Background and Objective: The biomedical fluid which fills the Synovial joint cavity is called Synovial fluid which behaves as in the fluid classifications to Non-Newtonian fluids. Also it’s described as a several mi- crometers thick layer among the interstitial cartilages with very low friction coefficient. Consequently, the present paper opts to investigate the influence of the concentration-dependent viscosity on Magne- tohydrodynamic peristaltic flow of Synovial Nanofluid in an asymmetric channel in presence of thermal radiation effect. Method: Our problem is solved for two models, in the first model which referred as Model-(I) , viscosity is considered exponentially dependent on the concentration. Model-(2) , Shear thinning index is considered as a function of concentration. Those models are introduced for the first time in peristaltic or Nanofluid flows literature. The governing problem is reformulated under the assumption of low Reynolds number and long wavelength. The resulting system of equations is solved numerically with the aid of Parametric ND Solve. Results: Detailed comparisons have been made between Model-(I) and Model-(2) and found unrealistic results between them. Results for velocity, temperature and nanoparticle concentration distributions as well as pressure gradient and pressure rise are offered graphically for different values of various physical parameters. Conclusions: Such models are applicable to rheumatoid arthritis ( RA ) treatment. Rheumatoid arthritis patients can be treated by applying the magnetic field on an electrically conducting fluid, due to the movement of the ions within the cell which accelerates the metabolism of fluids.