Histomorphometry

3.3.1.1 Precision o f measurements

The two methods of error assessment for the directly measured histomorphometry parameters are shown in Table 3.4. The results for %CV from the standard deviation from the 3 sets of measurements of 6 fields should give an upper bound for the precision error. The standard error method is likely to be more representative of the actual error which is 6-7 % for the area and perimeter measurements.

Table 3.4 Histomorphometry precision errors

Parameter %CV from the sd of 3

measurements on 6 fields

%CV from the standard error of the mean for 18

fields

Mean object length 8.8 1.6

No. of intercepts 4.5 3.6

Area of trabecular bone 7.3 6.6

Mean perim eter per arc 9.2 6.2

3.3.1.2 Histomorphometry results

Results for the histomorphometry variables are given in Table 3.5 for the bone cubes and sheep femur samples. The parameters have been defined in Table 3.1 The proximal sheep femur samples have a denser structure to the distal samples so the results represent an average.

Chapter Three In-vitro Investigations

Table 3.5 Histomorphometry results for bone samples

Parameter % bone Vertebral cubes mean ± sd 38.5 ±6.6 Sheep femurs mean ± sd 34.5 ± 10.6 N. int. 218 ± 2 2 165 ±31 T. Per. (pm) 7426 ± 694 6 8 2 7 ± 1149 P er./area (pm/pm ) 0.0084 ±0.0015 0.0883 ±0.0015 Tr. W. (pm) 277 ± 57 321 ± 4 7 Tr. N. (pm" 0.0014 ±0.0001 0.0010 ± 0.0002 Tr. S. (pm) 441 ±61 658 ± 223

3.3.1.3 Correlation within parameters

Some histomorphometry parameters are not independent e.g. trabecular number and trabecular separation. Also some parameters may be related to the amount of bone present. The relationships within parameters will depend on the type of bone sample. The correlations between the histomorphometry parameters for the vertebral cubes are shown in Table 3.6. For the vertebral cubes, number of intercepts, trabecular perimeter and trabecular number were not significantly correlated to %bone. The type of bone architecture observed in the vertebral cubes is of branching trabeculae running predominantly in one direction. In this arrangement it is easy to visualise that many thin trabeculae rather than few thick trabeculae will give very different results for trabecular perimeter and trabecular number but may give the same result for %bone. Trabecular separation and trabecular width may change independently of bone mass, as illustrated in Figure 3.13, but at constant trabecular separation a change in trabecular width will result in a change in bone mass and vice versa. For the sheep femur samples the bone architecture is more isotropic and all the histomorphometry variables were significantly correlated to each other.

Table 3.6 Significant correlation coefficients within histomorphometry parameters for

12 vertebral cubes

Nint. T. per. Per./area Tr. W. Tr. N. Tr. S.

% bone - - -0.87 0.86 - -0.74 N int. 1.00 0.98 - 0.85 0.997 -0.66 T. per. 0.98 1.00 - - 0.98 -0.70 P er./area - - 1.00 -0.97 - - Tr. W. - - -0.97 1.00 - - Tr. N. 0.997 0.98 - - 1.00 -0.66 Tr. S. -0.66 -0.70 - - -0.66 1.00

Figure 3.13 Illustration o f different trabecular architecture at constant bone mass

I

:

I

(a) (b)

Com pared to structure (a), structure (b) shows increased trabecular perim eter and trabecular num ber and decreased trabecular width and trabecular separation for the sam e am ount o f bone.

3.3.2 High resolution MR imaging

Figure 3.14 shows the high resolution images obtained of the bone samples on which the trabecular structure is clearly visible. A number of problems were encountered with this method. The proximal sheep femurs were imaged at an angle to the long axis of the sheep femur. Hence with the 5 cm FOV the image started and finished outside

Chapter Three In-vitro Investigations

bone (Figure 3.14b). With the distal end however the required image slice is along the axis of the sheep femur. Because the bone extends outside the FOV, image wrap occurs where the rest of image is superimposed on the region of interest. For this reason high resolution distal sheep femur images were not obtained.

Figure 3.14 High resolution images o f a vertebral cube and a proximal sheep femur

i

a) vertebral cube b) proxim al sheep fem ur

The SNR for all samples was poor and necessitated imaging times of the order of 5 hours per sample. Attempts to increase SNR would mean increasing slice thickness or pixel size. The ideal slice thickness for reducing partial volume effects to a minimum would need to be small compared to trabecular width which was of the order of 300 pm for the bone samples used in this study. However images obtained at a slice thickness less than 500 pm showed poor SNR and were found to be inferior to those obtained at a slice thickness equal to 500 pm.

The pixel size used in this study for the vertebral cubes was 60 pm which is similar to the resolution of 50 pm deemed suitable by Chung et al (1995b) based on the typical trabecular thickness found in human bone. For the sheep femur samples however the minimum pixel size obtained was 100 pm due to the FOV required to include the

femoral head. The width of the trabeculae may be as small as 200 p,m which means that a trabeculae could be only two pixels wide which would lead to a substantial partial volume effect.

Hence in terms o f either slice thickness, resolution or both, the images obtained in this study were considered unsuitable for computerised measurements o f bone morphometry. These are based on the assignment of pixels to either bone or marrow to produce binary images. The bone area is then determined by expressing the bone pixels as a fraction of the total number of pixels. The trabecular perimeter is obtained by identifying the interface between adjoining pixels o f value 0 and 1 in the binary image. Using these methods with images obtained at a slice thickness o f 200 pm and and a pixel size of 50x50 pm^, Chung et al (1995b) found that the errors in bone area fraction, trabecular perimeter, trabecular thickness and trabecular separation were 5- 6% which is comparable to the values obtained in this study for histomorphometry parameters. Hence at a greater slice thickness and pixel size (for the sheep femur samples), the precision of the high resolution MR imaging technique will be inferior to that of histomorphometry. Due to these considerations direct measurements of structural parameters were not taken from the high resolution images and histomorphometry results were used as the definitive measures of bone structure. However the 7 T images clearly show trabecular structure and would be suitable for texture analysis methods which are briefly discussed in the section on future work in Chapter Six.