has a weakness. It assumes that the jumper reaches the top of flight in the middle of flight, which is not always true. If our jumper lands in a very crouched position they can artificially increase their flight time and thus their jump height score, when in fact they didn’t jump higher (they just fell further). Luckily, jump height is a good example of a discrete outcome that can be determined in more than one way. Since force plate data can provide us with the take-off velocity, we can calculate jump height using another of Newton’s laws of motion that doesn’t assume anything about flight time

*change in position = ( v _{final} ^{2} * –

*v*)

_{initial}^{2}*/ 2a*

i.e.

*Jump Height*=

*v*

_{takeoff}^{2}*/ 2g*

Actually, this is essentially equivalent to calculating the area under the *v _{COM}* curve from take-off until

*v*reaches zero, or in other words taking the change in the

_{COM}*p*curve between take-off until the

_{COM}*v*reaches zero (see the figure below).

_{COM}*Challenge #5: Notice that the jump height values differ. Force-based calculations of jump height are usually preferred as more accurate than flight-time based calculations. Which one do you trust? Can you think of any reasons why using take-off velocity could be less accurate at times if data processing is imperfect? Hint: consider all the factors in this blog post that affect the calculated velocity curve and thus take-off velocity (body weight estimation, the Initiate event time, the take-off event time, force plate errors).*

## Conclusion

Biomechanists are facing the challenge of extracting value from increasingly large biomechanical datasets. This post offers only a basic introduction to this very broad topic. Whether you are working with outcomes that are provided by proprietary software or custom-built data processing pipelines, it is important to continuously engage individually and collectively – with analytical rigour – around the details of how these outcomes are extracted. This rigour is essential for building confidence in our biomechanical analyses and minimising the risks of serious error. Of course, for biomechanics enthusiasts, it can also be quite enjoyable to explore and master the technical aspects of a given set of analytical outcomes.

Please feel free to leave a comment if you are interested in sharing your experiences, asking questions or giving constructive feedback on how this post presents the topic. We can also discuss the answers to the challenges!