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Introduction: An important issue in multitracer studies is the separation of signals from the different radiotracers. This is especially the case when an early tracer has a long physical half-life and kinetic modelling has to be performed, because the early tracer can confer a long-lived contaminating background not only to images but also to a measured input function derived from blood samples. In this study, we examined data from a sequential multitracer infection study involving In (t1/2=2.8 days), investigating the influence on gamma counting of blood samples and on the kinetic modelling of subsequent PET tracers. Blood sample counts were corrected by recounting the samples a few days later. A more optimal choice of energy window was also explored. The effect of correction versus noncorrection was investigated using a two-tissue kinetic model with irreversible uptake (K1, k2, k3)., Results: K1 was least affected and k3 was most affected by the contamination, corresponding to the effect being relatively larger on the late part of the blood input function. A narrower energy window reduced the problem, but this will not be possible for all types of contaminating background., Conclusion: Gamma counting of blood samples can lead to a contaminating background not observed in PET imaging and this background can affect kinetic modelling. If the contaminating tracer has a much longer half-life than the foreground tracer, then the problem can be solved by late recounting of the samples.

The reliability of biokinetic models is essential in internal dose assessments and radiation risk analysis for the public, occupational workers, and patients exposed to radionuclides. In this paper, a method for assessing the reliability of biokinetic models by means of uncertainty and sensitivity analysis was developed. The paper is divided into two parts. In the first part of the study published here, the uncertainty sources of the model parameters for zirconium (Zr), developed by the International Commission on Radiological Protection (ICRP), were identified and analyzed. Furthermore, the uncertainty of the biokinetic experimental measurement performed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU) for developing a new biokinetic model of Zr was analyzed according to the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization. The confidence interval and distribution of model parameters of the ICRP and HMGU Zr biokinetic models were evaluated. As a result of computer biokinetic modelings, the mean, standard uncertainty, and confidence interval of model prediction calculated based on the model parameter uncertainty were presented and compared to the plasma clearance and urinary excretion measured after intravenous administration. It was shown that for the most important compartment, the plasma, the uncertainty evaluated for the HMGU model was much smaller than that for the ICRP model; that phenomenon was observed for other organs and tissues as well. The uncertainty of the integral of the radioactivity of Zr up to 50 y calculated by the HMGU model after ingestion by adult members of the public was shown to be smaller by a factor of two than that of the ICRP model. It was also shown that the distribution type of the model parameter strongly influences the model prediction, and the correlation of the model input parameters affects the model prediction to a certain extent depending on the strength of the correlation. In the case of model prediction, the qualitative comparison of the model predictions with the measured plasma and urinary data showed the HMGU model to be more reliable than the ICRP model; quantitatively, the uncertainty model prediction by the HMGU systemic biokinetic model is smaller than that of the ICRP model. The uncertainty information on the model parameters analyzed in this study was used in the second part of the paper regarding a sensitivity analysis of the Zr biokinetic models.

A physiological skeletal model (PSM) is described that represents the skeletal uptake, retention, and clearance of both bone-surface-seeking and bone-volume-seeking radionuclides and stable elements. A key objective of the PSM is to model the higher skeletal growth and bone turnover in infants and children (compared to adults) in order to account for their greater uptake and cancer risk from bone-seeking contaminants such as lead and plutonium. The PSM is a compartmental model that allows for the incorporation of organic and inorganic material in the bone volume via quiescent bone surfaces, forming bone surfaces and the lacuno-canaliculi system. The model uniquely incorporates a tertiary phase of mineralization via bone fluids. The PSM's structural concepts and biokinetic parameters--such as realistic mass transfers, organ and tissue masses, and bone remodeling half-times--are selected mainly on the basis of physiological and anatomical criteria. For brevity, model parameter values are evaluated for adults only. The PSM is an improvement on existing skeletal models that are based more on compartment structures and pathways that rendered good fits to biokinetic data rather than on being anatomically and physiologically accurate.

Experimental design includes decisions to perform measurements with intact animals or truncated in vivo measurements followed by dissection and ex vivo measurements. The design may be driven by advantages and disadvantages of the choices. Analytical results are presented here that can provide a basis for certain experimental design choices. Design considerations include longitudinal studies in the single animal that bracket a treatment, joint observations by supplementing the imaging data with plasma and/or ex vivo sampling after dissection, multiple injections of increasing molar base or administration of a molar dose that results in the occupation of a significant fraction of the target receptors. Of particular interest when constructing an experimental design is the reduction of bias. Analysis tools for this purpose include reparameterization and model application without the formation of time-based averaging.

Compartmental models are widely used for the mathematical modelling of dynamic studies acquired with positron emission tomography (PET). The numerical problem involves the estimation of a sum of decaying real exponentials convolved with an input function. In exponential spectral analysis (SA), the nonlinear estimation of the exponential functions is replaced by the linear estimation of the coefficients of a predefined set of exponential basis functions. This set-up guarantees fast estimation and attainment of the global optimum. SA, however, is hampered by high sensitivity to noise and, because of the positivity constraints implemented in the algorithm, cannot be extended to reference region modelling. In this paper, SA limitations are addressed by a new rank-shaping (RS) estimator that defines an appropriate regularization over an unconstrained least-squares solution obtained through singular value decomposition of the exponential base. Shrinkage parameters are conditioned on the expected signal-to-noise ratio. Through application to simulated and real datasets, it is shown that RS ameliorates and extends SA properties in the case of the production of functional parametric maps from PET studies.

This review article describes the principle and clinical applications of spectral analysis. Spectral analysis provides a spectrum of the kinetic components which are involved in the regional uptake and partitioning of tracer from the blood to the tissue. This technique allows the tissue impulse response function to be derived with minimal modeling assumptions. Spectral analysis makes no a priori assumptions regarding the number of compartments or components required to describe the time course of tracer in the tissue. Spectral analysis can be applied to various dynamic data acquired by planar scintigraphy, single photon emission computed tomography (SPECT) or positron emission tomography (PET) as an alternative approach to compartment analysis. This analysis appears to be clinically useful, because it not only facilitates the interpretation of dynamic scintigraphic, SPECT or PET data, but also simplifies comparisons between regions and between subjects.

The interest in the biokinetics of ruthenium and zirconium in humans is justified by the potential radiological risk represented by their radionuclides. Only a few data related to the biokinetics of ruthenium and zirconium in humans are available and, accordingly, the biokinetic models currently recommended by the ICRP for these elements are mainly based on data from animal experiments. The use of stable isotopes as tracers, coupled with a proper analytical technique (nuclear activation analysis with protons) for their determination in biological samples, represents an ethically acceptable methodology for biokinetic investigations, being free from any radiation risk for the volunteer subjects. In this work, the results obtained in eight biokinetic investigations for ruthenium, conducted on a total of three healthy volunteers, and six for zirconium, performed on a total of three subjects, are presented and compared to the predictions of the ICRP models.

Assessment of internal doses is an essential component of individual monitoring programmes for workers and consists of two stages: individual monitoring measurements and interpretation of the monitoring data in terms of annual intake and/or annual internal dose. The overall uncertainty in assessed dose is a combination of the uncertainties in these stages. An algorithm and a computer code were developed for estimating the uncertainty in the assessment of internal dose in the task of individual monitoring data interpretation. Two main influencing factors are analysed in this paper: the unknown time of the exposure and variability of bioassay measurements. The aim of this analysis is to show that the algorithm is applicable in designing an individual monitoring programme for workers so as to guarantee that the individual dose calculated from individual monitoring measurements does not exceed a required limit with a certain confidence probability.

A revised model of molybdenum biokinetics in humans was recently developed on the basis of experimental data gathered in specific investigations conducted with stable tracers. The model can be used for radiation protection purposes, and it is also a suitable working tool for designing new investigations aimed at further improvements to the model. For the latter goal, a sensitivity analysis was performed in order to determine the most significant model parameters in relation to output measurements performed in studies of molybdenum metabolism. A typical sensitivity analysis approach was adopted, considering the effects in variation of model parameters on the time courses of model outputs such as urinary excretion and blood clearance. A recent new sensitivity technique was considered too, based on the calculation of the so-called generalised sensitivity functions. This combines the sensitivities of the model output with respect to model parameters (as in the typical sensitivity analysis method), with the sensitivities of parameter estimates with respect to changes in model outputs. The results obtained in this analysis suggests that data collected in the first 7 h are critical for the definition of the process of blood clearance and related parameters, whereas reliable information at later times is required for a proper characterisation of urinary excretion.

The combination of analytical techniques such as PNA and SIMS with a compartmental approach enables the study of the metabolism and biokinetics in humans of several elements by using stable isotopes as tracers. The techniques developed for Te require the administration of greater masses than those used for similar studies performed with radioactive tracers, therefore a test was carried out in rabbits in order to assess the possible influence of the administered amounts on the determination of the biokinetic parameters. The behaviour of the tracers was found to be similar for Te administration of up to 70 micrograms/kg of body weight. An inter-individual variability in the size of the transfer compartment was observed and has to be taken into account.

In tracer kinetic modeling with Positron Emission Tomography (PET), the direct measurement (piecewise linear approximation) of plasma time-activity curve of tracer (PTAC) is often used as the input function to estimate regional physiological parameters. However, no explicit general model is available for PTAC itself, which limits the further study of the effects of PTAC, such as PTAC measurement noise or PTAC sampling schedules, on the physiological parameters estimation. A PTAC model is proposed in this paper and compared with other four possible candidates. Eight sets of [18F]-fluoro-2-deoxy-D-glucose (FDG) experimental data were used to test the models and several statistical criteria were used to validate their adequacy. An application of the model to improve the estimation of local cerebral metabolic rate of glucose (LCMRGlc) is presented. This model is also expected to be useful for generating realistic PTAC curves in computer simulation studies of other tracers and their kinetic modeling characteristics.