Raafat Hussein

Yann Landon

Anna Carla Araujo
email: araujo@insa-toulouse.fr

Bone properties -A Review for Drilling Application

Bone is the main organ of the skeletal system, composed of cells, collagenous fibers, non-collagenous proteins and minerals. The mechanical properties of bone maintain the shape of the body and transmit muscle contraction forces during movement. It is a dynamic, anisotropic, hierarchical, heterogeneous and time-dependent biological material. Its properties vary more than those of typical engineering materials due to various factors such as bone function, age, weight, and other characteristics. Bone has been shown to have high mechanical compressive properties as a highly calcified hard tissue. However, temperature and other factors affect the compressive strength and fracture morphology. Despite the high load-bearing capacity of bone due to its structurally optimized tissue, severe impact or trauma can weaken bone and cause fractures. Some types of fractures require internal fixation through surgical bone drilling. Orthopedic surgery exposes bones to higher stress and temperature, resulting in permanent or temporary damage. This can lead to certain healing complications and mechanical instability. Many researchers have investigated numerous factors to reduce heat generation and prevent osteonecrosis. These include processing parameters, drill specifications, and bone properties. However, it remains a problem to more accurately determine the behavior of the bone and the corresponding actual drilling conditions, as these factors and their effects are closely related. To accurately predict the temperature rise during bone drilling using experimental and computational models, it is necessary to understand the geometry, mechanical behavior, and thermal properties of the bone tissue. Therefore, it is important to analyze the bone as a thermo-mechanical element to predict its behavior. This article reviews the basic concepts of bone biomechanics, its complex hierarchical structure, and its mechanical and thermal properties at the macroscopic and microscopic levels. It also highlights the factors that influence the large variability in the mechanical behavior of bone, as well as the studies on the thermomechanical conditions of bone drilling. Many recent experimental and theoretical studies have investigated the influence of drilling techniques on the mechanical and thermal responses during bone drilling. Regardless of the used technique, there is a wide range of variation in the mechanical and thermal response of bone. This is constantly related to structural factors and is dependent on the direction of loading. This comprehensive review can help surgeons and drill manufacturers understand recent improvements through optimal strategies to reduce or limit thermal damage during bone drilling.

Introduction

Bone is a living tissue composed of cells embedded in an abundant hard intercellular material that makes up the skeleton of the body [START_REF] Clarke | Normal Bone Anatomy and Physiology[END_REF]. It has been the focus of interest of many researchers in the field of mechanics to understand and solve the problem of fractures related to the impairment of mechanical behavior by certain factors such as age and specific pathologies. Bone has the ability to renew itself after damage because its natural structural material repairs itself [START_REF] Cowin | Bone mechanics handbook[END_REF]. It is composed primarily of three cell types: osteoblasts, which are responsible for new bone formation, osteocytes, which are probably the sensors of mechanical stress and contribute to the degradation of the bone matrix, and osteoclasts which are multinucleated cells of the macrophage family that form from blood monocytes and responsible for aged bone resorption [START_REF] Clarke | Normal Bone Anatomy and Physiology[END_REF]. However, certain diseases and trauma damage the skeletal system, requiring clinical intervention in which bone drilling is involved for proper healing [START_REF] Kim | Orthopedic implants and devices for bone fractures and defects: Past, present and perspective[END_REF].

Bone drilling is a surgical method used in orthopedics, mainly for repairing internal fractures, inserting implants, or reconstructive procedures. In this surgical procedure, holes are drilled into the bone and the fracture is fixed with screws or wires to immobilize it [START_REF] Bohra | Bone drilling investigation and possible research: A state of the art review[END_REF]. It is an essential and universally demanding surgical procedure that generates both mechanical and thermal loading on the bone structure, resulting in an increase in bone temperature and stress. However, certain complications occur when drilling bone, such as uncontrolled plunging of the drill tip, mechanical instability, drill-bit breakage, lack of vascularization, in addition to bone loss and defects. The pivotal concerns of bone drilling are the time at which the temperature exceeds the threshold and the duration at constant temperature, which are detrimental to bone viability and can lead to osteonecrosis. According to the literature, the main sources of heat are plastic deformation of the produced chips and friction between bone and cutting surfaces of the drill [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF]. In addition, many processing parameters and drill specifications contribute to the temperature rise and drilling efficiency. The bone itself is also a source of heat generation due to its complex hierarchical structure and low thermal conductivity. Therefore, a successful bone drilling procedure requires adequate treatment of the mechanical and thermal aspects of bone.

In order to model drilling bones, it is important to understand the behavior of cortical bones submitted to a situation similar to orthogonal cutting model [START_REF] Baro | Investigation of cutting force and temperature variation in orthogonal cutting of cortical bone[END_REF]. The cutting parameters and cutting conditions play an important role in the temperature and the effect on the bones cells. Researchers have studied orthogonal cutting of bone to determine the cutting forces, chip geometry, surface quality and temperature. Despite the anisotropic nature of bone, Alam, Mitrofanov, and Silberschmidt [START_REF] Alam | Finite element analysis of forces of plane cutting of cortical bone[END_REF] developed a 2D isotropic finite element model for a bovine femur considering approximated as a fibre-reinforced composite to simulate its structure. Sugita et al. [START_REF] Sugita | A new cutting method for bone based on its crack propagation characteristics[END_REF] and Sugita and Mitsuishi [START_REF] Sugita | Specifications for machining the bovine cortical bone in relation to its microstructure[END_REF] also incorporated a one-dimensional continuous fiber reinforcement to analyse the bone using experimental approach and FEM on orthogonal cutting and analysing crack propagation and osteons alignment with cutting direction. Linear regression analysis was performed and a relationship between cutting force and crack length was suggested. Santiuste et al. [START_REF] Santiuste | The influence of anisotropy in numerical modeling of orthogonal cutting of cortical bone[END_REF] included the effects of anisotropy on cutting forces and temperature also modeling cortical bone as a long fiber-reinforced composite material. In another study, Childs and Arola [START_REF] Childs | Machining of cortical bone: Simulations of chip formation mechanics using metal machining models[END_REF] used finite element models of bone adapting metal cutting theory and a pressure dependent yield stress and a strain path dependent failure strain law and define the appropriate method for the bone cutting. Moreover, finite element models were used also by Baro and Deoghare [START_REF] Baro | Investigation of cutting force and temperature variation in orthogonal cutting of cortical bone[END_REF] to analyze the effect of orthogonal cutting parameters on three different models of cortical bone i.e., isotropic, anisotropic, and microscale models. They tested the effect of depth of cut, friction coefficient, cutting speed and rake angle on temperature and force levels. In microscale, Hage and Hamade [START_REF] Ilige | Micro-FEM orthogonal cutting model for bone using microscope images enhanced via artificial intelligence[END_REF] applied FEM using a data-driven approach using microscope images enhanced by Artificial Intelligence of orthopedic cutting in cortical bone containing only osteons and interstitial lamellae.

Experimental analysis of orthogonal cutting is analysed in some articles. Sui et al. [START_REF] Sui | Force analysis of orthogonal cutting of bovine cortical bone[END_REF] analyzed the significance of the parameters using experimental full factorial design of the cutting process when using stainless steel tools on bovine femur bones. ANOVA and regression analyses were used to determine the factors that have high and low significant influence. Recently, Zawadzki et al. [START_REF] Zawadzki | Influence of Machining Parameters on Cutting and Chip-Formation Process during Cortical Bone Orthogonal Machining[END_REF] analyzed experimental chip formation measuring cutting forces and evaluating the effects of the rake angle, clearance angle, and depth of cut on the orthogonal cutting process of cortical bone in three directions. In addition, Luo et al. [START_REF] Luo | Cutting Behavior of Cortical Bone in Different Bone Osteon Cutting Angles and Depths of Cut[END_REF] used experimental analysis along with analytical models on cortical bone to analyze chip formations, material removal behavior and cracks propagation and initialization under varying bone osteon cutting angles and depths. Besides, Bai et al. [START_REF] Bai | Mechanism of material removal in orthogonal cutting of cortical bone[END_REF] also performed experimental analysis to study the mechanisms of material removal and crack propagation in orthogonal cutting of cortical bone but with the consideration of microstructural and sub-microstructural features and material anisotropy.

In recent years, research in the field of bone drilling has come into focus and so the orthogonal cutting model is applied to drilling operations. The main focus is on predicting and controlling forces and temperature to ensure the success of operations and reduce damage to bone tissue, such as osteonecrosis. Many experimental analyses were done with various drill tools to investigate bone drilling. For example, Wang et al. [START_REF] Wang | Experimental analysis of drilling process in cortical bone[END_REF] used manual and automated drilling in bovine cortical bone to study the drilling process, drilling forces and torque. They investigated separately the effects of drilling speed, feed rate and drill-bit diameter on forces and torque. Chen et al. [START_REF] Chen | Thermal Management of Bone Drilling Based on Rotating Heat Pipe[END_REF] used novel rotary heat pipe drill, a different drill tool to investigate the thermal management and heat transfer mechanism at different heat fluxes and spindle speeds. Low-frequency vibration-assisted drilling was used by Han et al. [START_REF] Han | Influence of parameters on temperature rise and chips morphology in low-frequency vibration-assisted bone drilling[END_REF] to determine the effects of machining parameters such as feed rate, rotational speed, vibration frequency, and amplitude on drilling temperature rise and chip morphology. Moreover, conventional drilling was performed on Sawbones and bovine bone by Samarasinghe et al. [START_REF] Samarasinghe | Surgical Bone Drilling: A Review[END_REF] to comprehensively explore the effects of the processing parameters on drilling forces, temperature, osteonecrosis exposure and debris formation.

Shihao et al. [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF] implemented the drilling process on fresh bovine femur along wih for a comprehensive study of the thermal characterization of bones. Quasi-three-dimensional time-series temperature distributions were established and analyzed to formulate strategies to reduce thermal damage to bone. Other researchers conducted their investigations using non-conventional drilling. For example, Agarwal et al. [START_REF] Agarwal | Influence of cutting force on temperature, microcracks and chip morphology during rotary ultrasonic bone drilling: An in-vitro study[END_REF] conducted histopathological studies on porcine femur bone using rotary ultrasonic bone drilling technique. They studied cutting forces, temperature, microcracks and bone chips generated during drilling and compared the results with a conventional twisted drill-bit of the same diameter. They also intended to develop several machine learning algorithms to predict temperature increases during rotating ultrasonic bone drilling [START_REF] Agarwal | Prediction of Temperature Elevation in rotary ultrasonic bone drilling using machine learning models: An in-vitro experimental study[END_REF].

In addition, numerical modelling and simulations were implemented for the study of drilling process. Liu et al. [START_REF] Liu | Novel crescent drill design and mechanistic force modeling for thrust force reduction in bone drilling[END_REF] proposed a mechanistic model to predict thrust force and torque for a novel crescent-shaped drill with an improved positive rake angle. In the study by Wang et al. [START_REF] Wang | Evaluation of temperature distribution for bone drilling considering aging factor[END_REF], ABAQUS software was used to simulate the drilling of bone in a time-varying temperature field considering the aging factor. Additionally, the temperature of drilled bones was studied by Khan [START_REF] Khan | 3D Finite-Element Modelling of Drilling Cortical Bone: Temperature Analysis[END_REF] using a three-dimensional thermomechanical finite element model of bone drilling to determine the appropriate drilling parameters (cutting speed, feed rate) and cooling conditions. The latter was also investigated by Alam et al. [START_REF] Alam | In-vitro experimental analysis and numerical study of temperature in bone drilling[END_REF], where they performed a series of experiments and numerical studies to investigate the effects of cooling conditions on the increase in bone temperature during drilling.

Numerous investigations and research projects have been conducted to comprehensively evaluate the parameters in surgical bone drilling to mitigate thermomechanical damage to drilled bone. However, due to the complexity of parametric interactions, the problem of determining the ultimate ideal bone drilling parameters remains. This systematic review aims to understand the mechanical and thermal behavior of bone to achieve better surgical outcomes and reduce bone failure. It aims to provide an overview of the fundamental concepts of bone biomechanics and the mechanical tests that have been performed to characterize the multiscale mechanical behavior of bone. It also highlights various factors responsible for the wide variability in the mechanical and thermal properties of bone. In addition, the thermal characterization of bone in relation to specific factors will be examined. The relationships between the mechanical behavior of bone at different scales will allow a better understanding of the effects of changes in mechanical and thermal properties from one scale to another on damage and failure in drilling applications.

Bone structure

The structure and fracture strength of the bone itself should be considered to determine the mechanical behavior of the bone during drilling, i.e., whether the bone will fail under mechanical or thermal loading. The mechanical complexity of bone exceeds that of all other engineering composites because bone has a hierarchically organized structure. This means that it has an irregular but optimized arrangement and orientation of fibers. Because of its hierarchical structure, bone has defined properties at each structural level, making the material heterogeneous and anisotropic. Figure 1 shows the five levels of hierarchical structural organization.

As it is presented in Fig. 1, the macrostructure level takes place from 10mm to several cm. At this scale, bone can be divided into two parts: Cortical bone, the dense bone that makes up 80% of the volume of the entire skeleton, and trabecular or cancellous bone, which makes up the other 20%. The main difference between these two types of bone tissue is porosity. Cortical bone has a porosity of 5% to 15%, while trabecular bone has a porosity of 40% to 95% [START_REF] Morgan | Bone Mechanical Properties in Healthy and Diseased States[END_REF]. Adult long bones consist of two broad and rounded epiphyses on either side of a central cylindrical shaft. Cortical bone forms the diaphysis, while cancellous bone with a thin shell of cortical bone forms the epiphysis and metaphysis [START_REF] Cowin | Bone mechanics handbook[END_REF]. Cortical and trabecular bones also differ in their mechanical properties. The mechanical behavior of cortical bone is anisotropic. However, due to the small differences in mechanical properties in both radial and circumferential directions, it is considered a transversely isotropic material. The trabecular bone or spongy bone of the typical size of 5 -10mm, in which the trabeculae and the intervening pores can be observed simultaneously, is considered a highly porous anisotropic material [START_REF] Morgan | Bone Mechanical Properties in Healthy and Diseased States[END_REF]. This porosity mainly determines the mechanical properties of trabecular bone. The structural arrangement of the trabecular network and the tissue-level properties of a trabeculae also contribute to the apparent mechanical behavior. Moreover, the macroscopic mechanical properties of bone vary between regions of the same type of bone tissue [START_REF] Ovidiu | THE QUALITY OF TRABECULAR BONE AS-SESSED USING CONE-BEAM COMPUTED TOMOGRAPHY[END_REF].

The mesostructure level which is on a scale of 0.5 -10 mm where the osteons are randomly arranged within the interstitial lamellae with cavities for absorption. Furthermore, the microstructure level is on a scale of 10 -500 µm. At this level, the cortical bone can be seen as a Haversian system composed of a long narrow cylinder called the osteon consisting of concentric layers of lamellae that surrounds the Haversian canal. The mechanical properties of osteons vary with collagen fiber orientations, mineral density, and loading modes [START_REF] Atthapreyangkul | Effect of geometrical structure variations on strength and damage onset of cortical bone using multi-scale cohesive zone based finite element method[END_REF].

At the nanostructure level, the bone matrix can be described as a composite of collagen fibrils and mineral plateletes having an hexagonal lattice structure of hydroxyapatite [START_REF] Ma | Nanoscale mechanisms in age-related hip-fractures[END_REF]. Recently, researchers are focusing on the micro-mechanical properties of cortical tissue isolated using conventional machining technologies with length scales below a few hundred micrometers.

Mechanical characterisation of bone properties

The classical mechanics principles and solid mechanics are used to study the material fracture toughness when subjected to a certain load. Bone, the bio mechanical organ of the skeleton system, has always been a subject of great interest in mechanics. The analysis of bone biomechanics is vital to determine the mechanical properties of bone to detect failure and damage aspects during process.

Most of the studies in the literature have been performed on the cortical bone because of the importance of the multiscale structural function. Recently, researchers are moving toward analyzing and modeling the mechanobiology of trabecular bone since it is the main load-bearing bone in vertebral bodies and also it transfers the load from joints to the compact bone of the cortex of long bones [START_REF] Audekercke | Mechanical Properties of Cancellous Bone[END_REF], [START_REF] Giesen | Mechanical properties of cancellous bone in the human mandibular condyle are anisotropic. Response[END_REF], [START_REF] Michimoto | Effects of the cancellous bone structure in the skull on ultrasonic wave propagation[END_REF].

Due to bone's hierarchical structure and complexity, scale is of great importance when discussing bone architecture and properties. Every mechanical test has its own resolution for assessing the properties of a given structure [START_REF] Rho | Mechanical Properties and the Hierarchical Structure of Bone[END_REF]. Therefore, it is crucial to combine certain mechanical techniques to determine the properties of bone at its different scales using standard tests for mechanical characterization.

Mechanical properties of bones using macroscale tests

At the macroscale, the most common mechanical methods performed are the tensile, compression, bending and torsional [START_REF] Albert | A comparison of rib cortical bone compressive and tensile material properties: Trends with age, sex, and loading rate[END_REF], [START_REF] Atthapreyangkul | Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling[END_REF], [START_REF] Reilly | The elastic and ultimate properties of compact bone tissue[END_REF]. These methods are usually used to reveal bone stiffness represented by the elastic modulus (E), shear modulus (G), Poisson's ratio (ν), bone ultimate strength (σ ) and failure resistance.

The mechanical behavior of bone at the macroscale varies according to the type of bone, whether it is cortical or cancellous, and according to the anatomical function in the skeletal system. For example, femur is one of the longest and strongest bones in the body and is essential for standing and movement [START_REF] Reynolds | The Fractured Femur[END_REF]. Under various loading modes, the ultimate strength of human femoral cortical bone is greatest under compression in the longitudinal direction (135 ± 15.6 MPa) and weakest under tensile loading in the transverse direction (53 ± 10.7 MPa) performed on 1cm human femoral cortical bone [START_REF] Reilly | The elastic and ultimate properties of compact bone tissue[END_REF], [START_REF] Mirzaali | Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly[END_REF]. As cortical bone is loaded longitudinally, it is characterized by a bilinear stress-strain response that distinguishes linearly elastic and linearly hardening regions at a given yield point, fracturing abruptly at less than 3% fracture strain. [START_REF] Ascenzi | The torsional properties of single selected osteons[END_REF] calculated stiffness using shear experiments resulting 4GPa and by traction (tension and compression) as 5 -12GPa. A pull-out and push-out test also revealed that the cement line has a lower interfacial strength than the osteonal lamellae.

A summary of the values reported in some studies for the elastic mechanical properties for long bones assessed at the macro scale is presented in Tab. 1. According to the literature , the average Young's modulus of human long cortical bones under tension is approximated between the range of 17 GPa and 24 GPa in the longitudinal direction, and between 11.5 GPa and 15.2 GPa in the radial direction. In addition, it was reported that bovine bone properties are close to human properties, where its elastic properties vary between 21.9 GPa and 30.3 GPa in the longitudinal direction, and between 11.6 GPa and 17.3 GPa in the radial direction [START_REF] Morgan | Bone Mechanical Properties in Healthy and Diseased States[END_REF].

The trabecular tissue, as well, is considered to be linearly elastic material and the yield point is defined by a 0.2% offset method [START_REF] Birnbaum | Material properties of trabecular bone structures[END_REF]. The density of trabecular bone can be measured using several different methods. The ratio of mineralized tissue content to volume of bone of interest is defined as bone volumetric mineral density (vBMD). Alternatively, volume fraction can be defined as the ratio of the volume of mineralized tissue to the volume of the sample, or, equivalently, as one minus porosity. The vBMD of human trabecular bone ranges from 0.058 -0.263g/cm 3 , whereas the vBMD of human cortical bone ranges from 0.406 -1.018g/cm 3 . The variations in density depend on the anatomical region of the bone and the measurement and calculation technique used [START_REF] Liu | Bone Density, Geometry, Microstructure, and Stiffness: Relationships Between Peripheral and Central Skeletal Sites Assessed by DXA, HR-pQCT, and cQCT in Premenopausal Women[END_REF]. In the primary compression group of the femoral neck, the trabecular bone accounts for 60% of the total volume [START_REF] Morgan | Dependence of yield strain of human trabecular bone on anatomic site[END_REF]. Trabecular bone can exhibit considerable spatial diversity in terms of density and structure, which in turn can result in wide variability in apparent elastic modulus and strength properties. The human trabecular modulus of elasticity ranges broadly from 10 to 3, 000 MPa, while strength, which is linearly correlated with modulus of elasticity, ranges from 0.1 to 30 MPa [START_REF] Morgan | Dependence of yield strain of human trabecular bone on anatomic site[END_REF]. Like cortical bone, trabecular bone exhibits the highest value in compression rather than in tension, but has the lowest value in shear [START_REF] Yeni | The dependence between the strength and stiffness of cancellous and cortical bone tissue for tension and compression: Extension of a unifying principle[END_REF].

There are few studies in the literature on the dynamic response of bone at the macro level, though bone is a time-dependent biological material. Some studies reported stress, strain and strain-rate analyses at different test velocities [START_REF] Mcelhaney | Dynamic response of bone and muscle tissue[END_REF]. McElhaney [START_REF] Mcelhaney | Dynamic response of bone and muscle tissue[END_REF] showed, using an air-gun testing machine, that the mechanical properties of bone in compression depend on the rate of deformation and the critical velocity is detected at a strain rate of 1s -1 . This method is used to apply constant compression loads with a strain rate up to 4000s -1 . An increasing in the elastic modulus from 15.1GPa to 29.5GPa was reported with the increase in strain rate from 0.001s -1 to 300s -1 . Another method to measure the dynamic mechanical properties of the femoral cortical bone is using Hopkinson bar stress technique by which the measured Young's modulus (19.9 GPa) in dynamic conditions (ε = 100s -1 ) is 23% higher than the average Young's modulus (16.2 GPa) in static conditions [START_REF] Katsamanis | Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique[END_REF]. Also, Halldin et al. [START_REF] Halldin | On a Constitutive Material Model to Capture Time Dependent Behavior of Cortical Bone[END_REF] measured the behavior of anisotropic cortical bone in tension at a range of strain rate between 0.01s -1 and 200s -1 , where they found that at a strain rate of 0.1s -1 , bone has the maximum energy absorption capability.

Another reported dynamic method is based on ultrasound technique, a non destructive test and preserves the bone structure. It is performed with different ultrasound modes by varying the wave frequency (from kHz to MHz) and the propagation media. One of its main advantages is that the mechanical test can be performed in different directions within the same bone sample [START_REF] Bensamoun | Spatial distribution of acoustic and elastic properties of human femoral cortical bone[END_REF]. This technique is performed either by the reflection technique or by the transmission technique, where in the latter the ultrasound beam propagates through the bone interior and analyzes the entire bone volume, whereas in the reflection technique the bone surface is studied only [START_REF] Antich | Measurement of mechanical properties of bone material in vitro by ultrasound reflection: Methodology and comparison with ultrasound transmission[END_REF]. Therefore, the mass and structural density of the bone specimen affect the transmission technique rather than the reflection.

Reference

Bone

Mechanical properties of bones using micro and nanoscale tests

At the microstructure level, nanoindentation, micro/nanoscratch tests and micromechanical tests were processed on micropillars with a focused ion beam or femtosecond laser to explore the micro properties of the bone tissue. Nanoindentation is the most frequently used technique to characterize the local micromechanical properties, computed by the elastic-plastic Oliver-Pharr mechanical method [START_REF] Ma | Nanoscale mechanisms in age-related hip-fractures[END_REF]. The elastic moduli of human femoral osteonal and interstitial lamellae measured by nanoindentation, under dry conditions in longitudinal direction, are between the ranges of 16.1 -25.8 GPa and 15.1 -26.1 GPa respectively, and are about 45% lower in the transverse direction [START_REF] Franzoso | Erratum: "Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation[END_REF], [START_REF] Harun | Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue[END_REF]. The hardness was also detected to be between 0.30 and 0.65 GPa for the osteonal zone and between 0.51 and 0.8 GPa for the lamelar bone. However, compression tests on micropillars show that both strength and ductility of cortical tissue are higher at the microscale than at the macroscale [START_REF] Diab | Morphology, localization and accumulation of in vivo microdamage in human cortical bone[END_REF]. Casari et al. [START_REF] Casari | Microtensile properties and failure mechanisms of cortical bone at the lamellar level[END_REF] reported that the cortical bone strength at the lamellar level is affected by the orientation of the osteonal fibers of about ±30°, and the specimens showed highly anisotropic response compared to the macroscale under microtensile loading. Preliminary microscale fracture toughness values are comparable to those measured at the macroscale. The mechanical properties of cortical bone focused largely on porosity and mineralization. Cortical porosity is negatively correlated with elastic modulus, ultimate compressive stress, and fracture toughness [START_REF] Roy | Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone[END_REF]. Changes in porosity account for more than 75% of the variation in cortical bone strength. At the microstructural level of trabecular bone, the anisotropy is also found in the elastic modulus and strength [START_REF] Odgaard | Fabric and elastic principal directions of cancellous bone are closely related[END_REF]). However, the fracture toughness of trabecular bone has not been well studied because the porous and spatially heterogeneous microstructure don't meet the requirements for a fracture toughness test. Nevertheless, the cyclic compressive loading of trabecular bone, even at low loading rates, leads to the loss in stiffness and strength, in addition to the accumulation of residual strain [START_REF] Cook | The fracture toughness of cancellous bone[END_REF].

Concerning the viscoelastic response to detect the time-dependant properties of bone at the micro level, Oliver-Pharr mechanical method exhibited significant miscalculations. Therefore, researchers tended to use other methods to consider the effects of strain rate on the mechanical response of bone. The visco-elasticplastic (VEP) model and creep analysis were used to reveal the viscoelastic properties of bone at the microscale. In the former model, three extensive quadratic elements (viscous, elastic, and plastic) are used in series to create a time-dependent indentation model. In creep analysis, the usual method is to apply a constant load to . According to the data reported in Tab. 2, the mechanical response of bone depends on the loading direction, and the variations in the mechanical properties are due to the hydration state and the indentation zone (whether within the osteons or the interstitial lamellae). However, unlike the macro mechanical properties, small variations were found between cortical and cancellous bone at the microscale and this is due to the decrease in local porosity [START_REF] Ovidiu | THE QUALITY OF TRABECULAR BONE AS-SESSED USING CONE-BEAM COMPUTED TOMOGRAPHY[END_REF].

Factors affecting bone properties

Evaluating the mechanical properties of bone remains a challenge because bone qualities vary widely from species to species, depending on bone mass, mass distribution and material properties in addition to age, gender and diseases. The determined mechanical properties of bone vary according to different loading conditions, including loading types, loading rates, and boundary conditions. These results are inconsistent due to various intrinsic and extrinsic factors.

Intrinsic factors

The mechanical properties of bone depend on the total mass of the specimen, the geometric distribution of the mass and the material properties. Therefore, bone tissue can be strengthened by increasing the total mass or distributing the mass of the bone to locations where subjected to loads or by improving the material properties of the constituent tissue. As an example, some animal models have reduced material properties of their bone tissue compared to others, but its defined structural geometry makes the structural properties comparable and with reduced risk of fracture [START_REF]Adaptation of mouse skeletal muscle to a novel functional overload test: Changes in myosin heavy chains and SERCA and physiological consequences[END_REF], [START_REF] Bonadio | A murine skeletal adaptation that significantly increases cortical bone mechanical properties. Implications for human skeletal fragility[END_REF]. Cortical bone mass can be measured directly from the cross-sectional area, whereas cancellous bone is more complex and since it is spatially varying, its mass is measured in small homogeneous volumes of tissue at micro or nano level. Bone mass is usually measured as bone mineral content and it is determined through several in-vivo imaging technique such as QCT [START_REF] Luo | Bone Density and Mechanical Property[END_REF]. It is quantified including the bulk porosity for the cancellous bone by the apparent density, the mass of the bone tissue present in the total volume of the specimen. It can explain the 60% to 85% of the variability in the compression apparent stiffness measured experimentally [START_REF] Morgan | Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site[END_REF], [START_REF] Luo | Bone Density and Mechanical Property[END_REF]. According to literature, small variations in the bone mass have large variations in bone strength and elastic modulus due to the squared power law strength-density relationship and power law modulus-density relationship with exponent between 2 and 3 respectively [START_REF] Morgan | Trabecular Bone Modulus-Density Relationships Depend on Anatomic Site[END_REF], [START_REF] Rietbergen | Elastic Constants of Cancellous Bone[END_REF], [START_REF] Moshage | Elastic modulus and its relation to apparent mineral density in juvenile equine bones of the lower limb[END_REF]. However, measures of the bone mass take only the total bone tissue quantity and doesn't reflect the localisation of this tissue. Hence, as for engineering composite materials, same density materials may differ in their mechanical properties due to different parameters and structures at the micro level, e.g. the orientation of fibers, the amount non-collagenous and collagenous proteins, the density gradient of the Haversian canals and geometric parameters. The cross-sectional area, moments of inertia, and cross-sectional modulus are the geometric parameters that asses the geometric distribution of the bone material and modify its mechanical behavior under different types of loading. The effect of the geometric distribution of the bone mass on the section modulus and the whole bone strength -Adapted from [START_REF] Van Der Meulen | Understanding bone strength: Size isn't everything[END_REF] In particular, for bending and torsional loads, the strength of the material is higher when the tissue is further away from the bending plane or the torsional axis. Assuming that the structures in Fig. 2 consist of the same material, the section modulus increases exponentially with external diameter since the periosteal surface of the solid cylinder resist the bending load more than the central core [START_REF] Van Der Meulen | Understanding bone strength: Size isn't everything[END_REF]. A solid cylinder (test model 1) with the same periosteal diameter as the hollow cylinder (reference model) has 80% greater surface area, but only 25% greater bending strength. However, a solid cylinder of test model 2, which has only 7% less periosteal diameter compared to the reference model, has equivalent section modulus and thus equivalent strength. In contrast, the flexural strength of test model 3, a hollow cylinder, is 70% higher than that of the reference model when the bone mass is increased by 25% to the periosteal diameter. In cancellous bone, the homogeneous micro-volume taken from the sample showed that the sites with the same mineral density but different architectures and geometric distribution exhibited differences in strength and stiffness up to 50% [START_REF] Birnbaum | Material properties of trabecular bone structures[END_REF]. In addition, cancellous bone often shows different mechanical behavior when loading with different direction. For instance, in human vertebrae, the alignment of the trabeculae along the axis of the spine makes the bone specimen, when loaded along superior-inferior axis, two times stronger than when loaded along the anterior-posterior or right-left direction. Another determinant of the bone mechanical properties is the properties of the constituent material.

Naturally, cortical and cancellous bone consist of laminar tissue but with different microstructure organizations. The extracellular matrix of the bone primarly constitutes of an organic phase of collagen type I protein which can undergo various molecular level biochemical modifications such as intra-or inter-molecular cross-linking of enzymatic pathway. The impaired formation of enzymatic cross-links contributes directly to the decrease in bone strength and to the postyield deformation of the tissue [START_REF] Vashishth | Influence of nonenzymatic glycation on biomechanical properties of cortical bone[END_REF], [START_REF] Robins | Age-related changes in collagen: The identification of reducible lysinecarbohydrate condensation products[END_REF]. Bone tissue also constitutes of an inorganic phase of crystalline mineral where it contributes directly to the material stiffness at the nano level and therefore to the whole bone stiffness at the macro level [START_REF] Hasegawa | Contribution of collagen and mineral to the elastic anisotropy of bone[END_REF], [START_REF] Tsou | Ash Content Modulation of Torsionally Derived Effective Material Properties in Cortical Mouse Bone[END_REF]. Although the mineral content is not preserved where it is affected by the age, the cyclic loading due to daily activities and the temperature [START_REF] Sroga | Effects of Bone Matrix Proteins on Fracture and Fragility in Osteoporosis[END_REF], [START_REF] Ma | Mechanical properties of cortical bones related to temperature and orientation of Haversian canals[END_REF], [START_REF] Bumrerraj | Scanning Acoustic Microscopy Study of Human Cortical and Trabecular Bone[END_REF]. Microdamage induced by fatigue may be more likely to cause fractures near cortical pores than in areas of high mineral content. However, increased mineral content, as may occur with long-term therapy with bisphosphonates for the treatment of osteoporosis, is associated with fracture strength [START_REF] Lloyd | Atypical fracture with long-term bisphosphonate therapy is associated with altered cortical composition and reduced fracture resistance[END_REF].

Extrinsic factors

There are also external factors that contribute to the wide variability in bone mechanical properties. One of the time-dependent factor is the age of the living organisms. In addition to that, certain pathologies, gender and temperature alter the mechanical behavior of bone. Understanding these factors and their effects on the bone strength and stiffness from the nano level to the micro level is merely the first step to minimize fracture risk due to drilling applications. Material strengths and stiffness of bone decrease with age in both women and men. From the third decade of life, the strength of cortical bone in tension and compression decreases by about 2% per decade, while fracture toughness decreases by about 4% [START_REF] Sroga | Effects of Bone Matrix Proteins on Fracture and Fragility in Osteoporosis[END_REF]. In addition, under impact loading, the energy required to fracture a cortical bone specimen decreases by threefold from age 3 to 90 years [START_REF] Panagiotopoulos | Impact energy absorption by specimens from the upper end of the human femur[END_REF]. These deteriorated mechanical properties are due to the increased probability of being infected by osteoporosis, the increase in porosity and the susceptibility to fractures with aging [START_REF] Mccalden | Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure[END_REF], [START_REF] Ross | Pre-existing fractures and bone mass predict vertebral fracture incidence in women[END_REF].

Moreover, human trabecular bone also reveals a decrease in material properties with aging, as a result of a drop in the apparent density values. The ash density of the vertebral trabecula decreases by about 50% from the age of 20 to 80 years and also the compressive modulus, ultimate stress, and energy to failure decrease approximately 75% to 90% [START_REF] Tsou | Ash Content Modulation of Torsionally Derived Effective Material Properties in Cortical Mouse Bone[END_REF]. Not only does the density of bone tissue decrease with age, but also the microstructure undergoes modifications. For example, the osteonal density increases with age, as an indication of the presence of more small osteons in specific tissue area and therefore the density of the osteon cement lines increases. Hence, this density gradient affects the initiation of the microcrack and expands the direction of the fracture surface [START_REF] Ma | Mechanical properties of cortical bones related to temperature and orientation of Haversian canals[END_REF], [START_REF] Diab | Morphology, localization and accumulation of in vivo microdamage in human cortical bone[END_REF]. Therefore, the trabecular bone is weaker with age due to the perforation of the trabecular plates resulting in less connected thinner rod-like trabeculae. Although aging is an external factor, it is attributed to the constituent of the tissue such as the amount of collageneous and non-collagenous proteins. For example, the accumulation of AGEs changes microdamage production and morphology resulting in producing more fragile bones in olders. In addition, the orientation and spatial distribution of the collagenous fibers affect bone toughness. Furthermore, the non-collagenous proteins content are altered through age where up to fourfold non-collagenous quantity is found in younger bone tissue compared to older one [START_REF] Ascenzi | Non-osteoporotic women with low-trauma fracture present altered birefringence in cortical bone[END_REF], [START_REF] Van Der Meulen | Understanding bone strength: Size isn't everything[END_REF].

However, the loss and fragility in bone tissue with aging differ between genders. In woman, the volume fraction is decreased due to the trabecular loss, whereas in men, the decreased of volume fraction is referred to trabecular thinning. A study shows that for trabecular thinning (in men), a 10% drop in bone density results in 20% bone strength reduction. On the other hand, for trabecular loss (in women), bone strength is decreased by 70%, and 77% for both trabecular thinning and loss under the same percent of bone density reduction [START_REF] Stauber | Age-related changes in trabecular bone microstructures: Global and local morphometry[END_REF]. Hence, the mechanism of loss bone in women is more detrimental to the mechanical behavior even if the loss amount is restored by trabecular thickening. It is found in the literature that the cortical thickness of long bone is the same for both women and men with aging, though, men have greater section modulus due to the greater periosteal expansion resulting in more resistance to the applied loads. Therefore, women long bones are more susceptible to fracture due to the inability to compensate the periosteal apposition. Researchers have examined the microstructural changes in the cortical and trabecular compartments of the peripheral skeleton using high-resolution CT imaging. In men, the cortical area is nearly the same and the moment of inertia increases as they age. Whereas in women both of them decrease and thus osteoporosis puts them at the risk of fractures as they age [START_REF] Gold | Anatomy, Bony Pelvis and Lower Limb[END_REF].

In addition, many diseases affect the structure and material properties of bone tissue and therefore, they are detrimental to the mechanical behavior of the whole bone. According to the French Society of Rheumatology (SFR), around 145000 suffer from bone fracture due to diseases. Osteoporosis, for example, is a pathological state where bone density dropped below the average density of its age, which leads to the more fragile and weak bones as it increases the risk to break [START_REF] Morgan | Bone Mechanical Properties in Healthy and Diseased States[END_REF]. This disease leads also to change in the material constituent. During remodeling period with rapid alterations in bone density, mineralization is shifted towards hypomineralization (lower densities). For cancellous bone, several tests were performed at every level of bone hierarchical structure to determine diseases-related changes in mechanical properties and it was found that the trabecular number and the volume fraction deteriorated.

Thermomechanical conditions in bone drilling

Besides the mechanical properties, it is also difficult to asses the thermal properties of bone due to its wide quality variability. The thermal effect of bone drilling leads to an increase in temperature. This effect is crucial for bone injury, as it can lead to necrosis or irreversible loss of bone cells, resulting in infection and reduced mechanical strength. Bone drilling behavior is determined by several factors, including the cutting tools used, the machining conditions (feed rate and spindle speed), and the mechanical and thermal properties of bones. Drilling performance is evaluated by cutting forces (thrust and torque) and the resulting temperatures.

Bone thermal conditions in drilling

Bone exposed strong compressive resistances, but it is strongly affected by the loading direction and the fibrils' orientation. The compressive properties of cortical bone are also temperature dependent. Ma et al. [START_REF] Ma | Mechanical properties of cortical bones related to temperature and orientation of Haversian canals[END_REF] showed that the compressive properties of fresh tibial porcine cortical bone immersed in a 38 °C thermostat exhibit relatively low strength compared to specimens presented at room temperature. Strength attenuation is associated with temperature sensitivity of organic matter strength within cortical bone. Therefore, surgical bone drilling that generates high thermal and mechanical loads changes bone properties, and thus compromises bone healing and implant reliability. Applied cutting forces induce plastic deformation within the workpiece material, resulting in shear deformation and chip formation along the shear plane. A part of this mechanical work is converted in thermal work. The high heat generated during surgical drilling, resulting in excessively high tissue temperatures, can lead to thermal osteonecrosis, the phenomenon of bone death. Oblique drilling, processing parameters, drill geometry, and bone properties are factors that affect the maximum temperature, duration of overheating, and the thrust force.

Most of the drilling procedures discussed in the literature were examined at room temperature and under dry conditions. Bone drilling experiments, with different conditions, were performed on bone species to study the properties of the bone during the drilling process to avoid bone damage and failure. They investigated the relationship between drill-bit sizes, drill speed, bone stiffness, and triaxial compressive strength. The authors found that drill strength was directly correlated and proportional to bone triaxial compressive strength Karalis T [START_REF] Galanos | Research on the mechanical impedance of human bone by a drilling test[END_REF]. However, no linear correlations were found between hardness and drill strength. Robles Linares Alvelais et al. [START_REF] Robles | Machining-induced thermal damage in cortical bone: Necrosis and micro-mechanical integrity[END_REF] found different damage degrees induced by drilling in vitro bovine cortical bone. They performed micro-pillar compression tests to identify changes in properties and failure modes caused by drilling, and found that lower bone modulus (-42%) and strength (-41%) were revealed near the machined surface, in addition to brittle behavior, at high temperature. On the contrary, no damage was revealed at the bulk bone and pristine properties with ductile behavior were detected. Additionally, histology evaluated necrosis, revealing that the weaker and brittle bone layer accounts for more than three times as much area as the necrotic layer.

Hillerya and Shuaibb [START_REF] Hillerya | Temperature effects in the drilling of human and bovine bone[END_REF] studied the effects of temperature on the physical aspects of bone when drilling human and bovine bones. They found that temperature increased with increasing drilling depth. A higher temperature is observed when drilling bovine bone than human bone. This is because bovine bone has mean cortical thickness (7 to 9mm) greater than that of the human one (2 to 3mm), where increasing cortical thickness is positively correlated with increasing maximal mean temperature. Feldmann et al. [START_REF] Feldmann | The thermal conductivity of cortical and cancellous bone[END_REF] conducted experimental studies to analyze the thermal conductivity of bovine cancellous bone and human cortical bone. Cortical samples were tested using a custom steady-state and a widely used transient experimental setup, and the results were compared. Measurements were performed using micro finite elements (µFE) and microcomputed tomography (µCT ). The thermal conductivity of bovine cortical bone was found to be 0.64 ± 0.04 W/mK, while that of human cortical bone was 0.68 ± 0.01 W/mK. Shihao et al. [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF] also established and analyzed a pseudo-3D maximum temperature distribution, a temperature history at different distances, and a time series distribution of temperature at different times. The temperature distribution did not exhibit anisotropy under the different directions, and maximum temperature and exposure duration showed differences in the three different directions (parallel, perpendicular and transverse) due to the different removal mechanisms. The maximum temperature and exposure duration, in the vicinity of the hole wall, are mainly affected by the drill lip-cutting and margin friction stages. In addition, in inclined drilling, the temperature distribution showed a strong directionality due to the asymmetric friction caused by lateral forces. While the exact temperature at which necrosis occurs is not yet detected, the temperature of 47°C for a duration of 60s is considered a consensus threshold temperature [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF], [START_REF] Samarasinghe | Surgical Bone Drilling: A Review[END_REF], [START_REF] Ra Eriksson | Assessment of bone viability after heat trauma: a histological, histochemical and vital microscopic study in the rabbit[END_REF]. However, Samarasinghe et al. [START_REF] Samarasinghe | Surgical Bone Drilling: A Review[END_REF] showed that the threshold of 55°C for 30 seconds had a higher probability of thermal necrosis than 47°C for 60 seconds.

Cutting parameters for bone drilling

Numerous studies have focused on understanding the process behavior by examining the effects of spindle speed, feed rate, and applied forces on bone temperature. Samarasinghe et al. [START_REF] Samarasinghe | Temperature and force generation in surgical bone drilling[END_REF] found that increasing spindle speed from 1000 rpm to 2500 rpm increases temperature, and within the same range of cutting speed, increasing feed rate from 30 mm/min to 60 mm/min decreases temperature, while Alam et al. [START_REF] Alam | In-vitro experimental analysis and numerical study of temperature in bone drilling[END_REF] found that the temperature increases with increasing both, the spindle speed (from 1000 rpm to 3000 rpm) and feed rate (from 30 mm/min to 70 mm/min at constant cutting speed of 2000 rpm). Yang et al. [START_REF] Yang | Drilling Force and Temperature of Bone by Surgical Drill[END_REF] performed high-speed drilling on porcine bones to investigate the drilling temperature and axial force under different drilling parameters. The process variables were rotational speed, feed rate, and drill geometry. A newly developed drill-bit with a W-shape and three cutting tips at the drill tip was used. The results were compared with the SS drill commonly used in hospitals. It was found that feed rate and drilling speed have the greatest effect on the drilling force and temperature generated. The drilling speed varied with the drilling depth. The newly developed surgical drill-bit produced lower drilling force and temperature (less than 47°C) compared to SS and carbide drills.

Lee, Ozdoganlar, and Rabin [START_REF] Lee | An experimental investigation on thermal exposure during bone drilling[END_REF] performed drilling tests on bovine cortical bone and developed a mechanistic model to predict drilling torque and feed force. They performed a calibration test to investigate the variations of specific energies with cutting speed, feed rate, and radial position. It was found that torque increased at higher feed rates and higher rotational speeds due to chip evacuation force and friction between the drill rim and the hole. Karaca, Aksakal, and Kom [START_REF] Karaca | Influence of orthopaedic drilling parameters on temperature and histopathology of bovine tibia: An in vitro study[END_REF] conducted several experiments on male and female tibias to investigate the effect of sex, mineral density, drill speed and tool-tip angle, drilling forces, and feed on heat generation during orthopeadic drilling. It was found that the temperature increased directly with drilling speed, while it decreased at high feed rate and drilling forces. Drilling speed was found to be the most important process variable. They also found that temperature was higher in female bovine tibia than in male tibia. In addition, the effects of different drilling speeds on strain generation were studied [START_REF] Fonseca | Effect of drill speed on the strain distribution during drilling of bovine and human bones[END_REF]. They also studied the temperature distribution on the drill surface when drilling tibiae from human cadavers and femora from cattle. It was found that both bone strain and drill temperature were higher when drilling bovine femora compared to human tibial heads as drilling speeds increased.

Udiljak, Ciglar, and Skoric [START_REF] Udiljak | Investigation into bone drilling and thermal bone necrosis[END_REF] investigated the possibilities of high-speed drilling to avoid thermal bone necrosis, and it was found that cutting speed has no effect on axial drilling force but a significant effect on increasing bone drilling temperature. On the contrary, the increase in feed rate per tooth increases the axial drilling force but reduces machining time and friction duration. Therefore high feed rate results in lower bone drilling temperature. They recommended minimum cutting speed value of 6 m/min and high drilling feed rate at 0.1 mm/tooth for temperature reduction in classic drilling. Shihao et al. [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF] showed that the maximum temperature exhibited a declining trend with the feed rate but it increased with the increase in spindle rate. Whereas the exposure duration presented a declining trend with both the feed rate and the spindle speed. Similarly, Samarasinghe et al. [START_REF] Samarasinghe | Surgical Bone Drilling: A Review[END_REF] showed an opposite behavior of spindle speed and feed rate on temperature and force. Higher spindle speeds increased temperature but minimized forces, while higher feed rates decreased temperature but maximized forces. They also investigated the effect of the processing parameters on chip formation where they found that bone chips changed from a continuous spiral to a powdery shape as the spindle speed increased. In addition, Eriksson, Albrektsson, and Magnusson [START_REF] Ra Eriksson | Assessment of bone viability after heat trauma: a histological, histochemical and vital microscopic study in the rabbit[END_REF] performed drilling experiments on canine, human, and rabbit femoral cortex to measure temperature by attaching a Richards plate to stabilize a pertrochanteric fracture with a twist drill (θ = 3mm, tip angle = 118°, helix angle= 30°). The authors observed that at a drilling spindle speed of 20, 000 rpm, the measured temperatures in rabbits, canines, and humans, were 40°C, 56°C, and 89°C, respectively. Heydari et al. [START_REF] Heydari | Analytical and experimental study of effective parameters on process temperature during cortical bone drilling[END_REF] performed drilling studies on bovine bone and analyzed the drilling temperature using analytical models. It is reported that the process temperature increases with increasing drilling speed. The temperature also increases at low feed rates due to the longer contact time between bone and tool, and at high feed rates due to the high forces and friction.

Drilling tool specifications

Drill geometry, such as point angle, helix angle, drill diameter and affect drilling performance and bone final temperature [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF]. The entire heat generated during drilling increases with the increase in drill-bit diameter and thus temperature increases [START_REF] Lee | A new thermal model for bone drilling with applications to orthopaedic surgery[END_REF], [START_REF] Augustin | Thermal osteonecrosis and bone drilling parameters revisited[END_REF]. On the contrary, Shihao et al. [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF] found a non-monotonic relationship between the drill-bit diameter and the temperature elevation. Obviously, researchers showed conflicting observations on drill-bit diameter, temperature and thrust force [START_REF] Samarasinghe | Temperature and force generation in surgical bone drilling[END_REF].

For a drill diameter of 2.5 mm, the lowest process temperature (35.6°C) was obtained when drilling at a spindle speed and feed rate of 500 rpm and 30 mm/min respectively. In addition, Shihao et al. [START_REF] Shihao | Cortical bone drilling: A time series experimental analysis of thermal characteristics[END_REF] performed drilling experiments on fresh bovine femurs with different drill-bit diameters (2.5mm, 3.2mm, 4.2mm) and found that the highest temperature elevation (82.3°C), achieved by the 3.2mm drill bit, was approximately 10 and 21°C higher than those of the 2.5 and 4.2mm drill bits, where the highest temperature achieved did not exceed 47°C. By increasing the drill-bit diameter, chips can be evacuated more efficiently and the drill bit's heat capacity increases, reducing heat transfer to the surrounding tissues. But in this study, a non-monotonic relationship between the temperature elevation and drill bit diameter was detected.

Natali, Ingle, and Dowell [START_REF] Natali | Orthopaedic bone drills-can they be improved? Temperature changes near the drilling face[END_REF] performed an experiment on fresh human tibial cadavers to study different commercially available drills (θ = 2.5mm). Different drill-bits of same diameter (2.5 mm) were used, such as a used standard orthopaedic tool, a new standard orthopaedic drill tool, a standard orthopaedic bit with blocked flutes, a HSS tool (High speed steel) twist tool, and a HSS drill-bit with tip angles of 90 and 118°. The results showed that a split-point bit (tip angle=118°) of HSS caused the least thermal damage to nearby bone and also reduced the penetration force by half. Ultimately, the authors suggested using split-point drill-bit with a point angle of 118°and a quick helix with an additional parabolic flute to reduce the force required and therefore reduce thermal damage in orthopaedics. Similarly, Udiljak, Ciglar, and Skoric [START_REF] Udiljak | Investigation into bone drilling and thermal bone necrosis[END_REF] studied the effect of drill geometry on temperature and axial drilling force. They found that the axial drilling force is strongly influenced by the drill tip angle but the values of drill tip angle do not affect the drilling temperature. The axial drilling force is minimized when the drill tip angle is kept to a minimum (80°). They also concluded that in conventional bone drilling, a two-phase drill would be the suitable option to avoid temperature rise in the bone.

Conclusion

Bone drilling is essential in orthopaedic surgery to repair broken bones and replace damaged bones. High mechanical stress and temperature during drilling affect postoperative recovery and healing. In this review, extensive research has been conducted to understand the mechanical and thermal properties of bone. First, the structure and functions of bone were explained in detail. This was followed by a summary of the methods and results for multiscale mechanical testing of the hierarchical structure of bone and the extrinsic and intrinsic factors that contribute to the wide variability in the mechanical properties of whole bone. The variability of the macro-and micromechanical properties of the bone is also due to the test conditions, such as the specimen restraint, the type of loading, the loading rate, and the boundary conditions. The complexity of the bone structure and its anisotropy give it a high load capacity and resistance to compression.However, certain traumas or severe impacts may result in bone fractures and surgical procedures. In surgical bone drilling, the mechanical properties of the bone change, and the excessive rise in temperature leads to osteonecrosis. The reasons for the temperature and force increase are due to the drill specifications, machining parameters, and bone properties, as well as the complex interaction of the drilling environment. For better prediction and control of heat in surgical bone drilling, all these factors should be further investigated so that a parametric model can be developed and thus bone damage and osteonecrosis can be avoided. This comprehensive analysis of mechanical and thermal behavior under certain drilling conditions would lead to additional contributions toward identifying favorable conditions that are optimal for certain surgical conditions and thus improve the chance of successful surgery.

Figure 1 :

 1 Figure1: The five hierarchical structural levels in cortical bone: from the macroscale of cortical and cancellous bones to the nanoscale of collagen molecules -Adapted from[START_REF] Liu | Hierarchical Structures of Bone and Bioinspired Bone Tissue Engineering[END_REF]

Table 1 :

 1 Some literature review about bone mechanical properties assessed by several mechanical tests and ultrasound

			specie	Anatomical	Test	Loading	Elastic Modulus
				region		direction	(GPa)
	Reilly	and	Human	Femur	Compression/	Longitudinal/	E long = 17
	Burstein [38]			tension	radial/	E rad = 11.5
						transversal	E trans = 11.5
	Bayraktar et al.	Human	Rib	Compression	Longitudinal	E long = 12.51
	[52]
	Bayraktar et al.	Human	Femur	Compression	Longitudinal	E long = 17.04
	[52]
	Mirzaali et al.	Human	Femur	Tension/	Longitudinal	E tens = 18.16 ± 1.88
	[41]				compression/		E comp = 18.97 ± 1.84
					torsion		G tors = 6.07 ± 0.57
	Lipson	and	Bovine	Femur	Ultrasound	Longitudinal/	E long = 24.7 ± 1.0
	Katz [53]					radial	E rad = 16.7 ± 0.5
	Wang et al.	Bovine	Femur	Compression	Longitudinal	E long = 12.5 ± 1.9
	[54]


Siaka Sangare

Malinké

Dioula

Bambara Inverse Copular sentences

Bambara or bámanakan is a Niger-Congo language from the Mande family spoken mainly in Mali with its closer

Word-order

Bambara is a head final language; with a strict S-Part-O-V-(X) word order. Verbal particles are obligatory; they appear between S and O. V is final, but can be followed by oblique complements and adjuncts.

(1) Fanta bɛ ́ jɛ gɛ nyímin súgu kɔ ńɔ Fanta Prog fish eat market in 'Fanta is eating fish at the market.'

The syntax of intransitive predicates differs slightly, especially in the past. The same S-V-(X) order is exhibited, but the verbal particle is replaced in this case by an affixal TAM marker (the suffix -na/-ra/-la depending on verbal morphology and regional ) dialectal variations):

(2) Sitan ní Hawa nàna Sitan Conj Hawa come-Acc 'Sitan and Hawa came'

A tonal language

Bambara is a tonal language that distinguishes high, low and increasing tones. Tones have a lexical function (3),

(3) a. bá (river) c. bàn (refuse) e. fúru (mariage) g.jóli (wound) b. bà (goat) d. bán (die) f. fùru (stomach) h.jòli (blood)

as well as a grammatical function in the expression of definiteness ( 9)-( 10) [START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF] and Vydrin (2019:32-36)): definiteness is marked by a low tone [ ̀] added at the end of the nominal phrase (leading to possible modifications of the original lexical tones):

(4) Mùsò tɛ ́ yàn woman Cop-Neg here 'There is no woman in here.'

(5) Mùsó ̀ tɛ ́ yàn woman.Art Cop-Neg here 'The woman is not here.' This position is not yet a univocal agreement to the Bambara speaking community and remains a field of investigation.

Copular system

Bambara exhibits a multi-copular system that comprises four copulas [START_REF] Pustet | Copulas: Universals in the Categorization of the Lexicon[END_REF][START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF]: ká, bɛ ́, dòn and yé. Among the four copulative sentences, only yé-sentences allow for inversion.

Past descriptions [START_REF] Vydrin | Non-Verbal Predication and Copulas in Three Mande Languages[END_REF], 2020[START_REF] Pustet | Copulas: Universals in the Categorization of the Lexicon[END_REF][START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF][START_REF] Sauvant | Grammaire bambara[END_REF] • ká copula is used in predicational sentences:

(6) Búuru ká kálan bread Cop warm 'The bread is warm.'

• bɛ ́is used in locative and existential sentences (7) Oumou bá bɛ ́ só kɔ ńo

Oumou mother COP house in 'Oumou's mother is in the house' (locative) (8) Cɛ ẁ bɛ ́ yèn mùsow fàna man.pl COP there woman.pl also 'There are men but also women.' (existential)

• dòn is used in 'presentational' sentences (in the terminology used by [START_REF] Sauvant | Grammaire bambara[END_REF][START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF]; they are similar to Higgins' identificational sentences. In these sentences, however, and contrary to English, there is no deictic subject: the copula appears in final position and is directly preceded by the element that is being identified:

(9) M' fà dòn 1sg mother COP 'It is my mother.' / 'Here is my mother.'

• yé copula is used in 'equative' sentences [START_REF] Pustet | Copulas: Universals in the Categorization of the Lexicon[END_REF][START_REF] Vydrin | Non-Verbal Predication and Copulas in Three Mande Languages[END_REF], 2020[START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF]).

(10) Nìn yé námáasa yé this COP banana COP 'This is a banana' (Pustet 2003:23) (11) Jɛ kabaara ̀ fúrabulu ̀ yé náani yé Jɛ kabaara.ART leaf.ART EQU four PP 'Jɛkabaara (a monthly newspaper) has four pages' (litt. 'Jɛkabaara pages are four') (Vydrine, 2020:5) This paper focuses on yé…yé-sentences. Against the commonly accepted analysis, we will argue that yé…yé-sentences are not equatives and propose an analysis of canonical and inverse yé-sentences.

Copula and Verbal particle homophony

In Mande grammatical tradition [START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF], verbal particles are termed 'predicative markers' (PM); they express tense, aspect and mood.

(12) Ana ká dòn so Ana SUBJ enter house 'May Ana come home' (13) Fanta bɛ ́jɛ gɛ nyímin súgu kɔ ńɔ Fanta Prog fish eat market in 'Fanta is eating fish in the market.' (14) Tìle yé jɛ ǵɛ jà sun PAST fish dry 'The sun has dried the fish.'

Verbal particles are homophonous with the copulas (NB: There is no equivalent verbal particle for dòn.)

For some authors (e.g., [START_REF] Pustet | Copulas: Universals in the Categorization of the Lexicon[END_REF], there is no distinction between the verbal / non-verbal systems: copulas and verbal particles are the same grammatical items used with verbs and non-verbal predicates alike.

• In actuality, verbal particles and copulas are not the same grammatical items (cf., Sangare 2021):

-Their respective semantic contributions are not identical:

(15) Sara ká dòn só kɔ ńɔ Sara SUBJ enter house in 'May Sara come into the house now'

(16) Umu ká jàn Umu COP long 'Umu is tall' and not: 'May Umu be tall'

-TAM markers have positive and negative forms (like copulas do as well).

Negatives forms of TAM markers are not (always) identical to the negative form of the corresponding copula : Rosine PAST COP child good yé Rosine was a good child The complete study of the interaction between the four copulas and the TAM system is still under investigation.

yé…yé copular sentences

2.1-Two occurrences of yé Pustet (2003:23)

Against the equative analysis

The apparent symmetry in yé-sentences (two yé forms and the possibility of inversion) has led many researchers to assume that yé-sentences are equatives, ie. they express identity statements. [START_REF] Vydrin | Non-Verbal Predication and Copulas in Three Mande Languages[END_REF], 2020[START_REF] Pustet | Copulas: Universals in the Categorization of the Lexicon[END_REF], Dumestre 2003 and others) Arguments against this position:

➢ Interpretational problem

The meaning of yé-sentences is not that of an identity between two referential expressions. Not a single example in the literature can rightly be qualified as equative / identity. These sentences cannot mean We note that impossibility to realize plural is a property of predicates in general in Bambara (including verbs), suggesting again, that the post-copular expression is not a referential expression. NB: The plural marker .w always appears on the rightmost element in the DP:

(35) kálanden.w student.pl 'The students'

(36) kálanden nyùma sàba.w student good three Pl 'The three good student ➢ yé-sentences are not equatives; the post-copular expression is not referential.

Nominal predicates

Regarding the inventory of Bambara copulas, ká was said to be compatible with adjectives only and yé with nouns only (as early as [START_REF] Sauvant | Grammaire bambara[END_REF]. On the surface, however, Bambara seems to allow for certain adjectives in yé-sentences, and specifically adjectives derived in -man.

There are two classes of adjectives in Bambara: homorganic and heterorganic, or descriptively simplex and morphologically complex.

-Homorganic or simplex adjectives (e.g., nùgu (smooth), fɛ ǵɛn (light), súma (slow), bìlen (red)) are only compatible with ká copula.

(37) Jí ká kálan *ji yé kalan yé water hot 'The water is hot' -Heterorganic or complex adjectives are adjectives obtained by suffixation of a simplex adjective, for instance with the suffix -man. These (apparent) 2 adjectives are compatible with copula yé only, and not ká: -(38) Jíri yé sùrùman yé *jiri ká sùrùman tree COP short Foc 'The tree is short' There are reasons to believe that -man adjectives are in fact predicates inside a reduced relative clause. One argument comes from the copula; another argument comes from their contrastive interpretation (Acedo-Matellan & Roy in progress):

--man adjectives cannot take copula ká (39) Jíri ká súrun ≠ * Jíri ká sùrùnman Tree COP short 'The tree is short' -man adjectives in yé-sentences necessarily have a contrastive interpretation, where the subject is contrasted with a set of entities:

2 There exist also adjectivizing suffixes that attach to nouns -ma and verbs, -ta:

(40) 3-Topic-Focus structure

Introduction

Bambara yé-sentences (nominal copular sentences) allow for inversion. Inverse sentences are specificational sentences wherein the specificational subject is the topic and the complement the focus.

Question-test in Bambara

The unmarked way to ask the questions Who is John ? and Who is your best friend? is with the wh-expression after the copula and before yé2.

-"Who is John?"

3.3-Analysis of yé2

-yé2 is usually analyzed as the postposition yé [START_REF] Vydrin | Non-Verbal Predication and Copulas in Three Mande Languages[END_REF], 2020[START_REF] Dumestre | Grammaire fondamentale du bambara[END_REF]) -However, no one has provided empirical evidence beyond apparent homophony; but homophony within functional items is rampant in Bambara.

• Semantically, we note the absence of similarity with postposition yé (beneficiary, comitative, instrumental, etc...).

• Instead, we propose that yé2 is a marker of new information focus.

(54) N1 yé cop N2 yé FOCnew All yé-sentences, whether canonical or inverse, involve focalization.

Table 1

 1

	:	Copulas	positive form		negative form
			ká	/	mán
			bɛ ́/	tɛ ýé
				/	tɛ dòn
				/	tɛ verbal
		particles positive form	negative form
			ká	/	kàná
			bɛ ́/	tɛ ́4

  treats both occurrences of yé as a copula.We will come back to the analysis of the second yé, namely yé2, in section 3.3 This is not different from what we see in languages like English or French: *Blue is the table / *Bleue c'est la table. 'Inversable' expressions are not predicates; we analyze them as individual concepts[START_REF] Romero | Concealed questions and specificational subjects[END_REF], Heycock 2012, Roy 2022)

	tree Cop short		short Cop tree
	(20) Nìn yé 'the tree is small' nàmàsa yé
	this COP banana COP
	'This is a banana'	(Pustet 2003:23)
	However, only the first yé, namely yé1, is the actual copula in the sentence: only yé1
	changes to the negative form in a negative context: -In inverse sentences, yé1 remains the copula; this can be shown wiht the
	(21) Nìn negatives forms: yé / tɛ ́nàmàsa	yé/*tɛ this
	Cop NEG-Cop banana	yé
	'This is not a banana' (28) Né tɛ ́kàlàndèn yé		*Né yé kalanden te
	1sg NEG-COP student yé
	'I am a student'
	2.2-Inversion (29) Kàlàndèn tɛ ́né yé		*Kalanden yé ne te
	student NEG-COP 1Sg yé (22) John is the best candidate. The best candidate is John. 'The student is me'
	(25) Né yé kàlàndèn yé
	1sg COP student yé
	'I am a student'
	(26) Kàlàndèn yé né yé
	student COP 1Sg yé
	'The student is me'
	-yé-sentences are the only copular sentences that allow for inversion. In
	particular, true predicational sentences using the copula ká do not permit the
	raising of the predicate:
	(27) a. Jíri ká sùrun	b. *Sùrun ká jíri

•

[START_REF] Moro | The Raising of Predicates : Predicative Noun Phrases and the Theory of Clause Structure[END_REF]

: Predicate Inversion analysis: canonical and inverse copular sentences are derived by movement from the same underlying small clause (SC):

(23) John i is [ SC t i the culprit] = raising of the subject (24) The culprit i is [ SC John t i ] = raising of the predicate Bambara: yé-sentences allow for inversion:

[[X]] = [[Y]]

	-Specification
	(32) Kalanden yé Hawa yé
	Hawa Cop student YE
	'Hawa is a student'
	➢ Plural
	In yé-sentences the second nominal expression (i.e. post copular expression) is
	not pluralized even when the subject plural:
	(33) Né ní Umi yé kálanden yé
	1SG Conj Umi COP student yé
	'I and Umy are students.'
	(34) Né ní Umi	yé kálanden.(*w) yé
	1SG Conj Umi COP student.(*Pl) yé
	'I and Umy are the students.'
	-Identification
	(30) Nìn yé námáasa yé
	this COP banana YE
	'This is a banana'	(Pustet 2003:23)
	-Predication
	(31)Fanta kulibali yé muso hakilima yé
	fanta kulibali Cop woman intelligent YE
	'Fanta Kulibali is an intelligent woman' (Vydrin 2003)

Q= N1 yé jɔ ́n yé ?

	existence of a best friend together with his/her identity.
	-In this context the focus is not only on the identity of 'who' but also the
	existence or not of a best friend.
	-N2 is part of the new information focus.
	-importantly, the answer has to be in canonical order as well (N2 is new
	information focus)
	-The answer will be (45)
	(52) N'térifari yé Musa yé	→*not* (53)Musa yé n'terifari	yé
	1sg.friend.best COP Musa yé		Musa COP 1Sg friend.best yé
	'My best friend is Musa'		'Musa is my best friend'
	[A] (43) Musa yé jɔ ́n yé?
	Musa COP who yé
	'Who is Musa?'
	-We answer by :
	(44) Musa yé n' térifari yé		(45) N'térifari yé Musa yé
	Musa COP 1sg.best-friend yé	→*not*	1sg.best-friend COP Musa yé
	'Musa is my best friend.'		'My best friend is Musa'

➢ Conclusions: Bambara yé-sentences have a fixed information structure both in the canonical and the inverse orders: ○ Focus is always on DP2 DP1Cop DP2 FOCUS yé ➢ All nomical copular sentences in Bambara have the properties of inverse copular sentences in languages like English; and can potentially be analyzed by movement and focalization, along the lines of Shlonsky & Rizzi (2018) and

[START_REF] Isabelle | Aspects of the syntax of ce in French copular sentences[END_REF]

.

  • Bambara has a marker of contrastive focus: dè which can co-occur with yéMusa i subj [ AspP/TP yé [ FocP n't´erifari j yé [ PredP t j t i ]]]]-flat SC rather hierarchical SC? -syntax of copulas: yé inserted in T/Asp projection directly? -focalization of DP2 -movement of DP1 to Subj position 4 Conclusions yé…yé sentences are not equatives; instead they are asymmetric DP-Cop-Focus structures., in which DP2 is necesarily (new information) focus.

	Mariam COP 1sg best-friend FOC CONTRA FOC NEW
	'Mariam is my best friend (only friendship and nothing else ; not my fiancee
	for instance)
	Ingredients of the analysis:
	(56) [
	(55) Mariam yé n'térifari	dè	yé

Abbreviations :ACC: accomplished,ASP:aspect , CONJ: conjunction,COP:copula, FOC:focus, NEG: negative, POSS: possessive, Pl:plural, PM: predicative marker, QUAL:quality, SG:singular, SUBJ:subjunctive, PAST:passé

Bambara also allows for other question orders, where the wh-jon appears in sentence initial position. These questions, however, have a marked interpretation.

[C] (49) Jɔ ń yé Musa yé?

Who COP Musa yé 'Who is Musa?' Interpretational constraints: The question conveys an depreciative meaning (insult) cf. 'Who is this Musa?' / 'Who does he think he is?' 'C'est qui ce Moussa?' (our qui il se prend?, qu'est-ce qu'il pense qu'il est?) -The answer will be: (50) Musa yé Lajine nyɛ ́màa yé → *not* Lajine nyɛ ḿàa yé Musa yé Musa COP Guinea president yé 'Musa is the president of Guinea' So the new information focus necessarily is on the second DP, in this context as well.

[D] (51) Jɔ ń yé í térifari yé ?

Who COP 2sg best-friend yé 'Who is your best friend ?' context: I don't know if you have a best friend or not, I want to know the