## The Collimator Detector Response

The CDR of a single-photon nuclear medicine imaging system has 4 components the intrinsic response, due to uncertainty in position estimation in the detector system, and the geometric, septal penetration and septal scatter components that depend on the collimator characteristics. Suppose that we have a point at position r and we wish to know the probability that photons emitted at this point will be detected at some point in the detection plane, x. This is described by the collimator-detector...

## Compton Cameras

Except for those that use coded apertures, all collimated imaging systems exhibit a limiting detection sensitivity that is inversely proportional to the system's spatial resolution. This fundamental trade-off has motivated the development of Compton cameras (see Figure 4), which provide information about the incoming photon direction electronically without any restriction with respect to the solid detection angle.32 The mechanical collimation of the Anger camera is thus replaced by ''electronic...

## Explicit Correction Methods

Buvat et al.6 published a thorough review of explicit scatter correction methods as of 1994. Narita et al.41 provided a good, brief evaluation of possible methods as of 1996 in their introduction to a paper comparing two methods of SPECT scatter correction. They wrote ''The most commonly employed scatter correction techniques, due to their ease of implementation, are the convolution subtraction techniques42 and dual- or triple-energy window (TEW) techniques.35,43,44 These techniques have...

## Future of Dual Modality Imaging

Over the past 10 to 15 years, dual-modality imaging has progressed steadily from experimental studies of technical feasibility to the development of clinical prototypes to its present role as a diagnostic tool that is experiencing widening commercial availability and clinical utilization. Dual-modality imaging has advanced rapidly, primarily by incorporating the latest technological advances of CT, SPECT, and PET. Currently, combined MRI MRSI,152 153 PET CT,34 35 and SPECT CT125 systems are...

## References

Jones T., The role of positron emission tomography within the spectrum of medical imaging. Eur J Nucl Med 23 207-211 (1996). 2. Anger H., Scintillation camera. Rev Sci Instr 29 27-33 (1958). 3. Moore S. C., Kouris, K. and Cullum, I., Collimator design for single photon emission tomography. Eur J Nucl Med 19 138-150 (1992). 4. Jaszczak R. J., Greer, K. L. and Coleman, R. E., SPECT using a specially designed cone beam collimator. J Nucl Med 29 1398-1405 (1988). 5. Tsui B. M. and Gullberg, G. T.,...

## Convolution Deconvolution based Approaches

Techniques based on convolution or deconvolution estimate the distribution of scatter from the standard photopeak data. The scatter fraction (SF) which gives an indication about the expected amount of scatter and the scatter response function (srf) which defines the spatial distribution of scatter in the photopeak data are usually the two parameters required for estimation of scatter component and need to be determined a priori. A pure additive model of the imaging system is generally assumed...

## Septal Penetration and Septal Scatter Response Functions

The septal penetration response function (SPRF) describes the contribution to the total collimator-detector response by photons that penetrate through the collimator septa. To date there has been no analytic treatment of the septal penetration response for multi-hole collimators. However, the SPRF can be studied using ray tracing or Monte Carlo (MC) simulation tech-niques.66-9 The septal scatter response function (SSRF) describes photons that scatter in the collimator septa and are subsequently...

## Iterative Compensation Methods

Iterative reconstruction-based compensation for the CDRF is performed by including the effects of CDRF in the model of the image formation process. For simplicity, consider the maximum likelihood-expectation maximization (MLEM) algorithm28 (see chapter 4) In this expression, f(n+1) is the reconstructed image in the j-th voxel after n + 1 iterations, p is i-th projection bin from the measured projection data, and aij is the probability that a photon emitted in the j-th voxel is detected in the...

## Efficacy of CDRF Compensation

There have been a number of studies evaluating the efficacy of CDRF compensation. These include qualitative evaluations,38 evaluations in terms of quantitative of the effect of CDRF compensation on performance in estimation4242-45 and detection tasks.4646-50 Tsui demonstrated qualitative improvements in image quality in terms of noise and image resolution obtained using iterative 3D reconstructions with CDRF compensation compared to 2D reconstructions with or without compensation.38 Iterative...

## MAP with Gibbs Prior

As discussed above, maximising the likelihood is equivalent to maximising the posterior, if one can assume that nothing is known about the image, prior to the measurement. But obviously, some a-priori knowledge is available the image should not be too noisy. Somehow, this prior knowledge must be translated into a mathematical expression, which can be inserted in equation (4). A convenient way to define a prior distribution favouring smooth solutions is via a Markov random field (or equivalently...

## Subjective and Objective Assessment of Image Quality

Different approaches have been suggested to judge image quality when evaluating image reconstruction algorithms. As the 'best' reconstruction algorithm can only be selected with respect to a certain task, different 'basic' performance measures can be used. Basically, there is no single figure of merit that summarises algorithm performance, since performance ultimately depends on the diagnostic task being performed. Well-established figures of merit known to have a large influence on many types...

## Positron Emission Tomography 41 The Physical Principles of PET

When imaging positron-emitting radiopharmaceuticals, pairs of antiparallel 511 keV photons arising from electron-positron annihilations are recorded by block detectors surrounding the patient. A positron emission tomograph consists of a set of detectors usually arranged in adjacent rings that surround the field-of-view in order to image the spatial distribution of a positron-emitting radiopharmaceutical (Figure 5). In this case, the annihilation photons traverse a total tissue thickness that is...

## Transmissionless Approaches

In some cases, attenuation maps can be generated without adding a separate transmission scan to the emission acquisition. Algorithms in this class of methods either assume a known body contour in which a (uniform) distribution of attenuation coefficients is assigned or try to derive the attenuation map directly from the measured emission data. Only methods widely used in clinical routine and implemented on commercial systems will be described in this section. Other sophisticated and computer...

## Geometric Response Function

The geometric response function (GRF) is the portion of the total collimator response function that represents the distribution of detected photons that travel through the collimator holes without interacting with or passing through the collimator septa. The integral of the geometric response function, when normalized according to the convention described above, gives the geometric efficiency of the collimator. Of the three components of the collimator response, the geometric response is the...

## Spectct Imaging Systems

As noted earlier, the first SPECT CT imaging systems were developed at the University of California, San Francisco by Hasegawa and co-workers. The first prototype instruments (Figures 2 and 3) were configured as small-bore Figure 9. Precise characterization of increased 18F-FDG uptake and retrospective lesion detection on CT, after PET CT. The patient is a 35-y-old man, 22 months after treatment of colon cancer, with negative high-resolution contrast-enhanced CT and normal levels of serum...

## Small Animal Imaging Systems

The advantages of improved image quality and quantitative accuracy that are available for clinical applications of dual-modality imaging also are being investigated as a means of facilitating biological research, especially those that involve small animals such as mice and rats.37,111 Advances in molecular biology and genetic engineering, and the modern growth of the pharmaceutical and biotechnology industries have increased the need for biological studies that involve mice. Approximately 90 of...

## Implicit Correction Methods

One implicit scatter correction involved narrowing the photopeak energy window by moving the lower-energy cut-off energy up so it became less and less likely that scattered gamma rays were accepted. For 99mTc, this method worked better and better as the window was narrowed, but the number of unscattered counts being accepted was also being reduced.36 So this approach is usually not employed because one hardly ever is willing to sacrifice the good counts. Another implicit method simply required...

## Determination of the Attenuation Map in Emission Tomography

Reliable attenuation correction methods for emission tomography require determination of an attenuation map'', which represents the spatial distribution of linear attenuation coefficients and accurately delineates the contours of structures in the body for the region of the patient's anatomy that is included in the radionuclide imaging study. After the attenuation map is generated, it can then be incorporated into the radionuclide reconstruction algorithm to correct the emission data for errors...

## Correction Methods Based on Uniformly Attenuating Medium

Some of the first attenuation correction techniques used clinically in nuclear medicine, especially for SPECT, were designed to correct radionuclide images reconstructed using analytic techniques such as filtered backprojection. However, as noted above, it is difficult, if not impossible, to compensate the SPECT image for nonuniform attenuation using analytic reconstruction techniques. It is possible, however, to correct the radionuclide data assuming that the attenuation is uniform, for...

## Properties of MLEM Reconstruction

The EM algorithm results in an iterative process for estimation consistent with the general iterative flow-chart given in Figure 1. In this case the update is multiplicative, not unlike SMART, with the update simply being the ratio of measured over estimated projections. As the number of iterations increases the likelihood increases, providing an estimate that theoretically is more likely to be close to the true object distribution. In practice, however, the image reaches an optimal visual...

## General Design Features of Dual Modality Imaging Systems

Modern dual-modality imaging systems incorporate subsystems for radio-nuclide imaging and for x-ray computed tomography that essentially use the same components as those in dedicated nuclear medicine and CT systems. In PET CT, the radionuclide detector uses a scintillator bismuth germinate, lutetium orthosilicate, gadolinium orthosilicate coupled to an array of photomultiplier tubes for imaging the annihilation photons from the positron-emitting radiopharmaceuticals. Modern PET CT scanners also...