Bone quantitative ultrasound

1 Bone Overview, Pr. David Mitton, Pr. Christian Roux, Dr. Pascal Laugier 2 Introduction to the physics of ultrasound, Dr. Pascal Laugier, Dr. Guillaume Haiat.- 3 Quantitative ultrasound instrumentation for bone in vivo characterization, Dr. Pascal Laugier.- 4 Clinical applications, Dr. Reinhard Barkmann, Pr. C-C Gluer.- 5 Poromechanical Models: Biot's theory - Modified Biot's theory - Multilayer model, Dr. Michal Pakula, Pr. Mariusz Kaczmarek,Dr. Frederic Padilla.- 6 Scattering by trabecular bone, Dr. Frederic Padilla, Dr. Keith Wear.- 7 Guided waves in cortical bone, Dr. Maryline Talmant, Josquin Foiret,Dr. Jean-Gabriel Minonzio.- 8 Numerical methods for ultrasonic bone characterization, Dr. Emanuel Bossy, Dr. Quentin GRIMAL.- 9 Homogenization theories and inverse problems, Prof. Robert P. Gilbert, Dr. Ana Vasilic, Dr. Sandra Ilic.- 10 Linear acoustics of trabecular bone, Prof. Jukka S Jurvelin et al..- 11 The Fast and Slow Wave Propagation in Cancellous Bone -Experiments and Simulations, Prof. Atsushi Hosokawa, Dr. Yoshiki Nagatani, Prof. Mami Matsukawa.- 12 Phase Velocity of Cancellous Bone Negative dispersion arising from fast and slow waves, interference, diffraction, and phase cancellation at piezoelectric receiving elements, Prof. James G. Miller et al..- 13 Linear ultrasonic properties of cortical bone: in vitro studies, Dr. Guillaume Haiat.- 14 Ultrasonic monitoring of fracture healing, Dr. Vasilios Protopappas, Dr. Maria G. Vavva, Dr. Konstantinos N. Malizos, Prof. Dimitrios I. Fotiadis.- 15 Nonlinear acoustics for non-invasive assessment of bone micro-damage, Dr. Marie Muller, Dr. Guillaume Renaud.- 16 Microscopic elastic properties, Prof. Kay Raum.- 17 Ultrasonic Computed Tomography, Dr. Philippe Lasaygues.- Index.

[1]  S. Ortolani,et al.  Effects of long-term strontium ranelate treatment on vertebral fracture risk in postmenopausal women with osteoporosis , 2009, Osteoporosis International.

[2]  S. Goldstein,et al.  Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. , 1999, Journal of biomechanics.

[3]  L. Joseph Melton,et al.  Perspective how many women have osteoporosis? , 1992, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[4]  R. Andresen,et al.  Relationship Between Structural Parameters, Bone Mineral Density and Fracture Load in Lumbar Vertebrae, Based on High-Resolution Computed Tomography, Quantitative Computed Tomography and Compression Tests , 1999, Osteoporosis International.

[5]  G Boivin,et al.  The role of mineralization and organic matrix in the microhardness of bone tissue from controls and osteoporotic patients. , 2008, Bone.

[6]  Hwj Rik Huiskes.  The law of adaptive bone remodeling : a case for crying Newton? , 1995 .

[7]  V Bousson,et al.  In vitro ultrasonic characterization of human cancellous femoral bone using transmission and backscatter measurements: relationships to bone mineral density. , 2006, The Journal of the Acoustical Society of America.

[8]  J. Virieux.  P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method , 1986 .

[9]  S. Goldstein,et al.  Evaluation of a microcomputed tomography system to study trabecular bone structure , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[10]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[11]  J M Crolet,et al.  A new numerical concept for modeling hydroxyapatite in human cortical bone , 2005, Computer methods in biomechanics and biomedical engineering.

[12]  C. Langton,et al.  The measurement of broadband ultrasonic attenuation in cancellous bone. , 1984, Engineering in medicine.

[13]  Marco Viceconti,et al.  Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro. , 2008, Journal of biomechanics.

[14]  Maryline Talmant,et al.  Ultrasonically determined thickness of long cortical bones: Three-dimensional simulations of in vitro experiments. , 2007, The Journal of the Acoustical Society of America.

[15]  A. Larrue,et al.  Feasibility of Micro-Crack Detection in Human Trabecular Bone Images from 3D Synchrotron Microtomography , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[16]  Demosthenes Polyzos,et al.  Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone. , 2009, The Journal of the Acoustical Society of America.

[17]  A Hosokawa.  Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot's finite-difference time-domain methods. , 2005, The Journal of the Acoustical Society of America.

[18]  Pascal Laugier,et al.  Ultrasonic Propagation Through Trabecular Bone Modeled as a Random Medium , 2008 .

[19]  Christian Soize,et al.  A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation , 2008 .

[20]  D Mitton,et al.  An anatomical subject-specific FE-model for hip fracture load prediction , 2008, Computer methods in biomechanics and biomedical engineering.

[21]  L. S. Matthews,et al.  Comparison of the trabecular and cortical tissue moduli from human iliac crests , 1989, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[22]  Dennis M Black,et al.  Femoral Bone Strength and Its Relation to Cortical and Trabecular Changes After Treatment With PTH, Alendronate, and Their Combination as Assessed by Finite Element Analysis of Quantitative CT Scans , 2008, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[23]  T. Lang,et al.  What do we know about fracture risk in long-duration spaceflight? , 2006, Journal of musculoskeletal & neuronal interactions.

[24]  W. Parnell,et al.  The influence of mesoscale porosity on cortical bone anisotropy. Investigations via asymptotic homogenization , 2009, Journal of The Royal Society Interface.

[25]  O. Johnell,et al.  World-wide Projections for Hip Fracture , 1997, Osteoporosis International.

[26]  S Gheduzzi,et al.  Ultrasonic propagation in cortical bone mimics , 2006, Physics in medicine and biology.

[27]  R. Courant.  Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[28]  B. Stampa,et al.  Assessment of the Geometry of Human Finger Phalanges Using Quantitative Ultrasound In Vivo , 2000, Osteoporosis International.

[29]  V. Bousson,et al.  Prediction of mechanical properties of cortical bone by quantitative computed tomography. , 2008, Medical engineering & physics.

[30]  Hirotaka Imaizumi,et al.  Applicability of Finite-Difference Time-Domain Method to Simulation of Wave Propagation in Cancellous Bone , 2006 .

[31]  R Dumas,et al.  Mechanical characterization in shear of human femoral cancellous bone: torsion and shear tests. , 1999, Medical engineering & physics.

[32]  David Mitton,et al.  Assessment of femoral neck strength by 3-dimensional X-ray absorptiometry. , 2006, Journal of clinical densitometry : the official journal of the International Society for Clinical Densitometry.

[33]  K. F. Riley,et al.  Mathematical Methods for Physics and Engineering , 1998 .

[34]  Xiasheng Guo,et al.  Quantitative evaluation of fracture healing process of long bones using guided ultrasound waves: a computational feasibility study. , 2009, The Journal of the Acoustical Society of America.

[35]  H Follet,et al.  Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography. , 2007, Journal of biomechanics.

[36]  S. Dodd,et al.  Numerical and experimental simulation of the effect of long bone fracture healing stages on ultrasound transmission across an idealized fracture. , 2009, The Journal of the Acoustical Society of America.

[37]  Jacques Cornuz,et al.  Osteoporotic fracture risk in elderly women: estimation with quantitative heel US and clinical risk factors. , 2008, Radiology.

[38]  Dimitrios I Fotiadis,et al.  The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone. , 2008, Ultrasonics.

[39]  C-C Glüer,et al.  In vitro speed of sound measurement at intact human femur specimens. , 2005, Ultrasound in medicine & biology.

[40]  A Hosokawa.  Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods. , 2006, Ultrasonics.

[41]  S.,et al.  Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media , 1966 .

[42]  G. Pharr,et al.  Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. , 1997, Biomaterials.

[43]  R. B. Ashman,et al.  Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. , 1993, Journal of biomechanics.

[44]  E. Bossy,et al.  Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: a 2D simulation study. , 2002, The Journal of the Acoustical Society of America.

[45]  Christian Soize,et al.  Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission. , 2009, The Journal of the Acoustical Society of America.

[46]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

[47]  L. S. Matthews,et al.  Proximal femoral bone density and its correlation to fracture load and hip-screw penetration load. , 1992, Clinical orthopaedics and related research.

[48]  Maryline Talmant,et al.  Ultrasonically determined thickness of long cortical bones: two-dimensional simulations of in vitro experiments. , 2007, The Journal of the Acoustical Society of America.

[49]  O Johnell,et al.  Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures. , 1996, BMJ.

[50]  H. Skinner,et al.  Prediction of femoral fracture load using automated finite element modeling. , 1997, Journal of biomechanics.

[51]  S. Goldstein,et al.  Age, gender, and bone lamellae elastic moduli , 2000, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[52]  Robert Luben,et al.  Prediction of total and hip fracture risk in men and women by quantitative ultrasound of the calcaneus: EPIC-Norfolk prospective population study , 2004, The Lancet.

[53]  F. Padilla,et al.  Femur ultrasound (FemUS)—first clinical results on hip fracture discrimination and estimation of femoral BMD , 2010, Osteoporosis International.

[54]  Dimitrios I. Fotiadis,et al.  An ultrasound wearable system for the monitoring and acceleration of fracture healing in long bones , 2005, IEEE Transactions on Biomedical Engineering.

[55]  Ego Seeman,et al.  Bone modeling and remodeling. , 2009, Critical reviews in eukaryotic gene expression.

[56]  W. C. Hayes,et al.  Ultrasound and densitometry of the calcaneus correlate with the failure loads of cadaveric femurs , 1995, Calcified Tissue International.

[57]  Jeremy Magland,et al.  Implications of noise and resolution on mechanical properties of trabecular bone estimated by image‐based finite‐element analysis , 2009, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[58]  G. Pharr,et al.  The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. , 1999, Journal of biomechanics.

[59]  P. Delmas,et al.  Serum type I collagen breakdown product (serum CTX) predicts hip fracture risk in elderly women: the EPIDOS study. , 2000, Bone.

[60]  H H Bolotin,et al.  DXA in vivo BMD methodology: an erroneous and misleading research and clinical gauge of bone mineral status, bone fragility, and bone remodelling. , 2007, Bone.

[61]  Françoise Peyrin,et al.  Attenuation in trabecular bone: A comparison between numerical simulation and experimental results in human femur. , 2007, The Journal of the Acoustical Society of America.

[62]  V. Protopappas,et al.  Guided ultrasound wave propagation in intact and healing long bones. , 2006, Ultrasound in Medicine and Biology.

[63]  J. Currey,et al.  What determines the bending strength of compact bone? , 1999, The Journal of experimental biology.

[64]  Françoise Peyrin,et al.  Variation of Ultrasonic Parameters With Microstructure and Material Properties of Trabecular Bone: A 3D Model Simulation , 2007, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[65]  J. Katz,et al.  Ultrasonic wave propagation in human cortical bone-I. Theoretical considerations for hexagonal symmetry. , 1976, Journal of biomechanics.

[66]  P Zioupos,et al.  The fracture toughness of cancellous bone. , 2009, Journal of biomechanics.

[67]  S. Goldstein,et al.  The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. , 1990, Journal of biomechanics.

[68]  Julien Diaz,et al.  ROBUST HIGH ORDER NON-CONFORMING FINITE ELEMENT FORMULATION FOR TIME DOMAIN FLUID-STRUCTURE INTERACTION , 2005 .

[69]  S. Goldstein,et al.  Finite‐element modeling of trabecular bone: Comparison with mechanical testing and determination of tissue modulus , 1998, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[70]  S. Majumdar,et al.  A review of the recent advances in magnetic resonance imaging in the assessment of osteoporosis , 1995, Osteoporosis International.

[71]  A. Stewart,et al.  Long‐Term Fracture Prediction by DXA and QUS: A 10‐Year Prospective Study , 2005, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[72]  Pascal Laugier,et al.  Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz. , 2009, The Journal of the Acoustical Society of America.

[73]  Christian Soize,et al.  Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: application to cortical bone evaluation. , 2006, The Journal of the Acoustical Society of America.

[74]  Florian Hartl,et al.  Prediction of Hip Fracture Risk by Quantitative Ultrasound in More Than 7000 Swiss Women ≥70 Years of Age: Comparison of Three Technologically Different Bone Ultrasound Devices in the SEMOF Study , 2006, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[75]  M. Bouxsein,et al.  Digital X-ray Radiogrammetry Predicts Hip, Wrist and Vertebral Fracture Risk in Elderly Women: A Prospective Analysis from the Study of Osteoporotic Fractures , 2002, Osteoporosis International.

[76]  Chrysoula Tsogka,et al.  Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic hete , 1998 .

[77]  Pascal Laugier,et al.  Simulation of Ultrasound Propagation Through Three-Dimensional Trabecular Bone Structures: Comparison with Experimental Data , 2006 .

[78]  P. Rüegsegger,et al.  A microtomographic system for the nondestructive evaluation of bone architecture , 2006, Calcified Tissue International.

[79]  M Tanter,et al.  Experimental demonstration of noninvasive transskull adaptive focusing based on prior computed tomography scans. , 2003, The Journal of the Acoustical Society of America.

[80]  Maryline Talmant,et al.  Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius. , 2008, The Journal of the Acoustical Society of America.

[81]  Craig R. Slyfield,et al.  Quantitative Computed Tomography-Based Predictions of Vertebral Strength in Anterior Bending , 2007, Spine.

[82]  D. Mitton,et al.  Effect of a supercritical CO2 based treatment on mechanical properties of human cancellous bone , 2005, European Journal of Orthopaedic Surgery & Traumatology.

[83]  Judith E. Adams,et al.  Quantitative computed tomography. , 2009, European journal of radiology.

[84]  J A McGeough,et al.  Age-Related Changes in the Compressive Strength of Cancellous Bone. The Relative Importance of Changes in Density and Trabecular Architecture* , 1997, The Journal of bone and joint surgery. American volume.

[85]  Pascal Laugier,et al.  Potential of first arriving signal to assess cortical bone geometry at the Hip with QUS: a model based study. , 2010, Ultrasound in medicine & biology.

[86]  A. T. Hoop,et al.  A modification of cagniard’s method for solving seismic pulse problems , 1960 .

[87]  G Montaldo,et al.  Non-invasive transcranial ultrasound therapy based on a 3D CT scan: protocol validation and in vitro results , 2009, Physics in medicine and biology.

[88]  J. Eisman,et al.  Direct clinical and welfare costs of osteoporotic fractures in elderly men and women , 2005, Osteoporosis International.

[89]  W C Van Buskirk,et al.  A continuous wave technique for the measurement of the elastic properties of cortical bone. , 1984, Journal of biomechanics.

[90]  Rainer Thiel,et al.  Designing a Socio-Economic Assessment Method for Integrative Biomedical Research: The Osteoporotic Virtual Physiological Human Project , 2009, MIE.

[91]  A LeBlanc,et al.  Bone mineral and lean tissue loss after long duration space flight. , 2000, Journal of musculoskeletal & neuronal interactions.

[92]  F Peyrin,et al.  Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy. , 2008, The Journal of the Acoustical Society of America.

[93]  G. Van der Perre,et al.  The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[94]  Ryan K Roeder,et al.  Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur. , 2009, Journal of the mechanical behavior of biomedical materials.

[95]  S. Modak,et al.  The generalized method for structural dynamics applications , 2002 .

[96]  Christian Soize,et al.  Determination of the random anisotropic elasticity layer using transient wave propagation in a fluid-solid multilayer: model and experiments. , 2009, The Journal of the Acoustical Society of America.

[97]  Maryline Talmant,et al.  Effect of porosity on effective diagonal stiffness coefficients (cii) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study. , 2007, The Journal of the Acoustical Society of America.

[98]  Jonathan J. Kaufman,et al.  New ultrasound system for bone assessment , 2004, SPIE Medical Imaging.

[99]  Robert W. Graves,et al.  Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences , 1996, Bulletin of the Seismological Society of America.

[100]  E. Bossy,et al.  Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron microtomography , 2005, Physics in medicine and biology.

[101]  Dimitrios I Fotiadis,et al.  Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones. , 2007, The Journal of the Acoustical Society of America.

[102]  Juha Töyräs,et al.  Ultrasonic characterization of human trabecular bone microstructure , 2006, Physics in medicine and biology.

[103]  Atsushi Hosokawa,et al.  Effect of Minor Trabecular Elements on Fast and Slow Wave Propagations through a Stratified Cancellous Bone Phantom at Oblique Incidence , 2009 .

[104]  Gangming Luo,et al.  Ultrasound simulation in the distal radius using clinical high-resolution peripheral-CT images. , 2008, Ultrasound in medicine & biology.

[105]  E. Jaynes,et al.  Kramers–Kronig relationship between ultrasonic attenuation and phase velocity , 1981 .

[106]  Salah Naili,et al.  A theoretical analysis in the time-domain of wave reflection on a bone plate , 2006 .

[107]  D P Fyhrie,et al.  Human vertebral body apparent and hard tissue stiffness. , 1998, Journal of biomechanics.

[108]  T. Keaveny,et al.  Theoretical Implications of the Biomechanical Fracture Threshold , 2008, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[109]  Himadri S. Gupta,et al.  Mechanical modulation at the lamellar level in osteonal bone , 2006 .

[110]  I. Siegel,et al.  The determination of fracture healing by measurement of sound velocity across the fracture site. , 1958, Surgery, gynecology & obstetrics.

[111]  A. Hofman,et al.  Fracture incidence and association with bone mineral density in elderly men and women: the Rotterdam Study. , 2004, Bone.

[112]  M. Drezner,et al.  Bone histomorphometry: Standardization of nomenclature, symbols, and units: Report of the asbmr histomorphometry nomenclature committee , 1987, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[113]  C. Cooper,et al.  European guidance for the diagnosis and management of osteoporosis in postmenopausal women , 2008, Osteoporosis International.

[114]  David Mitton,et al.  ANTERIOR BENDING ON WHOLE VERTEBRAE USING CONTROLLED BOUNDARY CONDITIONS FOR MODEL VALIDATION , 2009 .

[115]  P. Rüegsegger,et al.  In vivo high resolution 3D-QCT of the human forearm. , 1998, Technology and health care : official journal of the European Society for Engineering and Medicine.

[116]  A. Hosokawa.  Development of a numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[117]  D B Burr,et al.  Alterations to the en bloc basic fuchsin staining protocol for the demonstration of microdamage produced in vivo. , 1995, Bone.

[118]  G Lowet,et al.  Assessment of the strength of the proximal femur in vitro: relationship with ultrasonic measurements of the calcaneus. , 1997, Bone.

[119]  Hiroshi Hosoi,et al.  Numerical and experimental study on the wave attenuation in bone--FDTD simulation of ultrasound propagation in cancellous bone. , 2008, Ultrasonics.

[120]  J. Katz,et al.  Ultrasonic wave propagation in human cortical bone--II. Measurements of elastic properties and microhardness. , 1976, Journal of biomechanics.

[121]  Sandra Schorlemmer,et al.  The role of cortical bone and its microstructure in bone strength. , 2006, Age and ageing.

[122]  G. Berger,et al.  Ultrasound parametric imaging of the calcaneus:In vivo results with a new device , 1996, Calcified Tissue International.

[123]  R. Huiskes,et al.  A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. , 1995, Journal of biomechanics.

[124]  P Zioupos,et al.  Mechanical properties and the hierarchical structure of bone. , 1998, Medical engineering & physics.

[125]  Armen Sarvazyan,et al.  Use of multiple acoustic wave modes for assessment of long bones: model study. , 2005, Ultrasonics.

[126]  R Huiskes,et al.  Comparison of micro-level and continuum-level voxel models of the proximal femur. , 2006, Journal of biomechanics.

[127]  Deepak Vashishth,et al.  Age-related change in the damage morphology of human cortical bone and its role in bone fragility. , 2006, Bone.

[128]  O. Johnell,et al.  Mortality after osteoporotic fractures , 2004, Osteoporosis International.

[129]  Maryline Talmant,et al.  Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models. , 2004, The Journal of the Acoustical Society of America.

[130]  G Berger,et al.  Analysis of the axial transmission technique for the assessment of skeletal status. , 2000, The Journal of the Acoustical Society of America.

[131]  L. S. Matthews,et al.  The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. , 1983, Journal of biomechanics.

[132]  R Barkmann,et al.  Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants. , 2006, Ultrasonics.

[133]  D. Hans,et al.  Prospective evaluation of risk of vertebral fractures using quantitative ultrasound measurements and bone mineral density in a population-based sample of postmenopausal women: results of the Basel Osteoporosis Study , 2008, Annals of the rheumatic diseases.

[134]  F. Padilla,et al.  Sensitivity of QUS parameters to controlled variations of bone strength assessed with a cellular model , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[135]  J A McGeough,et al.  Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure. , 1993, The Journal of bone and joint surgery. American volume.

[136]  R O Ritchie,et al.  On the origin of the toughness of mineralized tissue: microcracking or crack bridging? , 2004, Bone.