A review on finite element analysis of the anterior cruciate ligament reconstruction

A signifi cant number of papers relatively to the investigation made on Anterior Cruciate Ligament (ACL) Reconstruction (ACLR) has been published in orthopaedic related journals. Finite Element (FE) Analysis (FEA) has been used to predict the performance of biomechanical-biomedical systems as well as the effect of clinical factors on the ACLR success. This research tool presents some advantages relatively to experimental studies in assessing stresses and strains in soft tissues of the knee joint. By interpreting correctly FE results, it is possible to extrapolate them to clinical situations. This article reviews papers published from 2016 until nowadays on FEA for ACLR studies searched in Google Scholar, Medline and PubMed databases. Only studies that addressed surgery techniques, type and size of grafts, tunnel geometry and orientation, and fi xation devices are reviewed and presented. Research Article A review on fi nite element analysis of the anterior cruciate ligament reconstruction Simões1, O. J., Ramos2, A., Oliveira3, J. P., Noronha3, J. C., Simões2,4, J. A 1Faculty of Medicine of the University of Porto, Portugal 2University of Aveiro, Aveiro, Portugal 3Order of Saint Francisco Hospital, Porto, Portugal 4ESAD-College of Art and Design, ESAD.IDEA, Matosinhos, Portugal Received: 09 December, 2020 Accepted: 31 December, 2020 Published: 04 January, 2021 *Corresponding author: José António de Oliveira Simões, Associate Professor, Department of Mechanical Engineering, University of Aveiro, Portugal, Tel: +351917023952; E-mail:


Introduction
Anterior Cruciate Ligament (ACL) injuries are common in accidents and sports activities and its reconstruction is necessary to restore the static and dynamic stability of the knee. It is also performed in patients with functional instability following ACL injury, resulting in surgical repair or reconstruction [1][2][3]. The yearly incidence rate is of over two million injuries worldwide [4].
The knee joint is composed of structures with multiple body articulations that produce biomechanical complex responses to loads resulting from physical activities. The ACL is one of the main ligaments that connects the femur to the tibia and is often torn during certain pivot movements resulting in knee instability. The ACL after rupture leads to abnormal loading of the knee joint and does not have the biological ability to repair itself (self-healing) due to the intricate complexity of its structure and lack of vascular supply. Knee osteoarthritis can develop or progress under abnormal gait after ACL Reconstruction (ACLR). ACLR can be performed using different surgical techniques that need to be known to understand the mechanisms that lead to its failure.
Multiple underlying causes can be associated to the graft reconstruction failure like pain, stiffness or instability [5]. In this sense, many published studies have improved our understanding of the etiology, surgical reconstruction techniques and prevention of ACL injuries. Excessive knee valgus, poor trunk control, excessive quadriceps forces and leg asymmetries have been identifi ed as high risk biomechanical factors for ACL tear [6]. Some studies have emphasized the importance of an anatomical ACLR to restore normal knee anatomy and kinesiology [7].  [92]. FEA is a numerical tool that can be used to evaluate the performance of different types of research problems in orthopaedics and has been used for many years by researchers to determine how devices or structures may behave under different circumstances [49,50,111]. It is a powerful tool that can be used to predict biomechanical-biological performance, optimize design, screening, prediction, and treatment in orthopaedics [49].
FEA can also be used to anticipate complications or failures to prevent similar occurrences. This has been greatly enhanced by more powerful and advanced computer systems and has benefi tted the fi eld of orthopaedics. Surgical devices that have been developed using this technology are safer and more effective [112].
A signifi cant number of papers have addressed the modelling of the ACL, not so much the ACLR [64,82,83]. It is still unclear how ACLR techniques and materials affect knee joint motion and mechanics. As the in vivo measurement of knee joint loading is not possible, FEA are used to assess the infl uence of these in the outcomes of ACLR [72]. FEA has become an increasingly popular technique for the study of   and devices. Under several options to organize the literature review, we decided to organize the information in those interrelated topics which seem to be the most important ones concerning performance and outcomes of ACLR. The retrieved papers were screened in order to determine which suited adequately for FEA of ACLR. Table 1 presents the list of papers  identifi ed for each subtopic of the main topics considered. A total of 1180 hits was obtained with intersection of keywords "FEA" and "ACL" and "reconstruction", but only 190 papers were analyzed since these were the most suitable for the purpose of the study. Figures 4-6 [113] and is superior to open surgery [114] and provides faster rehabilitation [115].
A femoral tunnel can be created using the Transtibial (TT), Anteromedial (AM) portal, or Outside-in (OI) Technique [116]. TT technique has a tendency to produce a femoral tunnel in non-anatomic location and the graft may be placed too anteriorly and vertically and therefore might not be able to center the graft near the anatomic center of the ACL [117].
Postoperative complications including graft failure and rotational instability have been reported with this technique [116]. ACL reconstruction techniques have been transformed into anatomical and tibial tunnel-independent techniques and more anatomic reconstruction of the ACL can restore normal joint function and kinematics, since femoral tunnel placement has shown to play a vital role in the biomechanics, stability and clinical outcomes after ACLR [118]. Relatively to the TT approach, the independent AM portal technique is thought    to better position the femoral tunnel within the native ACL footprint and leave the graft more posteroinferior on the wall of the lateral femoral condyle [118]. However, this technique has complications such as short femoral socket, posterior wall blowout of the femoral socket [116]. The OI technique allows more freedom with positioning of the femoral tunnel and can be performed in retrograde fashion [116].
Extra-articular ACLR has been used over the last century to address ACL defi ciency but has not gained favor due to residual The most common treatment strategy for the injured ACL is either Single-Bundle (SB) or Double-Bundle (DB) ACLR [122].
Both surgical management approaches are relatively effective in restoring the native anatomy and kinematics of the joint [123]. The choice for SB or DB remains controversial. Some published studies compared the two procedures on human cadavers and have demonstrated better results for DB ACLR [124,125]. Several clinical studies have reported that anatomic DB ACL reconstruction might improve pivot-shift resistance, increase rotational knee control, decrease the rate of meniscal tears and postpone progression toward arthritis [126][127][128].
Other studies found no signifi cant differences between clinical outcomes [129].
Although ACLR can fail for a variety of reasons, the most common technical error is incorrect tunnel placement, with the femoral tunnel more commonly misplaced than the tibial tunnel. In fact, even small changes in tunnel placement have been shown to signifi cantly affect knee kinematics after ACLR [130]. The localization of the femoral tunnel is particularly important in terms of isometric placement of the graft. More anatomic placement of the tunnels can lead to greater knee stability and a more accurate reproduction of native knee kinematics. The all-inside AM portal technique requires only minimal surgical incisions and allows precise femoral tunnel placement. The OI technique may be more benefi cial in obese patients, skeletally immature patients or revision cases [131].
There are several methods to assess tunnel placement that  ACL is comprised mainly of two bundles: AM and posterolateral (PL) bundles. FE models have been developed to analyze the stress distribution in the internal fi bers under load [29]. There is a lack of knee joint FE models which include both AM and PL bundles to predict changes of articular cartilage contact pressures resulting from ACL injuries [28]. The type of reconstruction can include either using single bundle reconstruction, double-femoral-tibial tunnel reconstruction, single-femoral double-tibial tunnel reconstruction or doublefemoral single-tibial tunnel reconstruction, and certainly ones will present biomechanical and clinical advantages over others. In this sense, besides rotational stability, stresses of soft tissues can play a major role in the success of ACLR.

Surgery and reconstruction techniques
The effects of different ACLR techniques on the knee joint mechanics were studied by Halonen, et al. with six FE models during gait: healthy ACL; ACL rupture; single bundle ACLR; double bundle ACLR; weakened (softer) single bundle reconstruction; and single bundle reconstruction with less prestrain [72]. The results of the study of these authors suggest that rather than the choice of a reconstruction technique, stiffness and pre strain of the ACLR affect the motion and mechanics of the operated knee and an optimal choice of graft properties might help restore normal knee joint function and cartilage responses, thus, minimizing the risk of osteoarthritis [72].
The biomechanical properties of the ACL, tibial, femoral articular cartilage and meniscus in knee joints receiving computer aided or conventional ACLR were determined using 3D knee joint FE models of healthy volunteers (normal group) and patients receiving computer-aided surgery or conventional (traditional surgery) ACLR by He and co-authors [35]. The results evidence that computer-aided ACLR has advantages over conventional surgery approach in restoring the biomechanical properties of knee joints, thus reducing the risk of damage to the cartilage and meniscus after ACLR.

Graft and tunnel geometry and orientation
The importance of size and type of autograft, stiffness and tensioning, optimization placement, tunnel geometry and orientation are research issues in ACLR that have been addressed through FEA [60-62, 72, 73, 75, 92, 100]. Some studies have investigated the irregular geometry and the spirally oriented fi ber bundle organization with a realistic ACL geometry obtained using a digitizer and with an ACL geometry reconstructed by directly connecting the femur and tibia insertion sites. When evaluating the effect of fi ber bundle orientation, the models with unrealistic and realistic fi ber bundle orientation predicted similar ACL resultant forces and stress distributions. The results revealed that ACL geometry has a signifi cant effect on the FE model, while fi ber orientation does not [75].
Stiffness and graft tensioning on the knee joint biomechanics has also been studied using FE models. It has been shown that after reconstruction, the closest anterior tibial translation to that of the intact knee is obtained with  [60]. The material of the menisci was assumed to be transversely isotropic and the ligaments to be hyperelastic. These authors concluded that due to the stability and stresses in other tissues, the quadruple semitendinosus graft reconstruction was better than the others (bone-PT-bone and double semitendinosus) but can only restore the ACL function partially. Higher stresses induced in the medial collateral ligament and menisci may cause damage or degeneration in these tissues [60].
Tibial tunnel is an important factor for accurate anatomic graft tunnel positioning and adequate knee functionality.
How graft-tunnel friction affects the FEA of the ACLR is still unclear. Apparently it does not affect joint kinematics and the maximal principal strain of the graft. By contrast, both the relative graft-tunnel motion and equivalent strain for the bone tunnels are altered, which corresponded to different processes of graft-tunnel integration and bone remodeling [60,71].
This implies that the graft-tunnel friction should be defi ned properly for studying the graft-tunnel integration or bone remodeling after ACLR.
The effect of tibial tunnel orientation on the graft-bending angle and stress distribution in the ACL graft was investigated by Bracht, et al. [97]. These authors refer that the risk of graft rupture was similar for medial tibial tunnels and lateral tibial tunnels, but the location of graft rupture changes from the femoral tunnel aperture towards the tibial tunnel aperture respectively [97].
Graft tissues within bone tunnels maintain dynamic for a long time after ACLR. Simulation of graft-tunnel friction with FE models is a challenge. Different friction coeffi cients have been simulated and results show that friction does not affect joint kinematics, neither the maximal principal strain of the graft. However, the graft-tunnel motion and equivalent strain for the bone tunnels are changed indicating different mechanisms of graft-tunnel integration. In fact, friction must be defi ned properly to study the graft-tunnel integration or bone remodeling after ACLR when doing numerical simulations [60].

Fixation techniques and devices
There are a variety of fi xation devices to secure grafts within the femur and tibia and have also called attention in FEA because they can provide relevant information. The review of Hawkins. et al. gives an overview of ACL interference screw usage and design as well as an in depth review of studies that have used FEA to assess ACL interference screw performance [106]. trigonal, trilobe, and turbine) [107]. They concluded that it is possible to improve the designs of biodegradable interference screws for greater torque to be applied and greater screw fi xation between host bone and the graft for better integration, better patient healing, and improved patient outcomes [107]. properties of the GraftMax® with the EndoButton® and TightRope® to investigate whether knotting the free end of latter could improve biomechanical properties [105]. The study of Abdullah, et al. shows that the maximum von Mises stress that occurs on interference screws is less than 40 MPa at the femoral and tibial fi xation [104]. A stiffer screw is more prone to higher stress variations. According to Krasnoperov, cortical fi xators provoke widening of the canals that are larger than in those where interferent screws are used, but the difference does not seem to be signifi cant, only 5% for femoral side and 4% for tibia canals [89].

Conclusions
ACLR surgery is commonly performed using AM and TT techniques. Different results have been published and it seems that the AM surgical technique gives superior stability and clinical outcomes; others found no differences in terms of clinical function and knee joint stability. Based on the von Mises stresses on HT grafts, the AM portal technique is better than the TT technique in terms of the anatomical graft positioning. However, anatomic TT technique may be regarded as a superior surgical technique when compared with conventional TT and AM portal techniques. Stiffness and pre strain of the ACLR affect the motion and mechanics of the operated knee and suggest that an optimal choice of graft properties might help restore the normal knee joint function and cartilage responses, thus, minimizing the risk of osteoarthritis.
Graft performance has been studied using FE models, since these structures play an important role in the kinematics of the ligament reconstruction. Stresses occurring in the soft tissues, as well as contact pressures at the articular surfaces were found to be highly sensitive to graft size. Single-bundle hamstring ACLR using the AM technique has shown superior surgeonrecorded stability according to IKDC knee score, Lachman test, and pivot-shift test. But no difference in patient-reported functional outcome (Lysholm score) has been observed. The change in HT graft length can cause different strain and stress results in the grafts, but does not greatly infl uence joint stability. More graft tissues inside the femoral and tibial tunnels decrease stresses and strains at the femoral and tibial fi xation sites. The posterior stability and ligament stresses following double bundle augmentation is superior to those of single and double bundle reconstructions, especially after secondary defi ciency in the reconstructed grafts. Primary ACLR with 4-strand HT gives clinical results that are comparable with those obtained with PT and with less postoperative complications.
Stresses depend on the site placement and peak stresses and pressure in the ACL grafts increase with higher posterior and inferior placement from the anatomic location. The anterior femoral placement is less favorable for the knee joint biomechanics.
Graft-tunnel friction does not affect joint kinematics and the maximal principal strain of the graft. But relative graft-tunnel motion and equivalent strain for bone tunnels change corresponding to different processes of graft-tunnel integration and bone remodeling.