Optimisation using the model

The model can now be used to help decide on the best set of parameters to use for a given application. This study uses a one component system i.e. bone mineral only, in measurements on archaeological bone (see chapter three), and a two component system, i.e. bone tissue and bone marrow, in measurements on bone phantoms simulating in-vivo measurements. The material used to model the bone mineral is hydroxylapatite, which is the main mineral content of bone. The marrow is modelled using polyethylene as this gives a broad diffraction peak of momentum transfer value close to that of marrow fat.

2.3.1 The basis of the optimisation process

Although pencil beam geometry gives the best resolution in a measured spectmm i.e. it provides the minimum of angular blurring and hence improves energy resolution, it has

the disadvantage that long counting times are necessary to obtain good quality spectra. In any clinical application the measurement time has to be kept to a minimum and consequently for the purposes of this study ribbon beam collimation has been used and therefore all the modelling assumes this geometry. An important aspect of the optimisation procedure is taking into account how the spectra are to be analysed. In this study the diffraction peaks that are present in the spectra due to the two components being measured, i.e. bone mineral and bone marrow, will be analysed. (In the case of the archaeological bone it will be just the mineral). The peaks may or may not require good resolution depending on their position in the spectrum i.e. the proximity to each other or to other peaks present. If the resolution is not important then the collimation geometry can be widened allowing shorter measurement times and better counting statistics.

Chapter three describes work carried out on archaeological bone samples. This is a simple one component system to model i.e. bone mineral only. The model can be used to view peak positions and intensities as a function of scatter angle, and also as a function of the incident spectrum kV. The analysis of the recorded spectra is to quantify the bone mineral present which is achieved by integrating the number of counts in a region of interest (ROI) that contains peaks characteristic of hydroxylapatite. It should be noted for this application, the measuring time is not a limiting factor as it is not a clinical situation.

2.3.2 Variation of hydroxylapatite spectra with angle

Figure 2.17 shows a plot of the modelled spectra for hydroxylapatite with an incident spectrum of 70 kV and a range of scatter angles from 4 degrees to 10 degrees plotted at 0.25 degree intervals. It can be seen how the characteristic peak positions vary as a function of energy. The position of the peak of interest is an important consideration as it is desirable to position it such as to maximise the signal strength. As the peak shifts in relation to the angle the intensity varies as a function of the intensity of the incident spectrum. To demonstrate this more clearly the data has been replotted in figure 2.18 which shows the intensity as a function of momentum transfer and illustrates how the main peak intensity varies as the angle is increased.

Chapter Two Modelling Coherent Scattered Spectra

flngrlc ( d e g r e e s )

E n e rg y keV

Figure 2.17 : Variation o f the hydroxylapatite spectrum with changing scatter angle.

0 . 0 5

A n g le ( d e g r e e s )

Motnentum T r a n s f e r (A)

0 . 5

Figure 2.18 : The change in peak intensity as a function o f momentum transfer and changing angle fo r hydroxylapatite.

2.3.3 Variation of spectra with incident kV

It can be seen from figure 2.18 that the intensity of the main hydroxylapatite peak is maximised at a scatter angle of approximately 6 degrees. The peaks in the spectrum are present because the incident spectrum contains the wavelength necessary for the Bragg law to be satisfied. To see how the peaks vary in intensity with varying incident spectrum, and to see if any other peaks become significant, a plot such as that shown in figure 2.19 can be examined. The figure shows the variation of the hydroxylapatite spectra with increasing incident kV from 65 kV to 140 kV. It can be seen that by increasing the energy no further significant peaks appear i.e. there is no additional information in the increased energy range of 70 keV to 140 keV and the influence of the x-ray tubes characteristic lines become apparent.

Figure 2.19 : Variation o f the hydroxylapatite spectrum with change in incident kV at a scatter angle o f 5 degrees.

2.3.4. Modelling collimation geometry

The information described above is useful in the case of archaeological bone. However, perhaps one of the most useful aspects of the model is to investigate the change in spectra as a function of changing geometry. This is a useful tool because it enables the collimation geometry to be optimised such that the photon throughput of

Chapter Two Modelling Coherent Scattered Spectra

the system is maximised while retaining the useful information in the spectrum. In the case of archaeological bone this can be carried out using the model described in section 2.1 and is explained in context in chapter three. To perform this optimisation for a bone phantom simulating an in-vivo situation, it would be useful to be able to model both the bone mineral and the bone marrow as a mixture.