# Altered Mechano-Electrochemical Behavior of Articular Cartilage in Populations with Obesity
## 2 Material and Methods
### Simulation of the Articular Cartilage Behavior for People with Obesity  
To study the effect of the variation of mechano-electrochemical parameters on cartilage behavior, the experimental design described by [PERSON] et al. [21] is computationally reproduced. Thus, a cartilage specimen of 1.5 mm diameter and 0.5 mm depth is placed inside a circular impermeable confining ring and a loading permeable pattern is located at the top of the sample. Tissue samples are hydrated in NaCl solution of 0.15 M similar to the physiological state. Under these conditions, maximal compression loads relating to healthy people and people with obesity are applied on top of the sample. The applied pressure is that corresponding to the maximal pressure observed after 0.44 seconds of the human gait cycle. For the sake of simplicity, it is considered that, in later cycles, the tissue will exhibit similar behavior to that taken as a reference. The experimental data are extracted from [11]. Note that, for this study, they developed specific measurements in a total of 20 male subjects (10 normal and 10 obese) aged between eighteen and thirty-five volunteered for this study. Prior to experiments, anthropometric and body measurements were collected and recorded. Clinical guidelines are established to evaluate the grade of obesity in adults by considering the Body Mass Index (BMI). This measure correlates the weight with the height of an adult to assess obesity. Thus, values of BMI between 18.5 and 24.9 kg/m\({}^{2}\) represent a suitable weight for adults, whereas a BMI higher than 30 kg/m\({}^{2}\) indicates obesity. In the model calculations, the applied force and subsequent pressure are extracted from [11] who consider two groups of study: people of normal weight, BMI = 22.262 \(\mp\) 1.172 kg/m\({}^{2}\), and people with obesity, BMI = 33.978 \(\mp\) 3.629 kg/m\({}^{2}\). The other cartilage properties introduced into the computational model are listed in Table 1.  
Accurate quantifications of cation fluxes and distributions within the samples have been performed. Besides, monitoring of tissue changes during the loading processes was also carried out. Note that this model can be employed to study the cartilage behavior in function of the degree of obesity, how long an individual has been obese, co-morbidities, and sex of subjects. Besides, it can be a good tool to study specific cases such as normal and obese rats or rabbits. For all of these studies, experimental data are required to be carried out. Three linear 8-node hexahedral elements with 2 \(\times\) 2 \(\times\) 2 Gaussian integration points are used. The selected average mesh has a total number of 1680 elements. Small-deformation finite element formulation, similar to previous articular cartilage models [11; 22; 28], has been implemented in a user defined element subroutine (UEL subroutine following Abaqus standard names) of the commercial software package Abaqus 6.11 (Dassault Systemes, Paris, France, 2016). The implementation scheme of the 3D mechano-electrochemical model used for the loading problem is shown in Figure 2.