Kinematics of the Normal Knee: In Vivo Investigation Using Advanced Imaging Technique

Zhitao Rao, MD

Qidong Zhang, MD

Hany S. Bedair, MD

Timothy E. Foster, MD

Harry E. Rubash, MD FAOA

Guoan Li, PhD

INTRODUCTION

Accurate knowledge of knee joint kinematics is vital for understanding normal knee joint function and for investigation of knee joint injury/disease mechanisms as well as for development of efficient treatment methods for knee pathology.¹,²,³ The data on the characteristic motion of the knee is also necessary for design and evaluation of contemporary total knee arthroplasties (TKAs) that aim to restore normal knee function and achieve full range of knee flexion.⁴,⁵,⁶ In literature, numerous researches have reported on the investigation of knee joint kinematics using various measurement technologies.⁷,⁸,⁹,¹⁰,¹¹ These include skin/bone marker-based motion analysis systems⁷ and imaging-based technologies (including X-ray, CT, MRI, fluoroscopy, etc.).²,⁸,⁹,¹²,¹³,¹⁴,¹⁵,¹⁶,¹⁷ In general, these studies have revealed that the knee kinematics is activity- and loading-dependent.¹⁸,¹⁹,²⁰ The femoral condyles were shown to move posteriorly (or called rollback) with knee flexion.²¹,²²,²³ Further, the femoral condyles were found to rotate externally with knee flexion or described with respect to a long tibial axis located at the medial compartment of the tibial plateau (demonstrating a “medial pivoting” motion) during non-weight-bearing¹¹,²⁴ or weight-bearing flexion.²⁵,²⁶,²⁷ Data of these studies have greatly improved our understanding of physiological motion characters of the knee. These knowledges have also provided guidelines for development of contemporary TKA surgeries.²⁸,²⁹ For example, rollback and medial pivoting motion during knee flexion have been discussed in various contemporary TKA component designs.²,⁴,²⁷

The knee joint motion (tibiofemoral joint motion in this chapter) is achieved through articulation between the articular surfaces of the distal femur and proximal tibia. It is therefore critically important to examine the articular contact kinematics of the knee during various functional activities. However, traditional motion measurement technologies are limited to measure the intrinsic articular contact biomechanics of the knee during dynamic, functional activities. Recently, we developed a combined MRI and dual fluoroscopic image system (DFIS) technique for accurate investigation of the knee kinematics during various functional knee joint motion.¹,¹⁴,³⁰,³¹ Using this method, a three-dimensional (3D) model of the target knee, including the tibial and femoral bones and corresponding cartilage surfaces, was constructed using the 3D MR images of the knee. The in vivo knee motion is then captured using two orthogonally positioned fluoroscopy. Through a 2D to 3D matching algorithm, the in vivo knee motion can be reproduced using a series of the 3D knee models, representing accurate 6 degrees of freedom (DOFs) knee kinematics and articular cartilage contact kinematics. In this chapter, we first introduce the combined MRI and DFIS technique and then introduce the data on 6 DOF tibiofemoral joint motion and the articular contact kinematics of the knee during three functional knee activities: treadmill gait (low range knee motion), stair step-up (moderate range of knee motion), and weight-bearing deep flexion (full range of knee motion).

IMAGING TECHNIQUE FOR ACCURATE MEASUREMENTS OF KNEE MOTION

Tibiofemoral Kinematics and Relevant Coordinate Systems

Tibiofemoral kinematics refers to the relative motion of the femur and tibia. Motion of the knee is a synergistic function of many physiological factors around the joint, including the anatomy of the articular surfaces, the passive soft tissues such as ligaments and menisci, and active muscular structures. Cartesian coordinate systems are usually used to describe the relative motions between the tibia and femur (Fig. 8-1). The motion or kinematics of the knee can be described in 6 DOFs in 3 principle planes, i.e., sagittal, transverse, and frontal planes, including three translations along the principle axes and three rotations around the principle axes. The rotations are widely referred as internal-external rotation in transverse plane, varus-valgus rotation in frontal plane, and flexion-extension in sagittal plane.

In investigation of TKA kinematics, it is more conventional to use transepicondyle axis (TEA)³²,³³,³⁴ or geometric center axis (GCA)³⁵,³⁶ to describe femoral condyle motion (Fig. 8-2). The condyle motion and the articulating surface contact motion are not equivalent measurements
and cannot be used interchangeably. The in vivo knee kinematics represented by the 3D knee models at each flexion angle was combined with the anatomical surface models of the cartilage to determine cartilage contact during various activities (Fig. 8-3). The tibial and femoral cartilage surfaces were usually constructed from the MR images of each subject. The method for determination of cartilage contact has been described as the area of overlap of the cartilage models of tibia and femur.¹⁰ The articular contact kinematics is widely represented by an assessment of the positions of the contact point between the two articular surfaces. The contact point was defined as the location where the cartilage contact deformation was maximal in the contact area. To further quantify the geometry of the cartilage contact area, two orthogonal sectional planes, sagittal and coronal, were created at the contact point along the knee motion path. The profiles of the tibial and femoral cartilage in the contact area on these two planes were fitted using circles and the radii were measured (Fig. 8-4). For tibial cartilage, if the tibiofemoral cartilage is in a conforming contact, i.e., its curvature was in the same direction of the femoral cartilage, the radius value was defined as positive; if the tibiofemoral cartilage is in a convex contact, i.e., its curvature was in the opposite direction of the femoral cartilage, the radius value of the tibial cartilage was defined as negative.

FIGURE 8-1 Cartesian coordinate systems and 6 degrees of freedom (DOFs) motions of the knee joint. (Reproduced from Kozanek M, Van de Velde SK, Gill TJ, Li G. The contralateral knee joint in cruciate ligament deficiency. Am J Sports Med. 2008;36(11):2151-2157. Reprinted with permission.)

FIGURE 8-2 Schematic drawing showing (A) the transepicondylar axis (TEA) and the geometrical center axis (GCA); (B) the mediolateral axis connecting the centers of the medial and lateral compartments. (Modified from Li JS, Hosseini A, Cancre L, Ryan N, Rubash HE, Li G. Kinematic characteristics of the tibiofemoral joint during a step-up activity. Gait Posture. 2013;38(4):712-716. Reprinted with permission.)

Coordinate System for Measurement of 6 Degrees of Freedom Kinematics

To calculate the 6 DOF kinematics during various activities, a coordinate system was built for each femur and tibia (Fig. 8-1). In the femoral coordinate system, the medial-lateral axis was first defined as the TEA, which passed the most pivot points on the medial and lateral
condyles.³²,³⁴ The mid-point of the axis was defined as the femoral center. The femoral long axis was parallel to the shaft of the femur and passed through the femoral center. The anterior-posterior axis was perpendicular to the other two axes. In the tibial coordinate system, the tibial long axis was defined as the line parallel to the posterior tibial shaft wall. Two circles were created to fit the medial and lateral plateaus separately.³⁷ The line connecting the centers of these two circles was defined as the medial- lateral axis and the mid-point as the tibial center. The cross product of the medial-lateral axis and the tibial long axis was defined as the anterior-posterior axis of the tibia. In this chapter, we present the data of 6 DOF knee kinematics, including knee flexion, internal-external tibial rotation, and varus-valgus rotation, as well as anteroposterior translation, medial-lateral translation, and proximal distal translation.³⁸

FIGURE 8-3 A: Measurement of cartilage contact area and deformation of the knee joint. B: The coordinate system for measurement of cartilage contact locations on the tibial plateau. (Modified from Yin P, Li JS, Kernkamp WA, et al. Analysis of in-vivo articular cartilage contact surface of the knee during a step-up motion. Clin Biomech. 2017;49:101-106. Reprinted with permission.)

FIGURE 8-4 Schematic diagrams showing the measurement of cartilage surface geometry at the contact areas in the sagittal and coronal planes. (Reproduced from Yin P, Li JS, Kernkamp WA, et al. Analysis of in-vivo articular cartilage contact surface of the knee during a step-up motion. Clin Biomech. 2017;49:101-106. Reprinted with permission.)

Definitions of TEA/GCA for Measurements of Condylar Motions

The TEA was defined as the line connecting the sulcus of the medial condyle and the lateral condyle prominence,³²,³³,³⁴ whereas the GCA was constructed by fitting maximal circles to the posterior medial and lateral condyles in sagittal plane and by connecting the centers of these circles with a line (Fig. 8-2). The center points were defined as the
femoral condyle centers of the GCA. The medial and lateral condyle centers of the TEA were defined as the crossing points of the TEA and the two sagittal circle planes. The anatomical coordinate system of the proximal tibia was established to quantitatively describe the positions of the TEA or GCA on the tibial plateau surfaces. For measurements of the AP translations of TEA and GCA centers, the corresponding points were projected onto the transverse tibial plane.³⁷

Coordinate Systems for Cartilage Contact Kinematics/Deformation

Tibial coordinate systems constructed above using two circles to fit the medial and lateral plateaus were applied to describe the motion of the contact points²⁰,³⁹,⁴⁰ (Fig. 8-3B). The center of each circle was the origin of the coordinate system. The medial-lateral axis (X-axis) for the medial and lateral tibial plateaus was created by drawing a line through the origin of each coordinate system, parallel to the posterior edges of the tibial plateaus. The anterior-posterior axis (Y-axis) for each tibial plateau was created by drawing a line through the origin of the coordinate system perpendicular to the respective medial-lateral axis. The two quadrants nearest the tibial spine were defined as the “inner half,” and the remaining quadrants the “outer half.”

Dual Fluoroscopic Image System

The dual fluoroscopic imaging system (DFIS) setup (Fig. 8-5) is used for dynamic knee joint kinematics analysis.³⁰ The DFIS consists of two pulse fluoroscopes (BV Pulsera, Philips) that are set to generate 8 ms width X-ray pulses. A subject is free to move within the common imaging zone of the two fluoroscopes (corresponding to a 315 × 315 mm field of view). Various motions can be imaged this way such as treadmill gait, stair step-up, sit-to-stand, lunge, and squat, etc. The knee is imaged simultaneously by the fluoroscopes from two directions. The fluoroscopes took 30 evenly distributed snapshot images per second during dynamic knee joint motion. This procedure records the in vivo poses of the knee as a series of two-dimensional (2D) paired fluoroscopic images. The images are then segmented and corrected for distortion. The outlines of the knee structures from the edge detection are manually reviewed and saved. Next, a virtual replica of the DFIS is constructed in a solid modeling software. Two virtual source-intensifier pairs are created in the modeling software to recreate the geometry of the real fluoroscopic system. The outlines of the knee obtained from the DFIS are placed on their respective virtual intensifiers. Three-dimensional (3D) models of the knee are introduced into the virtual system. The tibial and femoral models can be manipulated independently in the virtual environment in 6 DOF and projected onto the virtual imaging intensifiers. If the projection outline matches the actual bony outline captured from the actual knee, the in vivo knee position in space is reproduced by the 3D knee models in the computer. In this manner, the knee motion can be represented by a series of 3D knee models reproduced along the motion path. Joint coordinate systems described previously can then be used to determine the 6 DOF knee joint kinematics.²⁵,³¹,³⁷,⁴¹

The DFIS technique has been rigorously validated for measurements of in vivo knee joint kinematics.³⁰ It could determine knee position with an accuracy of 0.16° ± 0.61° in rotation and 0.24 ± 0.16 mm in translation when compared to radiostereometric analysis (RSA). The cartilage contact area could be determined with 14% ± 11% error of measurement. Finally, the cartilage thickness based on MR meshed models could be constructed with an error of 0.04 ± 0.01 mm (corresponding to a 1.8% ± 1.6% difference).

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