Object Contrast. A main purpose of any imaging device is to record the details of an object faithfully in its image. What do we mean by the details of an object? These are the spatial variations of a given parameter, such as light intensity in photography, transmitted x-ray intensity in diagnostic radiology, and the concentration of radioactivity in scanning. Such a parameter, in the language of the physicist, is known as object contrast and is most important in the detectability of a lesion. In nuclear medicine, the object contrast is created in the organ of interest by the use of a radiopharmaceutical that either selectively localizes in the abnormal tissue as compared with the normal tissue (hyperintense uptake such as fluoro-deoxy-glucose [FDG] accumulation in a tumor) or vice versa (hypointense uptake such as a myocardial perfusion defect). In either case, the higher the variation between the concentration of radioactivity in the normal and abnormal tissues, the easier it is to detect an abnormality. Therefore, radiopharmaceuticals that produce greater contrast in the lesion have better detectability than those that produce smaller contrast.

For the quantitative purposes, we may define the object contrast C₀ as follows:

where C_a and C_n denote the concentration in abnormal and normal tissues, respectively. When there is no differential (variation) between the concentration of radioactivity in the abnormal and normal tissues, C₀ = 0 (i.e., there is no contrast). Such a radiopharmaceutical producing zero object contrast will be of no use in the detection of abnormal lesions. When the concentration of the radioactivity is higher in the abnormal area than that of the normal area, then C₀ is greater than 0, and the radiopharmaceutical produces a positive contrast. The majority of radiopharmaceuticals actively used for cancer imaging produce positive contrast. In cases where there is less radioactivity in a lesion than in normal tissue, radiopharmaceuticals produce a negative contrast (C₀ < 0). The value of C₀ for negative contrast cannot be increased more than -1, a value indicating almost no radioactivity in the lesion. For example, radiocolloids used for liver scanning are preferentially localized in normal tissue with almost no radioactivity in the abnormal lesions. Another example is myocardial perfusion defects in cardiac imaging; for example as seen in ^99mTc-Sestamibi single-photon emission computed tomography (SPECT) or ⁸²Rb positron emission tomography (PET) images. Because
radiopharmaceuticals producing positive contrast can achieve higher contrast values (C₀ ≥ 1) than those producing negative contrast, the former potentially have better detectability than the latter.

Spatial Resolution and Sensitivity of an Imaging Device. An imaging device, such as a scintillation camera, registers the details of the distribution of a radionuclide as a photographic camera records the details of an object or scene. In both cases, a physical device is used to form an image of an object. This is true, in fact, of any imaging process using such diverse instruments as an electron microscope, telescope, or x-ray tube. In all cases, the aim is to reproduce exactly the object contrast in the image.

Unfortunately, no imaging device is capable of reproducing all the details of an object in an image, and a certain loss of detail (object contrast) is inevitable. The parameter of an imaging device that characterizes the extent of the loss of object contrast or measures the faithfulness or the fidelity for reproduction of object contrast is called spatial resolution. An imaging device that possesses better spatial resolution is capable of reproducing finer details of an object (smaller object contrasts) and is able to detect smaller lesions than an imaging device with a poorer spatial resolution. Therefore, the spatial resolution of an imager is an important parameter that strongly influences the detectability of a lesion.

What limits the spatial resolution of an imaging device in nuclear medicine? Theoretically, there are no limitations in designing an imager with very fine spatial resolution capabilities in planer and SPECT imaging. In PET imaging, positron range and photon noncollinearity (Chapter 15) place a low limit of spatial resolution in the 1 to 2 mm range. However, practical limitations arise from two main constraints: the radiation dose to the patient must be kept low and the time of scanning should be reasonably short.

The effect of these two restrictions is to limit the number of γ-rays that can be detected and displayed in an image. As we see in the following section, the total number of γ-rays (photons) in an image is also an important parameter affecting the detectability of a lesion. To obtain a given number of photons in an image within a limited time, therefore, the imaging device should possess high sensitivity. The sensitivity of an imaging device is a measure of its ability to detect γ-rays efficiently. A more sensitive device will require a shorter interval of time to detect the same number of γ-rays than a less sensitive device.

Unfortunately, the sensitivity of an imaging device is commonly related inversely to its spatial resolution. For instance, as seen in Chapter 12 (see discussion following equations (12.4) and (12.5)), the relationship for a collimator design is in inverse squares. In other words, an imaging device with a spatial resolution better by a factor of 2 relative to another collimator design will have a fourfold loss of sensitivity. This loss of sensitivity theoretically necessitates either a fourfold increase in the scanning or imaging time or a fourfold increase in the radiation dose to the patient. In actuality, the cost to improve the spatial resolution by a factor of 2 will be more than fourfold, as will be seen in the following section.

Statistical (Quantum) Noise. For reproducing the details of an object, even with high contrast, an imaging device with good spatial resolution is not, in itself, enough. The human eye is capable of seeing minute details of a well-lit object but fails to perceive even large objects in a dark room. Hence, the amount of available light (number of photons) is another important parameter affecting the visualization of the details or contrast of an object.

This point is strikingly demonstrated in Figure 16.1, showing six photographs of a girl taken in succession with increasing numbers of total photons. With a smaller number of photons, only large details with high contrast are visible. As the number of photons increases, finer details of the object become visible in the image. In other words, the number of photons needed to visualize a given detail in an object is related to its contrast in the object. This relationship between the number of photons and the object contrast is not just limited to photography but is a generalized phenomenon of any imaging process as well.

Consequently, the net contrast in an image (it is the contrast in the image that allows us to determine the presence of a lesion) is derived from two components: the finite spatial resolution of the imaging device and the number of photons N detected that form the image. The latter component determines statistical noise in the image.
In a well-lit object (a large number of photons), the limiting factor for reproducing the object contrast is essentially the spatial resolution of the imaging device, whereas in a dark room (hardly any photons), the limiting factor is the statistical noise in the image. In a moderately lit room (a limited number of photons), the final contrast in the image is determined by both.

In nuclear medicine, the statistical noise of an image is related to the number of γ-rays detected.
The statistical noise can be reduced by increasing the total number of photons in the image. In planar imaging, the percentage statistical noise or error for N counts in an image equals × 100% (equation (3.11) in Chapter 3). Even in tomographic imaging (SPECT and PET), statistical noise in the reconstructed images is roughly proportional to . In other words, acquiring four times as many counts would reduce statistical noise in the generated image by ˜2. If we consider a lesion that is imaged by two different radiotracers that end up giving it different contrasts, offset by a factor of 2 from one another, the one with lower contrast would have to be imaged approximately four times longer, thus lowering its statistical noise by a factor of 2, so that the detectability of the two lesions becomes comparable. Overall, the total number of photons needed to properly visualize a lesion depends on its contrast, and therefore, a certain number of counts have to be acquired for a given imaging task to arrive at appropriate detectability. The use of too few counts (e.g., as obtained by acquiring data for too brief a time) may cause borderline lesions (with low contrast) to be overlooked. On the other hand, acquiring too many counts will not significantly affect the detectability because, beyond a certain level, the limiting factor for detectability is the resolution of the imaging device.