Trace element diffusivities in bone rule out simple diffusive uptake during fossilization but explain in vivo uptake and release

Abstract

Diffusion rates of numerous trace elements in bone at 20 °C were determined using laser-ablation inductively coupled plasma mass spectrometry analysis of experimentally induced diffusion profiles. Diffusivities are about 1 order of magnitude slower than current semiquantitative geochemical views and about 1.5 orders of magnitude faster than indirect radiotracer estimates. Intrabone volume diffusion is too slow and too similar among many elements to explain trace element profiles in young fossils and archeological materials. Diffusivity differences among elements do, however, explain disparate biokinetic washout of Sr vs. Ba and of light vs. heavy rare earth elements (REEs). These results improve the understanding of the physical principles underlying biokinetic models and rates and mechanisms of trace element alteration of phosphatic tissues in paleontological, archeological, and crystal-chemical contexts. Recrystallization and transport limitations in soils explain trace element profiles in young fossils better than intrabone volume diffusion alone and imply that diffusion of REE and other trivalent cations is likely controlled by a common charge–compensating species rather than ionic radii or partition coefficients.

Trace elements can pose major health risks, especially radioactive products of nuclear processes. Many of these elements concentrate in bone (bone-seeking elements), including P, Ca, Zn, Sr, Ba, lanthanides, Pb, and actinides, where they can reside for decades before being gradually eliminated from the body (1). Bone’s tenacious affinity for certain trace elements persists postmortem, as evidenced by orders of magnitude higher concentrations of trace elements in archeological bones and fossils compared with modern tissues (2). The question of how the bone mineral bioapatite—a calcium phosphate—takes up and releases these elements has launched a lively debate among numerous research groups. Health physicists have long debated in vivo remodeling (biologically controlled resorption and reprecipitation of bioapatite) vs. volume diffusion for explaining the slowest rates of uptake and release (3–8); such research is commonly termed biokinetics. Geochemists debate in vitro recrystallization and surface adsorption vs. diffusion for explaining trace element profiles in fossils, although diffusive processes are normally assumed (9, 10). Diffusion underpins both types of research because it provides a strict lower limit for rates of trace element uptake and release both in vivo and in vitro. Understanding diffusion rates therefore improves predictions of long-term clearance of trace elements from the body, as well as geological or archeological interpretations of trace elements or their isotopes, such as U-series geochronology, conditions of deposition and fossilization, and forensic discrimination among fossils (2).

Surprisingly, virtually no experiments constrain trace element diffusion rates in bone, and we can find no studies that measured diffusion profiles directly. Consequently, we conducted 18-mo experiments in which sections of cleaned cattle femora were immersed in a synthetic soil saturated with a trace element–spiked solution. Postexperiment diffusion profiles were measured via depth profile and spot analysis traverse (Fig. 1) using laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The diffusion coefficients are far more precise than prior measurements, cover a much larger range of elements than previously considered, and show important differences among some elements yet surprising similarities among others. These data help explain differential rates of trace element loss from the body but imply that trace element uptake during initial fossilization does not occur via volume diffusion. Note that modern bone contains considerably smaller apatite crystallites and considerably higher porosity than enamel, fossils, or inorganic apatites (11). These attributes imply faster diffusivities in modern bone and thus provide maximum limits on diffusive uptake in enamel or recrystallized fossils.

Fig. 1.

Schematic of postexperimental bone disk, showing methods of collecting trace element data (depth profiling into sides and ends vs. spot traverse). Reflected light photomicrograph shows 6-µm-diameter spots in traverse. Thin white line is bone-epoxy interface, and white dots in traverse show first analysis at bone-epoxy interface and two analyses close to Haversian canals (dark regions).

Results

Raw composition profiles (Dataset S1) show sharp concentration decreases away from bone edges (Fig. 2) and imply relatively slow diffusivities (Ds) for rare earth elements (REEs; steepest profiles), intermediate Ds for Pb and U, and fastest Ds for Zn and Sr (flattest profiles). Two prominent compositional humps appear for U in sample Mm (Fig. 2A), where the spot traverse approaches Haversian canals. Because only the outermost spots were fit to diffusion models, the humps do not adversely affect interpretations. Concentrations in deproteinated sample Jx relative to Mm are approximately 3 times higher for Sr and 60 times lower for U, indicating different partition coefficients for bioapatite mineral alone vs. collagen-bearing bone. Adsorption of U onto organic substrates (biosorption) is well documented (12). Plots of the inverse complementary error function (erfc⁻¹) vs. distance (Fig. 3A) are linear for the outer half of the spot traverses but exhibit compositional tailing for some elements such as U deeper into the bone. Multiple diffusion pathways produce compositional tailing and have been proposed as important for explaining trace element distributions in fossils (13), although their experimental contribution to calculated diffusivities is minor (<10%). In contrast, stronger tailing in depth profiles (Fig. 3 B and C) reflects an analytical artifact from compositional mixing of outer vs. inner bone from the walls of the ablation pit. These data nonetheless support differences in diffusivities among elements, and the outermost several analyses (5–6 analyses for REE and Ba; 10–20 for higher-concentration divalent cations) can be used to infer Ds quantitatively.

Fig. 2.

Composition vs. distance plots of raw data. (A) Spot traverse in Mm. (B and C) Transverse depth profile into side of Mm and Jx. (Inset) Generalized profile shapes for fast vs. slow diffusion. Note that scales for Sr, U, and Pb may be adjusted by a constant factor.

Fig. 3.

Inverse error function vs. distance plots corresponding to data shown in Fig. 2. (A) Spot traverse in Mm, showing good linearity for most of traverse. Tailing in Sr, U, and possibly Pb reflect additional fast-diffusion pathways. (B and C) Depth profiles for Mm and Jx. Tailing reflects analytical artifact, but near-edge data resolve differences in diffusivities. (Insets) Relative distribution of Ds based on near-rim profiles.

Diffusivities are lowest for Y, Ba, Th, and the lanthanides (<8 × 10⁻¹⁵ cm²/s), intermediate for B, Al, Pb, and U (∼1 × 10⁻¹⁴ cm²/s), and highest for transition metals and Sr (5 × 10⁻¹⁴ to >1 × 10⁻¹² cm²/s; Fig. 3; Table 1). Diffusivities decrease slightly with increasing atomic number in the lanthanide series. For example, plots of raw data (Fig. 2) and erfc⁻¹ (Fig. 3) consistently indicate slower D for Yb than Nd, which are both spiked tracers and well resolved. Longitudinal Ds (end profiles) are typically 2–10 times faster than transverse Ds (side profiles; Table 1), whereas Ds in deproteinated bone are scattered but generally <5 times faster than untreated bone.

Table 1.

Log₁₀ of trace element diffusion coefficients in bone

Element	Mm trans (spot), cm2/s	Mm trans (depth), cm2/s	Mm long (depth), cm2/s	Jx trans (spot), cm2/s	Jx trans (depth), cm2/s	Jx long (depth), cm2/s
B		−13.91 ± 0.02			−13.95 ± 0.06	−12.90 ± 0.38
Al	−14.18 ± 0.03	−14.15 ± 0.03	−14.02 ± 0.02	−14.24 ± 0.04	−13.90 ± 0.21	−13.03 ± 0.17
Cr		−13.33 ± 0.03	−13.53 ± 0.05		−13.18 ± 0.29
Fe		−12.91 ± 0.05			−13.17 ± 0.12	−12.38 ± 0.09
Zn		−13.17 ± 0.03	−12.90 ± 0.02		−13.29 ± 0.07	−13.16 ± 0.07
Sr	−12.46 ± 0.05	−12.85 ± 0.03	−12.28 ± 0.09		−11.86 ± 0.20	−11.34 ± 0.24
Ba		−14.38 ± 0.04	−14.58 ± 0.15		−14.06 ± 0.06	−14.34 ± 0.12
Y	−14.39 ± 0.06	−14.38 ± 0.02	−14.23 ± 0.04	−14.22 ± 0.01	−14.15 ± 0.19
La		−14.45 ± 0.04	−14.25 ± 0.04		−14.07 ± 0.33
Ce	−14.44 ± 0.09	−14.58 ± 0.03	−14.21 ± 0.03	−14.42 ± 0.02	−14.11 ± 0.20	−13.55 ± 0.16
Nd	−14.46 ± 0.05	−14.50 ± 0.03	−14.30 ± 0.02	−14.35 ± 0.01	−14.45 ± 0.05	−13.39 ± 0.21
Sm	−14.54 ± 0.07	−14.57 ± 0.02	−14.25 ± 0.03	−14.42 ± 0.01	−14.49 ± 0.03	−13.58 ± 0.17
Eu	−14.51 ± 0.07	−14.58 ± 0.03	−14.26 ± 0.04	−14.41 ± 0.01	−14.45 ± 0.07	−13.73 ± 0.03
Gd	−14.47 ± 0.05	−14.52 ± 0.03	−14.27 ± 0.02	−14.31 ± 0.01	−14.44 ± 0.07	−13.62 ± 0.04
Tb		−14.60 ± 0.06	−14.48 ± 0.11		−14.49 ± 0.16
Dy		−14.60 ± 0.04	−14.22 ± 0.06		−14.79 ± 0.10
Ho		−14.58 ± 0.03	−14.42 ± 0.03
Er		−14.53 ± 0.03	−14.36 ± 0.08		−14.43 ± 0.18
Tm		−14.63 ± 0.04	−14.56 ± 0.05		−14.60 ± 0.35
Yb	−14.59 ± 0.10	−14.68 ± 0.04	−14.41 ± 0.03	−14.49 ± 0.01	−14.57 ± 0.08	−13.63 ± 0.07
Lu		−14.51 ± 0.05	−14.43 ± 0.10		−14.71 ± 0.22	−14.00 ± 0.53
Pb	−13.93 ± 0.04	−13.95 ± 0.03	−13.88 ± 0.04		−14.28 ± 0.12	−13.24 ± 0.64
Th		−14.52 ± 0.06	−14.31 ± 0.10		−14.65 ± 0.16	−13.70 ± 0.25
U	−13.83 ± 0.02	−13.78 ± 0.03	−13.66 ± 0.02	−14.22 ± 0.03	−13.96 ± 0.27	−14.13 ± 0.33

In Mm experiments, bone contained collagen. In Jx experiments, collagen was first removed. depth, depth profile; long, longitudinal profile; spot, spot traverse; Trans, transverse profile. Errors are 2σ regression uncertainties.

Discussion

Diffusivities.

Our data follow many expected trends. Very generally, we expect higher Ds for divalent cations (Zn, Fe, Sr, Pb) than for higher valence cations (REE and Th) because exchange of 3⁺ and 4⁺ cations for Ca²⁺ in the bioapatite mineral structure requires movement of another charge-coupled species (coupled-substitution) such as vacancies, Na⁺ for Ca²⁺, Si⁴⁺ for P⁵⁺, etc. Decreasing Ds for Sr²⁺, Pb²⁺, and Ba²⁺ reflect increasing cation misfit as ionic radii exceed Ca²⁺ by ∼14%, 16%, and 30%, respectively (14). Note that strong similarities in biokinetic behavior and ionic radii suggest that Ra and Ba would have similar Ds (14–16). Adsorption of trace elements onto bone in vivo increases relative to other body pools in the order U, light REE (LREE: La, Ce, Nd), middle REE (MREE: Eu, Gd), and Th plus heavy REE (HREE: Yb, Lu; see review of ref. 17; Fig. S1). If higher partition coefficients between crystallite surfaces and fluids impart lower effective diffusivities (ref. 9, although see subsequent discussion), Ds should decrease in the order U, LREE, MREE, Th+HREE, as we observe, at least in comparing U, Nd, and Yb+Th. Faster longitudinal Ds mean either that bone is diffusionally anisotropic or that diffusion in osteonal bone is slightly faster than in outer circumferential lamellae. Diffusional anisotropy has been demonstrated in fossil teeth (13) but has not yet been studied in bone. Crystallite axes and elongation are both parallel to long-bone axes (18, 19), as are Haversian canals and bone lamellae, and would readily explain diffusional anisotropy.

The rates for Sr (≥1 × 10⁻¹³ cm²/s) and Ba (≥4 × 10⁻¹⁵ cm²/s) exceed estimates from indirect biokinetic studies of Ca, Sr, and Ra (∼1 × 10⁻¹⁶ cm²/s; ref. 4), whereas rates for U and REE (2 × 10⁻¹⁵ to 2 × 10⁻¹⁴ cm²/s) are about one order of magnitude lower than most geochemical estimates. The latter ranges from about 4 × 10⁻¹⁴ to 2 × 10⁻¹² cm²/s and is based indirectly on theoretical models of diffusion in fluid-saturated porous media, fluid-bioapatite partition coefficients for trace elements, and comparison with measured diffusivities for other elements and compounds in enamel (9, 10, 20).

Differences among REE Ds that have been predicted based on lattice strain models (20) are inconsistent with our data. Noting that the site occupancies of REE are not completely known, but appear to change between LREE (dominantly sevenfold coordination) and MREE (ninefold coordination; ref. 21), these models imply that Nd should diffuse roughly five times slower than Yb, whereas our data show the opposite, both with respect to retrieved Ds (Fig. 4) and the constancy of REE patterns with depth (Fig. S1). We propose that this disparity in predictions vs. observations reflects the fact that REE³⁺ cannot directly exchange for Ca²⁺ and instead require a charge compensating species, such as Na⁺. If such a species rate-limits REE diffusion, then all REEs will exhibit rather similar Ds, although one might also expect a systematic trend of D vs. a parameter like ionic radius. This expectation holds for the lanthanides, but Y diffuses faster compared with other REE than its ionic radius (similar to Dy and Ho) would imply.

Fig. 4.

Trace element Ds vs. atomic number for traverses shown in Figs. 2 and 3. See text for discussion. Vertical lines separate different general fields (labeled in A). Some elements are missing for spot profile because they are below detection limits. (A) Spot traverses. (B and C) Depth profiles.

Biokinetic Implications.

If diffusion ultimately limits long-term release of trace elements from the body (3–5, 7), then the diffusivities we measured bound long-term loss and help explain many classic observations. Researchers have long known that Ba and Ra exhibit faster initial washout than Ca and Sr (15) but persist much longer in the body at low levels (16). For example, Ba and Ra contents drop two to five times faster than Ca and Sr within 25 d of administration, yet Ba requires 5–10 y to fall to 2% of its initial dose, whereas Sr requires <1 y (1, 15, 16, 22). The measured diffusivities explain this behavior. Slow diffusion for Ba (and Ra) implies slow uptake into bone; therefore, they initially wash out more quickly than Sr. However, the small amount of Ba (and Ra) that does enter the bone diffuses back very slowly and therefore persists at low levels much longer.

In analogy to Sr and Ba, if Ds decrease in the order LREE > MREE > HREE, then heavier REEs should show faster initial washout but longer-term low-level retentions than lighter REE. This behavior may explain faster initial washout for MREE (Gd) than for LREE (Pm), and possibly also a longer half-life for long-term release of Yb than for Tm (see summary of ref. 23). Slower diffusivities for HREE vs. LREE may imply revision to biokinetic models of REE uptake. Recent models (24) use the same transfer coefficients between bone volume and other body pools. If diffusion rate-limits REE uptake and release, then HREE coefficients for bone volume should probably be lower (slower) than LREE.

Fossilization Mechanisms and Rates.

Fossil bone commonly shows relatively flat U profiles and steep REE profiles, which is especially marked in late Pleistocene fossils (13) (Fig. 5). If intrabone diffusion controls trace element uptake in fossils, then U must diffuse many orders of magnitude faster than REE. Until now, relative Ds among lanthanides and actinides remained unknown. Our recognition of similar Ds among them and slower diffusion than previously considered completely change our views on this process, at least for the initial stages of fossilization represented by young fossils. For example, the integrated value of Dt (diffusion coefficient times time) for ∼25-ka fossils from Montana along transverse chemical profiles ranges from 0.1 cm² for Ce to 1,000 cm² for U (13). Given Ds of ∼5 × 10⁻¹⁵ cm²/s for Ce and ∼2 × 10⁻¹⁴ cm²/s for U (Fig. 4; Table 1), diffusion alone would require >500,000 to >1 billion years to form such profiles—far exceeding the age of the fossils. Similarly, flatter profiles in fossils for HREE than for LREE (13, 20, 25, 26) conflict with slightly decreasing Ds with increasing atomic number in the lanthanides (Fig. 4). Discrepancies between the predictions of diffusive uptake and observations in fossils demand some additional process or factor that controls initial trace element uptake. The presence or absence of organic matter alone cannot be responsible because experiment Jx (initially deproteinated bone) shows similar Ds and trends as Mm (Fig. 4).

Fig. 5.

Evolution of trace element composition of soil water and bone through time. At t₀, soil water has constant composition and outer edge of bone recrystallizes to initial compositions. As time progresses from t₀ to t₁, trace element sink in bone is most effective for Nd, leading to a steep concentration gradient in the soil, and least effective for U, leading to a flat concentration gradient. As recrystallization propagates into the bone interior, U concentration decreases slightly, Yb moderately, and Nd substantially, reflecting differences in evolution of soil water compositions.

We propose two major revisions to current fossilization models. First, trace elements must be initially introduced into bone by some mechanism other than volume diffusion (alone); it is simply too slow both in fresh and deproteinated bone to account for profiles in fossils. Millard and Hedges (9) recognized that “early uptake” of U, in which U-series ages closely approximate depositional ages in archeological materials, could not be explained by then-estimated U diffusivities. Our observations for REE demonstrate that this problem encompasses numerous other elements. Wetting-drying cycles may enhance trace element movement into bone. Because pore diameters of bone’s Haversian-Volkmann canal system (∼50–100 µm) far exceed pore spaces in fine-grained soils (∼1 µm), capillary action during drying will withdraw trace element–depleted water from bone, whereas wetting will recharge it with trace element–loaded soil water (27). Alternatively, microbial processes different from our experiments might enhance rapid trace element movement. Second, we propose that recrystallization must propagate into the bone and control initial incorporation of trace elements in the fossil. The most important implication of this model is that the recrystallization front continuously equilibrates with (“sees”) the sediment–bone interface (Fig. 5) so that flat U vs. steep REE profiles reflect nearly constant U concentrations vs. rapidly decreasing REE concentrations at the bone surface and not inherent differences in intrabone trace element Ds. Diffusivities are simply too similar among REE and U to explain the disparate patterns observed among LREE, HREE, and U, and thus some other transport pathway must exist in bone during initial fossilization.

Our model implies that fossil bone depletes the surrounding sediment most quickly in LREE, somewhat more slowly in HREE, and hardly at all in U. Thus, trace element profiles in young fossil bones have virtually nothing to do with intrabone diffusion, in contrast to longstanding geochemical perspectives (2, 9, 10, 13, 20, 25), including our own. Instead, bone acts as a trace element sink that induces differential concentration gradients in the surrounding sediment and pore water. These gradients form because most trace elements in soils are hosted in specific minerals whose (non)reactivity may prevent buffering at high concentrations (13). The magnitude of the gradient depends on transport rates through the sediment and partition coefficients. Sandy soils (fast transport) will likely impart flatter trace element profiles in fossils than clayey soils (slow transport) or soils that do not undergo wetting-drying cycles. Predicted partition coefficients for REE in apatite are highest for Pr and Nd, decreasing slightly toward La and substantially toward Lu (20). The commonly observed greater depletion of Nd relative to La and HREE toward bone interiors (13, 20, 26) reflects more efficient removal of Nd from pore waters compared with lighter and heavier REE. Empirically determined partition coefficients between bone and soil water are highest for LREE, intermediate for HREE, and lowest for U (13), supporting this hypothesis. Partition coefficients and ionic radii are commonly assumed to directly impact diffusivities (9, 13, 20), but these principles no longer apply if disparate diffusants are charge-coupled to a single slow-diffusing species (28).

If our interpretation is correct, then inferences regarding durations of trace element uptake in fossils require reconsideration. The most commonly applied method for interpreting U-series ages in archeological bone assumes that U transport into bone interiors is rate-limited by simultaneous diffusion and adsorption onto bioapatite crystallites (9). Diffusion is also commonly implicated in the formation of REE profiles (13, 20). If, however, U and REE are taken up during recrystallization, no a priori reason exists that diffusion will rate-limit this process. Although recrystallization might respond to collagen loss that is controlled by diffusion (10), numerous factors that may not be diffusion-limited also occur during fossilization, including microbial degradation of collagen, hydrolysis of collagen to gelatin, apatite replacement of proteins, and fluid advection (27, 29). Although our hypothesis applies to initial fossilization, ancient fossils may experience continuous slow uptake via volume diffusion. With characteristic diffusion distances of centimeters, a 100-Myr fossil would be expected to show flatter trace element profiles than young fossils, as has been recently reported (26).

Archeological and Paleontological Forensics.

Trace elements in archeological remains and fossils are used in numerous endeavors, including estimating durations of burial from F diffusion profiles (30), sourcing fossils using trace element ratios (31), estimating redox conditions of early burial from REE patterns (32), and inferring paleodiets from Ba/Ca and Sr/Ca foodchain biopurification (33). Fluorine is thought to diffuse faster than cations (∼5 × 10⁻¹¹ cm²/s) (34), so in principle, diffusion might control F uptake. Bioapatite does act as a sink for F, however, so the same contradictions we encountered in understanding U and REE profiles in fossil bone within the context of diffusion rates may also apply to F.

Particularly slow diffusion of REEs and actinides (this study) and their general absence from alteration minerals (35) recommend their use over divalent cations for paleontological forensics. Similar diffusion rates for REEs suggest that bone does not inherently distinguish among them. Whereas differential partitioning will affect ratios compared with pore water, if pore water chemistry remains unchanged, then compositions in a bone interior vs. near the surface should be similar. This correspondence implies that bone acts as a faithful recorder of pore water chemistry. For example, use of Ce and Eu anomalies (disparities in Ce and Eu concentrations relative to their neighboring REEs) for interpreting redox states (32) would appear minimally biased by differential diffusion rates among REE (in contrast with ref. 13).

Our data have implications for paleodietary and other geochemical investigations of tooth enamel, which is more resistant to alteration and is emphasized analytically (2, 36). Coarser grain sizes and lower porosity generally imply Ds in enamel at least 50 times lower than in bone (9), or ∼1 × 10⁻¹⁶ cm²/s for most elements, but as high as 1 × 10⁻¹⁴ cm²/s for Sr. On time scales of 100s of kyr to Myr, these rates imply characteristic diffusion distances on the order of millimeters. Given that most enamel is thinner than ∼2 mm, it seems unlikely that it can withstand diffusive alteration, unless trace elements are preferentially adsorbed onto exchangeable crystallite surfaces and can somehow be removed before analysis rather than incorporated directly into crystallites via volume diffusion or recrystallization. Much faster diffusion for Sr compared with Ba generally implies that Ba/Ca ratios will be more resistant to alteration than Sr/Ca. For example, a characteristic diffusion distance for Sr of 1 mm would diffuse Ba only ∼30 µm. Fast Sr diffusion may also compromise retrieval of original biogenic ⁸⁷Sr/⁸⁶Sr in fossils.

Conclusions

Experimental diffusion coefficients for numerous elements in bone resolve long-standing questions about bone chemistry, particularly differential rates of long-term in vivo washout for different elements. Broadly similar diffusivities among disparate trivalent cations suggest that a common charge–coupled species controls diffusion rates. Similarities in these diffusion rates in comparison with disparate trace element profiles in fossils suggest that postburial intrabone diffusion does not control trace element uptake in archeological and young fossil bone. Rather, apparent diffusion profiles in such fossils result from bone’s role as a trace element sink in sediments, inducing chemical depletion haloes around the bone. Progressively recrystallizing bones encode these profiles, which then masquerade as having been formed by intrabone diffusion. Fossilization rates based on trace element profiles in fossils and assumed diffusivities will be grossly in error.

Methods

Moses (37) detailed the experimental methods used to induce trace element profiles in bone. Briefly, 25-mm-long transverse sections (disks) were cut from the femoral shaft of recently slaughtered cattle (Bos taurus) using a band saw. Marrow and the periosteum were removed. Disks were buried in 900 g of artificial sediment (854.5 g fine-grained quartz sand, 45g kaolin clay, 0.5 g minced straw) saturated with 300 mL of trace element–spiked solution, sealed in ∼1-L plastic sample jars, and stored at ∼20 °C for 18 mo, agitating periodically. Solutions were spiked with 10 ppm by weight Ce, Nd, Sm, Eu, Gd, Yb, Sr, and U. Slight impurities in the synthetic sediment and solutions allowed investigation of numerous other trace elements besides the spikes, including B, Al, Cr, Zn, Y, Ba, the remaining rare earths, Pb and Th, and Ca and P. We also measured Na, but high initial concentrations and high backgrounds precluded direct determination of diffusion profiles. Over the course of the experiments, pH values progressed from ∼7 to ∼9.

Two samples were chosen for detailed analysis. Sample Mm simulates trace element uptake by fresh bone under microbe-present conditions. Three milliliters of microbial solution was extracted from pond mud, horse manure, and decaying flesh and used to inoculate experiments together with 0.27 g of NH₄NO₃ (fertilizer). Specimen Jx simulates trace element uptake in a weathered bone with its organics removed. The bone disk was first dessicated and then soaked in ethanol, acetone, hydrogen peroxide (3% H₂O₂), and sodium hypochlorite (6% NaOCl) to remove organic compounds.

Trace element data were measured at Boise State University using a Thermo XSeries2 Quadrupole ICP-MS (inductively coupled plasma mass spectrometer) in conjunction with a NewWave UP-213 laser ablation system. Two types of analyses were performed: depth profiles and spot traverses (Fig. 1). Depth profiles were collected with 100-µm-diameter spots, 5 Hz, and 9–10 J/cm² into the sides and ends of bone disks. Side profiles penetrated outer circumferential lamellae (OCL) into osteonal bone, although only data from OCL were interpreted. End profiles sampled only osteonal bone and constrain diffusion anisotropy and differences in diffusion rates in different types of bone. Depth profiles provide the highest compositional resolution and readily discriminate relative diffusion rates, but data quality rapidly degrades down-hole from mixing between the near-surface, trace element–rich edge of the hole and deeper portions of the bone. Near-edge data are generally immune to these complications. Data were normalized to 37 wt% Ca (pure bioapatite), and concentrations of P did not vary significantly. Standardization errors propagate to uncertainties in absolute concentration of at least 10%. Distances were determined postanalysis by grinding a transverse section to intersect ablation pits and measuring their length. Each sweep through the element list corresponded to an ablation distance of 1.35 µm.

Spot analyses were collected using a 6-µm-diameter spot, 5 Hz, and ∼15 J/cm². Bone was embedded in epoxy and polished, and then spots were collected in an array at a shallow angle to the bone surface (Fig. 1). This approach allowed spots to be collected with a 1.3- to 1.4-µm spacing from the bone edge. The small spot size and low count rates allowed collection of only spiked trace elements, Al, P, Ca, and Pb (Mm only). The largest changes to composition occur in the outer ∼20 µm, which is dominated by OCL. This bone is structurally most homogeneous. Note that concentrations in fresh bone are negligible, except for Sr (∼300 ppm) and Zn (∼175 ppm), but Sr and Zn concentrations are so high near bone edges that these do not adversely affect calculations, and we correct for initial concentrations (C_o) in D calculations. Lead shows slight zoning from a few parts per million on fresh bone surfaces to ∼0.3 ppm within 20–50 µm. These concentrations imply that Pb Ds might be overestimated, although much less than an order of magnitude.

Diffusion coefficients were estimated by inverting composition vs. distance assuming a semi-infinite solution to the diffusion equation:

where C_x, C_s, and C_o are compositions at distance x at the surface, and initially (negligible for most elements), D is the diffusion coefficient, and t is time. A linear regression of the inverse complementary error function vs. distance provided a value and uncertainty for 1/2(Dt)^1/2, from which D was calculated. Only the outermost analyses (8–40 analyses for spot traverses, 5–20 for depth profiles) were used. For depth profiles, the first element sweep with comparably high Ca and P as for later sweeps was taken as the surface composition. For spot traverses, the first analysis that bisected the interface between epoxy and bone was taken as the surface composition. An error of ±1.5 µm affects diffusion coefficient estimates by ≤10%.