Clinical Radiopharmacology and Tracer Kinetic Modelling

The diversity of radiopharmaceuticals and of their applications

Radiopharmaceuticals and radioactive medical devices are used in all domains of medicine, particularly in oncology, neuroimaging, cardiology, and infectious diseases. Single photon- and positron emission-based imaging modalities capitalize on specific radionuclides selected on the basis of a variety of physical, chemical, and biological characteristics. First investigations on the use of radionuclides date back to the 1900th, short after Radium was discovered by Marie Curie. In the 1910-30th it was widely established for clinical use as sealed seed-sources. Used since the early 1940s for the treatment of thyroid and joint diseases, radionuclide therapy is gaining momentum in oncology and has been proposed to treat antibiotic-resistant infections. P32 was one of the first radionuclides systemically applied in an unsealed form for treatment of bone marrow diseases. Radionuclide therapy may be applied locally by implantation of radioactive seeds (brachytherapy), embolization of cancer tissues using radioactive microspheres, or direct injection into tumours, as well as systemically by intravenous or intra-arterial administration of radioactive drugs.

Nuclear medicine thus proposes a large variety of radionuclides, radiopharmaceuticals, and radioactive medical devices specifically adapted to the diversity of medical conditions. Radiopharmaceuticals may present in the form of radioactive ions, such as iodide or fluoride, salts of various metals (e.g. rubidium, gallium, strontium, radium…), or radiolabelled molecules of varying molecular structures and sizes, from small synthetic compounds, to peptides and antibodies, and supramolecular constructs such as liposomes, nanoparticles or microspheres. The radionuclides may have a variety of emissions (photons, positrons, alpha and beta particles, or Auger electrons) with very different energies (from a few eV to several MeV) and half-lives (from a few seconds for Rubidium-82 to months for Iodine-125).

Radiopharmacology is defined as the description and explanation of the mechanisms of distribution, disposition, and localization of radiopharmaceuticals in different tissues. It helps increase the accuracy of diagnosis, improve therapy, and assess therapeutic efficacy. Given the diversity of radiopharmaceuticals and radioactive devices, it is difficult to summarize all pharmacological aspects related to their use in the clinic. This chapter will focus on some prototypic examples of systemic administration of radioactive molecules.

 

Radiopharmaceuticals distribution, catabolism and disposition

Once injected into the bloodstream, radiopharmaceuticals are subject to various physiological and enzymatic actions. Very large differences are observed in the way the human body handles these labelled molecules. Enzymatic activity in the blood is low, and radiolabelling procedures are performed so that release of radionuclides by hydrolysis or trans chelation is generally not significant in vitro. Under physiological conditions, radiopharmaceuticals with molecular masses smaller than 40 kDa can extravasate from blood capillaries. Smaller molecules diffuse more rapidly across blood vessel walls, and here lipophilicity (measured as log P values) and binding to plasma proteins can have an impact on the rate. Molecules with a molecular mass up to 60 kDa may be cleared through the fenestrated capillaries of the kidneys. Larger molecules can only extravasate in the liver and bone marrow [1]. Some proteins, particularly albumin and antibodies, can bind neonatal Fc receptors (FcRn) after internalization in endothelial cells and are recycled in the bloodstream without degradation [2]. All these mechanisms can be quantified: vessel depletion can be described as the ratio between extravasation rate and blood flow, and range from 14.5 for oxygen, 3.0 for 2-[¹⁸F]fluoro-2-deoxy-D-glucose ([¹⁸F]FDG), and 0.0090 for antibodies [3]. The very large differences in residence times, from minutes to weeks, between commonly used radionuclide vectors can also be explained numerically. Small molecular weight compounds distribute rapidly in interstitial fluids, whereas larger compounds remain mostly confined to the bloodstream. As a result, clearance varies in terms of rates as well as in terms of routes of elimination.

Pathological conditions may alter blood vessel membranes and affect their permeability. Examples of this include inflammation and tumours, where abnormal vasculature is particularly leaky and allows antibodies and nanoparticles to reach tumour tissues [4]. Distribution to the brain is controlled by the blood brain barrier with a series of mechanisms of recapture and effusion that prevent brain uptake of most drugs [5]. Very specific chemical structures, summarized by Lipinski’s rules [6], are required for drugs and tracers to enter the central nervous system. Several pathological conditions (e.g. hypoxia, inflammation, and brain tumours) are associated with blood brain barrier breakdown and increased permeability. It is the leakiness of tumour blood vessels that allows imaging and therapy with large proteins such as antibodies.

Radiopharmaceuticals come into contact with cells expressing membrane proteins such as transporters. These transporters can take up ions, glucose, or amino-acids. They also come into contact with peptidases, such as neural endopeptidase, which very rapidly degrade peptides, unless they have been specifically engineered to withstand these enzymatic activities. They can also contact targets in the bloodstream or after extravasation [7]. The rates of these interactions vary greatly, and their outcome may be quite different. Radiopharmaceuticals may be released rapidly after they enter the cells, if they are not transformed into non-permeant entities or are catabolized into excreted radioactive compounds (e.g. radioactive iodo-tyrosine). For example, [18F]FDG shows long intracellular retention, because it is phosphorylated by hexokinase II after its uptake through the membrane transporter GLUT-1 [8]. Radiopharmaceuticals can also remain bound to the cell surface for long periods of time, if the interaction with their target is tight and shows slow off-rates. Finally, radiopharmaceuticals may be internalized by the cells, and this internalization is generally followed by lysosomal degradation [9]. Eventually, radioactivity will decay, but excretion of small molecular weight radiopharmaceuticals through the kidneys can be very fast, although reabsorption of metal radionuclides after catabolism results in long-lasting kidney uptake. Excretion through the gastro-intestinal tract is slower and can be a problem for imaging and a cause of toxicity (e.g. ²²³Ra).

In many instances, the part that really matters is the radionuclide. Then, the fate of the carrier molecule is relevant only by the way it interferes with the delivery of radioactivity to the various target and non-target tissues. For example, a PET scan will make no difference between 2-[¹⁸F]FDG and its phosphorylated metabolite ([¹⁸F]FDG-6-phosphate). Similarly, internalized peptides and antibodies are degraded within cells. The fate of their payload will be different if they are “residualizing”, e.g. most radioactive metals, not residualizing, e.g. halogens (iodine, fluorine), or metals that can be oxidized (technetium, rhenium) or reduced (copper). For imaging, in most cases, the single most important feature is the contrast ratio between target and non-target tissues that can be achieved, and the time needed to obtain it. For therapy, it is the ratio between the extent of radioactive disintegrations occurring in the target as opposed to normal tissue, especially in radiosensitive tissue that matter. Then, distinguishing between the parent radiopharmaceutical and its radioactive catabolites is not important. The situation is quite different for receptor quantification and receptor occupancy studies, for which it is mandatory to measure the concentration of the active radiopharmaceutical.

Radiopharmaceuticals must be selected using a complex set of characteristics involving pharmacokinetic properties that control delivery to targets versus disposition as well as its affinity to its molecular target, stability of activity uptake in targets, and they must be judged relative to the half-life of the radionuclide and specificity of radioactivity delivery. Specificity can be impaired by expression of the target in normal tissues, as, for instance, expression of PSMA in salivary glands [10], and by retention of radioactivity in organs, as, for instance, retention of radioactive metals in the kidneys after glomerular filtration, catabolism, and reabsorption [11].

 

Quantitative imaging

In preclinical studies, it is possible to count the activity in tissues after administration of radiopharmaceuticals. It is even possible to assess their microscopic distribution by autoradiography. Imaging can also be used to reduce the number of animals sacrificed in the necessary studies before human use, with limitations on the duration and number of imaging sessions. In humans, of course, only quantitative imaging can be used to monitor the biodistribution and pharmacokinetics of the radiopharmaceuticals after injection. Issues related to image quantification are numerous, and the process is far from straightforward. These issues remain a matter of intense research, and physicists have developed solutions that are now implemented in SPECT and PET cameras to make necessary corrections, e.g. attenuation correction, scatter correction and instrument calibrations. Tissue contouring and correction for partial volume effects remain problematic, because these are operator dependent [12]. It is common to express the results of these measurements in terms of Standardized Uptake Values (SUV, the ratio of the image derived radioactivity concentration in a region of interest to the injected activity times the patient’s body weight; instead of the body weight, the injected activity may also be corrected by the lean body mass or body surface area). SUVs allow meaningful semi-quantitative comparisons across tissues, patients, and radiopharmaceuticals.

To find the best time window of radiopharmaceutical uptake for static imaging, optimize the scheme of activity applications, and to make dosimetry calculations, the biodistribution of the radiopharmaceutical must be monitored over time. To that end, dynamic imaging may be performed for radiopharmaceuticals with fast kinetics and short-lived radionuclides in animals. In man, dynamic imaging is currently possible only if restricted to a part of the body, e.g. the brain, unless a PET system with a long axial field of view (LAFOV) is available, or when the system offers parametric imaging (such as Patlak) over multiple bed positions. Otherwise, for radiopharmaceuticals with slow kinetics and long-lived radionuclides (such as ⁸⁹Zr-labeled monoclonal antibodies), longitudinal imaging sessions may be performed, but these are perceived as a heavy burden by most patients. The number of sessions needed to collect enough data for pharmacokinetic analysis and calculation of the total number of disintegrations (also called cumulated activity) in the various tissues of interest depend on the nature and activity amount of radiopharmaceutical administered. 

 

Pharmacokinetics

The calculation of the total number of disintegrations in tissues of interest can be performed without any pharmacokinetic modelling using the trapezoidal rule, which only involves an estimation of a final activity half-life, to calculate the areas under the time-activity curves [13]. This half-life may even be set equal to the half-life of radioactive decay when tissue uptake is stable in time (e.g. fluoride uptake in bones). The error introduced by this approximation is low. However, pharmacokinetic modelling, and especially compartmental analysis, is a way to understand how the radiopharmaceutical and the injected activity distributes and is eliminated. For non-radioactive drugs, the pharmacokinetic analysis is usually limited to blood in order to rationalize dosing schedules. Radioactivity and quantitative imaging enable more extensive studies by considering blood and tissue measurements.

 

Kinetic modelling: blood and tissue distribution

Imaging studies in nuclear medicine provide measurements of radioactivity in an organ or tissue as a function of time. It is possible to build mathematical models that fit the observed time-activity curves and thereby derive parameters related to biological, metabolic, or physiological processes. Mathematical modelling can be based on the definition of compartments in which the tracer is uniformly distributed. The number and organization of compartments in the model depend on the tracer. Knowledge of the physiology and of blood flows, permeability coefficients, and surface areas may be used in a physiologically based approach [14]. Alternatively, transfer rate constants between blood, interstitial fluids, and deeper compartments as well as elimination rates may be considered as adjustable parameters. Analytical solutions of the systems of differential equations describing the pharmacokinetics may be derived in some cases, but usually software packages, such as WinSAAM [15] or Pmod (http://www.pmod.com), may be used to build multi-compartmental models and obtain estimations of the various micro-constants by non-linear weighted least square regression. The purpose of this modelling is to go beyond the calculation of areas under the time-activity curve, half-lives, and clearances so as to assess the consistency of the curve fitting in blood, which provides the input function, and in other tissues. It is easy then to distinguish tissues which show specific uptakes from those in which the radioactive content remains in fast exchange with the blood. A classical approach is to describe the blood pharmacokinetics (input function) using a compartment model (usually two compartments suffice), the uptake in specific tissues using one or two compartments, and reversible or irreversible kinetics as shown in Figure 1 [16]. A reference tissue may be used instead of a blood input curve to distinguish between specific and non-specific uptake. Parameters that can be easily determined are the apparent distribution volume (V_T) and blood clearance. For specific tissues, binding potential (BP_ND) or receptor occupancy may be extracted using these models.

 

In vivo assessment of receptor binding and receptor occupancy

Quantitative image studies are used in neurology (but also more frequently now in oncology) to assess receptor occupancy by injecting radioactive ligands and performing a quantitative imaging study. Graphical analyses can be performed using Logan plots and Patlak plots [17] or even calculation of SUV ratios between areas of interest and control areas are simpler substitutes to compartment models. The simplest compartmental model applied to receptor-ligand studies includes at least two compartments, namely free and bound compartments arranged in series with the plasma compartment (Figure 1). If experimental data are not adequately fitted with this model, a non-specifically bound compartment may be added. This approach is particularly useful using PET-scans and carbon-11 in preclinical studies in rodents and non-human primates, but clinical studies may also be performed in specific pathological conditions such as Parkinson’s disease with dopamine receptors. To derive receptor density and receptor occupancy data, it is important to have access to the concentrations of the active, intact, radiopharmaceutical [18].

 

Population pharmacokinetics and Bayesian estimations

Individual variations are common in pharmacokinetics, and studies are therefore conducted in groups of patients. Model-estimated pharmacokinetic parameters reflect this variability, which is explained by known differences between individuals, such as body weight or impairment of kidney function, interindividual differences that are not known or cannot be taken into account, and stochastic uncertainties in quantification. This is the basis of the so-called Nonlinear Mixed-Effects Modelling, in which data recorded for all patients are analysed simultaneously [19]. This approach is generally used for non-radioactive drugs and limited to blood data. It may be expanded to compartment modelling of radiopharmaceuticals distribution monitored by quantitative imaging. Then, parameters such as body weight, gender, or pathological conditions can be introduced in the pharmacokinetic model as covariates, which may be quantitative or qualitative. Their influence is analysed directly during the curve fitting process, instead of looking for correlations after individual parameter estimations. There are many sophisticated algorithms for population pharmacokinetics. They are all based on a likelihood maximization of the observed differences between observed values and values calculated for a single set of population-adjusted parameters and of the differences between individual-estimated parameters and population-adjusted parameters. This approach greatly increases the consistency in parameter estimation and is much less sensitive to outliers or missing data, because population-based parameters are evaluated from larger data sets, and the deviations of individual parameter estimations from the population-adjusted parameters are limited. It may even be used to develop imaging protocols in which not all individuals in the study cohort are submitted to imaging sessions at the same times, and in which the number of such imaging sessions for each patient is reduced.

Bayesian approaches may also improve parametric imaging using data acquired in a small group of patients and analysed in depth [20]. By using mean values and variability of pharmacokinetic parameters calculated from such small groups of patients as a priori knowledge, studies of larger populations of patients may be submitted to simplified and less demanding imaging protocols.

A more indepth view on the topics of Pharmacokinetic Modeling can be found in the Handbook of Nuclear Medicine and Molecular Imaging for Physicists by Michael Ljungberg [21, 22].

Altogether, the use of such pharmacokinetic modelling in radiopharmacology improves the accuracy of the determination of inter-individual differences in the way the human body handles radiopharmaceuticals while reducing the constraints for the patients.

Table 1. Basic radio pharmacological data for selected examples of radiopharmaceuticals

Figure 1. examples of frequently used compartment models.

Such compartment models have been particularly used in neuroscience to quantify tracer uptake in brain areas of interest and measuring binding potentials. The boxes represent compartments in which the tracer is uniformly distributed. Arrows and constants reflect the transfer of material and their rates. Here, two classical models are shown: the first is the one compartment – two constants model, which is often used to represent non-specific uptake, and the second is the two compartments – four constants model, which includes a binding compartment. Kinetics are “reversible” if all constants are non-zero, or “irreversible” if return to the input compartment or dissociation are not allowed. The input compartment is in general blood (arterial blood in brain studies) or plasma. Considerably more elaborate models have been developed to include, for instance, reference tissues, non-specific uptake, presence of blood activity in tissues and of catabolites. Differential equations for the kinetics may be written easily from the diagrams. Alternatively, appropriate software packages may deal with the problem, with no need for explicit differential equations. Curve fitting allows for estimation of the rate constants.

 

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