- Email: [email protected]
Stiffness analysis of tibia-implant system under cyclic loading
Materials Science and Engineering C 28 (2008) 1203–1208
Contents lists available at ScienceDirect
Materials Science and Engineering C j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m s e c
Stiffness analysis of tibia-implant system under cyclic loading Elmar K. Tschegg a,⁎, Stefan Herndler a, Patrick Weninger b, Michael Jamek a, Stefanie Stanzl-Tschegg c, Heinz Redl b a b c
Material Science Laboratory, Institute for Building Construction and Technology, University of Technology, Karlsplatz 13, A-1040 Vienna, Austria Ludwig Boltzmann Institute for Experimental and Clinical Traumatology, A-1200 Vienna, Austria Institute of Physics and Materials Science, BOKU University of Natural Resources and Applied Life Sciences, A-1190 Vienna, Austria
a r t i c l e
i n f o
Article history: Received 15 May 2008 Received in revised form 9 June 2008 Accepted 10 September 2008 Available online 23 September 2008 Keywords: Bone-implant-system Polymer-composite bone Distal tibia fracture Fatigue loading Stiffness Permanent deformation
a b s t r a c t A testing method has been developed to characterize stiffness and permanent deformation of bone-implant systems. The system consists of an artificial tibia with simulated distal fracture stabilized by an unreamed intramedullary nail. This system was loaded with three different sequences at 2 Hz, each consisting of 40,000 sinusoidal cycles, simulating clinical relevant loading conditions. Evaluation of the results showed a stiffness of 2782 N/mm with a standard deviation of 311 N/mm and a permanent deformation of 0.64 mm with a standard deviation of 0.21 mm. The locking screws broke exclusively during the third loading sequence starting with the most proximal of the distal screws. The study provides a standard technique for biomechanical testing and a comparison of different bone/implant-systems avoiding the variability of cadaver bone tests. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Use of surgical implants for the internal stabilization of fractures is a widely spread and commonly accepted orthopaedic technique. The mechanical behaviour of the entire bone-implant-system has been scarcely examined despite only particular components have been analyzed, yet [1–5]. Information about the mechanical implant behaviour was recorded under static loading [4–6], but not by cyclic loading, which would allow a simulation of physiological gait cycles in a walking subject. A testing method has been developed to analyze the biomechanical characteristics of the complete bone-implant-system under cyclic loading. The testing system allows for measuring the mechanical properties of different bone-implant systems by means of invitro-testing, avoiding the disadvantages of other techniques such as three-point bending tests, four-point bending tests and cadaver bone tests [4–6,7]. Our aim was to establish a basis for biomechanical testing and classification of a large spectrum of implants. As an example, an osteosynthetic system consisting of an artificial left tibia plus intramedullary nail and locking screws has been studied in this paper. The two main properties describing the mechanical characteristics of the bone-implant system are its stiffness and its permanent deformation. The stiffness which describes the relationship between applied load and resulting elastic deformation is an important ⁎ Corresponding author. Vienna University of Technology, Laboratory of Material Science, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria. E-mail address: [email protected] (E.K. Tschegg). 0928-4931/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msec.2008.09.022
characteristic in technical mechanics. Its measurement on boneimplant systems, however, has been scarcely verified. The stiffness of a system depends on the used materials as well as its geometry, thus always consisting of a material and a geometry term. Because the influence of the geometry stiffness is not a material property alone, the response of the system on the load is determined by both, modulus of elasticity and geometry of the specimen. Stiffness is only defined in the linear elastic range of the stress–strain curve where the modulus is defined. In practice it is often not the strain (relative length change) but the absolute change of length that is of interest. Thus stiffness is correlated to the absolute change of length and describes the load needed to change the length of the specimen by 1 mm elastically. The unit of the resulting stiffness, which is inversely proportional to the elastic deformation, is therefore N/mm. As mentioned above the second important characteristic to describe the mechanical behaviour of a specimen is the permanent deformation. This deformation characterizes the damage of the specimen under incremental loading. 2. System description This work aims to test the complete osteosynthetic system; the specimen therefore consists of a bone with an idealized fracture and an intramedullary nail with appropriate locking screws. The tested bone is an artificial model of a large left tibia from the 3rd generation of composite bones of the company Sawbones [8]. Its shape and behaviour simulate the human tibia bone. The model of the tibia is 405 mm long and has an intermedullary canal of 10 mm diameter
1204
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
beginning at the distal tibial plateau ranging into die proximal epiphysis of the bone. The intermedullary nail is placed in this canal. The composite bone consists of two different materials, a solid polyurethane foam (density 0.32 g/m3, compressive strength 5.4 MPa, compressive modulus 137 MPa) which forms the core and a mixture of short glass fibres and epoxy resin (density 1.7 g/cm3, compressive strength 120 MPa, compressive modulus 7600 MPa), which fills the space between the die external form and the polyurethane foam core. The polyurethane foam represents the cancellous bone of the human tibia and the mixture of epoxy resin and short glass fibres the corticalis. Before assessing the mechanical characteristics of an artificial tibia, one has to keep in mind that the shapes of the corticalis and of the cancellous bone are slightly different from those of the human bone. Before mechanical testing was performed, a comminuted distal fracture model was created by performing a saw cut in radial direction (shown in Fig. 1) and a tibial nail was inserted. The intramedullary nail was a product of the Expert Tibial Nail series of the company Synthes [9]. Its diameter was 9 mm, it was 375 mm long and it was inserted without reaming. We used two static locking screws to secure fit nail fixation in the proximal fragment. For the fixation in the distal fracture fragment, all four distal locking options were used. The locking screws originated from die Stardrive product series of the company Synthes. They were fully threaded with a self-tapping and self-drilling double helix thread, and their outer diameter was 4 mm, the screw lengths ranged from 34 mm to 50 mm dependent on the spans required. The intramedullary nail and the locking screws are made of TiAl6Nb7 (titanium–aluminium 6-niobium7)-alloy (tensile strength ≈ 1300 MPa, density ≈ 450 kg/mm2). 3. Specimen preparation As mentioned above the testing procedure was not limited to the testing of individual components of an osteosynthetic system, as described in many other papers, but it seemed appropriate to investigate the biomechanical characteristics of a complete boneimplant system. Therefore the specimen consists of a composite bone with a simulated comminuted fracture, which was stabilized by an intramedullary nail and the locking screws. While preparing the specimen it was important to simulate the clinical situation as close as possible. Therefore, a distal tibia fracture model was created in three specimens. The comminuted fracture zone was reduced to its fundamental biomechanical characteristics, consisting of a defect zone of 10 mm length, 60 mm proximal to the distal tibial plateau. The osteotomy was performed in the boundary region of the diaphysis and the distal metaphysis, to allow secure placement of up to four screws. In this setting, fragments had no cortical support and nail and locking screws had to transmit the loads applied. Locking screw insertion was performed according to the manufacturer's protocol [10]. At the point of insertion, the corticalis was opened with an awl to a diameter of 13 mm and a depth of approximately 30 mm. The nail was inserted into the center of the medullary canal by hand as far as possible and subsequently driven further by careful blows with a sliding hammer. This procedure was performed under permanent X-ray control (Mini-View 6800 General Electric). When the nail was directed into the desired position, the locking screws were implanted. Proximal locking was performed statically with two locking screws inserted from medial to lateral. The first screw was inserted into the most distal of the proximal wholes, thus securing rotational and axial stability. The second screw was placed through a long hole 15 mm apart of the first proximal screw. This way of locking allows secondary dynamization. The reason for using this technique may be explained easily from the clinical point of view. If the stabilization of the fracture is too rigid resulting in delayed healing, the screw of the round hole can be removed for dynamization of the fracture.
Distal interlocking is performed in the free hand technique under fluoroscopic guidance. To allow optimal stabilization of the distal fragment, all four interlocking options were used. One of the specimens can be seen in Fig. 1. 4. Testing routine The testing condition of the specimen was designed to simulate the clinical situation in the first instance, but goes beyond that for an estimation of safety margins. The “load to failure testing” technique for measuring the stiffness of a specimen is published in numerous papers. To simulate the clinical scenario as close as possible, cyclic loading with incremental sinusoidal loads were applied on the specimens. Such varying load is considered adequate to simulate the actual loading condition of the tibia. To cover a broad spectrum of strain, three different loading sequences were used. In Fig. 2, the three sequences are shown schematically. The first characterized the clinical situation, the second the technical investigation and the third the failure test. Each of these loading sequences consisted of 40,000 loading cycles with two loading cycles per second (2 Hz). The first sequence (a) consisted of a static compressive load of 700 N containing a superimposed cyclic load with an amplitude of 600 N. During the second sequence (b), 1300 N with an amplitude of 1200 N and during the third series (c) a static load of 1700 N with superimposed cyclic load of 1600 N were applied. Thus the maximum load of the first loading sequence simulated the forces during walking of a patient with a body weight of 87 to 130 kg [11], i.e. simulating approximately 1.5 times the body weight. This loading sequence is most important for the clinical investigation and therefore the resulting displacements of the specimen were examined exactly. The maximum load of the technical loading sequence simulated approximately 2 to 3 times of the average body weight of an adult
Fig. 1. Bone-implant system with bone of Sawbones and implant of Synthes.
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
1205
the whole testing routine is determined. In order to exactly document any changes at the locking screws of the specimen, five passive acoustic emission sensors [14] were attached to the screw heads. 6. Data acquisition
Fig. 2. Three different loading sequences are used: a) clinical investigation, b) the technical investigation and c) the failure test.
individual. Although an accurate analysis of the displacements is generally possible it was not considered as important for this study. Thus only a qualitative examination of the occurring damages was made. The peak load of the third (failure test) loading sequence corresponded with a load of up to 2.5 to 4 times of the body weight. As in the previous sequence the displacements were only examined qualitatively as to estimate the safety margin. Experiments were stopped after failure of the implant-boneconstruct leading to closure of the osteotomy gap. If specimens survived the testing, experiments were stopped after 3 series of 40,000 cycles. 5. Biomechanic test assembly The load was applied with a servo-hydraulic testing system (Schenck PSA 40) [12]. As the static preload is a compressive load there was no need for a stabilization against tensile forces. Therefore it was sufficient to prepare cast models of the distal and the proximal tibia plateaus and to mount the specimen onto the testing system between these moulds. The produced casts provide a 7° valgus alignment of the tibia simulating the physiological leg axis. In the experimental setup ten displacement transducers (Fig. 3), one load cell and five acoustic emission sensors (not all of them are shown) were used. A group of four displacement transducers measured the axial displacements of the specimen. The axial displacements were measured at the proximal tibial plateau (1), whereas the distal tibial plateau is immobile and therefore no measurement is needed. In addition, displacements are measured at the proximal fracture edge (3), and at the proximal (2) and the distal (4) end of the intramedullary nail. The signal of the displacement transducer which measures the displacement at the proximal tibial plateau (1) serves as shut-off criteria. The other six displacement transducers measure the radial displacement of the intramedullary nail at the fracture zone. The displacement transducers are mounted by dial gauge holders. Most of the measured displacements are located in the distal region of the specimen, but the distal tibial plateau is fixed. As a result of the design of the servo-hydraulic testing system the specimen was mounted–in contrast to Fig. 3–upside down (i.e. with distal end on top). Since the testing routine is load-controlled, use of a load cell is essential in the experimental setup. It supplies the signal for the closed loop control of the servo-hydraulic testing system where the actual value of the load is compared with the desired value and thus
The electric signals of the displacement transducers, besides the one which is used as shut-off signal, are amplified and led to the BNC connecting block. The electric signal was used as shut-off signal and the signal of the load cell is transmitted to the servo-hydraulic testing system. There, the signal of the load cell is fed into the loop circuit, and the displacement signal used as shut-off signal is controlled for finishing the testing sequence. Afterwards both signals are transmitted to the BNC connecting block. From here, the collected eleven signals are transferred to a data acquisition board and are recorded by the data acquisition software Dasy-Lab (National Instruments) [13]. The records thus attained can later be processed by spread-sheet analysis. The electrical signals of the five passive acoustic emission sensors are amplified and transmitted to the acoustic emission equipment AMS 3 of Vallen [14]. The acoustic emission equipment AMS 3 analyzes all signals of the acoustic emission sensors and passes the resulting analysis data and the shapes of the acoustic signals on to a data acquisition board. Subsequently the data are stored by an acoustic emission software. The records can later be processed by a special evaluation software, and they can also be exported as a text file and imported into a spread-sheet analysis. 7. Analysis of data The method of data analysis [15] can be performed for all three loading sequences in the same way and are described in the following. The acquired data of each single displacement transducer can be illustrated in a force-displacement-diagram as shown schematically in Fig. 4. Fig. 4 shows the first and the last loading cycles of a loading sequence. Loading of the specimen changes periodically, resulting in a defined displacement. As shown in Fig. 4 the stiffness of the specimen is defined by the gradient of the force-displacement-curve. Thus stiffness is determined by the elastic behaviour of the specimen. The
Fig. 3. Positions of displacement transducers and AE-sensors.
1206
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
Fig. 6. Schematic of the increase of “Permanent Deformation” with number of cycles.
Fig. 4. Stiffness obtained from the measured forces and axial displacements.
two most interesting values are the stiffness of the specimen at the beginning and at the end of the loading sequence, named “Stiffness A” and “Stiffness B.” The axial stiffness of the specimen is obtained by using the data of the displacement transducer no.1 as seen in Fig. 3. Fig. 4 also shows the most important displacements occurring during the loading sequence. The value named “Offset” indicates the measured permanent displacement before cyclic loading at the minimal load of the sequence. This is an important value, because it describes early permanent deformation. The values “Elastic Deformation A” and “Elastic Deformation B” describe the elastic behaviour of the specimen at the beginning and at the end of a loading sequence. Their values are inversely proportional to the ones of “Stiffness A” and “Stiffness B.” The value Permanent Deformation describes the amount of damage of the specimen induced by the periodical load. “Offset” contains elastic as well as irreversible displacements. “Offset” and Permanent Deformation together contribute to the displacements that remain after unloading the specimen. The axial displacement of the fracture gap is estimated by the given method using the data of displacement transducer no.3 as seen in the Fig. 3. Owing to the load-controlled testing method, the displacements may be plotted in a curve: displacement versus number of cycles—, as shown schematically in Fig. 5. Fig. 5 is just another way of visualizing the relevant displacements that have already been shown in Fig. 4. This also leads to the question how the Permanent Deformation increases with increasing number of cycles of the loading sequence. Fig. 5 shows a linear increase of the Permanent Deformation with an increase of the number of loading cycles. But there are in principal three different possibilities for the change of the Permanent Deformation with time, which are shown in Fig. 6.
Fig. 5. Axial displacements versus number of cycles.
As shown in Fig. 4, the Permanent Deformation may increase faster at the beginning or at the end of the loading sequence. It will be investigated in another study whether the linear or one of the two other changes is the actual behaviour of the Plastic Deformation. The data of the radial and the axial displacement transducers no.2 and no.4 are used to determine the bending of the intramedullary nail. The acquired data of the acoustic emissions of the screws were used to determine which screw is bearing the load in the course of the loading sequence and when does which screw break. To obtain information on screw breakage, values of the axial displacement transducers were checked additionally for abrupt non cyclic rises of their displacement values. 8. Results 8.1. Presentation of damages The easiest accessible results are the damages that occurred in the sample during the three loading sequences. Therefore after finishing the complete testing procedure the individual parts of the specimen are separated again following the preparation steps backwards. After the necessary working steps the damages on the locking screws, the artificial tibia and the intramedullary nail are documented. During the testing procedure locking screws only broke during the third loading sequence. Until closure of the fracture gap, which is the shut-off criterion of the testing procedure, all distal locking screws failed and only in one specimen one proximal locking screw failed. All fractures occur on the outside edge of the nail holes. Cracks in the bone were documented in all specimens. Cracks are located around the locking screws and are 6 mm long in average, but smaller than 10 mm. Formation of elongated holes has not been observed. No significant damage to the intramedullary nails was documented.
Fig. 7. Reduction of the fracture gap at the beginning and at the end of the first loading sequence.
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
At a whole, three specimens have been tested. The standard deviations of the obtained data have been determined and are added to the results in the following. 8.2. The stiffness The stiffness of the specimen is evaluated at the beginning and the end of the loading sequence, and before and after locking screw failure. The results show that the stiffness of the specimen hardly changes during all loading sequences. Mean stiffness was 2.782 N/mm with a standard deviation of 311 N/mm. Due to the fact that the specimen is statically over-dimensioned even a fracture of a distal locking screw would not result in a strong modification of the stiffness.
1207
Permanent Deformation over time is also analyzed. The results of this analysis are shown in Fig. 8. The diagram shows the increase of the Permanent Deformation during cyclic loading during the first sequence of testing, i.e. during the clinical investigation. As can be seen, the largest part of the Permanent Deformation takes place in the first half of the loading sequence. As the axial displacement shows a reduction of the fracture gap, it was then examined if this reduction was caused by bending of the intramedullary nail. Bending of the nail is calculated by measurement of the displacements with transducers no.2, 4 and 5–10. The measurements show that there is no bending of the nail. Therefore the reduction of the fracture gap can be solely attributed to bending of the locking screws and to damages of the artificial tibia and the screws. 8.4. Sequence of the screw fractures
8.3. The displacements The following results of the displacements of the specimens are obtained by analyzing the data of the first loading sequence (100– 1300 N) only. The displacements of the two other loading sequences are neglected here, since such high loads are not really of practical relevance. First, the results of the axial displacements, which correspond to the reduction of the fracture gap, are presented. Fig. 7 shows the average reduction of the fracture gap during the first loading sequence. The given standard deviation refers to the sum of the displacements situated below it. The “Offset” shows a displacement of 0.13 ± 0.08 mm. This indicates that a relatively high permanent deformation occurs already before the defined minimal load (100 N) of the first cycle is reached. The “Elastic Deformation A” has a value of 0.45 ± 0.05 mm and describes the early elastic behaviour of the specimen. This deformation is inversely proportional to the “Stiffness A.” The sum of the “Offset” and the “Elastic Deformation A” describes the maximum reduction of the fracture gap during the first loading cycles (~2000 cycles). During the loading sequence with a load periodically changing from 100 to 1300 N during 40,000 cycles the specimen is damaged irreversibly. This damage is described by the Permanent Deformation which was 0.52 ± 0.19 mm, meaning that the fracture gap is reduced by this amount even after unloading the specimen. If the specimen was to be unloaded after the first loading sequence only the sum of the permanent deformation (“Offset” & Permanent Deformation) would result in a permanent reduction of the fracture gap, with a deformation of 0.64 ± 0.21 mm in this case. The “Elastic Deformation B” describes the later (~ 38,000 cycles) elastic behaviour of the specimen and has a value of 0.43 ± 0.04 mm. This shows an increase of the stiffness of the specimen during the loading sequence. The maximum displacement of the fracture gap, i.e. the reduction of the gap, is obtained by summing up the displacements “Offset,” “Plastic Deformation” and “Elastic Deformation B” which is 1.07 ± 0.25 mm. As described earlier the growth of the
To determine timing and location of a locking screw's breaking, the acoustic emission technique is used. Additionally the data of the axial displacement transducers are utilized to recognize a fracture as one of a proximal or distal screw. All fractures of the screws can be identified unambiguously in time (number of cycles) and place. In the tested specimen, the first three screws broke at about the same time. Fracturing of the locking screws takes place only in the third, i.e. last loading sequence. The first screw to break is the most proximal of the distal screws. It breaks after approximately 11,000 loading cycles and leads to a reduction of the fracture gap of 2.83±0.06 mm. The distal neighbor of the above mentioned screw breaks after another 9000 cycles. After another 2000 cycles the third screw, which is the next distal one, breaks. 9. Discussion 9.1. The artificial tibia The artificial tibia offers several advantages in comparison to a cadaveric tibia: It is always available, easy to prepare, store and dispose and simplifies the testing procedure and evaluation. The crucial benefit, however, is the uniformity of the mechanical characteristics. This leads to identical boundary conditions for all testing procedures, causing a lower variance of the test results. As already mentioned the artificial tibia should imitate the global properties of the human bone. To achieve this, the thickness of the artificial corticalis has to be changed, due to its material properties that differ from those of the human corticalis. Furthermore the used polyurethane foam core fills the total inside of the artificial tibia, whereas in the epiphysis of the human tibia trabeculae are prevailing, which are increasingly replaced by bone marrow towards the diaphysis. In addition, the pervasive polyurethane foam core can lead to supports of the intramedullary nail, which is not possible in the natural bone. It is obvious that there are certain differences which may affect the results. Especially for intramedullary nails, which are fastened with locking screws, the local behaviour of the used components plays a larger role. Changed thicknesses and different mechanical properties of the artificial corticalis can, particularly in this case, influence the test results. Thus the results are not completely transmittable to the real patient. After all it is not the aim of this work to make a medical conclusion, but to establish a testing method with low scattering of the testing results in order to obtain typical values and characteristics of the mechanical behaviour of the specimen to compare different implants. Among these criteria the artificial tibia proves as ideal. 9.2. The origin of the damages
Fig. 8. Growth of the “Permanent Deformation” versus number of cycles.
Damages of the locking screws are most interesting and shall thus be discussed more closely. It is remarkable that all the distal screws have broken at least once or even twice in the three tested specimens.
1208
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
On the other hand the axial stable locking screw only broke in one of the three specimens, and this only after the described three distal screws failed. As described above, one axial stable screw is used for the proximal stabilization of the nail and four screws to ensure the distal fixation. The only difference between the proximal and the distal locking screws closest to the fracture, is their distance to the fracture and the diameter of the nail at the places of the locking screws. The proximal screw is situated 260 mm apart from the fracture, while the distal screw is only 10 mm apart. As the nail on the proximal side of the fracture gap is surrounded by the artificial tibia on a long distance, the tibia already shares part of the load directly with the nail. Thus the load on the proximal screw is reduced by this amount. Further the spans of the two screws are very similar, but as mentioned above, the diameter of the nail at the positions of the distal and proximal locking screws is different. At the hole of the proximal locking screw the diameter of the nail is 11 mm, whereas at the position of the distal screw the diameter is only 9 mm, which leads to a better distribution of the load around the proximal screw. This may be the reason for the earlier failure of the distal screw closest to the fracture gap, i.e. the proximal of distal screws. It is now to be discussed why the other distal screws broke earlier than the proximal as well. This may be explained in a similar way: the span of the screws more distant from the fracture gap is larger. Because of the increase in length at a constant diameter, the distal locking screws bend easier and are thus damaged sooner. Since they show a smaller resistance against the load, the deformations of these screws are larger. This leads to faster fatigue of the material and earlier failure. The effect is large enough that in two of the three specimens, all four distal locking screws break without any proximal screws breaking.
the “Offset” which contributes the largest part of these deformations. This strong offset even before the minimal load of 100 N is reached is very critical and efforts should be undertaken to minimize it.
9.3. Stiffness and displacements
The authors thank Ing. Karl Kropik and Dr. A. Schultz for the specimen preparation and Prof. Hartmut Pelinka and the Austrian Workers' Compensation Board (AUVA) for the research grant to realize this investigation.
A certain amount of stiffness is required and desired but very high stiffness is not useful, as it leads to a stress-shielding effect and thereby delays healing of the bone. Likewise a very low stiffness prevents healing. It is remarkable that the stiffness of the implant/bone system increases slightly and consistently from the beginning to the end of the loading sequence and although the effect is not pronounced, it is statistically significant for the first two loading sequences. This effect may be caused by a continuous and improving re-distribution of the load between the locking screws. Another explanation may be an effect similar to the “cold working” effect, which causes an increase of the strength of the locking screws by mechanical deformation. The stiffness corresponds only to the elastic deformations and is thus not sufficient to describe the entire behaviour of a specimen. Contrarily, the permanent deformation is not related to the stiffness. The results show that the fracture gap decreases while the stiffness of the specimen remains almost unchanged or slightly increases, which means that the deformations that cause the shortening have no effect on the stiffness. As no damages occur in the nail, the irreversible reduction of the fracture gap can only be caused by damages of the thread of the screws and/or the formation of elongated holes and cracks in the bone. Examination of the specimens leads to the assumption that the damages of the thread of the screws are mainly responsible for the displacements. It would therefore be advisable to use screws without thread in the area of contact with the nail. Also contributing to the “plastic” deformation is
10. Summary Fracturing of screws took place only during the third and final loading sequence of testing. In two of three specimens, all distal screws, but none of the proximal ones broke. The three screws breaking first are the same in the three samples, and break at about the same time and are the three distal screws closest to the fracture gap. The stiffness of the specimen remains almost constant and is approximately 2762 N/mm with a standard deviation of 280 N/mm. The axial displacements of the fracture fragments towards each other have been analyzed precisely during the first loading sequence and are stated below. The “Offset;” the displacement that occurs before reaching the minimal load of the first loading sequence, amounts to 0.13 ± 0.08 mm. The “Elastic Deformation A” and the “Elastic Deformation B;” elastic deformations at the beginning and at the end of the first loading sequence, are 0.45 ± 0.05 mm and 0.43 ± 0.04 mm respectively. The Permanent Deformation that describes the reduction of the fracture gap caused by the irreversible damages of the specimen during the loading sequence, is 0.52± 0.13 mm. The sum of the permanent deformations; those deformations that remain after unloading the specimen, is 0.64 ± 0.21 mm. The maximum difference at the beginning and the end of the loading sequence is 0.57 ± 0.13 mm and 1.07 ± 0.25 mm respectively. Acknowledgements
References [1] C. Gaebler, A. Speitling, E.L. Milne, S. Stanzl-Tschegg, V. Vecsei, L.L. Latta, Int. J. Care Inj. 32 (2001) 708–712. [2] C. Gaebler, S. Stanzl-Tschegg, W. Laube, V. Vecsei, Int. J. Care Inj. 32 (2001) 401–405. [3] C. Gaebler, S. Stanzl-Tschegg, G. Heinze, B. Holper, T. Milne, G. Berger, V. Vecsei, J. Trauma 47–2 (1999) 379–384. [4] J.T. Gorczyca, J. McKale, K. Pugh, D. Pienkowski, J. Orthop. Trauma 16–1 (2002) 18–22. [5] C. Kanchanomai, V. Phiphobmongkol, P. Muanjan, Eng. Fail. Anal. 15 (2008) 512–530. [6] C.C. Wu, C.L. Tai, Chang. Gung. Med. J. 29–3 (2006) 275–282. [7] J. Korner, G. Diederichs, M. Arzdorf, H. Lill, C.h. Josten, E. Schneider, B. Linke, J. Orthop Trauma 18 (5) (May/June 2004) 286–292. [8] http://www.sawbones.com/products/bio/composite.aspx. [9] http://www.synthes.com/html/Expert-Tibial-Nail.6885.0.html. [10] http://www.synthes.com/html/fileadmin/Shared/shop,/Printed_Materials/ Techique_Guide/trau ma/036.000.380.pdf. [11] R.R. Neptune, S.A. Kautz, F.E. Zajac, J. Biomech. 34 (2001) 1387–1398. [12] Standard-Handbuch für Hydropuls-Prüfmaschinen PSA mit Nennkräften von 10, 40 oder 100 kN. Ausgabe Januar 1992, Carl Schenck AG. [13] http://www.dasylab.com. [14] http://www.vallen.de. [15] E.K. Tschegg, S. Stanzl-Tschegg, Patent application 15.11.2007, Patent office Vienna, Austria.
Contents lists available at ScienceDirect
Materials Science and Engineering C j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m s e c
Stiffness analysis of tibia-implant system under cyclic loading Elmar K. Tschegg a,⁎, Stefan Herndler a, Patrick Weninger b, Michael Jamek a, Stefanie Stanzl-Tschegg c, Heinz Redl b a b c
Material Science Laboratory, Institute for Building Construction and Technology, University of Technology, Karlsplatz 13, A-1040 Vienna, Austria Ludwig Boltzmann Institute for Experimental and Clinical Traumatology, A-1200 Vienna, Austria Institute of Physics and Materials Science, BOKU University of Natural Resources and Applied Life Sciences, A-1190 Vienna, Austria
a r t i c l e
i n f o
Article history: Received 15 May 2008 Received in revised form 9 June 2008 Accepted 10 September 2008 Available online 23 September 2008 Keywords: Bone-implant-system Polymer-composite bone Distal tibia fracture Fatigue loading Stiffness Permanent deformation
a b s t r a c t A testing method has been developed to characterize stiffness and permanent deformation of bone-implant systems. The system consists of an artificial tibia with simulated distal fracture stabilized by an unreamed intramedullary nail. This system was loaded with three different sequences at 2 Hz, each consisting of 40,000 sinusoidal cycles, simulating clinical relevant loading conditions. Evaluation of the results showed a stiffness of 2782 N/mm with a standard deviation of 311 N/mm and a permanent deformation of 0.64 mm with a standard deviation of 0.21 mm. The locking screws broke exclusively during the third loading sequence starting with the most proximal of the distal screws. The study provides a standard technique for biomechanical testing and a comparison of different bone/implant-systems avoiding the variability of cadaver bone tests. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Use of surgical implants for the internal stabilization of fractures is a widely spread and commonly accepted orthopaedic technique. The mechanical behaviour of the entire bone-implant-system has been scarcely examined despite only particular components have been analyzed, yet [1–5]. Information about the mechanical implant behaviour was recorded under static loading [4–6], but not by cyclic loading, which would allow a simulation of physiological gait cycles in a walking subject. A testing method has been developed to analyze the biomechanical characteristics of the complete bone-implant-system under cyclic loading. The testing system allows for measuring the mechanical properties of different bone-implant systems by means of invitro-testing, avoiding the disadvantages of other techniques such as three-point bending tests, four-point bending tests and cadaver bone tests [4–6,7]. Our aim was to establish a basis for biomechanical testing and classification of a large spectrum of implants. As an example, an osteosynthetic system consisting of an artificial left tibia plus intramedullary nail and locking screws has been studied in this paper. The two main properties describing the mechanical characteristics of the bone-implant system are its stiffness and its permanent deformation. The stiffness which describes the relationship between applied load and resulting elastic deformation is an important ⁎ Corresponding author. Vienna University of Technology, Laboratory of Material Science, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria. E-mail address: [email protected] (E.K. Tschegg). 0928-4931/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msec.2008.09.022
characteristic in technical mechanics. Its measurement on boneimplant systems, however, has been scarcely verified. The stiffness of a system depends on the used materials as well as its geometry, thus always consisting of a material and a geometry term. Because the influence of the geometry stiffness is not a material property alone, the response of the system on the load is determined by both, modulus of elasticity and geometry of the specimen. Stiffness is only defined in the linear elastic range of the stress–strain curve where the modulus is defined. In practice it is often not the strain (relative length change) but the absolute change of length that is of interest. Thus stiffness is correlated to the absolute change of length and describes the load needed to change the length of the specimen by 1 mm elastically. The unit of the resulting stiffness, which is inversely proportional to the elastic deformation, is therefore N/mm. As mentioned above the second important characteristic to describe the mechanical behaviour of a specimen is the permanent deformation. This deformation characterizes the damage of the specimen under incremental loading. 2. System description This work aims to test the complete osteosynthetic system; the specimen therefore consists of a bone with an idealized fracture and an intramedullary nail with appropriate locking screws. The tested bone is an artificial model of a large left tibia from the 3rd generation of composite bones of the company Sawbones [8]. Its shape and behaviour simulate the human tibia bone. The model of the tibia is 405 mm long and has an intermedullary canal of 10 mm diameter
1204
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
beginning at the distal tibial plateau ranging into die proximal epiphysis of the bone. The intermedullary nail is placed in this canal. The composite bone consists of two different materials, a solid polyurethane foam (density 0.32 g/m3, compressive strength 5.4 MPa, compressive modulus 137 MPa) which forms the core and a mixture of short glass fibres and epoxy resin (density 1.7 g/cm3, compressive strength 120 MPa, compressive modulus 7600 MPa), which fills the space between the die external form and the polyurethane foam core. The polyurethane foam represents the cancellous bone of the human tibia and the mixture of epoxy resin and short glass fibres the corticalis. Before assessing the mechanical characteristics of an artificial tibia, one has to keep in mind that the shapes of the corticalis and of the cancellous bone are slightly different from those of the human bone. Before mechanical testing was performed, a comminuted distal fracture model was created by performing a saw cut in radial direction (shown in Fig. 1) and a tibial nail was inserted. The intramedullary nail was a product of the Expert Tibial Nail series of the company Synthes [9]. Its diameter was 9 mm, it was 375 mm long and it was inserted without reaming. We used two static locking screws to secure fit nail fixation in the proximal fragment. For the fixation in the distal fracture fragment, all four distal locking options were used. The locking screws originated from die Stardrive product series of the company Synthes. They were fully threaded with a self-tapping and self-drilling double helix thread, and their outer diameter was 4 mm, the screw lengths ranged from 34 mm to 50 mm dependent on the spans required. The intramedullary nail and the locking screws are made of TiAl6Nb7 (titanium–aluminium 6-niobium7)-alloy (tensile strength ≈ 1300 MPa, density ≈ 450 kg/mm2). 3. Specimen preparation As mentioned above the testing procedure was not limited to the testing of individual components of an osteosynthetic system, as described in many other papers, but it seemed appropriate to investigate the biomechanical characteristics of a complete boneimplant system. Therefore the specimen consists of a composite bone with a simulated comminuted fracture, which was stabilized by an intramedullary nail and the locking screws. While preparing the specimen it was important to simulate the clinical situation as close as possible. Therefore, a distal tibia fracture model was created in three specimens. The comminuted fracture zone was reduced to its fundamental biomechanical characteristics, consisting of a defect zone of 10 mm length, 60 mm proximal to the distal tibial plateau. The osteotomy was performed in the boundary region of the diaphysis and the distal metaphysis, to allow secure placement of up to four screws. In this setting, fragments had no cortical support and nail and locking screws had to transmit the loads applied. Locking screw insertion was performed according to the manufacturer's protocol [10]. At the point of insertion, the corticalis was opened with an awl to a diameter of 13 mm and a depth of approximately 30 mm. The nail was inserted into the center of the medullary canal by hand as far as possible and subsequently driven further by careful blows with a sliding hammer. This procedure was performed under permanent X-ray control (Mini-View 6800 General Electric). When the nail was directed into the desired position, the locking screws were implanted. Proximal locking was performed statically with two locking screws inserted from medial to lateral. The first screw was inserted into the most distal of the proximal wholes, thus securing rotational and axial stability. The second screw was placed through a long hole 15 mm apart of the first proximal screw. This way of locking allows secondary dynamization. The reason for using this technique may be explained easily from the clinical point of view. If the stabilization of the fracture is too rigid resulting in delayed healing, the screw of the round hole can be removed for dynamization of the fracture.
Distal interlocking is performed in the free hand technique under fluoroscopic guidance. To allow optimal stabilization of the distal fragment, all four interlocking options were used. One of the specimens can be seen in Fig. 1. 4. Testing routine The testing condition of the specimen was designed to simulate the clinical situation in the first instance, but goes beyond that for an estimation of safety margins. The “load to failure testing” technique for measuring the stiffness of a specimen is published in numerous papers. To simulate the clinical scenario as close as possible, cyclic loading with incremental sinusoidal loads were applied on the specimens. Such varying load is considered adequate to simulate the actual loading condition of the tibia. To cover a broad spectrum of strain, three different loading sequences were used. In Fig. 2, the three sequences are shown schematically. The first characterized the clinical situation, the second the technical investigation and the third the failure test. Each of these loading sequences consisted of 40,000 loading cycles with two loading cycles per second (2 Hz). The first sequence (a) consisted of a static compressive load of 700 N containing a superimposed cyclic load with an amplitude of 600 N. During the second sequence (b), 1300 N with an amplitude of 1200 N and during the third series (c) a static load of 1700 N with superimposed cyclic load of 1600 N were applied. Thus the maximum load of the first loading sequence simulated the forces during walking of a patient with a body weight of 87 to 130 kg [11], i.e. simulating approximately 1.5 times the body weight. This loading sequence is most important for the clinical investigation and therefore the resulting displacements of the specimen were examined exactly. The maximum load of the technical loading sequence simulated approximately 2 to 3 times of the average body weight of an adult
Fig. 1. Bone-implant system with bone of Sawbones and implant of Synthes.
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
1205
the whole testing routine is determined. In order to exactly document any changes at the locking screws of the specimen, five passive acoustic emission sensors [14] were attached to the screw heads. 6. Data acquisition
Fig. 2. Three different loading sequences are used: a) clinical investigation, b) the technical investigation and c) the failure test.
individual. Although an accurate analysis of the displacements is generally possible it was not considered as important for this study. Thus only a qualitative examination of the occurring damages was made. The peak load of the third (failure test) loading sequence corresponded with a load of up to 2.5 to 4 times of the body weight. As in the previous sequence the displacements were only examined qualitatively as to estimate the safety margin. Experiments were stopped after failure of the implant-boneconstruct leading to closure of the osteotomy gap. If specimens survived the testing, experiments were stopped after 3 series of 40,000 cycles. 5. Biomechanic test assembly The load was applied with a servo-hydraulic testing system (Schenck PSA 40) [12]. As the static preload is a compressive load there was no need for a stabilization against tensile forces. Therefore it was sufficient to prepare cast models of the distal and the proximal tibia plateaus and to mount the specimen onto the testing system between these moulds. The produced casts provide a 7° valgus alignment of the tibia simulating the physiological leg axis. In the experimental setup ten displacement transducers (Fig. 3), one load cell and five acoustic emission sensors (not all of them are shown) were used. A group of four displacement transducers measured the axial displacements of the specimen. The axial displacements were measured at the proximal tibial plateau (1), whereas the distal tibial plateau is immobile and therefore no measurement is needed. In addition, displacements are measured at the proximal fracture edge (3), and at the proximal (2) and the distal (4) end of the intramedullary nail. The signal of the displacement transducer which measures the displacement at the proximal tibial plateau (1) serves as shut-off criteria. The other six displacement transducers measure the radial displacement of the intramedullary nail at the fracture zone. The displacement transducers are mounted by dial gauge holders. Most of the measured displacements are located in the distal region of the specimen, but the distal tibial plateau is fixed. As a result of the design of the servo-hydraulic testing system the specimen was mounted–in contrast to Fig. 3–upside down (i.e. with distal end on top). Since the testing routine is load-controlled, use of a load cell is essential in the experimental setup. It supplies the signal for the closed loop control of the servo-hydraulic testing system where the actual value of the load is compared with the desired value and thus
The electric signals of the displacement transducers, besides the one which is used as shut-off signal, are amplified and led to the BNC connecting block. The electric signal was used as shut-off signal and the signal of the load cell is transmitted to the servo-hydraulic testing system. There, the signal of the load cell is fed into the loop circuit, and the displacement signal used as shut-off signal is controlled for finishing the testing sequence. Afterwards both signals are transmitted to the BNC connecting block. From here, the collected eleven signals are transferred to a data acquisition board and are recorded by the data acquisition software Dasy-Lab (National Instruments) [13]. The records thus attained can later be processed by spread-sheet analysis. The electrical signals of the five passive acoustic emission sensors are amplified and transmitted to the acoustic emission equipment AMS 3 of Vallen [14]. The acoustic emission equipment AMS 3 analyzes all signals of the acoustic emission sensors and passes the resulting analysis data and the shapes of the acoustic signals on to a data acquisition board. Subsequently the data are stored by an acoustic emission software. The records can later be processed by a special evaluation software, and they can also be exported as a text file and imported into a spread-sheet analysis. 7. Analysis of data The method of data analysis [15] can be performed for all three loading sequences in the same way and are described in the following. The acquired data of each single displacement transducer can be illustrated in a force-displacement-diagram as shown schematically in Fig. 4. Fig. 4 shows the first and the last loading cycles of a loading sequence. Loading of the specimen changes periodically, resulting in a defined displacement. As shown in Fig. 4 the stiffness of the specimen is defined by the gradient of the force-displacement-curve. Thus stiffness is determined by the elastic behaviour of the specimen. The
Fig. 3. Positions of displacement transducers and AE-sensors.
1206
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
Fig. 6. Schematic of the increase of “Permanent Deformation” with number of cycles.
Fig. 4. Stiffness obtained from the measured forces and axial displacements.
two most interesting values are the stiffness of the specimen at the beginning and at the end of the loading sequence, named “Stiffness A” and “Stiffness B.” The axial stiffness of the specimen is obtained by using the data of the displacement transducer no.1 as seen in Fig. 3. Fig. 4 also shows the most important displacements occurring during the loading sequence. The value named “Offset” indicates the measured permanent displacement before cyclic loading at the minimal load of the sequence. This is an important value, because it describes early permanent deformation. The values “Elastic Deformation A” and “Elastic Deformation B” describe the elastic behaviour of the specimen at the beginning and at the end of a loading sequence. Their values are inversely proportional to the ones of “Stiffness A” and “Stiffness B.” The value Permanent Deformation describes the amount of damage of the specimen induced by the periodical load. “Offset” contains elastic as well as irreversible displacements. “Offset” and Permanent Deformation together contribute to the displacements that remain after unloading the specimen. The axial displacement of the fracture gap is estimated by the given method using the data of displacement transducer no.3 as seen in the Fig. 3. Owing to the load-controlled testing method, the displacements may be plotted in a curve: displacement versus number of cycles—, as shown schematically in Fig. 5. Fig. 5 is just another way of visualizing the relevant displacements that have already been shown in Fig. 4. This also leads to the question how the Permanent Deformation increases with increasing number of cycles of the loading sequence. Fig. 5 shows a linear increase of the Permanent Deformation with an increase of the number of loading cycles. But there are in principal three different possibilities for the change of the Permanent Deformation with time, which are shown in Fig. 6.
Fig. 5. Axial displacements versus number of cycles.
As shown in Fig. 4, the Permanent Deformation may increase faster at the beginning or at the end of the loading sequence. It will be investigated in another study whether the linear or one of the two other changes is the actual behaviour of the Plastic Deformation. The data of the radial and the axial displacement transducers no.2 and no.4 are used to determine the bending of the intramedullary nail. The acquired data of the acoustic emissions of the screws were used to determine which screw is bearing the load in the course of the loading sequence and when does which screw break. To obtain information on screw breakage, values of the axial displacement transducers were checked additionally for abrupt non cyclic rises of their displacement values. 8. Results 8.1. Presentation of damages The easiest accessible results are the damages that occurred in the sample during the three loading sequences. Therefore after finishing the complete testing procedure the individual parts of the specimen are separated again following the preparation steps backwards. After the necessary working steps the damages on the locking screws, the artificial tibia and the intramedullary nail are documented. During the testing procedure locking screws only broke during the third loading sequence. Until closure of the fracture gap, which is the shut-off criterion of the testing procedure, all distal locking screws failed and only in one specimen one proximal locking screw failed. All fractures occur on the outside edge of the nail holes. Cracks in the bone were documented in all specimens. Cracks are located around the locking screws and are 6 mm long in average, but smaller than 10 mm. Formation of elongated holes has not been observed. No significant damage to the intramedullary nails was documented.
Fig. 7. Reduction of the fracture gap at the beginning and at the end of the first loading sequence.
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
At a whole, three specimens have been tested. The standard deviations of the obtained data have been determined and are added to the results in the following. 8.2. The stiffness The stiffness of the specimen is evaluated at the beginning and the end of the loading sequence, and before and after locking screw failure. The results show that the stiffness of the specimen hardly changes during all loading sequences. Mean stiffness was 2.782 N/mm with a standard deviation of 311 N/mm. Due to the fact that the specimen is statically over-dimensioned even a fracture of a distal locking screw would not result in a strong modification of the stiffness.
1207
Permanent Deformation over time is also analyzed. The results of this analysis are shown in Fig. 8. The diagram shows the increase of the Permanent Deformation during cyclic loading during the first sequence of testing, i.e. during the clinical investigation. As can be seen, the largest part of the Permanent Deformation takes place in the first half of the loading sequence. As the axial displacement shows a reduction of the fracture gap, it was then examined if this reduction was caused by bending of the intramedullary nail. Bending of the nail is calculated by measurement of the displacements with transducers no.2, 4 and 5–10. The measurements show that there is no bending of the nail. Therefore the reduction of the fracture gap can be solely attributed to bending of the locking screws and to damages of the artificial tibia and the screws. 8.4. Sequence of the screw fractures
8.3. The displacements The following results of the displacements of the specimens are obtained by analyzing the data of the first loading sequence (100– 1300 N) only. The displacements of the two other loading sequences are neglected here, since such high loads are not really of practical relevance. First, the results of the axial displacements, which correspond to the reduction of the fracture gap, are presented. Fig. 7 shows the average reduction of the fracture gap during the first loading sequence. The given standard deviation refers to the sum of the displacements situated below it. The “Offset” shows a displacement of 0.13 ± 0.08 mm. This indicates that a relatively high permanent deformation occurs already before the defined minimal load (100 N) of the first cycle is reached. The “Elastic Deformation A” has a value of 0.45 ± 0.05 mm and describes the early elastic behaviour of the specimen. This deformation is inversely proportional to the “Stiffness A.” The sum of the “Offset” and the “Elastic Deformation A” describes the maximum reduction of the fracture gap during the first loading cycles (~2000 cycles). During the loading sequence with a load periodically changing from 100 to 1300 N during 40,000 cycles the specimen is damaged irreversibly. This damage is described by the Permanent Deformation which was 0.52 ± 0.19 mm, meaning that the fracture gap is reduced by this amount even after unloading the specimen. If the specimen was to be unloaded after the first loading sequence only the sum of the permanent deformation (“Offset” & Permanent Deformation) would result in a permanent reduction of the fracture gap, with a deformation of 0.64 ± 0.21 mm in this case. The “Elastic Deformation B” describes the later (~ 38,000 cycles) elastic behaviour of the specimen and has a value of 0.43 ± 0.04 mm. This shows an increase of the stiffness of the specimen during the loading sequence. The maximum displacement of the fracture gap, i.e. the reduction of the gap, is obtained by summing up the displacements “Offset,” “Plastic Deformation” and “Elastic Deformation B” which is 1.07 ± 0.25 mm. As described earlier the growth of the
To determine timing and location of a locking screw's breaking, the acoustic emission technique is used. Additionally the data of the axial displacement transducers are utilized to recognize a fracture as one of a proximal or distal screw. All fractures of the screws can be identified unambiguously in time (number of cycles) and place. In the tested specimen, the first three screws broke at about the same time. Fracturing of the locking screws takes place only in the third, i.e. last loading sequence. The first screw to break is the most proximal of the distal screws. It breaks after approximately 11,000 loading cycles and leads to a reduction of the fracture gap of 2.83±0.06 mm. The distal neighbor of the above mentioned screw breaks after another 9000 cycles. After another 2000 cycles the third screw, which is the next distal one, breaks. 9. Discussion 9.1. The artificial tibia The artificial tibia offers several advantages in comparison to a cadaveric tibia: It is always available, easy to prepare, store and dispose and simplifies the testing procedure and evaluation. The crucial benefit, however, is the uniformity of the mechanical characteristics. This leads to identical boundary conditions for all testing procedures, causing a lower variance of the test results. As already mentioned the artificial tibia should imitate the global properties of the human bone. To achieve this, the thickness of the artificial corticalis has to be changed, due to its material properties that differ from those of the human corticalis. Furthermore the used polyurethane foam core fills the total inside of the artificial tibia, whereas in the epiphysis of the human tibia trabeculae are prevailing, which are increasingly replaced by bone marrow towards the diaphysis. In addition, the pervasive polyurethane foam core can lead to supports of the intramedullary nail, which is not possible in the natural bone. It is obvious that there are certain differences which may affect the results. Especially for intramedullary nails, which are fastened with locking screws, the local behaviour of the used components plays a larger role. Changed thicknesses and different mechanical properties of the artificial corticalis can, particularly in this case, influence the test results. Thus the results are not completely transmittable to the real patient. After all it is not the aim of this work to make a medical conclusion, but to establish a testing method with low scattering of the testing results in order to obtain typical values and characteristics of the mechanical behaviour of the specimen to compare different implants. Among these criteria the artificial tibia proves as ideal. 9.2. The origin of the damages
Fig. 8. Growth of the “Permanent Deformation” versus number of cycles.
Damages of the locking screws are most interesting and shall thus be discussed more closely. It is remarkable that all the distal screws have broken at least once or even twice in the three tested specimens.
1208
E.K. Tschegg et al. / Materials Science and Engineering C 28 (2008) 1203–1208
On the other hand the axial stable locking screw only broke in one of the three specimens, and this only after the described three distal screws failed. As described above, one axial stable screw is used for the proximal stabilization of the nail and four screws to ensure the distal fixation. The only difference between the proximal and the distal locking screws closest to the fracture, is their distance to the fracture and the diameter of the nail at the places of the locking screws. The proximal screw is situated 260 mm apart from the fracture, while the distal screw is only 10 mm apart. As the nail on the proximal side of the fracture gap is surrounded by the artificial tibia on a long distance, the tibia already shares part of the load directly with the nail. Thus the load on the proximal screw is reduced by this amount. Further the spans of the two screws are very similar, but as mentioned above, the diameter of the nail at the positions of the distal and proximal locking screws is different. At the hole of the proximal locking screw the diameter of the nail is 11 mm, whereas at the position of the distal screw the diameter is only 9 mm, which leads to a better distribution of the load around the proximal screw. This may be the reason for the earlier failure of the distal screw closest to the fracture gap, i.e. the proximal of distal screws. It is now to be discussed why the other distal screws broke earlier than the proximal as well. This may be explained in a similar way: the span of the screws more distant from the fracture gap is larger. Because of the increase in length at a constant diameter, the distal locking screws bend easier and are thus damaged sooner. Since they show a smaller resistance against the load, the deformations of these screws are larger. This leads to faster fatigue of the material and earlier failure. The effect is large enough that in two of the three specimens, all four distal locking screws break without any proximal screws breaking.
the “Offset” which contributes the largest part of these deformations. This strong offset even before the minimal load of 100 N is reached is very critical and efforts should be undertaken to minimize it.
9.3. Stiffness and displacements
The authors thank Ing. Karl Kropik and Dr. A. Schultz for the specimen preparation and Prof. Hartmut Pelinka and the Austrian Workers' Compensation Board (AUVA) for the research grant to realize this investigation.
A certain amount of stiffness is required and desired but very high stiffness is not useful, as it leads to a stress-shielding effect and thereby delays healing of the bone. Likewise a very low stiffness prevents healing. It is remarkable that the stiffness of the implant/bone system increases slightly and consistently from the beginning to the end of the loading sequence and although the effect is not pronounced, it is statistically significant for the first two loading sequences. This effect may be caused by a continuous and improving re-distribution of the load between the locking screws. Another explanation may be an effect similar to the “cold working” effect, which causes an increase of the strength of the locking screws by mechanical deformation. The stiffness corresponds only to the elastic deformations and is thus not sufficient to describe the entire behaviour of a specimen. Contrarily, the permanent deformation is not related to the stiffness. The results show that the fracture gap decreases while the stiffness of the specimen remains almost unchanged or slightly increases, which means that the deformations that cause the shortening have no effect on the stiffness. As no damages occur in the nail, the irreversible reduction of the fracture gap can only be caused by damages of the thread of the screws and/or the formation of elongated holes and cracks in the bone. Examination of the specimens leads to the assumption that the damages of the thread of the screws are mainly responsible for the displacements. It would therefore be advisable to use screws without thread in the area of contact with the nail. Also contributing to the “plastic” deformation is
10. Summary Fracturing of screws took place only during the third and final loading sequence of testing. In two of three specimens, all distal screws, but none of the proximal ones broke. The three screws breaking first are the same in the three samples, and break at about the same time and are the three distal screws closest to the fracture gap. The stiffness of the specimen remains almost constant and is approximately 2762 N/mm with a standard deviation of 280 N/mm. The axial displacements of the fracture fragments towards each other have been analyzed precisely during the first loading sequence and are stated below. The “Offset;” the displacement that occurs before reaching the minimal load of the first loading sequence, amounts to 0.13 ± 0.08 mm. The “Elastic Deformation A” and the “Elastic Deformation B;” elastic deformations at the beginning and at the end of the first loading sequence, are 0.45 ± 0.05 mm and 0.43 ± 0.04 mm respectively. The Permanent Deformation that describes the reduction of the fracture gap caused by the irreversible damages of the specimen during the loading sequence, is 0.52± 0.13 mm. The sum of the permanent deformations; those deformations that remain after unloading the specimen, is 0.64 ± 0.21 mm. The maximum difference at the beginning and the end of the loading sequence is 0.57 ± 0.13 mm and 1.07 ± 0.25 mm respectively. Acknowledgements
References [1] C. Gaebler, A. Speitling, E.L. Milne, S. Stanzl-Tschegg, V. Vecsei, L.L. Latta, Int. J. Care Inj. 32 (2001) 708–712. [2] C. Gaebler, S. Stanzl-Tschegg, W. Laube, V. Vecsei, Int. J. Care Inj. 32 (2001) 401–405. [3] C. Gaebler, S. Stanzl-Tschegg, G. Heinze, B. Holper, T. Milne, G. Berger, V. Vecsei, J. Trauma 47–2 (1999) 379–384. [4] J.T. Gorczyca, J. McKale, K. Pugh, D. Pienkowski, J. Orthop. Trauma 16–1 (2002) 18–22. [5] C. Kanchanomai, V. Phiphobmongkol, P. Muanjan, Eng. Fail. Anal. 15 (2008) 512–530. [6] C.C. Wu, C.L. Tai, Chang. Gung. Med. J. 29–3 (2006) 275–282. [7] J. Korner, G. Diederichs, M. Arzdorf, H. Lill, C.h. Josten, E. Schneider, B. Linke, J. Orthop Trauma 18 (5) (May/June 2004) 286–292. [8] http://www.sawbones.com/products/bio/composite.aspx. [9] http://www.synthes.com/html/Expert-Tibial-Nail.6885.0.html. [10] http://www.synthes.com/html/fileadmin/Shared/shop,/Printed_Materials/ Techique_Guide/trau ma/036.000.380.pdf. [11] R.R. Neptune, S.A. Kautz, F.E. Zajac, J. Biomech. 34 (2001) 1387–1398. [12] Standard-Handbuch für Hydropuls-Prüfmaschinen PSA mit Nennkräften von 10, 40 oder 100 kN. Ausgabe Januar 1992, Carl Schenck AG. [13] http://www.dasylab.com. [14] http://www.vallen.de. [15] E.K. Tschegg, S. Stanzl-Tschegg, Patent application 15.11.2007, Patent office Vienna, Austria.