1 Introduction

Healthy patellofemoral (PF) joint mechanics is crucial for the optimal function of the knee joint. Patella plays a vital role in distributing quadriceps load during knee extension. Patellar tracking, not physiological displacement, causes an increase of strains in PF ligaments, peaks of localized stress of soft tissues and articular cartilage and bony parts, and knee pain; these problems can lead to complications such as bone abnormalities and osteoarthritis.^1–3 The mechanical causes of PF joint malfunction can be different, for example, following cruciate ligament injury and repair; however, connections have been found between PF mal tracking and soft-tissue or bony areas pathologies.⁴ Some authors have performed probabilistic analyses to find relationships between the variability of material properties and PF instability.⁵ From a mechanical point of view, the stability of the PF joint is guaranteed by a correct interaction among the geometry of the patella and femur, quadriceps muscle forces, and strength of retinacular structures. The Q-angle is formed between a line representing the resultant line of force of the quadriceps, made by connecting a point near the ASIS to the mid-point of the Patella, see Fig. 1,.⁶

Close

Fig. 1 Q Angle and 3D FE model schematic representation.

Export to PPT

The quadriceps muscle tension imbalance can misalign the contact zone or cause the patella's regrettable displacements.^7–9 In the presence of unbalanced quadriceps forces, causing an incorrect Q-angle, added to an inadequate retinacular structures action, physiological displacements can be produced, modifying patellofemoral contact areas and pressures.^10–12 Another study also investigated patellar motion and contact area during knee flexion and the effects on the patellofemoral contact area with tibial rotation.¹³ Recently, research was focused on setting musculoskeletal in-vivo models by applying estimated loads placed instead of muscles to simulate contact stress ageing on the PF joint.^14,15 Another approach used to investigate this problem involves developing finite Element (FE) models using data obtained through MR and CT (computed tomography).

Moreover, in vivo experiments can provide valuable indications to validate material laws, loads, and constraints to apply. Numerical simulations allow investigating from a different point of view, including contour maps of forces, stresses, strains and displacements, offering the chance to investigate a singular part of the model alone. For example, kinematics and kinetics related to the PF joint during gait were investigated, considering muscle and ligament forces, contact stresses in cartilage and the menisci.^16,17 Also, the anterior cruciate ligament (ACL) can cause knee instability, pain, and patellar dislocation. The posterior cruciate ligament (PCL) regulates the posterior translation of the tibia in relation to the femur and guarantees stability at high flexion angles of the knee. Both these aspects, ACL and PCL deficiencies, can cause pathologic patellar instability uniquely for high flexion angles.¹⁸ From another point of view, if many studies have focused their investigations on a localized area of interest, others have tried to furnish a broader landscape giving information on the entire bony chain of the leg.^19-21

2 Material and methods

2.2

2.2 Material properties

The isotropic law was chosen to characterize cortical bone, cancellous bone, and cartilage material behaviour. The elastic moduli and Poisson's ratio were selected from the literature (Table 2).^25–27 Both the ACL and PCL ligaments were modelled as solid structures. At the same time, the lateral retinaculum was represented by applying a symmetric load of 100 N to the patella's left and right lateral sides.²⁸ Mesh convergence testing was conducted on the patella, tibial cartilage, and the upper part of the tibia. An iterative process decreased the average size of tetrahedral elements compared with the maximum value of Eq. Von Mises stress obtained (Fig. 2). Results revealed peak stress values comparable between the 1 mm and 0.80 mm conditions (average peak difference of 3.2%).

Table 2 Mechanical properties of FE parts.

	Elastic Modulus E [MPa]	Poisson ratio ν
Cortical Bone	17000	0.3
Cancellous Bone	350	0.25
Cartilage	12	0.45
Anterior cruciate ligament	366	0.4
Posterior cruciate ligament	366	0.4
Medial collateral ligament	366	0.4
Lateral collateral ligament	366	0.4

Close

Fig. 2 Convergence test of numerical simulation.

Export to PPT

2.3

2.3 Loading of the knee model

Loading setup was chosen by using literature data from Frigo and Donno,²⁹ who developed a musculoskeletal model to evaluate tensions of the knee joint ligaments during the contraction phase and their variations related to the magnitude of the muscle forces. The intensity of the muscle forces was calculated by a static optimization taking into account ground reaction and knee flexion/extension during walking. The other rotational and translational components were obtained due to the dynamic equilibrium of forces. Fig. 3 shows the curves calculated for the hamstrings, gastrocnemius and quadriceps during knee flexion at an angle of 40°.

Close

Fig. 3 Muscle forces applied to the model: a) Hamstrings, b) Gastrocnemius, c) Quadriceps.

Export to PPT

In particular, curve a) of the Hamstrings is obtained as the sum of four components (ST-semitendinosus, SM-semimembranosus, BF-lh - Biceps femoris –long head, and BF-sh - Biceps femoris –short head). On the other hand, curve b) of Gastrocnemius is obtained as the sum of two components (GaL-gastrocnemius lateralis. and GaM-Gastrocnemius medialis). Curve c) represents the quadriceps component. As depicted in Fig. 3, Peaks of forces were calculated for the hamstrings, gastrocnemius and quadriceps during knee flexion at an angle of 40° to simulate the ageing loads.

Based on the above considerations, the setting up configuration for FE analyses was chosen by fixing the tibia and loading the model with three different forces. The first force was the Hamstrings contribution, obtained by curve a) of Fig. 3, and applied on Point 1 (X = 124,63 mm, Y = −350,15 mm, Z = −70,84 mm), was chosen around the intercondylar line. The second one was the Gastrocnemius contribute, obtained by curve b) of Fig. 3, and applied on Point 2 (X = 98,36 mm, Y = −345, 56 mm, Z = −60, 05 mm) chosen between the medial epicondyle and the intercondylar line. Finally, the third one was the Quadriceps muscle, obtained by curve c) of Fig. 3, and applied to the quadriceps tendon.

Moreover, to simulate the effect of the medial retinaculum, a symmetric load of 100 N was applied to the left and right side of the patella, see Fig. 4. The effect of patellar instability was obtained by gradually unbalancing this symmetry, one side was unloaded till 90 N, and the other loaded till 110 N. Contact behaviour between tetrahedral (4 nodes) elements of the femur and patella was modelled as frictional with a friction coefficient of 0,2.³⁰ Tetrahedral (4 nodes) elements of cartilage, femur and tibia were glued to the bones, and a friction coefficient of 0.2³¹ was chosen.

Close

Fig. 4 Loading setup of numerical FE model.

Export to PPT

3 Results

In this paper, a FE model was developed to evaluate patellar instability, investigating the healthy and pathologic configurations during knee flexion. Simulations consider the effect of the hamstrings, gastrocnemius and quadriceps muscles during flexion. The medial retinaculum's contribution is obtained by loading with an equivalent distributed load on the patella's left and right sides. Results confirm increment of stress ageing on the contact area in the case of patellar instability. Clinical case reports confirm that restoration of the normal functionality of the knee in case of patellar instability is a challenging goal to achieve.

For this reason, a multidisciplinary approach to understanding mechanisms ruling the kinematic and kinetic of the knee are necessary and need more other speculations to calibrate the suitable surgical therapies.

Fig. 5 depicts the contour maps of stress and displacements evaluated for a healthy knee and an unhealthy one related to an unbalanced load of retinacula of 110 N. The Eq. Von mises stress is almost equivalent, with less than a 5% of difference, in each bony segment except for the patella, which shows higher stress of about 10% (33 MPa instead of 30 MPa) in the unhealthy configuration. The maximum peaks of stress obtained for every single part of the FE models are reported in Table 3. Analogue considerations could be done about displacements, which show differences only in translations related to the patella, (7.02 mm instead of 5.02 mm).

Close

Fig. 5 Contour maps of Eq. Von Mises stress and displacements of the FE models for healthy and unhealthy configurations.

Export to PPT

Different considerations must be made for stress ageing on ligaments. As shown by Fig. 6 and Table 3, ligaments and cartilages, which represent the elastic part in the kinematic of the model, play the vital role of absorbing increasing peaks of stress deriving by incorrect positioning of the patella.

Close

Fig. 6 Contour maps of Eq. Von Mises stress of ligaments for healthy and unhealthy configurations.

Export to PPT

In particular, on the medial collateral ligament and patellar tendon, a difference of about 42% in the peak of stress was registered. In this case, it is obviously due to the forces of ageing: the patella is laterally forced to translate while tendons try to drive it in the right position. For the same reasons, anterior and posterior ligaments are subjected to higher stress of 27% and 18%, respectively. The lateral collateral ligament suffers an increment of the stress of only 12%. As reported in Table 3, tibial and femoral cartilages are subjected to higher stress of 10% and 11%.

Finally, Fig. 7 is reported the comparative Eq. As mentioned in the Von mises contour map of the patella, essential differences are obtained regarding stress. As depicted in Fig. 7, the contact zone in the second case is translated on the right upper zone of the patella, not physiologically conceived to support that kind of contact and stress. Displacements are respectively 5 mm in case (a) and 7.02 mm in case (b). Fig. 8 reports curves of contact forces, calculated on the patella, vs its lateral displacement. The red curve represents the healthy configuration of the knee when the retinaculum is balanced. The curve shows a growing trend without particular slope variations because of the knee's physiological functioning. The maximum displacement is about 5 mm, while the contact force is approximately 320 N. The blue curve, related to the unhealthy configuration, shows displacements reaching a value of 7.02 mm and a contact force of about 480 N, with an essential variation of slope around 3 mm.

Close

Fig. 7 Contour maps of Eq. Von Mises stress of patella for healthy and unhealthy configurations.

Export to PPT

Close

Fig. 8 Curves of contact force vs lateral displacements.

Export to PPT

Fig. 9 shows curves of contact forces calculated on patella vs knee flexion angle. Simulations have been carried out until a knee flexion angle of 40°. Also, in this case, the red curve depicts a healthy knee. As it is possible to notice, at about 20° curve ends to growth and reaches a sort of plateau. The peak contact force is approximately 305 N. The blue curve confirms the trend shown in picture 8, and at 16° of, the knee flexion angle starts to grow suddenly.

Close

Fig. 9 Curves of contact force vs angle of knee flexion.

Export to PPT

4 Discussion

A patella pathological disarticulation causes patellar instability due to multiple factors such as trauma, ligamentous laxity, bony malalignment, connective tissue degradation, or anatomical deformities. Often, patients with patellar instability suffer debilitating pain, limitations in essential function, and arthritis.^32-34

The mechanical axis of the knee can be individuated through a line starting from the hip's centre to the ankle's centre. In contrast, the anatomic axis of the knee is a line lying from the centre of the femoral and tibial shaft. These two lines form an angle of approximately 6° of valgus in physiological conditions. Different values of this angle can encourage abnormal displacements of the patella and contribute to its instability.³² On the other hand, a femoral anteversion major of 20° deforms Q-angle's geometry because of a consistent lateral force ageing on the patella^35,36 and, consequently, abnormal displacements on it.

For this reason, a correct polygonal scheme of the Q-angle's geometry and an anatomic trochlear groove are necessary to prevent undesirable effects. In addition, tibia malpositioning, represented by a rotation major of 30°, has important consequences on Q-angle physiology.^37,38

In this paper an unbalanced medial retinaculum load, with a difference of 10 N, has been evaluated by comparing results with a healthy FE Knee model. Results confirm a determinant effect of the medial retinaculum in the lurch of the patella's equilibrium as it produces lateral forces directly acting on the left side of the patella. A lateral displacement of about 5 mm has been evaluated with an unaltered value of the Quadriceps muscle intensity. This effect is amplified when a reduced force, unable to oppose and contrast the lateral force induced by the left medial retinaculum, is applied. In literature, many studies demonstrate how the patella's restraining force is deeply influenced by slightly different force distributions among the quadriceps muscles.^39–41 Other studies consider the relationship between lateral patellar displacement and knee flexion, changing the quadriceps force distribution.⁴² Results obtained in this research demonstrate how at about 25–30° of knee flexion, after the first phase of adjustment, governed by the elasticity of ligaments and tendons. A second phase follows in which the patella displacement is guided to lay in the trochlear groove by the physiology of the bony anatomy. This phenomenon is accentuated in the case of the combined effect of a quadriceps force reduced at 90% and an unbalanced lateral load of 90 N and appears at about 15–20°. In the presence of the “patella alta”, the patella can't follow the physiology of the bony anatomy; thus, dislocations can occur.³² The kinematics of this phenomenon suggests that an angle of 25° during knee flexion is the most dangerous in the presence of possible patellar instability. Also, in literature, clinical investigations evidenced many cases of patellar subluxation and dislocation occurring at 30° of knee flexion.^43,44

Soft tissues, muscles, and retinacula are essential in containing and significantly restraining lateral patellar movements at full extension of the leg. In particular, at about 15° of knee flexion patella fits together with the trochlea; going on flexion, the compressive effect of retinaculum tends to decrease, replaced by bony assessment of the patella inside the femur, guaranteed by the articular cartilages. At about 30°–45° of knee flexion, the action of the retinaculum becomes almost insignificant, as reported in the literature.⁴⁵ At high knee flexion angles, on the sagittal plane, the directions of the quadriceps muscle and patellar tendon tend to reduce their angle, causing a resultant compressive force ageing on the bony surfaces involved, which finally can produce a certain stability of the patella.^46,47 The medial retinaculum constrains lateral patellar displacements starting from a fully extended knee configuration. Thus lateral patellar translations, happening between 0 and 30° of flexion, are probably due to abnormal medial retinacular structures.⁴⁸ In a cadaver knee, Nomura et al.⁴⁹ showed that by applying a lateral displacing force of 10 N, the patella displaced approximately 6 and 13 mm with an intact and transected MPFL, respectively; these results are in perfect agreement with ours. Other studies demonstrate how lateral unbalancing can reduce, by about 20%, the force to dislocate the patella of 10 mm at different angles.⁵⁰

This paper aims to demonstrate how an unbalanced forces of 10 N acting on the retinaculum alone can produce a real difference in displacements of about 40% and about 44% on contact patellar forces. Different techniques have been developed to study various pathologies; many FE models have been developed to establish stress shielding in the bony parts or the surgical tools describing the mechanical behaviour of the implanted bony parts.^51-55 In any case, the model appears to be an effective tool for further investigating knee joint biomechanics under dynamic conditions.

5 Conclusion

This research aimed to develop a FE model to evaluate patellar instability due to the effect of medial retinaculum asymmetric loading effect. Loading setup has been improved using simplified numerical data from the literature and replacing stance gait muscular activity quantifications. Results from this research demonstrate how unbalanced forces acting on the retinaculum can produce significant patellar instability, and consequently also increased contact patellar forces.

Funding/sponsorship

None.

Informed consent (patient/guardian), mandatory only for case reports/clinical images

This article does not contain any studies with human participants or animals performed by any of the authors.

Institutional ethical committee approval (for all human studies)

This article does not contain any studies with human participants or animals performed by any of the authors.

Author statement

Filardi V.: Investigation, Data curation, Software Validation, Conceptualization, Writing.

Risitano G.: Software Validation, Conceptualization, Writing.

Vaishya R.: Methodology, Supervision, Writing, review & editing.