Time-activity curves for most organs are usually characterized by one or more exponential terms, i.e., . The rate constants λ ₁ and λ ₂ describe the kinetics of removal of activity components A ₁ and A ₂; we can define half-times T ₁ and T ₂, by λ = 0.693/T; the half-time is the time needed for half of that component of activity to be removed from an organ. Each exponential term has two unknown variables; therefore, the time-activity curve has to have two data points for each phase of clearance for which we wish to define an exponential term. So, if a given time-activity curve is best characterized by two exponentials, an absolute minimum of four data points is needed to define the curve, with two points during each phase (i.e., not one during the first phase and three during the second). The starting point in a kinetic analysis is thus deciding on when to obtain samples, whether they are from a study involving animals or human subjects. For a completely new agent, this can obviously be a challenge, as the biokinetics are not yet known. An absolute limitation is the physical half-life of the radionuclide employed; F-18 has a half-life of 1.83 h, so data may be gathered over several hours after administration, but C-11 has a half-life of only 20 min, so data must be gathered much more quickly. Then, the biological clearance of the agent must be considered. The equation above with the exponential terms was not explicit, but the complete removal of activity from an organ or the body is due to both radioactive decay and biological clearance; this is characterized by a rate constant λ _e, an “effective rate constant,” which is the sum of the biological rate constant (λ _b) and the physical rate constant (λ _p). Some agents are cleared very quickly, others more slowly. So the study must be planned to get the needed number of data points taking into account both physical and biological clearance. Often experience with other similar agents can be helpful, or the data points can be spaced out over the range of times possible over several physical half-lives of the radionuclide, with several early time points and several later time points. There is not an exact formula for guiding the selection process of sampling times; care must be taken to provide enough data before spending the time and money on gathering the data so that the data collection process will be successful and the experiments will not have to be repeated. In addition to activity levels in organs and the body, an essential element of a biokinetic analysis is evaluation of the excretion of activity from the body (via the urinary or intestinal pathway). It is not uncommon for excretory organs to receive the highest doses of any other organ in the body, as often 100 % of the activity eventually passes through these organs (urinary bladder or intestines). For PET radiopharmaceuticals, excretion may be more limited than for other agents, due to their short physical half-lives. For C-11 compounds, for example, it is common to assume that there is no time for appreciable excretion from the body to occur, although activity might accumulate in the urinary bladder and decay there. So for studies using imaging data, if activity is seen in the urinary bladder, the activity levels may be quantified, and the activity may be integrated to get the number of disintegrations in the urinary bladder; collecting urine data is unlikely to provide any useful information. For F-18, it is common for there to be urinary excretion during the duration of the study, and the use of image data or urine collection may be helpful.

Preclinical studies are required for any New Drug Application (NDA) to the US Food and Drug Administration (FDA). Most research is done with some rodent species, but any animal species in theory is acceptable. Some have an inclination to use primate species, with the idea that they may produce results more similar to humans. Extrapolation of animal data to humans has produced misleading information in many cases, in most any animal species [2]. So, this is a necessary step in the process of evaluating the dosimetry of a new radiopharmaceutical, but one should bear in mind that the real dosimetry will not be known until well-designed and executed studies using human subjects are performed. Time-activity curves for radiopharmaceuticals using animals may be established by administering the radiopharmaceutical and either sacrificing the animals, extracting tissue samples, and performing a radioassay or by small animal imaging studies.

Imaging studies with either patients or healthy volunteers, required by the FDA for new drug approval (strict dose limits for new drugs do not exist, but dosimetry must be presented and is usually compared to other similar agents), need to be done according to the same requirements for number and spacing of time points as described above. The two basic imaging methods are planar imaging and tomographic imaging. For PET radiopharmaceuticals, tomographic methods are by far the most common approach, so an extensive description of planar methods will not be presented here. Briefly, anterior and posterior images are taken, regions of interest (ROIs) are drawn over recognized organs, and corrections for attenuation and scatter should be made [2]. Relating counts in an ROI to absolute values of activity is usually not straightforward, unless calibration factors have been developed from phantom image analysis, which is not common. Usually counts in the total body at the earliest imaging time, corrected for radioactive decay, are used to define 100 % of the administered activity, and counts in the body and organs at later times are related to this value. In tomographic images, as for animal studies, counts in voxels associated with an organ may be related to absolute values of activity via a calibration factor, and time-activity curves may be developed from this information. PET images are inherently quantitative, as PET analyses evaluate absolute levels of activity in organs and tumors (standardized uptake values, SUVs). In contrast, few centers practice quantitative analyses with single-photon emission computed tomography (SPECT); Dewaraja et al. [14] outlined the many steps required to obtain quantitative SPECT data for therapy dosimetry calculations, including choice of collimator, choice of energy windows, reconstruction methods, attenuation and scatter correction, dead time corrections, compensation for other image-degrading effects, choice of target regions, corrections for dose nonuniformities, and other aspects to be considered to obtain quantitative information in individual voxels used to define source and target regions.

The result of the biokinetic analyses described above is a series of values of percent or fraction of administered activity over time (Fig. 3.1). Values of doses for individual organs rely on the integration of these values over time. The most common method for performing this integration is to fit a function comprised of one or more exponential terms to the data. One may also integrate the data “directly,” i.e., by a “trapezoidal” integration, simply directly calculating the area under the curve between any two time points and adding up the values. A drawback of this approach is that estimating the area under the curve after the last data point is complicated; various approaches include assuming only radioactive decay after the last point, using a straight line defined by the last two or three data points, and other approaches. When an exponential function is fit to the data, the time-activity integral is easily calculated. If the function is , and the values of λ are effective rate constants (including both radioactive decay and biological removal), the integral of this function to infinite time is just A ₁/λ ₁ + A ₂/λ ₂. If values of A are in MBq and values of λ have units of s⁻¹, then the integral has units of MBq-s or millions of disintegrations. These integrals are often normalized to the amount of activity administered (MBq), so that doses are developed per unit administered activity. The units of this normalized integral are thus MBq-s/MBq. It is tempting to think of this as having units of time (here s), but this is not any measure of time.