Virtual axis finder: a new method to determine the two kinematic axes of rotation for the tibio-femoral joint

Contralateral preoperative templating of lower limbs' mechanical angles is a reasonable option

PURPOSE

In cases where the femur or tibia exhibits abnormal mechanical angulation due to degenerative changes or fracture, the contralateral leg is often used to complete preoperative templating. The aim of this study was to determine the degree of asymmetry between knee joints in healthy individuals and to determine whether it is affected by differing demographic parameters.

METHODS

A CT scan-based modelling and analysis system was used to examine the lower limb of 233 patients (102 males, 131 women; mean age 61.2 ± 15.2 years, mean body mass index 24.9 ± 4.4 kg/m²) The hip-knee angle (HKA), lateral distal femoral angle (LDFA), medial proximal tibial angle (MPTA), posterior proximal tibial angle (ppta) and posterior distal femoral angle (PDFA) were then calculated for each patient. Results were then analysed to calculate femoral symmetry based on absolute differences (AD) and percentage asymmetry (%AS) using a previously validated method.

RESULTS

Our results do not demonstrate any considerable asymmetry (percentage of asymmetry > 2%) for all the anatomical parameters analysed: HKA (mean AD = 1.5°; mean AS % = 0.8, n.s), MPTA (AD = 1.1°; AS % = 1.3, n.s), PPTA (AD = 1.4°; AS % = 1.0, n.s), LDFA (AD = 1.2 mm; AS % = 1.4, n.s) and PDFA (AD = 0.9°; AS % = 1.0, n.s). Gender and ethnicity were not associated with significantly higher AD asymmetry. A significant correlation of AD asymmetry was observed between BMI and HKA, BMI and MPTA, and between patients' age and the MPTA.

CONCLUSION

This data demonstrate that there is a non-statistically significant mechanical angle asymmetry between the two lower limbs. In cases where contralateral templating is used, such asymmetry will induce minimal (if any) clinical differences.

LEVEL OF EVIDENCE

IV.

In vitro determination of the passive knee flexion axis: Effects of axis alignment on coupled tibiofemoral motions

The natural passive flexion axis of human cadaveric knees was determined using a technique that minimized coupled tibiofemoral motions (translations and rotations), and the kinematic effects of mal-positioned flexion axes were determined. The femur was clamped in an apparatus that allowed unconstrained tibial motions as the knee was flexed from 0° to 90°. To establish the natural flexion axis, the femur's position was adjusted such that coupled tibiofemoral motions were minimized. Tests were repeated, first with the femur rotated internally and externally from its original position, and again after positioning the femur to flex the knee about the transepicondylar axis. Compared to the transepicondylar axis, flexion about the natural axis significantly reduced mean tibial translation by 66.4% (p < 0.01) and varus-valgus rotation by 70.1% (p <0.01). Mean varus-valgus rotation increased by 3.4° (factor of 4) when the femur was rotated 3° internally or externally from the optimum position. Differences in condylar location coordinates between the transepicondylar and natural flexion axes most likely indistinguishable clinically. Knee flexion about an axis that minimizes coupled tibiofemoral motions could be important for placement and orientation of a femoral total knee component and for specimen alignment during biomechanical knee testing.

Conceptual design and implantation of an external fixator with improved mobility for knee rehabilitation

A hinged external fixator is used to allow early knee rehabilitation in case of injury or trauma, as an alternative approach to immobilization. It is mainly adopted for the treatment of dislocations, which involve tearing of the ligaments, and it basically consists of two links connected to each other by a revolute joint. Each link is fixed to the femur and tibia via pin fixation, and the revolute joint is approximately aligned to the knee flexion-extension (FE) axis. The advantage in its implantation is to protect ligament reconstruction, while allowing for an aggressive rehabilitation. Traditional fixators only accommodate the functional flexion movement in a limited range, i.e. where the anatomical movement is closer to a planar circular trajectory. This paper presents the conceptual design and implantation procedure of a double-axis fixator, which accommodates both FE and longitudinal internal-external rotation. The procedure is based on accurate knee kinematics measurements and on computer-aided multibody simulations to assist clinicians in the implantation. An experimental test is presented using an artificial knee, and guidelines are given for in vitro studies. The proposed technique may allow for a better understanding of knee kinematics and have the potential advantage to increase the range of motion in postoperative rehabilitation.

Identifying the Functional Flexion-extension Axis of the Knee: An In-Vivo Kinematics Study

Purpose

This study aimed to calculate the flexion-extension axis (FEA) of the knee through in-vivo knee kinematics data, and then compare it with two major anatomical axes of the femoral condyles: the transepicondylar axis (TEA) defined by connecting the medial sulcus and lateral prominence, and the cylinder axis (CA) defined by connecting the centers of posterior condyles.

Methods

The knee kinematics data of 20 healthy subjects were acquired under weight-bearing condition using bi-planar x-ray imaging and 3D-2D registration techniques. By tracking the vertical coordinate change of all points on the surface of femur during knee flexion, the FEA was determined as the line connecting the points with the least vertical shift in the medial and lateral condyles respectively. Angular deviation and distance among the TEA, CA and FEA were measured.

Results

The TEA-FEA angular deviation was significantly larger than that of the CA-FEA in 3D and transverse plane (3.45° vs. 1.98°, p < 0.001; 2.72° vs. 1.19°, p = 0.002), but not in the coronal plane (1.61° vs. 0.83°, p = 0.076). The TEA-FEA distance was significantly greater than that of the CA-FEA in the medial side (6.7 mm vs. 1.9 mm, p < 0.001), but not in the lateral side (3.2 mm vs. 2.0 mm, p = 0.16).

Conclusion

The CA is closer to the FEA compared with the TEA; it can better serve as an anatomical surrogate for the functional knee axis.

Optimized Design of an Instrumented Spatial Linkage that Minimizes Errors in Locating the Rotational Axes of the Tibiofemoral Joint: A Computational Analysis

An accurate method to locate of the flexion-extension (F-E) axis and longitudinal rotation (LR) axis of the tibiofemoral joint is required to accurately characterize tibiofemoral kinematics. A method was recently developed to locate these axes using an instrumented spatial linkage (ISL) (2012, “On the Estimate of the Two Dominant Axes of the Knee Using an Instrumented Spatial Linkage,” J. Appl. Biomech., 28(2), pp. 200–209). However, a more comprehensive error analysis is needed to optimize the design and characterize the limitations of the device before using it experimentally. To better understand the errors in the use of an ISL in finding the F-E and LR axes, our objectives were to (1) develop a method to computationally determine the orientation and position errors in locating the F-E and LR axes due to transducer nonlinearity and hysteresis, ISL size and attachment position, and the pattern of applied tibiofemoral motion, (2) determine the optimal size and attachment position of an ISL to minimize these errors, (3) determine the best pattern of pattern of applied motion to minimize these errors, and (4) examine the sensitivity of the errors to range of flexion and internal-external (I-E) rotation. A mathematical model was created that consisted of a virtual “elbow-type” ISL that measured motion across a virtual tibiofemoral joint. Two orientation and two position errors were computed for each axis by simulating the axis-finding method for 200 iterations while adding transducer errors to the revolute joints of the virtual ISL. The ISL size and position that minimized these errors were determined from 1080 different combinations. The errors in locating the axes using the optimal ISL were calculated for each of three patterns of motion applied to the tibiofemoral joint, consisting of a sequential pattern of discrete tibiofemoral positions, a random pattern of discrete tibiofemoral positions, and a sequential pattern of continuous tibiofemoral positions. Finally, errors as a function of range of flexion and I-E rotation were determined using the optimal pattern of applied motion. An ISL that was attached to the anterior aspect of the knee with 300-mm link lengths had the lowest maximum error without colliding with the anatomy of the joint. A sequential pattern of discrete tibiofemoral positions limited the largest orientation or position error without displaying large bias error. Finally, the minimum range of applied motion that ensured all errors were below 1 deg or 1 mm was 30 deg flexion with ±15 deg I-E rotation. Thus a method for comprehensive analysis of error when using this axis-finding method has been established, and was used to determine the optimal ISL and range of applied motion; this method of analysis could be used to determine the errors for any ISL size and position, any applied motion, and potentially any anatomical joint.

Validation of a New Method for Finding the Rotational Axes of the Knee Using Both Marker-Based Roentgen Stereophotogrammetric Analysis and 3D Video-Based Motion Analysis for Kinematic Measurements

In a previous paper, we reported the virtual axis finder, which is a new method for finding the rotational axes of the knee. The virtual axis finder was validated through simulations that were subject to limitations. Hence, the objective of the present study was to perform a mechanical validation with two measurement modalities: 3D video-based motion analysis and marker-based roentgen stereophotogrammetric analysis (RSA). A two rotational axis mechanism was developed, which simulated internal-external (or longitudinal) and flexion-extension (FE) rotations. The actual axes of rotation were known with respect to motion analysis and RSA markers within ±0.0006 deg and ±0.036 mm and ±0.0001 deg and ±0.016 mm, respectively. The orientation and position root mean squared errors for identifying the longitudinal rotation (LR) and FE axes with video-based motion analysis (0.26 deg, 0.28 m, 0.36 deg, and 0.25 mm, respectively) were smaller than with RSA (1.04 deg, 0.84 mm, 0.82 deg, and 0.32 mm, respectively). The random error or precision in the orientation and position was significantly better (p=0.01 and p=0.02, respectively) in identifying the LR axis with video-based motion analysis (0.23 deg and 0.24 mm) than with RSA (0.95 deg and 0.76 mm). There was no significant difference in the bias errors between measurement modalities. In comparing the mechanical validations to virtual validations, the virtual validations produced comparable errors to those of the mechanical validation. The only significant difference between the errors of the mechanical and virtual validations was the precision in the position of the LR axis while simulating video-based motion analysis (0.24 mm and 0.78 mm, p=0.019). These results indicate that video-based motion analysis with the equipment used in this study is the superior measurement modality for use with the virtual axis finder but both measurement modalities produce satisfactory results. The lack of significant differences between validation techniques suggests that the virtual sensitivity analysis previously performed was appropriately modeled. Thus, the virtual axis finder can be applied with a thorough understanding of its errors in a variety of test conditions.