E. A. Messent¹, J. C. Buckland-Wright¹ and G. M. Blake²

Received: 2 August 2004  Accepted: 19 November 2004  Published online: 21 April 2005

Abstract  The purpose of this study was to determine whether fractal analysis (FSA) of macroradiographs or bone mineral density (BMD) is more sensitive in detecting disease-related cancellous bone alterations in knee osteoarthritis (OA). Differences in BMD between 11 OA (6 females) and 11 non-OA reference (7 females) tibiae were compared with differences in trabecular organization measured by computerized method of fractal signature analysis (FSA) of digitized macroradiographs (×3.5 to ×5). OA knees had anatomic and radiographic evidence of medial compartment disease. FSA measured cancellous bone organization at 4 regions of interest (ROI): medial and lateral subchondral (Sc) and subarticular (Sa) sites, dual X-ray absorptiometry (DXA) measured BMD at the same ROIs. Compared to non-OA, OA tibiae had significant increased (P < 0.05) in FSA of vertical trabeculae in the medial Sa region (trabecular size range: 0.42–0.54; 0.90–1.98 mm) and significant decrease (P < 0.05) in FSA for some horizontal trabeculae in the Sc region (trabecular size range: medial side 0.12–0.18 mm; lateral side 0.12–0.24 mm). Compared to non-OA, BMD of OA tibiae was not significantly different at any ROI. BMD was not sensitive to changes in trabecular organization detected by FSA. The increase in FSA of vertical trabeculae in the medial Sa region was consistent with trabecular fenestration and thinning, which may have been detected as decreased BMD in a larger sample. For studies involving small sample sizes, quantifying changes in trabecular organization is more sensitive than BMD for detecting bone alterations in knee OA.

Keywords  Knee osteoarthritis - Trabecular bone - Fractal analysis - BMD

Subchondral bone remodelling plays an integral role in the development of knee OA, as confirmed by animal models [1] and patient studies [2] in which thickening of the subchondral cortical plate was reported to occur prior to cartilage destruction. Subjacent to the thickened cortical plate, studies have reported hypomineralization of trabecular bone [3, 4]. This osteoporosis is possibly linked to abnormal bone cell behavior in OA joints, reported as imbalances in bone resorption, formation or both [5]. Recent studies have confirmed that increased bone resorption plays an integral role in the disease process, with increased levels of bone resorption markers reported in patients with radiolographic evidence of knee OA, including type I collagen [6], osteocalcin [7] and deoxypryidinoline [8]. In addition to bone being lost locally within the diseased joint, altered bone tissue contents has been reported in OA patients at sites distant from weight-bearing joints [9], including a study that demonstrated low BMD at the hip to be weakly correlated with OA knee progression [10].

Differences in tibial cancellous bone between patients with and without knee OA have been quantified using magnetic resonance imaging [11, 12], scintigraphy [13], dual energy X-ray absorptiometry [3, 14], and fractal analysis [15, 16]. These techniques quantify different bone parameters, such as structural organization [11, 12, 15], rate of turnover [13] and mineral density [3, 14]. A greater understanding of bone quality is achieved if data from two or more of these methods is acquired. For example, studies have shown that combining the fractal dimension and BMD data resulted in greater correlation with the biomechanical properties of the bone sample than when just one of these data sets was used [17–20]. Analyzed separately, fractal dimension of vertebral bone has been shown to be a better indicator of mechanical strength than BMD [21, 22]. However, we are not aware of any studies that have compared fractal analysis with BMD data from osteoarthritic and healthy bone specimens in order to determine which technique is more sensitive in detecting disease-related bone alterations.

Macroradiography, with its unusually good resolution, demonstrates the fine detailed structural organization of cancellous bone and this can be quantified by FSA. Structures within the tibia are more readily studied than those in the femur due to reproducible positioning of the former. Fractal analysis measures the degree of ‘roughness’ and ‘complexity’ of structures within an image, and also quantifies the change in ‘roughness’ with alterations in spatial scale [23]. Self-similar images (looking the same at all magnifications) [24] are said to be ‘fractal’ and have a fractal dimension (FD) associated with them, with a value between two and three for a surface [23]. When the pattern of a structure has altered at a particular size or sizes so as to be no longer self-similar, the ‘fractal signature’ of its image quantifies the alteration in the fractal dimension of the structure, and the size(s) at which those changes have occurred [25]. The fractal dimension, and similarly the fractal signature, has no units since it is calculated from the ratio of two areas [23]. The fractal dimension of cancellous bone assesses the composite nature of the tissue, which is determined principally by trabecular number, spacing and cross-connectivity [26]. Unlike other methods that calculate a mean fractal dimension from the overall appearance of cancellous bone [27], the FSA techniques measures the fractal dimension separately for vertical and horizontal trabeculae over a range of scales corresponding to a range of trabecular widths, identified as the ‘fractal signature’ [28]. A previous paper provides evidence of the robustness and applications of the technique [16].

Here, we obtained BMD and FSA measurements of the same regions of interest (ROI) within the proximal tibia of post-mortem knees with and without evidence of medial compartment knee OA in order to determine which technique is more sensitive in detecting OA-related bone differences.

Materials and Methods

Following Medical School authorization, permission was granted to image the following postmortem specimens; twenty-two knee joints from 19 cadavers. These were cleaned of surrounding soft tissue. Eleven (6 Females, mean (SD) age 89.9 (7.2)) were chosen because of evidence of medial compartment OA, including the presence of medial and/or lateral marginal osteophytes and/or substantially greater eburnated bone and damaged cartilage on the articular surfaces of the medial compartment of the tibia or femur compared to the lateral compartment. The remaining eleven (7 Females, mean (SD) age 71.2 (9.6)) were anatomically normal, with no evidence of osteophytosis, eburnation or cartilage damage upon visual inspection. Macroradiography confirmed that all knees selected for the non arthritic reference group had no evidence of OA and that those selected for the OA group had an osteophyte on either the medial or lateral tibial compartments.

Macroradiographs and Digitization of Macroradiographs

High-definition posteroanterior macroradiographs [29, 30] of the 22 tibiae were obtained at magnifications between ×3.5 and ×5 in the equivalent of the standing semi-flexed view [31]. Spatial resolution was between 25 and 50 μm [30]. The tibial shaft was positioned in a clamp so that the articular surface was horizontal relative to the floor, parallel to the central x-ray beam and perpendicular to the x-ray film. Correct positioning was confirmed using fluoroscopy. Radiographic magnification was determined from automated measurement of a metal ball (5-mm diameter) which was taped to the anterior surface of the proximal tibia. The joint was positioned with a film-to-object distance of 30 cm and a film-to-focus distance of 136 cm, resulting in radiographic magnification of between ×3.5 and ×5.

All macroradiographs were digitized using the high resolution Lumysis 200HR laser film digitizer (Lumysis, Sunny Vale, CA) at a pixel resolution of 60× by 60 μm (after correction for magnification) and the images were stored and analyzed with a Sun Sparcstation, model 20/61 (Sun Microsystems Ltd), and programs written in C++ were used to calculate the fractal signature of regions of interest within the images in Mdisplay.

Regions of Interest

Separate regions of interest (ROI) were identified for the assessment of trabecular bone structure consisting of the subchondral (Sc) and subarticular (Sa) regions within the medial (M) and lateral (L) compartments (Fig. 1). To account for variation in tibial size between patients, ROI width measured ³/₄ of tibial compartment width measured from a vertical line projected down from either the medial or lateral tibial spine to the outer tibial margin. The outer ¹/₄ of the width of the tibial compartment was not included for analysis due to the presence of periarticular osteopenia adjacent to marginal osteophyte formation [33]. The height of each ROI measured 100 pixels (6 mm). The Sc ROI commenced immediately beneath the inferior border of the medial or lateral cortical plates (Fig. 1), drawn onto the image by an automated ridge-tracing function in Mdisplay (Fig. 1). The Sa region commenced immediately below the inferior border of the Sc ROI.

Figure 1 Macroradiograph (×4) of a right proximal postmortem tibia showing placement of the medial (M) and lateral (L) subchondral (Sc) and subarticular (Sa) regions for FSA. Diameter of ball-bearing = 5 mm.

Measurement of Subchondral and Subarticular Cancellous Bone

Fractal analysis is a robust method [28, 34] that is independent of a range of factors that may vary during routine radiographic procedure, such as the effect of radiographic magnification and projection geometry [28, 34, 35] changes in object or patient positioning [23, 26, 28, 34–36] and variations in the sensitometric properties of radiographs such as film contrast and mean density [28, 34, 35]. FSA of vertical and horizontal trabecular structures for each ROI quantified trabecular structures ranging from 0.12 mm to 1.14 mm in increments of one pixel (0.06 mm). This range of sizes was chosen because trabecular thicknesses in the proximal tibia have been shown to fall within this range [37, 38]. The coefficient of variation for test re-test for FSA measurements was calculated as 1.8%.

Measurement of Subchondral Bone Mineral Density (BMD)

BMD of the four ROIs corresponding in size and position to those selected for FSA was quantified using the Hologic QDR4500 (Bedford, Massachusetts, USA) at the osteoporosis unit of Guy’s Hospital. Each tibia was positioned horizontally on the central region of the examination table, with the shaft parallel to the long axis of the table. The shaft of the tibia was supported by malleable dough such that the posterior and anterior lips of the articular surface of the medial tibial compartment aligned with each other in the vertical plane, perpendicular to the surface of the table and parallel to the X-ray beam. A soft-tissue substitute of 16 cm of water was used to eliminate the non-linearity in the BMD scale due to beam hardening. ROI placement was determined from the bone scan image (Fig. 2) using the manufacturer’s subregions software. BMD (g/cm²) for each ROI was computed. The precision error, based on repeat measures, was 2.5%.

Figure 2 A DEXA scan image of a right proximal postmortem tibia. BMD values were obtained from regions R1–R4. (R1 = M-Sc, R2 = M-Sa, R3 = L-Sc, R4 = L-Sa regions).

Statistical Analysis and Presentation of Data

Differences in the vertical and horizontal trabecular structures between the OA group and non-arthritic reference group were determined using 95% confidence intervals (CI) and the unpaired t-test. To simplify graphical presentation, the mean fractal signature for the ‘OA’ group was subtracted from that of the non-arthritic reference group (Fig. 3). Each graph presented the differences in fractal signature for the range of trabecular sizes from 0.12 mm to 1.14 mm. Data points below the abscissa corresponded to a decrease in complexity of the image texture (reduction in the FD), associated with a decrease in trabecular number, whereas those above the abscissa corresponded to an increase in complexity (increase in the FD), associated with an increase in trabecular number resulting from thinning and fenestration of coarser trabeculae. Differences in BMD between the OA and non-arthritic reference groups were identified in each ROI using unpaired t-tests. Differences in BMD or FD between medial and lateral compartments were identified using paired t-tests. The significance level for all tests was set at P = 0.05.

Figure 3 Mean difference in FD for vertical (i) and horizontal (ii) trabecular structures between the OA group and non-OA group in the M-Sc ⋅ ⋅ ⋅ ⋅ ⋅ ⋅, M-Sa – – – – – –, L-Sc _______, and L-Sa – ⋅ – ⋅ – ⋅ – ⋅ – regions. Significant differences indicated at P < 0.05 (■).

Results

Fractal Signature Analysis separately calculated the vertical and horizontal fractal dimension at trabecular sizes 0.12–1.14 mm at intervals of 0.06 mm for each ROI. Mean (SD) differences in fractal dimension between OA and non-OA groups are presented in Table 2. Separate graphs were produced for vertical and horizontal values (Fig. 3). See Statistical Analysis and Presentation of Data for further explanation of graphical presentation.

Differences in Trabecular Structure Between OA and non-OA Tibiae

Vertical Trabecular Structures

Compared to the non-OA group, FSA of cancellous bone of OA tibiae was significantly increased (P < 0.05) for vertical trabecular structures in the medial subarticular region at trabecular sizes 0.42–0.54 mm and 0.90–1.08 mm (Fig. 3(i)).

Horizontal Trabecular Structures

Compared to the non-OA group, FSA of cancellous bone of O A tibiae was significantly decreased (P < 0.05) for horizontal trabecular structures in the subchondral region (medial compartment: 0.12–0.18 mm, lateral compartment: 0.12–0.24 mm) (Fig. 3(ii)).

Differences in BMD Between OA and Non-OA Tibiae

Table 1 shows the mean (SD) BMD obtained from all ROIs in the OA and non-OA groups. No significant differences in BMD between OA and non-OA groups occurred at any ROI.

Table 1 Mean (SD) BMD (g/cm²) of the medial (M) and lateral (L) subchondral (Sc) and subarticular (Sa) regions in the OA and non-arthritic groups

Table 2 Mean difference and standard deviation (SD) in FD of (i) vertical and (ii) horizontal trabecular structures between the OA group and non-OA group in the medial (M) and lateral (L) subchondral (Sc) and subarticular (Sa) regions