Analysis of the effect of osteon diameter on the potential relationship of osteocyte lacuna density and osteon wall thickness

Abstract

An important hypothesis is that the degree of infilling of secondary osteons (Haversian systems) is controlled by the inhibitory effect of osteocytes on osteoblasts, which might be mediated by sclerostin (a glycoprotein produced by osteocytes). Consequently, this inhibition could be proportional to cell number: relatively greater repression is exerted by progressively greater osteocyte density (increased osteocytes correlate with thinner osteon walls). This hypothesis has been examined, but only weakly supported, in sheep ulnae. We looked for this inverse relationship between osteon wall thickness (On.W.Th) and osteocyte lacuna density (Ot.Lc.N/B.Ar) in small and large osteons in human ribs, calcanei of sheep, deer, elk, and horses, and radii and third metacarpals of horses. Analyses involved: (1) all osteons, (2) smaller osteons, either ≤150 μm diameter or less than or equal to the mean diameter, and (3) larger osteons (>mean diameter). Significant, but weak, correlations between Ot.Lc.N/B.Ar and On.W.Th/On.Dm (On.Dm = osteon diameter) were found when considering all osteons in limb bones (r values -0.16 to -0.40, P < 0.01; resembling previous results in sheep ulnae: r = -0.39, P < 0.0001). In larger osteons, these relationships were either not significant (five/seven bone types) or very weak (two/seven bone types). In ribs, a negative relationship was only found in smaller osteons (r = -0.228, P < 0.01); this inverse relationship in smaller osteons did not occur in elk calcanei. These results do not provide clear or consistent support for the hypothesized inverse relationship. However, correlation analyses may fail to detect osteocyte-based repression of infilling if the signal is spatially nonuniform (e.g., increased near the central canal).

Keywords: bone remodeling; osteocytes; osteon wall thickness; osteons; sclerostin.

Figure 1

Schematic diagram of the proposed mechanism for control of activation of bone remodeling. Within the bone tissue at top, the elliptical objects represent osteocytes. The heavy line at bottom indicates a quiescent (not remodeling) bone surface; five bone lining cells (BLCs) are shown on this surface. The multiple thin lines connecting the osteocytes to one another and to the bone lining cells schematically represent cell processes within canaliculi. The jagged horizontal line indicates microdamage (microcrack) to the calcified matrix, which interferes with generation or transmission of the osteocytic signal. Reduced signal generation/transmission is indicated as dotted lines for the canaliculi physically disrupted by the microcrack. In theory, when these inhibitory signals fall below a threshold value the bone lining cells initiate activation of remodeling. (Redrawn from Martin (2000b), figure 2, with permission of the author.)

Figure 2

Schematic representation of osteons that show the general hypothesis supported by data from Metz et al. (2003) in mature sheep ulnae. HC.Ar = Haversian canal area ( = central canal area).

Figure 3

The hypothesized areal inhibitory signal (normalized by volumetric signal strength), within a completed osteon, is plotted as a function of the cement line radius (R_C) for several values of the decay constant k (mm⁻¹). The radius of the Haversian canal is assumed to be 20μm. When k surpasses about 25 mm⁻¹, the inhibitory signal on the Haversian canal plateaus as the cement line radius (R_C) exceeds 100μm (0.10mm on the abscissa). S_NA is the inhibitory signal (S_N) per unit area (subscript A) on the surface of the Haversian canal. (Redrawn from Martin (2000a), figure 6, with permission of the author.)

Figure 4

Lateral-to-medial views of the right forelimb and hind-limb skeletons of an adult horse showing a spectrum from simple loading to complex loading, respectively: calcaneus (A), radius (B), and third metacarpal (MC3) (C). The drawings below are simplified renditions of each bone type, showing: A) the calcaneus as a cantilevered beam, B) the radius as a curved beam with longitudinal loading; the curvature accentuates bending. Torsion (dotted line) is also present but is less than the torsion in the MC3 (solid circular line in C), and C) the MC3 with off-axis longitudinal loading producing bending and torsion, the latter being greater than in the other two bones. Several studies reporting in vivo strain data were used to create these drawings (Lanyon, 1974; Turner et al., 1975; Rubin and Lanyon, 1982; Schneider et al., 1982; Biewener et al., 1983a; Biewener et al., 1983b; Gross et al., 1992; Su et al., 1999).

Figure 5

All calcanei in medial-to-lateral view; from top to bottom: sheep, deer, elk, and horse. Cross sections show image locations in gray. One section (60% location) was analyzed in sheep, elk, and horse bones, and two sections (50% and 70% locations) were analyzed in deer bones. Dor = dorsal, Pla = plantar, Med = medial, Lat = lateral. The inset drawing at the upper right shows an adult right deer calcaneus in lateral-to-medial view showing typical loading along the Achilles tendon (large arrow) producing net compression (“C”) and tension (“T”) on dorsal and plantar cortices, respectively. This loading regime is similar in all of the calcanei used in this study. In this figure the ‘Achilles tendon’ represents the common calcaneal tendon.

Figure 6

Lateral-to-medial view of a left forelimb skeleton of an adult horse showing the radius and third metacarpal (MC3). At near right are cross sections showing image locations, and at far right are the approximate typical ranges that the neutral axes (N.A.) moves during weight bearing. Several studies reporting in vivo strain data were used to create these drawings (Turner et al., 1975; Rubin and Lanyon, 1982; Schneider et al., 1982; Biewener et al., 1983a; Biewener et al., 1983b; Gross et al., 1992). “C” = compression region (darkened), “T” = tension region (oblique lines), Cr = cranial, Cd = caudal, Dor = dorsal, Pal = palmar, Med = medial, Lat = lateral.

Figure 7

At left is a tracing of an actual osteon showing the measured parameters, which are listed below the osteon. At right is the actual osteon converted to a perfect circle; below this drawing are the calculated parameters. Osteocyte lacunae are not shown in these drawings.

Figure 8

Histograms of frequency distributions of the outer diameters (microns) of all osteons analyzed in this study. The outer diameter is defined by the cement line.

Figure 9

Histograms of frequency distributions of the Haversian canal diameters (microns) of all osteons analyzed in this study.

Figure 10

Depicted are diagrams based on seven osteons from the equine radii (at top) and seven osteons from the human ribs (at bottom). They range from the smallest to largest osteon diameter (On.Dm). The intervening osteons are also depictions of actual osteons spaced at approximately equal intervals of diameters from this range. The osteons are drawn to scale with contours that are smoothed to make them circular; the distribution of osteocytes are shown to be quasi random for illustrative purposes. The chart in the center lists actual data for each osteon (1, 2, 3, … 7). Ot.Lc.N/B.Ar = no./mm² and other non-ratio values are in μm.

Figure 11

Three representative backscattered electron (BSE) images showing osteon size variations in: (A) equine radius, caudal cortex at 100X; (B,C) deer calcaneus, plantar cortex at 50X (B) and 100X (C). The counting of osteocyte lacunae in the 50X BSE images used in this study was facilitated with the aid of a magnifying lens.