Multidirectional morphology and mechanics of osteonic lamellae

• US 7,283,940 B2
• Filed: 02/03/2003
• Issued: 10/16/2007
• Est. Priority Date: 10/17/2001
• Status: Active Grant

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Ascenzi, Maria-Grazia, Kabo, John M.
• Primary Examiner(s): Thangavelu; Kandasamy
• Application Number:
  US10/357,090
• Publication Number:
  US 20030216899A1
• Time in Patent Office: 1,716 Days
• Field of Search: 703/2, 424/9.2, 424/49, 382/128, 600/586, 600/36, 600/449, 514/12, 623/23.56, 623/23.51, 623/23.61, 298/966
• US Class Current: 703/2
• CPC Class Codes: A61B 17/58 for osteosynthesis, e.g. bone plates, screws , setting implements or the like A61B17/14, A61B17/16 take precedence
• CPC Class Codes: A61B 2017/564 Methods for bone or joint treatment
• CPC Class Codes: A61B 34/10 Computer-aided planning, simulation or modelling of surgical operations
• CPC Class Codes: A61B 90/06 Measuring instruments not otherwise provided for
• CPC Class Codes: B33Y 80/00 Products made by additive manufacturing
• CPC Class Codes: G09B 23/30 Anatomical models G09B23/281 - G09B23/288 take precedence

Abstract

The present invention discloses a structural and mechanical model and modeling methods for human bone based on bone'"'"'s hierarchical structure and on its hierarchical mechanical behavior. The model allows for the assessment of bone deformations, computation of strains and stresses due to the specific forces acting on bone during function, and contemplates forces that do or do not cause viscous effects and forces that cause either elastic or plastic bone deformation.

Claims

1. A computer readable storage medium storing computer executable instructions which when executed on a computer determine a macrostructural mechanical response of a bone to at least one external force, comprising:

instructions for executing a computer based model of macrostructural properties of the bone, wherein the model comprises;

data corresponding to microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

a set of empirically-based mechanical properties of the microstructural elements comprising data generated by subjecting individual lamellae and individual osteons to external force; and

a set of corresponding macrostructural properties, based on the mechanical properties of the microstructural elements;

instructions for correlating one or more of the macrostructural properties of the bone with one or more mechanical properties of the microstructural elements of the bone when at least one external force is applied to the bone and data corresponding to at least one interaction of the bone is generated; and

instructions for determining a macrostructural mechanical response of the bone to the external force.

2. The model as defined in claim 1, wherein said bone is compact bone or cancellous bone.

3. The model as defined in claim 1, wherein said mechanical properties are selected from the group consisting of tension, compression, shear, bending, torsion, prestress, pinching, and cement line slippage.

4. The model of claim 1, wherein the data generated by subjecting individual lamellae to external force is obtained by a method comprising:

a) isolating individual bright and dark lamellae from secondary osteons;

b) measuring the length, thickness, width, and circumference of selected individual lamellae;

c) subjecting the selected individual lamellae to quasi-static tensional loading;

d) measuring the length, Thickness, width, and circumference of selected individual lamellae after loading; and

e) examining the selected individual lamellae using confocal microscopy, polarized light microscopy, and x-ray diffraction to determine a mechanical response of individual lamellae to force.

5. The model of claim 4, wherein individual lamellae are fully calcified osteonic lamella and the data generated by subjecting individual lamellae to external force is obtained by a method comprising:

subjecting the osteonic lamella to quasi-static tensional loading; and

collecting data comprising the geometry, distribution, and orientation of the bright or dark lamella components of the osteonic lamella.

6. The model of claim 1, wherein the data generated by subjecting individual lamellae to external force is obtained by amethod comprising:

a) isolating individual bright and dark lamellae from secondary osteons,

b) identifying regions of unidirectional collagen bundles,

c) measuring the length, thickness, and width of the unidirectional collagen bundles,

d) subjecting individual lamellae to quasi-static tensional loading in distinct orthogonal directions,

e) identifying fractures in the lamellae using an optical microscope, and

f) measuring the length, thickness, and width of the unidirectional collagen bundles after loading.

7. The model of claim 6, wherein the regions of unidirectional collagen bundles are identified using confocal microscopy.

8. A method of predicting deformation and fractures of bone, comprising:

obtaining at least one bone sample comprising microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

subjecting the bone sample to at least one external force that causes deformation and fracture;

collecting data comprising microstructural mechanical properties of the bone sample with and without application of the external force, including microstructural mechanical properties of individual larnellae and individual osteons;

inputting the data into a model of claim 1;

predicting deformation and fracture of the selected macrostructural iegion of the bone in response to at least one external force by correlating one or more of the macrostructural properties of the bone with one or more mechanical properties of the microstructural elements of the bone using the model; and

presenting deformation and fracture results to a user using a computer.

9. A method of identifying requirements of bone reconstruction and prosthesis, comprising:

obtaining at least one bone sample comprising microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

subjecting the bone sample to at least one external force;

collecting data comprising microstructural mechanical properties of the bone sample with and without application of the external force, including microstructural mechanical properties of individual lamellae and individual osteons;

inputting the data into a model of claim 1;

applying a finite element method to compute a response of a patient'"'"'s bone to at least one external force;

identifying requirements of bone reconstruction and prosthesis by correlating one or more of the macrostructural properties of the bone sample with one or more mechanical properties of the microstructural elements of the bone sample and comparing a computerized representation of the patient'"'"'s bone to the model; and

presenting identified requirements of bone reconstruction and prosthesis to a user using a computer.

10. A computer readable storage medium storing computer executable instructions which when executed on a computer determine a macrostructural mechanical response of a compact adult bone to at least one external force and/or biochemical testing, comprising:

instructions for executing a computer based model of macrostructural properties of the compact adult bone, wherein the model comprises;

data corresponding to microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

empirically-based viscoelastic properties of at least one type of secondary osteon and viscoelastic properties of bright and dark lamellae from secondary osteons, wherein the viscoelastic properties comprise data generated by subjecting at least one type of secondary osteon and individual lamellae to at least one external force and/or biochemical testing; and

a set of corresponding macrostructural properties, based on the viscoelastic properties of the microstructural elements;

instructions for correlating one or more of the macrostructural properties of the bone with one or more viscoelastic properties of the microstructural elements of the bone when at least one external force and/or biochemical testing is applied to the bone and data corresponding to at least one interaction of the bone is generated; and

instructions for determining a macrostructural mechanical response of the bone to the at least one external force and/or biochemical testing.

11. The model of claim 10, wherein said secondary osteon is a longitudinal osteon or an alternate osteon.

12. The model of claim 10, wherein the viscoelastic properties comprise at least one parameter selected from the group consisting of mechanical properties, collagen content, mucopolysaccbaride content, hydroxyapatite content, collagen bundle orientation relative to osteon axis, amount, of osteocytes, amount of osteoblasts, and content of porosity fluids.

13. The model of claim 12, wherein the viscoelastic properties comprise mechanical properties, collagen content, mucopolysaccharide content, hydroxyapatite content, and collagen bundle orientation relative to osteon axis.

14. The model of claim 12, wherein the viscoelastic properties are selected from mechanical properties and hydroxyapatite content, wherein the mechanical properties are selected from angle-of-twist as a function of torque, strain rate, and time.

15. The model of claim 14, wherein the angle-of-twist as a function of torque is derived from tests conducted under monotonic or dynamic loading.

16. The model of claim 14, wherein angle-of-twist as a function of torque at an approximately constant strain rate and approximately constant hydroxyapatite content is represented by a Ramberb-Osgood equation.

17. The model of claim 16, wherein a higher hydroxyapatite content leads to a higher angle-of-twist as a function of torque.

18. The model of claim 16, wherein a higher strain rate leads to a higher angle-of-twist as a function of torque.

19. The model of claim 10, comprising the viscoellastic properties of longitudinal and secondary alternate osteons.

20. The model of claim 19, wherein the viscoelastic properties comprise mechanical properties, collagen content, mucopolysaccharide content, hydroxyapatite content, and collagen bundle orientation relative to osteon axis.

21. The model of claim 20, wherein the contents of collagen and mucopolysaceharides in longitudinal osteons and the contents of collagen and mucopolysaceharides in alternate osteons are present in a ratio of less than 1 for longitudinal and alternate osteons with approximately equal hydroxyapatite contents.

22. The model of claim 10, comprising a reference osteon having an internal diameter, an external diameter, and a height, wherein the internal diameter of the reference osteon is about 40 μ

m, the external diameter of the reference osteon is about 210 μ

m, and the height of the reference osteon is about 500 μ

m.

23. The model of claim 22, wherein the reference osteon is a longitudinal reference osteon comprising about 12 lamellae.

24. The model of claim 22, wherein the reference osteon is an alternate reference osteon comprising about 36 lamellae.

25. The model of claim 10, comprising a Finite Element Model (FEM).

26. A method of predicting deformation and fractures of compact adult bone comprising:

obtaining at least one sample of compact adult bone comprising microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

subjecting the bone sample to at least one external force that causes deformation and fracture;

collecting data comprising microstructural viscoelastic properties of the bone sample, including microstructural viscoelastic properties of secondary longitudinal and alternate osteons and microstructural viscoelastic properties of bright and dark lamellae from secondary osteons;

generating data comprising a response of the sample bone to another external force including at least one change in at least one viscoelastic property in response to said another external force;

inputting the collected and generated data into a computer based model of claim 10;

predicting a deformation and fracture in a subject bone in response to at least one external force by correlating one or more of the macrostructural properties of the bone with one or more viscoelastic properties of the microstructural elements of the bone using the model; and

presenting the predicted deformation and fractures of compact adult bone to a user using the computer.

27. The method of claim 26, wherein the model further comprises empirically-based mechanical properties of compact adult bone, including simulation of fracture propagation by calculating stress distribution as a function of a torque applied to the bone.

28. A method of identifying requirements of bone reconstruction and prosthesis, comprising:

obtaining a bone sample comprising microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and individual secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

subjecting the bone sample to at least one external force;

collecting data comprising microstructural viscoelastic properties of the bone sample with and without application of the external force, including microstructural viscoelastic properties of at least one type of a secondary osteon, and microstructural viscoelastic properties of bright and dark lamellae from secondary osteons;

inputting the data into a model of claim 10;

applying a finite element method to compute the response of a patient'"'"'s bone to at least one external force;

identifying requirements of bone reconstruction and prosthesis by correlating one or more of the macrostructural properties of the bone sample with one or more viscoelastic properties of the microstructural elements of the bone sample and comparing a computerized representation of the patient'"'"'s bone to the model; and

presenting identified requirements of bone reconstruction and prosthesis to a user using a computer.

29. The method of claim 28, wherein the contents of collagen and mucopolysaccharides in a longitudinal osteon as compared to an alternate osteon are present in a ratio of less than 1, for a longitudinal and alternate osteon with approximately equal hydroxyapatite contents.

30. A method of preparing a computer based model of viscoelastic properties of bone for use in determining mechanical response of bone to at least one external force, comprising:

specifying data corresponding to microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and alternate and longitudinal secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

determining viscoelastic properties of alternate and longitudinal osteons and viscoelastic properties of bright and dark lamellae from secondary osteons, wherein the viscoelastic properties comprise data generated by subjecting alternate and longitudinal osteons and individual lameliae to at least one external force and/or biochemical testing;

preparing a computer based model of the bone using the viscoelastic properties of the microstructural elements;

determining corresponding macrostructural properties, based on the viscoelastic properties of the microstructural elements;

determining a mechanical response of the bone to at least one external force by correlating one or more of the macrostructural properties of the bone with one or more viscoelastic properties of the microstructural elements of the bone.

31. The method of claim 30, wherein the viscoelastic properties comprise mechanical properties, collagen content, mucopolysaccharide content, hydroxyapatite content, and collagen bundle orientation relative to osteon axis.

32. The method of claim 31, wherein the mechanical properties are determined by evaluating one or more parameters selected from angle-of-twist as a function of torque, strain rate, and time.

33. The method of claim 32, wherein angle-of-twist as a function of torque is determined by quasi-static torsional loading to rupture.

34. The method of claim 31, comprising determining a ratio of collagen and mucopolysaccharides in a longitudinal osteon as compared to those of an alternate osteon by the following method:

(i) drying the longitudinal and alternate osteons to constant weight;

(ii) separately contacting the longitudinal and alternate osteons with acid to promote hydrolysis of collagen to hydroxyproline and mucopolysaccharides to hexosamine;

(iii) separating hydroxyproline from hexosamine;

(iv) measuring the hydroxyproline and the hexosamine in the longitudinal and alternate osteons; and

(v) determining a ratio of hydroxyproline in the longitudinal osteon as compared to the hydroxyproline in the alternate osteon; and

(vi) determining a ratio of hexosamine in the longitudinal osteon as compared to the hexosamine in the alternate osteon;

wherein the ratio of hydroxyproline in the longitudinal osteon as compared to hydroxyproline in the alternate osteon represents the ratio of collagen in the longitudinal osteon as compared to collagen in the alternate osteon; and

wherein the ratio of hexosamine in the longitudinal osteon as compared to hexosamine in the alternate osteon represents the ratio of mucopolysaccharides in the longitudinal osteon as compared to mucopolysaccharides in the alternate osteon.

35. The method of claim 31, wherein the collagen bundle orientation relative to osteon axis is determined by circularly polarizing light microscopy, confocal microscopy, or X-ray diffraction.

36. A method of preparing a model of the macrostructural properties of a bone, comprising:

(a) obtaining a sample bone comprising selected microstructural elements of a bone, wherein the elements comprise bright and dark lamellae from secondary osteons and alternate and longitudinal secondary osteons, and are in a hierarchical relationship to a selected macrostructural region of the bone;

(b) isolating individual longitudinal and alternate osteons from the sample bone;

(c) mechanically testing individual longitudinal and alternate osteons under monotonic torsional loading to determine angle-of-twist per unit length as a function of torque;

(d) measuring and recording the angle-of-twist per unit length as a function of torque of the individual longitudinal and alternate osteons;

(e) using the recorded measurements from step (d) in the Ramberg-Osgood equation to create a microstructural model of the sample bone;

(f) determining corresponding macrostructural properties, based on the mechanical properties of the microstructural elements;

(g) determining a mechanical response of the bone to a torsional loading by correlating one or more of the macrostructural properties of the bone with one or more mechanical properties of the microstructural elements of the bone.