Content area
Abstract
In the absence of earlier detailed model studies and in continuation of our OKC flexion and extension simulations, this work aimed to perform a detailed computational model study. To do so, a complex, validated 3D knee joint model consisting of three bony structures and their articular cartilage layers, menisci, principal ligaments, patellar tendon, hamstrings and quadriceps muscle groups is used. For unconstrained boundary conditions, the femur is fixed while the tibia and patella are left free except in flexion that is prescribed. Ligaments are modeled by uniaxial elements with different prestrains and nonlinear properties (no compression). Cartilage layers are isotropic elastic whereas menisci are composite with collagen fibrils in radial/circumferential directions. After the application of ligament pre-strains, the tibia is flexed at an interval of 10° from 20° to 90°. Reaction force of 303.3 N (half a female body weight of 61.9 kg) is applied at foot at a sagittal lever arm generating moments reported in female subjects during squatting. At each flexion angle, quadriceps forces are then sought that counterbalance these moments. Nonlinear analyses are performed using ABAQUS 6.7 program.
In the reference case (a) with identical femoral and tibial orientations, vertical reaction force of 303.3 N at foot generates knee joint moments increasing from 14.59 Nm at 20° to 59.4 Nm at 90°. Similar cases but subjected to idealized pure moments with no reaction force (case b) are also considered. In case c, greater reaction force of 453.3 N (i.e., in presence of a 300 N in hands) at the same lever arms is applied at 20° and 90°. The role of 10% coactivity in hamstrings (178 N) is also investigated in case d at 20° and 50°. Finally at 90° and under the same moments as in case a, tibial and femoral orientations are altered from 45°-45° to either 60°-30° (case e) or to 75°-15° with 400 N load added in hands (case f).
Total force in quadriceps muscles substantially increase with flexion and joint moment reaching peak of 5560 N in the case c. They increase with loads in hands and hamstrings coactivity. Same trends are computed for patellar tendon (PT) force where it increases with flexion to 1575 N in case ( a) and 2312 N in case c. The ratio of PT force to quadriceps force diminishes in all cases from ∼0.95 to 0.40 as joint flexes from 20° to 90°. The effective lever arm estimated as the ratio of joint moment to PT force diminishes with joint flexion from 51.7 mm to 38.7 mm (case a). Small anterior cruciate (ACL) forces (<46 N, except in pure moment case b that reaches 141 N at 60°) are computed that disappear at flexions >50°. The posterior cruciate (PCL) (<20 N) as well as the medial collateral (MCL) (<50 N) and lateral collateral (LCL) (<35 N) ligament forces remain also small. The tibiofemoral (TF) contact force increases markedly with flexion from 598 N at 20° to 1689 N at 90° in case a and peak of 2507 N (>4 times body weight) at 90° in case c. Similarly, the patellofemoral (PF) contact forces increase substantially with flexion reaching peak force of 5677 N (>9 times body weight) in case c at 90°. Similar to contact areas, the average/peak TF contact pressures significantly increase with flexion in all cases reaching maximum at 90° of 2.2/1 0.9MPa and 2.86/12.1MPa in cases a and c, respectively. Similarly, average/peak PF contact pressures increase with flexion reaching maximum at 90° of 8.7/14.4MPa and 11.1/18.99 MPa, respectively in cases a and c.
Predictions are in agreement with results of earlier model and experimental studies. The drop in extensor lever arm with flexion indicates that quadriceps, in contrast to hamstrings, are much more efficient in resisting moments at smaller flexion angles. Estimation of small ACL/PCL forces in various CKC exercises with and without loads in hands advocate the use of squat exercises at all joint angles and external loads in post-ligament injury and reconstruction periods. Current results are helpful in comprehensive evaluation and design of exercise regimens allowing for effective exercise therapies and trainings involving minimal risk to various components. (Abstract shortened by UMI.)