Increase in pore area, and not pore density, is the main determinant in the development of porosity in human cortical bone

Authors


Mr C. David L. Thomas, School of Dental Science, University of Melbourne, Victoria 3010, Australia. E: cdthomas@unimelb.edu.au

Abstract

This study investigated the relative contributions of pore size and pore density (number of pores per mm2) to porosity in the midshaft of the human femur. Cross-sections were obtained from 168 individuals from a modern Australian population (mostly Anglo-Celtic). The study group comprised 73 females and 95 males, aged from 20 to 97 years. Microradiographs were made of 100-µm sections and porosity, pore areas and pore densities determined using image processing software. The cortex was divided into three rings radially and into octants circumferentially, and the porosity, pore area and pore density of each segment were calculated. Results show that 81% of the variance in porosity can be explained by changes in mean pore area with only a further 12–16% explained by changes in pore density. These effects were found to be constant across all areas of the cortex and in both sexes. These results are significant in their consistency and ordered gradation and indicate a well-regulated and systematic process of bone removal with ageing. The results show a regular progression from less porous to more porous bone; this is a uniform process that occurs in all individuals, and factors such as sex and rate of ageing determine where on this continuum any individual is at a particular time.

Introduction

Hip fractures, particularly in the developed world, are on the increase in both sexes due to the ageing of populations and a rise in the prevalence of osteoporosis (Boereboom et al. 1992; Cooper et al. 1992; Melton, 1993). However, bone mineral density (BMD) changes, the standard measure for predicting fracture risk, only account for a doubling of hip fracture risk between 60 and 80 years while the actual risk is much higher, a 13-fold increase (De Laet et al. 1997). Mainly cortical bone loss is implicated in hip fractures (Johnston et al. 1985; Bell et al. 1999) and it is the site-specific rather than the global changes in the cortices of susceptible bones that are thought to be a better predictor of fracture risk (Beck et al. 1992, 1993, 1996). Mayhew et al. (2005) recently showed that localized cortical thinning in the femoral neck, which occurred with age, particularly in women, compromised the elastic stability of the neck, greatly increasing the risk of hip fracture in a sideways fall: this was independent of osteoporosis but was enhanced in its presence. It is clear that a better understanding of how and where cortical thinning occurs and the principles underlying this process of bone loss are required. Geometric parameters (Ruff & Hayes, 1988; Simmons et al. 1991; Myers et al. 1993) as well as porosity (Schaffler & Burr, 1988; McCalden et al. 1993; Yeni et al. 1997, 1998) affect the mechanical properties of bone. Cortical bone strength (Wall et al. 1979; Dickenson et al. 1981), fracture toughness (Yeni et al. 1997, 1998), stiffness and the elastic modulus (Schaffler & Burr, 1988) are all affected by the porosity levels of bone. Yet despite this there is very little comprehensive data available on sex and age changes in the regional distribution of pore size and density, i.e. on the components of porosity, across complete cross-sections of bone. Early porosity studies (Jowsey, 1960; Atkinson, 1965; Martin et al. 1980; Martin & Burr, 1984) performed manually were necessarily limited in scope, in the number of individuals sampled, in the area of cortex examined and in the regional distribution and quantification of pore size and density. Unsurprisingly, results obtained from these studies were often in conflict. More recently, a few large studies, using automated or semi-automated methods, were carried out in an attempt to correct some of these deficiencies. Stein et al. (1999) examined complete midfemoral cross-sections in a modern, urban population sample but no attempt was made to determine the regional distribution of pore sizes and densities. Bousson et al. (2001) only studied the regional distribution of midfemoral porosity in the anterior cortex of a predominantly agrarian population of 163 individuals who died approximately a century ago and whose remains were exhumed 5–10 years after burial.

Over the last decade we have used material from the same collection as Stein et al. (1999) to study sex and age differences in total cortical bone loss, i.e. medullary plus intracortical (Feik et al. 1997), regional changes in cortical modelling (Feik et al. 2000), and distribution of porosity (Thomas et al. 2005), across entire transverse sections of the femoral midshaft. The current study logically follows on from the previous work in that the components of porosity are more closely examined. The aim of this study is to provide ‘normative’ data on the regional distribution of pore size (> 400 µm2) and density in the entire transverse cross-section of the midfemoral shaft across the adult lifespan of both sexes in a modern, urban Caucasian population. We also explore the relative contributions of pore size and density to porosity, noting sex and age differences if any.

Materials and methods

Bone specimens (n = 168) were collected at the Victorian Institute of Forensic Medicine, Melbourne, Australia, most between 1990 and 1993 and a smaller group in 1998. The people from whom samples were obtained were almost exclusively Anglo-Celtic in ethnic origin, as judged by names and facial appearance, and they had died suddenly with no known diseases directly affecting their bones. Information was available on the age, sex, supine length, weight and, in most cases, the cause of death. Details are presented in Table 1. The data groupings are described later in the section on data analysis. Specimens were sawn by mortuary staff from the midshaft of the femur and fixed in 70% ethanol but unfortunately, for the majority, the anatomical orientation of the specimens was not recorded. Only in the later small sample (20 specimens) was the orientation of the specimens known and all of these were obtained from the right femur. The specimens were cleaned manually and transverse sections, ∼300 µm thick, were cut from the femoral blocks using a Leitz 1600 sawing microtome (Leitz, Wetzlar, Germany). Plano-parallel sections with a nominal thickness of 100 µm were obtained from these by lapping on 1200-grade wet and dry carborundum paper.

Table 1.  Sex distribution of the study sample (grouped by MA/TSPA ratio)
Age group (years)FemalesMales
nMean age (years)SDFraction of totalnMean age (years)SDFraction of total
Low MA/TSPA group
 Young (20–44)2430.4 7.50.1432632.2 7.50.155
 Middle (45–64)1151.4 5.20.0662053.2 5.30.119
 Old (65+) 673.8 5.70.0362876.7 7.40.167
 Subtotal4142.420.50.2457454.720.20.441
High MA/TSPA group – sex distribution only
 All ages3276.617.70.1912173.213.30.125

Microradiography and image acquisition

The sections were microradiographed using a Matchlett Laboratories OEG X-ray tube with a copper target operated at 25 kV and 10 mA. The film used was Kodak SO-343 at a distance of 195 mm from the target. The microradiographs were mounted on glass slides and masked with black tape to define the borders and to control scattered light. An array of contiguous monochrome images from entire cross-sections was recorded by tiling on a computer-controlled X–Y stage (Prior ProScan) fitted to a Leitz Dialux 20 microscope. The camera used was a Diagnostic Instruments Spot 2 working at a resolution of 1315 × 1033 pixels. The image processing software used was Optimas (Media Cybernetics, Inc., Silver Spring, MD, USA) and data were recorded using Microsoft Excel. The field of view of the camera, using a 1× microscope objective (Leitz PL 1/0.04) and matching condenser, was ∼3.5 × 2.5 mm and most sections were contained within a rectangle of 30 × 35 mm, so that approximately 180 frames were needed to cover each specimen. Frame boundaries matched to a precision of 1 µm. In addition to the images of the bone, a bright-field image was acquired with a neutral density filter and this was used to correct for variations in illumination.

Montage reconstruction and data accrual

The images making up a single cross-section were combined into a montage (Fig. 1), from which the posterior surface of the femur was identified by the linea aspera and the medial and lateral aspects determined from macro- and microstructural features. The background and voids (pores) in the bone appeared black and were separated from the foreground bone on the basis of a threshold grey level of approximately 50. The outlines of the periosteal and endosteal boundaries of the bone, as well as all pores larger than ∼400 µm2 (∼23 µm diameter), were extracted automatically using the Optimas image-processing package. Having isolated the periosteal outline, Optimas calculated the location of the centroid and this value was recorded. The endosteal outline was reconstructed from a series of Fourier shape descriptors truncated at the eighth harmonic. More details of this process and of the image processing can be found in earlier papers based on the same material (Feik et al. 2000; Thomas et al. 2005). The total subperiosteal area (TSPA) and cortical area (CA) (as total foreground) were measured and the medullary area (MA) calculated from these measurements. At this stage of processing the data were in a series of Microsoft Excel spreadsheets, which contained the x,y coordinates of the linea aspera marker, the centroid of the periosteum and the centroid locations and areas (in mm and mm2, respectively) of all pores > 400 µm2 (Stein et al. 1999). Scatter plots created in Excel were used to check for, and remove, occasional spurious pore measurements that were due to image noise (mostly dust specks).

Figure 1.

Subdivisions of the cortex. A, anterior; AL, anterolateral; L, lateral; PL, posterolateral; P, posterior; PM, posteromedial; M, medial; AM, anteromedial. The three rings shown will be referred to as periosteal, midcortical and endosteal.

The cleaned data (4000–5000 pores in each specimen) were used to calculate average values of pore density (pores per mm2) and pore area (mm2) in anatomically defined subregions of the cortex (Fig. 1) using software written for Matlab V6.1 software (The MathWorks Inc., Natick, MA, USA). This software defined the boundaries shown in Fig. 1 in a polar coordinate system having its origin at the centroid of the periosteum. The original arbitrary Cartesian coordinates of all pore centroids were transformed into the same polar coordinate system. The total area of each segment of the cortex was calculated and the areas of all pores with a centroid falling within the area were summed.

Data analysis

Knowing the location and the area of each pore, we could determine the distribution of pore density and mean pore area (MPA) throughout the whole cross-section. Initially, we analysed the sample simply by age as we had done previously (Thomas et al. 2005) when describing the distribution of porosity in the same specimens. In this analysis the data were grouped by age into three (young 20–44, middle 45–64 and old 65+ years) and by position in the cortex, both radially (periosteal, midcortical and endosteal) and circumferentially (octants). Differences between mean values of pore density and MPA in each segment were assessed using one-way anova followed by Tukey's HSD tests where multiple comparisons were being made. This analysis revealed problems in specimens with very narrow cortices where division into rings and octants yielded such small segments that occasionally a single large pore comprised a significant proportion of an individual segment. To overcome this we decided on an additional grouping based on the MA/TSPA ratio (see table 2 in Thomas et al. 2005), which we previously found provided a biologically meaningful way of dividing the sample. For a fuller discussion and rationale for using this ratio, the reader is referred to our earlier work (Thomas et al. 2005). In the current analysis we grouped the whole sample into two (Table 1): in the first group were specimens with MA/TSPA values < 0.315 (the Low and Middle MA/TSPA groups in the earlier work); specimens with narrow cortices based on an MA/TSPA ratio = 0.315 (the earlier High MA/TSPA group) formed the second group. In an initial analysis the bones were separated into low- and high-ratio groups (wide and narrow cortices, respectively) and further grouped into sexes. The cortices were divided into octants, and values for porosity, MPA and pore density were calculated. In the wider cortex group a further analysis divided the cortex into three equal-width radial rings as well as octants and results were calculated for each sex divided into three age groups. Graphs of pore density and MPA were compared visually with the corresponding graphs of porosity (for detailed porosity results see Thomas et al. 2005). The results of this comparison were confirmed by a multiple regression analysis with porosity as the dependent variable and pore density, MPA, location within the cortex and age as predictors (SPSS v.13, SPSS Inc., Chicago, IL, USA).

Results

As shown in Table 1, in the first group, i.e. the low MA/TSPA ratio group, young males and young females make up approximately equal fractions (∼15%) of the total sample whereas old females (65+ years) comprise only ∼4% and old males ∼17% of the total. By contrast, the high MA/TSPA groups consist predominantly of old females (∼16% of total) with the old males in this group only accounting for < 1% of the total sample (data not shown). Hence, a marked sex difference with age is immediately apparent.

To obtain a clearer picture of the patterns of change in both sexes with increasing bone loss, in porosity, MPA and pore density we first compared the two groups with all ages and rings combined (Fig. 2) before proceeding with a detailed analysis of regional distributions in the low MA/TSPA ratio group (Figs 3 and 4). As can be seen in Fig. 2(a), in the low MA/TSPA ratio group, the patterns for porosity and MPA are very similar in that the greatest mean porosity and mean MPA are found in the posterior octants, followed by the anterior. This applies to both males and females, although males show consistently higher levels than females. The chief difference between the graphs Fig. 2(a.i) and Fig. 2(a.ii) is that in most octants the porosity is significantly different from the posterior whereas there are no significant differences in MPA between octants in either sex. Pore density (Fig. 2(a.iii)) differs from the aforementioned two parameters in that the highest level is seen in females in the anterolateral octant, this being the only measurement that is significantly different from the posterior in either sex. A multiple regression analysis (Table 2a) confirms that ∼81% of the porosity can be accounted for by MPA with an additional ∼16% due to pore density. Other factors such as location in the cortex and age play virtually no part in explaining porosity.

Figure 2.

Porosity (top), pore area (middle) and pore density (bottom) distribution around the cortex. Specimens grouped by sex. Graphs a(i), (ii) and (iii) are for subjects in the low MA/TSPA group, and b(i), (ii) and (iii) for those with high MA/TSPA ratios. Note the different vertical scales. Significant differences from the posterior octant (P = 0.05) are indicated by asterisks.

Figure 3.

Mean pore area distribution around the cortex, with specimens grouped by age. Graphs a(i), (ii) and (iii) are for females, and b(i), (ii) and (iii) for males. Note the different vertical scales. Significant differences from the posterior octant (P = 0.05) are indicated by lower-case letters for each age group (y, m or o).

Figure 4.

Pore density distribution around the cortex, with specimens grouped by age. Graphs a(i), (ii) and (iii) are for females, and b(i), (ii) and (iii) for males. Graphs (i) are for the periosteal ring, (ii) the mid cortex and (iii) the endosteal. Note the different vertical scales. Significant differences from the posterior octant (P = 0.05) are indicated by lower-case letters for each age group (y, m or o).

Table 2.  Predictors of log10(porosity), stepwise multiple regression results. (a) Low MA/TSPA ratio group, (b) high MA/TSPA ratio group

(a)

Model 1 Predictors: (Constant), Log10 mean pore area.

Model 2 Predictors: (Constant), Log10 mean pore area, Pore density.

Model 3 Predictors: (Constant), Log10 mean pore area, Pore density, Ring no.

Model 4 Predictors: (Constant), Log10 mean pore area, Pore density, Ring no., Octant.

Model 5 Predictors: (Constant), Log10 mean pore area, Pore density, Ring no., Octant, Age.

Model SSd.f.FPAdjusted R2
1Regression238.49   111453.50.0000.806
Residual 57.432758   
2Regression287.90   249486.30.0000.973
Residual  8.022757   
3Regression287.99   333332.30.0000.973
Residual  7.942756   
4Regression288.05   425205.00.0000.973
Residual  7.872755   
5Regression288.09   520254.80.0000.973
Residual  7.832754   

(b)

Model 1 Predictors: (Constant), Log10 mean pore area.

Model 2 Predictors: (Constant), Log10 mean pore area, Pore density.

Model 3 Predictors: (Constant), Log10 mean pore area, Pore density, Ring no.

Model 4 Predictors: (Constant), Log10 mean pore area, Pore density, Ring no., Age.

Model SSd.f.FPAdjusted R2
1Regression138.86   15400.90.0000.812
Residual 32.031246   
2Regression158.92   28264.70.0000.930
Residual 11.971245   
3Regression159.05   35566.20.0000.931
Residual 11.841244   
4Regression159.16   44217.10.0000.931
Residual 11.721243   

Figure 2(b) shows the equivalent graphs for the high MA/TSPA ratio group. Again the graphs for porosity and MPA closely resemble each other and the patterns are similar to those described for the first group, but here female samples are consistently more porous than males and the porosity levels are much higher. Note that the scaling of graphs in Fig. 2 (a.ii) and Fig. 2(b.ii) differs by a factor of four such that, for example, mean MPA in the posterior octant is up to eight times greater in females in the high MA/TSPA ratio group. The other obvious difference between the graphs is that there are many more significant differences posteriorly/anteriorly in a number of octants in both males and females in the second group, i.e. the regional distribution in MPA is more marked with increased bone loss. The graphs for pore density (Fig. 2(b.iii)) are almost the reverse of those for porosity and MPA, particularly in more porous areas; for example, in the posterior octants where MPA is highest, the pore density is lowest, in both sexes. In the less porous medial and lateral octants the pattern is not as clear, especially in males. Multiple regression analysis (Table 2b) reveals that again ∼81% of the variation in porosity can be accounted for by MPA with only a further ∼12% being due to pore density, bringing the total to ∼93% (vs. ∼97% for the low MA/TSPA ratio group). The other factors included in the equation, as before, contribute virtually nothing more.

Examining the data from the low MA/TSPA ratio group in more detail the following trends can be observed. In females (Fig. 3a) in each of the three rings, i.e. periosteal, midcortical or endosteal, the lowest values for MPA for each of the age groups are very similar but the upper values rise progressively as the group age increases, as does the range of MPAs. The actual values are given in Table 3 and the trends may be easier to discern here. When comparing rings we can see that MPA, not surprisingly, increases from the periosteal to the endosteal. The range of values also increases as the bones become more porous yet there is minimal overlap in each age group between these ranges from one ring to the next. Highest MPAs are generally found in the posterior and anterior regions with lower values in the lateral and medial, although there are some anomalies, e.g. the periosteal ring in the young group shows the greatest MPA in the lateral octant. The males (Fig. 3b, Table 3) show basically the same trends in MPA as the females; however, in all three rings and in all age groups, values generally tend to be slightly higher than in females. The spread of values is comparable with that for females in the periosteal and midcortical rings but greater in the endosteal in males. The regional distribution is also similar to females in that highest MPAs are usually found in the posterior and anterior regions but again there are some anomalies especially in the periosteal ring in the young group, as also found in the females.

Table 3.  Maximum, minimum and mean values of pore area (mm2) in the various subgroups of the low MA/TSPA ratio group
 FemalesMales
Min.Max.MeanRing meanMin.Max.MeanRing mean
Periosteal
 young0.00290.00380.0033 0.00310.00410.0036 
 middle0.00280.00480.00340.00330.00320.00500.00370.0039
 old0.00250.00540.0033 0.00340.00640.0043 
Midcortical
 young0.00350.00630.0043 0.00410.00690.0049 
 middle0.00370.00950.00570.00550.00480.01250.00690.0073
 old0.00290.01800.0065 0.00640.01780.0101 
Endosteal
 young0.00630.01670.0109 0.00800.03800.0221 
 middle0.01000.02140.01400.01390.01260.03520.02250.0248
 old0.00900.02330.0167 0.01480.04370.0297 

The mean pore density in females (Fig. 4a, Table 4) decreases from the periosteal to the endosteal and the range of values in each ring also becomes smaller as the medullary cavity is approached. When comparing each age group from ring to ring there is a tendency towards a progressive fall in pore density from the outer to the inner cortex. For example, the pore density in the young in the periosteal is less than it is in the young in the midcortical and even lower in the same group in the endosteal. The same trend is seen in the middle and old groups. The highest pore density in each ring is generally found in the middle group although this does not apply to the endosteal in females. When the regional distribution of pore density around the cortex is examined it can be seen that the lateral and anterolateral octants in the middle and young groups in all three rings generally display the highest pore densities, whereas in the old group the tendency is towards higher values in the posterolateral and anteromedial regions. In the males (Fig. 4b, Table 4) the mean pore density also decreases from the periosteal to the endosteal, although corresponding means tend to be slightly lower than in the females. The range of values in each ring is also lower than in females but does not show the same consistent decline towards the medullary cavity. From ring to ring the middle and old groups display reduced pore densities from the periosteal to the endosteal compared with values seen in the females; however, the young group does not quite conform to this pattern. Again, as with the females, the highest pore density in each ring is seen in the middle group. Owing to the smaller spread of pore density values in the males, in the periosteal and midcortical rings (Fig. 4b.i and ii) the middle and old groups are clustered together and clearly separated from the young group, unlike that in the endosteal ring (Fig. 4b.iii) or in the females. No clear pattern in the regional distribution of pore densities around the cortex can be seen in the periosteal and midcortical rings. In the endosteal ring higher pore densities are generally found in the medial and lateral octants in all age groups.

Table 4.  Maximum and minimum values of pore density (pores per mm2) in the various subgroups of the combined low MA/TSPA group
 FemalesMales
Min.Max.MeanRing meanMin.Max.MeanRing mean
Periosteal
 young9.0211.039.97 8.309.408.83 
 middle9.9914.2011.6710.7310.2212.0411.2510.26
 old9.0812.1810.47 9.7511.7510.70 
Midcortical
 young9.1410.839.73 9.289.469.34 
 middle9.8811.9610.7610.2610.3611.3410.8310.22
 old8.9610.9510.29 9.9210.8810.49 
Endosteal
 young6.968.087.34 6.507.386.95 
 middle6.488.447.36 7.617.328.167.827.45
 old7.418.938.13 7.118.327.59 

Discussion

In this study we measured the porosity, mean pore area and pore density in the midshaft femoral cortex of 73 females and 95 males from a modern Australian population. In order to study age and sex differences we divided the sample into three age groups, by sex, and into two groups based on MA/TSPA ratio, and we showed that these form two distinct populations in that all differences between mean values for MPA and pore density were highly significant (P = 0.000). Individual specimens were divided radially into octants and circumferentially into three rings to allow analysis of the distribution of measurements across the cortex.

Porosity can be almost wholly explained by MPA (∼81%), with a small contribution from pore density. A detailed examination of the regional distribution of MPA and pore density in the low MA/TSPA ratio group shows clear and consistent patterns. From the periosteal to the endosteal there is a progressive increase in MPA in each age group in both sexes. In addition, in both sexes the ring mean MPAs are significantly greater in the endosteal than in the two other rings. Males have significantly higher mean MPAs in all three rings than females. Highest MPAs are generally found in the posterior and anterior regions in both sexes, although there are some variations. Regional differences between octants become more marked as the age of the group increases and with proximity to the medullary cavity, i.e. the range of MPA values increases as the bone becomes more porous. Pore density values, in many respects, show the same trends as MPAs but in reverse. Ring mean pore densities and the mean range of values in each ring tend to decrease from the periosteal to the endosteal in both sexes. Within each ring, in all cases except the endosteal in females, the middle age group has the highest pore densities; by contrast, MPA values are always highest in the old. Although pore densities tend to be lower in males the differences between the sexes are not significant. Highest pore densities are generally found in the medial and lateral areas with only a few exceptions.

Having access to perhaps the largest collection of complete midfemoral cross-sections covering the adult lifespan of both sexes provided us with a unique advantage. The bones were well characterized, as has been previously reported in detail (Stein et al. 1999; Feik et al. 2000) and were obtained from a modern, prosperous and well-nourished, urban population largely Anglo-Celtic in origin. Hence, the results should be widely applicable to other developed countries; the prevalence of osteoporosis in Melbourne has been shown to resemble that of European and North American communities (Seeman et al. 1993). Automation of the data collection methods enabled a vast amount of data to be collected and also allowed the use of objective definitions for features such as the endosteal surface. For every specimen approximately 4000–5000 Haversian canals and resorption lacunae were located precisely and their areas determined.

The major limitation of the study was that the development of porosity could not be studied on a longitudinal basis: only a series of static pictures at different stages and ages from different individuals were available and a picture of how increasing porosity leads eventually to cortical thinning has to be inferred. In a study where invasive methods are used to obtain specimens, only a cross-sectional study is possible. Criticism can be levelled that the changes reported may be subject to cohort bias due to secular and lifestyle differences between generations, but this is unavoidable.

We discussed the rationale for using the MA/TSPA ratio rather than age alone in a previous paper (Thomas et al. 2005). In the current study use of this ratio proved particularly useful. It allowed us consistently to separate out the individuals with narrow cortices where radial subdivision into three rings often gave meaningless results as the delineated segments were too small or the spacing between ring outlines became close to zero. The resultant grouping of the sample into two broad categories seemed justified by the results in that the low vs. high MA/TSPA ratio groups form two distinct populations with highly significant differences between all mean MPA and pore density values. This further emphasizes the value of using a biologically meaningful measure such as MA/TSPA ratio as an alternative to simply grouping subjects by chronological age.

The relationships between porosity, MPA and pore density clearly show a consistent pattern of change that proceeds in a single direction. A change in porosity can only come about through an increase in pore area, an increase in the number of pores, i.e. pore density, or a combination of the two. We found that ∼81% of the change in porosity is explained by a change in pore area, and ∼16 and ∼12% by pore density in the low and high MA/TSPA ratio groups, respectively. The reduction in the independent contribution of pore density in the latter grouping implies an interaction between pore area and density when pore sizes are sufficiently large.

The generally higher MPA values in the anterior and posterior octants, compared with their medial and lateral counterparts, make sense when considered in the light of our previous findings on regional variations in cortical modelling (Feik et al. 2000) and intracortical porosity (Thomas et al. 2005). In these earlier studies we found evidence of progressive bone loss with increasing age occurring along a neutral axis of the cortex, i.e. porosity was greatest in the anterior and posterior, and least in the medial and lateral where periosteal apposition was greatest. Changes in the geometry of the femur resulted in more circular (eurycnemic) midshafts in the elderly and a concomitant shift in the neutral axis for bending towards the posterior and anterior poles where there would then presumably be greater resorption, i.e. a higher MPA value, something that has been corroborated by the current study. Further support for the results of our earlier work is found in this study in that in both older groups (males and females) the MPA values in the periosteal ring were lowest in the medial and lateral octants where, as described above, periosteal apposition has presumably been greatest and resorption least. The seemingly anomalous results in the periosteal ring in the young of both sexes in this study can perhaps be explained in terms of cortical ‘drift’ and as a result of remodelling lagging behind growth. Highest MPA values are found in the lateral followed by the medial, which would be consistent with a more rapid bone turnover rate in these periosteal regions, i.e. resorption on the lateral and apposition on the medial, as the bones are moved out and model back (‘drift’) into a position of equilibrium within their encasing soft tissues (Pollard et al. 1984).

The two most relevant recent articles on intracortical porosity in the midfemoral shaft are those of Stein and colleagues (including the present authors) (Stein et al. 1999) and Bousson and co-workers (Bousson et al. 2001). The former, investigating pore size and number across the entire cortex, concluded that age explains little of the interindividual variation found in these parameters and that the greater porosity in older specimens is due to greater pore size rather than a greater number of pores, findings that are consistent with those presented here. Bousson et al. (2001) also found that age per se bore little relation to porosity, explaining merely 13.5% of the variance in males and 52% in females. Results such as these provide further justification for our use of a geometric-based ratio such as MA/TSPA rather than age to explore the principles governing the process of bone removal.

A direct comparison of results between our study and that of Bousson et al. (2001) is difficult. The populations sampled were different, ours being modern, urban and prosperous, theirs from approximately a century ago and agrarian. They examined only the anterior cortex (∼200 pores per specimen) whereas we looked at the entire transverse cross-section (∼4000–5000 pores per specimen). However, our results are in broad agreement with theirs in that pore size and pore density increase from the young to the middle age groups with pore density reaching maximum values in the middle groups (with one case excepted). In the older groups in the present study pore size continues to increase but pore density declines, trends which are similar to those reported by Bousson and colleagues. When considering sex differences in the two studies, in both, higher pore densities were found in females than in males. However, Bousson and colleagues also found consistently higher mean pore sizes in females than in males, whereas we found this only in the high MA/TSPA group; in the low ratio group males had generally higher mean pore sizes. This difference may be due to the larger numbers of older men in the latter grouping as most of the older women, with their thinner cortices, fell into the high ratio grouping.

Data such as we have provided in this study are valuable for the verification of modelling of the structure of bone, particularly of models of cortical remodelling (Terrier et al. 1997; Hazelwood et al. 2001) and to provide reference data for non-invasive techniques, e.g. microcomputed tomography (Wachter et al. 2001, 2002), for determining the internal structure and porosity of bone. Many of the difficulties with the work reported in this paper are the consequences of using two-dimensional methods to study a three-dimensional structure. Current developments in micro-CT studies of bone (Cooper et al. 2004) will go a long way towards overcoming these problems. Future studies will examine more closely the relationship and subsequent interaction between pore size and density as pore size increases and cortical thinning proceeds. This process of cortical thinning in the midshaft will be compared with that in the femoral neck, an area of greater interest in ageing and osteoporosis studies.

Acknowledgements

We thank Professor Stephen Cordner, Director of the Victorian Institute of Forensic Medicine, and the staff of the mortuary and Donor Tissue Bank for their assistance in the collection of this series of bone specimens. We are also grateful to the next-of-kin of the donors for permission to remove bone for research purposes.

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