A mathematical model of forces in the knee under isometric quadriceps contractions

Objective. To predict the knee's response to isometric quadriceps contracti ons against a fixed tibial restraint. Design. Mathematical modelling of the human knee joint. Background. Isometric quadriceps contraction is commonly used for leg muscl e strengthening following ligament injury or reconstruction. It is desirabl e to know the ligament forces induced but direct measurement is difficult. Methods. The model, previously applied to the Lachmann or 'drawer' tests, c ombines an extensible fibre-array representation of the cruciate ligaments with a compressible 'thin-layer' representation of the cartilage. The model allows the knee configuration and force system to be calculated, given fle xion angle, restraint position and loading. Results. inclusion of cartilage deformation increases relative tibio-femora l translation and decreases the ligament forces generated. For each restrai nt position, a range of flexion angles is found in which no ligament force is required, as opposed to a single flexion angle in the case of incompress ible cartilage layers. Conclusions. Knee geometry and ligament elasticity are found to be the most important factors governing the joint's response to isometric quadriceps c ontractions, but cartilage deformation is found to be more important than i n the Lachmann test.