Basic parameters in collimator design

The collimator is the most critical component determining the quality of the images obtained with the Anger camera. The collimator performs the essential function of establish a geometrical relationship between the photons and the detector. The first characteristic of any collimator is the material selected for its construction. As the collimation process relies on the absorption of the photons travelling along certain directions, high-density materials with high atomic number (Z) are employed, such as lead and tungsten, in order to maximise the probability of photoelectric interactions.

The first Anger camera had a simple pinhole collimator, which is a small aperture at the apex of a cone located more than 20 cm away from the detector plane. Other designs have since been developed in order to increase efficiency. The most common collimator employed in nuclear medicine imaging is of the parallel-hale type, in which all the holes are arranged with their axes perpendicular to the collimator face. The orientation of the hole axes may follow a different pattern {converging or

diverging collimators) when specific applications require magnifying or minifying

properties.

Geometrical considerations in hole size and septa thickness are another fundamental aspect in collimator design (see for example [Moore et al., 1992], [Gunter, 1996]). The thickness of the septa is a function of the gamma-ray energy and it is designed to reduce penetration effects. A maximum septum penetration of 5% is usually accepted as reasonable criteria, thus resulting in a septum thickness t given by the following expression [Sorenson and Phelps, 1987]:

where d is the hole diameter, / is the physical length of the collimator holes and ju is the total linear attenuation coefficient of the collimator material at the energy of interest.

The physical dimensions of the holes play a major role in determining the system spatial resolution. The collimator spatial resolution is usually quantified by means of the width of its point spread function (PSF), which is the radiation profile obtained on the detector from a point source placed in front of the collimator. If the simple and most encountered case of a parallel hole collimator is considered and the thickness of the detector crystal is neglected, the following expression may be used for an approximate evaluation of the collimator resolution Rc, defined as the full width at half-maximum (FWHM) of the collimator PSF [Sorenson and Phelps, 1987]:

R,^d[l,+b)n,

where d is again the hole diameter, b is the distance between the source and the collimator and U is the collimator “effective length” or “effective thickness”. The quantity 4 is related to the physical thickness / of the collimator by the equation /g where p is the total linear attenuation coefficient of the collimator material at the given energy. The collimator effective thickness is introduced to account for the effect of penetration. As can be seen from equation (1.2), small values of the ratio {d/l^ provide better image quality.

The collimator geometric efficiency g, defined as the fraction of photons passing through the collimator per photon emitted by the source, can also be expressed in terms of the geometrical dimensions characteristic of the collimator (for a point source in air) [Sorenson and Phelps, 1987]:

Chapter 1 _________________________Collimation Approaches in M edical y-ray Imaging

g ^ K ^ { d H ^ f [ d ^ (1.3)

where d and 4 indicate the same physical quantities as in equation (1.2), t is the septal thickness and K is an adimensional constant that is a function o f the hole shape (e.g. Æ-0.24 for round holes in a hexagonal array). This equation shows that g increases as the quantity (d/leŸ is increased.

The sensitivity of an imaging system is the fraction of photons counted by the

system per photon emitted by the source. The sensitivity S^cs of a mechanically collimated system (MCS) can therefore be defined as the product of the geometric efficiency (equation (1.3)) and the photopeak detection efficiency s^et of the scintillator crystal in the camera:

^ M C S ~ (i-4)

The photopeak detection efficiency is a function of the source energy: for photon energies up to 100 keV, the Anger camera is over 90% efficient, but at 511 keV it has an efficiency of about 15%. In case of radioactive distributions different than a point source in air, corrections are required to account for the attenuation losses within the object. The sensitivity of a y-camera with a parallel hole collimator for ^^"’Tc is typically between 100 and 200 cps/MBq.

Relationships (1.2) and (1.3) indicate that if the collimator is designed so as to increase spatial resolution (i.e. Rc is decreased) then efficiency (or sensitivity) is necessarily decreased and vice versa, according to the approximate relationship

g cc . The appropriate geometric trade-off between efficiency and resolution is

usually tailored to specific applications by collimator manufacturers. Collimators for low-energy photons are therefore typically available in the following designs: high efficiency (low resolution), high resolution (low efficiency) or general-purpose with

intermediate efficiency and resolution. Table 1.1 summarises the typical performance characteristics of commercially manufactured parallel-hole collimators with different properties.

Table 1.1: Performance characteristics o f some typical commercially manufactured parallel-hole collimators [Sorenson and Phelps, 1987].

Collimator type Maximum

energy of operation (keV) Geometric efficiency g Resolution (FWHM in mm at 10 cm collimator-source distance) Low Energy, High Resolution 150 1.84 X 10"^ 7.4 Low Energy, General Purpose 150 2.68 X lO'"^ 9.1 Low Energy, High Sensitivity 150 5.74 X 10'^ 13.2 Medium Energy, High-Sensitivity 400 1.72 X 10"* 13.4

The total spatial resolution Rs of a gamma camera system is determined by the combination of the collimator resolution Rc with the intrinsic resolution Ri of the scintillation camera. The intrinsic resolution Ri is a measure of the precision with which interaction points can be localised in the uncollimated crystal. It is a function