The bone mineral density (BMD) of vertebrae probably influences their mechanical strength and thus the strength of the complete spinal structure. Hence, for all specimens harvested in this study, the BMD of the central part of each vertebra was determined based on the Hounsfield Units (HU) of the CT scans. BMD was expressed as the concentration of dipotassium phosphate in distilled water (mg K2HPO4 per ml).
To determine the bone mineral density of the bony structure inside the vertebrae, a 3D reconstruction program (Amira 3.0, Avizio 5.0, Mercury Computer Systems, Merignac, France) was used. DICOM files were imported directly. Because spongious bone is not a homogeneous structure and CT data are rather noisy, BMD values were mostly analysed within a defined volume (Figure II-9, Figure II-10).
Figure II-9 Location of the bounding box within two views of a vertebra
Figure II-10 Extracted bounding box and corresponding histogram of the voxels’
HU values
The measurement volume in this study was a bounding box of 30x30x15 voxels, manually placed in the centre of the analysed vertebral body. In cases where the
geometry of the vertebral body did not allow use of the standard size (e.g. if the vertebral bodies were too flat or had bony deformations), a smaller size was substituted to avoid inclusion of cortical bone and endplates (e.g. LWS 1103, L2:
30x30x10 voxels). Since the measured values might be influenced by the investigator’s choice of bounding box positioning and orientation, the measurements were performed by two individuals to evaluate the variability between different investigators. The derived values are given at the end of this section (Table II-4, Table II-5, Table II-6, Table II-7).
However, even though the HU scale appears to be rather objective, two problems are associated with it. First of all, this scale can hardly be transformed to material or mechanical properties like mineral content, ash weight or mechanical strength.
Second, this scale appears to be different for different types of CT scanners.
Therefore, the HU values were converted into the equivalent of BMD using a custom-made dipotassium phosphate (K2HPO4) phantom. Dipotassium phosphate is a secondary ortho-phosphate that is mainly used for the composition of buffer solutions. Since human bone also contains phosphate (calcium phosphate), the absorption of X-rays due to K2HPO4 is similar to that of the mineral fractions of the bone. However, in contrast to the description of the bone mineral density in HU, the description in equivalents of dipotassium phosphate is independent of the type and the setting of the CT scanner used and therefore allows better comparability – as long as the conversion formula is known.
K2HPO4 phantoms were used to estimate a linear conversion formula between the HU and K2HPO4 equivalents. A phantom made of three vials with different concentrations of K2HPO4 was made. One vial was filled with distilled water and the others contained 100 mg K2HPO4 per ml and 500 mg K2HPO4 per ml, respectively.
The phantom was scanned in both scanners (Siemens: 140 kV, 200 mAs, Kernel B70s and Philips: 140 kV, 200 mAs, Kernel D). The HU were measured in three perpendicular cutting planes and the mean value of the three measurements was calculated to account for deviations within the scanners (Figure II-11).
Figure II-11 CT slice from the same phantom recorded in different CT scanners
The phantom showed a high linearity between the concentration of K2HPO4 and measured HU; however, there were differences between the two scanners (Figure II-12 and also with respect to data in the literature (Brinckmann et al., 1998). Hence, different conversion parameters were needed to allow a comparison between the measured data.
Figure II-12 Relation between concentration of K2HPO4 and HU for both CT scanners
Regarding the measured HU as a function of the concentration of K2HPO4, the resulting curve does not cross the origin for the Philips scanner. The reason for this effect is the influence of the water in the phantom, which normally does not contribute to the attenuation (HUWater = 0) but changes the volumetric fraction of the K2HPO4
(20% in 500 mg K2HPO4 per ml, 4% in 100 mg K2HPO4 per ml). Since only the linearity between pure K2HPO4 and measured HU should be taken into account, the influence of the water has to be eliminated from the equation
W W K
K HU HU
HU = ν ⋅ +ν ⋅ , (II-11)
where vK is the volume fraction of K2HPO4, vW the volume fraction of water, HUK
the attenuation of K2HPO4 and HUW the attenuation of water. vK and vW are known values. By means of the measured Hounsfield Units (for Philips: 771 HU for 500 mg K2HPO4/ml, 212 HU for 100 mg K2HPO4/ml and 59 HU for water) HUK can be calculated with the equation
W K
W K
K 1 HU HU
HU ⋅
ν
− ν ν ⋅
= (II-12)
(for Philips this was 3536 HU, as calculated for 500 mg K2HPO4/ml concentration).
Now corrected values for the three calibration points can be calculated using the equation
K K
corrected HU
HU = ν ⋅ . (II-13)
The resulting corrected line crosses the origin (Figure II-13) and allows the correct conversion into Hounsfield Units for every concentration of K2HPO4.
Figure II-13 Relation between HU and concentration of K2HPO4 for the Philips and Siemens scanners (corrected)
In this study, the inverse relation is needed. Measured HU has to be expressed as the equivalent of K2HPO4. For the first scanner (Siemens), this is:
]
and for the second scanner (Philips), it is:
]
For 77 specimens of different spinal levels, the BMD values (in HU) were determined by two independent investigators. Vertebral bodies with deviations in BMD values of more than 10% were analysed repeatedly by both observers. Overall, the regression between the two data sets is sufficient (Figure II-14). The slope is 0.939 (±0.058) and the corrected coefficient of determination is R2corr =0.78 (p < 0.001).
It appeared that large deviations occurred mostly in cases where the size of the vertebral bodies was small or where bony damages were visible. In these cases the exact positioning within the spongy bone was difficult, and cortical bone and endplates might therefore have been included as well. The allowed reduction of the size of the measurement volume for flat or abnormal vertebrae was only done for the axial coordinate (from 15 voxels to 10 voxels). Some abnormal cases can be seen in Figure II-15. However, the quality of the results depends predominantly on the properties of the specimens and not on the choice of investigator.
Figure II-14 Regression between the BMD values determined by two independent investigators
Figure II-15 Positioning of the bounding box in extreme cases, where a smaller volume size was applied (L4, LWS 1103; L4, LWS 1114; L5, LWS 1118)
BMD1 [HU]
350 300
250 200
150 100
50
BMD2 [HU]
350 300 250 200 150 100 50
No differences between the mean BMD of different spinal levels were observed (Figure II-16). Table II-4 shows the measured data as well as the position of the bounding box defined by the minimal index in the x-, y- and z-directions.
spinal level
5 4
3 2
BMD [HU]
200
150
100
50
0
Figure II-16 Mean BMD of the four different spinal levels (error bars showing 95%
confidence interval)
Table II-4 Analysed measurement volume and BMD of vertebra L2
Table II-5 Analysed measurement volume and BMD of vertebra L3
Table II-6 Analysed measurement volume and BMD of vertebra L4
Table II-7 Analysed measurement volume and BMD of vertebra L5