Effects of variation on extensor elements and operative procedures in patellofemoral disorders

A detailed and validated three dimensional dynamic model of the patellofemoral joint

A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo experiment, involving MR imaging of a normal knee while performing isometric leg press against a constant 140 N force. The model was formulated within the framework of a rigid body spring model and solved using forth-order Runge-Kutta, for knee flexion angles between zero and 50 degrees. Results indicated a good agreement between the model predictions for patellar tracking and the experimental results with RMS deviations of about 2 mm for translations (less than 0.7 mm for patellar mediolateral shift), and 4 degrees for rotations (less than 3 degrees for patellar tilt). The contact pattern predicted by the model was also consistent with the results of the experiment and the literature. The joint contact force increased linearly with progressive knee flexion from 80 N to 210 N. The medial retinaculum experienced a peak force of 18 N at full extension that decreased with knee flexion and disappeared entirely at 20 degrees flexion. Analysis of the patellar time response to the quadriceps contraction suggested that the muscle activation most affected the patellar shift and tilt. These results are consistent with the recent observations in the literature concerning the significance of retinaculum and quadriceps in the patellar stability.

In vivo patellar tracking induced by individual quadriceps components in individuals with patellofemoral pain

Patellofemoral pain is a common knee disorder with a multi-factorial etiology related to abnormal patellar tracking. Our hypothesis was that the pattern of three-dimensional rotation and translation of the patella induced by selective activation of individual quadriceps components would differ between subjects with patellofemoral pain and healthy subjects. Nine female subjects with patellofemoral pain and seven healthy female subjects underwent electrical stimulation to selectively activate individual quadriceps components (vastus medialis obliquus, VMO; vastus medialis lateralis, VML; vastus lateralis, VL) with the knee at 0 degrees and 20 degrees flexion, while three-dimensional patellar tracking was recorded. Normalized direction of rotation and direction of translation characterized the relative amplitudes of each component of patellar movement. VMO activation in patellofemoral pain caused greater medial patellar rotation (distal patellar pole rotates medially in frontal plane) at both knee positions (p<0.01), and both VMO and VML activation caused increased anterior patellar translation (p<0.001) in patellofemoral pain compared to healthy subjects at 20 degrees knee flexion. VL activation caused more lateral patellar translation (p<0.001) in patellofemoral pain compared to healthy subjects. In healthy subjects the 3-D mechanical action of the VMO is actively modulated with knee flexion angle while such modulation was not observed in PFP subjects. This could be due to anatomical differences in the VMO insertion on the patella and medial quadriceps weakness. Quantitative evaluation of the influence of individual quadriceps components on patellar tracking will aid understanding of the knee extensor mechanism and provide insight into the etiology of patellofemoral pain.

Quadriceps cross-sectional area changes in young healthy men with different magnitude of Q angle

Knee pain and dysfunction have been often associated with an ineffective pull of the patella by the vastus medialis (VM) relative to the vastus lateralis (VL), particularly in individuals with knee joint malalignment. Such changes in muscular behavior may be attributed to muscle inhibition and/or atrophy that precedes the onset of symptoms. The aim of this study was to investigate possible effects of knee joint malalignment, indicated by a high quadriceps (Q) angle (HQ angle >15°), on the anatomic cross-sectional area (aCSA) of the entire quadriceps and its individual parts, in a group of 17 young asymptomatic men compared with a group of 19 asymptomatic individuals with low Q angle (LQ angle <15°). The aCSA of the entire quadriceps (TQ), VM, VL, vastus intermedius (VI), rectus femoris (RF), and patellar tendon (PT) were measured during static and dynamic magnetic resonance imaging (MRI) with the quadriceps relaxed and under contraction, respectively. A statistically significant lower aCSA was obtained in the HQ angle group, compared with the LQ angle group, for the TQ, VL, and VI in both static (TQ = 9.9%, VL = 12.9%, and VI = 9.1%; P < 0.05) and dynamic imaging (TQ = 10.7%, P < 0.001; VL = 13.4%, P < 0.01; and VI = 9.8%, P < 0.05) and the aCSA of the VM in dynamic MRI (11.9%; P < 0.01). The muscle atrophy obtained in the HQ angle group may be the result of a protective mechanism that inhibits and progressively adapts muscle behavior to reduce abnormal loading and wear of joint structures.

The effects of trochlear groove geometry on patellofemoral joint stability-a computer model study

The effect of the variation in the femoral groove geometry on patellofemoral joint stability was studied using a two-dimensional transverse plane model with deformable articular surfaces. The femoral and patellar bony structures were modelled as rigid bodies with their profiles expressed by splines. The articular cartilage was discretized into compression springs, distributed along the femoral and patellar profiles, based on the rigid-body spring model. The medial and lateral retinacula were modelled as linear tensile springs, and the quadriceps muscles and patellar tendon as strings with known tension. The anatomical data were obtained from the transverse plane magnetic resonance images of a normal knee flexed at 20° and from the literature. A dynamic analysis approach was employed to solve the governing equations of the model, i.e. three static equilibrium equations of the patella and a constraint equation for each cartilage spring, explicitly. The results of the model suggest that alteration of the sulcus angle from 139° to 169° causes a lateral shift and tilt of less than 3 mm and 4°. This effect increased slightly with increasing total quadriceps force, however, to significantly more than 7 mm and 18° respectively when the medial retinaculum was released. It was suggested that this might be the combined effect of the medial retinaculum deficiency and trochlear dysplasia that is responsible for patellar subluxation and, particularly, dislocation disorders.

A rigid body spring model to investigate the lateral shift - restraining force behavior of the patella

Patellar lateral stability was studied using a 2D transverse plane model with deformable articular surfaces. Quadriceps muscles and patellar tendon were considered as strings with predefined forces and lateral and medial retinaculum as tensile springs. Deformation behavior of articular cartilage was modeled by a set of compression springs perpendicular to articular surfaces, based on rigid body spring model method (RBSM). Patellar lateral stability was investigated using restraining force method (the external force required to cause up to 10 mm lateral displacement on patella). The results were in good agreement with experimental reports for normal joint, vastus lateralis and vastus medialis relieved. Small changes in the femoral trochlear groove geometry provided significant variation in patellar stability. Simulation of different surgical treatments showed that the tibial tubercle medialization is the most effective procedure for patellar subluxation and dislocation disorders.

Tension in a double loop tendon anterior cruciate graft during a simulated open chain knee extension exercise

Concerns exist regarding the tension developed in a reconstructed anterior cruciate ligament (ACL) during open chain knee extension exercises used to rehabilitate the knee. Therefore, the primary objective was to measure tension in an ACL graft during a simulated open chain knee extension exercise as a function of ankle weight. A secondary objective was to determine whether the graft tension was reduced with relatively high stiffness fixation. The open chain exercise was simulated in seven cadaveric specimens in which the ACL had been reconstructed with double loop tendon grafts. Graft tension was measured at 15 degrees of flexion as the effective ankle weight was increased from 22.5 to 67.5 and then to 112.5 N for three different fixation stiffnesses (25, 125, and 225 N/mm). The initial tension was set to restore the 225 N anterior limit of motion to that of the intact knee at 30 degrees of flexion. Increasing the ankle weight caused the graft tension to increase significantly (p<0.0001), but the increase with the highest ankle weight was only 62 N on average. Increasing the fixation stiffness caused the graft tension to decrease significantly (p<0.0001) because the initial tension decreased by 107 N as the fixation stiffness increased. Because the graft tension with the highest ankle weight was limited to 112 N on average, high stiffness fixation methods, which are also resistant to lengthening in the region of the fixation, may reduce the risk of graft construct lengthening during open chain knee extension exercises.

A new approach for surface fitting method of articular joint surfaces

The application of joint contact mechanics requires a precise configuration of the joint surfaces. B-Spline, and NURBS have been widely used to model joint surfaces, but because these formulations use a structured data set provided by a rectangular net first, then a grid, there is a limit to the accuracy of the models they can produce. However new imaging systems such as 3D laser scanners can provide more realistic unstructured data sets. What is needed is a method to manipulate the unstructured data. We created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces. We applied our polynomial model to unstructured data sets from an artificial joint, and confirmed that our polynomial produced a smoother and more accurate model than the conventional B-spline method. Next, we applied it to a diarthrodial joint surface containing many ripples, and found that our function's noise filtering characteristics smoothed out existing ripples. Since no formulation was found to be optimal for all applications, we used two formulations to model surfaces with ripples. First, we used our polynomial to describe the global shape of the objective surface. Minute undulations were then specifically approximated with a Fourier series function. Finally, both approximated surfaces were superimposed to reproduce the original surface in a complete fashion.

The effect of vastus medialis forces on patello-femoral contact: a model-based study

A mathematical model of the patello-femoral joint was introduced to investigate the impact of the vastus medialis (longus, obliquus) forces on the lateral contact force levels. In the model, the quadriceps were represented as five separate forces: vastus lateralis, vastus intermedius, rectus femoris, vastus medialis longus (VML), and obliquus (VMO). By varying the relative force generation ratios of the quadriceps heads, the patello-femoral contact forces were estimated. We sought to analytically determine the range of forces in the VMO and VML that cause a reduction or an increase of lateral contact forces, often the cause of patello-femoral pain. Our results indicated that increased contact forces are more dependent on combinations of muscle forces than solely VMO weakness. Moreover, our simulation data showed that the contact force levels are also highly dependent on the knee flexion angle. These findings suggest that training targeted to reduce contact forces through certain joint angles could actually result in a significant increase of the contact forces through other joint angles.

A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints

This study describes a general set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean +/- stand. dev. error in translation: 0.63 +/- 1.19 mm, 0.10 +/- 0.71 mm, -0.29 +/- 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 +/- 1.71 degrees, 0.27 +/- 2.38 degrees, -1.13 +/- 1.83 degrees in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room.

The use of basis functions in modelling joint articular surfaces: application to the knee joint

This article introduces a new method to represent bone surface geometry for simulations of joint contact. The method uses the inner product of two basis functions to provide a mathematical representation of the joint surfaces. This method guarantees a continuous transition in the direction of the surface normals, an important property for computation of joint contact. Our formulation handles experimental data that are not evenly distributed, a common characteristic of digitized data of musculoskeletal morphologies. The method makes it possible to represent highly curved surfaces, which are encountered in many anatomical structures. The accuracy of this method is demonstrated by modeling the human knee joint. The mean relative percentage error in the representation of the patellar track surface was 0.25% (range 0-1.56%) which corresponded to an absolute error of 0.17mm (range 0-0.16mm).

Quantitative study of the quadriceps muscles and trochlear groove geometry related to instability of the patellofemoral joint

This was a quantitative study of the major anatomical structures associated with instability of the patellofemoral joint: the quadriceps muscles and the femoral trochlear groove. The attachments of the muscles to the patella, their lines of action, and their relative sizes (physiological cross-sectional areas) were found. On the basis of the physiological cross-sectional areas, it was estimated that the central muscles-the rectus femoris and vastus intermedius-contributed 35% of the quadriceps strength, with 40% from the vastus lateralis and 25% from the vastus medialis. The vastus lateralis had the most variable results, with the ratio of the lateralis to the medialis ranging from 0.90 to 2.18; this may be associated with patellar instability. Both the long and oblique parts of the vastus medialis were more oblique than the corresponding parts of the vastus lateralis. Photographic "skyline" views of the trochlear groove produced data on the sulcus angle and ratio of depth to width. The data showed that the trochlear groove did not deepen in the area contacted by the patella with progressive knee flexion (p > 0.53), contrary to popular belief. These data are useful for objective analysis of patellofemoral stability and related surgical interventions.