Bone Fracture Prediction Using Computed Tomography Based Rigidity Analysis and the Finite Element Method

In this study two imaging modalities are proposed as a basis for fracture analysis in bone; Computed Tomography (CT) and Positron Emission Tomography (PET).

In the first part of this study, finite element analysis (FEA); CT based structural rigidity analysis (CTRA) and mechanical testing are performed to assess the immediate fracture risk of rat tibia with simulated lytic defects at different locations.

Twenty rat tibia were randomly assigned to four equal groups (n=5). Three of the groups included a simulated defect at various locations: anterior bone surface (Group 1), posterior bone surface (Group 2), and through bone defect (Group 3). The fourth group was a control group with no defect (Group 4). Micro computed tomography was used to assess bone structural rigidity properties and to provide 3D model data for generation of the finite element models for each specimen.

Compressive failure load was predicted using CT derived rigidity parameters (F_CTRA) and was correlated to failure load recorded in mechanical testing (R²=0.96). The relationships between mechanical testing failure load and the axial rigidity (R²=0.61), bending rigidity (R²=0.71) and FEA calculated failure load (R²=0.75) were also correlated. CTRA stress, calculated adjacent to the defect, were also shown to be well correlated with yield stresses calculated using the average density at the weakest cross section (R²=0.72). No statistically significant relationship between apparent density and mechanical testing failure load was found (P=0.37).

In the second part of this study, Positron Emission Tomography (PET) and Computed Tomography (CT) imaging modalities were utilized to study the implementation of a bone remodeling rule for the study of future fracture risk.

Eight rats were inoculated with MDA-MB-231 human breast cancer cells at T0 to induce osteolytic lesions that simulate skeletal metastasis. Fluorine 18 (¹⁸F) and fluoro-deoxy-glucose (FDG) PET and CT imaging were carried out weekly to correlate changes in local bone mineral density observed using CT, with radionuclide tracer uptake observed in 18F and FDG PET. Univariate relationships correlating pixel level density to standardized uptake values (SUV’s) were obtained (R²=0.4-0.72). These relationships can be applied in assigning material properties in finite element models studying future fracture risk. Furthermore, a tumor induced bone remodeling rule could be developed to allow determination of future fracture risk associated with a baseline CT scan taken at time T0.

In summary, the results of this study indicate that CTRA analysis of bone strength correlates well with both FEA results and those obtained from mechanical testing. In addition there exist a good correlation between structural rigidity parameters and experimental failure loads. In contrast, there was no correlation between average bone density and failure load. Furthermore, the positron emission tomography (PET) imaging modality offers a promising method of studying future fracture risk using the finite element method.

Year	Entry
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.
1998	Silva MJ, Keaveny TM, Hayes WC. Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections. J Orthop Res. May 1998;16(3):300-308.
2004	Bayraktar HH, Gupta A, Kwon RY, Papadopoulos P, Keaveny TM. The modified super-ellipsoid yield criterion for human trabecular bone. J Biomech Eng. 2004;126(6):677-684.
2002	Pistoia W, van Rietbergen B, Lochmüller E-M, Lill CA, Eckstein F, Rüegsegger P. Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone. June 2002;30(6):842-848.
2000	Whealan KM, Kwak SD, Tedrow JR, Inoue K, Snyder BD. Noninvasive imaging predicts failure load of the spine with simulated osteolytic defects. J Bone Joint Surg. September 2000;82A(9):1240-1251.
2004	Waarsing JH, Day JS, van der Linden JC, Ederveen AG, Spanjers C, De Clerck N, Sasov A, Verhaar JAN, Weinans H. Detecting and tracking local changes in the tibiae of individual rats: a novel method to analyse longitudinal in vivo micro-ct data. Bone. January 2004;34(1):163-169.
1984	Hart RT, Davy DT, Heiple KG. A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. J Biomech Eng. November 1984;106(4):342-350.
1996	Haapasalo H, Sievanen H, Kannus P, Heinonen A, Oja P, Vuori I. Dimensions and estimated mechanical characteristics of the humerus after long-term tennis loading. J Bone Miner Res. June 1996;11(6):864-872.
1991	Snyder SM, Schneider E. Estimation of mechanical properties of cortical bone by computed tomography. J Orthop Res. May 1991;9(3):422-431.
2008	Keaveny TM, Hoffmann PF, Singh M, Palermo L, Bilezikian JP, Greenspan SL, Black DM. 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. J Bone Miner Res. December 2008;23(12):1974-1982.
2010	Santos L, Romeu JC, Canhão H, Fonseca JE, Fernandes PR. A quantitative comparison of a bone remodeling model with dual-energy X-ray absorptiometry and analysis of the inter-individual biological variability of femoral neck T-score. J Biomech. December 1, 2010;43(16):3150-3155.
1999	Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.
2004	Hong J, Cabe GD, Tedrow JR, Hipp JA, Snyder BD. Failure of trabecular bone with simulated lytic defects can be predicted non-invasively by structural analysis. J Orthop Res. May 2004;22(3):479-486.
1999	Keaveny TM, Wachtel EF, Zadesky SP, Arramon YP. Application of the Tsai–Wu quadratic multiaxial failure criterion to bovine trabecular bone. J Biomech Eng. February 1999;121(1):99-107.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
2000	Keyak J, Rossi S. Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories. J Biomech. 2000;33(2):209-214.
2010	Doube M, Kłosowski MM, Arganda-Carreras I, Cordelières FP, Dougherty RP, Jackson JS, Schmid B, Hutchinson JR, Shefelbine SJ. BoneJ: free and extensible bone image analysis in ImageJ. Bone. December 2010;47(6):1076-1079.
1997	Jacobs CR, Simo JC, Beaupré GS, Carter DR. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. J Biomech. June 1997;30(6):603-613.
2005	Keyak JH, Kaneko TS, Tehranzadeh J, Skinner HB. Predicting proximal femoral strength using structural engineering models. Clin Orthop Relat Res. August 2005;437:219-228.
1997	Ulrich D, Hildebrand T, Van Rietbergen B, Müller R, Rüegsegger P. The quality of trabecular bone evaluated with micro-computed tomography, FEA and mechanical testing. Stud Health Technol Inform. 1997;40:97-112.
2011	Varghese B, Short D, Penmetsa R, Goswami T, Hangartner T. Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion. J Biomech. April 29, 2011;(7):1374-1379.
1972	Rybicki EF, Simonen FA, Weis EB Jr. On the mathematical analysis of stress in the human femur. J Biomech. March 1972;5(2):203-215.
2004	Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.
2011	Boyle C, Kim IY. Three-dimensional micro-level computational study of Wolff's law via trabecular bone remodeling in the human proximal femur using design space topology optimization. J Biomech. March 15, 2011;44(5):935-942.
2011	Schulte FA, Lambers FM, Kuhn G, Müller R. In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging. Bone. March 2011;48(3):433-442.
1988	Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.
1999	Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.
2000	Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech. December 2000;33(12):1575-1583.
1991	Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, I: linear analysis. J Biomech Eng. 1991;113(4):353-360.
1994	Bowman SM, Keaveny TM, Gibson LJ, Hayes WC, McMahon TA. Compressive creep behavior of bovine trabecular bone. J Biomech. March 1994;27(3):301-310.
2008	Sigal IA, Hardisty MR, Whyne CM. Mesh-morphing algorithms for specimen-specific finite element modeling. J Biomech. 2008;41(7):1381-1389.
2010	Cory E, Nazarian A, Entezari V, Vartanians V, Müller R, Snyder BD. Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-CT based mineral density. J Biomech. March 22, 2010;43(5):953-960.
2003	Crawford RP, Cann CE, Keaveny TM. Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone. 2003;33(4):744-750.
1995	van Rietbergen B, Weinans H, Huiskes R, Odgaard A. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech. January 1995;28(1):69-81.
1991	Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, II: nonlinear analysis. J Biomech Eng. 1991;113(4):361-364.
1991	Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of metaphyseal bone in the proximal femur. J Biomech. 1991;24(5):317-329.
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling—application: a preliminary remodeling simulation. J Orthop Res. September 1990;8(5):662-670.
1997	Rho J-Y, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997;18(20):1325-1330.
1986	Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.

Year

Entry

1990

Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.

1998

Silva MJ, Keaveny TM, Hayes WC. Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections. J Orthop Res. May 1998;16(3):300-308.

2004

Bayraktar HH, Gupta A, Kwon RY, Papadopoulos P, Keaveny TM. The modified super-ellipsoid yield criterion for human trabecular bone. J Biomech Eng. 2004;126(6):677-684.

2002

Pistoia W, van Rietbergen B, Lochmüller E-M, Lill CA, Eckstein F, Rüegsegger P. Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone. June 2002;30(6):842-848.

2000

Whealan KM, Kwak SD, Tedrow JR, Inoue K, Snyder BD. Noninvasive imaging predicts failure load of the spine with simulated osteolytic defects. J Bone Joint Surg. September 2000;82A(9):1240-1251.

2004

Waarsing JH, Day JS, van der Linden JC, Ederveen AG, Spanjers C, De Clerck N, Sasov A, Verhaar JAN, Weinans H. Detecting and tracking local changes in the tibiae of individual rats: a novel method to analyse longitudinal in vivo micro-ct data. Bone. January 2004;34(1):163-169.

1984

Hart RT, Davy DT, Heiple KG. A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. J Biomech Eng. November 1984;106(4):342-350.

1996

Haapasalo H, Sievanen H, Kannus P, Heinonen A, Oja P, Vuori I. Dimensions and estimated mechanical characteristics of the humerus after long-term tennis loading. J Bone Miner Res. June 1996;11(6):864-872.

1991

Snyder SM, Schneider E. Estimation of mechanical properties of cortical bone by computed tomography. J Orthop Res. May 1991;9(3):422-431.

2008

Keaveny TM, Hoffmann PF, Singh M, Palermo L, Bilezikian JP, Greenspan SL, Black DM. 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. J Bone Miner Res. December 2008;23(12):1974-1982.

2010

Santos L, Romeu JC, Canhão H, Fonseca JE, Fernandes PR. A quantitative comparison of a bone remodeling model with dual-energy X-ray absorptiometry and analysis of the inter-individual biological variability of femoral neck T-score. J Biomech. December 1, 2010;43(16):3150-3155.

1999

Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.

2004

Hong J, Cabe GD, Tedrow JR, Hipp JA, Snyder BD. Failure of trabecular bone with simulated lytic defects can be predicted non-invasively by structural analysis. J Orthop Res. May 2004;22(3):479-486.

1999

Keaveny TM, Wachtel EF, Zadesky SP, Arramon YP. Application of the Tsai–Wu quadratic multiaxial failure criterion to bovine trabecular bone. J Biomech Eng. February 1999;121(1):99-107.

1998

Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.

2000

Keyak J, Rossi S. Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories. J Biomech. 2000;33(2):209-214.

2010

Doube M, Kłosowski MM, Arganda-Carreras I, Cordelières FP, Dougherty RP, Jackson JS, Schmid B, Hutchinson JR, Shefelbine SJ. BoneJ: free and extensible bone image analysis in ImageJ. Bone. December 2010;47(6):1076-1079.

1997

Jacobs CR, Simo JC, Beaupré GS, Carter DR. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. J Biomech. June 1997;30(6):603-613.

2005

Keyak JH, Kaneko TS, Tehranzadeh J, Skinner HB. Predicting proximal femoral strength using structural engineering models. Clin Orthop Relat Res. August 2005;437:219-228.

1997

Ulrich D, Hildebrand T, Van Rietbergen B, Müller R, Rüegsegger P. The quality of trabecular bone evaluated with micro-computed tomography, FEA and mechanical testing. Stud Health Technol Inform. 1997;40:97-112.

2011

Varghese B, Short D, Penmetsa R, Goswami T, Hangartner T. Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion. J Biomech. April 29, 2011;(7):1374-1379.

1972

Rybicki EF, Simonen FA, Weis EB Jr. On the mathematical analysis of stress in the human femur. J Biomech. March 1972;5(2):203-215.

2004

Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.

2011

Boyle C, Kim IY. Three-dimensional micro-level computational study of Wolff's law via trabecular bone remodeling in the human proximal femur using design space topology optimization. J Biomech. March 15, 2011;44(5):935-942.

2011

Schulte FA, Lambers FM, Kuhn G, Müller R. In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging. Bone. March 2011;48(3):433-442.

1988

Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.

1999

Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.

2000

Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech. December 2000;33(12):1575-1583.

1991

Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, I: linear analysis. J Biomech Eng. 1991;113(4):353-360.

1994

Bowman SM, Keaveny TM, Gibson LJ, Hayes WC, McMahon TA. Compressive creep behavior of bovine trabecular bone. J Biomech. March 1994;27(3):301-310.

2008

Sigal IA, Hardisty MR, Whyne CM. Mesh-morphing algorithms for specimen-specific finite element modeling. J Biomech. 2008;41(7):1381-1389.

2010

Cory E, Nazarian A, Entezari V, Vartanians V, Müller R, Snyder BD. Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-CT based mineral density. J Biomech. March 22, 2010;43(5):953-960.

2003

Crawford RP, Cann CE, Keaveny TM. Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone. 2003;33(4):744-750.

1995

van Rietbergen B, Weinans H, Huiskes R, Odgaard A. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech. January 1995;28(1):69-81.

1991

Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, II: nonlinear analysis. J Biomech Eng. 1991;113(4):361-364.

1991

Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of metaphyseal bone in the proximal femur. J Biomech. 1991;24(5):317-329.

1990

Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling—application: a preliminary remodeling simulation. J Orthop Res. September 1990;8(5):662-670.

1997

Rho J-Y, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997;18(20):1325-1330.

1986

Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.

Year	Entry
2020	Mosleh H, Rouhi G, Ghouchani A, Bagheri N. Prediction of fracture risk of a distal femur reconstructed with bone cement: QCSRA, FEA, and in-vitro cadaver tests. Phys Eng Sci Med. March 2020;43(1):269-277.

Year

Entry

2020

Mosleh H, Rouhi G, Ghouchani A, Bagheri N. Prediction of fracture risk of a distal femur reconstructed with bone cement: QCSRA, FEA, and in-vitro cadaver tests. Phys Eng Sci Med. March 2020;43(1):269-277.