APPENDIX. Joint conformity in shoulder prostheses: In-vitro measurement of interface micromotions in a metal-backed glenoid implant.

Transcription

1 Joint conformity in shoulder prostheses: In-vitro measurement of interface micromotions in a metal-backed glenoid implant APPENDIX Master thesis Author: Willem Nerkens Student no: wb Date: Faculty of Mechanical, Maritime and Materials Engineering - 3mE Master: BioMedical Engineering - Tissue Biomechanics and Implants Examiner: Advisors: Supervisors: Prof.dr.ir. Fred van Keulen Prof. dr. P.M. Rozing Prof. dr. R.G.H.H. Nelissen Dr. ir. Edward Valstar Ir. Daniel Suarez

2 1. Background... 3 Features of the shoulder... 3 Total shoulder Replacement... 4 Osseointegration and Micromotions... 5 Micromotions threshold... 5 Fibrous tissue growth... 6 Fatigue... 6 Wear particles and Osteolysis... 6 Aseptic loosening... 7 Glenoid component failure... 7 Humeral component loosening Experimental setup design... 9 Past research... 9 Experimental setups at the TU Delft... 9 New experimental setup Measurement system Sensor choice DVRT principle DVRT Sensor specification Measurement system overview Labview program Low pass filter Preliminary experiments Calibration Sensor fixation Horizontal compression force Sublaxation force frequency Stabilization criterion Sources of error and variance Bone substitute geometry Glenoid component tilting Applied torque on central screw Angle of central screw Measurement surface on metal back Glenoid component alignment Material properties bone substitute Humeral head compression force Deterioration of PE inlay Deterioration of experimental setup Spring plate contact Total error per sensor Finite Element Model Cemented versus Uncemented experiment Detailed results Subluxation force Humeral head displacement Sample raw data References Author: Willem Nerkens 2

3 1. Background Features of the shoulder The shoulder girdle is a complex system, existing of the scapula the clavicle and the humerus. The scapula features the acromion, the coracoid process and the glenoid. The head of the humerus fits into the glenoid, forming a ball and socket joint, see Figure 1.1. Figure 1.1 Bones in the shoulder [encyclopaedia Britannica 2007] The glenohumeral joint is the main joint of the shoulder and the generic term "shoulder joint" usually refers to it see figure 1.2. It is a ball and socket joint that allows the arm to rotate in a circular fashion or to hinge out and up away from the body. It is formed by the articulation between the head of the humerus and the glenoid cavity of the scapula. The shallowness of the glenoid cavity (fossa) and relatively loose connections between the shoulder and the rest of the body allows the arm to have tremendous mobility, at the expense of being much easier to dislocate than most other joints in the body. The joint capsule is a soft tissue envelope that envolves the glenohumeral joint and attaches to the scapula, humerus, and head of the biceps. It is lined by a thin, smooth synovial membrane. This capsule is strengthened by the coracohumeral ligament which attaches the coracoid process of the scapula to the greater tubercle of the humerus. There are also three other ligaments attaching the lesser tubercle of the humerus to lateral scapula and are collectively called the glenohumeral ligaments. Author: Willem Nerkens 3

4 Figure 1.2 Joints of the shoulder [ Total shoulder Replacement In a total shoulder replacement (TSR) both the humeral head and the glenoid cavity are replaced, see figure 1.3. A TSR is only considered when more conservative treatment as physical therapy and/or drugs are no longer adequate. When placing a glenoid component in a shoulder joint damaged by rheumatoid-arthritis, is important that the rotator cuff is relatively healthy. A severely weakened rotator cuff can cause loosening and failure. There is a relation between the chance of a glenoid component revision and the presence of a rotator cuff tear [Kelly, 2003]. Data from a recent study indicates that there is marked long-term pain relief and improvement in motion with shoulder arthroplasty [Sperling et al, 2007]. The same study states that among patients with an intact rotator cuff, TSA appears to be the preferred procedure for pain relief, improvement in abduction, and lower risk of revision surgery. Figure 1.3. Total shoulder replacement [ Author: Willem Nerkens 4

5 Osseointegration and Micromotions There is no simple definition of osseointegration, although [Albrektsson, 1990] advocates the following: Osseointegration means a relatively soft-tissue-free contact between implant and bone, leading to a clinically stable implant. Early in the study of the osseointegration concept, Skalak found that osseointegration was promoted by a micro-rough surface more so than a smooth one [Skalak, 1983]. Since then, many animal experiments investigating the effect of plasma spraying on the surface, and various methods of creating a porous surface have been reported. Micromotion is the small movement between prosthesis and surrounding bone. Due to this motion, an implant s osseointegration can not take place in uncemented prostheses and debonding can occur in cemented prostheses. Figure 1.4. A porous-coated implant that was removed from a patient. Bone can be seen growing into the porous coating on the surface of the hip implant. This ingrowth anchors the implant in place, ensuring proper functionality. [Darthmouth Biomedical engineering centre] Figure 1.4. shows bone ingrowth into a porous coating of a femoral hip prosthesis. It can be observed that ingrowth is irregular; this is what is commonly found, even with successful implants retrieved at autopsy [Sychterz, 2002]; it is evident, therefore, that osseointegration is not required everywhere around the prosthesis for a successful fixation. Bone ingrowth is controlled by a combination of the mechanical environment and biological factors. Micromotions threshold When micromotions are high enough a fibruos tissue appears between implant and bone avoiding osseointergration of the implant This led Cameron et al. [Cameron et al., 1973] to introduce the concept of threshold micromotion. Micromotions of a certain magnitude were found to be tolerated for bone ingrowth into porous implants, but higher magnitude movements, prevented bone ingrowth and resulted in fibrous tissue interposition. That was confirmed by Maniatopoulos et al. [Maniatopoulos et al., 1986]. Initial estimates of the level of this threshold were around 30 µm [Pilliar, 1991], but in 1995, the same Pilliar et al [Pilliar et al., 1995] found that micromotions up to 50 µm were tolerated. The upper range of micromotion that did not interfere with osseointegration was around 150 µm for calcium phosphate coated titanium alloy implants. [Soballe et al., 1993]. Generally 30 µm of micromotion allows bone ingrowth into rough implant surfaces and above 150 µm micromotion induces fibrous tissue formation [Cehreli et al 2004]. The lowest known threshold of 20 µm was proposed by [Ramaumrti et al., 1997]. This value is sometimes used by researchers to give conservative ingrowth predictions [Andreykiv et al., 2004]. Author: Willem Nerkens 5

6 Fibrous tissue growth With fibrous tissue growth is meant the formation of soft bone material between implant and bone, thus at the implant-bone interface. This soft tissue formation is a result of micromotions between implant and bone in combination with shear stresses between two contact surfaces. The existence of this soft tissue layer between implant and bone decreases the stability of the implant fixation. The mechanical properties of the soft tissue are inferior, i.e. it is not capable to carry the loading or transmit the loading into the hard bone material. As a result of this soft tissue formation, the prosthesis is allowed to move even more resulting in the creation of more soft tissue material. This is an unstable situation and finally prosthesis loosening might occur [Weinans, 1991, Rubin et al., 1993, Weinans et al., 1993]. Fibrous tissue around an implant is visible as a radiolucent line, a dark line, on an x-ray image, see figure 1.5. Figure 1.5. X-ray of Fibrous tissue present around a hip implant. The fibrous tissue is visible as a radiolucent line. [ Fatigue In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The maxiumm stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material. Due to improvements in material and design fatigue failure has become rare in prosthesis Titanium and cobalt alloys have superior mechanical properties in relation to the earlier used stainless steel and cobalt-chromium. However, fatigue becomes an issue again because of the tendency now to use uncemented porous coated prosthesis. A coating gives high initial fixation strength, due to bone ingrowth in the pores of the material, see Figure 1.4. These coated prostheses often show weaker mechanical properties than the earlier used materials. The mechanical properties of the coated prostheses are influenced by the notching effect of the coating [Cook and Thomas, 1991]. The brittle coating material results in easier crack initiation in the bulk material. In the literature no information is found on fatigue failure of the metal back or humeral head. The reason for this might be that the loading in the shoulder joint is smaller as compared to the hip joint and with a smaller frequency. Wear particles and Osteolysis In materials science, wear is the erosion of material from a solid surface by the action of another solid. Wear particles will be generated as a result of shear stresses, friction, surface roughness and material hardness in combination with relative displacements of two surfaces. In shoulder replacement, these particles can be made out of polyethylene, metals and bone, due to abrasion of the glenoid component, the humeral component and the surrounding bone, respectively. Wear particles can result in implant-bone interface debonding, infection and, in case of metal and polyethylene particles, osteolysis [Klimkiewicz et al., 1998]. Osteolysis is the end result of a biologic process that begins when the number of wear particles generated in the joint space overwhelms the capsule's capacity to clear them. The residual particles stiumlate a macrophage-induced inflammatory response that can lead to bone loss and subsequent implant loosening. Any particle debris can result in bone resorption, see Figure 1.6. In healthy Author: Willem Nerkens 6

7 anatomical articular joints, there is almost no existence of wear, but in case of lubrication problems, for example as a result of the absence of synovial fluid, wear rates are no longer negligible. Figure 1.6. Wear debris can cause osteolysis [ Due to the fact that the shoulder joint is an articulation with a large range of motion, the wear particles in the shoulder joint don t remain in the articulation for a long time, but they are able to leave the joint. Wear particles in the shoulder range from 2 to 50 µm, which is an order of magnitude larger than the size of wear particles in the hip, which are less then 1 µm [Klimkiewicz et al., 1998]. The particles are able to move to the implant bone interface where they hasten the debonding process, generate more wear particles and are the cause of osteolysis [Chen et al., 1998]. Aseptic loosening Aseptic loosening is considered one of the main problems of joint replacement and accounts for the majority of prosthesis revisions. The definition of aseptic is free of pathological microorganisms. Aseptic loosening is the loosening of a prosthesis without an infection being present. Glenoid component failure Glenoid components failure is the most common complication of total shoulder arthroplasty [Bohsali et al., 2006]. Their failure is a result of their inability to replicate essential properties of the normal glenoid articular surface to achieve durable fixation to the underlying bone, to withstand repeated eccentric loads and glenohumeral translation, and to resist wear and deformation. The main cause for glenoid component loosening is incorrect positioning of the glenoid part into the scapula, inferior bone quality due to rheumatoid arthritis, in combination with peak loads due to instability, surgical mismatch and inferior cementing techniques [Skirving, 1999]. The trend now is to use glenoid parts with an increased radius of curvature to allow translation during movements of the shoulder [Skirving, 1999] as this is believed to reduce translational forces [Severt et al 1993]. A glenoid component which is too large will also result in aseptic loosening, because not every part of the glenoid prosthesis back is supported by the adjacent bone. The alternatively loading opposite sides of the glenoid component results in a tilting motion called the Rocking horse effect,see Figure 1.7 Matsen, 1999]. Author: Willem Nerkens 7

8 Figure 1.7. Rocking horse effect [Matsen, 1999] Humeral component loosening Loosening of the humeral component in shoulder arthroplasty is very uncommon, with a contribution of less then 1% to the complications [Bohsali et al., 2006]. The main cause is the generation of wear particles in the shoulder articulation, which are able to migrate quickly to the implant-bone interface [Klimkiewicz et al., 1998]. Here as well, wear particles cause an inflammatory reaction that will lead to bone resorption and osteolysis. Author: Willem Nerkens 8

9 2. Experimental setup design Past research The golden standard for the testing of glenoid components was set by Rebecca Anglin et al. in the year 2000 [Anglin et al., 2000]. Anglin and collegues applied a cyclic displacement to a cemented glenoid prosthesis while it was pressed against the humeral head by a constant horizontal force, see figure 2.1. The purpose of this study was to develop a test protocol that could detect relevant differences among prosthesis with respect to glenoid loosening. Figure 2.1 Anglin s experimental setup; The humeral head was compressed into the glenoid with 750 N, then vertically translated inferiorly and superiorly to 90% of the predetermined subluxation distance to mimic the rocking-horse phenomenon [Matsen, 1999]. The corresponding compression and distraction displacements of the glenoid s rim were measured before and after 100,000 cycles. [Anglin et al, 2000] Experimental setups at the TU Delft Based on the work done by [Anglin et al. 2000] Oosterom proposed a new method of glenoid component testing [Oosterom, 2005]. In this study Oosterom presented a method with physiological glenoid component loading as a result of force-controlled humeral head movements. The force-controlled experimental set-up was used for a more realistic evaluation of the component fixation. The new test set-up was used to study the effect of bone substitute stiffness on glenoid component tilting when physiological loads were applied, see Figure 2.2. It was the first glenoid prosthesis testing apparatus build at the TU Delft. It was capable of measuring rim displacements by placing metal strips with strain gages against pins on the prosthesis rim. Author: Willem Nerkens 9

10 Figure 2.2. Oosterom s experimental setup. Two bachelor students Ruit and Fintelman, from the faculty of mechanical engineering designed a new testing apparatus in 2008 [Ruit and Fintelman, 2008]. The goal of the study was to investigate the effect of the inclination angle of the prosthesis on initial stability. The setup was capable of measuring rim displacement with an optical sensor, Figure 2.3. Several practical issues made this setup somewhat unreliable and cumbersome to use. The bone substitute block holder moved with respect to the guidance rail as the construction was not rigid enough to cope with the applied shear load. Furthermore the bone holder fixated the sawbones by placing screws through the holder into the blocks. Not only does this damage the blocks, it leaves room for the block to move within the holder when the loading is applied. Changing the blocks was tedious because the threaded bars hindered the access of tools to the bone holder. Figure 2.3. Ruit and Fintelman 2008 Author: Willem Nerkens 10

11 New experimental setup The new experimental setup aims to measure interface micromotions in uncemented glenoid components. For the newly designed testing apparatus various parts were taken from the Ruit and Fintelman and Oosterom setups and were combined and supplemented with new parts [Ruit and Fintelman 2008, Oosterom 2009]. The design criteria were set as follows: The setup should be able to test both the block and adapted scapula geometry bone substitutes The bone holders need to be rigid and may not move when the load case is applied Changing the samples should be as consistent and fast as possible Bone substitute holder needs to constrain the testing blocks without disrupting the structural integrity of the blocks Bone holder must allow safe exit of DVRT sensor wires from the bone samples The frame was redesigned to grant easy access to the bone holders and to allow for both the block and the scapula geometry to be mounted within, see Figure 2.5. and 2.6. The guidance rails for the bone holders and the humeral head were taken from the previous [Ruit and Fintelman, 2008] setup. The cylinder can be fixed in two positions applying the compression force close to the centre of the inserted components in both the block and the scapula geometry. The block bone holder allows the exit of the DVRT sensor wires so these will not be in danger of damaging due to the clamping of the plates. The block is constrained in all sides with the exception of the front plane were the prosthesis is inserted. The plates clamp the bone substitute block and do not disrupt the structural integrity of the blocks. The plates are fixated using socket (inbus) bolts, thus allowing the samples to be replaced quickly between repetitions. The scapula bone holder uses threaded bars which pass through the rectangular back to fixate the adapted scapula geometry. Figure 2.5. The setup with mounted block bone holder Figure 2.6. The setup with mounted scapula bone holder Author: Willem Nerkens 11

12 The test setup was modelled in Catia and detailed drawings were made for production, see Figure 2.7. Most parts were produced by Patrick van Holst and Harry Jansen of the PME laboratory at the faculty of mechanical engineering. Some parts were manufactured at DEMO (Dienst Elektronische en Mechanische Ontwikkeling, TU Delft, Netherlands). Figure 2.7. Two out of fourteen production drawings made for this setup. The base of the block holder and the plate at the cylinder back respectively. Glenoid component implanted in bone substitute block The tensile testing machine clamps the humeral head plate to apply a cyclic vertical subluxation force N Cylinder applies a constant compression force 750 N Figure 2.8. The new experimental setup Bone substitute holder Humeral head 20 mm surface radius Author: Willem Nerkens 12

13 Sensor No. 3. Measurement system Sensor choice In the literature survey preceding this thesis an overview of all commercially available sensors capable of measuring micromotions was presented [Nerkens, 2008]. An ideal sensor was defined and the corresponding demands were given a weight factor, Table 1. Table 1, Demands and Weight No. Demand Weight Ideal 1 Probability of measuring relative micromotion 10 Certain 2 Intrusion on Bone foam material, sensor path diameter 8 <Ø 1 mm 3 Capability to measure multiple dimensions 6 3 D 4 Resolution 6 <1 µm 5 Linearity 5 <1 µm 6 Range 4 >3 mm Of each considered principle a sensor was chosen that best complied with the set demands. These specific sensors were then graded for their functioning per demand, Table 2. Table 2, Grading each sensor Points per demand [1-10] LVDT DVRT 1.5 DVRT 3.0 Potentiometer Laser triangulation 2D laser Fibre optic Confocal Prob Intr D Res Lin Ran Eddy Current These grades are multiplied by the weight factor attributed to each demand resulting in the final functioning grades for each sensor. Further considerations were the cost of the sensors and the mounting complexity. The overall performance ratio (functionality/cost) was calculated, Figure 3.1. Figure 3.1, Performance ratio of each sensor (Functionality/Cost) Based on these considerations the DVRT (Differential Variable Reluctance Transducer) sensor with a stroke of 3 mm was chosen. Author: Willem Nerkens 13

14 DVRT principle DVRT s (Differential Variable Reluctance Transducers) combined with their signal conditioners convert a linear displacement into a linear variable electrical output signal. The displacement is detected by the movement of a core within the coils inside of the sensor. The coil shown on the right is energized using an AC excitation through the center tap, Figure 3.2. The coil is usually arranged in a Wheatstone bridge with the Center Tap being the bridge excitation (forming a half bridge ). With the core in the central location (null) the signals Va and Vb are equal. When the core moves, Va and Vb vary proportionally, Figure X. Figure 3.2 Electrical schematic of DVRT sensor DVRT Sensor specification The DVRT sensor with DEMOD signal conditioner [Microstrain, USA] is a relatively small sensor with 1.8 mm sensor housing diameter, Figure 3.3. The tip of the sensor is spring gauged, ensuring contact with the metal back at all times. All specifications are listed in Table 4. Figure 3.3 Depiction of sensor size and sensor components [ Table 4, Electrical and Mechanical specifications Electrical specifications Linear stroke length 3 mm accuracy 1% straight line =30 µm 0.1% polynomial = 3 µm Sensitivity 1.66 Volts/mm Resolution 1.5 µm Hysteresis * 1 µm Repeatability * 1 µm Mechanical specifications Overall length Outside diameter Spring force tip Housing material * at constant temperature 24 mm 1.8 mm (smooth body) 0.2 N/mm Stainless steel Author: Willem Nerkens 14

15 Measurement system overview In general terms an observer is a person who needs information on a process. The purpose of the measurement system is to link the observer to the process, Figure 3.4. The input into the measurement system is the true value of the variable. The difference between the measured and true value of the variable is the measurement error. Process Input True value of variable Measurement system Output Measured value of variable Observer Figure 3.4, Purpose of measurement system A measurement system consists of four types of elements. Although in a given system each type may occur more than once. The four types are presented in figure 3.5. Input Output Sensing Element(s) Signal conditioning element(s) Figure 3.5, General structure of measurement system Signal processing element(s) Data presentation element(s) Sensing Elements Is in contact with the process and gives an output which depends on the variable to be measured. Signal conditioning elements - Takes the output of the sensing element and converts it into a form more suitable for further processing. Signal processing element Takes the output of the conditioning element and convert it into a form more suitable for presentation. Data presentation element - Presents the measured value in a form which can be easily recognized by the observer. The performed experiment measured micromotions, bone substitute deformation and rim displacement with DVRT sensors. The measurement system schematic is presented in figure 3.6. Input DVRT DEMOD-DC DAQ (ADC) Computer (Labview) Computer (Matlab) Computer (Matlab) Output Sensing Element Signal conditioning element Signal processing elements Data presentation element Displacement Milivolts Volts (0-5) Figure 3.6, Experiment measurement system DVRT (sensing element) The DVRT is in contact with the glenoid component. The relative displacement between the clamping of the sensor housing and the glenoid component produces an output in milivolts. DEMOD-DC (signal conditioning element) Operating from a DC power supply, the DEMOD-DC filters incoming transients from the line voltage, and supplies a sine wave excitation to the transducer. This excitation is used to measure minute impedance changes of the sensing elements. DAQ (signal processing element) Data acquisition device that digitalizes the DC output of the DEMOD-DC. (Analogue- Digital Conversion). Making the signal suitable for computer processing. Author: Willem Nerkens 15

16 Computer Labview (signal processing element) - The incoming digitalized signal is stored with a sample frequency of 50 Hz. A time vector is stored with at the same frequency. The output is a dataset containing the signals from all four DVRT s and the time vector. Computer Matlab (Signal processing element) The recorded signals are loaded and the specific factory specified polynomial fit of each sensor is applied. High frequent noise is reduced using a Butterworth lowpass filter. Computer Matlab (Signal processing element) The processed data is analyzed and plotted Author: Willem Nerkens 16

17 Labview program Labview was used to gather the data the data from the DVRT sensors. The schematic and the user interface created for this purpose are depicted below, see Figure 3.7 and 3.8. Figure 3.7, Schematic of Labview program; 5 physical channels and the passed measurement time are collected from the DAQ and stored in separate columns of a.mat file suitable for matlab. The gathered data is also displayed in a real time waveform chart on the user interface. The measurement time, sample time, and target file name are user inputs. The program stops if the measurement time is reached or is stopped manually with an overriding stop button on the interface. Figure 3.8, The user interface of the Labview program. Featuring the user inputs and realtime display of the acquired voltages. Author: Willem Nerkens 17

18 Low pass filter The signal that is measured contains high frequent noise, which results in an uncertainty of ~ 6 µm, Figure 3.9. To reduce the noise on the signal a low pass filter was used. A 8 th order Butterworth filter was set at a cutoff frequency of 1 Hz. The sample rate is 50 Hz. The applied load cycle has a frequency of 0.01 Hz. The effect on the measured signal is shown below, Figure X. The uncertainty is reduced to 1 µm. Deformation B sensor output [um] time [Sec] Figure 3.9, The low pass Butterworth filter applied to the deformation measurement on the conform I20 radius. The light (cyan) is the original signal, the black line in the centre of the high noise band is the filtered signal. Author: Willem Nerkens 18

19 4. Preliminary experiments Calibration The accuracy of a measurement of a variable is the closeness of the measurement to the true value of the variable. It is quantified in terms of the measurement error. To establish the accuracy of the DVRT sensors a displacement was applied with a calibrated micrometer. The micrometer applied a displacement of 0, 0.5, 1, 1.5, 2, 2.5 and 3 mm and the output voltages of the sensors were collected for these points, Figure 4.1. Output voltage [V] Sensor A Sensor B Sensor C Sensor D Applied displacement [mm] Figure 4.1, Applied displacement of a micrometer versus the output voltage of the sensors A factory supplied polynomial fit that is unique to each sensor was applied to these output voltages. The outcome is the measured displacement of the sensor, Figure 4.2. The maximum absolute error within the 0.5 to 2.5 mm range is 3 µm for all sensors. 3 Voltage -> Factory polynomial fit [mm] Polyfit Sensor A Polyfit Sensor B 0.5 Polyfit Sensor C Polyfit Sensor D y = x Applied displacement [mm] Figure 4.2, The measured displacement versus the applied displacement for all sensors Author: Willem Nerkens 19

20 Sensor fixation The sensors were placed in the bone substitute through predrilled sensor paths with diameter equal to the sensor housing (1.8 mm). Other sensor diameters considered were 1.7 mm in which the sensors were unable to enter the sensor path, and 1.9 mm which did not hold the sensor in place as the sensors spring force pushed the sensor housing from the interface. When a spring gauged sensor is placed in a sensor path the tip is always in contact with the metal back. Two states can occur during glenoid component loading, Figure 4.3. The metal back moves and opens the interface, a gap is formed and relative micromotion between the metal back and the clamping point in the bone substitute are measured. Or the metal back moves towards the sensor compressing the bone substitute, thus bone deformation with respect to the clamping point is measured. Points of bone sensor contact can not be specified Metal back displacement Comp. Gap Interface Figure 4.3, The exact clamping point of the sensor an experiment was needed to determine its location. When a spring gauged sensor is placed in a sensor path the tip is always in contact with the metal back. Two states can occur during loading. The metal back moves and opens the interface, a gap is formed and relative micromotion between the meal back and the bone substitute are measured. Or the metal back moves towards the sensor compressing the bone substitute, bone deformation is measured. Author: Willem Nerkens 20

21 Experiment sensor fixation To determine the fixation point of the sensors in the bone substitute, preliminary experiments were performed. Test with rigidly clamped sensor to check load case First a sensor was rigidly fixed in a holder, figure 4.4 (Left), and placed on a tensile testing machine (Z005, Zwick/Roell, Germany). A displacement of µm was applied on the sensor tip for 1000 cycles at 1 Hz. The resulting amplitude of the measurement equaled 110 µm. The error of the measurement was 3 µm (see calibration section), the actual applied displacement was therefore µm. Test output amplitude with single sensor in bone substitute A sensor was placed vertically in a predrilled sensor path with 1.8 mm diameter. A tensile testing machine applied a displacement of µm for 100 cycles at 1 Hz on the top surface of the bone substitute, Figure 4.4 (Right). The previous experiment showed that the actual applied displacement was 0 - ~110 µm. The resulting amplitude of the measurement was 45 µm. Assuming the deformation of the bone substitute was linear over the height of the sample, the fixation point was at 16.4 mm from the interface, 3.6 mm from the back of the enclosed sensor housing, Figure 4.5. The first cycles caused a shift of 3 µm in the mean of the signal, indicating the sensor housing had moved back from the interface before a stable sine was measured. Figure 4.4 (Left) Bottom sensor rigidly clamped in plastic holder. (Right) Top sensor in bone substitute on the tensile testing machine mm Disp Bone substitute 16.4 mm Fixation point 20 mm Figure 4.5, Schematic cross section of the bone substitute block. The fixation point of the sensor housing was at 16.4 mm from the interface, assuming the deformation was linear through the height of the bone substitute block. Author: Willem Nerkens 21

22 Test evaluating sensor housing motion in bone substitute during loading The motion of the sensor in the bone substitute was investigated using a second sensor which was placed under the first sensor in the bone substitute, Figure 4.5. The top sensor was placed in the sensor path with 1.8 mm diameter exactly as in the previous experiment measuring the bone substitute deformation. The bottom sensor is rigidly fixed in a holder, Figure 4.4 (Left), measuring the displacement of the top sensor housing. A tensile testing machine applied a displacement of µm for 100 cycles at 0.1 Hz on the top surface of the bone substitute. The first experiment showed that the actual applied displacement was 0 - ~110 µm. In the first cycles there was an increase in the amplitude of the top sensor of 10 µm, this was caused by the permanent movement of the sensor housing, Figure 4.6. The sensor housing moved away from the interface initially but remained fixed after 30 cycles (300 seconds). The bottom sensor confirmed these findings, as the sensor housing of the top sensor moves backwards the bottom sensor measured a smaller amplitude over time. The top sensor measured a deformation of 57 µm after 30 cycles. Again it was assumed that the deformation through the height of the block was linear. The fixation point of the top sensor was thus at the back of the sensor housing 20 mm from the interface. The bottom sensor measured a stable the motion of the top sensor housing to be 38 µm. The sum of the amplitudes of the top and bottom sensor was 95 µm in all cycles. 3 Disp 17 mm 20 mm Top sensor 20 mm Fixation point Bottom sensor Figure 4.5, (Left) Schematic cross section of the bone substitute block. The top sensor measured the deformation of the bone substitute while the bottom sensor measured the displacement of the top sensor housing. The fixation point of the top sensor housing was at 20 mm from the interface, assuming the deformation was linear through the height of the bone substitute block. 60 Top sensor 40 Bottom sensor sensor output [um] sensor output [um] time [Sec] time [Sec] Figure 4.6, The top sensor housing is sliding back from the interface in the first displacement cycles. After 30 cycles (300 seconds) both measurements are a constant sine. Author: Willem Nerkens 22

23 Relaxation of bone substitute To test the relaxation properties of the bone substitute on the deformation measurement the following load case was applied. A sensor was placed vertically in a predrilled sensor path with 1.8 mm diameter. A tensile testing machine applied a displacement of 150 µm on the top surface of the bone substitute and was halted position controlled. The duration of the measurement was 3 hours. Relaxation 60 umotion [um] time [Sec] Figure 4.7 sensor output after a single displacement step of -150 µm. Relaxation of the material causes the sensor housing to move 2 µm backwards from the interface over the experiment duration of three hours. The sensor ouput was 60 µm initially, Figure 4.7. Assuming the deformation of the bone substitute was linear over the height of the sample, the fixation point was at 16 mm from the interface, 4 mm from the back of the enclosed sensor housing, Figure 4.8. The measurement increased gradually over time with an output of 2 µm more than after the initial displacement step. This means the sensor housing has moved back from the interface as the relaxation of the bone substitute material takes place. The relaxation thus caused an average movement of the sensor housing of 0.66 µm/hour. Disp 3 17 mm Bone substitute 16 mm Fixation point 20 mm Figure 4.8, Schematic cross section of the bone substitute block. The fixation point of the sensor housing was at 16 mm from the interface, assuming the deformation was linear through the height of the bone substitute block. Author: Willem Nerkens 23

24 Fixation of the sensors in experiment Sensors A and B were placed in sensor paths perpendicular to the metal back, Figure 4.9. The fixation point of these sensors could not be determined as this point varies between repetitions. However preliminary experiments have shown that the fixation point is consistently located at the back side of the enclosed sensor housing. The minimum distance of fixation was found to be 16 mm from the interface. The maximum distance was the back of the enclosed sensor housing. The fixation point of the sensors A and B in the experiment was therefore defined to be mm from the interface (19 +/- 3 mm). Interface Sensor A 2 [mm] 22 [mm] 3 [mm] 18 [mm] Sensor path for sensor C Fixation 19 +/- 3 [mm] from the interface. Figure 4.9, (Left) Sensors A and B measuring micromotions and bone deformation perpendicular to the metal back, respectively, are placed in the bone substitute up to 22 mm of the sensor housing. The exact clamping point on these sensors will be different between repetitions. Preliminary experiments have shown the fixation point is at the back of the sensor housing mm from the interface. (Right) Sensor A is placed in its sensor path. The sensor path for the vertical micromotion measurement C is visible. Sensor C was placed vertically on the edge of the ingrowth surface on the metal back, Figure Fixation plate 5 [mm] Interface Figure 4.10, Sensor C measures the vertical micromotions through the predrilled sensor path. The depth of the sensor path is too small to clamp the sensor housing sufficiently to overcome the spring force of the sensor. The sensor is therefore fixed to a plate with two pins which enter the bone substitute on both sides of the senor. As this sensor is measuring the gap that is formed as the interface opens during loading, the exact fixation point was not vital. Author: Willem Nerkens 24

25 Sensor D Sensor C fixation plate Spring blade Figure 4.11, The mounted sensors C and D Sensor D Measured the rim displacement relative to the frame by means of a spring plate, Figure The spring plate pressed against a pin in the centre of the PE inlay with 2 N. The spring plate amplified the rim displacement by two factors, Figure 4.12, To negate the effects of these amplifications the measurements by sensor D were multiplied by the Rim displacement factor (16/17,5)/2 = Spring plate Sensor D PE inlay Pin Bone substitute Bone substitute holder 0,5L 0,5L Figure 4.12, (Left) A spring plate was pressed against a pin placed in the centre of the inferior side of the PE inlay. (Right) The spring plate amplifies the rim displacement the measured value was multiplied by a factor 1/2. 32 [mm] 17,5 16 +/- 0,5 Figure 4.13, (Left) As the component tilts during loading the pin in the PE inlay will have a larger displacement than the actual displacement of the rim. (Right) To negate this effect the measured value was multiplied with a factor (16/17,5) = 0.91.There is an uncertainty in the exact location of contact between the pin and the spring plate. In the section Sources of error and variance this is discussed further. Author: Willem Nerkens 25

26 Horizontal compression force The horizontal force was applied by a pneumatic actuator. (ADV-50-25, Festo BV, The Netherlands) The cylinder was placed on the tensile testing machine (Z005, Zwick/Roell, Germany) in contact with the 1 KN load cell (Load cell 1 KN, Zwick/Roel, Germany). Pneumatic pressure was increased manually using a regulator (B18-C4-GL00, Wilkerson, USA) until the actuator produced a force of 750N. The corresponding pressure was 3.8 Bar, this value was kept constant throughout all repetitions. A valve (valve 9982, Festo, ) was placed after the regulator enabling the controller to switch the horizontal compression force off for specimen changes. Sublaxation force frequency The experiments of Anglin and Oosterom applied a vertical subluxation displacement/force with a frequency of 1 Hz [Anglin et al., 2000, Oosterom 2005]. To investigate the influence of subluxation force frequency, a load case of 750 N compression and a N subluxation force was applied on the uncemented glenoid component ( with conform surface radius 20 mm inlay. The subluxation force frequency was applied with 0 (compression only), 0.01, 0.1, and 1 Hz. Results 0 Hz In all cases the horizontal compression force was applied first, Figure The 0 Hz result (no subluxation force) shows that some relaxation takes place over time. In the period 200 to 300 seconds the relaxation causes an increase of 9 µm of the measurement signal. In the period seconds the signal increases 3 µm. After 2300 seconds the signal no longer increased and had stabilized at a value 37 µm higher than after 200 seconds. sensor output [um] sensor output [um] sensor output [um] sensor output [um] Foam deformation R20 0[Hz] Single step time [Sec] Foam deformation R [Hz] time [Sec] Foam deformation R [Hz] time [Sec] Foam deformation R20 1 [Hz] time [Sec] Figure 4.14, Bone deformation measurement by sensor B, the output for frequencies 0, 0.01, 0.1 and 1 Hz subluxation force of N. Author: Willem Nerkens 26

27 Sensor output [um] hz hz 0.01 hz Time [sec] Figure 4.15, Sensor B output for frequencies 0, 0.01, 0.1 and 1 Hz subluxation force of 250 N. To make a visual presentation that compares the curves in the signals an offset to the 1 and 0.01 Hz measurements was applied. The timing of the first subluxation cycle was set equal as were the means of all signals at 1100 seconds. 1 Hz The tensile testing machine (Zwick/Roell Z005) was unable to apply a consistent load case at 1 Hz, Figure Peak loads in excess of 250 N were applied randomly during loading. However a 1000 seconds after the first subluxation force cycle the shifting of the mean of the cycle appears to stabilize. 0.1Hz When the subluxation force was applied with a frequency of 0.1 Hz the applied load case was stable without random force peaks. The initial load cycle brings the signal closer to its eventual equilibrium state compared to the 1 Hz load case. As the load case frequency decreases the dynamic damping properties of the bone substitute become less influential. A 1000 seconds after the initial subluxation force cycle the slope of the sine appears to be equal to that of the 1 Hz load case. The amplitude of the signal is smaller than in the 1 Hz case, this difference was not thought to be related to the frequency as the 0,01 Hz amplitude is equal to the 1 Hz measurement Hz A subluxation force applied at 0.01 Hz is stable and based on the changes in the signals between 1 Hz and 0.1 Hz the 0.01 Hz curve is as expected. The first cycle bring the sine closer to its equilibrium state as the damping of the material is less influential due to the slower force application. A 1000 seconds after the initial subluxation force cycle the slope of the sine appears to be equal to that of the 0.1 and 1 Hz load case. Overall The stabilization of the measurements at different frequencies is time dependent. The different load cases all become reasonably stable in time, to quantify this statement a stabilization criterion was made in the following section. Both the 0.1 and 0.01 Hz load cases provide a consistent load case. A large amount of load cycles fatigues the screw fixation. As we were interested in the relative motion between metal back and bone directly after surgery it was desirable to minimize the amount of cycles applied to the component. Therefore 0.01 Hz was used in the presented experiments. Author: Willem Nerkens 27

28 Stabilization criterion The stabilization of the measurements was time dependent. In the first load cycles the glenoid component tilts upward and after a certain time the movement of the component would be stable in its new position. For Sensor A which was measuring the micromotions in on the bottom of the metal back this means that the amplitude of the measurement would be large in the first cycles. This was the same for Sensor C which was measuring the vertical micromotions at the bottom of the metal back. Also Sensor D which was measuring rim displacement will have a larger amplitude for the first cycles. For sensor B which was located at the top of the metal back the component will compress the bone substitute causing the sensor housing of Sensor B to move backwards until the equilibrium state was found. This sliding of the sensor housing in the first cycles causes a change in the mean of the measured displacement. And also the plastic deformation of the material around sensor B will cause a change in the mean of the measurement. As we wanted to analyze the amplitudes of the micromotions, bone deformation and rim displacement measurements of the stable state a stabilization criterion was set, Figure Changes in the amplitude and mean of the measurements must be stable within 1% between cycles Perpendicular micromotion (u0/a) 3000 Perpendicular deformation (u1/b) umotion [um] umotion [um] % of next cycle % of next cycle time [Sec] Perpendicular micromotion Amplitude 100% Threshold 101% Cycle # Perpendicular micromotion Mean 100% Threshold 101% Cycle # % of next cycle % of next cycle time [Sec] Perpendicular deformation Amplitude 100% Threshold 101% Cycle # Perpendicular deformation Mean 100% Threshold 99% Cycle # Figure 4.16, The bar plots indicate the changes of one cycle to another in terms of amplitude and signal mean. (Left) Measurement of the micromotions perpendicular to the metal back by Sensor A (Right) Measurement of bone substitute deformation by Sensor B. Author: Willem Nerkens 28

29 After ~ 13 cycles the measurements of all sensors were stable within 1% between cycles, Figure To be certain that the measurements were sufficiently stable the amplitudes of cycles were stored for statistical analysis, Figure sensor output [um] umotion time [Sec] sensor output [um] time [Sec] Figure 4.17, cycles 20 to 25 are taken from the original measurements and the amplitude of each is computed. The mean amplitude of these 5 cycles is taken as the result of one measurement for one repetition per inlay size umotion3-20th cycle Author: Willem Nerkens 29

30 5. Sources of error and variance The variance found in the experiment, Figure 5.1, was quite large considering the uncertainty of the measurement system (calibration showed a residual error of 3 µm). However the magnitudes of the measurements relative to one another were highly consistent within the repetitions. Based on this observation one can conclude that the largest source of random error overall must have had influence on all measurements equally. In this section the causes of variance are described and quantified when possible. I [um] Rep1 Rep2 Rep3 Rep4 Rep Micromotion A Micromotion C Rim displacement D Deformation B Figure 5.1, Measured micromotions, bone substitute deformation and rim displacement per repetition for surface radius 20 mm inlay (conform). Notice the difference between repetition 2 and 3, the relative magnitudes of the measurements are consistent within the repetitions while the variance between repetitions is large. Bone substitute geometry Sensor path location The sensor paths in the bone substitute were made using a column drill. The locations of these points were not exactly equal in all bone substitute blocks. Visual inspection showed that the sensor path locations vary with ~ 2 mm. The reason for this variance was that the cell structure of the polyurethane foam caused the drill to deviate from the target position. In the next chapter a FE model is described which gives a mapping of all occurring micromotions on the metal back, Figure 5.1. From this modelled prediction we can conclude that the errors in the sensor path locations can cause only a small portion of the variance encountered in the experiment results. Author: Willem Nerkens 30

31 Sensor path angle Because of the open cell structure of the bone substitute the drill bends as the sensor paths were made. An estimated maximum error of 5 degrees was made in the sensor path angle. This caused a potential error of 0,38% to be made in the micromotions and bone substitute deformation measurement by sensors A and B, Figure 5.2. Glenoid component Measured displacement Max 5 0 Actual displacement Bone substitute Sensor paths Figure 5.2, An error of 5 degrees in the sensor path causes an error of 0,38 % in the measurement. Block dimensions -Clamping stress in material The bone substitute consisted of cellular rigid polyurethane foam block of 46 (+0.1/+0.5) x46 (+0.1/+0.5) x40 (+/- 0.1) mm. As the dimensions of the bone holder 46x46x33 mm, part of the block will not be clamped at the front, Figure The rest of the block will be subjected to strain as the block is fixed in the bone holder. This pre-strain will thus vary between repetitions. The material has a larger resistance against the shear subluxation force in its deformed state. Thus a larger bone substitute block will have decreased magnitudes of all measured variables, with respect to a block that is closer to the nominal geometry. The magnitude of the positive tolerances on the outer geometry of the bone substitute blocks may have been the cause of the large variance between repetitions. Glenoid component tilting Sensor A and C are measured relative micromotions perpendicular to the metal back. The sensors measure only relative displacement in one dimension. As the component makes a tilting motion the absolute relative micromotions are overestimated by 0.62%, Figure 5.3. Glenoid component Bone substitute Glenoid component Bone substitute Actual micromotion Measured micromotion Figure 5.3, Adjacent points (yellow) on the glenoid component and (red) on the bone are in contact in the initial state. The component is tilted by the load case and the adjacent points move away from one another in a circular motion. As the sensors only measure displacement in one direction an error is made. Based on an estimated maximum component rotation angle of 3 0 the measured micromotion was 0,62% larger than the actual occurring micromotion. Author: Willem Nerkens 31

32 Applied torque on central screw The torque that needs to be applied to the central screw for fixation of the glenoid component is not specified by the prostheses manufacturer. Before the experiments were performed the torque applied to the central screw was found experimentally. An orthopaedic surgeon of the LUMC was asked to apply the torque on the central screw as he would do in practice. A calibrated spring was then used to determine the applied torque, Figure 5.4. Figure 5.4, The spring and inbus used to apply the required torque on the central screw The applied torque on the central screw was Nm, based on this preliminary test. The same spring and inbus were used to apply the torque for each repetition. The uncertainty of the applied torque was estimated (13+/- 2 N at 45 +/- 2 mm) resulting in an uncertainty of / Nm. As a larger torque would strengthen the fixation of the glenoid component and thus decrease the magnitudes of all measured variables. The error in the applied torque may have been the cause of the large variance between repetitions. Angle of central screw As advised by an orthopaedic surgeon the central screw was placed in a predrilled path with 2mm diameter. The error in the implantation angle of the screw was estimated to be less than 10 degrees. This error could cause variance between repetitions. The magnitude of the effect on the measurements is undefined though the author considers the influence to be smaller than that of the errors in the applied torque and the pre-strain caused by the outer geometry of the bone substitute blocks. Measurement surface on metal back Sensors A and B measured micromotions and bone deformation perpendicular to the metal back. As the metal back had a rough surface structure direct contact with the DVRT s was undesirable. To increase the repeatability of the measurements and reduce the risk of damaging the sensors during the experiments the measurement locations were filled locally with tin, Figure 5.5. The measurement surfaces were not perfectly smooth attributing to the variance in the measurements of sensor A (Micromotions) and B (Bone deformation). The maximum absolute error was estimated to be ~20 µm. Figure 5.5, The metal backed implant (Multiplex, ESKA, Lübeck Germany) with tin measurement surfaces. Author: Willem Nerkens 32