When setting up the experimental test rig a problem with the damper was encountered. There were a large number of air bubbles present in the oil, which could be clearly heard passing the valve as the damper was moved manually. This issue corresponded to very inconsistent results, as can be seen in Figure A.4.5a. As well as problem of the force reaching a equilibrium value as if there was a parallel spring present to the Maxwell element, which was not the case. Examining the damper singularly by applying a simple loading ramp with constant speed showed that the force was larger when the piston was in the upper part of the damper and decreased significantly in the bottom part. This phenomena is not due to geometric inconsistencies on the inside of the damper (abrasions etc.) as this problem did not exist when the damper was simply filled with air.
It is therefore theorised that these issues originated from air bubbles present in the oil that cause a block-age in the valve. This explains the problem of the equilibrium as a blockblock-age in the valve prevents the piston from extending downward, meaning the spring bellow it maintains some tension. It also explains the problem of the inconsistency in results as repeating the same test could have moved or decreased the size of the bubbles giving a blockage at a different time.
The phenomena of the drop in force with the loading ramp tests is less intuitively explained, but a theory is that the bubbles are mostly present in the top part of the damper, meaning that once these are all pulled through the valve, the force drops as oil without bubbles is passed through.
The problem was eventually solved by filling the damper again using in a different method. Originally the damper was filled with a syringe through the opening at the top. Instead only the bottom part of the tube was disconnected and placed in a beaker of oil. Then the piston was pulled down, pulling the oil in the chamber above the piston, preventing any air bubbles. This method also ensures that the tube connecting the top and bottom of the damper also doesn’t contain any air as it is filled as well.
After filling the damper this way no bubbles could be heard in the damper and all described problems disappeared, proving that the problem was indeed related to the air bubbles.
Figure A.4.5: a) Relaxation results of the simple Maxwell element consisting of the damper and K-type spring. Three different valve openings are used and each test is performed twice. Shows that the air bubbles present in the oil result in very inconsistent results and an asymptote in force, where there should be none. b) The damper is subjected singularly to a loading ramp at a range of speeds with the same valve opening used in all cases. It is expected that the force remains constant as a constant speed is applied, but this is not the case. Illustrates that the air bubbles create a blockage in the valve, as there is a sharp drop when the bubble is passed.
Appendix B: Research proposal
Theoretical background
The anterior cruciate ligament (ACL) is one of five ligaments of the knee that make up the stability of the knee. The ACL runs diagonally from the front of the tibia (shin) to the back of the femur (thighbone), see figure B.0.1, and limits the anterior (to the front of the body) translation of the tibia relative to the femur [27]. In figure B.0.1 this is indicated as the z-direction, out of the page. In addition to this translation, the ACL also limits internal rotation of the tibia relative to the femur and hyper-extension of the knee.
An ACL tear or damage is a common injury in athletes, in particular in soccer players due to the way the tibia and femur twists around each other, over-extending the ACL, before a kick [27]. The ACL operates in tension, keeping the knee stable, which is why knee-instability is such a problem with ACL ruptures. A torn ACL will not heal on its own [27, 33], mainly because the torn ends contract due to the residual strain of the ACL: meaning the two ends cannot be bridged anymore. Simply stitching the torn ligament together will not be effective, however. There is evidence that the ACL will try to heal itself, but the scaffolding that forms during healing processes is broken down by the synovial fluid that is present inside the knee. This is known because the ligaments on the outside of the knee have no such problem with healing [27].
Therefore reconstruction of the ACL with a graft is a better option. There are many different recon-struction methods, but usually a graft is constructed from either the semitendinosus hamstring tendon, the gracilis hip adductor, or by harvesting part of the patella tendon (runs on the front of the knee and around the kneecap).
While ACL reconstruction has been helpful in restoring knee functionality, there are still some issues that have to be overcome. The main problem is increased knee-laxity in anterior-posterior direction (translation in front-to-back of the body) after reconstruction has taken place [4, 16]. This laxity is caused by stress relaxation of the graft, resulting in a loss of tension [27, 7, 26, 1, 18]. This increased knee-laxity can have serious consequences for the patient, with studies finding an increase in pain [6], increase in knee-instability, increased risk of reoccurring ACL injuries, and even a significant increase in the risk of developing early knee osteoarthritis [27].
Figure B.0.1: Schematic view of the location of the ACL between the tibia and femur [8].
Since the stress relaxation of the graft is such a serious problem, much progress has been made in un-derstanding this effect. Ciccone et al.[7] found that in vitro experiments where the stress was allowed to fully relax, the tension and stiffness in a hamstring graft decrease by 50% and 80% respectively. They
also found that the increase in temperature due to insertion into the body decreased the tension and stiffness even further: to 40% and 70% respectively.
Similarly Meike et al.[26] looked at the long term increase in knee-laxity and found that the increase in laxity from 1 to 7 years after reconstruction was not significant, whereas the increase from the day of the surgery to 7 years after was significant. This indicates that the stress relaxation of the graft completes shortly after the surgery. This is in line with Ciccone et al.[7] who found that stress relaxation of a hamstring graft completes within three hours after reconstruction.
In order to try to limit the stress relaxation problem, a lot of research has been done on the the optimal initial tension value applied to the graft during surgery. With Yasuda et al.[46] in 1997 being one of the few to test the effect of the initial tension value in patients, they found that initial tension in the range of 20 to 80 N results in the least amount of knee-laxity. While some recommend an initial tension magnitude of around 60 N or higher [7, 5, 15, 28, 46, 1], there is no consensus yet on what the optimal value should be.
The initial tension can be applied manually or with the use of a tensiometer. However as Lee et al.[23]
found, when applied manually, the initial tension was considerably lower and less accurate than was needed. Therefore the use of a tensiometer or weights to apply the initial tension was recommended.
A final issue with the application of the initial tension is that there is not yet an agreed upon rate at which the initial tension needs to be applied. A hamstring tendon consists of bundles of crimped fibers which allow the tendon to stretch easily, but also support high loads when needed. This means that when loaded the initial deformation will be due to the ”un-crimping” of the fibers, and is not part of the linear elastic region [21], but called the toe region (figure B.0.2a). Because most normal activities occur at low loads, the length of this toe-region is important. A toe-region too short will give the graft not enough stretch, resulting in unnecessary strain of the fibers. However a toe-region too long will allow too much stretch, which reduces support [27].
Figure B.0.2: a) Schematic view of the stress-strain curve of a tendon or ligament [27]. b) Schematic view of part of the femur after ACL reconstruction using suspension fixation.
In addition to initial graft tension, other means of limiting the stress relaxation problem have been de-vised as well. Preconditioning is a process whereby the graft is loaded for an extended period of time to eliminate the visco-elastic creep of the graft as much as possible before applying the initial tension [30, 11]. The goal of preconditioning is thus to have some of the stress relaxation already take place
before the graft is secured inside the body, to try to maintain as much of the initial tension applied. It is however not yet clear what the optimal preconditioning protocols should be [30].
The type of graft used is also important, with each type having its advantages and disadvantages. As of yet, no difference has been found in the functionality of hamstring and patella grafts, however there is some evidence that the use of a patella graft can cause pain while kneeling [6]. Hamstring grafts do not have this problem, however do experience more stress relaxation than patella grafts [13].
The configuration of the graft is also an issue that could have an impact on the knee-laxity due to stress relaxation. Standard ACL reconstruction is performed with a single graft bundle being secured in one tunnel in the tibia and one tunnel in the femur. However because a functional ACL in essence consists of two bundles, it was hypothesised that replacing these bundles separately would better mimic the func-tionality of a functional ACL. This is done by constructing two smaller grafts and running them through each their own set of tunnels: so in total there are four tunnels, two in the tibia and two in the femur.
The separate grafts are then joined together in the middle by sutures [27]. It is however not yet known whether this method improves outcomes, with studies finding no clinical differences between a single or double bundle construction [27]. Because of this uncertainty and because of the increased complexity of this procedure, this study will not focus on double graft bundle reconstruction methods, but design for single bundle reconstruction.
Another aspect of ACL reconstruction that can influence knee-laxity is the fixation method by which the graft is secured inside the bone tunnels. There are many different fixation methods for ACL recon-struction: the simplest being metallic or bio-degradable interference screws which clamp the graft in the bone tunnels [33, 2]. Another method is inserting cross-pins through the bone perpendicular to the graft, fixing it in place. More complex is the suspension fixation method (figure B.0.2b): where the graft is secured by means of an adjustable loop woven suture device, passing through a button outside of the bone-tunnel [3, 33, 27]. It has been shown that for securing hamstring grafts, screws may experience more graft slippage and have lower failure loads. Cross-pin devices allow for a more rigid fixation and higher failure loads, however are associated with other complications during and after surgery [3]. For hamstring grafts, suspension fixation remains therefore the best option.
In summary, many different methods have been developed to understand the behavior of ACL-reconstruction grafts, and try to limit the problem of knee-laxity due to stress relaxation in particular. However no so-lution to the problem has yet been found. This study will approach the problem differently by designing an additive device that will manage the stress relaxation, by absorbing the loss of tension. In addition the device will standardize and control the application of the initial tension.
Problem definition
An important problem with ACL reconstruction remains the laxity in the knee due to loss of tension, due to primarily stress relaxation of the graft. Attempts at limiting the problem in the form of optimizing the amount of initial tension and different preconditioning protocols, have yet to solve this problem. To complicate matters, often the application of the initial graft tension is not accurately controlled, resulting in an inconsistent initial tension or a tension that is applied too quickly.
The goal of this study is to design a device that can be incorporated into the current fixation system with the following objectives:
• control the rate at which the initial graft tension is applied.
• control the precise amount of initial graft tension.
• counteract the stress relaxation of the graft and maintain the initial tension during the healing process.
• develop a preconditioning protocol that matches the design.
Since the stress relaxation of the graft is a complex problem to solve, the focus of the design will be on the other three objectives. Thus keeping the counteraction of the stress relaxation as a secondary goal,
if the other three are met as well.
The design of the device will be based on a few initial boundary conditions. The type of graft is a single semitendinosus hamstring tendon in a quadruple loop configuration. The fixation method is by means of suspension fixation in both the femur and the tibia, with the device added on the femur’s side (figure B.0.2b). For now the fixation in the tibia is assumed to be a fixed loop-length suture, or EndoButton CL Ultra, and on the femur side a adjustable loop-length suture, or TightRope RT [3]. However based on the design of the added device, the type of suspension fixations may be changed. The procedure may need to be altered slightly the accommodate the added device, however overall it should remain the same procedure.
Research plan
This study is set up in a few different phases, starting with a short literary review, working towards a concrete design for the device, and finally testing the device numerically and possibly in practice as well.
The purpose of the first phase, the literary review, will be to further understand the behavior of the hamstring graft during and after reconstruction surgery. In this way specific boundary conditions can be developed, upon which the design can be based. This also means that some preliminary decisions need to be made about the surgery, in particular the amount of pretension and preconditioning protocol.
Both are based on current standards, derived from the literary review. Both will likely be adjusted in the final phases of the project, to fit better with the final design.
With the boundary conditions defined, designs for the device can be made. The focus of the designing phase is on the two pretension objectives (as stated before) as these are simpler to achieve and stress relaxation can be a complex problem to counteract. The purpose of this phase is to come to one design, including dimensions and material choices, that achieves as many of the objectives as possible.
Based on this specific design a numerical model can be developed in order to validate whether the design functions as intended. In this modeling phase the design will be tested and tweaked to come to a final optimal design that can possibly be made and tested in practice as well. It is expected that the mod-elling phase will take a longer time as, in addition to the development of a model, this is the part of the project when limitations of the design or preliminary decisions present itself and a lot of problem-solving is needed. Therefore the model will feed back into the design, helping to finalize it.
The next phase is for practical experiments of the developed device in an experimental setup, including a hamstring graft. The experiments will match the conditions in reconstruction surgery as closely as possible. This includes the decided on preconditioning protocol, as well as a creep test simulating the application of the pretension and relaxation period. Based on the amount of graft tissue that is available, the experiment can be performed multiple times to achieve more reliable results.
The final phase of the project will focus on compiling the results from the numerical simulations and the practical experiments, and drawing conclusions from them about the functionality of the designed device. This phase will include summarizing the findings of this study as well as some recommendations on further improvements of the design and areas of further research.
Preliminary designs
Based on the objectives outlined in the section Problem definition, some preliminary designs for the device have been made. Figure B.0.3 shows two design options incorporated in the femur bone tunnel (see figure B.0.2b for a full view of suspension fixation reconstruction) that achieve some or all of the design options. The simplest design is one that aims to solve the two objectives related to controlling the application of the initial tension. It is a simple rubber ring that will implemented before the narrowing of the bone tunnel, through which a Tightrope RT suture will pass (see figure B.0.3a). The end of the TightRope will have a metallic button that will rest on the rubber ring, and another fixed-length loop suture (green) will connect the graft to the TightRope.
The functioning is as follows: the initial tension is applied by pulling the TightRope tight, which causes the rubber ring to compress. The effort required to compress the rubber ring allows for a slower appli-cation of the initial tension, and the limiting depth of the bone tunnel gives a maximum initial tension level. This design however does nothing to address the problem of stress relaxation.
Figure B.0.3: a) Design of a rubber ring (dark blue) inserted before the narrowing of the bone tunnel.
b) Design of a rubber band (dark blue) that will counter stress relaxation.
A second design that will address this objective is seen in figure B.0.3b. It consists of a rubber band encased in a woven sleeve (similar to a hair-tie) that is passed through the graft on one side and through a TightRope (light blue) on the other side. The device (dark blue) functions as follows: when the initial tension is applied by tightening the TightRope, the rubber band expands until the woven encasing limits further extension. With the device fully expanded the load is transferred to the graft, allowing the initial tension to be applied. Once the graft starts to elongate due to stress-relaxation, the device will contract:
maintaining the initial tension.
Project planning
Below is a general overview of the different phases of the project in a monthly time-frame. Light-colored areas indicate some buffer where it is expected that work can be done earlier or will experience some delay. The last month is kept free for any delays in the project.