Analysis of three- and four-compartment models for in vivo radioligand-neuroreceptor interaction

Exploring a mathematical model for the kinetics of beta-amyloid molecular imaging probes through a critical analysis of plaque pathology

Amyloid plaques are highly heterogeneous in content, size, density, and macromolecular crowding, as they are composed of masses of fibrils and other cellular material. Given this target architecture, the aggregated microenvironment offers a unique imaging target for ligands and positron emission tomography (PET) molecular imaging probes (MIPs). In this work, we address how the heterogeneous microenvironment of a plaque and its evolution may affect the kinetic rate constant of PET MIPs. We argue that macromolecular crowding will result in anomalous diffusion within plaque regions. To account for anomalous diffusion within plaques, we propose a diffusion-limited ligand-receptor compartmental model. Given the current state of knowledge about the pathological progression of Alzheimer's disease (AD), the model's parameters may be a function of the pathological progression of AD, which could result in biased estimates of the true amyloid load. The bias may be partially overcome through evaluation in conjunction with other measures of AD progression including cerebral glucose metabolism rate, neuronal cell loss, and activated inflammatory presence.

Theoretical relationships of receptor and delivery sensitivities and measurable parameters in in vivo neuroreceptor-radioligand interactions

In vivo quantification of neuroreceptors in human brains by PET or SPECT is complicated by the fact that a number of variables other than receptor concentration may influence the observed radioactivity in a brain region. This consideration has led the authors to formulate rigorous mathematical definitions of the concepts of receptor and delivery sensitivities. It has been speculated that a neuroreceptor-radioligand system having a high (low) receptor sensitivity would have a low (high) delivery sensitivity, and that the receptor sensitivity of a neuroreceptor-radioligand system can be determined by observing the time-course of the brain radioligand concentration following injection of no carrier added (nca) radioligand. Computer simulation studies of the characteristics of a simple model for in vivo neuroreceptor-radioligand interaction show that, under a set of realistic restrictions, there is a unique and intuitively satisfying relationship between receptor and delivery sensitivities: receptor sensitivity+delivery sensitivity approximately 1. In addition, the receptor sensitivity can be computed as a function of the observable parameters of the nca radioligand time course. These straightforward relationships are surprising in light of the complexity of the analytical solutions.

Estimation of relative regional neuroreceptor concentration by PET or SPECT: Theoretical comparisons of using a single late image or a late plus early image

The potential for using a single (SPECT) single-photon-emission computed tomography or (PET) positron emission tomography image to estimate quantitatively the relative regional neuroreceptor concentration depends on acquiring the image at a time when changes in the regional radioactivity localization are much more sensitive to changes in receptor concentration than to changes in delivery. Using the binding of [(11)C]carfentanil to the opiate receptor as a model, the authors have applied a computer simulation approach to determine the joint and marginal probability distributions for the ipsilateral/contralateral ratio of receptor concentrations and delivery. They have found that the probability distributions depend on the sensitivities for both delivery and receptor. Incorporation of data at an early time point results in a significant sharpening of the probability distributions. There is an insignificant effect of subtraction of the radioactivity localization in a control region.

Uses and limitations of positron emission tomography in clinical pharmacokinetics/dynamics (Part II)

Positron emission tomography (PET) involves imaging the biodistribution and tissue localisation of small amounts of radiolabelled biomolecules or drugs. In Part I of this article, which appeared in the previous issue of the Journal, the applications of pharmacokinetics in PET were discussed in order to derive quantitative measures of physiological function. Part II examines the use of PET imaging as a tool to study the pharmacokinetics and pharmacodynamics of specific drugs.

Theoretical investigation of the estimation of relative regional neuroreceptor concentration from a single SPECT or PET image

The validity of estimating changes in regional neuroreceptor concentration based upon a single ECT (emission computed tomography) image is examined to determine whether an image can be acquired at a time when changes in the observed regional radioactivity are much more sensitive to changes in receptor concentration than to changes in radioligand delivery. These sensitivities are defined as the normalized partial derivatives of the regional radioactivity signal (S) with respect to the total receptor (R(t)) and with respect to radioligand delivery (k(1)). Using computer simulations, it is found that ( partial differentials/ partial differentialR(t))/( S/R(t)) can be less than unity (receptor hyposensitivity), approximately equal to unity, or significantly greater than unity (receptor hypersensitivity). It is possible to find classes of parameter sets under which the receptor sensitivity is close to unity and the delivery sensitivity is of much lower magnitude. The results indicate that if the parameters for a given radioligand-neuroreceptor system can be established as belonging to one of these classes, then changes in regional neuroreceptor concentration can be estimated based upon a single ECT image.

Quantification of the dopamine D2 receptor in the living human caudate nucleus by PET: comparison of in vivo and in vitro kinetic parameters

It is demonstrated that the set of kinetic parameters (including first-order rate constants for the dissociation of N-methylspiperone (NMSP) from, and second-order rate constants for the association of NMSP to, the dopamine D2 and serotonin S2 receptors of the caudate nucleus) which can be derived from previously reported human caudate PET (positron emission tomographic) data is not uniquely determined, but that multiple sets generate approximately equivalent curve fits. In particular, the set consisting of the in vitro values can generate the PET data. Thus, the in vitro rate constants may apply in vivo.

Accuracy of in vivo neuroreceptor quantification by PET and review of steady-state, transient, double injection, and equilibrium models

The accuracy of in vivo dopamine D2 receptor quantification by positron emission tomography (PET) was determined for several models by means of singular-value decomposition, and some of the model assumptions were reviewed. These include steady-state, transient, double injection, and equilibrium approaches. All four modes are augmented by including a realistic kinetic interaction of the radioligand with the striatal serotonin S2 receptor. When a set of parameters derived specifically with reference to the equilibrium model was applied, it was found that a reversible radioligand used in conjunction with the equilibrium model permits accurate quantification. However, an assumption of the equilibrium model-that equilibrium is achieved during the time of measurement-is shown to be unsupported by the published experimental data. These results indicate that the equilibrium approach can provide an alternative to the kinetic approaches, but that additional experimental evidence is required to demonstrate the validity of the equilibrium assumption.