Sensitivity analysis of the knee ligament forces to the surgical design variation during anterior cruciate ligament reconstruction: a finite element analysis

Development of a novel geometrically-parametric patient-specific finite element model for anterior cruciate ligament reconstruction

PURPOSE

A personalized model of the knee joint, with adjustable effective geometric parameters for the transplanted autograft diameter in Anterior Cruciate Ligament Reconstruction (ACLR) using the bone-patella-tendon-bone (BPTB) technique, has been developed. The model will assist researchers in understanding how different graft sizes impact a patient's recovery over time.

METHODS

The study involved selecting a group of individuals without knee injuries and one patient who had undergone knee surgery. Gait analysis was conducted on the control group and the patient at various time points. A 3D model of the knee joint was created using medical images of the patient. Forces and torques obtained from the gait analysis were applied to the model to perform finite element analysis.

RESULTS

The results of the finite element (FE) analysis, along with kinetic data from both groups, indicate that models with diameters of 7.5 mm and 12 mm improved joint motion during follow-up after ACLR. Additionally, a comparison of the stress applied to the ACL model revealed that a 12 mm autograft diameter showed a more favorable trend in patient recovery during the three follow-up intervals after ACL reconstruction surgery.

CONCLUSION

The development of a personalized parametric model with adjustable geometric parameters in ACLR, such as the transplanted autograft diameter, as presented in this study, along with FE using the patient's kinetic data, allows for the examination and selection of an appropriate autograft diameter for Patella Tendon grafting. This can help reduce stress on the autograft and prevent damage to other knee joint tissues after ACLR.

The effect of body weight on the knee joint biomechanics based on subject-specific finite element-musculoskeletal approach

Knee osteoarthritis (OA) and obesity are major public health concerns that are closely intertwined. This intimate relationship was documented by considering obesity as the most significant preventable risk factor associated with knee OA. To date, however, the effects of obesity on the knee joint's passive-active structure and cartilage loading have been inconclusive. Hence, this study investigates the intricate relationship between obesity and knee OA, centering on the biomechanical changes in knee joint active and passive reactions during the stance phase of gait. Using a subject-specific musculoskeletal and finite element approach, muscle forces, ligament stresses, and articular cartilage contact stresses were analyzed among 60 individuals with different body mass indices (BMI) classified under healthy weight, overweight, and obese categories. Our predicted results showed that obesity significantly influenced knee joint mechanical reaction, increasing muscle activations, ligament loading, and articular cartilage contact stresses, particularly during key instances of the gait cycle-first and second peak loading instances. The study underscores the critical role of excessive body weight in exacerbating knee joint stress distribution and cartilage damage. Hence, the insights gained provide a valuable biomechanical perspective on the interaction between body weight and knee joint health, offering a clinical utility in assessing the risks associated with obesity and knee OA.

Sensitivity analysis of paediatric knee kinematics to the graft surgical parameters during anterior cruciate ligament reconstruction: A sequentially linked neuromusculoskeletal-finite element analysis

BACKGROUND AND OBJECTIVE

Incidence of paediatric anterior cruciate ligament (ACL) rupture has increased substantially over recent decades. Following ACL rupture, ACL reconstruction (ACLR) surgery is typically performed to restore passive knee stability. This surgery involves replacing the failed ACL with a graft, however, surgeons must select from range of surgical parameters (e.g., type, size, insertion, and pre-tension) with no robust evidence guiding these decisions. This study presents a systemmatic computational approach to study effects of surgical parameter variation on kinematics of paediatric knees.

METHODS

This study used sequentially-linked neuromusculoskeletal (NMSK) finite element (FE) models of three paediatric knees to estimate the: (i) sensitivity of post-operative knee kinematics to four surgical parameters (type, size, insertion, and pre-tension) through multi-input multi-output sensitivity analysis; (ii) influence of motion and loading conditions throughout stance phase of walking gait on sensitivity indices; and (iii) influence of subject-specific anatomy (i.e., knee size) on sensitivivty indices. A previously validated FE model of the intact knee for each subject served as a reference against which ACLR knee kinematics were compared.

RESULTS

Sensitivity analyses revealed significant influences of surgical parameters on ACLR knee kinematics, albeit without discernible trend favouring any one parameter. Graft size and pre-tension were primary drivers of variation in knee translations and rotations, however, their effects fluctuated across stance indicating motion and loading conditions affect system sensitivity to surgical parameters. Importantly, the sensitivity of knee kinematics to surgical parameter varied across subjects, indicating geometry (i.e., knee size) influenced system sensitivity. Notably, alterations in graft parameters yielded substantial effects on kinematics (normalized root-mean-square-error > 10 %) compared to intact knee models, indicating surgical parameters vary post-operative knee kinematics.

CONCLUSIONS

Overall, this initial study highlights the importance of surgical parameter selection on post-operative kinematics in the paediatric ACLR knee, and provides evidence of the need for personalized surgical planning to ultimately enhance patient outcomes.

Polynomial chaos expansion based sensitivity analysis of predicted knee reactions-assessing the influence of the primary ligaments in distraction based models

Computational knee models have shown that predicted condylar reactions are sensitive to the utilized ligament mechanical parameters. These models, however, are computationally expensive with multiple sources of uncertainty. Traditional uncertainty analysis using Monte-Carlo (MC) inspired methods are costly to perform. The purpose of this study was to use two example calibrated knee models to compare quasi-MC versus polynomial chaos expansion (PCE) sensitivity analyses of predicted condylar reactions that included uncertainty in the mechanical parameters of the ligaments. PCE was practically identical versus quasi-MC with 95% and 98% reductions in model evaluations for analyses with 10 and 6 uncertain variables, respectively.

Bayesian Calibration of Computational Knee Models to Estimate Subject-Specific Ligament Properties, Tibiofemoral Kinematics, and Anterior Cruciate Ligament Force With Uncertainty Quantification

High-grade knee laxity is associated with early anterior cruciate ligament (ACL) graft failure, poor function, and compromised clinical outcome. Yet, the specific ligaments and ligament properties driving knee laxity remain poorly understood. We described a Bayesian calibration methodology for predicting unknown ligament properties in a computational knee model. Then, we applied the method to estimate unknown ligament properties with uncertainty bounds using tibiofemoral kinematics and ACL force measurements from two cadaver knees that spanned a range of laxities; these knees were tested using a robotic manipulator. The unknown ligament properties were from the Bayesian set of plausible ligament properties, as specified by their posterior distribution. Finally, we developed a calibrated predictor of tibiofemoral kinematics and ACL force with their own uncertainty bounds. The calibrated predictor was developed by first collecting the posterior draws of the kinematics and ACL force that are induced by the posterior draws of the ligament properties and model parameters. Bayesian calibration identified unique ligament slack lengths for the two knee models and produced ACL force and kinematic predictions that were closer to the corresponding in vitro measurement than those from a standard optimization technique. This Bayesian framework quantifies uncertainty in both ligament properties and model outputs; an important step towards developing subject-specific computational models to improve treatment for ACL injury.

Evaluation of anterior cruciate ligament surgical reconstruction through finite element analysis

Anterior cruciate ligament (ACL) tear is one of the most common knee injuries. The ACL reconstruction surgery aims to restore healthy knee function by replacing the injured ligament with a graft. Proper selection of the optimal surgery parameters is a complex task. To this end, we developed an automated modeling framework that accepts subject-specific geometries and produces finite element knee models incorporating different surgical techniques. Initially, we developed a reference model of the intact knee, validated with data provided by the Open Knee(s) project. This helped us evaluate the effectiveness of estimating ligament stiffness directly from MRI. Next, we performed a plethora of “what-if” simulations, comparing responses with the reference model. We found that (a) increasing graft pretension and radius reduces relative knee displacement, (b) the correlation of graft radius and tension should not be neglected, (c) graft fixation angle of 20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}∘ can reduce knee laxity, and (d) single-versus double-bundle techniques demonstrate comparable performance in restraining knee translation. In most cases, these findings confirm reported values from comparative clinical studies. The numerical models are made publicly available, allowing for experimental reuse and lowering the barriers for meta-studies. The modeling approach proposed here can complement orthopedic surgeons in their decision-making.