Validation of a computational knee joint model using an alignment method for the knee laxity test and computed tomography

Abstract

Background:

Computational models have been identified as efficient techniques in the clinical decision-making process. However, computational model was validated using published data in most previous studies, and the kinematic validation of such models still remains a challenge. Recently, studies using medical imaging have provided a more accurate visualization of knee joint kinematics.

Objective:

The purpose of the present study was to perform kinematic validation for the subject-specific computational knee joint model by comparison with subject’s medical imaging under identical laxity condition.

Methods:

The laxity test was applied to the anterior-posterior drawer under 90° flexion and the varus–valgus under 20° flexion with a series of stress radiographs, a Telos device, and computed tomography. The loading condition in the computational subject-specific knee joint model was identical to the laxity test condition in the medical image.

Results:

Our computational model showed knee laxity kinematic trends that were consistent with the computed tomography images, except for negligible differences because of the indirect application of the subject’s in vivo material properties.

Conclusions:

Medical imaging based on computed tomography with the laxity test allowed us to measure not only the precise translation but also the rotation of the knee joint. This methodology will be beneficial in the validation of laxity tests for subject- or patient-specific computational models.

Keywords

3D imaging computed tomography computer simulation knee joint laxity test

1. Introduction

Precise and clinically relevant modeling of complex biological systems, such as the knee joint, remains a challenge; however, it also holds the potential to enhance the quality of patient care significantly. Computational analysis is recognized as an important tool in various biomedical fields and has been widely adopted for analyzing knee joint biomechanics [1]. Computational models are fundamental to the development of clinical and surgical assessment techniques as well as surgical instruments [2]. Recently, subject-specific computational models have been identified in biomechanics. This approach can produce significant results and aid in the assessment of various factors such as forces and strains, contact forces and areas of ligaments, and the stress and strain distribution across various tissue structures, which have been challenging to obtain from experimental studies [2]. However, the validation of subject- or patient-specific computational models can be challenging.

The knee laxity test with various devices has been widely used in clinical diagnosis and for research purposes to evaluate the severity of injuries related to the human knee joint [3]. Jacobsen et al. evaluated the anteroposterior, medial, and lateral stability of the knee joint using stress radiography [4]. Li et al. validated kinematic laxity testing in a computational knee joint model, showing its similarity to experimental laxity testing [5]. Wang et al. performed a laxity test simulation with cartilage contact in an anterior cruciate ligament reconstruction using a validated computational model [6]. Quatman et al. studied an anterior cruciate ligament injury mechanism using a validated computational model [7]. However, a representative model was used for clinical relevance to be evaluated in these previous studies rather than subject-specific computational models [5–7].

Subject-specific models have been applied to other aspects of biomechanics. Yang et al. recently reported the development of a subject-specific model intended to predict forces in the knee ligaments at high flexion angles [8]. Shim et al. used subject-specific finite element analysis to characterize the influence of geometry and material properties on the rupture of the Achilles tendon [9]. A study by Lenhart et al. focused on the prediction and validation of load-dependent behavior in a subject-specific model of the tibiofemoral and patellofemoral joints during movement [10]. However, previous subject-specific models were validated using the results from previous studies or were based on data collected from cadaver specimens. There have been studies with regard to subject-specific model validation as well as postoperative assessments; these models have implemented recent advances in medical imaging techniques [11–14]. Computed tomography (CT) imaging has been widely used for relatively easy 3-dimensional (3D) visualization and for assistance with reconstruction techniques, particularly for tunnel length and position measurements in knee joint arthroscopy. Using magnetic resonance imaging (MRI), Kang et al. validated a in vivo subject-specific weight-bearing model of the cartilage contact area and deformation; this is a relatively convenient method for users [12]. However, this study only considered a simple vertical loading condition; thus, in vivo validation is required for the more complex loading conditions that apply to the knee joint anatomy to create a more realistic simulation.

The objective of the present study was performed in vivo kinematic validation of a subject-specific computational model using subject’s own data under laxity test conditions. The laxity test was applied to the anterior–posterior drawer in 90° flexion and to the varus–valgus in 20° flexion for both subject and its computational model with a series of stress radiographs, CT scans and quantitative stress examinations using a Telos device to validate a in vivo subject-specific computational model. Finally, translations and rotations of the subject-specific computational model were compared with CT images.

2. Methods

2.1. Laxity test

The data for the present study was measured from a 35-year-old male volunteer with a normal healthy knee. Both stress radiography with a Telos GA II stress device (Telos, Weterstadt, Germany) and CT were used with the subject in the lateral decubitus position in 20° and 90° knee flexion conditions.

To make our testing clinically relevant to the current guidelines, the angle of 90° was selected for testing the anterior-posterior (AP) laxity of the knee, and 20° was selected as a testing variable in lateral and medial compartment joint openings in accordance with the guidelines authorized by the International Knee Documentation Committee [15,16].

To determine AP laxity, the limb was positioned in neutral rotation, and load was applied to the anterior proximal tibia or the posterior proximal calf at the level of the tibial tubercle. To determine medial or lateral laxity, the knees were flexed 20° in neutral rotation with the subject in the supine position. For each examination, the applied load on the limbs was determined to be 150 N in accordance with the Telos device guidelines [15,16].

CT images were taken with a 1-mm slice thickness using a 64-channel CT scanner (Somatom Sensation 64; Siemens Healthcare, Erlnagen, Germany) while Telos exerted a load on the knee joint. The tube parameters were 120 kVp and 135 mA, and the acquisition matrix was $512 \times 512$ with a 200-mm field-of-view.

The reconstructed 3D-CT images were evaluated on the basis of the technique of Jacobsen and Staubli using peripheral bony landmarks to determine relative tibial displacement of the femur [4,17].

In measurement of AP laxity, after a horizontal line was drawn along the medial tibial plateau, two vertical lines perpendicular to the horizontal line were constructed through the midpoint between the most posterior contours of the medial and lateral femoral and tibial condyles, respectively. The distance between these two points along the plateau line was then measured to displacement of the knee (DOK). Anterior tibial translation (ATT) was calculated by substracting DOK in unloading condition from DOK in anterior loading condition, and posterior tibial translation (PTT) was calculated by the same manner (Fig. 1).

Fig. 1.

Measurement of ATT–PTT and varus–valgus displacement on a stress radiograph in 90° and 20° of flexions, respectively. (ATT and PTT were distance of black line translated from red line, varus and valgus were distance between two lines).

To measure the valgus–varus laxity, the medial and lateral joint gaps between the bony components of the joints were measured in anteroposterior views. Two lines were drawn along the bony margin of the femoral condyle and tibial plateau. The femoral line was drawn along the lowest margin of the medial and lateral femoral condyle and the tibial line was drawn along the lowest sclerotic lines of the medial and lateral tibial plateau. Lines perpendicular to the tibial line were drawn tangentially to the medial or lateral tibial condyle. The medial and lateral joint gaps were defined as the distances between the two crossing points along the perpendicular line (Fig. 1). Tibial rotation was measured based on the method of Cobb et al. [18]. An axial plane was defined 20 mm below the tibial spines. The center of each tibial condyle was calculated from ten points around the condylar cortex. Three different sagittal axes were then defined. The posterior condylar axis was defined as the axis perpendicular to the posterior condylar line at its midpoint. The sagittal tubercle axis was generated by connecting the lateral tibial spine and the center of the tibial tubercle. The anatomical tibial axis was defined as the perpendicular at the mid-point of the line connecting the medial and lateral condylar centers.

2.2. Evaluation of intra-observer repeatability and inter-observer reproducibility

To verify the results of Telos stress radiography, scan–rescan reproducibility analysis was performed by following the initial radiography with a one-month follow-up scan. To evaluate inter-observer reproducibility, two trained observers segmented the CT images of the knee joint and developed independent tibiofemoral (TF) models. CT data was imported into Mimics software version 17.1 (Materialise, Leuven, Belgium) to develop the 3D TF models.

The 3D reconstruction reproducibility analysis suggested by Koo et al. was used [19]. Both observers were experienced; the first had previously segmented and reconstructed knee joints for 150 sets of knee CT images, and the second was an orthopaedic surgeon who had previously segmented and reconstructed 30 sets of knee CT images. Thus by adjusting the threshold to exclude those of soft tissues, it was possible to display the geometry of the bone in the CT image, which were then assembled to construct a 3D volumetric model of femur and tibia. The observers were trained to follow a rule-based protocol, including prior instruction of common rules between the observers in the 3D reconstruction, and performed the same segmentation and reconstruction processes on the CT images [19]. Intra-observer and inter-observer reliability were measured by having the two examiners measure the medial and lateral ATT and PTT on each set of radiographs twice; this was followed by 3D reconstruction of the CT images. The trials were spaced a minimum of two weeks apart to prevent recall bias. Cobb et al.’s landmarks were the bony landmarks used in scan–rescan repeatability and reconstruction reproducibility [18].

Inter-observer measurements were determined by calculating coefficients of variation (CV, %) for the bony landmarks (Fig. 2). Intra-observer and inter-observer reliability were evaluated by comparing the means of the ATT and PTT translations on the lateral and medial compartment gapping and by calculating intraclass correlation coefficients (ICC).

Fig. 2.

The points that were used for verification of scan–rescan reproducibility test and for measurement of tibial displacement between CT image and computational model.

The knee joints in full extension, 20 and 90 flexions, and under the laxity test condition in CT images were fully reconstructed and the femur was aligned in order to visualize its movement in the Mimics software. Deviation analysis for alignment error between images was performed using Rapidform version 2006 (3D Systems Korea, Inc., Seoul, Republic of Korea). This was similar to the technique used by Kurmis et al. [20].

2.3. The subject-specific finite element model

A 3D computational knee model was developed using CT and MRI images of a 35-year-old healthy male subject [12,21,22]. The contours of the tibia, fibular, and femur bones and those of the cartilage, menisci, and ligaments were digitized from the CT and MRI images, respectively, to construct the 3D bony models and soft tissue geometry of the knee. The distal of the reconstructed femur was 10.2 cm, and the proximal of the tibia was 7 cm in MRI. To match the positional coordinates of each model, we defined three anatomical reference points in the reconstructed CT and MRI models: the central point of the diaphysis of the femur, the midpoint of the trans-epicondylar axis, and the intercondylar notch. The combination of the reconstructed CT and MRI models with the positional alignment for each model was achieved with the Rapidform commercial software.

The computational knee joint model was described and validated in previous reports [12,21,22]. In the model, the bony structures were modeled as rigid bodies [21,22]. The articular cartilages were defined as isotropic, linear elastic materials with a moduli of 15 MPa and Poisson’s ratios of 0.47, owing to the time-independent and simple compressive load applied to the knee joint [23]. The menisci were modeled as a transversely isotropic, linearly elastic, homogeneous material with a Young’s moduli of 120 MPa in the circumferential direction and 20 MPa in the axial and radial directions. The Poisson’s ratio was 0.2 in both the circumferential and radial directions and 0.3 in the axial direction [24]. The subject-specific computational models of the soft tissue included articular cartilage, 14 of the major ligaments, the menisci, and the meniscal horn attachments. The 14 primary non-weight-bearing soft tissue structures in the TF joint were the anterior and posterior cruciate ligaments, medial and lateral collateral ligaments, anterior and posterior bundles of the deep medial collateral ligament, popliteal fibular ligament, oblique popliteal ligament, medial and lateral posterior capsules, and an anterolateral structure with non-linear and tension-only spring elements in full extension, as shown in Fig. 3 [25–27]. A contact between the combinations of the femoral cartilage, meniscus, and tibial cartilage was modeled for both the medial and lateral sides. A frictionless contact between the articular structures was defined according to a literature-based pressure-overclosure relationship [28]. Convergence was noted if the relative change between two adjacent meshes was less than 5%. The mean element size was 0.8 mm for the cartilage and menisci. Loading conditions in subject’s Telos testing method and computational model were identical. The total number of nodes and elements for subject-specific knee joint computational model were 177,587 and 177,564, respectively. In addition, ATT, PTT, varus and valgus telos were constrained opposite direction to the loading applied.

Fig. 3.

Computational model used in this study.

3. Results

The results were verified using Rapidform software and the analysis of deviation for the error from model alignment was established for the combined model (Fig. 4). To validate the accuracy of model alignment, the mean mesh size was determined in each model and was found to vary within $0.23 \pm 0.13$ mm and $0.25 \pm 0.11$ mm in the coronal and sagittal views, respectively.

Fig. 4.

3D femoral geometry differences for femur alignment under laxity test conditions: (a) medial sagittal plane; (b) lateral sagittal plane; (c) coronal plane.

The results of the 3D reconstruction reproducibility test performed for the ATT–PTT and varus–valgus tibia translations are summarized in Table 1, and it was demonstrated that inter-observer reproducibility was improved in segmentation using a rule-based approach. The inter-observer reproducibility test showed good reproducibility (CV = 0–1%) for tibial displacement (Table 1). Under 90° flexion, the ATT was 3.32 mm and the PTT was 2.64 mm. With 20° flexion, the varus and valgus gaps were 2.15 and 1.83 mm, respectively. The mean intra-observer change was 0.52 ± 0.13 mm and the intra-observer ICCs for the scan–rescan reliability were 0.99 for each observer. In the assessment of inter-observer reliability, the mean difference between the two examiners was 0.68 ± 0.31 mm. Inter-observer ICCs for scan–rescan reliability were 0.98 for each observer.

Table 1

The inter-observer reproducibility test results

	First observer	Second observer
Anterior tibia translation
Average CV (%)	0.93	0.98
Average movement (mm)	$3.33 \pm 0.17$	$3.30 \pm 0.19$
Posterior tibia translation
Average CV (%)	0.90	0.94
Average movement (mm)	$2.66 \pm 0.10$	$2.61 \pm 0.15$
Varus
Average CV (%)	0.95	0.97
Average displacement (mm)	$2.17 \pm 0.18$	$2.12 \pm 0.19$
Valgus
Average CV (%)	0.98	0.99
Average displacement (mm)	$1.85 \pm 0.11$	$1.82 \pm 0.12$

The ATT–PTT and varus–valgus differences in the subject-specific CT images and computational model are summarized in Table 2. The differences between ATT and PTT with respect to tibial displacement were 1.19 and 1.85 mm in the CT images and the computational model, respectively. The differences between the varus and valgus with respect to tibial displacement were 0.95 and 0.66 mm in the CT images and the computational model, respectively.

Table 2

Difference in displacements for the laxity test and computational model under the laxity test condition

	CT laxity test	Computational model
Anterior tibia translation (mm)	3.32	2.13
Posterior tibia translation (mm)	2.64	0.79
Varus (mm)	2.15	3.10
Valgus (mm)	1.83	1.17

The mean absolute difference in the bony landmarks among the points selected for tibial translation between ATT and PTT was 5.21 mm (standard deviation, SD: 1.25 mm, range: 0.89 to 1.43 mm). The mean absolute difference in the bony landmarks among the points selected for tibial translation between the varus and valgus was 2.21 mm (SD: 1.08 mm, range: 0.96 to 2.13 mm).

The benchmark CT model is displayed graphically with overlapping layers in the supplementary information for the ATT–PTT and varus–valgus conditions in the subject-specific computational and CT image models (Fig. S1).

4. Discussion

This study demonstrated an innovative approach to in vivo validation of kinematics for a subject-specific computational model of the knee joint. Our approach primarily involved innovative methodology using a direct comparison of predictions using an computational model with in vivo measurements under active laxity conditions.

With the majority of current studies using representative computational models, the models have been accepted as validated if their results lie within a certain range of standard deviation of results reported in previous cadaver experiments [1,2,7,16]. As computer technology has developed, the subject-specific model has come to the fore in biomechanics; however, its material non-linearity, irregular loading, geometrical and material domains of the anatomy, and validation remain as challenging issues [10–12]. Until recently, most subject-specific knee models were developed using experimental data from cadavers for the evaluation of kinematic or contact pressure on articular cartilage [5,6,8,29,30]. However, with the rapid development of medical imaging, methods that use medical imaging for the validation of computational models have attracted attention. MRI is beneficial for the validation and in vivo and in vitro material property evaluation of subject-specific models due to its potential to incorporate accurate tissue morphology and boundary conditions [10,12,21,29].

Yao et al. primarily studied the material properties of menisci and articular cartilage for subject-specific cadaver images under anterior loading based on optimization using a design of experiments approach [31]. In addition, Kang et al. used five different MRI images of subjects’ flexion and studied in vivo material properties of meniscal horn attachments using probabilistic subject-specific computational models [21]. Recently, Lenhart et al. reported kinematic validation of a subject-specific model using dynamic MRI images [10]. Previously, based on alignment techniques involving MRI and X-ray images, we have reported in vivo validation of a subject-specific computational model of contact pressure and the area of articular cartilage [12]. However, unlike CT imaging, MRI imaging is not cost-effective and reduces the efficiency and accuracy of 3D reconstruction procedures [32]. Development of a 3D reconstructed model using MRI requires detailed handwork and takes a long time to ensure accuracy and precision; in contrast, the use of CT imaging is a relatively efficient process due to the initial automatic functions.

CT imaging is widely used in the orthopaedic biomedical field, and currently, computational simulation is actively used in pre- and post-operative assessments of knee joints [13,14]. Particularly for ligament reconstruction, computational simulation has been recognized as the gold standard as it does not require the consideration of soft tissues in the reconstruction process [13,14,33].

Objective knee laxity measurement has been a long-cherished desire for physicians and other professionals in the field of orthopaedic surgery [3]. The quantitative analysis of TF displacement with respect to various directions of force in the knee joint has repercussions for both clinical surgeons and biomechanics researchers in orthopaedic surgery [3]. The reliability of knee-testing devices has been extensively studied, and they have been used as validated techniques for long- or short-term follow-up and experimental research [3]. The Telos laxity test device, a mechanical stress device for measuring laxity in injured knees, was used in the present study. This device has been shown to have both superior and inferior reliability in assessing anterior knee laxity when compared with the KT-1000 arthrometer (MedMetric Corp., San Diego, CA, USA) [3]. It was also beneficial that this device could be aligned with the CT scanner during diagnosis.

The reproducibility tests for the 3D reconstruction development in this study demonstrated accuracy and precision because of the use of a rule-based protocol [19]. Inter-observer tests showed that each observer was highly consistent in segmenting tibial displacement from CT images. ICCs as a measure of scan–rescan correlation indicated high reliability. Although the subject in this study was not a patient and had a normal healthy knee, the ATT–PTT and varus–valgus trends showed good agreement with the results from previous studies using stress radiography [4,34]. Our result showed a greater variance in movement in the PTT and valgus compared to that in the ATT and varus, respectively.

Our subject-specific computational model showed knee laxity kinematic trends that were consistent with the CT images, with only negligible differences due to the indirect application of the subject’s in vivo material properties. It would be the global standard in the field of biomechanics to evaluate and validate the subjects’ knee joint properties in vivo.

We have proposed a relatively simple in vivo validation technique for a computational knee joint model under the laxity test conditions. We believe that stress radiographs are a feasible and cost-effective objective measurement tool using alignment with X-ray images for clinicians to document their patients’ pre- and post-operative results based on computational model validation. Ligament instability is a major field of research in sports medicine with the increasing popularity of sports [6,13,14,33,35]. The findings of this study can be beneficial for patient-specific rehabilitation or surgical techniques for common knee injuries, such as ligament rupture, instability, or reconstruction by using surgical simulation given that accurate validation was allowed by the subject-specific model.

This study had some limitations. First, the posterior lateral corner ligament structures were developed based on data from the literature because of uncertainty in the location of the ligament attachment areas in the MRI images. Second, the validation method in high kinematic would be necessary. Third, the articular cartilage was considered to be an elastic material, and the effects of anisotropy and viscoelasticity were not considered. Finally, we used the newly developed method for validation in a single subject of normal knee joint. In order to prove its validity, more subjects are required for study.

Future studies should focus on the evaluation of material properties for major ligaments with supplement of limitations mentioned using medical imaging techniques.

5. Conclusion

This study has introduced a new validation method for a computational model using subject’s own medical image. The potential of effective kinematic validation method for subject-specific model using medical image and laxity test was suggested through this approach.

Supplement

Fig. S1.

The difference between CT image and FE model overlapped under loading condition: transparent femur in FE model (a) ATT, (b) varus, (c) PTT and (d) valgus conditions.

Conflict of interest

The authors have no conflict of interest to report.

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