# A Novel Criticality Analysis Method for Assessing Obesity Treatment Efficacy
## 3 Methodology
### Data Collection  
The study assembled a heterogeneous cohort of 50 adolescent subjects, comprising individuals diagnosed with obesity, those with diabetes, and a cohort of healthy controls, all of whom were thoroughly recruited from Mexico Children's Hospital. Among the healthy control group, 19 were males, and there was one female participant, with ages ranging from 10 to 15 years, weights spanning from 40 to 83 kg, heights from 133 to 172.9 cm, and BMIs from 21.16 to 34. The participants with obesity included 16 males and 4 females, aged between 10 and 17 years, with weights ranging from 36 to 106.4 kg, heights spanning from 129 to 179 cm, and BMIs from 17.64 to 35.5. Meanwhile, diabetic participants consisted of 10 females aged 12 to 13 years, with weights ranging from 74.5 to 76.2 kg, heights from 159 to 159.7 cm, and BMIs from 29.5 to 30.4. It is crucial to underscore that due to an inadequate volume of available diabetic data points, the analysis was restricted to data from 20 healthy controls and 20 participants diagnosed with obesity, ensuring the robustness of the findings while acknowledging data limitations. The participants underwent a 6-week intervention program aimed at improving fitness and reducing weight. Gait analysis was conducted at baseline, immediately after the intervention, and at 3- and 6-month follow-ups. Gait analysis involved participants walking back and forth over a 30 m track for 6 min while  
Figure 1: The flowchart of the proposed CARDIGAN methodology is presented.  
wearing an inertial measurement unit sensor on their lower back. The gait data were anonymised, and approval was obtained before analysis.  
Assessment was based on the use of an inertial measurement movement sensor (IMU), placed on the fourth lumbar verteba located on the top left of the anatomical position of the lumber spine, known as the body Centre of Mass (CoM). The sensor was designed to be incredibly flexible, providing for mobility in many different planes including flexion, extension, side bending, and rotation. Gait analysis was conducted for participants using a standardised 6 m test, wherein an IMU was attached to the lower back to capture triaxial accelerometer and gyroscope data at a frequency of 100 Hz. For individuals with DPN (Diabetic Peripheral Neuropathy), the assessment took place at OCDEM (Oxford Centre for Diabetes, Endocrinology, and Metabolism) in a dedicated obstacle-free corridor. The methodology employed for deriving gait parameters has been comprehensively described in previous studies. The spatiotemporal parameters obtained from the 6 min walking test encompassed step time (measured in milliseconds), cadence (expressed in steps per minute), stride length (in meters), and walking speed (in meters per second). Furthermore, gait control parameters, which encompass measures of dynamic stability and gait variability, were evaluated utilising various instruments such as accelerometers, force plates, or motion capture technology. These assessments aimed to quantify fluctuations in temporal aspects (e.g., stride time), spatial aspects (e.g., step length), and comprehensive whole-body kinematics (e.g., segment angles). The parameters assessed included Beta (expressed in degrees), SDa (measured in arbitrary units), SDb (also in arbitrary units), ratio (in a dimensionless unit), and walk ratio (in millimeters per steps per minute). These parameters have been identified as indicators of neuro motor control [16; 17]. The dynamics of their walking activity were monitored using the Polar Team tracking system [18].