Hierarchical Nature of Nanoscale Porosity in Bone Revealed by Positron Annihilation Lifetime Spectroscopy

Abstract

Bone is a hierarchical material primarily composed of collagen, water, and mineral that is organized into discrete molecular, nano-, micro-, and macroscale structural components. In contrast to the structural knowledge of the collagen and mineral domains, the nanoscale porosity of bone is poorly understood. In this study, we introduce a well-established pore characterization technique, positron annihilation lifetime spectroscopy (PALS), to probe the nanoscale size and distribution of each component domain by analyzing pore sizes inherent to hydrated bone together with pores generated by successive removal of water and then organic matrix (including collagen and noncollagenous proteins) from samples of cortical bovine femur. Combining the PALS results with simulated pore size distribution (PSD) results from collagen molecule and microfibril structure, we identify pores with diameter of 0.6 nm that suggest porosity within the collagen molecule regardless of the presence of mineral and water. We find that water occupies three larger domain size regions with nominal mean diameters of 1.1, 1.9, and 4.0 nm-spaces that are hypothesized to associate with intercollagen molecular spaces, terminal segments (d-spacing) within collagen microfibrils, and interface spacing between collagen and mineral structure, respectively. Subsequent removal of the organic matrix determines a structural pore size of 5-6 nm for deproteinized bone-suggesting the average spacing between mineral lamella. An independent method to deduce the average mineral spacing from specific surface area (SSA) measurements of the deproteinized sample is presented and compared with the PALS results. Together, the combined PALS and SSA results set a range on the mean mineral lamella thickness of 4-8 nm.

Keywords: bone; collagen; hierarchical structure; mineral lamella; nanocomposite; porosity; positron annihilation lifetime spectroscopy (PALS).

Figure 1.

Schematic showing a hierarchical nature of the bone structure from macro to molecular level. This study probes the nanostructure, ultrastructure and molecular structure of bone by utilizing positron annihilation lifetime spectroscopy (PALS). Reprinted with permission from ref . Copyright 2014 Elsevier.

Figure 2.

NLDFT pore size distribution from nitrogen adsorption data of the deproteinized bovine femur based on a cylindrical/ spherical pore model shows a bimodal distribution.

Figure 3.

Four fitted Ps lifetimes and their corresponding fitted Ps intensities for dehydrated bovine cortical femur bone. Dehydrated 1 and dehydrated 2 were dehydrated under vacuum with heat. Dehydrated 3 was dehydrated under vacuum with no heat. Dehydrated 4 (two bovine femur pieces surrounding the source) had its fitted intensities reduced by a normalization factor to account for its special source geometry. The four independent sample treatments showed consistent results.

Figure 4.

PALS discrete lifetime fitting results for deproteinized 1, 2, and 4 bone samples. Average data for dehydrated 1, 2, and 3 bone is provided for comparison. Dehydrated 3 and deproteinized 4 data are from the same bovine femur piece. The black dotted line guides the eye through dehydrated sample data. The blue dotted line connects data from the deproteinized samples.

Figure 5.

Typical distribution in plate/lamella spacing X (based on the infinite plate model) deduced using the continuum fitting program, CONTIN. The area under the curve is normalized to unity. For deproteinized 1, the average of this distribution is X_mean = 5.38 ± 0.03 nm.

Figure 6.

(A) Calculated pore size distribution (PSD) functions of collagen molecule (blue color) and collagen microfibril (red color) assuming spherical geometry. Three gray dotted lines indicate experimentally determined pore diameter sizes, corresponding to 2.16, 6.5, and 21.4 ns Ps lifetimes, based on the spherical pore shape. Three gray circles on the gray dotted lines indicate experimentally determined Ps intensity values for each lifetime component from Table 4. (B) Visualization of the collagen microfibril illustrating where three pore sizes are located. α indicates pores within collagen molecules. β indicates pores between collagen molecules. γ indicates pores that are located at the termini of collagen molecules within the collagen microfibril.

Figure 7.

Example of how finite size mineral lamella effects the deduced lamella thickness for a rectangular plate model. Lamella spacing X is linearly related to mineral plate thickness t with porosity fixed at 55.6% for four different rectangular shapes of mineral plates. Constraints on the average value of X imposed by results from PALS and SSA from BET and NMR (plus porosity measurement) determine a range in the deduced average mineral plate thickness in bovine femur. Selected plate sizes for rectangular plates are assumed to have length that is twice the width.