PhD thesis “Experimental and computational investigation on the mechanical characteristics of a self-setting calcium phosphate bone cement intended for biomedical applications”

Στη παρούσα διδακτορική διατριβή παρουσιάζεται ένας ενδελεχής χαρακτηρισμός ενός οστικού τσιμέντου φωσφορικού ασβεστίου, το οποίο παρασκευάστηκε από την ανάμειξη καθαρής σκόνης α-TCP και υδατικού διαλύματος Na2HPO4 και εν συνεχεία σκληρύνθηκε με την αντίδραση της υδρόλυσης. Ο διεξαχθείς χαρακτηρισμός καλύπτει πέντε βασικούς τομείς: i) Ανίχνευση των όποιων μικροδομικών αλλαγών κατά τη διάρκεια της περιόδου σκλήρυνσης, ii) Αξιολόγηση του επιδεικνυόμενου πορώδους, iii) Μηχανική δοκιμή του υλικού, iv) Προσροφησιμότητα του υλικού σε υγρά περιβάλλοντα, v) Οι αναπτυχθείσες παραμορφώσεις σε χαρακτηριστικές φάσεις της παρασκευής του υλικού. Επιπλέον δύο μοντέλα προσομοίωσης δημιουργήθηκαν και παρουσιάζονται, με σκοπό την περιγραφή του φαινομένου της διάχυσης σε υγρά περιβάλλοντα και των επαγόμενων υγροσκοπικών παραμορφώσεων, αντίστοιχα. Επιπροσθέτως προσομοιώθηκε επίσης μια μελέτη περίπτωσης, στην οποία διερευνάται η χρήση του εξεταζόμενου οστικού τσιμέντου σε μια ρεαλιστική εφαρμογή του.


Information about biomaterials and bone cements
From ancient times, humans started to seek solutions to relieve illnesses and heal injuries, wounds, bone fractures/defects etc. Surgical instruments, medicines and other elements, discovered throughout all these years, proved the continuous evolvement of medical field from the early ages of human civilization. Also, an initial development of intervening in the human body by adding materials either for decorative or medical purposes is also evident, such as dental implants that were used to substitute rotten or damaged teeth ( Fig. 1.1.). The outburst of technology, in the recent years, led to a strong systematic development of medical field, while a lot of new innovative materials intended for medical reasons (e.g. implants) are being researched, like biomaterials. The term "biomaterials" refers to any material or substance that has been engineered to interact with biological systems for a medical purpose -either a therapeutic (treat, augment, repair or replace a tissue function of the body) or a diagnostic one (2). The field of this class of materials is quite extended and several examples are illustrated in Fig. 1.2. Some typical biomaterials, such as bone implants, metals plaques, polymers and scaffolds are used in orthopedics, dentistry and cardiology. A useful and widespread category of biomaterials involves ceramics, polymers and glasses, mainly used as bone defect fillers or cements in orthopedics and dentistry, termed as "bone cements". The use of bone cements is met in occasions where parts of the human bones are destroyed (e.g car/sport accidents, diseases like cancer etc.), hence the use of proper materials for mechanical support and bone structural integrity is of significant importance. A well-known bone cement is polymethylmethacrylate (PMMA) cement, discovered in the 1950s, which is widely used in various orthopedic and trauma surgery (e.g. total hip arthroplasty-THR). It is consisted of two primary components: (i) a powder consisting of copolymers based on the substance polymethylmethacrylate and (ii) a liquid monomer, methylmethacrylate (MMA). Upon the mixture of these two components, the liquid monomer polymerizes around the pre-polymerized powder particles, forming hardened PMMA (4). During this process heat is generated, due to a strong exothermic reaction between the powder and the liquid. Although the overall mechanical properties of this bone cement are shown to be able to lead to long-term stability (5), several disadvantages are reported: generation of heat during curing, that causes necrosis of the surrounding tissue (6), exhibited toxicity of the monomer (7), embrittlement of the PMMA bone cement due to aging (8), osteolysis caused by wear debris formation (9) etc.
In 1980s a new promising biomaterial was discovered: Calcium Phosphate Cements (CPCs).
This class of materials exhibits excellent biocompatibility, bioactivity, osteoconduction and osteogenesis. Moreover, CPCs are more biocompatible with the human bone than many other ceramic and inorganic nanoparticles (10). For the fabrication of CPCs, a calcium phosphate compound [e.g α or β Tricalcium Phosphate (α/β-TCP), TeTracalcium Phoshate (TTCP)] is mixed with an aqueous solution. The mixture results in a malleable paste that progressively solidifies and subsequently hardens in a liquid media.Water, aqueous solutions of various salts or acid-based solutions are used as hardening liquid of CPCs (12), while a hardening process by sintering CPCs in high temperatures (>700 0 C) is also reported in the literature (13), (14). Unlike acrylic bone cements, which harden through a polymerization reaction, CPCs set as a result of a dissolution and precipitation process, in the case of hardening in a liquid media. Specifically, 3 stages occur: (a) dissolution of particles of solid phases in the hardening liquid until its saturation, with respect to calcium ions and phosphate ions, (b) interaction of these ions in solution to form nuclei of crystallization from solution phase and (c) crystal growth of this phase ( Fig. 1.4). The recrystallization can occur in parallel with the change in the crystal size and phase transformation (12). The dissolution of a-TCP is an exothermic process, while the formation of crystals (precipitation process) from an aqueous solution without foreign ions is endothermic (15). Despite the large number of possible formulations, the CPCs developed up to now have only two different end products: precipitated hydroxyapatite (HA) or brushite (DCPD) (16).
All the above are characteristically illustrated in Fig. 1.3. Calcium phosphate cements also exhibit variable stoichiometry, functionality, and dissolution properties (10) which, combined with their intrinsic porosity, enable the potential to be used as drug delivery systems. Currently 3 ways could achieve this goal: (a) as individual molecules dissolved in the liquid within the pores, (b) adsorbed or chemically bound to the crystals surface or (c) in a solid form, as drug crystals or aggregates ( Fig. 1. Despite CPCs' numerous advantages, a number of limitations have to be addressed in order to satisfy the clinical requirements. Apart from bad injectability (18), (19) and weak cohesion of CPC pastes (20), they also exhibit low mechanical properties (6), thus their use is limited to low-load bearing applications (6), (21). Several published works have focused on dealing with the aforementioned challenges by adding various additives either to the powder or to the liquid of CPCs (22), (23), (24), (25), (26). In these works, an improvement in handling properties, desired porosity or bioactivity was achieved, but a decrease in the mechanical strength was also reported. Moreover, the category of self-setting CPCs, like α-TCP, present a unique feature: their mechanical properties can be improved when are immersed in a liquid of similar composition of human body fluids because of occurred microstructural changes (6), (27), hence are considered as promising CPCs to overcome current mechanical challenges.

5)
As it is demonstrated in Chapter 2, most of the studies that deal with CPCs measure their strength by conducting only compression tests. However compression strength cannot be the only criterion in order to assess the mechanical performance of a CPC, since they are meant to be subjected to complex stress fields developed in human bones (28). Moreover, porosity is not always evaluated despite the fact that is the most detrimental factor to CPC mechanical properties (6). Last but not least, little information exist in the literature about the induced strains during self-setting cements' fabrication. This parameter should be considered of significant importance since any strain fields developed during this period can affect the way CPCs fail under loading.

Thesis goals and structure
In this work a thorough characterization of a calcium phosphate bone cement is presented, that was fabricated from the mixture of pure α-TCP powder and Na2HPO4 aqueous solution and subsequently hardened through hydrolysis reaction. The conducted characterization covers five main sections:  Detection of any occurred microstructural changes during hardening period  Evaluation of the exhibited porosity  Material's mechanical testing  Material's absorbability in wet environment  The developed strains throughout characteristic phases of the material's fabrication.
Moreover 2 simulation models are implemented and presented, in order to describe the diffusion phenomenon in wet environments and the induced hygroscopic strains, respectively.
Additionally a case study was also simulated in which the use of the studied bone cement in a real life application is investigated. Based on the frame that is set from the abovementioned sections and implemented models, the structure of this thesis was accordingly formed and is described in the following paragraph, while a characteristic illustration can be found in Fig.

1.6.
Initially, in Chapter 2 are reported several studies that set the context within the research falls, as far it concerns calcium phosphate bone cements. Afterwards, in Chapter 3, are presented the used materials and the implemented steps that were followed in order to fabricate the needed bone cement specimens. Moreover, the design and dimensions of the moulds that were used are also presented.
Chapter 4 is composed of 4 main sub-chapters that concern an equal number of the aforementioned main sections of the conducted characterization. Specifically, in the first one are reported the results from scanning electron microscopy (SEM) and X-ray diffractometry (XRD) in samples that were hardened at different levels, in order to investigate the development of any crystal structures during hardening period. The second sub-section concerns the evaluation of the material's porosity with 3 different methods: micro computed tomography (μ-CT), microscopy investigation and confocal microscopy. In the third one the material properties of the examined biocement are determined from the conduction of compressive and diametral compressive testing, as well as from low-load indentations.
Furthermore, based on the presented results a failure model is proposed. In the last sub-chapter of Chapter 4 the material's absorbability is investigated by conducting immersion experiments in bone cement samples, in liquid environments.
Passing to Chapter 5, the experimental results of the developed strains are presented and discussed, obtained throughout three characteristic stages during material's fabrication: (i) solidification (ii) hardening and (iii) re-immersion. The experimental data were obtained with the use of non-destructive, optic method (Fiber Bragg Grating-FBG sensor), whose working principle is described in details at the start of the chapter. Furthermore, the strain results are also coupled with the experimental results presented in Chapter 4, in order to investigate any correlation between them.
Chapter 6 includes the implemented models and their results for the diffusion phenomenon, during re-immersion, and the corresponding developed hygroscopic strains. Also the input data and the obtained results are presented and discussed for a simulated case study in which the examined bone cement was used as a fixation mean of a stem implant, in a Total Hip Replacement (THR) case. Finally, in Chapter 7 are summarized the exported conclusions from this work and several ideas are proposed as future work, in order to further deepen the characterization of such materials.  Combes and Rey (31) published a review paper on amorphous calcium phosphates (ACPs) that provide an update on several aspects of these compounds, since there is lack of indisputable proof of the occurrence of an ACP phase in mineralised tissues of vertebrates. The various synthesis routes of ACPs with different compositions are reported as well as the techniques used to characterise this phase. The study focuses on various physico-chemical properties of ACPs and especially the reactivity in aqueous media, which have been exploited to prepare bioactive bone substitutes for medical or/and dental applications.
The work conducted from Zhang et al. (32) concerned apatite cements, fabricated through α-TCP (α-tricalcium phosphate) hydrolysis, that were subjected in various tests in order to assess their mechanical properties (Young's modulus, fracture toughness and compressive strength), as a function of various parameters (particle size, liquid-to-powder ratio, amount and morphology of porosity, including macropores). The aim of this study was to find a better compromise between strength and biological behaviour. which is strongly dependent on the injection system (e.g. type of syringe, needle size, injection speed). Moreover, it appears that injectability and ease of injection differ between them, since the latter does not consider the quality of the extruded paste in which phase separation may occur and could lead in deviations of the actual composition of the extruded paste from the initial one (39), (37). Consequently, it becomes unclear whether various properties, including mechanical ones, of the extruded cement are still clinically acceptable (40).
Also, numerous scientific articles exist that deal with the chemistry and kinetics of CPCs setting, although the chemistry of the setting reaction in these cement systems does not significantly differ and can be understood by investigating the solubility behavior of the compounds involved (41), (42), (43). Moreover, several researchers deal with the use of additives in powder of liquid compound (44), (45), (46) or composite fibers (47), (48), (49), (50) in order to enhance various properties of the resulting CPC.

Materials used and sample handling
In order to fabricate the specimens needed for this work, amounts of α-TCP powder were produced and provided by Prof. Bouropoulos (Department of Material Science, University of Patras), that required a specialized procedure. Specifically, ball milling was performed in equimolar quantities of calcium carbonate and calcium pyrophosphate for a certain period.
Then the resulted mixture was placed in alumina crucible and absolute ethanol was also added to prepare a suspension. The suspension was homogenized using magnetic stirring, dried, then placed in a furnace at high temperature for several hours and eventually rapidly quenched on a metallic surface. The resulted material was finally crushed in the ballmill for certain time periods in order to obtain the powder in its final form. The granules' size (diameter) of the powder varied between 0.5 and 5 μm (51), with a mean particle size diameter of 4.5 μm. More details about powder fabrication can be found in (14). The fabrication of the samples was implemented through three different steps and more specifically: (I) manual mixture of the α-TCP powder and Na2HPO4 aqueous solution , in a ratio of 1 ml : ~2.06 gr, that resulted in a malleable paste ( Fig. 3.1b) and casted with a spatula in the moulds (II) the casted paste was let to solidify for at least 4 days, in room temperature (~23 0 C) and (III) the solidified samples were recovered and placed in the Ringer solution that acted as a hardening liquid, as reported in the literature (27), for at least 15 days. The hardening process took place also in a temperature of ~23 0 C except for a number of the specimens intended for low-load indentation (see 4.3.2.2), that were hardened in human body temperature (~37 0 C). Since several specimens were tested in dry state, upon the completion of hardening stage they were dried in an oven at a temperature of ~50 0 C for at least two hours.

Moulds design and samples geometry
The resulted paste from the mixture was casted into three different type moulds in order the specimens to have the desired geometry. The first one (Type I), made of ABS, was built by a closed chamber FDM Stratasys Elite 3D Printer and consisted of 2 parts that could be assembled and create a cylindrical cavity of 12 mm in diameter and 40 mm in length ( Fig.   3.3a,b). Three samples recovered from this mould, labeled as A, B, D, and subsequently were hardened in the Ringer solution. Afterwards in sample A a cut was performed, perpendicular to its longitudinal symmetry axis ( Fig. 3.4) using a diamond wire saw. As a result two new cylindrical specimens, of 12 mm in diameter and 20 mm in length, were created and denoted as AW1 and AW2. Specimen AW1 was used for μ-CT imaging while AW2 was further cut in 4 pieces, using the same technique, in order to create 4 cross sections that were thoroughly investigated with a microscope. Sample B was also cut perpendicular to its longitudinal symmetry axis with the same way and 8 cylinders, of 12 mm in diameter and 5 mm in length, were created (labeled as BW1-BW8) and intended for indirect compression test. The remaining specimen D was used for the investigation of induced strains with a camera as well as for weight gain measurements, when the specimen was immersed in liquid media. The second mould (Type IIa) was made of silicon, having 10 rectangular cavities of 6x6x12 mm 3 (width x length x height) as it is seen in Fig. 3.5b, in order to recover the specimens easily without damaging their shape. It was fabricated by casting silicon in a "negative" mould ( Fig. 3.5a) with attached aluminum blocks that created the desired cavities. Alternatively small 3-D printed moulds (Type IIb) having the same cavity dimensions were used in some cases for the fabrication of same dimensions block CPC samples ( Fig. 3.6). Overall, forty two (42) block samples came up from these moulds and were used for XRD, SEM investigation, confocal microscopy and compression tests, after the hardening period was completed.     In Fig. 4.1 some representative SEM images from the examined samples at different reaction times are presented. By comparing them one concludes that microstructural changes took place when the bone cement was immersed into the hardening liquid. Initially, after 48 hours of immersion commencement a-TCP particles exhibit a sandy texture and on these particles an early creation of a layer composed of small crystal structures can be distinguished as seen in (4a). After 72 hours (3 days) and 96 hours (4 days) of immersion significantly larger crystal structures were observed having either leaf-like or needle-like shapes, leading to the conclusion that growth of these structures was taking place (4b and 4c). In the next presented image (4d), referring to 144 hours (6 days) of immersion, an entanglement of the previously observed structures having uniform size is observed. However, there are also areas on cement's surface where the size of the crystal structures varies. This finding is also verified by (4.3a) where a higher resolution was applied, suggesting that the growth of these structures was still in progress. After 192 hours (8 days) of immersion, as seen in (4.1e), the created layer on a-TCP particles has now become an entangled network of crystals and it is enough dense so that particles' initial geometry has altered. Finally, after 240 hours (10 days) of immersion, in (4.1f), the crystals' network appears to be more compact, clearly supported from the image of a higher magnification presented in (4.2b). It is seen that a thick layer of a complex crystals network has been created occupying the existing voids between α-TCP particles. The findings demonstrated that microstructural changes took place during the followed hardening stage, as it is also supported by several studies (27) 6) reports that various parameters such as smaller particle size, higher setting temperature and low liquid-to-powder ratio can affect kinetics and as a consequence CPCs' setting time.
Considering that the aforementioned parameters were not the same with the ones of the present study, such differences in the time period where microstructural changes take place are expectable.

X-Ray Diffractometry
Ten prismatic specimens (X1-X10) recovered at 72, 120, 168, 264 and 432 hours (i.e. 3, 5, 7 ,11, and 18 days) after their immersion in the hardening liquid, were dried and then used for XRD characterization of the material. All solids were characterized using a Siemens/Bruker D5000 X-ray diffraction with CuKα radiation. Moreover, in the following days the peaks of apatite correspond to (211), (112) and (300) reflections are overlapped, due to peak broadening. This is probably due to the presence of carbonate ions in the apatite structure or to the formation of calcium deficient hydroxyapatite because of a-TCP conversion (55), which is directly related with the crystal structure growth.
In addition, the fact that a-TCP was detected for the last time after 7 days, since hardening a) b) period started, suggests that a-TCP conversion was nearly completed around this time period.
Finally, residual α-TCP was detected for the last time in the specimens recovered after 7 days of immersion in the hardening liquid.

Micro computed tomography imaging
Micro computed tomography or "micro-CT" is a three dimensional (3-D) imaging using Xrays. Specifically a micro-focus X-ray source penetrates the examined object and a planar xray detector collects the projection images. Based on hundreds of angular views acquired ( Fig.   4.5), a 3-D reconstruction of a stack of virtual cross section slices through the object is achieved with the use of a software program. One of the two cylindrical specimens, denoted as AW1, was dried and used for micro computed tomography (μ-CT) imaging (Bruker microCT, Kontich, Belgium). In this work, the highest resolution was applied which corresponds to 9 µm voxel size. The resulting images were software processed (CTAN image analysis) to construct the 3-D image of the specimen. The calculation of the material's porosity is based on voxel's brightness: low brightness voxels represent low density areas (pores) while high brightness voxels represent bulk material (56), (57). Then porosity is given as the fraction of the low brightness voxels over the total amount of them. However, the main challenge of this technique is the definition of a threshold in brightness value that distinguishes the two different voxel "categories". In this work, the resulted μ-CT images were mainly employed to check the extent of pores due to the trapped air and the uniformity of the material microstructure. imaging since their size is on the edge or lower than 9 μm that corresponds to lowest applicable voxel size. Consequently, a value for the threshold brightness can't be defined with certainty.
However if the threshold brightness value is increased several regions of higher brightness voxels, compared to the rest of the specimen, are revealed ( Fig. 4.6b). These regions are dispersed in a uniformly way and the high brightness suggests that the density of these regions is higher than the rest of the material. In the literature is well established that during hydrolysis of α-TCP (hardening period), crystal structures are developed and entangled that enhance the bone cement's mechanical response (12), (27), (54). Thus, the distribution of the crystals has a significant influence in the mechanical behavior of the material. The 3D images obtained from the micro-CT investigation can provide qualitative information on the crystals distribution. a) b)

Microscope investigation
Specimen AW2 was dried and the 4 created cross sections from the performed cut (see Section 3.2) were polished with a 4000 paper grid before observed with an optical microscope in order to investigate the porosity. Characteristic images were captured and afterwards processed with software, in order to estimate the porosity based on the occupied surface of the pores. the ones detected in μ-CT imaging. This is supported by the fact that their shape is close to a circular geometry and not irregular, like the rest of the pores. The porosity was calculated as a fraction of the pixels surrounded by the yellow lines over the total amount of pixels the image has. In the four presented pictures it varies between 27% and 32.1%.
This evaluation comes in accordance with the calculated porosity that was based on experimental data, presented in Section 4.4. The specimen used to acquire these results was cylindrical, having 12 mm in diameter and 40 mm in length (i.e., same dimensions with the specimen used for microscope investigation), with a weight at the dry state equal to ~6 gr. The specimen was immersed in the Ringer solution and weighted after saturation. Saturation was considered when additional weight gain is negligible for relatively long time (for this study, saturation was achieved in ~5 minutes and the experiment was interrupted after 13 days of immersion). The results indicated a mass increase of ~25 % (or ~1.5 gr). Considering a density of ~1.007 gr/cm3 for Ringer solution (58), which is a typical value provided by the material suppliers, the volume of the absorbed liquid was found. By dividing it over the volume of the specimen specimen's porosity was obtained: ~33 % which is very close to the porosity evaluated using the optical microscope images. It is worth noticing that since saturation of the specimen in the Ringer solution is achieved very fast, diffusion, as relatively slow process, is considered negligible. The data also suggest that the specimen possess a network of open porosity.

Confocal microscopy
Confocal microscopy is an optical imaging technique that gives the ability for enhanced optical resolution and contrast of a micrograph by adding a spatial pinhole positioned at the confocal plane of the lens to eliminate out-of-focus light. Through this technique a 3-D reconstruction of 3 the acquired images can be succeeded, by collecting sets of images at different depths within a thick object (59). The specimens intended to be investigated with the confocal microscopy technique (F1 and F2) were cut perpendicular to their longindutinal axis with a razor, mounted on the cross head of a testing machine and as a result a raw planar surface was created in each specimen ( Fig. 4.8).

Compressive testing
The compressive testing was carried out in specimens that were hardened in the hardening liquid (Ringer solution) for several days, in order to obtain the final mechanical strength.
Specifically nine block specimens, denoted as C1 -C9, were recovered in preselected time periods: after 9 and 14 days after the hardening process started, in groups of three, that were tested in wet state. Additionally three fully hardened specimens (14 days of hardening) were also tested in dry state. Each specimen was loaded up until its catastrophic failure (Fig. 4.10b).
The compressive strength tests were performed using a MTS Insight testing machine equipped with a 10 kN load cell and metallic platens while the cross head was displacement controlled with a rate of 1.5 mm/min. It is noted that the followed testing method is also reported in several published studies that conducted compressive testing in CPCs (14), (60).

Low-load indentation
Instrumented indentation is a common method for characterizing the mechanical properties of a material. This technique is capable of testing small volumes of material at low loads and small displacements and allows for simple sample preparation compared to traditional tension or compression tests (63). In this work, a spherical indenter was chosen in order to test a relatively large zone, as compared to a sharp one, and reduce the influence of material's porosity (64).
Where (P) is the applied load and (S) is the stiffness ( ℎ ), in the unloading part, that was calculated by linear fitting of the first 25% of the unloading curve. The value of e depends on the indenter's geometry: for a spherical indentor e=0.75 (66). Then the specimen's Young's modulus (Es) was obtained using Eq. (4.6): For the given bone cement and indentor, the following values were used respectively: =0.28 (67), =220 GPa, =0.3. The measurements were repeated at least 3 or 4 times in every indented surface in order to determine the error in the presented results and the maximum error in the Young modulus was found to be ±25 MPa. However for the unhardened specimen as well as the specimens hardened for 2 and 4 days, only one measurement was successful due to the fact that the material was too brittle for the applied load. The latter is attributed in low crystal development since the hydrolysis of the bone cement was still in early stages.

Room temperature
Seven prismatic specimens (L1-L7) were recovered at 48, 96, 144, 192 and 240 hours (i.e. 2, 4, 6, 8, 10, 12 and 14 days) after the immersion in the hardening liquid commenced, under a room temperature (~25 0 C) while one specimen was indented unhardened. In Fig. 4.14 the loaddisplacement curves from the obtained test data, are presented. As it can be observed the achieved maximum load was low in the unhardened specimen but was considerably increased during bone cement's stay in the hardening period. Based on these data, the corresponding effective Young modulus was obtained and presented in the Fig. 4.16 while the dependence of (Er) on the indentor's penetration depth (hcontact) is shown in the inset graph of Fig. 4.14, indicating that it was levelled off at the achieved depth in the conducted experiments. It is evident that Young modulus increased at least 50%, reaching a value up to ~721 MPa, due to crystal structure's development that were observed in μ-CT imaging, SEM investigation and also reported in the literature (6), (27), (54). The measurements were repeated at least 3 or 4 times in every indented surface and the error in the Young modulus was found to vary 1.5-3.5%. However for the unhardened specimen as well as the specimens hardened for 2 and 4 days, only one measurement was successful due to the fact that the material was too brittle for the applied load. This is attributed to the limited crystal development in these specimens. As one can conclude, the obtained Young modulus of the studied material after 14 days hardening in the Ringer solution based on compression tests (4.3.1) is considerably higher. Specifically, it was found to be 1.7 GPa, instead of 721 MPa. However in compression tests, as already been reported, after the initial loading the material is becoming more and more compact due to the fact that the pores start to crush (densification) and eventually fails when enough cracks form the fracture surface (68). Consequently, a higher compressive strength and Young modulus of the material is achieved. On the other hand, a low-load indentation with a spherical indentor causes a purely elasto-plastic response of the material (64). The above lead to the conclusion that the Young modulus, obtained from the conducted indentations, apply during the early stages of loading, until the densification phenomenon starts to occur.   In this work, the hardened cylindrical specimens, intended for diametral compression test

Failure model
The results presented from compression (4.3.1) and indirect compression tests (4.3.2) were exploited in order to propose a failure criterion for the examined bone cement. Mohr Coulomb criterion has been commonly used to characterize the failure of granular materials with different tensile and compressive strengths such as soils (73), rocks (74) and concrete (75). The biocement in this study is also a granular material and the use of a Mohr-Coulomb criterion seems adequate. The strength quantities experimentally obtained suggest that a Mohr-Coulomb failure criterion may be appropriate to predict the CPCs strength in combined loads (76). In

Absorption phenomenon
The denoted D cylindrical specimen was fully dried, after the completion of hardening process, and then re-immersed in a small bath filled with Ringer solution. At certain time periods it was recovered, its weight was measured and then re-immersed until it was fully saturated. The weight gain of the hardened samples during their exposure in liquid and humid environment was expressed as follows: where, Wref is the specimen's weight at dry state and W(t) its weight at time t. A digital balance of 10 -3 gr resolution was used for measuring Wref and W(t). Each time the specimen was recovered from the liquid media and before it was weighed, a gentle shake was applied to it in order to remove the excessive amount of liquid on the sample's surface. In Fig. 4.20 the weight gain as a function of sample's immersion time in a liquid environment, is presented and labeled as "C". Since the experiment was conducted twice, the obtained results were numbered as (I) and (II), respectively Both times, the sample's weight gain exhibited two distinct stages: (a) a rapid liquid uptake during the first two minutes of immersion and (b) further evolution of liquid absorption with a lower rate in the following days. More measurements were taken regularly over the next days, since the experiment started, and the results are presented in Fig. 4.21 :. It can be observed that after three days of immersion the weight measurements were practically stabilized indicating that saturation levels were reached. The measurements taken after 11, 12 and 13 days of immersion, of the first experimental run, confirm the latter allegation. As it is obvious, the weight gain evolves rapidly during the first three minutes, while after 14 minutes more than 85% of the total absorbed liquid media has been gained. Hence, the time period of the first 15 minutes is the most crucial for the absorption phenomenon. In order to assure that the results were unaffected from the sample's geometry and size, the experiment was conducted again, using a small block specimen (dimensions: 6x6x12 mm). The results obtained from the block specimen are presented in Fig. 4.20 :, labeled as (B). It is evident that they are practically the same, compared with the results obtained from the cylindrical specimen, apart from the first two minutes of immersion. This difference, reaching up to ~20%, is noted during the period of rapid liquid uptake (first 2 minutes of immersion) and can be attributed to the measurements' error related with the amount of excessive liquid in the specimen's surface.  A change in either one of the above parameters changes the reflected wavelength. A temperature increase causes a thermal expansion of the grating resulting to a change of its period and refractive index. A mechanical strain deforms the FBG and thus changes its period and modifies also the refractive index by photoelastic effects (79). When a FBG sensor experiences a three-dimensional homogeneous thermomechanical strain field, where εx≠ εy≠ εz (z is the direction of the fiber axis) and ΔΤ≠0, the induced change of the refractive index in the cross section of the fiber causes the Bragg peak to split into two distinct ones. Additionally, in order to calculate the developed hygroscopic strains due to moisture uptake Eq. 4 takes the following form: Where ℎ are the obtained strains during liquid/moisture absorption and is the bone cement's coefficient of moisture expansion (CME). In section 5.1.2 is being discussed why the recorded strains and ℎ from the FBG sensors correspond to the applied induced strains in the studied bone cement, assuming a perfect interface between the fiber and the material.

Isostrains justification
In order to assume that the recorded strains from the FBG sensors correspond to the applied induced strains from the host material, assuming a perfect interface between the fiber and the material, the strain field must be unaffected from any edge effects. According to a published study (81) in a cylindrical specimen, having the same dimensions as the ones used in this work, the strain field is homogeneous along its longitudinal axis apart from a zone of 8 mm towards cylinder's upper and bottom face. Hence, the strain field in the middle of the specimen, where all the FBG sensors were placed in this study, is certainly not affected by any edge effects.
Additionally, when the cylindrical specimen is subjected to an external strain, a fraction of the applied strain is transferred to the embedded FBG. The amount of strain measured by the FBG is strongly dependent on the ratio of the volume stiffness between the host material and the fiber (82). More specifically, this dependence can be defined from Eq. 5.6: Where E and E is the Young modulus of the material and fiber, respectively and A , A is the cross section of the cylindrical specimen and fiber, respectively. Numerical studies carried out for the cylindrical specimens employed in this study have shown that values of K as low as ~25 lead to deviations from the isostrains assumption below ~3.2%. This error significantly decreased for higher values of K encountered in this study. Considering

Multiplexed sensing
As one can conclude, single FBG sensors can be used in order to monitor effectively the strains induced in the host material, in which are embedded. However these measurements concern only the near area close to Bragg grating and as a consequence provide limited information about the overall strain field in the material. Multiplex sensing was developed in order to face this crucial limitation, with two different concepts: serial and parallel multiplexing (84). The working principle is similar as in the case of a single FBG: a broad band light source is introduced through fiber's core however each FBG sensor reflects back a different, unique wavelength. The serial multiplexing has the advantage of using a single source of light while interrogating all the FBG sensors simultaneously. As a result in this work, apart from using single FBGs, serial multiplexing also assisted the investigation of the host material's strain field in order to interrogate a wider area as well as to corroborate the results obtained from single FBGs. Attention was given from the manufacturer in order the response of each sensor won't overlap the reflected wavelength of the sensors next to them, in loading conditions. On the other hand, in large structures parallel multiplexing is more common since it allows sensing at different locations that can be very distant among each other.

Single FBGs
Six cylindrical specimens, denoted as S1-S6 in Section 3.2, were fabricated with embedded FBG optical sensors placed along their longitudinal axis while Bragg gratings were located in the middle of them (~20 mm) (Fig. 5.2). Full spectrum measurements from the FBGs were taken using a Micron Optics sm125 optical sensing interrogator, from which the reflected wavelength was obtained. The length of Bragg gratings were of a few millimeters and varied between 1 and 10 mm. The specimens with embedded single FBG sensors underwent through the 2 main stages of a CPC preparation: (a) solidification and (b) hardening. Additionally, a third stage was added, in which the specimens were dried and subsequently exposed to a liquid and humid environment, respectively. At the same time, the embedded FBGs were interrogated frequently. The ultimate goal was to investigate if any strains are induced in the material, during the main stages of a CPC preparation (solidification and hardening), as well as to monitor the material's hygroscopic response in liquid and wet environment.

Multiplexed FBGs
The investigation of induced strains during solidification and hardening period was repeated, by fabricating two more cylindrical specimen (M1, M2), of the same dimensions, with 5 embedded multiplexed FBGs each. The optical sensors were placed again in specimen's longitudinal symmetry axis and the Bragg gratings were located around the specimen's medial.
The objective was to investigate if the strain field is homogeneous, in the area where single FBGs were located, and corroborate the already obtained results. For the needs of this work, the distance between the multiplexed sensors was decided to be 5 mm while FBG sensors had a length of 1 mm (Fig. 5.3). In order to define accurately the location of Bragg gratings, in reference to the specimen's longitudinal axis, Optical Low Coherence Reflectometry (OLCR) technique was employed, after specimen's solidification stage was completed. OLCR setup, schematically depicted in Fig. 5.4, is based on Michelson interferometer whose arms are labeled as test and reference arm. Light from the broadband source and tunable laser are alternatively introduced using the optical switch. The transferred signal passes through an optical circulator and subsequently into the test and the reference arm, using a 3dB directional coupler. Afterwards, the light from reference and test arm is reflected back and enters the coupler, only if the optical length difference of the two arms is smaller than the coherence length (~25μm) of the light source. The resulting interference signal corresponds to the impulse response, smoothed over a few micrometers, and also to the half of the coherence length.
Moving the mirror of the reference arm, the optical distance is changing the causing light, reflected from the mirror, to interfere with the light coming from different FBG positions. An induced displacement Δz of the mirror in the reference arm "selects" the light back reflected from the FBG in the test arm at a slightly different distance from the previous point. The FBG in the test arm is then completely scanned with a maximum spatial resolution given by half the coherence length of the light source (83). hardly deviated from specimen's midst (z=0), as their between distance was found to be only 0.1 mm. Additionally, FBG 2 and FBG 4 had a distance, from z=0, of 5.4 mm and 5.7 mm, respectively, while FBG 1 and FBG 5 were found to abstain (from z=0) 11.3 mm and 11.9 mm, respectively. Since all embedded Bragg gratings had a distance more than 8 mm from the edges of the specimens, there were no edge effects that could affect the calculated strains (85).

Solidification
As far it concerns solidification period, the interrogated wavelengths (λB0, λB) and corresponding strains (εs) for single and multiplexed embedded FBGs are presented in Table   5.1, for two characteristic stages (initial and final) of this time period. The first one (before FBG embedment) corresponds in a state where the optical sensor is mounted on the mould, but no CPC paste has been casted in the mould's cavity. The reflected wavelength of this state will be considered as a reference value (λB0). As final stage of the solidification period was chosen the state where each specimen was recovered from the mould and before its immersion in the hardening liquid, at a free state. The two different interrogated wavelengths (λB0, λB) were used in Eq. 5.4, from which the induced strains (εs) were calculated. Each presented value is the mean value obtained from 10 consecutive measurements during FBG's interrogation and the maximum difference between them was found to be ~25 με.
It can be seen that the strains obtained from single FBGs are compressive which means that there were induced residual strains during solidification. Nevertheless are of low magnitude, while a variation is exhibited. More specifically, in S1, S2, S3 and S5 specimens the exhibited strains were between -514 and -795 με, while for S4 specimens the calculated strains are -1113   as it has been demonstrated in section 4.2.2, one can conclude that FBG measurements can be affected from local edge effects, because of the voids, in the examined material.

Hardening
In Fig. 5.8 the strain values (εh), obtained from the implementation of Eq. 5.4, that concern the hardening stage are presented in a diagram. Hardening process lasted at least 15 days, since during in this time interval microstructural changes take place as demonstrated in section 4.1, and was completed when the stain values were levelled off. The interrogated reflected wavelength from specimens S2 and S3 coincided with the reference wavelength (when the optical fiber was not embedded), suggesting that the interface between the bone cement and the optical fiber was severely damaged. As a result they were not taken into account. It is also noted that the strain values of "0 day" were obtained after several minutes passed since  (Fig. 4.1d). In the following days, the entanglement became more complex as it is depicted from Fig. 4.1e and f, recorded at 8 and 10 days of immersion. The entanglement of the crystal structures that resulted in a complex network, appears to be the cause that strain values exhibited a different linear slope. The obtained strain values from specimen S1 exhibits a different strain pattern. Specifically, during the first 12 days of immersion in the Ringer solution, strain values exhibit a plateau of a mean value of -230 με, while afterwards a new, second plateau appears where the strains retain a mean value of -90 με. However, in the case of S1 specimen hardening stage took place in a room environment while for the rest specimens in an environmental chamber, with settable temperature. Thus, it is concluded that unavoidable room temperature variations, during hardening of S1 specimen, have affected the strain measurements. reports that various parameters such as smaller particle size, higher setting temperature and low liquid-to-powder ratio can affect kinetics and as a consequence CPCs' setting time.
Considering that the aforementioned parameters were not the same with the ones of the present study, such differences in the time period where microstructural changes take place are expectable.
the second one, not that steep as the first one, which is defined from the rest strain values and is similar to the slope exhibited from strains values of M1 specimen.
The low magnitude of the obtained strains, also corroborated from the multiplexed FBGs, suggest that no significant residual strains were created during the bone's cement immersion in the Ringer solution and the subsequent hardening. Thus, deformation due to hardening is negligible and the specimen preserves its dimensions when immersed in the liquid media. This later property is crucial since parts made from this material in the human body can preserve their dimensions during hardening.

Liquid environment
After hardening period, one of the single FBG instrumented specimen (S5) was dried in 50 0 C for 2 hours, in order to subtract the liquid content absorbed during hardening period, and then re-immersed in the Ringer solution. Meanwhile the reflected wavelength from the Bragg gratings was interrogated every minute for the first 13 minutes. Thus, the developed c strains (εhygro) were calculated and presented in Fig. 5.10, by implementing Eq. 5.5. More measurements were also taken from the Bragg sensor in the following days, every 24 hours, until saturation levels were reached and the calculated strains are presented in Fig. 5.12. Since the experiment was conducted twice, the obtained results were numbered as (I) and (II), respectively Additionally, in the presented graphs are also included the results reported in section 4.4, that concern the weight gain (WL) of a same cylindrical CPC specimen without embedded FBG sensor (specimen D). For both experimental runs, designated as εhygroI and εhygroII, a rapid strain evolution takes place reaching values of -305x10 -6 (με) and -254x10 -6 (με) respectively, within the first two minutes of immersion into the Ringer solution, while at the same time a rapid liquid uptake occurred. In the following minutes and days, a further evolution of the hygroscopic strains is exhibited, but with a lower rate, until saturation levels were reach and the developed strain values were levelled off at -290 x10 -6 and -250 x10 -6 (με), at the first and second conduction of the experiment respectively. It is noted that the differences in the recorded strain values can be possibly attributed to the fatigue of the interface between the FBG sensor and the bone cement material, due to the successive drying-swelling process that the sample had to undergo to repeat the re-immersion experiments. Moreover, the fact that the measured hygroscopic strains exhibited the same behavior as the specimen's liquid gain, suggest that the material's absorption process can be monitored in an effective way leading to the conclusion that FBGs can be used to investigate CPCs kinetics. where 0 is the pre-marked length measured from the camera when the specimen was placed in the empty bath at a dry state. The above described configuration is illustrated in Fig. 5.11. From the obtained results no developed strains were found, suggesting that their magnitude was wellbelow the resolution of the method, which corresponds to ~1000 με for a change of 1 pixel in the measured length. The developed hygroscopic strains are also presented as a function of sample's weight gain in Fig. 5.13 where the data can be approximated by two slopes. The first slope is exhibited when the sample's weight gain is between 0≤W<29 % and its value was calculated to be B(1Ι)=3.75x10 -6 /%w/w (r 2 =0.971) and B(1ΙΙ)=2.74x10 -6 /%w/w (r 2 =0.9059) for the two experimental trials (I and II), respectively. The second slope is appearing for a liquid uptake range of 29≤W<37 %, where the corresponding values were B(2Ι)=16.2x10 -6 /%w/w (r 2 =0.9856) and B(2ΙΙ)=11.3x10 -6 /%w/w (r 2 =0.9929). In order to calculate the material's coefficient of moisture expansion (CME), designated as β in Eq. 5.5, an equilibrium must be achieved between the specimen and the surrounding environment, when the weight gain and the hygroscopic strains were obtained. Hence, the value of β can be approximated βI=7.02x10 -6 /%w/w, βII=4.96x10 -6 /%w/w.

Humid environment
Specimen S6, after the hardening period, was also dried for at least 2 hours in an oven and then was placed in an environmental chamber with settable values of relative humidity (RH), under a stable temperature of 23 0 C. The initial set value of RH was 25%and was increased by 5% each time, when equilibrium between the sample and the surrounding environment was achieved, and up to a maximum value of RH (80%) reached by the environmental chamber. At the end of each RH increment, the sample was weighed using the same method followed in section 5.2.2.3.1 and the peak wavelength from the optical fiber was recorded. In Fig. 5.14 the developed hygroscopic strains as a function of sample's moisture content, designated as WH, in a humid environment are presented. The strains values exhibit a variation trend that was found to have a slope value of β=3.98x 10 -4 /%w/w for a moisture uptake range of 0.9≤WH<3.8.
The calculated slope was found to be two orders of magnitude higher than the ones obtained for the case of the liquid immersed specimens. As one can conclude, the hygro-strain values range between the magnitudes exhibited when the specimen is dried (solidified) and fully fabrication parameters such as pore size, interconnectivity of pores, tortuosity, and in general to the different way with which the pores are filled in a humid environment, seem to have contributed in this exhibited difference of CME values between humid and liquid environment for the examined material.  The use of simulation models aims either to validate any obtained experimental results or to investigate a case which is too challenging to be implemented in reality for various reasons e.g.
need of complex configurations, limitations in material quantities etc. The first simulation attempts were achieved using analytical models, at times where the development of computers was still in early stages and the available computational power was limited. Hence, several drawbacks existed in developing reliable models and any obtained results often suffered in terms of accuracy since the models concerned over-simplified cases which abstained a lot from the reality. However, in the recent years the use of computers became widespread and the processing power has greatly increased, leading to a wider development of complex, credible simulation models which verge on reality and provide high precision results. Moreover, finite differences method as well as Finite Element Method (FEM), that require high computational resources, are now broadly used for implementing 2-D and 3-D models. In this work, an implementation of simulation models, using the above mentioned methods, was achieved: the first one simulated the absorption phenomenon, using finite differences method, and its results were imported in a FEM model in order to calculate the induced strains, when the studied CPC is immersed in wet environments. Moreover, a complex 3-D model was developed in a simulation software, using Finite Element Analysis, for the investigation of the distributed stress fields in the examined CPC as well as for the whole system configuration, in a real-life application (case study).
Finite difference is a numerical method for solving differential equations, based on the following equation: The explicit scheme (forward difference) is the least accurate and can be unstable, however is the easiest to implement and the least numerically intensive. As a result, this approach was adopted.
In the case of Finite Element Method the area or volume to be modelled is sub-divided into smaller, elementary parts ( Fig. 6.2). As a result a mesh of finite elements is created, where each element is constituted of a number of nodes. Then for a given set of boundary and initial conditions, field parameters such as stress, strain, displacement, temperature distribution, etc.
can be obtained in these nodes and consequently for the whole modelled area or volume. This is achieved by solving a system of N equations with N unknowns ([N]x[N] system), where N corresponds to the number of nodes times the number of unknown field parameter components per node (85). The above described procedure is achieved through the use of a user-friendly commercial software, in which suitable commands are given. For the needs of this work, Abaqus 6.11 ® simulation software package was employed for the implementation and analysis of Finite Element models.

Absorption phenomenon and developed hygro strains
In order to model the absorption phenomenon with the use of finite difference method, 3 different models that describe the diffusion phenomenon were developed: From the three diffusion models, Fick's and Langmuir law diffusion models were successfully implemented in Matlab ® software. In order to face the instability issues short spatial increments were used in the nodes that were close to the edges and increased towards the symmetry axis.
The same approach was also used for the time increments: the first time increments were short and were increased towards the end of analysis. As weight gain results, in each time increment, was considered the sum of the calculated ( ) values from all calculated time increments.
Random values were given to the unknown parameters for the implementation, however they were defined though a process described in the next paragraph. where ′ is the diffusion coefficient of the cement's crystals, is the exhibited porosity and accounts for the tortuosity of the interconnected porosity (11).  Ultimately, for a value of = 5.32x10 -6 /% w/w, the simulation results presented the best achieved convergence with the corresponding experimental results, as it can be observed in can be observed, that varies between ~1-16%.

Exp. Data
Simulation results

Where Total Hip Replacement is implemented?
The human hip bone is one of the body's largest joints, considered as a ball-and-socket joint.
The socket is formed by the acetabulum, which is part of the large pelvis bone, while the ball is the femoral head, which is the upper end of the femur (thighbone). The bone surfaces of the ball and socket are covered with articular cartilage, a smooth tissue that preserves and protects the ends of the bones and enables them to move easily. Also, a thin tissue called synovial membrane surrounds the hip joint. In a healthy hip, this membrane makes a small amount of fluid that lubricates the cartilage and ensures a frictionless hip movement (91). One of the most common hip disease is arthritis, where the cartilage cushioning the bones of the hip, wears away. As a result, the bones rub against each other, causing hip pain and stiffness.
In this case a Total Hip Replacement (THR) surgical procedure is necessary, in which the damaged femoral head is removed and replaced with a metal stem that is placed into the hollow center of the femur. The femoral stem may be either cemented or "press fit" into the bone. (Fig.   6.7). For the needs of this work, a cemented stem placed in a femoral bone will be investigated through a developed simulation, thoroughly presented in the next section. The main goal is to evaluate the mechanical performance of the bone cement in such application as well as to discuss the developed stress fields and their patterns in the components of the whole configuration system.

 CAD models
Initially, a replicated model of a femur bone was created by 3-D scanning a femur sawbone.
The resulting CAD file ( Fig. 6.8) was consisted of small surfaces, stitched between them, which formed a closed shell-type model. Afterwards, the obtained CAD file was imported in Abaqus ® simulation software package where a number of steps were followed, in order to create the final model that was used for the implemented simulation. Initially, as soon as the CAD model was imported in the simulation software, the shell-type geometry was converted into a solid 3-D model Then, the bottom part of the femur model was subtracted, since the area of interest concerns the upper half part of the femur bone, where the stem implant is placed. This consideration is also found in several studies, in which loading of a stem implant placed in a femur bone was also simulated (92), (93), (94), (95). Subsequently, the femoral head was subtracted with a cut perpendicular to its basis, like the one performed in THR surgery. Also, a refinement of the model's external surfaces was conducted by merging the small surfaces, since the quality of the generated mesh is strongly depended on them. Afterwards, a cavity was created on the inside of the femur model in which the stem implant as well as a structure that will surround the stem implant and resemble the bone cement, will be placed in. The above-described are illustrated in Fig. 6.9. In reality, the human femur bone is consisted of 2 different structures that exhibit different material properties: the trabecular (or cancellous/spongy) bone which is located on the inside of the femur bone, having a spongous structure, and the cortical bone on the outside that acts as a hull (Fig. 6.10). Thus, the femur bone CAD model was partitioned in 2 different structures: a "shell" of variable thickness along its longitudinal axis (1.8-3 mm) and the inner "core". This way, a more realistic approach of the femur bone was also simulated, where the "shell" and the "core" resembles the cortical and spongy bone, respectively ( Fig. 6.11).  Based on the CAD model of the stem implant, a new structure was created which surrounded the stem implant and simulated the bone cement. This was achieved through 3 steps: (I) creation of a main 3-D structure having a similar, simplified geometry as the one of the stem implant ( Fig. 6.13a), (II) sufficiently increase its thickness (Fig. 6.13b) (III) subtraction of the volume that corresponds in the stem implant, which led to a cavity creation (Fig. 6.13c). The thickness varied between 1-3.5 mm, since in reality a small amount of bone cement is used in cemented THR.   Generated mesh 10-node quadratic tetrahedron type elements (C3D10) were used in order to mesh all the femur component models, which is suggested for 3-D stress simulations. A total number of 828588 elements was generated for all meshed models, which was considered enough in order to avoid the generation of distorted elements, either in shape or size that would have an impact in the results. A mesh refinement was also implemented in the areas where the geometry was more complicated as well as in the surfaces in which a friction model was assigned. Afterwards, the meshed models were suitably assembled, as Fig. 6.14 illustrates.

Results
The stress field, obtained from the analysis run, which concerns the stem implant is presented in Fig. 6.15. As one can observe the developed stresses range between ~0.1 and ~250 MPa, where the high stress values are located around the edges of the backside (~180 MPa) and foreside (~250 MPa). The low stress values, observed in Fig. 6.16a for a higher accuracy stress scale, are exhibited around the neck of the stem (1-20 MPa) and are increased to ~30 MPa, along a zone between posterior and anterior side of the stem. A node-defined path was set at the backside of the stem implant, indicated with a red line, and the corresponding stress graph ( Fig. 6.16b), according to maximum principle stress, was plotted as a function of the stem's posterior length. Oshkour et al. (93), also conducted a FEM simulation on a cemented femur stem implant and among other results a similar stress graph is also presented (Fig. 6.16c). In this graph, if the part of the first ~50 mm of prosthesis length is ignored since in the referred study the head of the femoral implant was included, it can be observed that it is very comparable with the one of this work not only in terms of stress value interval but also in the exhibited stress magnitudes for the same prosthesis lengths.  Passing to the bone cement, the exhibited stress field is presented in Fig. 6.17 for the case its The exhibited stress field in the spongy bone, for the case where bone cement's Young modulus was set to 721 MPa, is presented in Fig. 6.19. The majority of the exhibited stress values range between 1 and ~40 MPa while in some areas are too low (<0.1 MPa). However, the corresponding node(s) in this area were successfully tied to the cortical bone and consequently higher stresses were obtained. It can be also observed that the exhibited stress values are lower for the part area where the femoral head is located and are progressively increased towards bottom. The same loading scenario was ran again but this time the Young modulus of the bone cement was set to 1.7 GPa. Interestingly, similar stress fields were obtained and little changes were observed, when compared with the previous results.
In Fig. 6.20 the stress field of the cortical bone, for a bone cement's Young modulus equal to 721 MPa, is presented. Its mechanical response due to stem's loading is similar to the one  In a local area, indicated with yellow, vivid red and grey color, stress values exceed that limit due to the fact that the thickness of the cortical bone in this region is too thin (>0.5 mm), compared to the thickness of a real human femur bone. As a result, they should not be taken into account. Moreover the obtained results, using a higher value in bone cement's Young modulus (1.7 GPa instead of 721 MPa) are very similar with the above presented and almost no differences can be found.

Chapter 7
Conclusions and future work

Conclusions
In this thesis a thorough mechanical characterization on a self-setting apatitic cement, fabricated from pure α-TCP powder, is conducted and driven by the following sections:  FBG-based strain investigation before, during and after material's hardening stage  Material's compressive strength and Young modulus is considerably increased during hardening stage, due to crystals' development. Although the Young modulus obtained from compression and low-load indentation tests considerably differ, this is justified from the fact that the latter applies only during the early stages of loading.
 A Mohr-Coulomb failure criterion is proposed for the examined hardened biocement, based on the obtained results from compression and indirect compression test.
However, the conduction of more tests is suggested that would further contribute to obtain cohesion (c) and internal friction angle (φ) values with higher accuracy.
 The hardened material exhibits an intrinsic porosity while pores' size vary within the order of magnitude of few microns. In the material's porosity are also included cavities, created due to air entrapment during paste casting in the moulds.

Future work
Through the conduction of this work a number of proposals can be made and suggested as future work, to further enrich the mechanical investigation on self-setting calcium phosphate bone cements:

I) Incorporation of geopolymers in calcium phosphate cements
Geopolymers have been proven to be non-toxic and eco-friendly materials. Their potential use in calcium phosphate bone cements would be very interesting, both in a scientific and a medical point of view. Hence, several experiments which will investigate if and in which degree the addition of geopolymers in CPCs have a positive impact on the material's mechanical properties and performance, are strongly suggested.

II) Investigation of TCP powders with different characteristics (granulometry, stoichiometry, sample volume etc.) and variable curing conditions (pH, hardening solution etc)
In this work it was demonstrated that the mechanical performance of hardened self-setting calcium phosphate bone cements is strongly dependent on the developed crystal structures, during hardening stage. However those crystals are actually products of a chemical reaction (hydrolysis), which can be affected by several parameters such as grains size, pH of hardening liquid, temperature of the surrounding environment etc. As a result, a parametric study in which these parameters will be investigated and determined in order to achieve the optimum mechanical properties in a hardened CPC, is considered of high value. Although several works have been conducted which investigate some of these parameters, no systematic study exists in the literature.

III)
Conduction of more experiments (i.e biaxial testing, pure shear tests) through which the mechanical performance of CPCs will be further researched.
As it was noted, the mechanical strength of the examined CPC in tensile stress, obtained from diametral compression testing, was ~7 times lower that the exhibited mechanical strength in compression stress. Consequently, the failure of CPCs may be dominated from their strength in tensile stresses and not in compressive stresses. The investigation of such allegation becomes more important considering that the developed stress fields in potential applications of CPCs, like Total Hip Replacement, are complex and include tensile stresses. Moreover, such information would provide more precise information to better assess the Mohr-Coulomb failure criterion, though which CPC mechanical performance in shear stresses can be evaluated.

IV)
Further investigation on the exhibited ability of FBGs to sense the development of microstructural changes during hardening period.
The finding that the linear patterns of the recorded hardening strains are correlated with the development of crystal structures is considered of high value. However the crystals development rate is affected not only from temperature changes but also by several other parameters (pH, grain size etc.), which in this study were not controlled. Hence, deviations may were introduced in strain readings. For this reason, the conduction of more experiments that concern FBG-based strain investigation during hardening period are suggested, in which any parameter that influence the α-TCP hydrolysis rate will be controlled.