Modeling of the knee joint load in rehabilitative knee extension exercises under water

A biomechanical and hydrodynamical theoretical model has been developed in order to calculate the knee joint load during underwater knee extension exercises. The hydrodynamic force has been evaluated within the framework of a strip-theory approach, when a blunt rectangular resistive device is applied proximally to the shank to increase its frontal area. Analytical expressions of the patellar tendon force (F_pt), the axial (phy_n) and the shear (phy_t) component of the tibiofemoral joint load have been derived as a function of joint angle (theta), angular velocity (omega), angular acceleration (alpha), resistive device density, length (Lx), width (Lz) and thickness, and average hydrodynamic drag and added mass coefficients. An inverse dynamic problem has been solved, assuming for alpha and omega a dependence on theta consistent with the experimental kinematical data available in the literature. The results highlight that the characteristics of the resistive device and the level of muscular activation can be adjusted reciprocally in order to control the peak value of F_pt, phy_n and phy_t, and the position of these peaks within the joint range of motion (ROM). No anterior cruciate ligament (ACL) stress is observed (phy_t>0) over the whole ROM, independent of the level of muscular activation, for a light resistive device with Lx<0.3 m and Lz<0.4 m. This work highlights that aquatic exercises can be usefully and safely implemented in the rehabilitation program following ACL surgery, and whenever it is important to avoid excessive shear joint forces that constrain the tibial plateau anterior translation with respect to the femur.