Assessing osteosynthesis techniques for pelvic fractures using Digital Image Correlation

Assessing osteosynthesis techniques for pelvic fractures using Digital Image Correlation

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Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2016) 000–000 Structural Integrity Procedia 00 (2016) 000–000

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Procedia Structural 2 (2016) 1252–1259 Structural IntegrityIntegrity Procedia 00 (2016) 000–000

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21st 21st European European Conference Conference on on Fracture, Fracture, ECF21, ECF21, 20-24 20-24 June June 2016, 2016, Catania, Catania, Italy Italy

a a

Assessing osteosynthesis techniques for pelvic fractures Assessing osteosynthesis techniques for pelvic fractures XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal using using Digital Digital Image Image Correlation Correlation a a b a of an Thermo-mechanical modeling of a bhighPapadogoulas pressure turbine blade M. M. Karanika Karanikaa,, D. D. Georgiou Georgioua,, S. S. Darmanis Darmanisb,, Α. Α.a Papadogoulasb,, E. E. D. D. Pasiou Pasioua,, a* engine S. Kourkoulis airplane turbine S. K. K.gas Kourkoulis *

Laboratory of Testing and Materials, Department of Mechanics, Unit of Biomechanics, National Technical University of Athens, 157 73, Greece a Unit of Biomechanics, b c University of Athens, 157 73, Greece Laboratory of Testing and Materials, Department of Mechanics, National Technical b b NIMITS Hospital, Monis Petraki 10-12, 115 21, Athens, Greece NIMITS Hospital, Monis Petraki 10-12, 115 21, Athens, Greece

P. Brandão , V. Infante , A.M. Deus *

a

Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal

Abstract b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal

c Various techniques used of in orthopedicEngineering, surgery for the fixation of pelvic fractures are assessed experimentally from the biomechCeFEMA, Department Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Various techniques used in Mechanical orthopedic surgery for Instituto the fixation of pelvic fractures are assessed experimentally from the biomechanical point of view. The protocol designed consisted of twenty five experiments with cadaveric semi-pelvises which were artificialPortugal anical point of view. The protocol designed consisted of twenty five experiments with cadaveric semi-pelvises which were artificially fractured. The fractures simulated the extremely dangerous T-type ones. Five fixation techniques, comprising of simple and selfly fractured. The fractures simulated the extremely dangerous T-type ones. Five fixation techniques, comprising of simple and selflocking plates with fixation screws, were assessed. For the determination of the displacement field developed three-dimensional locking plates with fixation screws, were assessed. For the determination of the displacement field developed three-dimensional Abstract Digital Image Correlation (3D-DIC) was used. It was indicated that 3D-DIC is advantageous against classical sensing techniques Digital Image Correlation (3D-DIC) was used. It was indicated that 3D-DIC is advantageous against classical sensing techniques since it allows convenient selection of critical pairs of material points (both prior and after the experiments, without any limit as to since it allows convenient selection ofaircraft critical engine pairs of material points prior and after the experiments, without any limit as to During theirfor operation, modern are(both subjected to determination increasingly demanding operating conditions, their number) the estimation of the opening of thecomponents fracture. Moreover it permits of the pure relative sliding bettheir number)the forhigh the estimation of the (HPT) opening of theSuch fracture. Moreover it permits determination of the pure relative sliding betespecially pressure turbine blades. conditions cause these parts to undergo different types of time-dependent ween the various parts of the T-fractured pelvises as it allows isolation of rigid body displacement and rotation. From the clinical ween the various parts of the is T-fractured pelvises as itthe allows of rigid body displacement and rotation. From the clinical degradation, of which creep. A model using finiteisolation element (FEM) wasoffers developed, in order to be able to predict point of view it one appears that combination of locking reconstruction platesmethod with simple ones increased stability. point view behaviour it appears that combination locking plates simple ones offers increased theofcreep of HPT blades. of Flight datareconstruction records (FDR) for with a specific aircraft, provided bystability. a commercial aviation © 2016 The Authors. Published bythermal Elsevier B.V.mechanical company, wereThe used to obtain and foraccess three article different cycles. In order to create the 3D model Copyright © 2016 Authors. Published by Elsevier B.V. This is data an open underflight the CC BY-NC-ND license © 2016 TheforAuthors. Published by aElsevier B.V. scrap was scanned, and its chemical composition and material properties were (http://creativecommons.org/licenses/by-nc-nd/4.0/). needed the responsibility FEM analysis, HPT blade Peer-review under of the Scientific Committee of ECF21. Peer-review under responsibility of Scientific the Scientific Committee ofmodel ECF21. Peer-review the of FEM ECF21. obtained.under The responsibility data that wasofgathered was Committee fed into the and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with plates; the realDigital 3D mesh from the blade scrap. The Keywords: pelvic fractures; T-type fractures, osteosynthesis; fixation techniques; locking Imageobtained Correlation Keywords: fractures; T-typeinfractures, techniques; plates; Digital Imageedge Correlation overall pelvic expected behaviour terms ofosteosynthesis; displacementfixation was observed, in locking particular at the trailing of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

1. Introduction 1. Introduction

© 2016 The Authors. Published by Elsevier B.V. Pelvic fractures are classified among the mostofdangerous since they are related to high mortality. In Peer-review under (Fig.1a) responsibility of the Scientific Committee PCF 2016.ones Pelvic fractures (Fig.1a) are classified among the most dangerous ones since they are related to high mortality. In

addition the fixation of these fractures is a demanding task given that even the slightest misalignment of the fractured addition the fixation of these fractures is a demanding task given that even the slightest misalignment of the fractured parts duringHigh the Pressure fixationTurbine operation ofModel; the femur’s cartilage rendering hip artrhoplasty unKeywords: Blade;may Creep;cause Finite severe Element damage Method; 3D Simulation. parts during the fixation operation may cause severe damage of the femur’s cartilage rendering hip artrhoplasty unavoidable. Fixation of pelvic fractures is an extremely complicated operation, as it can be seen in Fig.1b, in which avoidable. Fixation of pelvic fractures is an extremely complicated operation, as it can be seen in Fig.1b, in which

* Corresponding author. Tel.: +30-210-7721263; fax: +30-210-7721302. * Corresponding author. Tel.: +30-210-7721263; fax: +30-210-7721302. E-mail address: [email protected] E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. 2452-3216 © 2016 Authors. Published Elsevier B.V. * Corresponding author. Tel.: +351 Peer-review underThe responsibility of218419991. theby Scientific Committee of ECF21. Peer-review under responsibility of the Scientific Committee of ECF21. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of PCF 2016.

Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.160

2 M. Karanika, D. Georgiou, S. Darmanis, Α. M.Papadogoulas, Karanika et al.E.D. / Procedia Integrity 2 (2016) 1252–1259 1253 Pasiou,Structural S.K. Kourkoulis / Structural Integrity Procedia 00 (2016) 000–000

(a)

(b)

(c)

Fig. 1. A typical pelvic fracture before (a) and after (b) fixation. (c) Sketch of a “B2 T-type” fracture according to Letournel and Judet (1993).

the typical fracture of Fig.1a is shown fixated by a combination of two fixation plates and a number of screws. The complex geometry of the specific anatomic region results to quite a few types of pelvic fractures. Their most widely adopted classification is the one proposed by Letournel and Judet (1993). According to this classification the fracture of the anterior column of the pelvis combined with a semi-transverse posterior fracture is called “B2 T-type” fracture (Fig.1c) and is common in case of osteoporotic bones. It is a variance of this fracture that is studied in the present paper. The number of accidents resulting to “B2 T-type” pelvic fractures increases steadily and it is expected that it will increase even further in the future due to increased life expectancy. As a result the need for efficient fixation techniques becomes demanding. From the biomechanical point of view the experimental assessment of pelvis fracture fixation techniques is a quite challenging task due to the pelvis complex geometry, the difficulties in reproducing the actual boundary and loading conditions and also the difficulties in measuring the relative displacements of the fractured parts. In addition the respective experimental procedure is not as yet standardized and a variety of experimental setups and protocols are introduced, rendering the comparative consideration of published data quite subjective. The topic is very hot and the respective literature is relatively rich. Attention is focused, among others, to the proper application of novel, sophisticated sensing techniques, which permit accurate determination of the displacement field and of the distance between the fixated parts of the fracture during loading. Recently Culemann et al. (2009) assessed conventional and modern osteosynthesis techniques using a combination of cadaveric and artificial pelvises. The specimens were subjected to loading-unloading loops, simulating single-leg stance and the relative displacements were measured using two properly positioned pairs of ultrasounds microphones. It was concluded that long periarticular screws offer better stabilization of the specific type of fracture. An alternative sensing and recording system was used by Mehin et al. (2009) consisting of a system of optoelectronic cameras. From a clinical point of view it was pointed out that the use of self-locking plates offers to the osteosynthesis the same stability with that offered by traditional plates. The use of self-locking plates is suggested only in case interfragmentary screws cannot be used. Later on Yuntong et al. (2013) using cadaveric pelvises attempted assessment of three fixation techniques, i.e. simple screws, simple plates with screws and locking plates with screws. The relative displacement of the fractured parts was measured with a device based on the principles of the ultrasounds method. The specimens were subjected to six loading-unloading loops and it was concluded that the differences between the three techniques were not statistically significant. Along the same lines Wang et al. (2015) compared four fixation techniques, i.e. simple plate, locking plate, combination of simple and locking plates, and combination of simple plate with interfragmentary screws. Using data concerning the stiffness of the fixated complex and also the displacement of the fractured parts within two normal planes they concluded that the last technique (simple plate with interfragmentary screws) offered increased stability. At the same period Liu et al. (2015) tested twenty pelvises in the direction of comparing five fixation techniques. Among others they concluded that increased stability of the osteosynthesis is achieved in case implants are applied in both the posterior and anterior columns of the fractured pelvis.

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The short survey of previous paragraphs clearly indicates that the problem is still open and the conclusions drawn are not always towards the same direction. As already mentioned this could be attributed to improper laboratory simulation of the actual loading and supporting conditions, the different displacement measuring techniques used and the lack of any standardization. Moreover the number of tests per fixation technique is limited (usually two to five specimens are used), for obvious reasons, resulting inevitably to difficulties in the statistical correlation of the results. In the present study the problem is addressed by taking advantage of the three dimensional Digital Image Correlation (3D-DIC) technique (in conjunction with traditional clip gauges) for the determination of displacements. The object is two-folded: To assess the applicability and efficiency of 3D-DIC when it is used in experiments with fractured and fixated pelvises and to comparatively assess the efficiency of some widely used fixation techniques. 2. The experimental protocol 2.1. The specimens and the experimental set-up For the needs of the study about thirty cadaveric semi-pelvises were used with considerable degree of osteoporosis. The semi-pelvises were artificially fractured. Every effort was paid for the fractures of all pelvises to be identical to each other. All fractures were of the “B2 T-type” according to Letournel and Judet (1993). Five of the specimens were used during a preliminary protocol which permitted optimum spatial arrangement of the constituent elements of the experimental set-up (loading frame, cameras and white light sources of the 3D-DIC system), design of a proper system for supporting the specimens and applying the load, and finally calibration of a number of experimental parameters, like for example the loading rate, the sampling rate, the data acquisition and storage constants etc. The remaining twenty five pelvises were classified in five groups of five specimens each. The fractured pelvises of each group were fixated following five different techniques as it is shown in Table 1. Some characteristic specimens are shown in Fig.2. After fixation the specimens were painted white and then using a black spray a random pattern of black dots was created on their surface (as it is shown in Fig.3a) to assist application of 3D-DIC. Using a suitable adhesive two pairs of knife edges were attached on either side of the fourth fracture (at the outer surface of the anterior column, Fig.3b). A semi-spherical implant made of material simulating the properties of articular cartilage mounted in the acetabulum assisted uniform distribution of the load. Then the specimen was attached to the loading frame. Table 1: The five specimen groups used in the present study, classified according to the fixation system used in each group. Specimens’ Class I II III IV V

Anterior column Plate Plate Locking Plate Plate Plate (Stoppa)

Fixating system Posterior column Plate Screw Screw Locking Plate Locking Plate

Fig. 2. Typical fractured semi-pelvises used in the experimental protocol, fixated according to various techniques.

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Fig. 3. (a) a fixated specimen after painted and sprayed. The random pattern of black dots is clearly visible. (b) the knife edges, applied on either side of the fracture at the outer surface of the anterior column, used to keep the clip-gauges in place. (c) the semi-spherical head placed in the acetabulum to simulate articular cartilage and assist uniform load distribution.

The experimental protocol was implemented at the Unit of Biomechanics of the Laboratory of Testing and Materials of the National Technical University of Athens. The set-up consisted of an electromechanical loading frame (MTS Insight 10 kN), equipped with a load cell of sensitivity equal to 0.01 N and the Testworks 4 software, a 3D-DIC system (Limess) with an accuracy for the displacement measurements equal to 0.01 pixel (two cameras, two sources of white light and the corresponding software Istra4D), two clip-gauges (Instron) and the respective data logger (Kyowa). Before each test the specimens were photographed using a digital camera. 2.2. The experimental procedure and raw experimental data The experiments were implemented under quasi-static loading conditions. Displacement control mode was adopted at a rate equal to 0.2 mm/min. The load was applied monotonically and the test was completed when either the load attained a value equal to 3 kN (about four times the weight of a normal person) or when the displacement induced by the loading frame’s traverse exceeded 15 mm. The cameras of the DIC system were arranged at angle equal to 40 o (Fig.4a) focused to the fractures of the upper and rear side of the pelvis. The system was calibrated before each test with the aid of the AI119x9_BMB Calibration Panel (Limess). The two clip-gauges were mounted on either side of the fracture at the outer surface of the anterior column (Figs.4b,c). The specimens were properly supported to the loading frame in order to simulate loading during single-leg stance. The load was applied to the artificial articular cartilage with the aid of a semi-spherical metallic punch simulating the femour’s head (Fig.4c). During each test the following quantities were recorded (sampling rate equal to 1 Hz): The displacement of the frame’s traverse (mm), the load induced (N) and the indications of the two clip-gauges. At the same time photos of the specimen were taken by the cameras of the DIC at a rate equal to 1 photo every 10 seconds, resulting to a number of about 250 photos for each experiment. The variation of the load applied versus the displacement is shown in Fig.5a for a characteristic specimen of Class I, i.e. fixation with simple plates for both the anterior and posterior columns. It is seen from this figure that the load-displacement curve is more or less linear up to a load equal to about 800 N. This linear portion was systematically observed in almost all specimens independently of their specific class. (b)

(a) 40

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45

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Fig. 4. (a) the experimental set-up. (b), (c) a typical specimen mounted on the loading frame while tested.

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Fig. 5. (a) load versus displacement induced for a typical specimen of Class I. (b) dependence of the distance between the lips of the fracture of the anterior column as measured by the two clip-gauges on the applied load.

It is to be mentioned, however, that the terminal load, FL, for this linearity portion is not constant even for specimens of the same class. After FL all the graphs deviated from linearity following paths without any common characteristics. The raw data recorded by the two clip gauges measuring the distance between the lips of the fracture at the outer surface of the anterior column are plotted in Fig.5b for the same specimen as in Fig.5a. As it is expected the distance of the two lips remains almost constant for a significant portion of the maximum load induced (for the specific specimen up to a load level equal to about 400 N). From this point on, the distance between the lips changes according to an almost linear law (up to a load level of about 600 N). It is noted that for the specific specimen of Fig.5 the signs of the graphs of the two gauges are opposite indicating a kind of rigid body rotation of the two lips. Further increase of the load results to rapid change of the relative position of the fracture’s lips. Again the behaviour of the graphs after the linearity portion is somehow random even for specimens with the same fixation technique. 3. Results from the 3D-DIC technique The data recorded from the 3D-DIC system are stored by its software in the form of displacements along the axes of a Cartesian reference with x-axis vertical and z-axis normal to the plane of the image. A typical set of such data is shown in Fig.6. Clearly this way of representing the data is not efficient for the specific application considered here. In this context an alternative method was developed as it can be seen in Fig.7: Three axes were introduced along the

Fig. 6. The displacement field along the axes (x,y,z – from left to right) of a Cartesian reference introduced by the software of the 3D-DIC system (axis x is vertical and axis z is normal to the image’s plane). The fourth figure and the scale correspond to the total displacement.

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Fig. 7. The method developed to elaborate the data of the 3D-DIC system. The lines of the three fractures are marked red and the “virtual gauges” formed to measure the distance between the lips of each fracture are shown for each fracture in the right photo.

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Fig. 8. The variation of the distance between the fractures’ lips as obtained by the “virtual gauges” introduced in Fig.7. The same colour code is adopted, i.e. blue lines correspond to the blue “virtual gauge” and red ones to the red “virtual gauge”.

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three fracture lines of the “B2 T-type” fractures. On either side of each fracture (denoted from here on as fracture 1, 2 and 3, respectively) two pairs of points were considered forming six “virtual gauges”. For example, for fracture 1 in Fig.7, points 1 and 2 form the first “virtual gage” while points 3 and 4 form the second one. Similarly points 5 and 6 form the first virtual gauge for fracture 2 and points 3 and 7 the second one. Finally points 10 and 11 form the first “virtual gauge” for fracture 3 and points 8 and 9 the second one (recall that the actual clip gauges are mounted on the other side of the pelvis measuring the distance of the fracture of the outer surface of the anterior column. Recall that this fracture is denoted as fracture 4. Taking advantage of these “virtual gauges” it is possible to determine the relative distance between the lips of all four fractures characterizing the “B2 T-type” pelvis fractures within any plane and for any load level. Typical results of this procedure are plotted in Fig.8 for the same as above specimen. In Fig.8, axis x corresponds to the line of the fracture, axis z is normal to the fracture plane, and finally axis y is normal to the previous two ones. Therefore, it is straightforward to conclude that displacements along axis z (Fig.8a) correspond to the motion of any fracture’s lip normally to the fracture line, or in other words they represent the pure “opening” of the fracture. On the other hand, the displacements along axes x and y (Figs.8b,c) correspond to relative “slip” of the fracture’s lips within the plane of the fracture, either along the line of the fracture (axis x) or along the line normal to axes x and z (axis y). 4. Discussion and Conclusions To achieve optimum exploitation of the huge volume of data gathered during the tests of this protocol some convenient and objective assessment criteria should be introduced. The main obstacle hard to overcome in this direction was that each specimen is characterized by the existence of four fractures. It was quite often observed that while one of the fractures was well fixated (very small changes of the distance between its lips) another fracture (of the same specimen) was poorely fixated (increased change of the distance between its lips for the same load level). It was therefore necessary to introduce a “homogenization” procedure by considering some average values. In this direction, and taking into account the lack of any standardization, it was decided to introduce an assessment criterion based on the minimization of some kind of “average” displacement of the fractures’ lips (for a common predefined load level) considering all four fractures of each specimen. For the comparison to be as objective as possible a relatively low value of the load was chosen, equal to 450 N, which lies within the linearity region of all the tests. Based on the above thoughts the maximum value of the relative displacement of all four fractures of each specimen is plotted in Fig.9a for the five classes of fixation techniques. From this figure it can be concluded that the fixation techniques used in the specimens of classes IV and V appear more effective. It could be anticipated at this point that the choice of a different kind of displacement as an assessment criterion could yield different conclusions. To cope with this objection, some alternative “homogenized” measures of the displacement between the lips of the fractures were considered, including the average “opening” of each fracture, the minimum of the maximum relative displace-

I

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Fig. 9. (a) the maximum value of the relative displacement of all the fractures for all the specimens of each class. (b) the maximum of the minimum relative displacement of all fractures of each class.

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ment of all the fractures of all specimens of a given class (minimum maximorum), and the maximum of the minimum relative displacement of all fractures of all specimens of a given class (maximum minimorum) etc. It was extremely encouraging to observe that all alternative criteria, based on a “homogenized” value of the relative displacement of the fractures’ lips, resulted to the same conclusion, concerning the efficiency of the fixation techniques used (Kourkoulis et al., 2015; Georgiou and Karanika, 2016). To support this conclusion the maximum minimorum of the relative displacement of all fractures of all specimens of a given class is plotted in Fig.9b for all five classes. The similarity with Fig.9a, concerning the superiority of the fixation techniques of the IV and V classes is obvious. It is to be mentioned at this point that any conclusion drawn based on the results of an experimental protocol with five specimens per class is rather risky. Indeed the statistical analysis of the results is characterized by marginal statistical significance. In this direction and before definite conclusions are drawn the authors of this study believe that additional experiments should be implemented (with specimens of identical material properties). In spite of the above limitation the conclusions drawn and the quantitative data presented here could be valuable in the direction of validating and calibrating numerical models which could be used for detailed parametric analysis of the (quite a few) factors influencing the overall mechanical response of the fixated pelvis after “B2 T-type” fracture. Recapitulating, and besides the difficulties in reaching a definite clinical suggestion, it can be definitely stated that the 3D-DIC technique was proven very effective for the study of fixation techniques of pelvic fractures. Its main advantage is that it allows the “construction” of any number of “virtual gauges” over the surface of the specimen tested, by considering two arbitrary points and following their spatial displacement (in three dimensions). In this way it is possible to determine the change of the distance along any fracture line or determine the strain field at any region of the specimen independently of its complex geometry. What is, also, important is that the choice of these “virtual gauges” may be realized either before the test or “post mortem”, i.e. after the test is completed or during the elaboration of results. In addition to the estimation of the “normal opening” (or perhaps “closure”) of the fracture (i.e. the change of the distance of the fractured parts normally to the fracture plane) 3D-DIC offers the possibility to determine the relative sliding of the fractured parts within the fracture plane, which is not possible using traditional sensing techniques. This feature is very efficient when geometrically complex fracture lines (or fractures with more than one fracture lines) are studied (like the ones considered here), since in such cases it is quite possible that while one of the lines is “opening” normally to the fracture plane a second fracture exhibits a kind of shear displacement. Equally important is the fact that 3D-DIC permits isolation of the rigid body displacements and rigid body rotations of the specimen as a whole body, providing the pure relative displacements of the fractured parts. References Culemann, U., Holstein, J.H., Köhler, D., Tzioupis, C.C., Pizanis, A., Tosounidis, G., Burkhardt, M., Pohlemann, T., 2010. Different stabilisation techniques for typical acetabular fractures in the elderly - A biomechanical assessment. Injury, 41(4), 405-410. Georgiou, D., Karanika, M., 2016. Using Digital Image Correlation for the biomechanical assessment of pelvic fractures (in Greek), Diploma Thesis, Supervisor: Kourkoulis, S.K., National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, Athens, Greece. Letournel, E., Judet, R., 1993. Fractures of the acetabulum, 2nd ed. Springer-Verlag, Heidelberg, Germany. Kourkoulis, S.K., Darmanis, S., Papadogoulas, A., Georgiou, D., Karanika, M., Pasiou, E.D., 2015. A study of fixation techniques of pelvic fractures using DIC (in Greek). In Proceedings of the 8th National Conference of the Hellenic Society for Non Destructive Testing, p. 74, May 8-9, Athens, Greece. Liu, H., Li, L., Wu, X., Xu, H., Zhang, R., 2015. Biomechanical research of different internal fixations using locking reconstruction plate for acetabular transverse fracture. Chinese Journal of Reparative and Reconstructive Surgery, 29(9), 1084-1087. Mehin, R., Jones, B., Broekhuyse, H., 2009. A biomechanical study of conventional acetabular internal fracture fixation versus locking plate fixation. Canadian Journal of Surgery, 52(3), 221. Wang, L., Wu, X., Qi, W., Wang, Y., He, Q., Xu, F., Liu, H., 2015. Biomechanical comparative study on four internal fixations for acetabular fractures in quadrilateral area. Chinese Journal of Reparative and Reconstructive Surgery, 29(10), 1235-1239. Zhang, Y., Tang, Y., Wang, P., Zhao, X., Xu, S., Zhang, C., 2013. Biomechanical comparison of different stabilization constructs for unstable posterior wall fractures of acetabulum. A Cadaveric Study. PloS one, 8(12), e82993.