# Use of Wearable Sensor Technology in Gait, Balance, and Range of Motion Analysis
## 5 A Taxonomy for Gait, Balance, RoM Analysis
### Gait Analysis
#### 5.2.1 Postural Sway  
A common parameter used by researchers and clinicians in static balance assessment is _postural sway_. Postural sway is the horizontal movement of the person's center of mass (CoM) in all directions. Postural sway during quiet stance has helped differentiate age-matched healthy controls from those with early untreated Parkinson's Disease and helped determine changes with disease progression in early PD [131]. Studies that use IMUs and smart devices vary in terms of where to place the sensor to measure postural sway. The studies in this review vary in terms of the sensor's location used to measure postural sway. There are some that attach the device to the lower back or lumbar spine [23; 32; 33; 47; 49; 50; 52; 55] while others have the subject hold the device on their chest/sternum with their dominant hand [29; 68]. The most common measures that describes postural sway are _sway area_, _sway range_, _sway velocity_, and _sway jerk_.  
Sway area approximates the area enclosed by the acceleration path in each axis of movement [132]. Studies vary between enclosing the path with a circle or enclosing the path with an ellipse. In both approaches, the acceleration in both the mediolateral (ML) and anteroposterior (AP) direction can be extracted using the acceleration signal at the X-axis and the acceleration signal at the Z-axis, respectively. Figure 5 shows the typical 'Spaghetti' plot that represents the acceleration sway path using ML and AP planes.  
Figure 5: Postural Sway Acceleration in ML and AP Planes (‘Spaghetti’ Plot).  
The acceleration path can be enclosed using an ellipse fitting or ellipse enclosing algorithms [133]. These algorithms can be difficult to implement with datasets that have a lot of data points. To reduce the size of the problem, researchers often use an approach called _convex hull_. A convex hull is a subset of points that defines a convex polygon that encloses all the points in the set [133]. The minimum enclosing ellipse for the convex hull is the same as the minimum enclosing ellipse for the set of points (Figure 6).  
Sway range is the maximum distance between any two points in the accelerometer data [132]. Sway range estimates how wide the acceleration was at a particular assessment time point. It can be calculated in all the different axes using Equation (12), where \(P_{axis}\) is the set of points in a particular axis [132].  
\[Range_{axis}=|max(P_{axis})-min(P_{axis})| \tag{12}\]  
Sway velocity is the velocity at which the trunk sways. Similar to gait velocity, sway velocity can be estimated using abstraction models or by direct integration.  
Sway jerk is the smoothness of the trunk sway. One of the first reviews on jerk defined the term as the \"rate of change of acceleration\" [134]. [PERSON] and [PERSON] (1985) formulated a mathematical model to predict features of coordination of voluntary human arm movements. More recently, jerk is used in many varied applications including postural sway analysis using sway jerk. Sway jerk is typically calculated for the ML-AP plane using Equation (13), where \(t\) is the time that the trial lasted and \(N\) the size of the set of points of the acceleration signal [132]. Since Equation (13) involves integration of time derivatives of acceleration components, it is important to make sure that the signal is clean and does not contain much noise since dealing with noisy differentiation signal may amplify the noises on the signal to be estimated.  
\[Jerk_{ML-AP}=\frac{1}{t}\sum_{i=1}^{N-1}\sqrt{(AP_{i+1}-AP_{i})^{2}+(ML_{i+1}- ML_{i})^{2}} \tag{13}\]