Background This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk.
Background
This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk.Methods Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for analysis. The power spectrum was obtained from the Fourier transform of each region and three profiles were produced; a circular profile and profiles parallel and perpendicular to the preferred orientation of the trabeculae. PCA was used to generate a score from each profile, which we hypothesised could be used to discriminate between the fracture and control groups. The fractal dimension was also calculated for comparison. The area under the receiver operating characteristic curve ( A z ) discriminating the hip fracture cases from controls was calculated for each analysis.
Methods
Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for analysis. The power spectrum was obtained from the Fourier transform of each region and three profiles were produced; a circular profile and profiles parallel and perpendicular to the preferred orientation of the trabeculae. PCA was used to generate a score from each profile, which we hypothesised could be used to discriminate between the fracture and control groups. The fractal dimension was also calculated for comparison. The area under the receiver operating characteristic curve ( A z ) discriminating the hip fracture cases from controls was calculated for each analysis.AzResults Texture analysis of standard radiographs using the fast Fourier transform yielded variables that were significantly associated with fracture and not significantly correlated with age, body mass index or femoral neck bone mineral density. The anisotropy of the trabecular structure was important; both the perpendicular and circular profiles were significantly better than the parallel-profile ( P  < 0.05). No significant differences resulted from using the various ROI within the proximal femur. For the best three groupings of profile (circular, parallel or perpendicular), method (PCA or fractal) and ROI ( A z  = 0.84 – 0.93), there were no significant correlations with femoral neck bone mineral density, age, or body mass index. PCA analysis was found to perform better than fractal analysis ( P  = 0.019).
Results
Texture analysis of standard radiographs using the fast Fourier transform yielded variables that were significantly associated with fracture and not significantly correlated with age, body mass index or femoral neck bone mineral density. The anisotropy of the trabecular structure was important; both the perpendicular and circular profiles were significantly better than the parallel-profile ( P  < 0.05). No significant differences resulted from using the various ROI within the proximal femur. For the best three groupings of profile (circular, parallel or perpendicular), method (PCA or fractal) and ROI ( A z  = 0.84 – 0.93), there were no significant correlations with femoral neck bone mineral density, age, or body mass index. PCA analysis was found to perform better than fractal analysis ( P  = 0.019).PAzPConclusions Both PCA and fractal analysis of the FFT data could discriminate successfully between the fracture and control groups, although PCA was significantly stronger than fractal dimension. This method appears to provide a powerful tool for the assessment of bone structure in vivo with advantages over standard fractal methods.
Conclusions
Both PCA and fractal analysis of the FFT data could discriminate successfully between the fracture and control groups, although PCA was significantly stronger than fractal dimension. This method appears to provide a powerful tool for the assessment of bone structure in vivo with advantages over standard fractal methods.

Background The NIH Consensus Statement defines Osteoporosis as "a skeletal disorder characterised by compromised bone strength predisposing to an increased risk of fracture" [ 1 ]. Bone strength was defined as "the integration of two main features: bone density and bone quality". Currently, clinical diagnosis is based solely on bone mineral density (BMD) in accordance with the World Health Organisation guidelines [ 2 ]. Previous studies, however, have found that trabecular bone structure also plays a significant role in determining bone strength [ 3 - 5 ] with BMD explaining only 60 to 80 % of the variability in mechanical resistance [ 6 ]. Trabecular bone structure is visible on standard pelvic radiographs and many attempts have been made to quantify the quality of the structure and assess its relationship to osteoporosis and BMD. These range from visual scoring systems, such as the Singh index [ 7 ], through to sophisticated computerised methods based on fractals [ 8 - 10 ] and other image processing methods [ 11 - 13 ]. A review of the literature suggests that fractal analysis has been a method of choice in recent years for the analysis of trabecular bone structure in CT scans [ 14 , 15 ], MRI [ 16 ], histology [ 17 ] and radiographs [ 18 - 21 ], although it has not been established categorically that it is preferable to other methods of texture analysis [ 22 , 23 ]. By reducing all the information in the image to one descriptor, the fractal dimension [ 24 ], a large part of the information is lost. The Fourier transform of an image expresses the information in the image in terms of spatial frequencies rather than distances. Various methods can be applied to extract information from the Fourier transform [ 25 ], including the fractal dimension [ 24 ]. However such methods have not been fully exploited for analysing bone structure [ 8 , 26 - 30 ]. In this study we investigate the use of Fourier transforms and Principal Components Analysis to generate a mathematical model of the data which can be used to help classify individuals according to the presence or absence of a hip fracture. Principal component analysis (PCA) [ 31 ] is a data reduction technique that has been applied in many fields of study, including investigation of gene expression [ 32 ], development of an electronic nose [ 33 ] and tracing of the evolutionary changes in fish morphometry [ 34 ]. It describes data in terms of a small number of orthogonal, linearly independent components which contain the majority of the information. PCA has no preconditions, such as relying on the data to fit a normal or fractal distribution, but builds a mathematical model based on the correlations present in the data. An eigenanalysis of the correlation or covariance matrix is used to perform PCA. The resulting components are then selected in order of the amount of variance they account for, enabling an efficient mapping of the data. As the first few components account for the vast majority of the variance in the original data, they can be selected for analysis whilst the remainder are discarded as 'noise'. In this way, the number of variables can be greatly reduced whilst maintaining the information present in the original data. In this pilot study we used these methods to investigate the similarities and differences between trabecular bone structure in fracture and control groups using standard radiographs of the proximal femur.
Background
The NIH Consensus Statement defines Osteoporosis as "a skeletal disorder characterised by compromised bone strength predisposing to an increased risk of fracture" [ 1 ]. Bone strength was defined as "the integration of two main features: bone density and bone quality". Currently, clinical diagnosis is based solely on bone mineral density (BMD) in accordance with the World Health Organisation guidelines [ 2 ]. Previous studies, however, have found that trabecular bone structure also plays a significant role in determining bone strength [ 3 - 5 ] with BMD explaining only 60 to 80 % of the variability in mechanical resistance [ 6 ].Trabecular bone structure is visible on standard pelvic radiographs and many attempts have been made to quantify the quality of the structure and assess its relationship to osteoporosis and BMD. These range from visual scoring systems, such as the Singh index [ 7 ], through to sophisticated computerised methods based on fractals [ 8 - 10 ] and other image processing methods [ 11 - 13 ]. A review of the literature suggests that fractal analysis has been a method of choice in recent years for the analysis of trabecular bone structure in CT scans [ 14 , 15 ], MRI [ 16 ], histology [ 17 ] and radiographs [ 18 - 21 ], although it has not been established categorically that it is preferable to other methods of texture analysis [ 22 , 23 ]. By reducing all the information in the image to one descriptor, the fractal dimension [ 24 ], a large part of the information is lost. The Fourier transform of an image expresses the information in the image in terms of spatial frequencies rather than distances. Various methods can be applied to extract information from the Fourier transform [ 25 ], including the fractal dimension [ 24 ]. However such methods have not been fully exploited for analysing bone structure [ 8 , 26 - 30 ].In this study we investigate the use of Fourier transforms and Principal Components Analysis to generate a mathematical model of the data which can be used to help classify individuals according to the presence or absence of a hip fracture. Principal component analysis (PCA) [ 31 ] is a data reduction technique that has been applied in many fields of study, including investigation of gene expression [ 32 ], development of an electronic nose [ 33 ] and tracing of the evolutionary changes in fish morphometry [ 34 ]. It describes data in terms of a small number of orthogonal, linearly independent components which contain the majority of the information. PCA has no preconditions, such as relying on the data to fit a normal or fractal distribution, but builds a mathematical model based on the correlations present in the data. An eigenanalysis of the correlation or covariance matrix is used to perform PCA. The resulting components are then selected in order of the amount of variance they account for, enabling an efficient mapping of the data. As the first few components account for the vast majority of the variance in the original data, they can be selected for analysis whilst the remainder are discarded as 'noise'. In this way, the number of variables can be greatly reduced whilst maintaining the information present in the original data. In this pilot study we used these methods to investigate the similarities and differences between trabecular bone structure in fracture and control groups using standard radiographs of the proximal femur.Methods Study data A set of digitised standard pelvic radiographs was available from a previous investigation into the morphology of the proximal femur [ 35 ]. These radiographs were taken from an earlier study [ 36 ], that had examined three groups (osteoporotic, osteoarthritic and control) of age matched, postmenopausal women (30 subjects per group). Subjects with osteoarthritis were excluded from the present study. All patients had undergone a scan of the unfractured hip by dual-energy x-ray absorptiometry (DXA) using a Norland XR-26 scanner (CooperSurgical Inc, Trumbull, CT). The controls had had their left hip scanned. All patients and controls had had a pelvic antero-posterior radiograph recorded within a year of the DXA scan. We used those radiographs and the femoral neck BMD (Neck-BMD) data in the current study. A data set of 50 digitised radiographs was available comprising 26 hip fracture patients (HIP) and 24 controls (CNT). The radiographs were digitised, using a Howtek MultiRAD 850 scanner (Howtek, Hudson, New Hampshire) at a resolution of 584 dpi (44 μm per pixel) and a depth of 12 bits. The age, height and weight of each subject were also recorded. Region selection Five regions of interest (ROIs) were selected relative to the principal trabecular systems in locations known to be related to hip fracture via the Singh index [ 7 ] and BMD analysis [ 37 ]. To ensure reproducibility, their locations were determined in relation to the centre and angle of the narrowest part of the femoral neck and the centre and radius of the femoral head on each image, as shown in Figure  1 . Figure 1 Regions of interest.  Displays the five regions of interest, upper femoral head (UH), central femoral head (CH), upper femoral neck (UN), Ward's triangle area (WA) and the lower femoral neck (LN) used for analysis. Points A to G are determined by the femoral head and neck and used to locate the ROIs. Points A and E mark the femoral neck width. Points B, C and D lie at 1/4, 1/2 and 3/4 along this line. Point F is the centre point of the femoral head, point G at 1/2 the radius of the femoral head at an angle of 45 degrees to the neck width, 135 degrees to the neck shaft, shown as a dashed line through point C. Each ROI was 256 × 256 pixels (11.3 mm square), to enable use of the fast Fourier transform, and were selected as follows. The upper region of the head (UH) lies on the upper part of the principal compressive trabeculae, the central region of the head (CH) is at the intersection of the principal compressive and tensile trabeculae, the upper region of the neck (UN) lies on the principal tensile trabeculae, the lower region of the neck (LN) is at the base of the principal compressive trabeculae and finally Ward's triangle (WA) which lies between these structures. The points and regions were identified using a macro written for Image Pro Plus software (version 4.1.0.0, Media Cybernetics, Silver Spring, Maryland). The femoral head was described by a best-fit circle, calculated from a series of manually marked points around the outline of the femoral head. Between 15 and 20 evenly spaced points were used to describe the outline, depending on the size of the head. The radius and centre (marked as F in Figure  1 ) of the femoral head were then taken from this circle. The narrowest part of the neck (neck-width) was determined using two automatic edge traces, marking the upper and lower outlines of the femoral neck. The first point and the direction for each trace were marked manually; the edge of the neck could then be identified automatically by the software. The neck width (A – E in Figure  1 ) was calculated by finding the smallest Euclidean distance between the traces. The centre of the neck was located at the mid-point of this line (point C) and the axis of the femoral neck was taken to be a line perpendicular to this through the centre of the neck (dashed line). The top right corner of the WA region was located at the midpoint of the neck width (point C). Points B and D were placed 25% and 75% of the way along the neck width and used as the midpoints of the UN and LN regions respectively. Point F, the centre of the femoral head marked the centre of the CH region and point G, the centre of the base of the UH region. Point G was placed one half of the femoral head radius above point F, at a 45-degree angle to the neck width (A-E). Region analysis Analysis was performed using Matlab software (version 6.1.0, MathWorks Inc, Natick, Massachusetts). A fast Fourier transform was generated for each ROI and three profiles were generated using data from the power spectrum. Firstly a global or circular profile (CircP) was generated, composed of the magnitude at each spatial frequency averaged across all angles, resulting in a profile with 128 data points. To create this profile, each pixel in the Fourier transform was assigned to the integer spatial frequency that most closely matched its' distance from the zero'th component. The angle of preferred orientation was calculated by finding the angle of the maximum value in the power spectrum for the first 25 spatial frequencies [ 38 ]. The maximum value over this range relates to the dominant texture orientation within the image, the trabecular structure. As data in the frequency domain relate to features in the spatial domain rotated by 90°, the median of the values plus 90° was taken as the angle of preferred orientation for each image. Due to the symmetry of the Fourier power spectrum, angles were only calculated between 0° and 180°, rather than 0° and 360°. Two more profiles were then generated, parallel with (ParP) and perpendicular to (PerP) the angle of preferred orientation. In this case the average value was calculated at each spatial frequency from all points lying within ± 5° of the desired angle (Fig.  2 ). Figure 2 Profile generation.  (A) Shows a typical region of interest (contrast enhanced for visualisation) showing the trabecular bone structure, in this case aligned approximately 22° to the vertical. (B) The central section of the FFT (128 × 128 pixels). The horizontal and vertical axes have been marked with a mid-grey tone to indicate that they have been excluded from the angle calculation. The bright strip at the centre (running from top left to bottom right) shows the preferred orientation of the trabeculae. Angles calculated from the Fourier power spectrum correspond to the same angles in the spatial domain, rotated by 90°. (C) The pixels with the maximum values are marked using white squares for the first 25 spatial frequency values of the Fourier power spectrum. The median angle, lying 21.8° from the horizontal is shown by a dashed white line. (D)_The regions used to generate the parallel (shaded black) and perpendicular (shaded white) profiles, based on the orientation of the trabecular structure. Principal component analysis Principal component analysis [ 31 ] was used to model statistically the shape of each set of profiles (parallel, perpendicular and circular). This was performed using an eigenanalysis of the correlation matrix. The eigenvectors then become the principal components and are selected in order, depending on their eigenvalue. The eigenvalues are associated with the components in decreasing order, the largest eigenvalue is associated with the first component and the smallest with the last. In order to choose the number of components for analysis, a scree plot [ 31 , 39 ] was generated by plotting the eigenvalues (representing the proportion of variance described by each component) against the component number (Figure  3 ). In each case, the first few principal components were selected for analysis using the scree test [ 39 ] to find an 'elbow' in the slope of the plot. This is used as a threshold between the components that contained useful information, which were then used as input variables for further analysis, and those that could be attributed to noise. Figure 3 Scree plot.  Example of a scree plot from the perpendicular profile. The first component typically accounts for the largest amount of variance. The components are chosen to the left of an 'elbow' in the plot. Here components 1 to 5 are included in the analysis as they lie before the 'elbow' at point6 (eigenvalue = 1.63). Fractal analysis Fractal analysis was performed on each profile using a method similar to the Fourier transform technique described by Majumdar et al [ 40 ]. The average power spectrum of the circular profile was plotted on a log-log scale, three approximately linear regions were defined and the gradient ( slope ) of a straight line fitted to each region was found;  slopeA , a 'coarse' slope, where the log of the spatial frequency is less than or equal to 1.0,  slopeB  a 'medium' slope, where the log of the spatial frequency lies between 1.0 and 1.75 and  slopeC , a 'fine' slope where the log of the spatial frequency is above 1.75. The fractal dimension was calculated for each slope using the formula suggested by Majumdar et al [ 40 ] Statistical analysis Stepwise discriminant analysis was used to select principal components that could be combined to build a linear classifier. If the stepwise procedure failed to select any components, the most accurate of the individual components was chosen. The same procedure was used to discriminate between the groups using the fractal dimension. Measurement of the area under the ROC curve was used to compare the classifiers built using the discriminant analysis [ 41 ]. A three way ANOVA was applied in order to determine whether there were significant differences between the performance of classifiers depending on the type of analysis, the profile used or the region analysed. Pearson product moment correlation was applied to examine the relationship with age, BMI and Neck BMD for the strongest classifiers. A one-way ANOVA was used to test for significant differences in the performance of the slopes from each spatial frequency band used in the fractal analysis. T-tests, correlation and ANOVA were performed using SigmaStat (version 2.03, SPSS Science, Chicago). Principal component analysis, discriminant analysis, and measurement of the area under the ROC curve were calculated using SPSS (version 10 SPSS Science, Chicago).
Methods
Study data A set of digitised standard pelvic radiographs was available from a previous investigation into the morphology of the proximal femur [ 35 ]. These radiographs were taken from an earlier study [ 36 ], that had examined three groups (osteoporotic, osteoarthritic and control) of age matched, postmenopausal women (30 subjects per group). Subjects with osteoarthritis were excluded from the present study. All patients had undergone a scan of the unfractured hip by dual-energy x-ray absorptiometry (DXA) using a Norland XR-26 scanner (CooperSurgical Inc, Trumbull, CT). The controls had had their left hip scanned. All patients and controls had had a pelvic antero-posterior radiograph recorded within a year of the DXA scan. We used those radiographs and the femoral neck BMD (Neck-BMD) data in the current study. A data set of 50 digitised radiographs was available comprising 26 hip fracture patients (HIP) and 24 controls (CNT). The radiographs were digitised, using a Howtek MultiRAD 850 scanner (Howtek, Hudson, New Hampshire) at a resolution of 584 dpi (44 μm per pixel) and a depth of 12 bits. The age, height and weight of each subject were also recorded.
Study data
A set of digitised standard pelvic radiographs was available from a previous investigation into the morphology of the proximal femur [ 35 ]. These radiographs were taken from an earlier study [ 36 ], that had examined three groups (osteoporotic, osteoarthritic and control) of age matched, postmenopausal women (30 subjects per group). Subjects with osteoarthritis were excluded from the present study. All patients had undergone a scan of the unfractured hip by dual-energy x-ray absorptiometry (DXA) using a Norland XR-26 scanner (CooperSurgical Inc, Trumbull, CT). The controls had had their left hip scanned. All patients and controls had had a pelvic antero-posterior radiograph recorded within a year of the DXA scan. We used those radiographs and the femoral neck BMD (Neck-BMD) data in the current study. A data set of 50 digitised radiographs was available comprising 26 hip fracture patients (HIP) and 24 controls (CNT). The radiographs were digitised, using a Howtek MultiRAD 850 scanner (Howtek, Hudson, New Hampshire) at a resolution of 584 dpi (44 μm per pixel) and a depth of 12 bits. The age, height and weight of each subject were also recorded.Region selection Five regions of interest (ROIs) were selected relative to the principal trabecular systems in locations known to be related to hip fracture via the Singh index [ 7 ] and BMD analysis [ 37 ]. To ensure reproducibility, their locations were determined in relation to the centre and angle of the narrowest part of the femoral neck and the centre and radius of the femoral head on each image, as shown in Figure  1 . Figure 1 Regions of interest.  Displays the five regions of interest, upper femoral head (UH), central femoral head (CH), upper femoral neck (UN), Ward's triangle area (WA) and the lower femoral neck (LN) used for analysis. Points A to G are determined by the femoral head and neck and used to locate the ROIs. Points A and E mark the femoral neck width. Points B, C and D lie at 1/4, 1/2 and 3/4 along this line. Point F is the centre point of the femoral head, point G at 1/2 the radius of the femoral head at an angle of 45 degrees to the neck width, 135 degrees to the neck shaft, shown as a dashed line through point C. Each ROI was 256 × 256 pixels (11.3 mm square), to enable use of the fast Fourier transform, and were selected as follows. The upper region of the head (UH) lies on the upper part of the principal compressive trabeculae, the central region of the head (CH) is at the intersection of the principal compressive and tensile trabeculae, the upper region of the neck (UN) lies on the principal tensile trabeculae, the lower region of the neck (LN) is at the base of the principal compressive trabeculae and finally Ward's triangle (WA) which lies between these structures. The points and regions were identified using a macro written for Image Pro Plus software (version 4.1.0.0, Media Cybernetics, Silver Spring, Maryland). The femoral head was described by a best-fit circle, calculated from a series of manually marked points around the outline of the femoral head. Between 15 and 20 evenly spaced points were used to describe the outline, depending on the size of the head. The radius and centre (marked as F in Figure  1 ) of the femoral head were then taken from this circle. The narrowest part of the neck (neck-width) was determined using two automatic edge traces, marking the upper and lower outlines of the femoral neck. The first point and the direction for each trace were marked manually; the edge of the neck could then be identified automatically by the software. The neck width (A – E in Figure  1 ) was calculated by finding the smallest Euclidean distance between the traces. The centre of the neck was located at the mid-point of this line (point C) and the axis of the femoral neck was taken to be a line perpendicular to this through the centre of the neck (dashed line). The top right corner of the WA region was located at the midpoint of the neck width (point C). Points B and D were placed 25% and 75% of the way along the neck width and used as the midpoints of the UN and LN regions respectively. Point F, the centre of the femoral head marked the centre of the CH region and point G, the centre of the base of the UH region. Point G was placed one half of the femoral head radius above point F, at a 45-degree angle to the neck width (A-E).
Region selection
Five regions of interest (ROIs) were selected relative to the principal trabecular systems in locations known to be related to hip fracture via the Singh index [ 7 ] and BMD analysis [ 37 ]. To ensure reproducibility, their locations were determined in relation to the centre and angle of the narrowest part of the femoral neck and the centre and radius of the femoral head on each image, as shown in Figure  1 .Each ROI was 256 × 256 pixels (11.3 mm square), to enable use of the fast Fourier transform, and were selected as follows. The upper region of the head (UH) lies on the upper part of the principal compressive trabeculae, the central region of the head (CH) is at the intersection of the principal compressive and tensile trabeculae, the upper region of the neck (UN) lies on the principal tensile trabeculae, the lower region of the neck (LN) is at the base of the principal compressive trabeculae and finally Ward's triangle (WA) which lies between these structures. The points and regions were identified using a macro written for Image Pro Plus software (version 4.1.0.0, Media Cybernetics, Silver Spring, Maryland). The femoral head was described by a best-fit circle, calculated from a series of manually marked points around the outline of the femoral head. Between 15 and 20 evenly spaced points were used to describe the outline, depending on the size of the head. The radius and centre (marked as F in Figure  1 ) of the femoral head were then taken from this circle. The narrowest part of the neck (neck-width) was determined using two automatic edge traces, marking the upper and lower outlines of the femoral neck. The first point and the direction for each trace were marked manually; the edge of the neck could then be identified automatically by the software. The neck width (A – E in Figure  1 ) was calculated by finding the smallest Euclidean distance between the traces. The centre of the neck was located at the mid-point of this line (point C) and the axis of the femoral neck was taken to be a line perpendicular to this through the centre of the neck (dashed line). The top right corner of the WA region was located at the midpoint of the neck width (point C). Points B and D were placed 25% and 75% of the way along the neck width and used as the midpoints of the UN and LN regions respectively. Point F, the centre of the femoral head marked the centre of the CH region and point G, the centre of the base of the UH region. Point G was placed one half of the femoral head radius above point F, at a 45-degree angle to the neck width (A-E).Region analysis Analysis was performed using Matlab software (version 6.1.0, MathWorks Inc, Natick, Massachusetts). A fast Fourier transform was generated for each ROI and three profiles were generated using data from the power spectrum. Firstly a global or circular profile (CircP) was generated, composed of the magnitude at each spatial frequency averaged across all angles, resulting in a profile with 128 data points. To create this profile, each pixel in the Fourier transform was assigned to the integer spatial frequency that most closely matched its' distance from the zero'th component. The angle of preferred orientation was calculated by finding the angle of the maximum value in the power spectrum for the first 25 spatial frequencies [ 38 ]. The maximum value over this range relates to the dominant texture orientation within the image, the trabecular structure. As data in the frequency domain relate to features in the spatial domain rotated by 90°, the median of the values plus 90° was taken as the angle of preferred orientation for each image. Due to the symmetry of the Fourier power spectrum, angles were only calculated between 0° and 180°, rather than 0° and 360°. Two more profiles were then generated, parallel with (ParP) and perpendicular to (PerP) the angle of preferred orientation. In this case the average value was calculated at each spatial frequency from all points lying within ± 5° of the desired angle (Fig.  2 ). Figure 2 Profile generation.  (A) Shows a typical region of interest (contrast enhanced for visualisation) showing the trabecular bone structure, in this case aligned approximately 22° to the vertical. (B) The central section of the FFT (128 × 128 pixels). The horizontal and vertical axes have been marked with a mid-grey tone to indicate that they have been excluded from the angle calculation. The bright strip at the centre (running from top left to bottom right) shows the preferred orientation of the trabeculae. Angles calculated from the Fourier power spectrum correspond to the same angles in the spatial domain, rotated by 90°. (C) The pixels with the maximum values are marked using white squares for the first 25 spatial frequency values of the Fourier power spectrum. The median angle, lying 21.8° from the horizontal is shown by a dashed white line. (D)_The regions used to generate the parallel (shaded black) and perpendicular (shaded white) profiles, based on the orientation of the trabecular structure.
Region analysis
Analysis was performed using Matlab software (version 6.1.0, MathWorks Inc, Natick, Massachusetts). A fast Fourier transform was generated for each ROI and three profiles were generated using data from the power spectrum. Firstly a global or circular profile (CircP) was generated, composed of the magnitude at each spatial frequency averaged across all angles, resulting in a profile with 128 data points. To create this profile, each pixel in the Fourier transform was assigned to the integer spatial frequency that most closely matched its' distance from the zero'th component.The angle of preferred orientation was calculated by finding the angle of the maximum value in the power spectrum for the first 25 spatial frequencies [ 38 ]. The maximum value over this range relates to the dominant texture orientation within the image, the trabecular structure. As data in the frequency domain relate to features in the spatial domain rotated by 90°, the median of the values plus 90° was taken as the angle of preferred orientation for each image. Due to the symmetry of the Fourier power spectrum, angles were only calculated between 0° and 180°, rather than 0° and 360°. Two more profiles were then generated, parallel with (ParP) and perpendicular to (PerP) the angle of preferred orientation. In this case the average value was calculated at each spatial frequency from all points lying within ± 5° of the desired angle (Fig.  2 ).Principal component analysis Principal component analysis [ 31 ] was used to model statistically the shape of each set of profiles (parallel, perpendicular and circular). This was performed using an eigenanalysis of the correlation matrix. The eigenvectors then become the principal components and are selected in order, depending on their eigenvalue. The eigenvalues are associated with the components in decreasing order, the largest eigenvalue is associated with the first component and the smallest with the last. In order to choose the number of components for analysis, a scree plot [ 31 , 39 ] was generated by plotting the eigenvalues (representing the proportion of variance described by each component) against the component number (Figure  3 ). In each case, the first few principal components were selected for analysis using the scree test [ 39 ] to find an 'elbow' in the slope of the plot. This is used as a threshold between the components that contained useful information, which were then used as input variables for further analysis, and those that could be attributed to noise. Figure 3 Scree plot.  Example of a scree plot from the perpendicular profile. The first component typically accounts for the largest amount of variance. The components are chosen to the left of an 'elbow' in the plot. Here components 1 to 5 are included in the analysis as they lie before the 'elbow' at point6 (eigenvalue = 1.63).
Principal component analysis
Principal component analysis [ 31 ] was used to model statistically the shape of each set of profiles (parallel, perpendicular and circular). This was performed using an eigenanalysis of the correlation matrix. The eigenvectors then become the principal components and are selected in order, depending on their eigenvalue. The eigenvalues are associated with the components in decreasing order, the largest eigenvalue is associated with the first component and the smallest with the last. In order to choose the number of components for analysis, a scree plot [ 31 , 39 ] was generated by plotting the eigenvalues (representing the proportion of variance described by each component) against the component number (Figure  3 ). In each case, the first few principal components were selected for analysis using the scree test [ 39 ] to find an 'elbow' in the slope of the plot. This is used as a threshold between the components that contained useful information, which were then used as input variables for further analysis, and those that could be attributed to noise.Fractal analysis Fractal analysis was performed on each profile using a method similar to the Fourier transform technique described by Majumdar et al [ 40 ]. The average power spectrum of the circular profile was plotted on a log-log scale, three approximately linear regions were defined and the gradient ( slope ) of a straight line fitted to each region was found;  slopeA , a 'coarse' slope, where the log of the spatial frequency is less than or equal to 1.0,  slopeB  a 'medium' slope, where the log of the spatial frequency lies between 1.0 and 1.75 and  slopeC , a 'fine' slope where the log of the spatial frequency is above 1.75. The fractal dimension was calculated for each slope using the formula suggested by Majumdar et al [ 40 ]
Fractal analysis
Fractal analysis was performed on each profile using a method similar to the Fourier transform technique described by Majumdar et al [ 40 ]. The average power spectrum of the circular profile was plotted on a log-log scale, three approximately linear regions were defined and the gradient ( slope ) of a straight line fitted to each region was found;  slopeA , a 'coarse' slope, where the log of the spatial frequency is less than or equal to 1.0,  slopeB  a 'medium' slope, where the log of the spatial frequency lies between 1.0 and 1.75 and  slopeC , a 'fine' slope where the log of the spatial frequency is above 1.75. The fractal dimension was calculated for each slope using the formula suggested by Majumdar et al [ 40 ]slopeslopeAslopeBslopeCStatistical analysis Stepwise discriminant analysis was used to select principal components that could be combined to build a linear classifier. If the stepwise procedure failed to select any components, the most accurate of the individual components was chosen. The same procedure was used to discriminate between the groups using the fractal dimension. Measurement of the area under the ROC curve was used to compare the classifiers built using the discriminant analysis [ 41 ]. A three way ANOVA was applied in order to determine whether there were significant differences between the performance of classifiers depending on the type of analysis, the profile used or the region analysed. Pearson product moment correlation was applied to examine the relationship with age, BMI and Neck BMD for the strongest classifiers. A one-way ANOVA was used to test for significant differences in the performance of the slopes from each spatial frequency band used in the fractal analysis. T-tests, correlation and ANOVA were performed using SigmaStat (version 2.03, SPSS Science, Chicago). Principal component analysis, discriminant analysis, and measurement of the area under the ROC curve were calculated using SPSS (version 10 SPSS Science, Chicago).
Statistical analysis
Stepwise discriminant analysis was used to select principal components that could be combined to build a linear classifier. If the stepwise procedure failed to select any components, the most accurate of the individual components was chosen. The same procedure was used to discriminate between the groups using the fractal dimension. Measurement of the area under the ROC curve was used to compare the classifiers built using the discriminant analysis [ 41 ]. A three way ANOVA was applied in order to determine whether there were significant differences between the performance of classifiers depending on the type of analysis, the profile used or the region analysed. Pearson product moment correlation was applied to examine the relationship with age, BMI and Neck BMD for the strongest classifiers. A one-way ANOVA was used to test for significant differences in the performance of the slopes from each spatial frequency band used in the fractal analysis. T-tests, correlation and ANOVA were performed using SigmaStat (version 2.03, SPSS Science, Chicago). Principal component analysis, discriminant analysis, and measurement of the area under the ROC curve were calculated using SPSS (version 10 SPSS Science, Chicago).Results There were no significant differences between the age, height, weight or body mass index (BMI) of the fracture and control groups (Table  1 ). As expected femoral neck-BMD was significantly lower in the fracture group in comparison to the control group ( P  = 0.001). Table 1 Summary of anthropometric variables for the fracture and controls groups. Mean and standard deviation (SD) of the age, height, weight, BMI and BMD of the fracture and control groups.  P  values were obtained from a two-tailed t-test. Variable Control Group (n = 24) Fracture Group (n = 26) Mean SD Mean SD P Age, years 69.1 6.5 69.2 6.3 0.97 Height, cm 158.6 7.1 157.1 0.4 0.38 Weight, kg 63.4 9.5 61.0 9.0 0.38 Body Mass Index, kg/m 2 25.2 3.2 24.8 4.1 0.72 Femoral neck BMD (g cm -2 ) 0.70 0.11 0.604 0.066 0.001 The Receiver Operating Characteristic (ROC) curve is a plot of True Positive Fraction v False Positive Fraction (or Sensitivity v 1 – Specificity). The area underneath the curve ( A z ) represents the performance of the classifier ranging from a value of 0.5 if it is no better than chance to 1.0 for a perfect discriminator. Table  2  shows  A z  for PCA analysis by region for the circular, perpendicular and parallel profiles respectively, discriminating fracture and control cases. A wide range of values was observed (overall mean 0.70, standard deviation 0.11). Some were little better than chance ( A z  = 0.5) (mostly derived from the parallel profile) and the strongest ones were from the perpendicular profiles. The 5 largest areas under the ROC curve were obtained by PCA of the perpendicular profile of the lower neck, upper and central head regions (Table  3 ) ( A z  = 0.93, 0.84 and 0.84 respectively), followed by PCA analysis of the circular profile in the upper head region ( A z  = 0.76) and, finally, fractal analysis of the parallel profile in the upper neck region ( A z  = 0.75). Femoral neck BMD lay between the third and fourth best texture measures ( A z  = 0.79 95% CI = 0.66 – 0.91). Plots of the ROC curves for the strongest combinations of image analysis classifier are shown in Figure  4 . Table 2 Classification accuracy for each region-profile combination. Area under the ROC curve for principal component analysis of each profile by region of the femoral neck. Analysis using three-way ANOVA found that the area under the ROC curve was significantly higher in the perpendicular profile than in the parallel profile. ( P  < 0.05) Region Circular (95% CI) Parallel (95% CI) Perpendicular (95% CI) Upper head 0.76 (0.63 – 0.89) 0.57 (0.41 – 0.73) 0.84 (0.73 – 0.95) Central head 0.59 (0.43 – 0.75) 0.56 (0.40 – 0.73) 0.84 (0.72 – 0.95) Upper neck 0.72 (0.58 – 0.86) 0.72 (0.57 – 0.86) 0.67 (0.52 – 0.82) Wards triangle 0.74 (0.61 – 0.88) 0.61 (0.45 – 0.76) 0.71 (0.56 – 0.86) Lower neck 0.71 (0.56 – 0.85) 0.55 (0.39 – 0.71) 0.93 (0.87 – 1.00) Table 3 The best five classifiers: Area under the curve and correlation with BMD, age and BMI. Area under the ROC curve ( A z ) for each of the best 5 classifiers and the correlation with age R age , femoral neck BMD (R BMD ) and body mass index (R BMI ) and associated significance values ( P ). Analysis Profile ROI A z (95% CI) R BMD ( P ) R age ( P ) R BMI ( P ) PCA PerP LN 0.93 (0.87 – 1.00) 0.09 (0.55) 0.14 (0.34) -0.08 (0.58) PCA PerP UH 0.84 (0.73 – 0.95) 0.09 (0.52) -0.17 (0.24) -0.03 (0.86) PCA PerP CH 0.84 (0.72 – 0.95) 0.06 (0.70) 0.27 (0.055) -0.11 (0.46) PCA CircP UH 0.76 (0.63 – 0.89) -0.16 (0.28) -0.15 (0.29) 0.07 (0.62) Fractal ParP UN 0.75 (0.61 – 0.89) -0.30 (0.034) 0.25 (0.081) -0.04 (0.78) Figure 4 Comparison of ROC curves.  Comparison of the ROC curves for the strongest classifier from the combination of (A) PCA analysis of the perpendicular profile (Lower neck region), (B) PCA analysis of the circular profile (Upper head region) and (C) Fractal analysis of any profile (Upper neck region). Table  3  also shows the correlations between the top five classifiers with age, BMI and Neck-BMD. No significant correlations were found between any of these classifiers and either age or BMI and, for the top three, there was also no significant correlation with Neck-BMD ( P  > 0.05). The fifth placed classifier, fractal analysis of the parallel profile in the upper neck region, was the only one significantly associated with Neck-BMD ( P  = 0.034). A three-way analysis of variance was used to examine differences in performance due to the region, profile or type of analysis used. It showed that overall PCA analysis performed significantly better than fractal analysis ( P  = 0.019) and that analysis of both the perpendicular and circular profiles performed significantly better than the parallel profile ( P  = 0.003 and 0.011 respectively). No significant differences were found between the different regions of the femoral neck ( P  = 0.241) (despite the apparently large differences in  A z ). The power of this test was 0.69, 0.97 and 0.15 for the investigation of differences due to the method of analysis, type of profile used and the region analysed respectively. Table  4  presents the mean A z  for the slope from each of the spatial frequency bands for all regions of interest. This was assessed for each profile individually and also for all the profiles together. A one-way ANOVA was used to test for significant differences in Az between slopes A, B and C. In the individual profiles,  slopeA  performed significantly better than  slopeC  for the circular profile ( P  = 0.008), however when all the profiles were considered, no significant differences were apparent ( P  = 0.26). Table 4 Comparing  slopeA ,  slopeB  and  slopeC . The average and standard deviation of the area under the ROC curve ( A z ) are presented for each of the slopes used in the fractal analysis for all regions of interest. A significant difference was found between  slopeA  and  slopeC  in the circular profile, however when all the profiles were compared, no significant differences were found. SlopeA SlopeB SlopeC P All profiles 0.601 (0.074) 0.598 (0.055) 0.565 (0.067) 0.260 Circular 0.670 (0.072) 0.611 (0.022) 0.531 (0. 026) 0.008 Parallel 0.544 (0.042) 0.620 (0.083) 0.563 (0.037) 0.140 Perpendicular 0.589 (0.047) 0.563 (0.032) 0.600 (0.104) 0.678
Results
There were no significant differences between the age, height, weight or body mass index (BMI) of the fracture and control groups (Table  1 ). As expected femoral neck-BMD was significantly lower in the fracture group in comparison to the control group ( P  = 0.001).PSummary of anthropometric variables for the fracture and controls groups. Mean and standard deviation (SD) of the age, height, weight, BMI and BMD of the fracture and control groups.  P  values were obtained from a two-tailed t-test.PVariableControl Group (n = 24)Fracture Group (n = 26)MeanSDMeanSDPPFemoral neck BMD (g cm -2 )0.700.110.6040.0660.001The Receiver Operating Characteristic (ROC) curve is a plot of True Positive Fraction v False Positive Fraction (or Sensitivity v 1 – Specificity). The area underneath the curve ( A z ) represents the performance of the classifier ranging from a value of 0.5 if it is no better than chance to 1.0 for a perfect discriminator. Table  2  shows  A z  for PCA analysis by region for the circular, perpendicular and parallel profiles respectively, discriminating fracture and control cases. A wide range of values was observed (overall mean 0.70, standard deviation 0.11). Some were little better than chance ( A z  = 0.5) (mostly derived from the parallel profile) and the strongest ones were from the perpendicular profiles. The 5 largest areas under the ROC curve were obtained by PCA of the perpendicular profile of the lower neck, upper and central head regions (Table  3 ) ( A z  = 0.93, 0.84 and 0.84 respectively), followed by PCA analysis of the circular profile in the upper head region ( A z  = 0.76) and, finally, fractal analysis of the parallel profile in the upper neck region ( A z  = 0.75). Femoral neck BMD lay between the third and fourth best texture measures ( A z  = 0.79 95% CI = 0.66 – 0.91). Plots of the ROC curves for the strongest combinations of image analysis classifier are shown in Figure  4 .AzAzAzAzAzAzAzClassification accuracy for each region-profile combination. Area under the ROC curve for principal component analysis of each profile by region of the femoral neck. Analysis using three-way ANOVA found that the area under the ROC curve was significantly higher in the perpendicular profile than in the parallel profile. ( P  < 0.05)PRegionCircular (95% CI)Parallel (95% CI)Perpendicular (95% CI)The best five classifiers: Area under the curve and correlation with BMD, age and BMI. Area under the ROC curve ( A z ) for each of the best 5 classifiers and the correlation with age R age , femoral neck BMD (R BMD ) and body mass index (R BMI ) and associated significance values ( P ).AzPAnalysisProfileROIA z (95% CI)AzR BMD ( P )PR age ( P )PR BMI ( P )P-0.30 (0.034)Table  3  also shows the correlations between the top five classifiers with age, BMI and Neck-BMD. No significant correlations were found between any of these classifiers and either age or BMI and, for the top three, there was also no significant correlation with Neck-BMD ( P  > 0.05). The fifth placed classifier, fractal analysis of the parallel profile in the upper neck region, was the only one significantly associated with Neck-BMD ( P  = 0.034).PPA three-way analysis of variance was used to examine differences in performance due to the region, profile or type of analysis used. It showed that overall PCA analysis performed significantly better than fractal analysis ( P  = 0.019) and that analysis of both the perpendicular and circular profiles performed significantly better than the parallel profile ( P  = 0.003 and 0.011 respectively). No significant differences were found between the different regions of the femoral neck ( P  = 0.241) (despite the apparently large differences in  A z ). The power of this test was 0.69, 0.97 and 0.15 for the investigation of differences due to the method of analysis, type of profile used and the region analysed respectively.PPPAzTable  4  presents the mean A z  for the slope from each of the spatial frequency bands for all regions of interest. This was assessed for each profile individually and also for all the profiles together. A one-way ANOVA was used to test for significant differences in Az between slopes A, B and C. In the individual profiles,  slopeA  performed significantly better than  slopeC  for the circular profile ( P  = 0.008), however when all the profiles were considered, no significant differences were apparent ( P  = 0.26).slopeAslopeCPPComparing  slopeA ,  slopeB  and  slopeC . The average and standard deviation of the area under the ROC curve ( A z ) are presented for each of the slopes used in the fractal analysis for all regions of interest. A significant difference was found between  slopeA  and  slopeC  in the circular profile, however when all the profiles were compared, no significant differences were found.slopeAslopeBslopeCAzslopeAslopeCSlopeASlopeASlopeBSlopeBSlopeCSlopeCPP0.670 (0.072)0.531 (0.0.008Discussion and conclusions In these short series, this study found that texture analysis of standard radiographs using the fast Fourier transform can yield variables that are significantly associated with fracture but not significantly correlated with age, body mass index or Neck-BMD. Both PCA and fractal analysis of the FFT data could be used to discriminate successfully between the groups, although overall PCA was significantly stronger than fractal dimension. The best results from this study were not significantly correlated with femoral neck-BMD, age or BMI, indicating their potential for use as an independent predictor of fracture. The radiographic appearance of bone is known to be affected by factors including the size of the patient. As there was no significant difference in the BMI of the fracture and control groups, it is unlikely that this has influenced the results, however it is an issue that will need addressing in future studies. The PCA method extends a method previously developed for analysis of histological sections [ 26 ]. The use of oriented profiles improved the performance of the analysis by selecting directions in which there was the most information about bone structure i.e. perpendicular to the preferred orientation of the trabeculae. PCA considerably reduces the number of variables required to characterise the image via its power spectrum. For example, in this study, we start with a 256 × 256 pixel ROI (65,536 pixels), the Fourier transform is performed and a profile of 128 spatial frequency values is generated. For each profile, PCA was able to describe over 70 % of the variance present in the data using only 5 components or fewer. Overall, the performance of principal components analysis was significantly stronger than that of fractal analysis ( P  < 0.01). One advantage of PCA that may contribute to this finding is the ability to summarise the information present in the dataset with a small number of components via an economical mapping of the variance present in the data. In addition, the property of orthogonality between these components ensures that the variables generated are linearly independent (Fig.  5 ). Benefits can also be found by the use of a model built on the mathematical distributions present in the data, rather than expecting the data to meet a given mathematical property, such as fitting a fractal distribution. Figure 5 Plot of two principal components.  Example of a scatterplot of two principal components. For FFT/PCA analysis of the upper head region, principal components 4 and 5 were selected by stepwise analysis and are shown here. They are plotted against each other with fracture and control subjects identified using separate markers. The lack of correlation between the components can be seen ( r  = 0.040,  P  = 0.997). Previous studies using non-fractal analysis of the Fourier power spectrum have focussed on images of the spine or wrist, where the alignment of trabeculae is generally orthogonal [ 28 - 30 ]. In such images, analysis of trabecular orientation can be performed by examining the vertical and horizontal sectors as the trabeculae lie predominantly in these directions. The trabecular structure of the femur is more complicated as the trabeculae are aligned in arcs, so the preferred orientation changes throughout the proximal femur. Analysis parallel to the preferred orientation of the trabeculae was significantly poorer than analysis using either the perpendicular or circular profiles ( P  < 0.05). Analysis in the perpendicular direction was strongest overall, although it was not significantly better than the circular profile. This accords with the increasingly anisotropic nature of trabecular bone with aging; bone loss is not evenly distributed but is lost primarily at angles perpendicular and oblique to the preferred orientation of the trabeculae [ 30 ]. This loss heightens the risk of fracture, especially if the impact is from the side, as expected from a typical fall from standing height, as there are fewer trabeculae orientated in this direction to absorb the force of impact. In summary, this paper presents a new method for analysing the structure of trabecular bone from standard radiographs. It demonstrates that the Fourier transform can be used to describe structural information in images which may be related to fracture, independently of BMD. This study is limited by the small size of the data set and further analysis is needed to validate these findings. This should be performed on a similar series of radiographs, consisting of fracture and control subjects scanned at the same resolution. The methods from this study could then be applied directly to this group (without recalculating the PCA) to evaluate whether they were generally applicable. However the success of both this and our previous study, using similar techniques to analyse histological sections, indicates that this may be an effective method with clinical utility for describing bone quality statistically in terms of structural parameters.
Discussion and conclusions
In these short series, this study found that texture analysis of standard radiographs using the fast Fourier transform can yield variables that are significantly associated with fracture but not significantly correlated with age, body mass index or Neck-BMD. Both PCA and fractal analysis of the FFT data could be used to discriminate successfully between the groups, although overall PCA was significantly stronger than fractal dimension. The best results from this study were not significantly correlated with femoral neck-BMD, age or BMI, indicating their potential for use as an independent predictor of fracture. The radiographic appearance of bone is known to be affected by factors including the size of the patient. As there was no significant difference in the BMI of the fracture and control groups, it is unlikely that this has influenced the results, however it is an issue that will need addressing in future studies.The PCA method extends a method previously developed for analysis of histological sections [ 26 ]. The use of oriented profiles improved the performance of the analysis by selecting directions in which there was the most information about bone structure i.e. perpendicular to the preferred orientation of the trabeculae. PCA considerably reduces the number of variables required to characterise the image via its power spectrum. For example, in this study, we start with a 256 × 256 pixel ROI (65,536 pixels), the Fourier transform is performed and a profile of 128 spatial frequency values is generated. For each profile, PCA was able to describe over 70 % of the variance present in the data using only 5 components or fewer. Overall, the performance of principal components analysis was significantly stronger than that of fractal analysis ( P  < 0.01). One advantage of PCA that may contribute to this finding is the ability to summarise the information present in the dataset with a small number of components via an economical mapping of the variance present in the data. In addition, the property of orthogonality between these components ensures that the variables generated are linearly independent (Fig.  5 ). Benefits can also be found by the use of a model built on the mathematical distributions present in the data, rather than expecting the data to meet a given mathematical property, such as fitting a fractal distribution.PPrevious studies using non-fractal analysis of the Fourier power spectrum have focussed on images of the spine or wrist, where the alignment of trabeculae is generally orthogonal [ 28 - 30 ]. In such images, analysis of trabecular orientation can be performed by examining the vertical and horizontal sectors as the trabeculae lie predominantly in these directions. The trabecular structure of the femur is more complicated as the trabeculae are aligned in arcs, so the preferred orientation changes throughout the proximal femur. Analysis parallel to the preferred orientation of the trabeculae was significantly poorer than analysis using either the perpendicular or circular profiles ( P  < 0.05). Analysis in the perpendicular direction was strongest overall, although it was not significantly better than the circular profile. This accords with the increasingly anisotropic nature of trabecular bone with aging; bone loss is not evenly distributed but is lost primarily at angles perpendicular and oblique to the preferred orientation of the trabeculae [ 30 ]. This loss heightens the risk of fracture, especially if the impact is from the side, as expected from a typical fall from standing height, as there are fewer trabeculae orientated in this direction to absorb the force of impact.PIn summary, this paper presents a new method for analysing the structure of trabecular bone from standard radiographs. It demonstrates that the Fourier transform can be used to describe structural information in images which may be related to fracture, independently of BMD. This study is limited by the small size of the data set and further analysis is needed to validate these findings. This should be performed on a similar series of radiographs, consisting of fracture and control subjects scanned at the same resolution. The methods from this study could then be applied directly to this group (without recalculating the PCA) to evaluate whether they were generally applicable. However the success of both this and our previous study, using similar techniques to analyse histological sections, indicates that this may be an effective method with clinical utility for describing bone quality statistically in terms of structural parameters.Competing interests The authors declare that they have no competing interests.
Competing interests
The authors declare that they have no competing interests.Authors' contributions Author JG helped design the study, performed the image and data analysis and drafted the manuscript Author AS collected the data/images used within this study and helped with writing of the paper. Author PU assisted with some of the practical approaches, and the writing of the paper Author DMR designed the initial case control study and assisted with interpretation of the results and writing the paper Author RMA helped with the design of the study, the interpretation of the results and the writing of the paper. All authors read and approved the final manuscript
Authors' contributions
Author JG helped design the study, performed the image and data analysis and drafted the manuscriptAuthor AS collected the data/images used within this study and helped with writing of the paper.Author PU assisted with some of the practical approaches, and the writing of the paperAuthor DMR designed the initial case control study and assisted with interpretation of the results and writing the paperAuthor RMA helped with the design of the study, the interpretation of the results and the writing of the paper.All authors read and approved the final manuscriptPre-publication history The pre-publication history for this paper can be accessed here:
Pre-publication history
The pre-publication history for this paper can be accessed here:


Retroviruses are unique among virus families in having dimeric genomes. The RNA sequences and structures that link the two RNA molecules vary, and these differences provide clues as to the role of this feature in the viral lifecycles. This review draws upon examples from different retroviral families. Differences and similarities in both secondary and tertiary structure are discussed. The implication of varying roles for the dimer linkage in related viruses is considered.

Introduction With relatively few genes compared to many other virus families, the retroviridae have evolved over the millenia to maximise the functions of their RNA genome. The genome serves as a versatile template from which various proteins can be translated by the use of splicing and by translational flexibility using scanning, IRES and frameshifting. It is also an RNA molecule capable of interacting with itself, and cellular and viral proteins. By these means, from an RNA around 7 – 12 kilobases long, the retroviridae have evolved to infect a wide range of species and cell types. A unique characteristic of retroviral genomes is the fact that they are dimeric. The reasons for this are as yet unclear, and are discussed below. In brief, it is thought that the diploid genome allows template switching during reverse transcription and may be linked to recombination in some viruses. It may also play a role in translation of proteins and packaging of the RNA. Much of the work on the nature, structure(s), and role of the dimer linkage has been based on Human Immunodeficiency Virus Type 1, and this has been recently reviewed ([ 1 ] and Russell  et al  this issue [ 2 ]). Whether or not HIV-1 is a representative model for other retroviruses is open to debate. However, there have been important contributions from investigators studying other retroviruses. They have shown both similarities with the HIV-1 motifs, and also, importantly, differences. The fact that distinct RNA structures are used by different retroviruses to perform the same purpose, namely to link their two RNA molecules, tells us something very important. For these viruses, whatever organism or cell they are infecting it has been advantageous to evolve to do so with a double complement of genome in their virion particles. However, diploidy may be used to benefit the virus in a number of ways and for different viruses the priorities may vary. This review will attempt to draw on several examples from viruses other than HIV-1, whilst of necessity drawing comparisons with the latter.
Introduction
With relatively few genes compared to many other virus families, the retroviridae have evolved over the millenia to maximise the functions of their RNA genome. The genome serves as a versatile template from which various proteins can be translated by the use of splicing and by translational flexibility using scanning, IRES and frameshifting. It is also an RNA molecule capable of interacting with itself, and cellular and viral proteins. By these means, from an RNA around 7 – 12 kilobases long, the retroviridae have evolved to infect a wide range of species and cell types.A unique characteristic of retroviral genomes is the fact that they are dimeric. The reasons for this are as yet unclear, and are discussed below. In brief, it is thought that the diploid genome allows template switching during reverse transcription and may be linked to recombination in some viruses. It may also play a role in translation of proteins and packaging of the RNA.Much of the work on the nature, structure(s), and role of the dimer linkage has been based on Human Immunodeficiency Virus Type 1, and this has been recently reviewed ([ 1 ] and Russell  et al  this issue [ 2 ]). Whether or not HIV-1 is a representative model for other retroviruses is open to debate. However, there have been important contributions from investigators studying other retroviruses. They have shown both similarities with the HIV-1 motifs, and also, importantly, differences. The fact that distinct RNA structures are used by different retroviruses to perform the same purpose, namely to link their two RNA molecules, tells us something very important. For these viruses, whatever organism or cell they are infecting it has been advantageous to evolve to do so with a double complement of genome in their virion particles. However, diploidy may be used to benefit the virus in a number of ways and for different viruses the priorities may vary. This review will attempt to draw on several examples from viruses other than HIV-1, whilst of necessity drawing comparisons with the latter.et alThe dimeric genome Retroviruses were discovered at the beginning of the 20th century [ 3 , 4 ]. The unique nature of their genome was first discovered in the 1960s [ 5 , 6 ] but the actual dimeric genomes were elucidated, and visualised by electron microscopy, a decade later [ 7 , 8 ]. Bender and colleagues extracted the RNA from several different retroviruses and examined it by electron microscopy under denaturing conditions. The RNA appeared to be joined at a discrete point, termed the dimer linkage site (DLS). Using bromodU to label the RNA at one end, they were able to show that the molecules were joined at their 5' ends [ 9 , 10 ]. Under less stringent conditions the genomes can be demonstrated to interact along their lengths [ 11 ] and it is this that probably contributes to confusing reports on the exact location of the primary DLS in different viruses. RNA dimerisation in the primate lentiviruses, predominantly HIV-1, has subsequently been extensively studied [ 1 ], yet little has been published on this process in the non-primate lentiviruses. Early studies of rapid harvest virions of the prototype lentivirus, Maedi Visna virus (MVV), identified viral RNA with a Svedberg coefficient of 35S immediately post-budding, which increased with time to 70S. It is possible that weakly interacting dimers formed during RNA encapsidation may have been denatured during purification, however these observations are supportive of a progression from monomeric to dimeric RNA associated with viral maturation [ 12 ]. Since 1990 [ 13 ] it has been possible to study  in vitro  the RNA elements involved in the dimer linkage first observed by EM. It was shown that RNA transcripts comprising sequences from the 5' end of the viral genome would migrate as two species of RNA when subjected to electrophoresis. By this means many subsequent studies were able to focus on isolating the elements and structures involved in dimerisation, and to investigate the role of the viral structural proteins in this process.
The dimeric genome
Retroviruses were discovered at the beginning of the 20th century [ 3 , 4 ]. The unique nature of their genome was first discovered in the 1960s [ 5 , 6 ] but the actual dimeric genomes were elucidated, and visualised by electron microscopy, a decade later [ 7 , 8 ]. Bender and colleagues extracted the RNA from several different retroviruses and examined it by electron microscopy under denaturing conditions. The RNA appeared to be joined at a discrete point, termed the dimer linkage site (DLS). Using bromodU to label the RNA at one end, they were able to show that the molecules were joined at their 5' ends [ 9 , 10 ]. Under less stringent conditions the genomes can be demonstrated to interact along their lengths [ 11 ] and it is this that probably contributes to confusing reports on the exact location of the primary DLS in different viruses.RNA dimerisation in the primate lentiviruses, predominantly HIV-1, has subsequently been extensively studied [ 1 ], yet little has been published on this process in the non-primate lentiviruses. Early studies of rapid harvest virions of the prototype lentivirus, Maedi Visna virus (MVV), identified viral RNA with a Svedberg coefficient of 35S immediately post-budding, which increased with time to 70S. It is possible that weakly interacting dimers formed during RNA encapsidation may have been denatured during purification, however these observations are supportive of a progression from monomeric to dimeric RNA associated with viral maturation [ 12 ].Since 1990 [ 13 ] it has been possible to study  in vitro  the RNA elements involved in the dimer linkage first observed by EM. It was shown that RNA transcripts comprising sequences from the 5' end of the viral genome would migrate as two species of RNA when subjected to electrophoresis. By this means many subsequent studies were able to focus on isolating the elements and structures involved in dimerisation, and to investigate the role of the viral structural proteins in this process.in vitroMultiple functions for the dimeric genome? As yet investigators have not been able to agree on a distinct role for the dimer linkage. The fact that it is conserved amongst the retroviridae does not guarantee that its role will be the same in all retroviral families. The following section of the review will endeavour to explore some of the proposed roles, and examine the evidence from different retroviruses.
Multiple functions for the dimeric genome?
As yet investigators have not been able to agree on a distinct role for the dimer linkage. The fact that it is conserved amongst the retroviridae does not guarantee that its role will be the same in all retroviral families. The following section of the review will endeavour to explore some of the proposed roles, and examine the evidence from different retroviruses.The dimeric linkage and recombination Several studies have demonstrated that, in HIV-1 and MLV, the dimer linkage serves as a "hotspot" for recombination [ 14 , 15 ]. It is an obvious hypothesis, that in viruses which are known for their hypervariability, there exists the capacity to jump from one RNA molecule to another. Researchers have compared dimerising to non-dimerising controls, and the frequency and distribution of template switching. Templates containing the dimerisation site had a 4-fold higher transfer efficiency than the non-dimerising control [ 14 ]. This result implies that recombination would occur preferentially at the site where the RNA molecules were in close proximity. In the case of HIV-1, whilst it has been shown that template switching is facilitated by template homology [ 16 ], it has also been demonstrated that recombination can occur between viruses of different subtypes which might have different dimer initiation sequences (DIS) [ 17 ]. Bearing in mind the fact that the genome is linked at other sites besides the DIS [ 11 ], it seems probable that other hot spots for recombination exist. Interestingly, it has been suggested that the nucleocapsid protein (NC) promotes or stimulates the strand transfer reaction. As will be discussed below, NC and the precursor Gag protein both bind the RNA close to the DIS in HIV-1. In addition, there is evidence that the presence of a dimer in the virus particle facilitates the first strand-transfer reaction of reverse transcription [ 18 ]. Work in our laboratory has shown that the Maedi Visna Virus DIS is centred on a helix terminating in a GACG tetraloop between positions 281 and 300 in the viral genome; a region which is highly conserved between the ovine and caprine lentiviruses (Monie, personal communication, see Figure  3d ). Intriguingly, this structure shows homology with structural motifs in the  Alpha-  and  Gammaretroviruses , but not with DIS regions identified in the primate lentiviruses. Within the  Alpha - and  Gammaretroviruses  GACG tetraloops are involved in the packaging of viral RNA [ 19 , 20 ] and whilst not a component of the core M-MLV DIS motif [ 21 ], they may contribute to the process of dimerisation and the stability of the resultant dimer [ 22 ]. Importantly, it is possible to form heterodimers between transcripts from these viruses containing the GACG tetraloops and between MVV and M-MLV (personal observations). This raises parallels with recent studies of the dimerisation of murine leukaemia viruses and Harvey Sarcoma virus in which GACG tetraloops were found to regulate inter-species RNA heterodimerisation [ 23 ], whilst other linkage elements were postulated to mediate homodimerisation. Recombination, and the genomic variability it confers cannot be the sole function of the dimeric genome, since retroviruses with highly conserved genomes and little sequence variability such as HTLV-1 [ 24 ] are also dimeric.
The dimeric linkage and recombination
Several studies have demonstrated that, in HIV-1 and MLV, the dimer linkage serves as a "hotspot" for recombination [ 14 , 15 ]. It is an obvious hypothesis, that in viruses which are known for their hypervariability, there exists the capacity to jump from one RNA molecule to another. Researchers have compared dimerising to non-dimerising controls, and the frequency and distribution of template switching. Templates containing the dimerisation site had a 4-fold higher transfer efficiency than the non-dimerising control [ 14 ]. This result implies that recombination would occur preferentially at the site where the RNA molecules were in close proximity. In the case of HIV-1, whilst it has been shown that template switching is facilitated by template homology [ 16 ], it has also been demonstrated that recombination can occur between viruses of different subtypes which might have different dimer initiation sequences (DIS) [ 17 ]. Bearing in mind the fact that the genome is linked at other sites besides the DIS [ 11 ], it seems probable that other hot spots for recombination exist.Interestingly, it has been suggested that the nucleocapsid protein (NC) promotes or stimulates the strand transfer reaction. As will be discussed below, NC and the precursor Gag protein both bind the RNA close to the DIS in HIV-1. In addition, there is evidence that the presence of a dimer in the virus particle facilitates the first strand-transfer reaction of reverse transcription [ 18 ].Work in our laboratory has shown that the Maedi Visna Virus DIS is centred on a helix terminating in a GACG tetraloop between positions 281 and 300 in the viral genome; a region which is highly conserved between the ovine and caprine lentiviruses (Monie, personal communication, see Figure  3d ). Intriguingly, this structure shows homology with structural motifs in the  Alpha-  and  Gammaretroviruses , but not with DIS regions identified in the primate lentiviruses. Within the  Alpha - and  Gammaretroviruses  GACG tetraloops are involved in the packaging of viral RNA [ 19 , 20 ] and whilst not a component of the core M-MLV DIS motif [ 21 ], they may contribute to the process of dimerisation and the stability of the resultant dimer [ 22 ]. Importantly, it is possible to form heterodimers between transcripts from these viruses containing the GACG tetraloops and between MVV and M-MLV (personal observations). This raises parallels with recent studies of the dimerisation of murine leukaemia viruses and Harvey Sarcoma virus in which GACG tetraloops were found to regulate inter-species RNA heterodimerisation [ 23 ], whilst other linkage elements were postulated to mediate homodimerisation.Alpha-GammaretrovirusesAlphaGammaretrovirusesRecombination, and the genomic variability it confers cannot be the sole function of the dimeric genome, since retroviruses with highly conserved genomes and little sequence variability such as HTLV-1 [ 24 ] are also dimeric.Translation and packaging? Another possible role is that of the dimer linkage acting as a switch, its presence permitting or restricting the packaging of RNA. In HIV-2 two regions were originally suggested as dimer initiation sites, one analogous to the palindromic sequence identified as the principal DIS in HIV-1 (termed SL1), one close to the PBS [ 25 - 27 ]. Recently, a region upstream of SL1 (also called the DIS, see Figure  1a ) was identified as being critical for packaging [ 28 ]. An extensive deletion analysis of the 5' leader of HIV-2 was carried out, and removal of nucleotides 380–404 (HIV ROD ), termed the DM region, rendered the virus severely packaging deficient. The mutation had been designed based on the mfold [ 29 , 30 ] prediction, that removal of these sequences would disrupt the SL1 structure and hence dimerisation (Figure  1b ).  In vitro  studies using RNA transcripts comprising the leader region with and without the DM deletion, reveal that it does, indeed, render the viral RNA monomeric (personal observations). Using antisense oligonucleotides, another group have demonstrated that this region may, in fact, play a role in the dimerisation process itself [ 31 ]. By free energy minimisation this region is predicted to be unstructured, so it is not clear how the RNAs would interact with one another. In addition, whilst the SL1/DIS sequence is conserved amongst HIV-2 and SIV sequences in the database, that within the DM region is less so, and the substitutions which exist would affect the auto-complementarity of the sequence. Figure 1 Structure of the HIV-2 leader region. 1a. Secondary structure model of the HIV-2 leader region based on mfold predictions. Indicated are the putative dimer linkage sites (in red). Also highlighted is the DM region defined as being critical for packaging [28], in blue). 1b. The effect of the DM deletion on the SL1/DIS stem loop. The stem is truncated and the internal bulge altered in approximately half the predicted structures. Figure 2 Structure of the key elements involved in HIV-1 RNA dimerisation. 2a. Secondary structure model of the packaging signal of HIV-1 Lai  ([64] [65]), containing the principal DLS. 2b Proposed sequence of the RNA dimerisation process in HIV-1 Lai . The initial kissing hairpin interaction (including loop B) followed by formation of the extended duplex ([1]). 2c. Loop B, one of the critical elements in the dimer interaction. The flexibility of this internal loop allows the duplex to form ([44]). Figure 3 Dimer linkages of the retroviridae (excluding the lentiviruses). 3a. Loose and tight dimers ([51]). 3b. Imperfect repeats ([66]). 3c. Palindromes ([38]). 3d. GACG loops ([23]). 3e. CAG tri-loops (see Figure 4). Figure 4 Proposed tertiary structure of the HTLV-1 dimer linkage. 4a Stereoview of 3D molecular modelling of a potential structure of the HTLV-1 DIS from nucleotide A730 to A744 using JUMNA ([61]). 4b. Close up of the terminal loop. Bases are coloured as follows: adenine, grey; cytosine, yellow; guanine, orange; and uracil, cyan. One of the key differences between HIV-1 and HIV-2 replication is their modes of packaging [ 32 ]. Whilst the Gag protein of the former captures the genomic RNA  in trans , the latter uses predominantly a  cis  mechanism. One might postulate therefore, that, if retroviruses must package a dimeric genome, it is critical in the case of HIV-2 that the genome is dimeric before interacting with the Gag polyprotein. Hence, the effect of mutations in the DM region may be to render the RNA monomeric and thus to severely impair packaging. It is attractive to speculate that the reason packaging itself is not affected by DIS mutations to the same degree in HIV-1 [ 33 ] is this difference in protein:RNA interaction. If the RNAs can interact at points other than the principal DIS over time, then perhaps the  trans  mechanism is less dependent on a high affinity dimer linkage?
Translation and packaging?
Another possible role is that of the dimer linkage acting as a switch, its presence permitting or restricting the packaging of RNA. In HIV-2 two regions were originally suggested as dimer initiation sites, one analogous to the palindromic sequence identified as the principal DIS in HIV-1 (termed SL1), one close to the PBS [ 25 - 27 ]. Recently, a region upstream of SL1 (also called the DIS, see Figure  1a ) was identified as being critical for packaging [ 28 ]. An extensive deletion analysis of the 5' leader of HIV-2 was carried out, and removal of nucleotides 380–404 (HIV ROD ), termed the DM region, rendered the virus severely packaging deficient. The mutation had been designed based on the mfold [ 29 , 30 ] prediction, that removal of these sequences would disrupt the SL1 structure and hence dimerisation (Figure  1b ).  In vitro  studies using RNA transcripts comprising the leader region with and without the DM deletion, reveal that it does, indeed, render the viral RNA monomeric (personal observations). Using antisense oligonucleotides, another group have demonstrated that this region may, in fact, play a role in the dimerisation process itself [ 31 ]. By free energy minimisation this region is predicted to be unstructured, so it is not clear how the RNAs would interact with one another. In addition, whilst the SL1/DIS sequence is conserved amongst HIV-2 and SIV sequences in the database, that within the DM region is less so, and the substitutions which exist would affect the auto-complementarity of the sequence.In vitroOne of the key differences between HIV-1 and HIV-2 replication is their modes of packaging [ 32 ]. Whilst the Gag protein of the former captures the genomic RNA  in trans , the latter uses predominantly a  cis  mechanism. One might postulate therefore, that, if retroviruses must package a dimeric genome, it is critical in the case of HIV-2 that the genome is dimeric before interacting with the Gag polyprotein. Hence, the effect of mutations in the DM region may be to render the RNA monomeric and thus to severely impair packaging.in transcisIt is attractive to speculate that the reason packaging itself is not affected by DIS mutations to the same degree in HIV-1 [ 33 ] is this difference in protein:RNA interaction. If the RNAs can interact at points other than the principal DIS over time, then perhaps the  trans  mechanism is less dependent on a high affinity dimer linkage?transParticle maturation and viral infectivity A recurring observation amongst investigators is the fact that mutation or deletion of dimer linkage sites causes viral infectivity to be decreased [ 33 ]. One explanation for this might be that a dimeric genome is a prerequisite for maturation of virus particles. Certainly, immature HIV-1 particles are non-infectious, and viruses with their DLS mutated have been demonstrated to form only immature particles [ 34 ]. The DLS of Human T Cell Lymphotropic Virus Type 1 (HTLV-1) was identified as a 14-nucleotide sequence just downstream of the splice donor [ 35 ]. Removal of this region from the leader sequence rendered the RNA monomeric  in vitro  [ 24 , 36 ]. When this deletion was introduced into the wildtype genome sequence, the only viral replication defect that was observed, following transfection and subsequent infection, was that of impaired infectivity [ 37 ]. Likewise, a similar effect was observed when the DLS of Human Foamy Virus was mutated [ 38 ]. Parent  et al  showed that if the RNA of Rous Sarcoma Virus (RSV) was engineered so that it was monomeric, the virus was non-infectious [ 39 ]. Interestingly, this group suggested that it might be a difference in localisation of structural proteins and RNA affecting subsequent dimer formation and viral infectivity [ 40 ]. This is an area that has not been explored to any extent. Also working with RSV, Bieth and colleagues found that, in an  in vitro  system, dimer formation appeared to inhibit synthesis of the Gag polyprotein precursor [ 41 ].
Particle maturation and viral infectivity
A recurring observation amongst investigators is the fact that mutation or deletion of dimer linkage sites causes viral infectivity to be decreased [ 33 ]. One explanation for this might be that a dimeric genome is a prerequisite for maturation of virus particles. Certainly, immature HIV-1 particles are non-infectious, and viruses with their DLS mutated have been demonstrated to form only immature particles [ 34 ].The DLS of Human T Cell Lymphotropic Virus Type 1 (HTLV-1) was identified as a 14-nucleotide sequence just downstream of the splice donor [ 35 ]. Removal of this region from the leader sequence rendered the RNA monomeric  in vitro  [ 24 , 36 ]. When this deletion was introduced into the wildtype genome sequence, the only viral replication defect that was observed, following transfection and subsequent infection, was that of impaired infectivity [ 37 ]. Likewise, a similar effect was observed when the DLS of Human Foamy Virus was mutated [ 38 ].in vitroParent  et al  showed that if the RNA of Rous Sarcoma Virus (RSV) was engineered so that it was monomeric, the virus was non-infectious [ 39 ]. Interestingly, this group suggested that it might be a difference in localisation of structural proteins and RNA affecting subsequent dimer formation and viral infectivity [ 40 ]. This is an area that has not been explored to any extent. Also working with RSV, Bieth and colleagues found that, in an  in vitro  system, dimer formation appeared to inhibit synthesis of the Gag polyprotein precursor [ 41 ].et alin vitroStructure of the dimer linkage Undoubtedly the best defined dimerisation structure is that involved in the dimer linkage of HIV-1. The discovery of the sequences involved, the subsequent description of the RNA:RNA interaction, and the elucidation of the tertiary interaction are described elsewhere [ 1 ]. The initial interaction between the two RNAs appears to be a kissing loop interaction (similar to that seen in the regulation of plasmid replication, [ 42 ]) followed by annealing of the two RNAs into an extended duplex (Figure  2b ). The sequences contained within the palindrome are remarkably conserved. Using an  in vitro  selection system it has been possible to demonstrate that the DIS has evolved to satisfy both constraints for optimal dimerisation affinity, and the potential to homodimerise [ 43 ]. The dimer linkage is found at the terminal end of Stem Loop 1 (SL1) within the packaging signal region of HIV-1 (Figure  2a ). The tertiary structure of the whole SL1 RNA has been determined [ 44 , 45 ] and the structures have helped to determine exactly how the RNAs interact with one another. A number of elements appear to be critical for the dimer interaction: flanking purines and central nucleotides in the palindromic sequence [ 46 ] and loop B [ 47 - 49 ]. The tertiary structure of the latter has been described (Figure  2c ), and there is some debate as to how flexible this internal loop might be. However, work by Borer  et al , examining the interaction of NC with elements of the packaging signal, of which loop B is one, showed that, in fact, both structures might exist, the flexible one allowing NC binding at high affinity [ 50 ]. There are similar linkages in other retroviruses. The Avian Leukosis Viruses also interact firstly in a kissing hairpin manner, and then form an extended duplex (Figure  3a , [ 51 ]). Palindromes remain a theme throughout many of the viruses investigated to-date. As already mentioned, the DIS of HIV-2 is less well defined than that of HIV-1. Whilst there is a palindromic sequence at the top of a stem loop structure that closely resembles the HIV-1 DIS (see Figure  1 ), there are other regions which have also been demonstrated to be important for dimer formation [ 25 , 26 ]. Other viruses with palindromic sequences as their DLS include HFV (Figure  3c ) and MoMLV. In the case of MLV there are other sequences and structures which may play a role in dimer formation, including the GACG tetraloops mentioned previously [ 52 ]. The tertiary structure of this stem loop is the only proposed dimer linkage element yet to be determined in a retrovirus other than HIV-1 ([ 53 ]). RSV and VL30, also have imperfect repeat sequences in their dimer linkages [ 54 , 55 ] (Figure  3b ). Recent work by Monie and colleagues [ 36 ] describes the potential tertiary structure of the HTLV-1 dimer linkage, capped by a novel CAG tri-loop (Figure  3e  and Figure  4 ). This tri-loop is formed by an unusual C:synG base pair closing the loop. Other similar loops have been described, in the domain IIId terminal loop of the hepatitis C virus internal ribosomal entry site (IRES) [ 56 ] and in stem loops required for initiation of transcription within the Bromoviridae [ 57 ]. Although sequence heterogeneity between HTLV-1 isolates is rare, distinct mutations identifying individual strains can be identified. Of 101 HTLV-1 sequences identified from the EMBL database, 90 showed sequence homology with HTLV-1 CH , the strain used in the study. The other 11 sequences comprised three different variants. Eight contained a deletion of C736 (see Figure  4 ), two possessed the substitution A737G, and one possessed the substitution C733U. The substitution mutants have minimal impact on regional secondary structure, while the deletion may induce formation of a CAGG tetraloop. Interestingly, the A737G mutation possesses homology with 150 deposited HTLV-II sequences, suggesting a conservation of the DIS between HTLV-I and -II.
Structure of the dimer linkage
Undoubtedly the best defined dimerisation structure is that involved in the dimer linkage of HIV-1. The discovery of the sequences involved, the subsequent description of the RNA:RNA interaction, and the elucidation of the tertiary interaction are described elsewhere [ 1 ]. The initial interaction between the two RNAs appears to be a kissing loop interaction (similar to that seen in the regulation of plasmid replication, [ 42 ]) followed by annealing of the two RNAs into an extended duplex (Figure  2b ). The sequences contained within the palindrome are remarkably conserved. Using an  in vitro  selection system it has been possible to demonstrate that the DIS has evolved to satisfy both constraints for optimal dimerisation affinity, and the potential to homodimerise [ 43 ]. The dimer linkage is found at the terminal end of Stem Loop 1 (SL1) within the packaging signal region of HIV-1 (Figure  2a ). The tertiary structure of the whole SL1 RNA has been determined [ 44 , 45 ] and the structures have helped to determine exactly how the RNAs interact with one another. A number of elements appear to be critical for the dimer interaction: flanking purines and central nucleotides in the palindromic sequence [ 46 ] and loop B [ 47 - 49 ]. The tertiary structure of the latter has been described (Figure  2c ), and there is some debate as to how flexible this internal loop might be. However, work by Borer  et al , examining the interaction of NC with elements of the packaging signal, of which loop B is one, showed that, in fact, both structures might exist, the flexible one allowing NC binding at high affinity [ 50 ]. There are similar linkages in other retroviruses. The Avian Leukosis Viruses also interact firstly in a kissing hairpin manner, and then form an extended duplex (Figure  3a , [ 51 ]).in vitroet alPalindromes remain a theme throughout many of the viruses investigated to-date. As already mentioned, the DIS of HIV-2 is less well defined than that of HIV-1. Whilst there is a palindromic sequence at the top of a stem loop structure that closely resembles the HIV-1 DIS (see Figure  1 ), there are other regions which have also been demonstrated to be important for dimer formation [ 25 , 26 ]. Other viruses with palindromic sequences as their DLS include HFV (Figure  3c ) and MoMLV. In the case of MLV there are other sequences and structures which may play a role in dimer formation, including the GACG tetraloops mentioned previously [ 52 ]. The tertiary structure of this stem loop is the only proposed dimer linkage element yet to be determined in a retrovirus other than HIV-1 ([ 53 ]). RSV and VL30, also have imperfect repeat sequences in their dimer linkages [ 54 , 55 ] (Figure  3b ).Recent work by Monie and colleagues [ 36 ] describes the potential tertiary structure of the HTLV-1 dimer linkage, capped by a novel CAG tri-loop (Figure  3e  and Figure  4 ). This tri-loop is formed by an unusual C:synG base pair closing the loop. Other similar loops have been described, in the domain IIId terminal loop of the hepatitis C virus internal ribosomal entry site (IRES) [ 56 ] and in stem loops required for initiation of transcription within the Bromoviridae [ 57 ]. Although sequence heterogeneity between HTLV-1 isolates is rare, distinct mutations identifying individual strains can be identified. Of 101 HTLV-1 sequences identified from the EMBL database, 90 showed sequence homology with HTLV-1 CH , the strain used in the study. The other 11 sequences comprised three different variants. Eight contained a deletion of C736 (see Figure  4 ), two possessed the substitution A737G, and one possessed the substitution C733U. The substitution mutants have minimal impact on regional secondary structure, while the deletion may induce formation of a CAGG tetraloop. Interestingly, the A737G mutation possesses homology with 150 deposited HTLV-II sequences, suggesting a conservation of the DIS between HTLV-I and -II.Conclusions The retroviral RNA genome structure does not stay static during the course of transcription, translation and ultimately packaging. Various investigators have suggested that this constantly changing RNA structure plays an intimate role in the viral replication [ 58 - 61 ]. It seems possible that linkage of the two RNA molecules constituting the genome is integral to the changes in RNA structure. As described in the article above, the dimer also acts as a mechanism for promoting recombination; may be a signal for packaging to occur; may be an inhibitory signal; may direct processes to occur in specific cellular compartments; and lastly, may be capable of interacting with cellular proteins. In vivo  data has revealed just how important an intact dimmer linkage may be to a retrovirus. For instance, there are intriguing differences in the effect of dimer mutations on viral infectivity depending on the cell type being infected [ 62 ]. What the significance of this might be in the context of a viral infection is, as yet, unclear. The importance of the dimer linkage is perhaps most clearly exemplified by the observation that a patient infected with a viral isolate having a defective DLS, had a low viral load. The subsequent switch in the predominant virus to that with a competent DLS coincided with a rise in viral load [ 63 ]. One can speculate that, at least in the case of HIV-1, only those viruses with a whole, optimised dimer linkage are capable of efficient infectivity. For the purposes of examining the role of retroviral RNA dimer sequences in the context of animal models, the non-human retroviruses, including the non-primate lentiviruses will be of great importance. To sum up, retroviral dimeric genomes are linked by a variety of RNA structures, including kissing hairpins, GACG tetraloops and unusual CAG-tri loops. The differences in these interactions, and when or where they occur, may reflect different demands upon this unique feature, and highlight the elasticity of the RNA genome.
Conclusions
The retroviral RNA genome structure does not stay static during the course of transcription, translation and ultimately packaging. Various investigators have suggested that this constantly changing RNA structure plays an intimate role in the viral replication [ 58 - 61 ]. It seems possible that linkage of the two RNA molecules constituting the genome is integral to the changes in RNA structure. As described in the article above, the dimer also acts as a mechanism for promoting recombination; may be a signal for packaging to occur; may be an inhibitory signal; may direct processes to occur in specific cellular compartments; and lastly, may be capable of interacting with cellular proteins.In vivo  data has revealed just how important an intact dimmer linkage may be to a retrovirus. For instance, there are intriguing differences in the effect of dimer mutations on viral infectivity depending on the cell type being infected [ 62 ]. What the significance of this might be in the context of a viral infection is, as yet, unclear. The importance of the dimer linkage is perhaps most clearly exemplified by the observation that a patient infected with a viral isolate having a defective DLS, had a low viral load. The subsequent switch in the predominant virus to that with a competent DLS coincided with a rise in viral load [ 63 ]. One can speculate that, at least in the case of HIV-1, only those viruses with a whole, optimised dimer linkage are capable of efficient infectivity. For the purposes of examining the role of retroviral RNA dimer sequences in the context of animal models, the non-human retroviruses, including the non-primate lentiviruses will be of great importance.In vivoTo sum up, retroviral dimeric genomes are linked by a variety of RNA structures, including kissing hairpins, GACG tetraloops and unusual CAG-tri loops. The differences in these interactions, and when or where they occur, may reflect different demands upon this unique feature, and highlight the elasticity of the RNA genome.Competing interests None declared.
Competing interests
None declared.