Introduction

The biomechanical approach to cross-sectional geometry (CSG) analysis has a long tradition in biological research when studying an environmental impact (i.e., external mechanical stimuli) on bone tissues (for review, see Ruff 2007). The biomechanical approach is to analyse long bone cross sections with respect to engineering beam theory (Rybicki et al. 1972). Biomechanical parameters, such as areas and moments of area, are calculated from distribution and geometry of cortical tissue defined by periosteal and endosteal boundaries (Fig. 1).

It has been shown that the reliability of long bone CSG estimates used in biomechanical analysis is dependent not only on the technique used in taking the cross section but also upon the accurate determination of periosteal and endosteal contours in later processing (Stock 2002), when the periosteal contour of a bone is the most relevant to bone mechanical competence and the endosteal contour has less influence (Stock & Shaw 2007).

In deciding how to obtain the raw cross sections from long bone shaft, researchers may choose among noninvasive and invasive groups of methods (Ruff 2007; see summary of techniques in Table 1). Non-invasive methods estimate cross sections using external measurement (Pfeiffer 1980), moulding (Trinkaus & Ruff 1989, Trinkaus et al. 1999), Xray (O'Neill & Ruff 2004), computed tomography [CT] (Ruff et al. 1993, Ruff et al. 1994, Lieberman et al. 2004, Sládek et al. 2006a, b, 2007), micro-computed tomography [µCT] (Fritton et al. 2005), or peripheral quantitative computed tomography [pQCT] (Sone et al. 2006). If available, CT is the foremost method of choice (Sumner et al. 1985), because the method is very rapid and produces accurate two-dimensional images of inner and outer bone contours. Standard CT cannot be used, however, when analysing bones of small size (e.g., mouse bone). Therefore, µCT is often used for evaluating bone morphology and microarchitecture ex vivo in mice and other small animal models (Bouxsein et al. 2010). pQCT uses a small, highresolution CT machine that has builtin software for calculating section properties as well as bone density (Ferretti et al. 1996). There are alternative methods of CT technique, the most common using bi-planar radiography (Trinkaus & Ruff 1989), which can be used alone (the ellipse model method [EMM]; Stock 2002) or in combination with direct measurement of external bone contours (the latex cast method [LCM]; Trinkaus & Ruff 1989). LCM shows generally good correspondence to the true cross-sectional properties while EMM generally overestimates the true parameters (O'Neill & Ruff 2004). Previous research suggests that cross-sectional contours derived from LCM are within 5 % of those of the original bones (Trinkaus & Ruff 1989, Stock 2002).

Invasive methods visualizing periosteal and endosteal contours directly on natural or artificial cuts of the diaphyseal shaft include direct cutting of a section (Ruff & Hayes 1983), histological processing (Diab & Vashishth 2007), or using broken bone section (Ruff 2009). Cross sections can be either manually transformed into the image or scanned in using an optical scanner (Stock 2002). The choice between invasive and non-invasive techniques depends on the purpose of the given analysis. One of the main disadvantages of CT technique is an absence of histological information for cortical tissues between the periosteal and endosteal boundaries. Several techniques have been developed in recent years to obtain nondecalcified histological sections whereby both cross-sectional geometry as well as histology can be studied (Ciani et al. 2009).

What remains similar between invasive and noninvasive methods is how the raw periosteal and endosteal contour is later processed. In each case, the contour must be transferred in order to be useful for calculating cross-sectional properties. Several software applications have been developed for deriving cross-sectional geometric properties either from section images directly (Ruff 2007) or from digitized pictures [CT-i] (Sailer et al. 2003), [MomentMacro for ImageJ] (Ruff 2006). These all work according to basic engineering principles (for a description of the algorithms, see Nagurka & Hayes 1980). The most reliable transfer of periosteal and endosteal contour is direct digitization by setting points on the periosteal and endosteal boundaries. Experience shows that it is difficult to produce reliable estimates using an automated digitization approach (i.e., whereby contours are estimated automatically using pixel values for boundaries between ‘air’ and ‘bone’ that are defined a priori). The raw cross sections are usually accompanied by artefacts introduced by technique as well as preservation. Since cross-sectional properties are calculated as ‘ideal’ geometry of cortical tissue between periosteum and endosteum, the artefacts are not of interest per se. The points must therefore be carefully located manually on the cross-sectional boundary, with the researcher deciding whether is artefact unimportant for estimated values, what is the effect of preservation, where is the natural boundary of the cross section, and how to set up the points to best reflect the natural geometry of the cross section.

It is clear that part of variability differences in later biomechanical analysis of CSG properties is due to intra- and inter-observer error introduced by digitizing. The goal of this paper is to determine intra-observer measurement error in calculating CSG parameters based on the digitizing of periosteal and endosteal contours. It is assumed that the intra-observer measurement error of the digitization method tested in this study will be similar to that of CT digitization (Sailer et al. 2003) and can be minimized by the observer's acquiring experience in the cross-sectional digitizing.

Fig. 1.

The left tibia cross-section at 50 % biomechanical length [A] with the detail of cortical bone [B]. The periosteal (1) and endosteal (2) digitalized margins are distinguished by black lines. The artefacts (3, 4) are pointed out in the detailed picture.

Table 1.

Summary of techniques used for cross-sectional geometry analysis.

Material and Methods

Laboratory mice (Mus musculus) of the B6CBA strain were used (males: n = 10; females: n = 7) for the CSG parameters analysis. The animals were nine months old and kept in standard laboratory conditions. All procedures involved in obtaining bone samples were in compliance with EU guidelines for scientific experimentation on animals and with the permission of the Ethical Commission of the Faculty of Medicine in Pilsen, Czech Republic.

Intra-observer error measurement

Intra-observer error was tested in two different samples (set I and set II measurements). The set I measurement (n = 10; males) was performed by nine repeated measurements of CSG parameters. The first to eighth measurements were performed during one month's time. The ninth measurement was made six months later on the same sample. The eighth measurement was chosen as the reference, because it was assumed that the error of repeating measurements should be smallest between the seventh and eighth measurement and that the error decreases with the number of measurements performed. Intra-observer error of the set II measurements (n = 7; females) was tested one week later after the set I measurement by eight repeated measurements to determine whether the intra-observer error of the set I measurements could be influenced by memorizing of each cross section instead of from experiencing the section digitizing. Intra-observer error was tested according to the method used in a study by Sládek et al. (2012). Intra-observer error was calculated for TA, CA, I_max, I_min, I_min/I_max and J. The difference between each measurement was estimated by mean difference (MD). MD varies from negative to positive values. The MD was calculated by the following formula used in the study by Sládek et al. (2012):

Where M1_i is the first compared (first-seventh; ninth) measurement, M2_i is the eighth measurement and n = 10 (for set I measurements) and n = 7 (for set II measurements) is the sample size.

Fig. 2.

The mean error (%) from first to ninth measurements compared to eighth (reference) measurement for total area (TA), cortical area (CA) and polar moment of area (J).

The overall error was expressed by mean absolute difference (MAD). MAD has only positive values and is computed as follows (Sládek et al. 2012):

The symbols are described above.

Table 2.

Total area (TA). Numbers 1–9 in column headings indicate measurement record for ten tested individuals. For computation and abbreviation, see Material and Methods.

The interval within which we would expect to find 95 % of differences between the first and second recordings is estimated by the limit of agreement (95 % LA). The 95 % LA was computed using the approach of Bland & Altman (1986):

Table 3.

Cortical area (CA). Number 1–9 in column headings indicate measurement record for ten tested individuals. For computation and abbreviation, see Material and Methods.

Results

The results for the set I measurements are presented in Tables 2-4, Appendices 1-2 and Fig. 2. Each studied parameter showed decreasing error with increasing number of repeats. The greatest difference (MD) as well as overall error (MAD) between first and eighth measurements was found for I_min (3.63 %), J (3.41 %) and I_max (3.40 %). Compared to I_max, I_min and J, the I_max/I_min (1.68 %), CA (2.41 %) and TA (2.52 %) were less susceptible to error at the start of the digitization learning (Fig. 2). By the completion of eight consecutive measurements, each parameter was reduced below 2 % error: TA (0.73 %), CA (1.14 %), I_max/I_min (1.19 %), I_max (1.60 %), J (1.73 %) and I_min (1.94 %). The availability of a measurement after the interval of six months showed no effect in relation to the time that had passed since the digitization skill was acquired. However, the measurement errors for I_max (1.66 %) and I_max/I_min (1.42 %) were slightly increased while those for TA (0.54 %), CA (0.97 %), I_min (1.25 %) and J (1.33 %) were decreased.

Table 4.

Polar moment of area (J). Numbers 1–9 in column headings indicate measurement record for ten tested individuals. For computation and abbreviation see Material and Methods.

The results from the set II measurements confirm learning of the digitization process, rather than simply learning of the given sample. The measurement error of the new sample was below 1 % for each parameter during each of the consecutive measurements. For the first measurement, the error was highest for I_min (0.48 %), I_max (0.46 %) and J (0.43 %) and lower for TA (0.18 %), I_max/I_min (0.21 %) and CA (0.32 %). In the last measurement, the intra-observer error was only slightly changed: I_max (0.62 %), J (0.47 %), I_max/I_min (0.37 %), CA (0.35 %), I_min (0.32 %), and TA (0.20 %). These results confirm our findings from the set I measurements that I_max, I_min and J are the most susceptible to measurement error in the first measurement on an unknown sample.

Discussion

The results of this study demonstrate that crosssectional parameters derived from the tested digitization of periosteal and endosteal contours can be accurately used to estimate cross-sectional areas (TA, CA) and second moments of areas (I_max, I_min, I_max/I_min, J). Digitization of periosteal and endosteal cross-sectional contours of further use for histological processing is probably more difficult to be compared with methods using CT (e.g., Sailer et al. 2003). Histological samples are obtained invasively and undergo longer preparation processes that include cutting, grinding and histological staining of the cross section. The great advantage of the method used in this study, however, is the possibility to analyse both histological and CSG parameters of the long bones. Although we expected that intra-observer error of the tested method would be similar to that of CT, the results do not confirm our assumption. Intra-observer error from the digitization method used in this study was lower compared to the intra-observer error of the CT method used in Sailer et al. (2003). In the study by Sailer et al. (2003), however, the intra-observer error was calculated for measurements of human tibia cross sections. It remains unclear whether error differences between the two data sets could be influenced by the much different sizes of the measured cross sections.

Accuracy of the tested method was estimated by intra-observer error measurement according to the study by Sládek et al. (2012). Accuracy and precision can be interpreted only with respect to the level of error that is acceptable. The accepted error is frequently specified by a value derived from empirical observations (Hunter 1980, Meloun & Militký 1998) and is defined as the numerical accepted error (Sládek et al. 2010). A standard for acceptable error has not been developed for CSG comparison. Trinkaus & Ruff (1989) suggested a 5 % level of accepted difference to characterize reasonably accurate cross section measurements. Although the 5 % level of accepted error was later used in other methodological studies (Stock 2002, O'Neill & Ruff 2004), the established level was used only for human CT cross sections.

The intra-observer error measurement was tested in two samples. The first sample (set I) was digitized nine times. The last digitization was performed six months later to test the affect of placing a time interval between each measurement. Thus, this tested whether experience of a digitization process can be forgotten after some period of time. The results showed that the difference between intra-observer error for the eighth and ninth measurements was not influenced by the longer time interval between those measurements (see Fig. 2).

We assumed the possibility of memorizing each cross section during the digitization. According to this assumption, two different samples (set I and set II) were used to test whether the intraobserver error could be influenced by repeating and memorizing one sample digitization. Because intra-observer error of set II measurement was from the beginning smaller than that at the end of the set I measurement, we confirmed learning of the digitization process rather than learning of the sample.

Intra-observer measurement error could also be affected by the quality of the tested sample. The technique of obtaining the cross section and the process of histological staining can produce artefacts. Because the cross sections were calculated as an ‘ideal’ geometry of cortical tissue, the researcher had to decide which artefacts were unimportant for the estimated values. It is assumed that the intra-observer error could be affected by the frequency and size of artefacts in the raw cross sections. Learning of the digitization process could be slowed by a higher frequency of the cross-section artefacts.

Our results show that second moments of area (I_max, I_min and J) are more susceptible to intra-observer error than are cross-sectional areas (TA, CA). This could be caused by computational algorithms used for calculating second moments of area from defined periosteal and endosteal contour information. In our study, the intra-observer error in measuring total area was generally lower than was the intra-observer error in measuring cortical area. Cortical area is calculated using values from both periosteal and endosteal contours and total area is calculated using only values from the periosteal contour. These facts suggest that the digitization of endosteal contour might be more difficult to learn. Difficulties in digitizing of endosteal contour could be caused by a greater presence of artefacts on the endosteal boundary. While during the preparation of histological samples the soft tissue was removed from the periosteal and endosteal surface to reduce the presence of artefacts, it was more complicated to remove soft tissue from the endosteal surface.

Conclusion

Intra-observer error in the bone cross-section digitization technique used in this study was within 2 % for all the analysed CSG parameters (TA, CA, I_max, I_min, I_max/I_min, J). The intra-observer error attained cannot be interpreted as being either high or low, because the necessary level of accuracy and precision must be determined with reference to the specific research. Our results can serve the purpose of estimating accepted error for future studies. The results of this study confirm our assumption that the impact of intra-observer error during digitizing of periosteal and endosteal contour on CSG properties decreases with the number of repeated measurements. Thus, intra-observer measurement error for the digitization method used in this study can be minimized by acquiring experience in the section digitizing. This phenomenon is not caused by the memorization of measured bone cross sections and is not affected by the time interval between each measurement. Our results show that TA, CA and J are more susceptible to intra-observer error than are I_max, I_min and I_max/I_min. The results do not confirm our assumption that intraobserver measurement error for the tested digitization method is similar to that for CT digitization used in some previous studies. Even though digitization of histological sample can be more difficult to perform, the intra-observer error of the digitization method used in this study was lower than that reported earlier for CT digitization.