Fig 1.
Schematic inflammatory network of cartilage including the concentrations of PICs, AICs, MMPs, adipokines and Fn-fs as denoted respectively by .
Adipokines stimulate the production of PICs and MMPs as a source mediator of which concentration is regulated by adiposity. Adiposity can be varied by the system status including PAL, BMI and nutrition. Each mediator group has a rate of natural decay and the rate of production consists of the production from background, stimuli and inhibitors. Since Fn-fs are only released due to the deconstruction of tissue, the production is determined by mechanical damage and the catabolism of MMPs.
Table 1.
The classification of the obesity level using BMI [8].
Fig 2.
The sensitivity of (a) nex and (b) to the adipokine concentration at equilibrium.
nex is numerically correlated to obesity level so it measures the sensitivity of adipokine reduction due to different PALs at a certain level of obesity (EO: Extreme obesity; O: Obesity; OW: Overweight; NW: Normal weight; ND: Nutritional deficiency). is the dimensionless coefficient that determines the amount of adipokine reduction due to PAL (S: Sedentary; LA: Low active; A: Active; VA: Very active).
Table 2.
The category of PAL [65].
Table 3.
The estimated dimensionless parameters of the inflammation model.
Fig 3.
The equilibrium adipokine concentration against PAL and BMI.
Fig 4.
The boxplots of the LSA for dimensionless parameters in (a) Baker’s model [43] and (b) the adipokine-mediated inflammation model.
The values of datasets represent the percentages of change in the measured responses from the system outputs perturbed by 1 percent change of a specified parameter at the inflamed limit cycle and the healthy state. Parameters that result in output changes over 1 percent are highlighted in blue for (a) and in red for (b). Pbp: The background production rate of PICs; Ppp: The production rate of PICs driven by PICs; Pfp: The production rate of PICs driven by Fn-fs; App: The production rate of AICs driven by PICs; Aph: The concentration of AICs at which the production rate of AICs driven by PICs is half of the maximum; Afp: The production rate of AICs driven by Fn-fs; Afh: The concentration of AICs at which the production rate of AICs driven by Fn-fs is half of the maximum; Mbp: The background production rate of MMPs; Mpp: The production rate of MMPs driven by PICs; Mph: The concentration of MMPs at which the production rate of MMPs driven by PICs is half of the maximum; Fdam: Mechanical damage parameter; : Decay rate of PICs;
: Decay rate of MMPs;
: Decay rate of Fn-fs.
Table 4.
The types of dynamics presented in bifurcations. S: Quiescent stable state; L: Limit cycle; S in superscript: Stable; U in superscript: Unstable.
Fig 5.
Bifurcation diagrams of parameters in the production of PICs and MMPs: (a) Production rate of PICs driven by adipokines; (b) Production rate of MMPs driven by adipokines; (c) Saturation rate in the stimulation of MMPs by adipokines; (d) Saturation rate in the inhibition of MMPs by AICs.
Solid black lines where the pro-inflammatory is at a higher level represent the inflamed states; solid black lines where the pro-inflammatory is at a lower level represent the healthy states; dash blue lines represent the unstable states; solid blue lines represent unstable states; The scatter of blue points represents the average maximum and minimum concentration in the oscillated limit cycle.
Fig 6.
Bifurcation diagrams of parameters in the production of adipokines: (a) Production rate of adipokines due to the number of adipocytes; (b) Production rate of adipokines due to the size of adipocytes; (c) Decay rate of adipokines.
Fig 7.
Bifurcation diagrams of where (a)
,
; (b)
,
, and codimension-2 bifurcations of (c)
and
; (d)
and
Fig 8.
Bifurcation diagrams of PAL when (a) BMImeas = 25; (b) BMImeas = 35 in the production of adipokines, and (c) Codimension-2 bifurcation of and PAL.
Fig 9.
Bifurcation diagrams of Damage under different physical activity interventions when (a) BMImeas = 25 ; (b) BMImeas = 35; (c) BMImeas = 45 in the adipokine-mediated inflammation model.
The dynamics transition is presented when PAL = 2 as an example
Fig 10.
The sensitivity of the minimum damage leading to inflammation in the evolution of inflammatory activities.
Fig 11.
The evolution of inflammatory activities under different strategies of physical activity intervention in the non-dimensionalised model.