# A Novel Criticality Analysis Method for Assessing Obesity Treatment Efficacy
## 3 Methodology
### Feature Extraction Method for Analysing Gait Data  
The CARDIGAN dataset, which was collected utilising a 3-dimensional accelerometer, gyroscope, and magnetometer IMU sensor, was analysed utilising DataGait Analysis Software (DGAS) (v11.1, 2019). Developed as a standalone software analysis package by the Movement Science Group at Oxford Brookes University using LabVIEW2011 (National Instruments, Ireland), DGAS employs quaternion rotation matrices and double integration to transpose the accelerations frame of the \(z\)-axis from the object to the global system, thereby allowing for the measurement of translatory vertical CoM accelerations during walking and the achievement of a relative change in position. As referenced in [18], upward CoM measurements determine the global quality of human gait parameters. DGAS extracts critical features of individuals' gait for the purpose of classification. In this context, it becomes feasible to differentiate between biologically distinct masculine and feminine gait patterns, taking into account not only the spatiotemporal parameters that capture gait dynamics at specific time points but also the potential impact of their respective body shapes or dimensions on these distinctions. In gait analysis, a multitude of parameters are employed to comprehensively understand the complexities of human locomotion. Temporal parameters encompass fundamental measurements such as Step Time, which quantifies the duration from the initial contact of one foot to the subsequent contact of the opposite foot, and Stride Time, which denotes the time interval between successive initial contacts of the same foot. Cadence adds another layer of insight, representing the number of steps taken per unit of time. Meanwhile, spatial parameters offer dimensions to gait assessment; Step Length measures the distance between successive initial contacts of the same foot, and Stride Length extends this to cover the span from one foot's initial contact to the following foot's contact. The rate of position change during gait, known as Velocity, is calculated by the ratio of stride length to stride time. In addition, multi-dimensional parameters introduce complexity: Duty Factor gauges the percentage of the gait cycle during which each foot remains on the ground, while the Froude Number serves as a dimensionless speed parameter reflecting the interplay of centripetal and gravitational forces during walking. Finally, the Walk Ratio denotes the relationship between cadence and mean step length, offering insights into the neuromotor control of gait. Within the realm of Phase Plot Analysis, distinctive parameters emerge: Beta Angle, a measure of stability, is the angle of the primary gait phase plot axis relative to the vertical axis; SDa and SDb represent standard deviations describing the distribution of phase plot points, with SDa reflecting stability and SDb pertaining to rhythm; and Ratio (SDa/SDb) serves as a relative rhythm stability indicator. The raw data from the accelerometer are processed using DGAS software, which is founded on the inverted pendulum approach. This conversion results in 17 parameters that are used to assess the physical characteristics of each individual. These 17 gait features serve as inputs for perturbing the criticality analysis model, as represented by Equations (4) and (7), respectively. Table 1 displays the list of the 17 gait parameters.