Statistical Representation and Rendering of Trabecular Bone Microstructure

Microstructure plays a pivotal role in the bulk mechanical behavior of materials. That is why proper understanding of trabecular bone microstructure is of great importance to assess the risk of bone fragility fracture. Current studies of trabecular microstructure are still relying on µCT-based finite element models due to the lack of standard mathematical method to render random cellular structures like trabecular bone. µCT-based models are costly and time consuming .Such models are individual specific, incapable of parametric analyses and lack flexibility correlating different microstructural features to the overall mechanical properties. In this work, a statistical representation of trabecular bone microstructure was defined by means of suitable parametric models for various microstructural features. These parametric models will allow for quantitative comparison of trabecular bone samples from different anatomical locations and of different bone diseases. A novel method was developed for rendering digital microstructure that is quantitatively similar to real trabecular bone sample using Voronoi Tessellation, Inverse Monte Carlo algorithm and a series of geometric constructions. The parametric models and the method of rendering trabecular microstructure developed in this work will accelerate studying microstructure-property relationships and also facilitate bio inspired design for engineering applications. Finally, a 3D model of the trabecular bone was generated which can be useful for designing and rapid prototyping of artificial bone.

Year	Entry
1997	Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. 2nd ed. Cambridge, UK: Cambridge University Press; 1997. Cambridge Solid State Science Series.
1997	Saha PK, Chaudhuri BB, Dutta Majumder D. A new shape preserving parallel thinning algorithm for 3D digital images. Patt Recogn. December 1997;30(2):1939-1955.
1987	Goldstein SA. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomech. 1987;20(11-12):1055-1061.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
1996	Saha PK, Chaudhuri BB. 3D digital topology under binary transformation with applications. Comput Vis Image Und. May 1996;63(3):418-429.
1996	Marshall D, Johnell O, Wedel H. Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures. BMJ. May 18, 1996;312(7041):1254-1259.
2006	Stauber M, Müller R. Volumetric spatial decomposition of trabecular bone into rods and plates: a new method for local bone morphometry. Bone. 2006;38(4):475-484.
2008	Liu XS, Sajda P, Saha PK, Wehrli FW, Bevill G, Keaveny TM, Guo XE. Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone. J Bone Miner Res. February 2008;23(2):223-235.
2009	Liu XS, Bevill G, Keaveny TM, Sajda P, Guo XE. Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods. J Biomech. February 9, 2009;42(3):249-256.
2008	Meyers MA, Chen P-Y, Lin AY-M, Seki Y. Biological materials: structure and mechanical properties. Prog Mater Sci. January 2008;53(1):1-206.
2009	Liu XS, Zhang XH, Guo XE. Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone. Bone. August 2009;45(2):158-163.
2004	Schuit SCE, van der Klift M, Weel AEAM, de Laet CEDH, Burger H, Seeman E, Hofman A, Uitterlinden AG, van Leeuwen JPTM, Pols HAP. Fracture incidence and association with bone mineral density in elderly men and women: the Rotterdam Study. Bone. January 2004;34(1):195-202.
2011	Mueller TL, Christen D, Sandercott S, Boyd SK, van Rietbergen B, Eckstein F, Lochmüller E-M, Müller R, van Lenthe GH. Computational finite element bone mechanics accurately predicts mechanical competence in the human radius of an elderly population. Bone. June 1, 2011;48(6):1232-1238.
2006	Liu XS, Sajda P, Saha PK, Wehrli FW, Guo XE. Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone. J Bone Miner Res. October 2006;21(10):1608-1617.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
1998	Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech. December 1998;31(12):1187-1192.

Year

Entry

1997

Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. 2nd ed. Cambridge, UK: Cambridge University Press; 1997. Cambridge Solid State Science Series.

1997

Saha PK, Chaudhuri BB, Dutta Majumder D. A new shape preserving parallel thinning algorithm for 3D digital images. Patt Recogn. December 1997;30(2):1939-1955.

1987

Goldstein SA. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomech. 1987;20(11-12):1055-1061.

2007

Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.

1996

Saha PK, Chaudhuri BB. 3D digital topology under binary transformation with applications. Comput Vis Image Und. May 1996;63(3):418-429.

1996

Marshall D, Johnell O, Wedel H. Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures. BMJ. May 18, 1996;312(7041):1254-1259.

2006

Stauber M, Müller R. Volumetric spatial decomposition of trabecular bone into rods and plates: a new method for local bone morphometry. Bone. 2006;38(4):475-484.

2008

Liu XS, Sajda P, Saha PK, Wehrli FW, Bevill G, Keaveny TM, Guo XE. Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone. J Bone Miner Res. February 2008;23(2):223-235.

2009

Liu XS, Bevill G, Keaveny TM, Sajda P, Guo XE. Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods. J Biomech. February 9, 2009;42(3):249-256.

2008

Meyers MA, Chen P-Y, Lin AY-M, Seki Y. Biological materials: structure and mechanical properties. Prog Mater Sci. January 2008;53(1):1-206.

2009

Liu XS, Zhang XH, Guo XE. Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone. Bone. August 2009;45(2):158-163.

2004

Schuit SCE, van der Klift M, Weel AEAM, de Laet CEDH, Burger H, Seeman E, Hofman A, Uitterlinden AG, van Leeuwen JPTM, Pols HAP. Fracture incidence and association with bone mineral density in elderly men and women: the Rotterdam Study. Bone. January 2004;34(1):195-202.

2011

Mueller TL, Christen D, Sandercott S, Boyd SK, van Rietbergen B, Eckstein F, Lochmüller E-M, Müller R, van Lenthe GH. Computational finite element bone mechanics accurately predicts mechanical competence in the human radius of an elderly population. Bone. June 1, 2011;48(6):1232-1238.

2006

Liu XS, Sajda P, Saha PK, Wehrli FW, Guo XE. Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone. J Bone Miner Res. October 2006;21(10):1608-1617.

1993

Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.

1998

Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech. December 1998;31(12):1187-1192.

Year	Entry
2017	Kirby ML. Digital Modeling of Trabecular Bones: Structural Analysis and Probabilistic Modeling Techniques [Master's thesis]. San Antionio, TX: University of Texas at San Antonio; August 2017.
2022	Xiao P. Medical Image-Based AI Techniques in Prediction of Trabecular Bone Microarchitecture and Mechanical Properties [PhD thesis]. San Antionio, TX: University of Texas at San Antonio; December 2022.

Year

Entry

2017

Kirby ML. Digital Modeling of Trabecular Bones: Structural Analysis and Probabilistic Modeling Techniques [Master's thesis]. San Antionio, TX: University of Texas at San Antonio; August 2017.

2022

Xiao P. Medical Image-Based AI Techniques in Prediction of Trabecular Bone Microarchitecture and Mechanical Properties [PhD thesis]. San Antionio, TX: University of Texas at San Antonio; December 2022.