Histomorphometric Assessment of Haversian Canal and Osteocyte Lacunae in Different-Sized Osteons in Human Rib

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1 THE ANATOMICAL RECORD PART A 272A: (2003) Histomorphometric Assessment of Haversian Canal and Osteocyte Lacunae in Different-Sized Osteons in Human Rib SHIJING QIU, 1 DAVID P. FYHRIE, 2 SAROJ PALNITKAR, 1 AND D. SUDHAKER RAO 1 * 1 Bone and Mineral Research Laboratory, Henry Ford Hospital, Detroit, Michigan 2 Bone and Joint Center, Henry Ford Hospital, Detroit, Michigan ABSTRACT There is no detailed information available concerning the variations in bone, the Haversian canal, and osteocyte populations in different-sized osteons. In this study a total of 398 secondary osteons were measured in archived rib sections from nine white men (20 25 years old). The sections were stained with basic fuchsin. The parameters included the osteon area (On.Ar), Haversian canal area (HC.Ar) and perimeter (HC.Pm), bone area (B.Ar), and osteocyte lacunar number (Lc.N). From these primary measurements the following indices were deduced: 1) lacunar number per bone area (Lc.N/B.Ar) and per osteon (Lc.N/On); 2) the ratio between Haversian canal perimeter and bone area (HC.Pm/B.Ar); and 3) the fraction of Haversian canal area (HC.Ar/On.Ar) and its complement, the fraction of bone area (B.Ar/ On.Ar). The results showed that the osteons varied greatly in size, but very little in the fraction of bone area. Regression analyses showed that HC.Ar, HC.Pm, and Lc.N/On were positively associated with On.Ar (P for all). A significant negative correlation was found between On.Ar and Lc.N/B.Ar (P 0.05) and HC.Pm/B.Ar (P ). HC.Ar and HC.Pm increased significantly with increasing Lc.N/On (both P ) rather than Lc.N/B.Ar. Lc.N/B.Ar had a significant positive correlation with HC.Ar/On.Ar (P 0.05) and HC.Pm/B.Ar (P 0.01). We conclude that: 1) the size of the osteon is determined by the quantum of bone removed by osteoclasts, 2) the osteon is well designed for molecular exchange, and 3) a well designed osteon may be produced via the regulation of bone apposition by osteocytes during the process of osteon refilling. Anat Rec Part A 272A: , Wiley-Liss, Inc. Key words: osteon; Haversian canal; osteocyte lacunae; anatomical correlation Bone remodeling in cortical bone produces an elongated and roughly cylindrical structure called the secondary osteon (Frost, 1973; Parfitt, 1994). A typical secondary osteon is separated from its surrounding bone by a thin cement line, and has a centrally located Haversian canal that contains blood vessels, a nerve, and some space occupied by interstitial fluid (Cooper et al., 1966; Cowin, 1999). The wall of the Haversian canal, which is also the bone surface of the osteon, is covered with flat lining cells (Cooper et al., 1966; Parfitt, 1983). Groups of osteocytes, which are enclosed within the interconnected lacunae and canaliculi in lamellar bone, form a complex cellular network by connecting with each other and with the cells on the bone surface via their long slender cytoplasmic processes (Marotti et al., 1990; Aarden et al., 1994). There are numerous canalicular openings on the bone surface (Marotti et al., 1985), which serve as a pathway for osteocyte processes as well as for transport of interstitial fluid. Based on morphology, the secondary osteon can be regarded as an independent bone unit because it contains its own cellular and blood supply systems. Grant sponsor: National Institutes of Health; Grant number: DK *Correspondence to: D. Sudhaker Rao, Bone and Mineral Research Laboratory, E&R Building 7071, Henry Ford Hospital, 2799 W. Grand Blvd., Detroit, MI Fax: (313) danrao47@yahoo.com Received 31 August 2002; Accepted 18 February 2003 DOI /ar.a WILEY-LISS, INC.

2 Much of the information concerning osteon anatomy was first published over 30 years ago (Frost, 1961; Enlow, 1962; Cooper et al., 1966), and mainly involved the areas of osteons and their Haversian canals. Takahashi and Frost (1965) suggested that these indices could be used to explore the characteristics of cortical bone remodeling. The size of the osteon, marked by the cement line, represents the extent of bone that has been resorbed by osteoclasts, whereas the area between the cement line and the Haversian canal represents the amount of bone formed by osteoblasts (Landeros and Frost, 1964; Takahashi and Frost, 1965). One can speculate that different-sized osteons also have different Haversian canals, bone volumes, and osteocyte numbers. A larger osteon would be expected to have a larger Haversian canal in order to provide sufficient nutrients to the osteocytes. However, to the best of our knowledge, there is no evidence to prove this hypothesis. Accordingly, we conducted a histomorphometric assessment of secondary osteons in the ribs of young white men. The changes in bone volume, Haversian canal, and osteocytes in different-sized osteons were investigated. MATERIALS AND METHODS Specimen Preparation Archived human rib sections were used for this study. The sections were obtained from nine healthy white men, years old. The method of sample processing has been previously described (Frost, 1960). In brief, the 3-inch rib segments were placed in 1% basic fuchsin and 40% ethyl alcohol for 4 weeks, and then immersed in a large volume of tap water for 48 hr. After the samples were hydrated, cross and longitudinal sections were cut from each rib, ground to a thickness of about 50 m, and mounted on the slide. Histomorphometry Microscopy of osteons and osteocyte lacunae was performed on the cross sections using a Nikon microscope equipped with a CCD video camera (Optronics, Goleta, CA). The microscopic image was imported to a Bioquant NOVA image analysis system (R&M Biometrics Inc., Nashville, TN) with a panel sized pixels. The length and width of the panel under 1 objective was mm. All of the secondary osteons that met the following criteria were examined: 1) an intact osteon with a clear boundary of cement line; 2) an Haversian canal area less than one-quarter of the osteon area, with no osteoid on its surface; 3) no Volkmann s canals crossing the osteon; and 4) no interference from the basic fuchsin intensity with the measurement of osteocyte lacunae. Based on these criteria, a total of 398 osteons from nine subjects were measured. The boundaries of the osteon and the Haversian canal were traced under bright light using a 10 objective, and then the stained lacunar profiles were counted under blue-violet epifluorescent light using a20 objective. Osteocyte lacunae can be readily identified under blue-violet light due to the strong fluorescence of basic fuchsin. Because epifluorescent light penetrates only a few microns below the specimen s surface, a thin section can be assumed for measuring osteocyte lacunae even though the bone section is thick ( m) (Mori et al., 1997; Vashishth et al., 2000). The primary measurements included the osteon area (On.Ar), Haversian canal area (HC.Ar) and perimeter HISTOMORPHOMETRY OF DIFFERENT-SIZED OSTEONS (HC.Pm), bone area (B.Ar On.Ar HC.Ar), and osteocyte lacunar number (Lc.N). From these parameters the following indices were deduced: 1) lacunar number per bone area (Lc.N/B.Ar) and per osteon (Lc.N/On); 2) the ratio between Haversian canal perimeter and osteonal bone area (HC.Pm/B.Ar), which is equal to the ratio of bone surface (BS) and bone volume (BV); and 3) the fraction of Haversian canal area (HC.Ar/On.Ar) and the fraction of bone area (B.Ar/On.Ar). Statistics The mean, standard deviation (SD), coefficient of variation (CV), and range of each variable were calculated. The relative frequency for different-sized osteons was calculated. Best-fitting nonlinear as well as linear regressions were used to test the associations among the variables. P 0.05 was considered significant. RESULTS 521 There was a great variety of sizes in the human rib osteons; even adjacent osteons varied greatly (Fig. 1A). In a comparison of different-sized osteons, a higher bone volume and a capacious Haversian canal were observed in the larger osteon, but the bone area fraction was similar. In longitudinal sections, the distance between two cement lines had changed little at various levels on the longitudinal axis of the osteon (Fig. 1B), indicating that an osteon has similar profiles at any given cross-sectional level. Because all bone sections were obtained from white men of similar age and without metabolic bone disease, the histomorphometric results were pooled. The numerical data for the 398 osteons are presented in Table 1. Among variables, bone area fraction (B.Ar/On.Ar) and lacunar density (Lc.N/B.Ar) had a relatively lower CV (particularly the former; see Table 1). Although the differences in osteon area could reach 10-fold, most of them (86%) were concentrated between 0.02 mm 2 and 0.07 mm 2 (Fig. 2). The scatterplots and linear and nonlinear regression lines between variables are shown in Figures 3 6, and their detailed parameters are given in Table 2. Relationship of Osteonal Size to Haversian Canal and Osteocyte Lacunae To examine the effect of osteonal size on the Haversian canal and osteocytes, On.Ar was used as an independent variable. Both HC.Ar and HC.Pm had a significant positive correlation with On.Ar (HC.Ar: r 0.643, P ; HC.Pm: r 0.673, P ) (Fig. 3A and B). The relationship between On.Ar and HC.Pm/B.Ar, however, was strongly negative (r 0.700; P ) (Fig. 3C). Lc.N/On significantly increased with the growth of On.Ar (r 0.927, P ) (Fig. 4A), but Lc.N/B.Ar showed a weak but significant negative correlation with On.Ar (r 0.143; P 0.05) (Fig. 4B). A similarity of regression lines was present for the association of Lc.N/B.Ar and HC.Pm/ B.Ar with On.Ar (Figs. 3C and 4B), in which a very steep downward slope occurred in the osteons smaller than 0.03 mm 2, after which the variation was very small. We did not examine the relationship between On.Ar and HC.Ar/ On.Ar because of their correlated derivation. Relationship Between Osteocyte Lacunae and Haversian Canal Lc.N/On and Lc.N/B.Ar were used as independent variables to determine their correlation with HC.Ar and

3 522 QIU ET AL. Fig. 1. A: Secondary osteons of various sizes are shown in cross section ( 10). B: In longitudinal section, the distance between two cement lines shows little change at various levels on the longitudinal axis of the osteon ( 4). TABLE 1. Histomorphometric values from 398 osteons in human rib Mean (S.D.) CV (%) Range On.Ar(mm 2 ) (0.018) Hc.Ar(mm 2 ) (0.001) Hc.Pm(mm) (0.054) Hc.Pm/B.Ar (mm/mm 2 ) 4.31 (1.71) HC.Ar/On.Ar (mm 2 /mm 2 ) 4.64 (2.23) B.Ar/On.Ar(%) 95.4 (2.23) Hc.Pm/On.Ar (mm/mm 2 ) 4.08 (1.52) Lc.N/B.Ar 848 (129) Fig. 2. Relative frequency for osteon areas. In 86% of the osteons the cross-sectional areas range from mm 2. HC.Pm, because osteocytes were formed before the Haversian canal. HC.Ar and HC.Pm increased significantly with increasing Lc.N/On (HC.Ar: r 0.555, P (Fig. 5A); HC.Pm: r 0.579, P (Fig. 5B)), but not with Lc.N/B.Ar. Lacunar density (Lc.N/B.Ar) had a significant positive correlation with HC.Ar/On.Ar (r 0.104, P 0.05) (Fig. 6A) and HC.Pm/B.Ar (r 0.136, P 0.01) (Fig. 6B). DISCUSSION To eliminate the potential effects of gender, race, and disease on the results, we restricted the examination only to young white men who had no history of bone disease. It has previously been shown that osteocytes decrease in number with age (Qiu et al., 2002a). Therefore, we chose a narrow age range (20 25 years) to reduce the effects of aging. In general, the values from a single osteon or subject may have a poor credibility, but values from multiple osteons in people of identical gender and race, and similar ages ( 5 years difference) could exhibit a high credibility. In recent years, the association between osteocytes and microdamage has been investigated using sections stained with basic fuchsin (Mori et al., 1997; Vashishth et al., 2000). In fact, these investigations (including the current study) observed osteocyte lacunae, rather than osteocytes, because basic fuchsin can stain both the osteocytes and the wall of lacunae. Sometimes it is difficult to distinguish stained osteocytes from stained lacunae. However, since the empty lacunae that remain after osteocytes die will be filled by mineralized osteoid tissue (Parfitt, 1993), the loss of osteocytes may be associated with a decrease in total lacunae. Our previous studies demonstrated a very strong positive correlation between total lacunar density and the lacunae occupied by osteocytes (r ) in human iliac bone, indicating that the total lacunar density explains about 97% of the variance in osteocyte density (Qiu et al., 2002b). Accordingly, the changes in osteocyte number can be predicted from the changes in total lacunar number, although the loss of osteocytes could be underestimated

4 HISTOMORPHOMETRY OF DIFFERENT-SIZED OSTEONS 523 Fig. 4. Relationship of osteon area to lacunar number per osteon (upper panel: r 0.927, P 0.001) and lacunar number per bone area (lower panel, r 0.143, P 0.05). Fig. 3. Relationship of osteon area to Haversian canal area (upper panel: r 0.643, P 0.001), Haversian canal perimeter (middle panel: r 0.673, P 0.001), and the ratio of Haversian canal perimeter/bone area (lower panel: r 0.700, P 0.001). Fig. 5. Relationship of lacunar number per osteon to Haversian canal area (upper panel: r 0.555, P 0.001) and Haversian canal perimeter (lower panel: r 0.579, P 0.001). because some empty lacunae are stained. In addition, we have found that the empty lacunae in superficial cancellous bone, equivalent to the osteon in cortical bone, account for only 3% of the total lacunae (Qiu et al., 2002a). On the basis of these results, we believe that extensive death of osteocytes may not occur in osteons because of their younger bone age. Therefore, all of the stained lacunae were regarded as osteocytes in this study. This and previous studies show that the osteons in cortical bone vary greatly in size, even between two adjacent osteons (Landeros and Frost, 1964; Martin and Burr, 1989). The mechanism(s) for the genesis of different-sized osteons remains unclear. It has previously been suggested that the cross-sectional size of an osteon is determined by the quantum of bone removed by osteoclasts in one resorption tunnel (Landeros and Frost, 1964; Takahashi and Frost, 1965). A well-known example is the repair of microdamaged bone. As many authors have suggested, bone remodeling (at least part of it) is targeted to repair microdamage in bone (Burr, 1993; Parfitt, 1993; Bentolila et al., 1998). For an entire crack to be removed, the size of an osteoclastic resorption cavity must be close to, or slightly larger than, the area of damaged bone. Therefore, different-sized areas of microdamage may result in different quanta of bone to be resorbed, which would produce different-sized osteons after the resorption cavities are refilled by new bone. We have found that microcracks in human ribs range in length from 20 m to200 m, and that 97% of the cracks are shorter than 150 m (unpublished data). Thus, the range of the osteon size suggests that the extent of bone resorption is sufficient to remove most of the microcracks. Our results demonstrate that HC.Ar, HC.Pm, and Lc.N/On are positively associated with On.Ar. Moreover, HC.Ar and HC.Pm grow with increasing Lc.N/On. These

5 524 QIU ET AL. Fig. 6. Relationship of lacunar density to the ratio of Haversian canal area/bone area (upper panel: r 0.104, P 0.05), and the ratio of Haversian canal perimeter/bone area (lower panel: r 0.136, P 0.01). relationships imply a potential coordination between the Haversian canal and the osteocytes. The Haversian canal contains blood vessels and interstitial fluid, and its wall, which is the osteonal bone surface, is the interface for molecular exchange between blood circulation and bone tissue (Martin and Burr, 1989; Cowin, 1999). There are two plausible explanations for the positive association between Haversian canal and osteon size. First, increased osteocytes in larger osteons need more nutrients, so a corresponding increase in the bone surface may be required to ensure adequate molecular exchange. Second, osteocytes are connected with osteoblasts and lining cells on the bone surface via their processes residing in the canaliculi (Marotti et al., 1990; Aarden et al., 1994). Accordingly, the number of osteocytes may determine the number of canalicular openings on the bone surface (Marotti et al., 1995). In order to maintain a relatively consistent density of canalicular openings in differentsized osteons, the osteon containing more osteocytes may need a larger bone surface. The bone surface and osteocytes could be regarded as structures responsible for molecular supply and demand in bone. The total amount of molecular exchange may be positively associated with the size of the bone surface, but the amount of molecules distributed to each unit of bone is probably determined by the BS/BV ratio. Likewise, the total amount of molecules in need may be positively associated with the total number of osteocytes, but the molecules in need by each unit of bone is probably determined by the osteocyte density. According to the ASBMR Histomorphometry Nomenclature Committee (Parfitt et al., 1987), the 2D parameters (bone area (B.Ar) and Haversian canal perimeter (HC.Pm/B.Ar)) in osteons can be defined as the 3D parameters (BV and BS). Thus, HC.Pm/ B.Ar can be regarded as the BS/BV ratio. Our results show that there is very little alteration of these two variables in most ( 75%) of the osteons. An exception to this is the smaller osteons ( 0.03 mm 2 ), in which the Lc.N/B.Ar and HC.Pm/B.Ar are inversely correlated with On.Ar. Many have reported that the osteon diameter in human cortical bone ranges from 150 m to300 m, and the cross-sectional area is about mm 2. The present study shows that about 86% of the osteons sized within that range, and the extremely large or small osteons, may be formed under abnormal conditions (Bell et al., 2001). Accordingly, we suggest that the osteocyte density and BS/BV ratio both remain relatively constant in the osteons sized within reference range. In addition, an intimate relationship between osteocyte density and BS/BV ratio in osteons could be derived from the significant positive correlation between Lc.N/B.Ar and HC.Pm/B.Ar. The relationships among On.Ar, Lc.N/B.Ar, and HC.Pm/B.Ar indicate that a similar homeostasis is present in the osteons. The strongly positive association between Lc.N/On and HC.Ar implies that osteocytes may be responsible for the formation of an optimal Haversian canal. Since the osteocyte system is formed before the completion of the Haversian canal, if there is any cause-and-effect relationship between them, osteocytes should be the cause. During the process of osteon refilling, some osteoblasts are entombed in bone matrix to become osteocytes, and many of them die by apoptosis (Weinstein and Manolagas, 2000). The bone apposition rate may gradually decline as a consequence of decreasing osteoblasts (Martin and Burr, 1989). However, because osteoblasts would not completely disappear as the osteon refilling continues (if no other factors are implicated in arresting their work), the only things stopping bone apposition may be the blood vessels, nerve, and other soft tissues in the Haversian canal. According to this scenario, the size of the Haversian canals may not vary with the size of the osteons. Therefore, the formation of an ideal Haversian canal in a given osteon likely depends on ending the bone apposition at the right time. It has been postulated that osteocytes produce signals to inhibit the secretory activity of osteoblasts (Marotti et al., 1990; Marotti et al., 1992). This inhibitory effect may contribute to the regulation of bone apposition during osteon refilling (Martin, 2000). At the beginning of osteon refilling, the new bone quickly deposits in the resorption cavity. With the thickening of the bone layer, the bone apposition rate progressively slows down until it completely stops (Jee, 1954; Lee, 1964; Manson and Waters, 1965; Polig and Jee, 1990; Martin, 2000). Our explanation for this is that during the process of osteon refilling, inhibitory signals originating from osteocytes may grow stronger (Martin, 2000). On the other hand, osteoblasts decrease in number as the Haversian canal becomes smaller (Martin and Burr, 1989). When the accumulated osteocytes can completely inhibit the activity of osteoblasts, bone formation is terminated. The inhibition of bone apposition by osteocytes is probably relevant to the reduction in interstitial fluid flow in forming bone. During the initial period of osteon refilling, there is a large central canal and few osteocytes. Thus, every osteocyte shares abundant interstitial fluid and nutrients. As the bone apposition progresses, the number of osteocytes increases but the size of the Haversian canal contracts, resulting in a reduction in interstitial fluid flowing to each osteocyte. In order to be well nourished and stimulated by interstitial fluid flow, osteocytes may pro-

6 HISTOMORPHOMETRY OF DIFFERENT-SIZED OSTEONS TABLE 2. Summary of regression analyses Variable Equations r P Independent (x) Dependent (y) On.Ar (mm 2 ) HC.Ar (mm 2 ) y e (9.38*x) HC.Pm (mm) y e (11.5*x) HC.Pm/B.Ar (mm/mm 2 ) y e ( 87.0*x) Lc.N/On (#/On) y * x Lc.N/B.Ar (#/mm 2 ) y e ( 273* x) Lc.N (#/On) HC.Ar (mm 2 ) y * x HC.Pm (mm) y * x Lc.Dn (#/mm 2 ) HC.Ar (mm 2 ) NS HC.Pm (mm) NS HC.Pm/B.Ar (mm/mm 2 ) y *x HC.Ar/On.Ar (%) y *x duce inhibitory signals to suppress bone apposition. The intensity of the inhibitory signals may be elevated with increasing osteocytes (Martin and Burr, 1989; Marotti et al., 1992). Once the interstitial fluid provided by the Haversian canal could not support more osteocytes, osteoblastic bone formation would be completely suppressed. Based on the regression of On.Ar on HC.Ar (Fig. 3A, Table 1), it can be concluded that the activity of bone apposition terminates when the Haversian canal area contracts to about 4 5% of the osteon area. However, in a few smaller osteons this percentage can approach 7%. With regard to the entire osteon, 3% of bone area (or volume fraction) is a small portion that would not severely affect bone structure, but could cause a remarkable change in the size of the Haversian canal. LITERATURE CITED Aarden EM, Burger EH, Nijweide PJ Function of osteocytes in bone. J Cell Biochem 55: Bell KL, Loveridge N, Reeve J, Thomas CD, Feik SA, Clement JG Super-osteons (remodeling clusters) in the cortex of the femoral shaft: influence of age and gender. Anat Rec 264: Bentolila V, Boyce TM, Fyhrie DP, Drumb R, Skerry TM, Schaffler MB Intracortical remodeling in adult rat long bones after fatigue loading. Bone 23: Burr DB Remodeling and the repair of fatigue damage. Calcif Tissue Int 53:S75 S80; discussion S80 S81. Cooper RR, Milgram JW, Robinson RA Morphology of the osteon. An electron microscopic study. J Bone Joint Surg Am 48: Cowin SC Bone poroelasticity. J Biomech 32: Enlow DH Function of the Haversian system. Am J Anat 110: Frost HM Presence of microscopic cracks in vivo in bone. Henry Ford Hosp Med Bull 8: Frost HM Human Haversian system measurements. Henry Ford Hosp Med Bull 9: Frost HM Bone remodeling and its relationship to metabolic bone disease. Springfield, IL: Charles C. Thomas. p Jee WSS Rate of individual Haversian system formation. Anat Rec 118:315. Landeros O, Frost HM The cross section size of the osteon. Henry Ford Hosp Med Bull 12: Lee WR Appositional bone formation in canine bone: a quantitative microscopic study using tetracycline markers. J Anat 98: Manson JD, Waters NE Observations on the rate of maturation of the cat osteon. J Anat 99: Marotti G, Remaggi F, Zaffe D Quantitative investigation on osteocyte canaliculi in human compact and spongy bone. Bone 6: Marotti G, Cane V, Palazzini S, Palumbo C Structure function relationship in the osteocyte. Ital J Miner Electrol Metab 4: Marotti G, Ferretti M, Muglia MA, Palumbo C, Palazzini S A quantitative evaluation of osteoblast osteocyte relationships on growing endosteal surface of rabbit tibiae. Bone 13: Marotti G, Ferretti M, Remaggi F, Palumbo C Quantitative evaluation on osteocyte canalicular density in human secondary osteons. Bone 16: Martin RB, Burr DB Structure, function, and adaptation of compact bone. New York: Raven Press. p Martin RB Does osteocyte formation cause the nonlinear refilling of osteons. Bone 26: Mori S, Harruff R, Ambrosius W, Burr DB Trabecular bone volume and microdamage accumulation in the femoral heads of women with and without femoral neck fractures. Bone 21: Parfitt A The physiologic and clinical significance of bone histomorphometric data. In: Recker RR, editor. Bone histomorphometry: techniques and interpretation. Boca Raton: CRC Press, Inc. p Parfitt AM, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR Bone histomorphometry: standardization of nomenclature, symbols, and units. Report of the ASBMR Histomorphometry Nomenclature Committee. J Bone Miner Res 2: Parfitt AM Bone age, mineral density, and fatigue damage. Calcif Tissue Int 53:S82 S85; discussion S85 S86. Parfitt AM Osteonal and hemi-osteonal remodeling: the spatial and temporal framework for signal traffic in adult human bone. J Cell Biochem 55: Polig E, Jee WS A model of osteon closure in cortical bone. Calcif Tissue Int 47: Qiu S, Rao DS, Palnitkar S, Parfitt AM. 2002a. Age and distance from the surface but not menopause reduce osteocyte density in human cancellous bone. Bone 31: Qiu S, Rao DS, Palnitkar S, Parfitt AM. 2002b. Relationship between osteocyte density and bone formation rate in human cancellous bone. Bone 31: Takahashi H, Frost HM The presence of frequency maxima in histograms of resorption space sizes in human rib cortex. Henry Ford Hosp Med Bull 13: Vashishth D, Verborgt O, Divine G, Schaffler MB, Fyhrie DP Decline in osteocyte lacunar density in human cortical bone is associated with accumulation of microcracks with age. Bone 26: Weinstein RS, Manolagas SC Apoptosis and osteoporosis. Am J Med 108:

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