A digital computer handles information in discrete, digitized form, and these too in binary form only (base 2 instead of base 10; i.e., using only the two digits: 0 and 1). Therefore, any instrument from which data are to be acquired and analyzed by a digital computer in an automatic manner has to present the data to the computer in digital form. Unfortunately, most electronic instruments produce signals or data in an analog form. Analog signals are continuously varying and do not produce data in finite (discrete) numbers. For example, the needle of a car speedometer moves in a continuous manner from one end of the dial to the other as the speed of the car is increased from zero to a certain maximum. The higher the speed of the car, the farther the needle moves. The digital information (in finite numbers) about the car’s speed is derived from a scale printed on the dial. The scale printed on the dial is, in a way, manual digitization of an analog signal (continuous movement of the needle). Now, if the speedometer or a radiation detector has to be coupled to a digital computer to record the analog output of these devices automatically, some electronic device will have to be used that will digitize the information provided by the speedometer.

In nuclear medicine, radiation detectors produce analog signals, for example, light produced in a scintillator or pulse height produced by a photomultiplier (PM) tube. Hence, all analog signals have to be digitized before entering a computer. This process is also referred to as quantization. An example of an analog signal and a digital signal is shown in Figure 11.1. A device, which automatically converts (quantizes) analog signals into digital (binary) signals, is known as an analog-to-digital converter, or simply an ADC. Many times, we also need to convert the output of the computer to an analog signal, for example, audio output from a computer. This is achieved by a digital-to-analog (DAC) converter. Examples of both are shown in Figure 11.1.

Two parameters of an ADC, accuracy and speed, are important for our purpose. The accuracy of ADC tells how close the numeric data is
to the analog signal. Let us consider the example of the speedometer again and assume this time for simplicity that the minimum speed of the car is zero and the maximum speed is 100 miles per hour (mph). Now to read any speed in between these two extremes, the scale on the dial has to be divided into equal divisions. If there are only 10 divisions, then we will be able to measure the speed of a car accurately only in steps of 10 mph. When the scale is divided into 100 equal parts, the speed could be read in steps of 1 mph. One thousand equal divisions will provide an accuracy of 0.1 mph and so on. The more divisions on the scale (in a given range), the better the accuracy. Similarly, in an ADC, a given range of signals is broken into divisions; the more divisions, the better its accuracy. In the example shown in Figure 11.1, the analog signal has been sampled 13 times using a 3-bit ADC. The unit of divisions in the case of an ADC is a bit. A one-bit (2¹) ADC divides a given range only into two equal parts, a two-bit (2² = 4) ADC divides it into four equal parts, a three-bit ADC (2³ = 8) into eight equal parts, and so on. The more bits an ADC has, the better its accuracy. However, it takes more time to digitize a signal as the number of bits in an ADC increases. This brings us to the second parameter of an ADC, speed. The faster an ADC is, the higher the rate of data it can digitize. Thus, speed and accuracy are inversely related. More accuracy means reduced speed.

Presently, all scintillation cameras are either completely integrated with a digital computer
(all-digital cameras) or interfaced with a dedicated computer. In a scintillation camera, unless it is an all-digital scintillation camera in which case the digitization is already perfomed at the PM tube, the X, Y, and Z pulses are analog and have to be digitized before being recorded by a digital computer. The ADCs used for digitizing X and Y signals of a scintillation camera are 7 to 9 bits, which means that the X and Y ranges are equally divided into 2⁷ = 128, 2⁸ = 256, or 2⁹ = 512 equal divisions, respectively.

In a scintillation camera, the maximum range of X or Y signals equals to the diameter d of the crystal. Therefore, each division of an ADC corresponds to either d/128, d/256, or d/512 cm of distance, depending on whether the ADC is 7, 8, or 9 bits. For an 11-inch (28 cm) diameter crystal and 7-bit ADC, or for a large field of view 20-inch-diameter crystal with an 8-bit ADC, this value equals ˜0.2 cm. Because the intrinsic spatial resolution of a scintillation camera is presently around 0.4 cm, greater accuracy is not needed (according to the so-called “sampling theorem” in digital signal processing, a system with a certain resolution is properly sampled at twice the rate; i.e., half the resolution). In terms of the speed of the ADC, the system should be able to handle over 100,000 signals per second because higher count rates are seldom encountered in nuclear medicine.

Pixel and Matrix. The digitization of X and Y signals into 64, 128, 256, or N (variable number) divisions yields, 64 × 64, 128 × 128, 256 × 256, or N × N, two-dimensional (2D) matrices, respectively (64, 128, 256, or N rows giving y locations along Y axis and 64, 128, 256, or N columns giving x locations along X axis). Thus, the analog image (which is a 2D or planar distribution) is divided into 64 × 64 = 4096, 128 × 128 = 16,384, or 256 × 256 = 65,536, or N × N = N² equal small areas known as picture elements or pixels that are distributed in a 2D matrix. This is graphically illustrated in Figure 11.2 using a 4 × 4 matrix comprising of 16 pixels, shown for simplicity, instead of 64 × 64, 128 × 128, or 256 × 256, which are used in practice. A specific area on the crystal corresponds to a specific pixel (given by its column and row number). For example, the top left corner of the crystal is represented by x = 1 and y = 1, the area of the crystal with seven counts is represented by x = 2 and y = 2 and so on. Thus, each distinct area of the crystal and therefore the patient is assigned a specific pixel (location) in the computer memory. In summary, when a γ-ray interacts within a crystal, its pixel location (x, y, coordinates) is determined by the two ADCs, and a count is stored in the corresponding location in the computer in a matrix form called a frame, or as a list as described later under acquisition mode. As more γ-rays interact, they are stored in the appropriate locations, and a digitized frame or list is stored in computer for subsequent display.

Pixel versus Voxel. A digital image acquired in planar nuclear medicine consists of a two-dimensional (2D) matrix formed with multiple rows and columns. Image dimensions involve powers of 2—for example, 2⁷ or 2⁸—arriving at 128 × 128 or 256 × 256
matrices, as explained earlier. Each element in such an image is referred to as a pixel, and has a digital location or coordinate; for example, “x = 31, y = 6.” In contrast, data acquisition in emission computed tomography (Chapter 13) in specific forms of SPECT (Chapter 14) and PET (Chapter 15) ultimately produces multislice images. Such three-dimensional (3D) or volumetric images are represented by three coordinates; for example, “x = 25, y = 46, z = 18.” An individual element within a volumetric image is referred to as a voxel. At the same time, the term pixel can still be used when discussing a single 2D slice through the 3D image.

Acquisition Modes. There are two general kinds of acquisition in nuclear medicine: frame-mode (2D matrix) versus list-mode (linear array). In frame-mode, all counts occurring within a prespecified time-span (e.g., 0 to 5 seconds) are integrated (accumulated) for the image produced for that frame. An example of this was shown in Figure 11.2. In contrast, in list-mode acquisition, the counts are recorded in the form of time series (e.g., count1: position (x₁, y₁), time t₁ ms; count2: position (x₂, y₂), time t₂ ms; etc.). Data acquired in list-mode can then be sorted, integrated and converted to frame-mode. List-mode data acquisition is more flexible because the data can be framed in different ways as desired following acquisition. For instance, in a dynamic scan lasting 2 minutes, one may generate 10 images each spanning 12 seconds, or reprocess the same list-mode data to produce 20 images each spanning 6 seconds, and so on. Both frame-mode and list-mode acquisition allow three different kinds of imaging, as described next.

Static, Dynamic, and Gated Imaging. Static imaging is obtained when a single time-frame, generally lasting for multiple minutes or for a certain number of counts acquisition (say 500,000 counts) is produced. In dynamic studies, images are recorded at a fast speed, similar to a movie or a video. Digitization has enabled very efficient recording of fast dynamic studies. For instance, images can be acquired every 0.5 second for a period of 100 seconds or more. A digital acquisition is the only practical way to acquire such a fast and large amount of data accurately and efficiently.

Another type of imaging known as gated imaging is also made practical by digital acquisition of data. In planar imaging of the heart, this is referred to as multiple-gated acquisition (MUGA), whereas in SPECT or PET imaging it is simply referred to as gated imaging. Gated imaging is desired where the organ to be imaged moves in a periodic manner (e.g., heart) (Fig. 11.3). To acquire images in various phases of a heartbeat (such as systole or diastole), the beat is divided into a number of
time segments, usually 8 or 16. Each time segment corresponds to a particular phase of the heartbeat.

In frame-mode data acquisition, onset of the first-time segment is triggered by the R wave of an electrocardiogram (ECG or EKG) monitor attached to the patient, and data during this segment are collected as a distinct frame 1. At the end of this time segment, data acquisition for the second time segment takes place that produces frame 2. Thus, data recorded by the scintillation camera during each time segment (62.5 ms in this example) result in multiple-gated frames or images (16 in this case). Each time segment corresponds to a particular frame or image. At the beginning of the next beat, as indicated by the second R wave, the data acquisition reverts back into frame 1 for the first time segment and frame 2 for the second time segment and so on. This process continues for a large number of beats, quite often up to 1,000 beats or more. Alternatively, in list-mode acquisition, the recorded EKG data are inserted within the list-mode data as they are being produced. Gated images can then be generated following gamma camera data acquisition, given knowledge of the time of arrival for the individual detected events, and their correspondence to different cardiac cycles.

The reason for summing the data for each time segment of a heartbeat during many heartbeats has to do with the number of counts in the image of each time segment (also called “gate”). For a heartbeat of about 1 second, when divided into 8 or 16 time segments, each time segment is about 125 or 62.5 ms, respectively. Actual duration of the time segment will vary with the actual time of the heartbeat. The number of counts detected by the scintillation camera during such small time-intervals is quite small, even for a 20 mCi ^99mTc administrated to the patient, and will have large statistical errors. Therefore, by adding counts from a large number of beats within each time segment, images with statistically sufficient numbers of counts for each time segment of heart cycle (phase) can be obtained.