Biomechanics: The Late Effects Of Meniscectomy

Introduction
Biomechanics (the science of analyzing the mechanics of biological systems) provides useful insight to current global healthcare issues such as cardiovascular problems and musculoskeletal disorders (MSDs). Cardiovascular diseases and stroke account for 1 in 4 deaths in US (CDC Wonder Online Database) and account for more than $312.6 billion in cost (AHA Statistical Update 2014). MSDs such as Osteoarthritis (OA) – a joint disease that deteriorates the articular cartilage - reduce the quality of life and are estimated to cost a total of $125 billion per year [Gallagher et al. 2013]. OA accounts for a considerable portion of this cost. Lawrence et al. (2008) estimated that 13.9% of adults aged 25 year and older are affected by OA.

And it results in a $28.5 billion and $13.7 billion for total knee and hip joint replacements respectively per year [Murphy and Helmick 2012].
Rigid Body Dynamics, Solid Mechanics and Fluid Mechanics are the three main mechanical engineering principles that are used to answer research questions in the fields of Musculoskeletal System, Tissue deformities and Cardiovascular System respectively. Cardiovascular systems are beyond the scope of this manuscript and will not be discussed any further (The field is discussed in detail by K. B. Chandran).
Numerous treatments of musculoskeletal disorders consider the joint as an organ and not as a collection of individual independent tissues. The interaction of tissues with each other in every organ, play an important role in the well-being of the whole organ. Any change to even one of the tissues might jeopardize a healthy joint. A follow up study on 1337 John Hopkins medical students (91% male, 91% white and mean age 22 years) reported an increased risk of developing OA significantly following a joint injury (relative risk of 5.17) [Gelbar et al. 2000]. Abnormal joint pressure is regarded as one of the common pathways leading to degenerative joint diseases such as OA. Therefore, mechanical environment in the joint and any disturbance of it (either by impact injuries or musculoskeletal disorders) has been the subject of many studies.
For example Meniscal tears and the subsequent meniscal surgery is believed to be one of the established risk factor in onset of OA in the knee. Out of the 155 patients (mean age = 54 years old) who had undergone partial meniscectomy surgery with no other injury, 43 percent had radiographic features of osteoarthritis while 59% of those were symptomatic after 16 years [Englund et al. 2003]. Conservative treatments are usually considered for patients with less physically demanding life styles. However, they have been proved to be ineffective in response to joint injuries such as ACL ruptures. Out of the 73 patients with acute ACL ruptures classified suitable for primarily conservative treatment after a preoperative screening, only one third show a good or very good result [Strehl A and Eggli, 2007].
Notion of treating the joint as a whole organ, not as individual tissues, has resulted into elimination of invasive surgeries such as meniscectomy (complete removal of injured menisci).

A study on the late effects of meniscectomy ten to thirty years after surgery revealed that only 10 percent of women who underwent the surgery had symptom-free knees [TAPPER et. al, 1969]. Less invasive methods such as arthroscopic surgeries have been introduced to preserve the joint capsule as much as possible and have provided satisfactory results. For instance, central quadriceps tendon-bone autograft performed on patients with ACL injuries produced successful results in a majority of patients 27 to 49 months post operatively [Lee et. al, 2004]. Therefore, the complicated interaction of tissues inside the knee plays a crucial role in the well-being of the organ. Thorough understanding of this complex interaction enables the healthcare professionals to design better treatment plans and also provide better injury prevention

methods.
Injuries and chronical musculoskeletal problems often times lead to abnormal joint kinematics and kinetics. Therefore, the best outcome of a treatment plans is restoring the joint kinematics and kinetics. However, the normal kinematics and kinetics of the joint is not completely understood. Therefore, the surgical interventions to restore the joint to the initial condition are limited. Information about internal mechanics of the joints as well of forces exerted by the muscles during ambulatory activities can help solve this problem.
Experimental studies, both in-vitro cadaveric studies and in-vivo (experiment whithin the living organism) gait measurements, have provided insight into musculoskeletal disorders and also the interactions of the nervous and musculoskeletal systems of the body, interactions that result in coordinated motion of body segments relative to each other.
Cadaver experiments are used for different purposes; for example, measuring material properties of soft tissue, studying the mechanical response of the joint to specific loading conditions and also serving as a validation tool for computational studies.

For instance, industrial six-degree of freedom robots matched with a universal force-moment sensor (UFS) have been used recently to calculate the internal forces of the joint in addition to measuring accurate kinematics in the 3-D envelope of motion. One example was the Kawasaki ZX165U matched with a Delta UFS (ATI). Heyse et al. (2015) analyzed the ability of Unicondylar Knee Arthroplasty (UKA) to restore the kinematics of the knee both in Balanced (normal installation of the implant) and Overstuffed (thicker inlay of polyethylene in the medial compartment) implant. The kinematics were measured in response to axial loading of 200 N in addition to a 15 Nm Abduction moment. Another example of utilizing an industrial robot matched with a UFS was presented by Kanamori et al. (2000). A Puma robot model 762 (Unimate, Pittsburgh, PA) was matched with model 4015 UFS (JR3, Inc, Woodland, CA) in order to compare the kinematics of intact and ACL deficient knee in response to tibial torque of 10Nm and pivot shift test (A combination of 10-Nm internal tibial torque and 10-Nm Valgus). Moreover, the ACL force was calculated at specific knee angles by serial sectioning method, a method in which the force taken by a constraint (ACL in this

case) is measured by comparing the loading applied by the robotic arm before and after dissection, when the knee is in that specific spot. Mechanical testing equipment has also been used to explore the joint kinematics and kinetics in only one or two degrees of freedom. For example Senavongse and Amis (2005) used an Instron 1122 materials testing machine (Instron Ltd., Massachusetts, US) to analyze the medial-lateral stability of the patella after injury on eight cadaver knees.
Another avenue in experimental biomechanics is gait analysis. Motion capture systems track the position and orientation of body segments while force plates determine the direction and magnitude of the resultant ground reaction force and surface electromyography (EMG) electrodes as well as indwelling EMG sensors record the activation of muscles. Indwelling EMG electrodes such as quadrifilar needle sensors and quadrilfilar wire sensors have been used in the past (De Luca, C.J et. al, 1972) to record EMG signals from individual muscles. Due to the fact that they are inserted into the muscle, indwelling electrodes do not record any cross talk providing a more accurate activation signal. Moreover, indwelling electrodes have access to muscles in deeper layer of the body. On the other hand, surface EMG electrodes provide a better indication of overall muscle activation, thus, surface EMG electrodes are mainly used in the field musculoskeletal biomechanics.
Gait analysis can be used to evaluate athletic performance in addition to analyzing injury probability among other applications. Gait measurements provide useful information on the moments acting on the joint and also ground reaction force but they are inadequate when it comes to internal loading of the joints and mechanical interactions of the joint’s tissues. Hewett et al. (2004) used an Eagle camera system (Motion Analysis) combined with force measurement from AMTI force plates to determine that increased valgus moment and valgus motion of the knee at the impact phase of landing are key predictors of an increased potential for ACL injury.
Experimental studies provide valuable insight into the kinetics and kinematics of the joint. However, there are so many limitations to these types of experiments. Cadaveric studies mostly use old subjects and there is no data on whether old cadavers and young cadavers have the same mechanical characteristics [Couppé et al. 2009]. Thus, application of the results in clinical settings is under question. Moreover, muscle forces, which play an important role in stability and load distribution of the joints, cannot be utilized. In gait analysis, joints torques are calculated by modeling the human joints as simplified engineering joints, for example, hip is modeled as a ball and socket joint. Joint torques provides useful information especially in injury prevention and athletic training. However the results do not provide any information about the internal mechanics of the joint such as ligament forces and contact pressure. Another downside of experimental analysis is the expensive cost of the equipment and also availability of the subjects. Moreover, experimental methods are prone to operator errors and equipment malfunction. For instance, in cadaveric studies, a malfunctioning digitizer might threaten the integrity of the data. Furthermore, quantities such as tissue deformation are almost impossible to measure in-vivo and in-vitro(experiment performed outside the normal biological contex).
In Silico Methods (using computational models to conduct a biological experiment) in contrast to experimental methods are capable of examining the loading environment of the joint. Computational models will be helpful in understanding the mechanical interaction of tissues within a joint and enables researchers to answer the questions that are not possible in the real world. Most importantly, computational models can answer “What if” scenarios easily by modifying a few parameters. Due to the complex non-linear nature of soft tissues material properties (Anisotropy, Inhomogeneity and Viscoelasticity), computational methods are widely used to study the function and structure of soft tissues. For example Lai et al. (2015) developed a Finite Elements (FE) technique (a computational method that finds approximate solution to a partial differential equations system) to study the knee laxity. Nine anatomical knees were modeled using the femoral and tibial cartilage, menisci, cruciate and collateral ligaments. The only difference between the models was the stiffness of the PCL. Posterior translation of the tibia was examined in result of a 100 N posterior tibial drawer load.
FE provides detailed data into mechanical environment of the biological tissue. For example, strain within tissue can only be studied using FE methods. However, FE models are computationally intensive; those models are used to analyze specific loading conditions that result in small deformations or vice versa. For instance, Kiapour et al. (2014) predicted the contact mechanics and kinematics of an anatomical knee in response to only four simple quasi-static loading profiles. Thus, FE models typically only analyze a small portion of the 3-D envelope of motion and understanding of joint mechanics in a dynamic situation is not feasible.
In contrast to FE models, rigid multi-body dynamics modeling (modeling the systems as a group of interconnected rigid bodies, which may undergo significant translation and rotational motion relative to each other) provides a system of equations that is noticeably less computationally intensive and requires considerably less time to solve. Therefore, enables the researchers to examine more complex models both in terms of structure and boundary conditions. Simulating ambulatory activities is possible in multi-body environment with the current state of processing technology available to public. But modeling the full range of motion of the knee in the finite elements model requires a considerable computational effort as well as oversimplification the boundary loading condition [Shim et al. 2015].
For example, Shelburne et al. (2006) developed a computational model of the leg in rigid body environment to predict the knee contact force. They used a dynamic optimization solution of normal walking to calculate ground reaction force, joint angle and muscle forces.
Rigid multi-body modeling is an efficient method in modeling the contact mechanics of articular cartilage. Due to the high deformability of the menisci, modeling the menisci in the multi-body environment is a challenging process. Therefore modeling the menisci is avoided in many of the computational studies (Bei et al, 2004). However, a larger number of studies model menisci in the FE environment (Peña et. al, 2006).
This manuscript presents two separate studies designed to develop a multi-body model of the human body to simulate ambulatory activities such as gait. The goal of the computational method is to predict the loading environment of the knee by calculating the muscle forces.
Chapter two presents a method to calculate the resting length or zero load length of the bundles of ligaments of the knee using an iterative process. A multi-body computational model of the right leg of the subject is developed using magnetic resonance imaging (MRI) of the lower leg in addition to the motion measurements of the lower and upper leg in the kinematic envelope of motion.
Chapter three presents development and validation of a full body computational model of gait using the data from chapter two in addition to motion data recorded from the subject during the gait trial. Ground reaction forces (GRF) recorded from force plates in the ground and the joint angles during the Inverse kinematic simulation are used as means of validation for the model. Following the validation of the model by comparing the ground reaction forces predicted by the model and measured during the experiment, two different objectives were achieved.
1. Patellofemoral pressure distribution was studied in response to manipulation of patellofemoral tendon, both in terms of insertion and laxity of the tendon to analyze two pathological situations.
2. The motion of menisci with respect to tibia was examined during gait in response to different horn attachment stiffness.
Chapter Four presents a conclusion and summarizes the points covered in the manuscript.

Knee Ligament’s Resting Length in a Subject Specific Model
Introduction
The knee joint is one of the most important joints in the body and it is vulnerable to both acute and chronic injuries. ACL rupture, the most common knee injury [Woo et al. 2002], accounts for approximately $3 billion dollars of healthcare cost [Brophy et al. 2009]. ACL injury leads to kinematic changes in the knee, leading to abnormal loading distribution of contact pressure on the articular cartilage [Imhauser et al. 2013]. Due to this change in the contact area, some of the areas that have not been under compression loads are now under dynamics loading. Andraicchi et al. (2004) suggested that changes in mechanical loading of the joint results in the onset and progression of OA. Chronic debilitating conditions such as OA and patellofemoral pain syndrome are also very common. OA affects over 20% of adults over the age of 25 in hip or knee [Helmick et al. 2008].
Understanding this mechanical environment requires a deep knowledge of interaction of soft tissues, mainly articular cartilage, menisci and the ligaments. However in-vivo measurement of forces acting on the ligaments, articular cartilage and menisci is not feasible. Computational models on the other hand provide researchers with tools that enable them to study almost every aspect of the joint biomechanics.
Ligaments are often modeled as bundles of elastic nonlinear springs, with a piece-wise function, modeling the two elastic loading regions; nonlinear toe region and linear region [Blankevoort et al. 1991 and Guess, Stylianou and Kia 2014]. The toe region ends when all of the fibers have become taut [Weiss et al. 2005] and the ligaments can be modeled as a constant stiffness linear spring.
The length at which the ligament starts carrying load (the beginning of the toe region) is called the ligament resting length or the zero-load length. Previous sensitivity studies conducted in our lab suggest that the force predicted by the model in the ligament is highly sensitive to the zero-load length. Therefore, calculating an accurate value for the ligament resting length in each bundle is crucial in developing a computational musculoskeletal model.
This chapter presents a method to measure this length for each the ligament bundles using MRI and motion data recorded during the knee laxity test (the medical procedure that attempts to put force only on the passive elements of the joint). 
Methods
Experimental Procedure
The Experimental Procedure was conducted by researchers in the Musculoskeletal Biomechanics Research Laboratory (MBRL) of the University of Missouri – Kansas City (UMKC). This section is presented here for the sake of better understanding of the material.
A young female with no prior lower extremity injuries have been selected for the study (age: 20 years, height: 159.5 cm, mass: 59 kg). The subject signed a written consent approved by the Internal Review Board (IRB) of the UMKC to participate in the study.
Two Bone Localizers, one for Tibia and one for Femur were fitted on to the subject prior to MRI. The purpose of the localizers is to register segments of lower body to the motion capture coordinate system for modeling purposes. Radius of curvature was different between the localizers in order to fit the upper leg and lower leg properly. Mustard is visible in the MRI and it was used in the two orthogonal hollow tubes inside the localizers. Those cylinders were later used in developing the computational model to register the bone geometries to motion capture data.

Figure 2-1. Custom Designed Localizers. The localizer on the femur (a) has a different radius of curvature than the localizer on the tibia (b).
The localizers have 4 small spots that house reflective markers. After the MRI four markers are attached in order to capture the motion of lower and upper segment of the leg. A second localizer was attached on the shin bone in order to provide better information on the location of the lower body. Since there is almost no soft tissue on the shin bone, the markers attached to the second localizer provide more accurate information with less skin artifact.

Figure 2-2.

In the next step a surgeon manipulated the knee in the whole range of motion in order to examine the kinematic envelope of motion (KEM). The subjects were instructed to lay on their back and relax their leg muscles while the surgeons was moving the knee through the complete range of flexion-extension, abduction-adduction and internal-external rotations in addition to translation in anterior-posterior, medial-lateral and vertical direction. The surgeon was instructed to minimize the force on the passive elements of the knee.
Computational Model
After the imaging, 3D Slicer (www.slicer.org), was used to segment the geometries from MRI. The geometries were saved as STereoLithography (STL) files. Post processing of the geometries such as smoothing, reducing noise, removing spikes, removing tunnels and holes was performed using Geomagic Studio (Geomagic, Inc. Research Triangle Park, NC).The final geometries are shown in Figure 2-3.

Figure 2-3.

In order to model the contact mechanics of the articular cartilage, the modeling software, MSc Adams (MSC Software Corporation, Santa Ana, Ca), calculates the penetration and the speed of penetration of the geometries (Equation). The only geometries that were used to define the contacts were femoral cartilage and tibial cartilage. Therefore, the surface of those geometries should match the MRI exactly. In the rest of the geometries, the number of surface elements was reduced as much as possible to help reducing the size of the files, making the model more efficient. In the geometries that were used to define contact (Tibial and femoral cartilage), the number of surface elements were reduced too. However, the majority of the reduction in size is only performed on the side that is not involved in any contact interactions. For example, number of elements in the upper side of femoral cartilage (concave side) is significantly reduced while the articulating side is only slightly reduced (convex side). The final element count between 10,000 and 20,000 provides an appropriate file size and also simulation time. It should be noted that after the final processing of the geometries, all of them were imported into the Slicer environment and the contact surface the geometries were compared against the MRI.
A multibody computational model of the right leg was created from the geometries in the MRI position in MSC Adams environment. The femoral and tibial cartilages were attached rigidly by a fixed joint to the upper leg and lower leg respectively. The fixed joints are located at the center of mass for each cartilage part which is calculated automatically in ADAMS based on the volume and the density (1.08E-006 kg/mm3) of the geometry. Contact force elements are created between tibial articular cartilage and femoral articular cartilage. The contact force is predicted by combining a Hertzian contact model with a damper to allow for energy dissipation [Sharf and Zhang, 2006]. Contact force is defined as a function of geometry penetration depth and penetration depth velocity:
〖Equation 2-1 F〗_c=kδ^n+B(δ)(δ ̇)
Where F_c is the contact force, k is the contact stiffness, B(δ)is the damping coefficient, k is the contact stiffness, δ is the penetration of the contacting geometries and δ ̇ is the velocity of interpenetration. Contact parameters in tibio-femoral joint have been found by a recent Optimization study to be Kc, = 327, B = 5 and n = 2.07[Guess et al, 2010]. In that optimization study, contact parameters were systemically modified as design variables so that the Multibody model prediction matches the model of the same knee in the finite element environment.
The ligaments were represented as one-dimensional nonlinear springs. The model included two bundles for the Anterior Cruciate Ligament (ACL) and Posterior Cruciate Ligament (PCL). The Lateral Collateral Ligament (LCL) was divided into three bundles. And Medial Collateral Ligament (MCL) was modeled in order to define the functions of both deep bundle and superficial bundles of the ligament. The deep bundle is divided into two bundles (anterior and posterior dMCL) and the superficial bundle is divided into three bundles (anterior, intermediate and posterior sMCL). Ligaments were attached to bone based on the origin and insertions identified from the MRI. A complete overview of ligament attachments and mechanical properties has been presented in Appendix A. Ligament Force elements predict the force by combining the static and dynamic response of the ligament to movement of lower leg relative to upper leg.
The static response is defined based on the force length relationship described by Blankevoort (1991) and Wismans J (1980).

0 ε2ε_1

Where ε=((l-l_0)/l_0 ) is defined as the engineering strain. K is a stiffness parameter with dimension of force. (Table) presents the values used for k in different ligaments of the knee. ε_1 was assumed to be 0.03 in order to include the non-linear toe region of the force-length curve [Li G et al. 1999]. The objective of this study is to calculate an accurate value of l_0. The initial value for l_0 was set to the distance between the insertion and origin of each bundle measured from MRI.
The active component of ligament response is defined as a parallel damper. The damping coefficient is different when the ligament is lengthening and shortening. Damping coefficient for lengthening is assumed to be 0.5 Ns/mm while the value for shortening was assumed to be 0.01.

Figure 2-4.

The motion data during the laxity test records the location of each motion marker in space. There may be a difference between the relative location of localizer and bone between MRI and the laxity test. This difference is caused by the movement of soft tissue beneath the markers also known as the skin motion artifact [Nester et al. 2007].
In order to address this problem, an equilibrium simulation was performed. Femur and Tibia Localizer geometries were imported into the model as individual parts. The lower leg and upper leg were attached to the localizers via a 6 degree of freedom spring parallel with a damper. Such element is defined as a Bushing element in ADAMS. Each of the motion markers were also attached via a bushing to four motion markers. The stiffness and damping of mentioned bushing are presented in the (table). The bushings between body segments and localizers are defined at a single location (2 parts 1 Location). However, the bushing between the motion markers and localizers are defined between two different locations (2 Parts 2 Points). This equilibrium (10 seconds of simulation) allows the localizers to move slightly in the space to match the “best fit position” before starting the simulation of laxity test.
After adjusting the location of the localizers relative to the bone, the localizers were rigidly attached to the bone by deleting the bushings between the localizer and the leg segments with fixed joints. The stiffness of the bushings between motion constrains and the localizers were reduced too. The stiffness and damping values for the bushings are presented in the table.

Bushing between body segment and localizer Bushing between motion marker and localizer Bushing between motion marker and localizer After Equilibrium
Translational Stiffness 80 100 10
Translational Damping 10 10 1
Rotational Stiffness 10 100 0
Rotational Damping 1 10 0
Table 2-1
Simulation
An iterative procedure was performed to determine the zero-load length for each ligament bundle. The goal was to reduce the load taken by each ligament bundle during the simulation. Despite the careful manipulation of the surgeon while performing the laxity test, ligaments carry a minimal load through the KEM. Therefore, a threshold of 50N was set and the objective of the study was to reduce the maximum load on each ligament bundle during simulation below the threshold. 50N corresponds to 3-5.5% ligament strain which is approximately the ligament strain at the transition between nonlinear to linear portions of the force length relationship.
At each iteration step, a simulation of knee laxity test was performed (approximately 2 minutes simulation) with a step size of 0.01 s. Each simulation takes about 40 seconds on a machine with Intel Core i7-4770 @ 3.40 GHz with 16.0 GB of RAM. The forces carried by each ligament bundle and also the distance between origin and insertion of each ligament were recorded during the simulation.
If the predicted force carried by a ligament bundle stays below 50N, the zero load length stays the same in the next iteration. However, if the force reaches values above 50N, zero-load length for that specific bundle is increased to the midpoint between the previous value and the maximum length recorded.
The iterations stop at a point where all of the ligaments predict tension values less than 50N. The zero-load lengths in the final step are recorded as the subject specific zero-load lengths for each bundle. It should be noted that the contact between the tibial cartilage and femoral cartilage was maintained during the simulation.

Results
It took ten iterations for the model to reach the goal where the forces carried out by all the ligament bundles were below 50 N during the simulation of KEM. The values in the first iteration (MRI distance between insertion and origin of each bundle) as well as final values are presented in the table below.
MRI origin and Insertion Distance Final Zero-Load Length Values
AM_ACL 33.4 35.23
PL_ACL 25.7 26.43
AL_PCL 35.8 42.31
PM_PCL 35.4 46.31
A_LCL 46 52.03
C_LCL 46.7 53.63
P_LCL 43.9 51.86
aSMCL 90.1 94.38
cSMCL 91.9 93.58
pSCML 94.3 96.98
aDMCL 34.7 40.91
pDMCL 33.8 36.76
Table 2-2
The distance between medial and lateral condyles of femur (74.2mm) was used as a measure of the knee joint size for the subject to normalize the data for comparison purposes. Ligament bundles lengths were graphed against the flexion angle in (Figures).
Figure

Discussion
The length at which the ligaments start carrying loads, called Ligament resting length or zero-load length, is an important parameter in computational biomechanics. In computational modeling, zero-load lengths usually come from cadaveric studies and are not subject specific. This chapter presents a method that can calculate subject specific zero-load lengths using MRI and knee laxity measurements conducted in a gait lab.
The same method discussed in this chapter was performed on two other female subjects by other researchers (Subject 2: Age: 22, Height: 172 cm, Weight: 73 kg and Subject 3: Age: 29, Height: 170 cm, Weight: 70kg). The medial-lateral distance of knee condyles was measured to be 81.0 mm and 73.49 mm respectively. The reported zero-load length values are presented in (Table).
Subject 1 Subject 2 Subject 3 Mean (SD)
AM-ACL 35.23 46.16 37.25 39.55 (5.82)
PL-ACL 26.43 40.26 3