PHYSICS -DEPARTMENT

Improvement of a biokinetic model for cerium in humans by tracerkinetic studies

Dissertation of Teresa Maria Keiser

TECHNISCHE UNIVERSITÄT MÜNCHEN

TECHNISCHE UNIVERSITÄT MÜNCHEN

Fachbereich Strahlenphysik

Improvement of a biokinetic model for cerium in humans by tracerkinetic studies

Teresa Maria Keiser

Vollständiger Abdruck der von der Fakultät für Physik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigten Dissertation.

Vorsitzender: Univ.-Prof. Dr. Martin Zacharias Prüfer der Dissertation: 1. Hon.-Prof. Dr. Herwig G. Paretzke 2. Univ.-Prof. Dr. Thorsten Hugel

Die Dissertation wurde am 27.04.2011 bei der Technischen Universität München eingereicht und durch die Fakultät für Physik am 25.05.2011 angenommen.

Table of contents

Abstract ______1 List of acronyms, symbols and abbreviations______2 1 Introduction ______5 2 Theoretical considerations ______7 2.1 The element cerium ______7 2.1.1 Natural isotopes of cerium______7 2.1.2 Applications of cerium salts in medicine______10 2.1.3 Radioactive isotopes of cerium ______11 2.2 Analytics of cerium ______13 2.2.1 History of mass spectrometry ______14 2.2.2 Thermal ionisation mass spectrometry (TIMS) ______16 2.2.3 Isotope dilution technique for tracer concentration calculation______18 2.3 Calculation of internal doses ______19 2.4 Current biokinetic models of cerium ______25 2.5 Fractional absorption ______30 2.6 First order kinetic compartment modelling ______32 3 Materials and Methods ______35 3.1 Collection of human biokinetic data ______35 3.1.1 Preparation of tracer solutions______37 3.1.2 Implementation of volunteer tests ______39 3.1.3 Test persons______41 3.2 Measurement of Ce tracer concentration in biological samples______42 3.2.1 Mass spectrometric method ______43 3.2.2 Sample preparation ______46 3.2.3 Isotope dilution technique for tracer concentration calculation______48 3.3 Model development for data interpretation ______50 3.3.1 Fractional absorption ______50 3.3.2 Approaches and software used for modelling in this work ______53 3.3.3 Model development process ______55 3.4 Improved Dosimetry of cerium ______57 3.5 Errors and uncertainties ______61 4 Results and discussions ______63 4.1 Development and optimization of sensitive Ce analytics______63

ii 4.2 Sample measurements ______71 4.2.1 Measurements in blood plasma samples ______72 4.2.2 Measurements in urine samples______76 4.2.3 Comparison of the own newly measured human data with model predictions of the ICRP and of Taylor and Leggett ______79 4.3 Fractional absorption without compartment modelling ______83 4.4 Tracer kinetics and the corresponding development of a new compartmental model ______86 4.5 Proposed new model ______94 4.6 Implications of the new model for dosimetry______102 4.6.1 Dosimetry with the old ICRP model ______102 4.6.2 Dose coefficients of 144 Ce of the new cerium biokinetic model ______108 5 Conclusions ______114 Bibliography______115 Appendix ______121 Acknowledgments ______135

iii

Abstract

Abstract

The calculation of internal doses from incorporated radionuclides depends critically on the biokinetic behaviour of the substances. Internal radiation dosimetry relies on biokinetic models, which link exposure and dose, because internal dose cannot be measured directly in exposed persons. The data for the biokinetic model should preferably be derived from experimental investigations on humans. However, far a number of radiological important elements there are still inconsistencies in the current knowledge of the biokinetic behaviour and thus in dose estimates. Therefore, there is a persisting need for further examination of biokinetic parameters of incorporated radionuclides. The purpose of the present work is to improve current knowledge about the element cerium. The structure and parameters of the current cerium model presented from the International Commission on Radiological Protection (ICRP) have been estimated from animal data. In ICRP 30 (ICRP, 1979) only one case of human data is reported, but of accidental inhalation (Sill et al., 1969). In this work, for the first time data on cerium metabolism, especially fractional absorption, retention in the body and excretion, are obtained directly from humans by the use of enriched stable cerium isotopes as tracers. The use of stable tracer instead of radionuclides represents an ethically justifiable method. For analysis purpose, thermal ionization mass spectrometry (TIMS) method has been developed for being able to simultaneously detect different cerium isotopes in biological samples (i.e. blood and urine) at very low concentrations. Twelve adult volunteers (7 female, age range 21-62 years; 5 male, age range 29-54 years) who did not have chronic illness such as diabetes, heart disease, or gastrointestinal disorders participated in the study. Blood plasma and urine data from double tracer studies with up to 30 d duration serve as input for developing a new first order kinetic compartment model. The data were compared with the current ICRP cerium model. The model was further on validated and improved by establishing a more physiologic logical model. The new measured data show a series of deviations from the current model predictions. A satisfactory exact conformation of the data is only possible after modification of the model. Ingestion dose coefficients for 144 Ce were evaluated with the new proposed model. The resulting dose coefficients differ significantly from the old ICRP estimated values about 70 %.

1 List of acronyms, symbols and abbreviations

List of acronyms, symbols and abbreviations

This list comprises only expressions used commonly in different sections of the work. Expressions specific to single sections or equations are explained at their respective first occurrence.

AFi(T ←S) absorbed fraction AIC Akaike information criterion and the

ASj Cumulative activity of radionuclide j in source organ S aw atomic weight APCI Atmospheric Pressure Chemical Ionisation BIC Bayesian information criterion CE capillary electrophoresis CI Chemical Ionisation

DT Absorbed dose to a target region T

DT,R Absorbed dose averaged over tissue or organ T, due to radiation R

DL Detection limit E Effective dose

Ei energy of radiation i per transformation EI Electron Impact EM electron multiplier EOID electro-optical ion detector ESI Electro spray Ionisation ET Extrathoracic tissues FAB Fast Atom Bombardment FCC Fluid catalytic cracking f1, f A Fractional absorption FD Field Desorption

2 List of acronyms, symbols and abbreviations

FI Field Ionisation GC gas chromatography GI tract gastrointestinal tract GUM ISO-Guide to the expression of uncertainties in measurement HAT Human alimentary tract (model) HAECs Human aortic endothelial cells HMGU Helmholtz Zentrum München, German Research Centre of Environmental Health HPLC high pressure liquid chromatography

HT Equivalent dose to a target region T i.v. intravenous ID(-MS) Isotope dilution (mass spectrometry) ICP-MS Inductively-coupled plasma mass spectrometry ICP-OES inductively coupled plasma optical emission spectrometry ICRP International Commission on Radiological Protection ISO International Organization for Standardization IUPAC International Union of Pure and Applied Chemistry k Boltzman constant ki→j Transfer rate (of a substance) from a model compartment i to compartment j MALDI Matrix assisted laser desorption Ionisation MIRD Medical Internal Radiation Dose

MT mass of target organ T

N+ Number of positive ions

N0 Number of neutral atoms ORNL Oak Ridge National Laboratory p.o. per-oral (used to denote tracer administration by ingestion) PNA Proton nuclear activation (analysis) S spike SAF specific absorbed fraction

3

SEE (T←S) Specific effective energy absorbed in a target region T from a nuclear transformation in a source region S TIMS Thermal ionisation mass spectrometry TLM Taylor and Leggett model UNSCEAR United Nations Scientific Committee on the Effects of Atomic Radiation u(x) Standard uncertainty of a quantity x wR Radiation weighting factor wT Tissue weighting factor yi yield radiation I per transformation

4 Introduction

1 Introduction

The aim of this study is to obtain and evaluate data for the first time on the human biokinetic behaviour of the rare earth element cerium in order to validate and improve the biokinetic model of this element and further on give dose estimation for the element after accidental exposure. Cerium can cause a potential radiological risk after incorporation of its radionuclides into the human body. The International Commission on Radiological Protection (ICRP) has developed or proposed mathematical compartment models for nearly all radionuclides of interest. A model that describes uptake, distribution and excretion in the human body is therefore required to estimate the risk associated to the incorporation. The biokinetics of cerium had already been investigated in dogs, mice, rats, guinea pigs, hamsters, rabbits, cats, and miniature swine (NCRP, 1978). Only one case of human data are known, after accidental exposure (Sill et al., 1969), but no experimental data derived from humans are known about the biokinetic behaviour of cerium. The biokinetic models recommended by the ICRP for this element are mainly derived by extrapolation from the animal data and from the biokinetic behaviour of chemical analogues, like lanthanum, americium. Consequently, biokinetic models developed from such a variety of data sources can only be applied to humans with a limited degree of confidence. The above mentioned issues suggest that a systematic study on healthy humans can substantially improve the current knowledge of cerium biokinetics and render a benefit to internal dosimetry. Therefore, a project has been launched in order to determine the biokinetic behaviour of cerium directly in humans. Since a volunteer study with radioactive cerium would not represent an ethically justifiable method, a technique making use of stable isotopes instead of radionuclides as tracers (Werner et al., 2002) was applied. This prevents the unnecessary exposure of volunteers to ionizing radiation. The method consists in the administration of two stable tracer isotopes at the same time, one orally and the other one intravenously. By measuring the time dependent tracer concentrations in blood and urine samples, information about their gastrointestinal absorption, blood clearance, and urinary excretion can be obtained. It is important that the measurement technique is able to determine isotopic compositions in biological samples below an uncertainty of several percent. There are two main measurement methods applicable for this purpose: Neutron activation analysis and mass spectrometry. Neutron activation analysis (Henry et al., 2001) is probably the most frequently used technique for determination of rare earth elements (REE) (Cantone et al., 2007; Sabbioni et al., 1982); unfortunately it is not suitable for routine

5 Introduction

analyses because the method requires the availability of a nuclear reactor, an elaborate separation before measurements and it is in general only possible to separate one isotope. Mass spectrometry can use different ionisation methods for biological samples, the two most important are thermal ionization mass spectrometry (TIMS) and inductively coupled plasma mass spectrometry (ICP-MS). The main advantages of TIMS over ICP-MS, which have been the decisive factors for choosing it, are the fewer problems with interference because the degree of purity required for analysis is much higher. Its measurement precision and accuracy are also considerably higher than that of ICP-MS (Turnlund and Keyes, 2002; Walczyk, 2004) for the determination of the isotope ratios. For this purpose, TIMS was the method of choice and was therefore used in the present work. Still, this technique had to be optimized for the determination of stable cerium isotopes in biological samples due to the challenging demands within a human tracer study. On the one hand, the concentration of the administered tracers in blood should be as low as possible in order to not disturb the metabolism of the naturally occurring isotopes in the body. On the other hand, the method must be eligible for isotope separation to distinguish between one or more tracers and the natural element content in the sample. For this reason, it must be possible to measure low amounts of cerium in human blood and urine samples down to 1 ng/ml. Interference from other elements must be controllable or even completely avoided. After collection of the human data it can be used for model validation or development of a new model, respectively, which is the main aim of this study.

In order to reach this aim the work was structured in following main topics:

- collection of human data was reached by a double tracer method, which contained of a simultaneously administration of one intravenously and one orally applied stable tracer of cerium; - to determine the amount of the tracers in biological samples, e.g. blood plasma and urine, the analytics in biological samples and a fitting measurement method with TIMS were established; - the obtained data were compared with the current compartment model for cerium of the ICRP and a new biokinetic model for cerium was established; - based on the new cerium biokinetic compartmental model it is possible to give an estimation of a possible risk because of internal exposure. Dose calculations were done for the new biokinetic model.

6 The element cerium

2 Theoretical considerations

In this chapter, the theoretical background for this work will be established. First the element cerium will be introduced, including the natural isotopes of cerium, application of cerium salts in medicine and radioactive isotopes of cerium. Further on it is demonstrated, how to calculate internal dose. For that, biokinetic models of cerium are necessary. The current two models, one of the ICRP and the other one from Taylor and Leggett, are introduced, followed by an introduction into compartment modelling and the methods of cerium analytics.

2.1 The element cerium

Cerium with the atomic number 58 is the second element of the lanthanide group also called rare earth elements (REE), the elements in the periodic table in which the inner 4f electron shell is being filled. First isolated as an impure oxide in 1803, the element was named after the earliest recognized asteroid Ceres that, in turn, was named for the roman goddess of food plants. The recognition that cerium was a unique element and its relationship to other elements were factors in the gradual development of the periodic table concept. The separation and identification of all the individual 4f elements, cerium included, caused considerable confusion one hundred years ago but helped to understand the atomic structure (NCRP, 1978).

2.1.1 Natural isotopes of cerium

Cerium has 20 isotopes that range in its atomic mass from 129 through 148. Only four are naturally occurring (136, 138, 140, and 142). Cerium-142 is actually radioactive but has a half live of 5·10 6 years, that is why it is classified as stable. The abundances of the four isotopes are shown in Table 1.

7 Theoretical considerations

Table 1: The four naturally occurring cerium isotopes and their relative atomic mass and isotopic composition in mass% (Coursey et al., 2010).

Isotope Relative atomic mass isotopic composition (mass%)

136 135.907172 0.00185 138 137.905991 0.00251 140 139.905438 0.88450 142 141.909244 0.11114

In the earth’s crust cerium is the 25 th most common element with a mean concentration of 60 ppm. Cerium, the most abundant lanthanide, has been found in many minerals (Clack, 1984), usually present in trace amounts. There are just two minerals that supply by far the bulk of the world’s cerium: bastnasite and monazite. These two minerals both contain, as far as the lanthanide fraction is concerned, predominantly light-lanthanides and, furthermore, both have very similar cerium contents (Table 2).

Table 2: Distribution of the constituents of the minerals Bastnasite and Monazite in % of total Lanthanum (Molycorp, 1992).

Source Minerals Relative Lanthanide Proportions (Total Ln = 100 %)

Bastnasite Monazite

Ln Ln FCO 3 (Ln , Th) PO 4

Ce ≈ 49 % ≈ 47 % La ≈ 33 % ≈ 22 % Nd ≈ 12 % ≈ 18 % Others ≈ 06 % ≈ 13 %

One hundred years ago, cerium made its first major contribution to chemical technology in 1891 outside the Opera café in Vienna. The successful installation of gas lights, using the Welsbach gas mantle based on a thorium- and cerium-oxide impregnated fabric, was soon followed by the rapid widespread adoption of this form of illumination (Molycorp, 1992). Some cerium-containing materials which are available commercially are summarized in Table 3. Cerium and the other lanthanides have no known metabolic role and only minute amounts occur naturally in living systems (Evans, 1990). The elements have a

8 The element cerium

very limited ability to travel up through the food chain (Evans, 1990). There are reports that they can selectively interact, possibly by binding, with external surfaces with certain organisms and plants. It is one of the main components of the rare earth containing micro-fertilizers manufactured in China (Guo, 1991). In general, the lanthanides, including cerium, have a low toxicity rating (Haley, 1965), especially when they are present in material with low aqueous solubility. Oral toxicity of the lanthanide oxides in rats and mice has been compared to that of table salt, being as difficult to determine. Cerium-oxide, because of its potential use as a diesel-fuel additive, has been specifically tested for acute effects and found to have a very low toxicity (Cosandey, 1986; de Bartolo et al., 2000; HEI, 2001).

Table 3: Cerium containing materials, which are available commercially (Evans, 1990).

Cerium – containing Materials and their Application

Nature of cerium content Example Commercial Application in Material Major component of Fluid catalytic cracking Rare earth chloride, mixed-lanthanide (FCC) catalysts composition metal composition Fe metallurgy Minor component of Lanthanum concentrate, mixes-lanthanide FCC catalysts La-Ln chloride composition Dominant element in Glass polishing, Cerium concentrate oxide-type composition glass decolorizing Relatively pure compound Auto-emission, Oxide, nitrate, metal > ≈ 90 % catalysts, etc. Highly pure compound Oxide, salts Luminescence, catalysts > ≈ 99 %

9 Theoretical considerations

2.1.2 Applications of cerium salts in medicine

The first documented medical use of cerium dates back to the mid nineteenth century when the obstetrician James Y. Simpson reported on satisfactory therapeutic results obtained with cerium nitrate for the relief of vomiting (Simpson, 1854). Especially in vomiting of pregnancy, oral administration of cerium(III) oxalate has been widely practiced during the following decades. Its use has also been proposed for other forms of vomiting such as in cases of sea-sickness, for other gastrointestinal disorders such as chronic diarrhoea and even in neurological disorders such as epilepsy and chorea. The medical preparations used until the early twentieth century contained substantial and varying amounts of other lanthanides, however, supposedly without altering its therapeutic effects (Böhm, 1915; Wilcox, 1916). As controversial as the opinions regarding the therapeutic value of cerium(III) oxalate were the tentative explanations for its effects, ranging from sedative effects on the cerebral vomiting centre on the pneumogastric nerve and a lowering effect on the reflex excitability of the gastrointestinal tract to astringent properties or the mere formation of a protective coating on the wall of the stomach (Baehr and Wessler, 1908; Hara, 1923; Umezawa, 1925). A formulation described as colloidal cerium(III) oxalate (Lange, 1933) was available until the 1950s, with vomiting of pregnancy and all forms of motion sickness as primary indications, but it was later blended with the antihistaminic medicine (Giggelberger and Höhn, 1958). Hunter and Walker (Hunter and Walker, 1956) referred 1956 to antagonism of rare earth elements and calcium concerning blood coagulation. Calcium is needed for the last four reactions of the coagulation cascade. Because of the competition with calcium a blockade of the forced enzymatic reactions needed for blood coagulation was shown. Furthermore, rare earth elements have an inhibiting effect on platelet aggregation. However, it was not used anymore because of side effects like fever and abdominal convulsion (Evans, 1990). At the moment rare earth elements are used for treatments of external combustions (burns), and for therapy and diagnostic of cancer. The main cause of death after external combustions is the infection of respective bodily parts. Cerium- silver-sulfadiazine is used for fire victims against infection of the wound. Secondary of the anti-inflammatory character it is conducive for wound healing. The third application area of rare earth elements is renal failure and the resulting hyperphosphatemia and osteodystrophy (Joy and Finn, 2003; Locatelli et al., 2003).

In current studies the determination of the ability of cerium oxide (CeO 2) nanoparticels to protect against monocrotaline (MCT)-induced hepatoxicity in a rat model is of major interest (Kamal et al., 2011). CeO 2 has a protective effect against radiation-induced oxidative damage and pneumonitis, and it has the ability to scavenge oxygen free radicals and reactive oxygen species. In addition, CeO 2 nanoparticels offer many active sites for free radical scavenging due to their large surface/volume ratio and also the mixed valence states for unique redox chemistry. Furthermore, CeO 2 nanoparticels have

10 The element cerium

been revealed to effectively protect mammalian cells against damage caused by increased reactive oxygen species or nitrogen species (Kamal et al., 2011).

2.1.3 Radioactive isotopes of cerium

Apart from the four stable isotopes of cerium, 24 different radionuclides are known, whose half times are between a few seconds and 33 days, and normally do not represent a radiological hazard to humans. The radioactive isotopes of cerium with half-life times over 15 h are shown in Table 4 along with their decay products. Only three longer-lived isotopes, 141 Ce, 143 Ce and 144 Ce with half-life times from 32.5 d, 33 h, 284 d have been identified among the nuclear wastes present in the environment.

Table 4: Radioactive decay chains for the longer-lived radioisotopes of cerium including those which have been identified in environmental studies ( a All are stable except for La-137 which has a half-live of 6 × 10 4 years, but may be considered to be stable for purpose of radiation dosimetry; b Electron capture; c isomeric transition) (NCRP, 1978).

Isotope Half-life Mode of Decay Decay Mode of Decay Decay product product decay product a half-life Ce-144 284.9 d β- Pr-144 17.3 m β- Nd-144 Ce-139 137.6 d EC b La-139 stable Ce-141 32.5 d β- Pr-141 stable Ce-134 03.16 d EC La-134 6.45 m β+ Ba-134 Ce-137m 34.4 h IT c Ce-137 9.0 h EC La-137 Ce-143 33.04 h β- Pr-143 13.6 d β- Nd-143 Ce-135 17.70 h EC La-135 19.5 h EC Ba-135

The primary source of environmental radiocerium has been from nuclear explosive devices and nuclear power facilities in the past. The release took place in huge amounts during nuclear tests until the beginning of the 1980´s. The important isotopes of cerium released to the atmosphere have been 141 Ce, 143 Ce and 144 Ce. The high temperature reactions in nuclear explosive devices are generally thought to result in release of refractory, insoluble chemical forms (Palumbo, 1963). However, in some studies of environmental samples as much as one half of the radiocerium was in readily soluble forms (NCRP, 1978). Radiocerium in the environment can be taken up by plants through roots or other plant surfaces. Plants have achieved concentrations up to 0.5 times the surrounding soil concentration although there are many reports of

11 Theoretical considerations

radiocerium contamination of food crops with existing measurements of its presence in animal products (Chhabra and Hukkoo, 1962; Merk, 1967; Selders et al., 1953). This is due to poor absorption and transfer of cerium through biological food chains. Studies in human population indicate that inhalation, beside ingestion, is the major route of entry into the body for radiocerium released into the atmosphere from testing of nuclear explosive devices. According to United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) (UNSCEAR, 2000) the worldwide annual average exposition through inhalation of 144 Ce adds up to 52.5 µSv. In comparison, the mean value for all redundant radionuclides together is about 149 µSv per year. Furthermore, 144 Ce was released in the environment by nuclear production facilities. In the plutonium factory Majak in the area of Tscheljabinsk (former Soviet Union), from the overall 74 × 10 15 Bq total activity 66 % was from the radionuclide 144 Ce and has been laid off because of an incident (UNSCEAR, 2000). For the fissioning of 235 U, 238 U, or 239 Pu by thermal neutrons, fission-spectrum neutrons, and high-energy (~14.7 MeV) neutrons, the cumulative fractional yields of 141 Ce, 143 Ce and 144 Ce range from 0.034 to 0.062 (Meek and Rider, 1974). All of these radionuclides can readily be detected in fresh nuclear debris, but 141 Ce and 144 Ce are measured more often than 143 Ce in fallout because of their longer half-lives (Noyce et al., 1973; UNSCEAR, 1964). From the above fission isotope yield information and nuclear weapon test data, it is estimated that about 600·10 +19 Bq of 144 Ce and 8,500·10 +19 Bq of 141 Ce have been produced in weapon tests and injected into atmosphere through 1976. Both of these radionuclides were monitored in seawater, plankton, and marine foodstuffs in the Central Pacific after weapon tests (Held, 1963; Welander, 1969; Welander and Palumbo, 1963). In Table 5 equilibrium concentration ratios (activity per gram wet weight/activity per ml water) for 144 Ce in aquatic foodstuff adapted from Thompson are shown (Thompson et al., 1972). In addition, at nuclear reactor incidents or accidents like in Tschernobyl and Fukushima radioactive materials, including radioactive isotopes of cerium, can be released. The radionuclides are distributed in the environment and can be absorbed in the human food chain and hydrological cycle respectively and can be incorporated into men. After the nuclear accident in Tschernobyl and atomic bomb tests an activity in soil was measured of about 0.4 kBq/m 2 in Munich (Paretzke, 2000). Cerium can enter the human body by ingestion, inhalation, or absorption through wounds. For that it is important to know the human risk and to determine this is important as a first step to calculate the internal dose by dosimetry.

12 Analytics of cerium

Table 5: Equilibrium concentration ratios (activity per gram wet weight/activity per millilitre water) for 144 Ce in aquatic foodstuffs adapted from Thompson et al. (Thompson et al., 1972).

Min Max Average Reference (Activity per gram wet weight/activity per millilitre water)

Seawater Plants 700 (Mauchline and Templeton, 1963) 300 900 (Bryan et al., 1966) Crustaceans 100 (Bryan et al., 1966) Molluscs 2,000 (Mauchline and Templeton, 1963) 200 2,000 (Bryan et al., 1966)

Freshwater Plants 2,000 10,000 (Bryan et al., 1966) Crustaceans 1,600 6,500 (Polikarpov, 1966) Molluscs 37 720 (Polikarpov, 1966) Fish 1 (Polikarpov, 1966)

2.2 Analytics of cerium

In order to be able to measure cerium in non biological and biological samples the measurement technique is one of the most essential issue. It is important that the measurement technique is able to determine isotopic compositions in biological samples as accurate as possible. There are two main mass spectrometry methods applicable for this purpose: Thermal ionization mass spectrometry (TIMS) and inductively coupled plasma mass spectrometry (ICP-MS). The main advantages of TIMS over ICP-MS, which have been the decisive factors for choosing it, are the fewer interference problems. Its measurement precision and accuracy are also considerably higher than that of ICP-MS (Turnlund and Keyes, 2002; Walczyk, 2004). For the purpose of analysing isotopic compositions of cerium in biological samples, TIMS is the method of choice. In the next sections a short introduction into the history of mass spectrometry and the mass spectrometric method is given.

13 Theoretical considerations

2.2.1 History of mass spectrometry

The foundation of mass spectroscopy was laid in 1898, when Wilhelm Wien, a German physicist, discovered that beams of charged particles could be deflected by a magnetic field. In more refined experiments carried out between 1907 and 1913, the British physicist J.J. Thomson, who had already discovered the electron and observed its deflection by an electric field, passed a beam of positively charged ions through a combined electrostatic and magnetic field. The two fields in Thomson’s tube were situated so that the ions were deflected through small angles in two perpendicular directions. The net result was that the ions produced a series of parabolic curves on a photographic plate placed in their paths. Each parabola corresponded to ions of a particular mass-to-charge ratio with the specific position of each ion dependent on its velocity; the lengths of the parabolic curves provided a measure of the range of ion energies contained in the beam. Later, in an attempt to estimate the relative abundances of the various ion species present, Thomson replaced the photographic plate with a metal sheet in which a parabolic slit was cut. By varying the magnetic field, he was able to scan through a mass spectrum and measure a current corresponding to each separated ion species. Thus, he may be credited with the construction of the first mass spectrograph and the first mass spectrometer. Nowadays mass spectrometers are used in industry and academia for both routine and research purposes. The operation of a mass spectrometer is described in the following part. Mass spectrometers can be divided into three fundamental parts

the ionisation source,
the analyser
the detector

The sample has to be introduced into the ionisation source of the instrument. Once inside the ionisation source, the sample molecules are ionised, because ions are easier to manipulate than neutral molecules. These ions are extracted into the analyser region of the mass spectrometer where they are separated according to their mass-to-charge ratios (m/z). The separated ions are detected and this signal sent to a data system where the m/z ratios are stored together with their relative abundance for presentation in the format of an m/z spectrum. The analyser and detector of the mass spectrometer, and often also the ionisation source too, are maintained under high vacuum to give the ions a reasonable chance of travelling from one end of the instrument to the other without being stopped by hitting air molecules. The entire operation of the mass spectrometer, and often the sample introduction process as well, is under complete data system control on modern mass spectrometers. The method of sample introduction to the ionisation source often depends on the ionisation method being used, as well as the type and

14 Analytics of cerium

complexity of the sample. The sample can be inserted directly into the ionisation source, or can undergo some type of chromatography en route to the ionisation source. This latter method of sample introduction usually involves the mass spectrometer being coupled directly to a high pressure liquid chromatography (HPLC), gas chromatography (GC) or capillary electrophoresis (CE) separation column; hence the sample is separated into a series of components which then enter the mass spectrometer sequentially for individual analysis.

Many ionisation methods are available and each of these methods has its own advantages and disadvantages (Ashcroft, 1997).The ionisation method to be used should depend on the type of sample under investigation and the mass spectrometer available.

Atmospheric Pressure Chemical Ionisation (APCI)
Chemical Ionisation (CI)
Electron Impact (EI)
Electro spray Ionisation (ESI)
Fast Atom Bombardment (FAB)
Field Desorption / Field Ionisation (FD/FI)
Matrix Assisted Laser Desorption Ionisation (MALDI)
Thermo spray Ionisation
Thermal Ionisation

The main function of the mass analyser is to separate, or resolve, the ions formed in the ionisation source of the mass spectrometer according to their mass-to-charge (m/z) ratios. All mass analysis methods use static or dynamic electric and magnetic fields than can be used alone or in a combined form. Different set-ups are shown in Table 6.

Table 6: Types of analysers used in mass spectrometry (Edmond de Hoffmann, 2007).

Type of analyser Principle of separation

Electric sector Kinetic energy Magnetic sector Momentum Quadrupol m/z (trajectory stability) Ion trap m/z (resonance frequency) Time-of-flight Velocity (flight time) Fourier transformation ion cyclotron resonance m/z (resonance frequency) Fourier transform orbitrap m/z (resonance frequency)

15 Theoretical considerations

The ions, that passed through the mass analyser are then detected and transformed into a usable signal by a detector. Detectors are able to generate from incident ions an electron current that is proportional to their abundance. The most common types are faraday cups, electron multipliers (EM) and electro-optical ion detectors (EOID).

2.2.2 Thermal ionisation mass spectrometry (TIMS)

A TIMS is a magnetic sector mass spectrometer that is capable of producing very precise measurements of isotope ratios of elements that can be ionized thermally, usually by passing a current through a thin metal ribbon or ribbons under vacuum. The ions created on the ribbon(s) are accelerated across an electrical potential gradient and focused into a beam via a series of slits and electrostatically charged plates. This ion beam then passes through a magnetic field and the original ion beam is dispersed into separate beams on the basis of their mass-to-charge ratio. These mass-resolved beams are then directed into collectors where the ion beam is converted into voltage. Modern instruments are composed of three primary components: 1) ion source, the region in which ions are produced, accelerated, and focused; 2) analyzer, the region in which the beam is separated based on mass/charge ratios; and 3) collector, a region in which the ion beams are measured either sequentially (single collector) or simultaneously (multi-collector). The electronics of these instruments must operate to very close tolerances in order to produce isotope ratios that are precise to 0.01-0.001 %. The advantage of TIMS compared to other isotope ratio techniques include:

the chemical and physical stability of the measurement environment, which lead to highly precise measurements,
the ability to ionize and evaporate samples at different temperatures by using multiple filament assemblies,
lower and more consistent average mass fractionation,
the possible use of single element solutions to eliminate isobaric interferences,
production of ions with a restricted range of energies (eliminates the need for an energy filter),
almost 100 % transmission of ions from source to collector.

Thermal ionisation in TIMS is realised by thermal desorption of ions from a heated metal surface, a narrow flat filament. According to temperature, valence electrons of atoms adsorbed to the hot surface will occupy excited states or even be transferred into conducting band of the bulk solid (Kienitz, 1968) prior to desorption of the atom or ion.

16 Analytics of cerium

The Saha-Longmuir equation describes the ratio of ions and atoms desorbed from the surface governed by the probability distribution of their electron states:

N g  Φ − I  + = + exp   (1) N 0 g0  kT  with

N+ Number of positive ions

N0 Number of neutral atoms

g+, g 0 respective statistical weights Φ Electron work function of the filament material I first ionisation energy of the adsorbed element k Boltzmann constant T filament temperature in Kelvin

The Saha-Longmuir equation is based on several assumptions, some of which are not strictly valid in the following cases:

the ionisation energy I of an atom in close proximity to a conducting surface

can be different from the ionisation energy I 0 of a free atom;
Equation 1 is valid only, if the adsorbing atoms are in their ground state,

which means I ~ I0;
Atoms can be lost by elastic scattering on the ionisation filament surfaces, when multiple filament sources, with one sample evaporation filament and one ionisation filament are used.

Depending on the filament material and temperature-constraining conditions, the ionisation yield, calculated as N +/(N 0 + N +), can be below 1 %. This can be a drawback of the TIMS ion source, unless enough sample material is available. There are some possibilities to overcome this drawback like by improving the low ion yield by applying additives to the filaments surface, e.g. colloidal carbon, boron or rhenium suspensions, boric acid in order to modify the work function Φ. Samples must be purified for TIMS to avoid a suppression of the ionisation of the target element. This purification is usually performed by chemical sample digestion with various acids and subsequent extraction of the relevant element, e.g. column chromatography.

17 Theoretical considerations

2.2.3 Isotope dilution technique for tracer concentration calculation

Isotope dilution mass spectrometry (IDMS) is an isotope-specific method which can provide very good values for element amounts of concentration. The use of isotopes is an excellent representation of the element to be determined (Heumann et al., 1998). IDMS is used because thermal ionisation mass spectrometry does not allow direct measurement of the mass or concentration of cerium in a sample. Absolute calibration is not possible with TIMS, because the ion yield of the thermal ion source can vary by orders of magnitude between different samples with identical filament heating and focussing voltages of the ion optics system. In order to enable concentration measurement by TIMS, isotope dilution (ID) can be implemented. The technique is based on a mixture of an elemental sample ( E) with a spike ( S), i.e. a known amount of the same element with artificially altered isotope ratios (Fassett and Paulsen, 1989). From the measured isotope ratio R M= Y M/X M and the relative abundances hx and hy in spike S and natural element E the mass mE of the natural element in the sample can then easily be derived by:

m ⋅ aw h − h R m = S E ⋅ ,Sy ,Sx M (2) E − aw S h ,Ex RM h ,Ey aw denotes atomic weights. After the sample and the spike isotopes have been completely mixed, loss of the elements to be determined normally has no effect on the analytical results. The condition that no quantitative isolation of the isotope diluted element is necessary is a major advantage of IDMS, especially for analyses at very low concentration levels, like it is the case in this study. To guarantee a complete mixture of the sample isotopes with the spike isotope as quickly as possible is therefore an important feature in IDMS. The selection of the spike isotope should be based on the following points:

Preferably, an isotope with low abundance in the sample should be selected.
The spike isotope should not interfere with isotopes of another element or with molecular ions in the mass spectrum.
In cases where more than one isotope with relatively low natural abundance exists, the cost of the isotope can be used as a criterion for its selection.

IDMS is internationally accepted as a method of proven high accuracy. However, it must be taken into consideration that systematic errors can also occur when using this technique. The following points can contribute to possible errors in IDMS:

18 Analytics of cerium

Isotope fractionations
Mass spectrometric interferences
No equilibration between sample and spike

For TIMS possible fractionation effects can be checked with a standard material. This type of error usually does not influence the result substantially, in particular not if the measurements are carried out under standardized conditions, which is the case in this study. Most of the natural isotope variations are in the range of a few parts per thousand or less and can therefore usually be negligible for IDMS because of resulting errors ≤ 0.1 %. Thermal ionization is one of the most selective ionization methods for the analysis of elements. Therefore interferences in TIMS are not a problem.

2.3 Calculation of internal doses

In the case of incorporation or inhalation of cerium radionuclides, it is necessary to give risk estimation by calculating the internal dose. The ICRP represents the basic intention of radiological protection, which is to prevent or minimise damage by ionising radiation. Recommendations to explain this intention have been published by the ICRP. Within the field of radiation protection, internal dosimetry is concerned with limiting the intake of radionuclides by workers or members of the public in order to limit radiation damage by radionuclide transformations within the body. Deterministic radiation effects, whose severity depends on the amount of absorbed radiation above certain threshold, or stochastic effects, e.g. the modification of DNA, are the resulting damage effects which can lead to cancer or hereditary diseases. Exposure limits proposed by the ICRP are set to prevent deterministic effects and constrain the incidence of stochastic effects to a level “as low as reasonably achievable, economic and social factors being taken into account” (ALARA). For the estimation of health risks related to incorporated cerium isotopes, both chemical toxicity and radiotoxicity is important to be known for the biokinetics of the particular isotopes in the human body. For the incorporation of radionuclides the resulting internal radiation dose is the essential parameter. The concept of “dose” was introduced to quantify the effect of exposure to ionising radiation, in turn being able to give a quantitative estimate of the risk of stochastic effects, since their incidence is supposed to be related linearly of the dose. The basic quantity is the “absorbed dose” D, defined as the energy of ionising radiation absorbed in a volume element, divided by the mass of this volume element. Its unit is

19 Theoretical considerations

J·kg -1, named gray (Gy) and defined as 1 Gy = 1 J·kg -1. The absorbed dose is usually averaged over a target region of tissue T for practical purposes of dosimetry. It must be noted that the concept of tissue-averaged equivalent dose is usually not valid for localised effects, e.g. radiation damage from low energy Auger electron emitters selectively attached to DNA. Since radiation effects on tissues can be dependent on type and energy of radiation, it is useful for the risk estimation to introduce radiation weighting factors wR and calculate an “equivalent dose” H T to a tissue T from the contributions of adsorbed doses DR from different radiation qualities R:

= ⋅ H T ∑ wR D ,RT (3) R

-1 -1 Its unit is J·kg , named sievert (Sv) and defined as 1 Sv = 1 J·kg . The value wR given in the current ICRP recommendation (ICRP, 2007) is 1 for photons and electrons, 2 for protons, 20 for alpha particles and ranges between 2 and 20 for neutrons, depending on their energy. Various tissues have differing sensitivities to radiation effects. This characteristic can be dealt with by tissue weighting factors wT, which can be used to combine individual organ equivalent doses HT to an “effective dose” E, estimating the risk of stochastic effects for the whole human organism. The effective dose is calculated by

= ⋅ E ∑ wT H T (4) T

Its unit is also J·kg -1, named sievert (Sv) and defined as 1 Sv = 1 J·kg -1.

However, equivalent and effective doses after incorporation of radionuclides cannot be measured, and have to be calculated on the basis of physical, radiobiological and biokinetic parameters. The solution is to calculate the internal dose by introduction of two mathematical models: a) the biokinetic model, which describes the biokinetic behaviour of incorporated radionuclides, i.e. uptake, retention, excretion, in order to assess the number of nuclear transformations in each source organ and b) the dosimetric model, which assess the dose in the target organs on the basis of the numbers of nuclear transformations in the source organs. The biokinetic model describes the main step between the intake of radionuclides and the number of transformations within the body, which pictures the biokinetic behaviour, the so called “biokinetics”. The dosimetric model describes the step between the number of transformations in the body and the calculation of the equivalent dose HT.

In the case of incorporation HT is expressed as:

20 Calculation of internal doses

⋅ ⋅ ⋅ ← ∑ wR yi Ei AF i (T S) = ⋅ i H T ∑ ASj ( ) j (5) S M T

with HT equivalent dose in target organ T

ASj cumulative activity of radionuclide j in source organ S

AF i(T ←S) absorbed fraction: relation of absorbed energy in target organ T and emitted energy from source organ S

MT mass of target organ T

yi yield radiation i per transformation

Ei energy of radiation i per transformation

wR radiation weighting factor

wT tissue weighting factor

It can be seen that there exist several factors which influence the internal dose, e.g. half- life of radionuclides; yield, type and energy of emitted radiation; organ sensitivity; human anatomy; spatial distribution of radionuclides in the body and temporal distribution of radionuclides in the body. These factors can be subdivided basically into different fields:

a) The specific absorbed fraction belonging to “anatomy”; b) The yield and energy of radiation belonging to “physics”; c) The radiation weighting factors belonging to “radiation biology”; d) The number of decays belonging to “biokinetics”.

For calculating the doses a biokinetic model is necessary. A biokinetic model is the mathematical description of the uptake, retention and excretion of substances. Hence, it is the connective link between exposure and effects of substances, e.g. pharmaceuticals or radionuclides.

The ICRP recommends models in form of compartment models, which is used as approach to describe the real biokinetic behaviour of substances in biological systems. A compartment is described by its kinetic property and it can be an anatomical, physiological, chemical or physical part of a system. In 1982, the ICRP published in recommendation ICRP 30 the Gastrointestinal Tract (GIT) model (ICRP, 1982). The GIT model has been developed for use in internal dose estimations to the wall of the GIT and to the organs and tissues of the body from radionuclides deposited in the luminal contents of the five sections of the GIT. These sections were the oesophagus, the stomach, the small intestine, the upper large intestine, and the lower large intestine

21 Theoretical considerations

(Poston et al., 2005). This model was replaced 2006 by the ICRP in the “Human alimentary tract model for radiological protection” through the Human Alimentary Tract (HAT) Model (ICRP, 2006). The new HAT model is applicable to children and adults under all circumstances of exposure. It considers the movement of radionuclides throughout the alimentary tract from ingestion to elimination. It takes account of sites of radionuclide absorption and retention in the alimentary tract and routes of excretion of absorbed radionuclides in the alimentary tract. The dose is calculated for sensitive cells in each region: mouth, oesophagus, small intestine and stomach and colon. Beside the GIT/HAT-model also the Respiratory-Tract-Model (ICRP, 1994) and Systemic Models for the different radionuclides (ICRP, 1993) exist. In this work the attention is turned to the systemic model of cerium.

In conclusion, in order to evaluate the ‘committed’ equivalent or effective doses ( HT(τ) or E(τ)) from an intake of a given radionuclide, i.e. the dose received from transformations of this radionuclide occurring within a set time interval τ after intake, the following steps are necessary:

estimation of the amount of radionuclides incorporated and time course of intake;
identification of the organs and tissues the radioactive material is transferred to and from and in which it is retained;
determination of the time course of retention and distribution of radionuclides in the body organs and tissues and excretion from the body;
calculation of the number of radionuclide transformations in relevant source regions S, i.e. organs or tissues containing the radionuclide, within the time interval τ or parts of it,
calculation of the fraction of radiation emitted from each source region S and absorbed in each target region T;

derivation of DT,R and subsequent calculation of H T(τ) and E( τ);

Dose coefficients for internal dosimetry calculations are calculated from the number of transformations US,j (τ) of a radionuclide j in the time period τ as predicted from the respective elements biokinetic model for each source region S. A further set of coefficients, the specific effective energies (SEE), is then used to characterize the equivalent dose received by a target region T per transformation in S:

70 = τ ← H T (t0 ) c∫∑∑U j )( SEE j (T S)dt (6) 0 S j

Equation 6 can be simplified for the committed equivalent dose in adults, which is exclusively used in the current study, since only investigations with adult test persons

22 Calculation of internal doses

were performed. However, the ICRP has also given recommendations concerning dose calculations for infants and children. In the case of intake at any early age, biokinetic model parameters and SEE values have to be interpolated between age groups and Equation 6 has to be used. The characteristic time period τ is 50 y as a default for adults and hence Equation 6 can be written as follows:

= ⋅ ← H T )50( ∑∑U , jS )50( SEE j (T S) (7) S j

The number of transformations US(50) was calculated with the SAAM II software. For this purpose, each compartment CS of the respective biokinetic model was linked to a closed compartment CS,0 receiving the transformed radionuclides. The respective transfer rates k was set to the radionuclide half-lives in analogy to Equation 7. With an experiment duration of 50 y and a unit intake of activity, the contents in the closed compartments CS,0 are equal to Us(50).

The specific energy SEE j(T ←S) in Equation 7 is defined as

w Y E AF (T ← S) ← = , kkkR k SEE j (T S) ∑ , (8) k mT with

w ,kR The radiation weighting factor of radiation k Y the yield of radiation k per transformation

Ek the energy of radiation in Joule

mT the mass of target T

AF k(T ←S) the absorbed fraction of radiation k in T per transformation in S

Apart from geometrical relations of source and target regions, the AF values are dependent on energy and type of nuclear transformations according to the penetration depth of each radiation caused by a transformation. Non-penetrating radiations like α-, and β-particles, recoil atoms and fission fragments are assumed to be absorbed within the source region. Exceptions to this general assumption are source regions distributed over the whole body, the radiosensitive target regions in bone (red bone marrow and endothelial tissue), as well as walled compartments, e.g. stomach, intestine, colon and urinary bladder; here the wall is the target region and the contents are the source. Tabulated SEE values were taken from the SEECAL software package (Eckerman, 1993), which was also used for calculation of ingestion dose coefficients in ICRP publication 56 (ICRP, 1990). These coefficients were derived from mathematical defined phantoms on human body, termed MIRD phantoms.

23 Theoretical considerations

The committed effective dose over 50 y is calculated from the individual dose coefficients in analogy to Equation 4. The tissue weighting factors wT used in this study are from ICRP publication 103 (ICRP, 2007) and are presented in Table 7.

Table 7: Tissue weighting factors proposed in ICRP recommendation 103 (ICRP, 2007).

Tissue or organ Tissue weighting factor wT

Gonads 0.08 Red bone marrow 0.12 Colon 0.12 Lung 0.12 Stomach 0.12 Bladder 0.04 Breast 0.12 Liver 0.04 Oesophagus 0.04 Thyroid 0.04 Skin 0.01 Bone surface 0.01 Remainder 0.08

In order to calculate the internal dose biokinetic models are necessary, which are described in the next paragraph.

24 Current biokinetic models of cerium

2.4 Current biokinetic models of cerium

In 1979, in its Publication 30 (ICRP, 1979), the ICRP issued a set of biokinetic models of the distribution of various radionuclides within the human body. These models serve to provide a mean to calculate element uptake, distribution and retention in the human body, or allow for intake estimation from excretion measurements (bioassay measurements). The general structure of the most metabolic models in these publications consists of compartments, which contain the modelled substance, and transfers of this substance between the compartments. By design, the compartments represent functional units of the human metabolism rather than the individual organs, although often some compartments can be identified with certain cell types, e.g. red bone marrow or individual organs. For a lot of radionuclides, the publications of the ICRP are based on old information of animal experiments, so that the actual relationship is wrong or imprecise for humans. That is the case for the lanthanides in general and may be especially for cerium. The biokinetics of cerium in humans are hardly known. The existent results for the biokinetics of cerium are limited to experiments with animals (NCRP, 1978). A comparison of the biokinetic data for cerium and americium in large animals indicates that the initial distribution of both elements is similar. Cuddihy et al. (Cuddihy et al., 1975) developed a biokinetic model for cerium from data of beagles inhaling 144 Ce aerosols. In their model, cerium is removed from blood with a half-life of about 25 min, with about 2 % going to urine, 12.5 % to the intestinal contents, 35.5 % to the liver compartment, 27 % to skeleton, and 23 % to soft tissues. A portion of depositions in liver, skeleton, and soft tissue returned to blood over a period of days, and the remainder entered long-term compartments in these tissues. A biological half-life about 144 10 y (3283-3873 d) was estimated for beagles after intravenous injection of CeCl 3 (Richmond and London, 1966). In Publication 30 (ICRP, 1979; ICRP, 1989) the ICRP produced a common model for lanthanides. The assumptions made for this model were that 60 % of the lanthanides in blood deposit in the liver, 5 % in the spleen, 20 % in the skeleton and 15 % in other soft tissues. Subsequently, they were assumed to be lost from all tissue compartments, directly to excretion, with a retention half-life of 3,500 days. This corresponds to a half- life for the whole body retention of cerium in beagles (Richmond and London, 1966). Experimental results reported by Cuddihy (Cuddihy et al., 1975) and Guilmette (Guilmette et al., 1987) in dogs and by Durbin (Durbin, 1960) in rats show that for cerium entering the blood, about 50 % of it is translocated to the liver, 30 % to the skeleton and 20 % to other tissues. These values have been adopted in ICRP publication 56 (ICRP, 1989) and the corresponding transfer coefficients are shown in Table 8. The schematic presentation of the model is shown in Figure 1.

25 Theoretical considerations

.

ICRP publication 30 / 56 / 67 Systemic model Stomach

Transfer compartment

Small intestine

Other Skeleton Liver tissues Upper large intestine Urinary Bladder contents Lower large intestine Urine

Excreted faeces

ICRP publication 30 GI tract model

Figure 1: The current biokinetic model of cerium proposed by the ICRP (ICRP, 1990).

26 Current biokinetic models of cerium

Table 8: Transfer coefficient values k of the ICRP model publication 56 (ICRP, 1989). All parameter values are given in h-1. (C-Bone stands for cortical bone, T-bone stands for trabecular bone).

Transfer k [h -1]

Blood to C-Bone 4.1589·10 -01 Blood to T-Bone 4.1589·10 -01 Blood to Liver 1.3863·10 +00 Blood to other 5.5452·10 -01 C-Bone to Urinary Bladder 1.9804·10 -05 C-Bone to Upper large intestine 1.7824·10 -04 T-Bone to Urinary Bladder 1.9804·10 -05 T-Bone to Upper large intestine 1.7824·10 -04 Liver to Urinary Bladder 1.9804·10 -05 Liver to Upper large intestine 1.7824·10 -04 Other to Urinary Bladder 1.9804·10 -05 Other to Upper large intestine 1.7824·10 -05

The structure of many models, including the ICRP model of cerium, is unidirectional, i.e. there is no possibility of recycling once the substance has left a compartment. While this model is still used for radiation protection dosimetry calculations it is now widely recognised to be flawed and is to be replaced by a more realistic model that allows for the recycling of metal between tissue compartments and blood published by Taylor and Leggett (Taylor and Leggett, 2003). The Taylor and Leggett model (TLM) was developed as a generic biokinetic model for predicting the behaviour of lanthanides elements in the human body. Data on the known depositions, tissue retention and excretion patterns of lanthanides in animals (Palmer et al., 1970; Roth et al., 1997; Shutt et al., 2002) were used to specify element-specific rate-constants to describe the kinetics of their transfer between tissue compartments and excretion. A schematic presentation of the TLM is presented in Figure 2. The model is a re-cycling box model comprising 19 compartments that represent either tissue or excreta sinks. The model uses compartments to represent various sections of the body with transfer coefficients between the compartments representing their pathways. The values of these coefficients determine the relocation pattern of the lanthanide in the model. The compartments can be split into groups representing blood, bone, liver, soft tissues and excretion. The compartment representing blood is the main re-circulating compartment and is the primary route for the lanthanides to relocate from one group of compartment to another. The transfer coefficients for the TLM are shown in Table 9.

27 Theoretical considerations

Figure 2: Schematic representation of the Taylor and Leggett model for predicting the behaviour of lanthanides in the human body (Taylor and Leggett, 2003).

28 Current biokinetic models of cerium

Table 9: Transfer coefficient values k of the Taylor and Leggett model (Taylor and Leggett, 2003). All parameter values are given in h -1. (C-Bone stands for cortical bone, T-bone stands for trabecular bone).

Transfer k [h -1]

Blood to Liver 1 11.645 Blood to ST 0 10.0 Blood to ST 1 1.85250 Blood to ST 2 0.46579 Blood to C-Bone 3.49350 Blood to T-Bone 3.49350 Blood to Kidney 0.34935 Blood to Urine large intestine 1.39740 Blood to Urinary path 0.11645 Blood to Urinary bladder 0.46580 Liver 2 to Blood 0.00095 Liver 1 to GI 0.0231 ST 0 to Blood 1.3863 ST 1 to Blood 0.00190 ST 2 to Blood 0.0001266 C-Bone to Blood 0.000760 T-Bone to Blood 0.000760 Urinary Path to Urinary bladder 0.099 Other kidney tissue to Blood 0.00139

29 Theoretical considerations

2.5 Fractional absorption

A characteristic value of specific importance for many radionuclides is the fractional absorption, i.e. the fraction of substance transferred from the alimentary tract into the systemic part of the model. It has two consequences.

1) If the amount of an element ingested shall be derived from urinary data to bioassay measurement, the result is directly proportional to fractional absorption. Any associated dose estimate will be scaled by the fractional absorption value and also be subject to a corresponding uncertainty. This is relevant to occupational exposure monitoring, e.g. of thorium (Baglan et al., 2001). 2) For long-lived radionuclides with half-lives significantly longer than the transfer time of substances through the alimentary tract, e.g. 137 Cs (30.2 y) of 90 Sr (28.5 y), the internal absorbed dose is approximately directly proportional to the amount of substance transferred into the systemic circulation.

Since the transfer rates are constant over time, the fractional absorption from small intestine to transfer compartment can be calculated at any time by

k → f = f = SI transfer (9) 1 A + kSI →transfer kSI →colon

In the new HAT model, the total fractional absorption f A is identical to f1 as long as the uptake of an element only takes place from the small intestine. This is the standard assumption of the HAT model, unless information is available on specific uptake from other compartments of the alimentary tract. Therefore, in the current study, fA and f1 are treated as synonyms, unless otherwise stated. There are various techniques available to determine this parameter (Roth and Werner, 1985), the double tracer technique and the convolution integral technique beside determination via modelling procedure. In general fractional absorption fA can be derived from the transfer rated of a first-order kinetic compartment model (Equation 9), if a model is available. The quality of this approach relies both on the appropriateness of the model, as well as on the uncertainty of the relevant parameter values. A large amount of data may be needed for a well-defined and appropriate model. As already mentioned information about fractional absorption can also be obtained from comparatively simple investigations with fewer assumptions concerning the metabolism under study (Roth and Werner, 1985). One very basic technique is the measurement of the fraction of an orally (p.o.) administered substance which is directly excreted in faeces, i.e. passed through the alimentary tract without being absorbed. This method

30 Fractional absorption

requires the complete collection of faeces within a few days after administration, with only one substance concentration measurement of the collected sample. It is however limited in its informative value due to endogenous excretion of the substance, which can yield a biased result, i.e. an artificially low fractional absorption value. In addition, this method is not suitable if fA is of the order of the relative measurement uncertainty, since the measured excreted amount of substance will not be significantly different from the ingested amount in this case, hence the measured value of fA is zero. Hence this method is presumably not applicable for cerium. For elements with low fractional absorption values it is preferable to measure the amount of absorbed substance rather than the remaining excreted amount. Various techniques have been reviewed concerning their effectiveness for radioisotopes of calcium (Roth and Werner, 1985), but not all of them are applicable for stable cerium tracers:
Absorbed radioactive isotopes can be quantified by whole-body counting, but the exposure to radioactive substances without special necessity is generally not accepted. In addition, inhomogeneous tracer distribution in the body, excretion process prior to measurement and retention of non-absorbed tracer in the alimentary tract may be sources of errors.
The tracer concentration in plasma, which can easily be obtained from a single

plasma sample, can allow for quantification of fA. This technique requires a scaling factor which related the plasma concentration at the time of measurement to the whole-body concentration after completed absorption. It is therefore only applicable if further information on the metabolism of the element is available, e.g. plasma content of the body, and clearance rate of the tracer from plasma.
The double tracer technique circumvents the latter problem by using a second intravenously (i.v.) administered tracer. This tracer can serve as a reference for clearance processes from the plasma and thus provide the scaling factor relating oral tracer concentration in plasma with whole-body absorbed amount. The central assumption of this technique is that both tracers are metabolised identically after simultaneous administration. In principle, the double tracer technique requires only one plasma or urine sample, probed after the absorption process from the alimentary tract is completed. This method is discussed in paragraph 3.3.1.
The convolution integral technique is a modified extension of the double tracer technique, and discussed in section 3.3.1. In brief, it uses the time course of the concentrations of one orally and one intravenously administered tracer to derive the time-dependent absorption rate. The fractional absorption is then calculated from the time integral of the absorption rate. This technique relies on the same basic assumptions as the double tracer technique. It requires several plasma samples, but also yields additional kinetic information.

31 Theoretical considerations

Further on, the value of fA can be heavily dependent on the chemical form in which an element is ingested (Höllriegl et al., 2004). The ICRP (ICRP, 1990) act on the assumption that for adults the fractional intestinal absorption (f 1-value) of cerium is 4 about 5 × 10 , according to the fA-value of the actinides (ICRP, 1993) due to of the physicochemical similarity between cerium and the actinides, e.g. plutonium, americium. Owing to the relevance for the dose estimation, fractional absorption is one of the most interesting parameters investigated in this work.

2.6 First order kinetic compartment modelling

The ICRP use first-order kinetic compartment models to estimate the distribution and retention of most radionuclides in the human metabolism, as well as to calculate the number of radionuclide transformations giving rise to the internal absorbed doses. Since the aim of this work is to support, improve or replace the current biokinetic model of cerium, this type of model was used in this study. Compartmental analysis is a common approach in biokinetics. The following outline of the main concepts of first order kinetic compartment models is based on the book by Carson, Cobelli and Finkelstein (Carson et al., 1983). Such a model consists of several compartments. Each compartment is characterized by its state variable that generally corresponds to the time dependent amount or concentration of a substance. These compartments can represent the physiological or physical location or the metabolic or chemical state of the substance under investigation, e.g. selected organs or tissues or parts of them. It is important to mention that a compartment not necessarily represents a physiological entity like an organ, but it is far more an abstract construct. In most cases the mathematical model is only a very simplified representation of the complex biological system. The possible transformations and translocations are described by connections between the compartments that allow an exchange of the substance. The relation between compartments can be described by a mass balance equation

dc t)( i = − ∑Ril ∑ Rmi , (10) dt l m

where ci(t ) is the state variable of compartment i and ∑ Ril is the sum of all transfer l rates into compartment i from all compartments l. If the transfer rates are dependent on the substance concentration or amount cl in compartment l, often the simplifying

32 First order kinetic compartment modelling

assumption is made that these general transfer rates can be described by a first-order relationship Ril =k il ·c l(t). In these first order processes the rate coefficients kil are positive as well as constant and describe which fraction of the molecules of the radioactive substance will move from compartment l to compartment i within a defined time. Equation 10 can then be rewritten as a set of first order linear differential equation.

dc t)( i = − ∑kil *cl t)( ∑kmi *cm t)( (11) dt l m

This system of coupled differential equation can be solved given some initial values or boundary conditions of the state variables ci(t) . The solutions are sums of exponential functions with constant coefficients. This approach is implemented in several different computer programs with iterative algorithms to solve these differential equations and fit the model to the measured data. The software used in this work is described in detail in chapter 3.3.2. Therefore, with the measured data, it is possible with this method to determine the unknown values of the rate constants k il . The easiest way to evaluate a model is to fit the model to the measured data of each project in a study individually and evaluate the resulting sets of model parameters. A key element for the modelling is the input function, describing the application of the substance. A usual starting condition for stable isotopes is the assumption of no substance in the system. The substance can then be applied at one or more times either as a rapid bolus or as a slower infusion over a certain period of time depending on the clinical protocol. In this case it was a rapid bolus. If the substance is administered, the total absorption fraction fA is of special interest. It is defined in ICRP publication 100 (ICRP, 2006) as the fraction of incorporated material that is absorbed to blood in the human alimentary tract in the absence of radioactive decay. The term f A describes the fraction of the administered cerium amount that is available for the metabolism and is more discussed in paragraph 3.3.1. Compartment modelling depends on a number of assumptions that are more or less met in the experiments. The first one is that mass is conserved, meaning that all influxes and losses can be accounted for the model. Another one is that the administered substance (in the present case the isotope solution) does not disturb the normal physiological and metabolic processes; furthermore, that the system is in a steady state so that the parameters of the model will be constant over time.

33 Theoretical considerations

Before it is possible to use the first order compartment modelling procedure the data must be measured. The measurement technique is introduced in paragraph 3.1 and 3.2. Examples for the application of biokinetic models can be found

a) in toxicology, in order to assess dose limits for pollutants; b) in medicine, in order to assess the relationship between dose administration and effects of pharmaceuticals and in order to perform optimal nuclear diagnostics by using radionuclides as radiopharmaceuticals; c) in nutrition science, in order to explore the physiological properties of essential or toxic trace elements; d) in radiation protection, in order to assess the resulting radiation dose after the incorporation of radionuclides.

34 Collection of human biokinetic data

3 Materials and Methods

3.1 Collection of human biokinetic data

In this work the biokinetic of the radionuclide cerium is the main interest. It was investigated by using stable isotopes of cerium as tracers. Since it can be assumed that they have the same biokinetic behaviour as the radionuclides. Kinetic distributions of target substances in a steady state condition can be difficult to observe, especially if small changes, e.g. a slow flux between two large substance pools, shall be investigated. This is critical for biokinetic studies, since many substance concentrations in living beings are governed by dynamic equilibriums. Stable substance concentrations may easily be measured, but flux reaction rates, which are attributed to metabolic activity, are more difficult to determine. Tracer investigations attempt to bypass this problem by determining the kinetics of a tracer instead of a target substance, the tracee, with both substances being similar in respect to their metabolic characteristics. A meaningful tracer/tracee investigation should fulfil further requirements:

The tracer should not be present in the metabolism before the investigation;
The amount of applied tracer should be small as possible in order not to disturb the normal trace metabolism;
At least in studies with human test persons, a tracer substance is not allowed to be toxic, nor may its application cause harm to the persons under study.
Furthermore, stable isotopes can be applied as tracers if more than one stable isotope of an element exists, and if the natural isotopic composition of an element is known and stable.

Depending on investigation design, stable tracers can be more complicated to measure and yield less information than radioactive tracers, which are detectable from outside the body. Although latter are used e.g. in PET diagnosis, ethical concerns reflected above prevent their application to healthy test persons, unless individually justified. In contrast, stable tracers can be used for special test persons like pregnant women or

35 Materials and Methods

children. Stable isotopes can be applied as tracers if more than one stable isotope of an element exists, and if the natural isotopic composition of an element is known and stable, at least within an investigation. Cerium fulfils these prerequisites so its biokinetic can be investigated using its stable isotopes and is used in this work. For the purpose to determine the kinetic profile of the absorption process, the blood clearance and the excretion kinetic it is important to have suiting methods. Except for sacrificial animal experiments, the condition that the measurement process should not disturb the metabolism limits the choice of sample types to blood, hair or various excreta, all of which can be obtained without anaesthesia. The information contained in such samples is limited to parameters describing uptake and clearance from these sample materials. The double tracer method as introduced by de Grazia et al. (de Grazia et al., 1965) is a powerful method to determine the fractional absorption of an ingested substance. The technique which was originally performed with radioactive tracers and only one urine and two blood samples was modified and applied to several elements over the last few years (Cantone et al., 1997; Höllriegl et al., 2002; Keiser et al., 2011; Veronese et al., 2000). According to this methodology two tracers are applied simultaneously; one tracer is administered orally (p.o.), the other injected intravenously (i.v.). The behaviour of the two tracers is considered to be similar when they are both in the systemic metabolism. Tracer excretion can be calculated by measurements of urine or faecal samples. Urine samples have three advantages for intended tracer measurements. Firstly, urine sampling is easier and more acceptable than the collection of faecal samples for many test persons; secondly urinary excretion occurs usually more often, thirdly tracer excretion in faeces is a mixture of two components: tracer directly transferred through the alimentary tract and tracer which has been transferred into the systemic circulation and excreted back to the alimentary tract. Tracer in urine must have entered the systemic circulation prior to excrete in the urinary pathway. Therefore at least in the first few days after tracer administration, urine measurements are better suited to estimate excretion from the systemic circulation. The concentration curves of the two tracers in blood plasma are compared and the fractional absorption from the alimentary tract into the systemic circulation can be evaluated. The i.v. tracer serves as a reference for the clearance process from blood plasma. In conclusion, the double tracer technique with urine and plasma samples provides data on tracer absorption from the alimentary tract, tracer retention in plasma and tracer elimination through the urinary pathway.

36 Collection of human biokinetic data

3.1.1 Preparation of tracer solutions

Reagents The reagents used were “suprapure” grade acids from Merck KGaA, Darmstadt,

Germany. Nitric acid (HNO 3, 65%) and hydrochloric acid (HCl, 30%) were further purified by subboiling distillation (“distillacid BSB-939-IR”, Berghof Products + Instruments GmbH, Eningen, Germany). For dilution of acids and rinsing of Teflon parts, deionised “Milli-Q” water (18.2 M Ω/cm) was used (Millipore GmbH, Schwalbach, Germany). Teflon vessels, which are used for sample preparation, were cleaned prior to use by concentrated nitric acid as described by Tschöpel (Tschöpel et al., 1980).

Natural cerium standard solutions For the in vitro experiments regarding the assessment of the TIMS properties and reproducibility, a standard solution of natural cerium (PLCe2-2X/2Y; SPEX CertiPrep, Metuchen, NJ, USA) was employed as an in-house reference.

Cerium tracer stock solutions Three different cerium tracers (T-136, T-138, T-142) as cerium oxide powder with different, highly enriched isotopic compositions were purchased from Campro Scientific GmbH, Berlin, Germany. The isotopic compositions of the tracers are listed in Table 10.

Table 10: Isotopic composition of cerium stock solutions given in the suppliers´ certificate and composition of natural cerium.

Type Relative isotope abundances (atom%)

136 Ce 138 Ce 140 Ce 142 Ce

Natural Ce 0.19 0.21 88.5 11.1 T-136 30.6 0.7 64.2 4.5 T-138 0.04 41.6 55.81 2.55 T-142 0.02 0.1 6 93.88

An aliquot of 20 mg of the cerium powder was dissolved in 3 ml 1 M HNO 3 (subboiled) and 100 µl H 2O2 and heated in a closed Teflon vessel for 4 h at 140 °C. Then, 30 ml 1

M HNO 3 were added and the solution was filled up to 100 ml with MilliQ water. In this way, three different tracer stock solutions (T-136: enriched in 136 Ce; T-138: enriched in

37 Materials and Methods

138 Ce; T-142: enriched in 142 Ce) with a nominal concentration of 100 mg/l Ce-isotope were obtained and used for further application.

Cerium spike solution By diluting the T-142 stock solution down to a concentration of 175 µg/l of 142 Ce, a spike solution was obtained and used for quantification of other cerium isotopes in the samples.

Oral and intravenous tracer solutions For the investigations within the volunteer study, two different tracer solutions (one for oral and one for intravenous administration) have been produced as described in the following: The tracer solution for oral application (enriched in 136 Ce) was prepared by taking an aliquot of 100 µg cerium from the T-136 solution and mixing it with about 80 ml MilliQ water. Then 2 µl HCl and 1 ml sodium citrate (10 % solution) were added for pH stabilization. The solution was filled up to 100 ml with MilliQ water. The pH of the solution was 4.4. The final concentration of the oral tracer solution was 1 µg/l of T-136. The tracer solution for intravenous application (enriched in 138 Ce) was prepared by addition of 400 ml NaCl (0.9 %, sterile), 180 µl HCl (conc., subboiled), 60 ml sodium citrate (10 % solution, sterile), and 0.7 ml of the solution T-138 (86 mg/l). The solution was filled up to 600 ml with sterile MilliQ water. The pH was adjusted to 6.1. From this solution, aliquots of 10 ml were filled into glass ampoules, melted tight and sterilized at 120 oC within 20 min. Sterility of samples was checked according to German European Pharmacopoeia. The recommended minimum sample amount of 10 % of the ampoules per charge was randomly selected and checked for microbial infection by the Institute of Microbiology, Immunology and Hygiene of the Technical University Munich, Germany. The cerium concentration in the ampoules was 0.1 µg/ml which was proved by using ICP-MS and TIMS measurements.

38 Collection of human biokinetic data

3.1.2 Implementation of volunteer tests

The cerium tracer study in this work was approved by the Ethics Commission of the Medical Faculty of the Technical University of Munich and supervised by Prof. Dr. M. Göttlicher (Helmholtz Zentrum München, Institute of Toxicology). It was conducted in cooperation with Prof. Dr. T. Zilker and Dr. N. Felgenhauer of the Department of Toxicology in the II. Medical Clinic of the Technical University of Munich, where the tracer administration took place. The tracer administration was limited based on body weight to 0.0143 µg/kg for the i.v. tracer and 1.43 µg/kg for the oral tracer. Possible impairments to the test persons were covered by a special insurance. Investigations were carried out according to the following pre-defined scheme:

Written informed consent was obtained from volunteers preceding the investigations.
Test persons´ health was checked out by medical examinations and a complete blood count.
Sampling vessels were labelled in advance.
Test persons had to be fasting overnight preceding the start of the investigation and further two hours thereafter.
Oral tracer solutions were prepared fresh from stock solution in advance.
Test person was driven to the clinic where he or she would be kept under medical control for the first 60 min of the investigation.
An in-dwelling catheter was intravenously inserted in one arm and fixed by the physician in charge.
2-4 ml blood were drawn and discarded to avoid sample contamination by catheter material.
A blank sample of ~ 10 ml was drawn.
The investigation was started by intravenous injection of one ampoule of i.v. tracer solution in the arm opposite the catherized arm. The time of injection was noted in the investigation record form.
As soon and fast as possible, the test person drank the oral tracer solution. The time of drinking was noted in the investigation record form.
The actually administered amounts of both tracers were determined by weighing the beaker and syringe when empty, and when containing the tracers before and after application.
In pre-defined time intervals, blood samples of ~ 10 ml each were drawn. All urine was collected after the start of the investigation at collection intervals of 4, 12 h or 24 h.
After 60 min the test person was driven back to the Helmholtz Zentrum München, where consecutive blood samples were drawn by a physician.

39 Materials and Methods

Two hours after injection the test person was offered a standardised breakfast, consisting of coffee, sugar, milk, and two bread rolls with butter and jam. Half an hour after breakfast the test person was free to drink and eat ad libitum.
The in-dwelling catheter was removed either if necessary or after 8 h after its insertion. After removal of the catheter, and in the following days, blood samples were drawn by butterfly needles.

Blood sampling time was scheduled for 5, 10, 15, 30, 60, 120 min and 3, 4, 6, 8, 24, 48 h, as well as 7 d and 30 d after tracer injection. Urine was collected completely over the first 12 h, from 12 – 24 h, and every 24 h until 7 d. All relevant sample data such as time after injection, duration of drawing, time of centrifugation of blood samples, and urine weight were noted in a record form. Blood plasma samples were prepared for storage at the Helmholtz Zentrum München as soon as possible by centrifuging at 3,000 rpm for 10 min. and removing the plasma and freezing it. Urine samples were weighed for later calculation of excreted tracer amounts. From each collected urine sample, two aliquots of 15 ml each and two of 100 ml each were mixed with 0.75 ml and 5 ml HNO 3 (conc., sub-boiling), respectively, and stored frozen until preparation for analysis. For the preparation of the biological samples (blood plasma and urine), a microwave digestion system with built in, non contact temperature measurement (Berghof, Eningen, Germany) was used for digesting the samples. It consists of a rotor carrier in which the pressure vessels containing the samples were screwed.

40 Collection of human biokinetic data

3.1.3 Test persons

Until April 2010, 19 test persons were accomplished at the Helmholtz Zentrum München after administration stable isotopic tracers of cerium, German Research Centre for Environmental Health (HMGU). Within this study 12 investigations were performed with the double tracer method. Table 11 gives an overview of the investigations performed during this study. In the personal code, e.g. Ce 06 20 01, 06 stands for the year, 20 identifies the test person and 01 stands for the investigation.

Table 11: Overview of investigations subjected to measurement within this study.

Study code Sex Age i.v. Tracer p.o.Tracer (y) Type ( µg) Type (µg)

Ce 06 20 01 female 32 138 Ce 0.99 Ce 07 24 04 female 50 138 Ce 0.965 136 Ce 99.6 Ce 07 26 03 male 29 136 Ce 98.6 Ce 07 27 02 male 28 136 Ce 98.8 Ce 07 29 05 female 21 138 Ce 0.99 136 Ce 96.4 Ce 07 30 06 female 54 138 Ce 0.99 136 Ce 99.7 Ce 09 33 07 female 28 136 Ce 98.8 Ce 09 34 08 male 42 136 Ce 99.8 Ce 10 35 10 male 31 138 Ce 0.99 136 Ce 99.8 Ce 10 36 12 male 44 138 Ce 0.99 136 Ce 99.8 Ce 10 37 13 female 39 136 Ce 99.9 Ce 10 38 14 male 54 138 Ce 0.98 136 Ce 99.8 Ce 10 39 15 female 47 138 Ce 0.99 136 Ce 99.8 Ce 10 40 16 male 22 138 Ce 0.99 136 Ce 99.8 Ce 10 41 17 male 27 138 Ce 0.98 136 Ce 99.9 Ce 10 42 18 male 28 138 Ce 0.99 136 Ce 99.9 Ce 10 43 19 male 27 138 Ce 0.99 136 Ce 99.8 Ce 10 44 20 male 28 138 Ce 0.99 136 Ce 99.9 Ce 10 45 21 female 62 138 Ce 0.99 136 Ce 99.8

Among the 19 test persons were 8 female in the age of (42 ± 14) years (mean ± SD) and 11 male in the age of (33 ± 10) years (mean ± SD). The plasma samples were collected according to the following time scheme after injection: 5 - 10 - 15 - 30 - 45 - 60 - 120 - 180 - 240 - 360 - 480 - 1440 - 2880 min.

41 Materials and Methods

The urine samples were collected by the test persons following the time scheme after ingestion: 4 - 4 - 4 - 12 - 24 - 24 - 24... h up to six days. In experiments of the years 2007 and 2009, the time interval was 12h – 12h- followed by 24 h each.

3.2 Measurement of Ce tracer concentration in biological samples

Measurement methods for the tracer investigations must necessarily fulfil two requirements:

1) They must be able to distinguish between different stable isotopes of the investigated element, 2) And be sensitive enough to quantify or at least detect trace amounts of these isotopes in most samples.

The necessary detection limit for cerium isotopes can be obtained from a simple estimation. It is based on a reference person of 70 kg, with a blood volume of ~ 3 l, daily urine excretion of ~ 1 l, and the administration of the maximum permitted amount of tracer, i.e. 1 µg by injection or 100 µg by ingestion. The tracer is further assumed to be isotopically enriched in 100 % and to distribute according to the current ICRP biokinetic model presented in paragraph 2.3. with its standard parameters. Blood plasma and urine are considered as sample materials. In this case, the oral tracer would be the quantity constraining the necessary measurement detection limit, since the amount of tracer adsorbed in plasma is 100 µg · fA, i.e. only 0.5 µg, resulting in a maximum concentration in plasma of ~ 33 ng/ml. The tracer is cleared from plasma with a half- life of 6 h, hence its estimated concentration will be 1 ng/ml after 1 d and 0.1 ng/ml after ~ 2 d. Tracer concentrations in urine can be estimated from the literature data given in ICRP publication 56 (ICRP 1990) without using the model. Any measurement method applicable for cerium stable tracer investigations must therefore be able to detect ~ 1 ng/ml or less of at least two cerium isotopes in both blood plasma and urine. The measurement method used in this work was therefore thermal ionisation mass spectrometry and how it is used will be discussed in the following section.

42 Measurement of Ce tracer concentration in biological samples

3.2.1 Mass spectrometric method

In this work, a TRITON thermal ionisation mass spectrometer from Thermo Fisher, Bremen, Germany, as shown in Figure 3 is used.

Figure 3: Photograph and scheme of the TRITON instrument (courtesy of the Thermo Fisher Scientific GmbH).

The ion source chamber (to the left in Figure 3) features the sample carrier wheel, a heating current system with glide contacts, and the ion optics. The filament temperature can be monitored by a pyrometer. A 90° magnet is used to deflect the ions according to their mass-to-charge ratio, optionally supported by two quadrupoles. These quadrupoles serve to deform the beam in measurements which use two or more magnet settings and static multicollectors. The detector distance between neighbouring isotopic ion beams is dependent on the central ion mass selected by the magnet. Since the detectors are not moved when the magnet current is changed, the ion beam can not be centred on all detectors with all magnet settings. By using the quadrupoles it is possible to deform the beam slightly and correct such small deviations.

43 Materials and Methods

The ion detection system of the TRITON consists of three subsystems:

A set of nine carbon faraday-cups, movable individually either direct or indirect by 4 motors, and used for high-precision isotope ratio measurements with strong ion beams;
A single secondary electron multiplier for low signals or large isotope ratios; in the latter case, the more abundant isotope is measured with a faraday cup and the less abundant isotope with the SEM;
A set of up to 8 channeltron detectors, mounted onto selected faraday cups. This arrangement is specific to one or a few elements, since the relative distances of the detectors can not easily be altered.

The instrument is operated exclusively by a software suite provided by the manufacturer. This software provides access to all necessary operational tests and measurements as well as to diagnostic information.

A typical sample measurement of cerium samples in the current study proceeds according to the following scheme: The sample is heated slowly to a temperature where ion beam formation can be expected, trying to avoid sample loss due to local stress deformations from an inhomogeneous temperature distribution, or complete untimely evaporation. The heating scheme is for ionisation is 400 mA/min up to 2000 mA, then 250 mA/min up to 3000 mA, followed by 100 mA/min up to 4600mA and finally 50 mA/min for th evaporation filament and 200 mA/min up to 1100 mA for the ionisation filament until a signal of 142 Ce can be observed. To reach optimal transmission through the instrument the ion beam is focused to obtain optimal transmission. An automated optimisation routine, which is included in the software, was alternated with fine tuning of the filament position. The combination of both focusing operations can improve the ion count rate by several orders of magnitude. Especially for small sample amounts it is a critical step because overheating of the filaments can consume the sample in a few minutes. Therefore, it is more important to focus as effectively as possible. After focussing the ion beam the measurement routine is started. In an initial reference measurement current setting of the magnet is calibrated to centre the beam on the detectors which takes ~ 5 – 8 min. The standard measurement consists of 50 measurement cycles grouped in 5 blocks with 10 cycles. In each cycle the count rate of the masses 136, 138, 140 and 142 amu is recorded. The measurement routine calculates all count rates ratios relative to 140 Ce, taking into account the barium isobaric correction, the detector dead time and dark noise. The isotope ratio measurement takes about 35 min.

44 Measurement of Ce tracer concentration in biological samples

The measured data can be viewed during and after the measurement with the instrumental software. The calculation of isotope ratios is interactive in that only the count rates of each cycle are stored as numbers; all derived quantities can be recalculated or modified in case an error is found. The results were exported as ASCII files. They were further evaluated with Microsoft Excel. In a thermal ion source, the probability of an atom or ion emission from the surface is dependent on the mass of the particle. Lighter ions of an element are preferably emitted; leading to depletion in light ions over time and a change in measured isotope ratios, an effect termed “mass fractionation”. In high-precision isotope ratio measurements, this effect is usually corrected by using a known isotope ratio of the investigated element as reference (Habfast, 1998). However, in the current study, each cerium type (i.e. the different tracers and natural cerium) contains all of the naturally-occurring isotopes in non-negligible amounts. This makes internal mass fractionation correction impossible, because none of the cerium isotope ratios are known in mixed samples. Three total evaporation experiments during development of the method showed that the change in cerium isotope ratios was negligible for the ratio 142/140 until 70 % of a sample was evaporated, while during a routine measurement, typically only 10 – 50 % of a sample was consumed. The change in isotope ratios 136/140 and 138/140 was greater, but still below 5 % during a typical measurement duration. Care must be taken, if a sample is nearly depleted during measurements, indicated by a declining signal despite a continuous increase of the heating current. In such an extreme case, the relative change in the isotope ratio 138/140 can exceed 15 %. Since no reliable correction mechanism is available, such sample measurements should be rejected and repeated. Repeated measurements of laboratory standards have shown that the range of isotope ratios due to mass fractionation is usually negligible compared to the random fluctuations of the isotope ratio in the course of a typical measurement procedure. A further source of mass-dependent bias is “mass discrimination” introduced by the ion detector. Secondary electron multipliers (SEM) have different electron emission efficiencies for ions with differing velocities (Adams et al., 1988). This bias can be assessed in the same way as thermal ionisation mass fragmentation, i.e. by comparison of the measured count rates with reference isotope ratios or abundances. However, the effect is negligible if the detector is operated in ion counting mode, and if the ions of all isotopes generate enough secondary electrons to exceed the SEM´s pulse-generating threshold value. Therefore, the channeltron measurements should not be subject to mass discrimination effects.

45 Materials and Methods

3.2.2 Sample preparation

Blood plasma and urine samples were first subjected to microwave-assisted acid pressure digestion (Berghof, Eningen, Germany). In a second step, cerium was extracted by column chromatography to obtain pure cerium salts, which can be optimally ionised in the TIMS ion source without interfering elements. The third step was the preparation and loading of TIMS sample carriers. The digestion and extraction procedure was derived from previous experiences with biological samples in the department of medical radiation physics and diagnostic, Helmholtz Zentrum München. It was optimised for cerium based on literature examples of cerium extraction from various materials (Esser et al., 1994; Goswami and Das, 2004; Misawa et al., 2000) and supplier’s recommendations on the treatment of chromatography resin.

Chromatography columns were prepared as follows Re resin material, which consist of 1 M octyl(phenyl)-N,N-diisobutylcarbamoyl- methylphosphine oxide (abbreviated as CMPO) in tributyl phosphate (TBP) coated on an inert methacrylic polymeric support and with a particle size of 100-150 µm, and column assembly parts were purchased from Eichrom Environment, SAS, Bruz, France.

Prior to the first use, the loose resin was repeatedly elutriated in 0.1 M HNO 3; floating particles were removed. Aliquots of the resin slurry were filled into polypropylene columns of 8 mm inner diameter. During filling, air bubbles were removed through stirring the resin with a glass rod in order to prevent the columns from becoming impermeable for solutions. The resin was firmly fixed in place by porous polypropylene frits to prevent loss of resin and disturbances when adding sample solutions or acids during chromatography. The typical height of the resin beds was 20 mm, resulting in a resin volume of ~ 1 ml. Assembled columns were successively rinsed with 20 ml 0.1 M HCl, 15 ml 6 M HCl and 15 ml 0.1 N HCl prior to their first use. They were stored in 0.1 M HCl at 4°C.

Sample preparation was done for several samples in parallel and included the following steps:

a) Spiking of 1 ml urine or 500 µl plasma with 10 µl of reference tracer solution 142 Ce, commensurate to a tracer mass of 1.75 ng; b) Incubation at 37°C in a heating cabinet for 8 h;

c) Addition of 6 ml concentrated HNO 3 (sub-boiling distilled grade) to plasma

and 4.5 ml HNO 3, 0.5 ml H 2O2 to urine; d) Microwave digestion; Plasma: 15 min-140 °C/30 min-220 °C/10 min-230 °C, Urine: 10 min-145 °C10 min-160 °C/20 min-190 °C;

e) Plasma: Addition of 0.4 ml H 2O2; f) Transfer of the samples to Teflon beakers (~ 10 ml volume);

46 Measurement of Ce tracer concentration in biological samples

g) Evaporation to dryness at 120°C over 7 h on a hot plate with extraction of the acid vapour to avoid cross-contamination of the samples; h) For plasma: repeat step c -g once again;

i) Re-dissolution of the residue in 2 ml 1 M HNO 3 by using a ultrasonic bath over 15 min;

j) Preconditioning of the Re resin with 10 ml 1 M HNO 3, followed by loading the sample solution directly on the top of the frit, i.e. when the sinking fluid level coincides with the upper fringe of the resin;

k) Rinsing of the emptied Teflon beaker with 1 ml 1 M HNO 3 and loading of this solution on the respective column;

In every following chromatography step, the solutions were not applied until the fluid level on the columns reached the upper fringe of the resin, in order to prevent mixing of the different solutions. Extracting chromatography was continued with:

l) Applying 10 ml 1 M HNO 3;

m) Applying 10 ml 4 M HNO 3;

n) Elution of cerium with 3.2 ml of 0.015 M HNO 3; the first 0.7 ml were discarded, the following 2.5 ml collected in a Teflon beaker;

The resulting cerium solution was evaporated to dryness under the same condition as in step (g) above but only for 4 h. Chromatography columns were regenerated for repeated use by consecutive rinsing with 10 ml 0.1 M HCl, 30 ml of the mixture 0.1 M HCl-0.29 M HF, and again 30 ml 0.1 M HCl.

TIMS sample carriers, i.e. single tantalum filament assemblies, were prepared onsite using filament holders (Thermo Fisher Scientific (Bremen) GmbH, Germany) and a zone-refined tantalum ribbon (H.Cross Company, Weekhawken, USA) of 99.999 % purity, 0.28 mm width and 15 µm thicknesses. Tantalum filaments were cut to appropriate length and electro welded to filament holders. The assembled sample carriers were washed in 99.9 % denatured ethanol in an ultrasonic bath and successively baked out in high vacuum over 30 min at an electric current of 4.5 A, corresponding to a temperature of 1600°C. Baking was used both for cleaning the filaments after handling as well as to reduce the isobaric signals of trace impurities of barium from the filament. For application to TIMS, samples were redissolved each in a droplet of ~ 3 µl of concentrated HNO 3 of sub-boiling distilled grade, by placing the Teflon beakers in an ultrasonic bath over 15 min. The sample solution was consecutively transferred from its beaker to the filament and dried at an electric current of 0.5 A.

47 Materials and Methods

Before reuse, the Teflon beakers were cleaned by

Rinsing with tap water and allowing to dry;

Dissolving large remnants in 2 ml HNO 3 conc. (analytical grade) using an ultrasonic bath over 15 min;
Rinsing with distilled water and allowing to dry;

Filling with 5 ml HNO 3 conc. (analytical grade), letting trace impurities dissolve over more than 48 h;
Again rinsing with distilled water and allowing to dry;

Subjecting the beakers to a flow of hot HNO 3 vapour over 4 h;
Finally rinsing with MilliQ water over 24 h and allowing to dry;

Up to 21 samples at a time, including at least one standard sample of 10 ng natural cerium, were assembled in a sample carrier wheel and introduced into the Triton ion source chamber. Prior to measurement, the source chamber was evacuated, aiming at a pressure of ~ 10 -7 hPa.

3.2.3 Isotope dilution technique for tracer concentration calculation

The Isotope Dilution Mass Spectrometry (IDMS) concept is used in the current study, however adapted to four different types of cerium in each sample. As required in the current double tracer study, four types must be considered in each sample:

A: Orally administered tracer: T-136 ( 136 Ce)
B: Intravenously injected tracer: T-138 ( 138 Ce)
C: Reference tracer or spike: T-142 ( 142 Ce)
D: Natural cerium, present in the sample or introduced from the external environment through contamination

The concentration of each type can be calculated straight forward, similar to Equation 2, if the number of stable isotopes is equal to or even greater than the number of types in the sample, including the reference tracer. The calculation demands a high effort due to many mixed products of isotope abundances and ratios. Hence, the calculation was done with the symbolic programming language Mathematica 5 (Wolfram Research Inc., Champaign, IL, USA). The major steps are described in the following.

48 Measurement of Ce tracer concentration in biological samples

The measured sample M, which consists of NM atoms, is composed of four different stable isotopes i ( i=v,x,y,z ) according to the relative abundances hM,I (expressed in atom %):

= ⋅ ( + + + ) = + + + N M N M h ,vM h ,xM h , yM h ,zM N ,vM N ,xM N ,yM N ,zM (12)

The number of atoms NM,i of each isotope i in M is in turn composed of contributions from all types T ( T = A,B,C,D ):

= ⋅ = ⋅ + ⋅ + ⋅ + ⋅ N ,iM N M h ,iM N A h ,iA N B h ,iB NC h ,iC N D h ,iD (13)

If the resulting system is solved with the assumption that the number of atoms of one type is known (the spike), the number of atoms of all other types is obtained in analogy to Equation 2. The number of atoms can be converted to masses by scaling them with atomic weights of the respective isotopic mixtures:

z = ⋅ = ⋅ ⋅ mT NT aw T NT ∑h ,iT im i (14) =vi

with im i as respective isotope masses.

In order to obtain a direct link between the masses mT and measured values, i.e. isotope ratios, the relative abundances hT,i can be described by the isotope ratios RT,ij . This conversion has no effect on the mass values but is relevant for the calculation of their uncertainties. Sometimes the measured isotope ratios are strongly correlated, and their correlation coefficients can be easily included in the uncertainty calculations if the masses are related to the ratios:

N h = ,iT = ,iT R ,ijT (15) N , jT h , jT

R h = ,ijT (16) ,iT + + + R ,viT R ,xiT R , yiT R ,ziT

49 Materials and Methods

The isotope j has a special role in Equation 15 as a reference isotope. In the current study, 140 Ce was chosen for this purpose, since it was the most abundant isotope in all relevant types, excluding the spike.

3.3 Model development for data interpretation

A set of experimental data, although possibly comprehensive, generally consist of discrete measured values. A suitable method can allow interpolation and extrapolation in multidimensional parameter space, offering further insights or enabling predictions beyond the set of previously collected data. The methods, tools, and assumptions which were used to evaluate data in this study are discussed in this section. Two major topics are addressed:

a) Fractional absorption: As introduced in paragraph 2.4, the fractional absorption

fA, i.e. the fraction of substance transferred from the alimentary tract into the systemic circulation, is an important parameter for internal dose estimates. Various techniques are available for the determination of this parameter (Roth et al., 1985), two of them are dealt with in section 4 in this work. b) First order kinetic models: The ICRP uses this class of models to estimate the distribution and retention of most radionuclides in the human metabolism, as well as to calculate the number of radionuclide transformations giving rise to the internal absorbed dose. Since the aim of this work is to support, or improve or even replace the current biokinetic model of cerium, this type of model was used in this study. A software method for simple numeric solution of this class of models is introduced in section 3.3.2 and the model development process is introduced in section 3.3.3.

3.3.1 Fractional absorption

As introduced in paragraph 2.5, the fractional absorption fA, i.e. the fraction of substance transferred from the alimentary tract into the systemic circulation is an important parameter for internal dose estimates. Various techniques are available for the determination of this parameter (Roth and Werner, 1985). Two methods to estimate fractional absorption fA beside the estimation via the modelling process are following: the double tracer technique and the convolution integral technique. Whereas the double tracer method requires only a single blood or urine sample, the convolution integral technique needs information of the time course of both tracer concentration in blood

50 Model development for data interpretation

plasma after oral and intravenous administration until gut uptake is complete. Moreover, this technique provides additional information on the kinetics of gastrointestinal absorption. The advantage of estimating the fractional absorption by these two methods is that it depends only on data and is not constrained by assumptions as the model.

The double tracer technique The double tracer method was introduced by de Grazia. (de Grazia et al., 1965) for the determination of intestinal absorption of calcium. De Grazia originally used radioisotopes of calcium as tracers, but the method is applicable just as well to stable tracers, if there are more than three stable isotopes available of an element. The generalized experimental procedure of the double tracer method consists of the following steps:

Simultaneous administration of tracers, one ingested orally and one injected intravenously after overnight fasting to establish a metabolic reference condition.
A waiting period of 6-24 h to complete the absorption process, time is depending on the form in which the oral tracer was administered, either as solution or with a meal.
Collection of one urine or plasma sample and measurement of the tracer concentration.

136 The fractional absorption ( fA) can be determined from the ratio of the oral Ce to the intravenously injected 138 Ce in a plasma or cumulated urine sample taken 24 h after simultaneous administration, according to the following equation:

z m = po iv f A * (17) ziv m po

136 138 where z = Ce (z po ) and Ce ( ziv ) tracer concentrations in plasma or urine 24 h after 136 138 administration; m = Ce ( mpo ) and Ce ( miv ) amounts administered. But after 24 h the plasma concentration is very small, huge uncertainties are the consequence. The deduction of the fA equations is shown in Appendix I.

Convolution integral technique The convolution integral focuses on the kinetics of the absorption process in plasma in comparison to the double tracer technique, which evaluates the concentration data in plasma or urine after completed absorption. The tracer concentrations in plasma are described by time-dependent concentration functions cpo (t) and civ (t) , which are normalised on the respective administered amount

51 Materials and Methods

of tracer. These functions can be derived by stepwise interpolation or by fitting a suitable curve to the data that was used in this work and will be explained in section 4.3.

In general, civ (t) is observed to decline after its bolus injection into the circulation. In contrast, cpo (t) rises from an initial zero value to a peak value and declines afterwards.

The function cpo (t) can be interpreted as a linear superposition of infinitesimal short bolus entries a( τ) dτ of oral tracer from the gut into the blood plasma, which are afterwards cleared from the plasma in the same way as the intravenous tracer. This relation can be formulated as the convolution integral

t = τ −τ τ c po t)( ∫ a )( civ (t )d , (18) 0 which is a special case of a Volterra integral equation. It may be solved by a Laplace transformation, yielding a simple equation for the transformed functions:

C s)( A s)( = po (19) Civ s)(

where A(s) , Cpo (s) and Civ (s) is the Laplace Transform of a(t) , cpo (t) and civ (t) , respectively. The reverse Laplace transformation leads to the function a(t) , which describes the absorption rate; its time integral from 0 to ∞ is the total fractional absorption f A. The reverse transformation can however be complicated, depending on the analytical forms of the equations describing cpo and civ . Instead of an analytical solution, it is also possible to apply a numerical approach to the reverse Laplace transformation. In the current work a short FORTRAN program written by Paul Roth, former scientist of the Helmholtz Zentrum München was used for the calculation of the absorption rates and fractional absorption values for the investigations with stable isotopic tracers of cerium.

52 Model development for data interpretation

3.3.2 Approaches and software used for modelling in this work

The modelling process used in this work consists of several steps:

• First a new model is devised or a previously existing model is modified according to a previous evaluation. • The model is then fitted to the sets of measured data.

In this modelling process the software package SAAM II (Barrett et al., 1998a) was applied. In the individual analysis the model parameters are estimated for each person. SAAM II was originally developed for the development and solution of individual kinetic models. The following description of the computational features is taken from the SAAM II User’s guide and from tutorials provided with the software. SAAM II fits a model to data in a series of iterations. In these it modifies the values of the adjustable parameters to obtain the best agreement between the calculated model predictions and the data. The best fit produced by minimizing an objective function R θ )( that is calculated for each iteration:

2 1 J N j (y − h θ ))( R θ)( = (log[ V (h θ ),( y ,v )] + , ji , ji ) (20) ∑∑ , , jiji , ji j θ M j=1i = 1 V , (h , jiji ),( y , ji ,v j ) with θ (estimated) vector of adjustable parameters (transfer rates and blood volume) M total number of data points J number of data sets (measurements in blood plasma and urine)

Nj number of data points in the j-th data set vj variance parameters for the j-th data set yi,j the i-th datum of the j-th data set hi,j (θ) the model prediction corresponding to yi,j

SAAM II implements a generalised variance model for all data points without individual uncertainty values. The variance model is based either on a compartmental model estimates or data values. Even if the input data file for SAAM II contains explicit uncertainties for each data point, the type of the variance model must be specified. The data based option, described in Equation 21, and was exclusively used in the current work:

53 Materials and Methods

= + C V , ji (y , ji ,v j ) v j (* A B * y , ji ) (21)

For a weighting factor vj = 1, a combination of the weighting parameters ( A,B,C ) = (0, B,2) is equal to a constant relative standard deviation of B, whereas ( A,B,C ) = ( A,0,0) defines a constant absolute standard deviation A for all data points with unspecified variance. The latter option was used as a default according to the uncertainties given as absolute uncertainties; however, explicit individual uncertainty values do override the value of A, making the value of A arbitrary. The variance model also allows using the specified uncertainties without further weighting, i.e. vj = 1 (‘absolute’ variance model), or the estimating of the weighting factor from model and data according to Equation 21 for each data set j (‘relative’ variance model):

2 N j − θ 1 (y , ji h , ji ))( v j = (22) ∑ θ N j=1 V , (h , jiji ),( y , ji )1,

The differences of the weighting factor vj for the data sets can indicate the differences in their influence on the result of the fit. On the other hand each set of data can be assigned to a different value for the fractional standard deviation reflecting the assumed uncertainties of each data set. For each adjustable parameter an initial value as well as upper and lower boundaries, in which the parameter value can be varied, have to be specified before the fitting process. If a parameter value is known a priori (like the physical decay constant) it is possible to indicate it as fixed and this parameter value is not changed during the fitting process. During each iteration, the algorithm searches for parameter values that result in a reduced value of the objective function R( θ) relative to that of the previous iteration. This optimization is performed by the modified Gauss-Newton method, while the Rosenbrock integrator is used to solve the differential equations. The iteration process is continued until the convergence criteria are satisfied or the maximum number of iterations is reached. As a result, the software gives the final parameter estimate and the associated covariance matrix.

54 Model development for data interpretation

3.3.3 Model development process

In the current study, several compartment model candidates were evaluated, inspired by certain observations of measured data, the current ICRP biokinetic model, and experiences during the modelling process itself. Therefore, detailed information on the development of models is given together with these observations on section 4.4, while the tools and concepts used for model evaluation are discussed in the current paragraph. The general approach to each modelling cycle contained the following steps:

A new model structure was designed, or a previously evaluated model was altered according to observations made from the measured data.
The model was built with the modelling software SAAM II.
Initial parameter values were adopted from ICRP publications 67 (ICRP, 1993) and 100 (ICRP, 2006) if applicable.
The built up model was solved and fitted to each investigation data set.
Parameters boundaries were set to zero (lower limit) and to 10 times the starting values (upper limits).
If a parameter reached the upper limit during fitting, the respective upper limit was increased one-time by a factor 10.
If the model led to an improvement, certain statistical parameters calculated by SAAM II were evaluated to compare quantitatively the goodness of the fit.

The modelling software SAAM II (Saam Institute 1992-2002) (Barrett et al., 1998b) was used to describe and solve compartmental models in the current work, as well as to fit models to data and thus evaluate the respective parameters. This software allows constructing compartmental models by drawing the compartments and transfers; the associated differential equations are generated by the software, according to the model structure. Experimental data, including uncertainties, can be provided to SAAM II by pre-formatted text files. Multiple data sets, i.e. measured data of different tracers in different compartments can be handled at once during a fit of the model. For a given experimental setup (duration, tracer administration…) the model is then solved numerically.

After a successful fit SAAM II reports the optimised parameter values pˆ k together with σ an estimated standard deviation k . This standard deviation is derived from the diagonal elements of the covariance matrix of parameters, which is calculated by SAAM II during the fitting process:

σ = [ − 2 ] k E ( pk pˆ k ) (23)

55 Materials and Methods

Apart from the subjective assessment of a fit quality by comparing visually data and model graphs, three quantities generated by SAAM II were used to judge the relative fit quality of different model candidates. The first of these quantities is the minimised value of the objective function R( θ) as defined in Equation 20. For any unique data set with accordingly unique unweighted variances, a lower value means that the residuals, i.e. the differences between each data point and its respective model estimate, are smaller on average; thus, the modelled curve is closer to the data. Two other quantities were used to compare the models: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). They are calculated by SAAM II as follows:

1 N AIC = (R θ )( + log( 2π )) + θ (24) 2 M

N log( M ) BIC = R θ )( + log( 2π ) + θ (25) 2M

In these expressions, M is the total number of data points as defined above and Nθ is the number of adjustable parameters θ. Both expressions AIC and BIC are based on the minimised value of the objective function R( θ), but penalise the number of adjustable parameters.

56 Improved Dosimetry of cerium

3.4 Improved Dosimetry of cerium

In ICRP publication 67, dose coefficients for 141 Ce and 144 Ce were published, because these isotopes of cerium are the most common by produced ones in nuclear technology, and have a half-live of 32.5 d and 284 d, which make them relevant for internal dose calculations after accidental exposure of the environment. 144 Ce has a radioactive daughter nuclide 143 Pr in the decay chain (Figure 4), while 141 Ce has a direct radionuclide transformation to the stable 141 Pr (Figure 5). In ICRP publication 67 (ICRP, 1993) the equivalent and the effective dose coefficients after ingestion of 144 Ce have been calculated based on the compartmental model described in section 2.5. There values are shown in Table 12 and illustrated in Figure 6.

144 = 58 Ce (T 2/1 284 3. d)

1 2 3 4 5 6 133.5

- β (49.35 keV, 19.6 %)

100 β- (65.26 keV, 4.6 %)

80.1 β- (90.23 keV, 75.8 %)

59 144 = 59 Pr( T 2/1 28.17 m)

7 8 9 10 2185 - β (26.69 keV, 1.08 %)

2084 β- (89.47 keV, 1.17 %)

- 696 β (122 keV, 97.7 %) 144 60 Nd (stable ) 0.0

Figure 4: Decay scheme of 144 Ce and daughter product according to the ICRP publication 38 (ICRP, 1983). Excitations energies of the nuclides are stated in keV, as are the mean β- energies; the levels are not drawn to scale. The γ emission yields Y are 1) 0.248 %, 2) 0.468 %, 3) 0.0119 %, 4) 1.64 %, 5) 0.0396 %, 6) 10.8 %, 7) 0.774 %, 8) 0.3 %, 9) 0.00659 % and 10) 1.48 %. X-rays, Auger electrons and internal conversion electrons are not shown.

57 Materials and Methods

141 = 58 Ce (T )2/1 501.32 d)

β- (129 keV, 70 %) 145.4 1 - 141 β (180 keV, 30 %) 59 Pr( stable ) 0.0

Figure 5: Decay scheme of 141 Ce. according to the ICRP publication 38 (ICRP, 1983). Excitations energies of the nuclides are stated in keV, as are the mean β- energies; the levels are not drawn to scale. The γ emission yield Y is 1) 48 %.

Table 12: Ingestion dose coefficients and effective dose of 144 Ce given in ICRP 67 (ICRP, 1993).

Organ HT(70) (Sv/Bq)

Adrenals 1.6·10 -11 Bladder Wall 3.0·10 -11 Bone Surfaces 3.3·10 -10 Brain 1.2·10 -11 Breast 1.2·10 -11 St Wall 1.1·10 -09 SI Wall 3.7·10 -09 ULI Wall 1.6·10 -09 LLI Wall 3.5·10 -09 Kidneys 2.0·10 -11 Liver 9.6·10 -10 Lungs 1.3·10 -11 Muscle 1.8·10 -11 Ovaries 7.5·10 -11 Pancreas 1.9·10 -11 Red Marrow 1.9·10 -10 Skin 1.4·10 -11 Spleen 1.7·10 -11 Testes 1.7·10 -11 Thymus 1.2·10 -11 Thyroid 1.2·10 -11 Uterus 3.8·10 -11 Remainder 9.5·10 -11

Effective dose 5.2·10 -09

58 Improved Dosimetry of cerium

ULI Wall: 23.5 % LLI Wall: 68.5 % St Wall: 2.7 % Bladder w all: 0.013 % Bone surface: 0.028 % Breast: 0.005 % Liver: 0.9 % Lungs: 0.03 % Red Marrow : 0.47 % Skin: 0.002 % Thyroid: 0.01 % Remainder: 0.09 %

144 Figure 6: Contribution of the single target regions wT·H T(50) to the effective dose for ingestion of Ce according to the values given by the ICRP.

Several of the tissue dose coefficients covered by the tissue weighting factors are subject to a special treatment. The gonad dose included in the effective dose coefficients given by the ICRP is the higher value of both ovaries and testes dose coefficients, weighted by the gonads weighting factor. As recommended by the ICRP publication 67 (ICRP, 1993), the colon dose coefficient is composed of the dose coefficients of its sections by Hcolon = 0.57 · HULI + 0.43 · HLLI . Furthermore the lung dose coefficient is composed of the dose coefficients to the thoracic tissues, i.e. Hlung = 0.333· Hbronchial + 0.333· Hbronchiolar + 0.333· Halveolar-intestinal + 0.0001· Hlymphatics . The dose coefficients of Extrathoracic tissues (ET) of the respiratory tract are included in the remainder region, combined as HET = 0.001· Hanterior nose + 1· HET2 +

0.001· Hlymphatics . The regions ET2 are posterior nasal passages, larynx, pharynx and mouth. The remainder dose coefficient is composed of the dose coefficients of all further target regions, weighted by their relative mass contribution. The respective target regions and their masses are given in Table 13. The uterus is taken to contribute only to the female effective dose coefficients in the current study.

59 Materials and Methods

Table 13: Masses of tissues contributing to the remainder dose coefficient as used in the SEECAL software.

Target region Mass male (g) Mass female (g)

Adrenals 14 14 Brain 1400 1200 Small intestine wall 640 600 Kidneys 310 275 Extrathoracic tissue 15.47 12.71 Muscle 28000 17000 Pancreas 100 85 Spleen 180 150 Thymus 20 20 Uterus 80 80

The target regions gonads, i.e. upper large intestine and lower large intestine, stomach, liver and red marrow consists of a higher dose than the others in which the subject matter can be deposited. Some compartments of the HAT model are not included in the SEECAL SEE values, nor are the oesophagus included as a target region in the SEECAL software. Therefore, the following adoptions were made: Oral cavity and oesophagus were introduced as additional source regions S. For the purpose of dose calculation, the oral cavity was identified with the brain, and the oesophagus with the thymus. Both organ pairs are in close proximity to each other and have similar sizes; this may result in a small error if the same SEE values are used within each region pair. Furthermore, the masses of these tissues are small, and the error introduced by removing them from the “other tissues” source region is small. The following equations were used for the relevant values of SEE(T ←S) , with existing SEECAL values marked by *:

SEE(T ←oral cavity) = SEE*(T ←brain) SEE(T ←oesophagus) = SEE*(T ←thymus) SEE(brain ←oral cavity) = 0 SEE(oesophagus ←oesophagus) = SEE*(thymus ←thymus) SEE(thymus ←oesophagus) = 0

The calculation of the thymus and oesophagus dose coefficients is therefore not identical in that the latter includes the self-absorbed dose component

Uoesophagus (50)·SEE(oesophagus ←oesophagus) , whereas this contribution is neglected

60 Errors and uncertainties

for the thymus dose. The brain dose coefficient is also calculated without self absorption, i.e. the brain, as a surrogate for the oral cavity, is used as a source region for all target regions except for itself. Furthermore, the upper large intestine is identified with the colon, i.e. UULI (50) = URC (50) . The lower large intestine is taken to be composed of the left and recto sigmoid colon, i.e. ULLI (50) = ULC (50) + URS (50) .

3.5 Errors and uncertainties

Uncertainties of the measurements are calculated based on the recommendations in the “Guide to the expression of uncertainties in measurement” (GUM) (ISO et al., 1995) to give a quantitative and reproducible indication of the quality of the measurement results done in this work. In general, components of uncertainty must be categorized according to the method used to evaluate them. “Type A” standard uncertainties are uncertainties, which are evaluated by statistical means from repeated observations of single quantities. This type of uncertainty was used for the error calculation in tracers. Uncertainties u(y) of a quantity y can be expressed as standard deviations of the mean sM(y) of repeated observations qk:

n − 2 ∑(qk qM ) u y)( = s q)( = k =1 (26) M n(n − )1 with

n = 1 qM ∑qk (27) n k =1 and represents the mean of a number n of observations. If uncertainties cannot be estimated from repeated observations by statistical mean, then they are called “Type B” uncertainties. A Type B evaluation of a standard uncertainty is usually based on scientific judgement using all of the relevant information available, which may include: previous measurement data, experience with general knowledge of the behaviour and property of relevant materials and instruments, manufacturer’s specifications, data provided in calibration and other reports, and uncertainties assigned to reference data taken from handbooks. Uncertainties in tracer concentration in stock solutions were calculated according to Type B. Type B uncertainties are treated in the same way as Type A standard uncertainties.

61 Materials and Methods

The “combined standard uncertainty” uc(y) of the measurement results obtained from a functional relation f of different influencing quantities xi are stated.

N ∂f N −1 N ∂f ∂f u 2 y)( = ( ) u 22 (x ) + 2 u(x u() x () xr , x ) (28) c ∑∂ i ∑ ∑ ∂ ∂ i j i j i=1 xi i=1ij += 1 xi x j

Each u(x i) is a standard uncertainty evaluated as Type A evaluation or Type B evaluation. The combined standard uncertainty uc(y) is an estimated standard deviation and characterizes the dispersion of the values. The combined standard uncertainty is based on a first-order Taylor series approximation. If all influencing quantities are uncorrelated the second term with the correlation factor r(x i,x j) can be neglected and Equation 28 reduces to

N ∂f u 2 y)( = ( ( ) u(x )) 2 (29) c ∑ ∂ i i=1 xi

The standard uncertainty uc(y) is thus simply a sum of squares representing the variation of the output estimate y generated by the standard uncertainty of each input estimate xi. Depending on the probability distribution of a measurand, different estimations of its excepted value can be given in a Typ A evaluation. Commonly, a normal or at least symmetrical distribution is assumed for a measurand, and the estimate of the expectation value is stated as the arithmetic mean µa of the measurement results. In case that only a small number of observations is available as in the current study, the weighted arithmetic mean µa can be calculated in the current study, in order to avoid a biased value of µa due to a single uncertain observation. The weighted arithmetic mean is calculated as n

∑ x wkk µ = k =1 a n (30)

∑ wk k =1

With the weight wk being the inverse square of the uncertainty attributed to the value xk, i.e. it inverse variance.

62 Development and optimization of sensitive Ce analytics

4 Results and discussions

4.1 Development and optimization of sensitive Ce analytics

For the development and optimization of the whole measurement technique for cerium in biological samples, first of all the TIMS analysis of cerium in aqueous solutions had to be focused on. For this reason, different ribbon materials for the filament assemblies and different kinds of sample applications were tested. Several combinations of the material of the ribbon (rhenium, tungsten, and tantalum) as well as different methods for sample coating with silica gel or graphite, single filament (Evaporation and Ionization at the same surface temperature) or double filament (sample evaporation and ionization are separated, ionizations happens on the hot surface of the ionization filament) method were compared. Several combinations of ribbon materials and different methods for sample coating and ionizing were checked as shown in Table 14.

Table 14: Combinations of ribbon material and coating possibility used for single and double filament method, Re (rhenium), W (tungsten), Ta (tantalum).

EVAPORATION & RIBBON MATERIAL COATING IONIZATION

double Evaporation ionization silica gel graphite single filament filament

Re X X X W X X Ta X X Re Re X Re W X W Re X Ta Re X Ta Ta X

63 Results and discussions

Natural cerium standard solutions were measured corresponding to 10 ng and 1 ng on the ribbons. The ratios 136 Ce/ 140 Ce, 138 Ce/ 140 Ce and 142 Ce/ 140 Ce were assessed. The best signal results were achieved for the Ta-Ta double filament method by drying the sample with a current below 500 mA and without coating of the sample with silica gel or black lead. In this way, a sufficient signal and a constant trend of the signal during the measurement were achieved. Furthermore, the interferences due to barium and neodymium stemming from the biological samples as well as from the ribbon material were significantly reduced when using tantalum rather than rhenium. The sample is heated slowly to a temperature where the ion beam formation can be expected. The heating procedure for the ionisation filament is 225 mA/min up to 4800 mA and then 50 mA/min, the evaporation filament is heated up to 1200 mA in steps of 55 mA/min until a signal of 142 Ce can be observed which is sufficient to focus the ion beam. Furthermore, measurements with different amounts of cerium in aqueous solutions were performed to assess the precision and the accuracy of the method. Stability of the measurement technique was controlled by measuring cerium standard solutions (10 ng and 1 ng) with a known enrichment of the fraction of the ratios of the four isotopes from the manufacturer. The results were compared with the reference value given by the International Union of Pure and Applied Chemistry (IUPAC). An absolute deviation below 1 % was achieved for the amount of 10 ng. In Figure 7 the relative deviation of the measured ratios in comparison to the values given by the IUPAC is shown. In the first weeks of the measurements the method was not good enough to be in a range below 1 % deviation (see Figure 7, Section a). After modification of the method (optimization of cup positions and heating procedure) the measurements are below 1 % deviation (Figure 7, section b). The low deviation and the narrow range of variation over time indicate the accuracy and precision of the measurement method.

64 Development and optimization of sensitive Ce analytics

0,03

0,02

0,01

0,00

-0,01

136 Ce/ 140 Ce -0,02 138 140 a) b) Ce/ Ce 142 Ce/ 140 Ce -0,03 1% deviation relative deviation in comparison to IUPAC to comparison in deviation relative

-0,04 04 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72

sample number

Figure 7: Relative deviation of cerium standard solution ratios in comparison to the desired value of the IUPAC is below 1 %; a) first weeks of measurements with TIMS; b) better results after modification of the method.

With the amount of 1 ng of cerium only a relative deviation of 3-5 % was achieved because of the considerably low signal to noise ratio and the shorter measuring time due to a faster evaporation of the sample. Beside the standard solution, also ratios of the tracer solutions of T-136, T-138, T-140 were measured. The isotopic composition of the measured ratios, 136 Ce/ 140 Ce, 138 Ce/ 140 Ce and 142 Ce/ 140 Ce, in comparison to the expected values as given by the manufacturer are shown in Table 15. The deviation of all measured ratios was below 1%, which could be regarded as a very good proof for accuracy and precision of the method. Isotope ratios of all tracers were measured by TIMS and compared to the corresponding manufactures certificates. The results show only small differences. The TIMS measured ratios were used for an evaluation of TIMS. Type A relative standard uncertainties of the tracer measurements were calculated as 0.07 – 0.8 %. Tracer concentrations in stock solutions were measured by the Central Inorganic Analysis Service of the Helmholtz Zentrum München with inductively coupled plasma optical emission spectrometry (ICP-OES). Type B relative standard uncertainties from one to three measurements of each tracer solution were estimated to be ~ 2 %.

65 Results and discussions

Table 15: Measured ratios of tracer solutions and theoretical ratios.

Tracer 136/140 138/140 142/140

136 Ce 0.47570 ± 0.00142 0.01087 ± 0.00013 0.06993 ± 0.00412 0.47703 ± 0.00101 0.01083 ± 0.00020 0.06991 ± 0.00026 0.47495 ± 0.00120 0.01083 ± 0.00008 0.07013 ± 0.00033 0.48697 ± 0.00096 0.01093 ± 0.00017 0.07018 ± 0.00021 0.47553 ± 0.00096 0.01081 ± 0.00010 0.07102 ± 0.00018 0.47812 ± 0.00117 0.01091 ± 0.00010 0.07059 ± 0.00034 0.46126 ± 0.00099 0.01088 ± 0.00011 0.06994 ± 0.00003 0.47126 ± 0.00095 0.01090 ± 0.00001 0.07009 ± 0.00001 0.47616 ± 0.00094 0.01085 ± 0.00008 0.06879 ± 0.00033 0.47713 ± 0.00084 0.01085 ± 0.00010 0.07009 ± 0.0000

Mean 0.47441 ± 0.00104 0.01087 ± 0.000112 0.07006 ± 0.00021

Expected Value 0.47664 0.01090 0.070093

Deviation +0.47 % +0.33 % +0.04 %

138 Ce 0.00073 ± 0.00002 0.74786 ± 0.00106 0.04536 ± 0.00020 0.00071 ± 0.00002 0.74854 ± 0.00067 0.04536 ± 0.00009 0.00072 ± 0.00003 0.74552 ± 0.00114 0.04572 ± 0.00024 0.00072 ± 0.00011 0.74922 ± 0.00267 0.04550 ± 0.00044 0.00072 ± 0.00001 0.75002 ± 0.00438 0.04498 ± 0.00021 0.00071 ± 0.00001 0.74621 ± 0.00092 0.04568 ± 0.00033 0.00072 ± 0.00011 0.74125 ± 0.00703 0.04512 ± 0.00028 0.00072 ± 0.00002 0.74598 ± 0.00608 0.04499 ± 0.00037 0.00072 ± 0.00001 0.74530 ± 0.00118 0.04567 ± 0.00034 Mean 0.000717 ± 0.000022 0.746616 ± 0.002853 0.04535 ± 0.00288 Expected Value 0.000717 0.745386 0.045690 Deviation +0.08 % -0.16 % +0.74 %

142 Ce 0.00345 ± 0.00003 0.01625 ± 0.00046 15.57227 ± 0.03996 0.00337 ± 0.00004 0.01661 ± 0.00008 15.60606 ± 0.05954 0.00313 ± 0.00003 0.01678 ± 0.00021 15.44559 ± 0.03467 0.00335 ± 0.00003 0.01512 ± 0.00084 15.54353 ± 0.01420 0.00346 ± 0.00003 0.01701 ± 0.00021 15.71904 ± 0.00766 0.00335 ± 0.00003 0.01663 ± 0.00004 15.57064 ± 0.01485 0.00335 ± 0.00003 0.01665 ± 0.00008 15.58277 ± 0.01505 0.00336 ± 0.00003 0.01678 ± 0.00016 15.54049 ± 0.01480 0.00333 ± 0.00003 0.01664 ± 0.00009 15.58876 ± 0.01690 0.00336 ± 0.00002 0.01678 ± 0.00017 15.59325 ± 0.00920 0.00313 ± 0.00003 0.01726 ± 0.00021 15.54265 ± 0.01262 0.00333 ± 0.00003 0.01732 ± 0.00019 15.56689 ± 0.01502 0.00331 ± 0.00012 0.01659 ± 0.00007 15.54825 ± 0.00700 0.00313 ± 0.00002 0.01670 ± 0.00011 15.50788 ± 0.00961 Mean 0.00331 ± 0.00003 0.01665 ± 0.00021 15.56629 ± 0.01936 Expected Value 0.00333 0.01667 15.64666 Deviation +0.59 % +0.09 % +0.51 %

66 Development and optimization of sensitive Ce analytics

After the optimization of the measurement method for cerium in aqueous solutions, the next step was to devise the method to measure cerium from biological samples. First a methodology for extraction of cerium from biological samples, e.g. blood plasma and urine, using column chromatography was proved; an optimization of the chromatography technique was established by using different acids for elution with a known amount of cerium concentration and followed by measuring the elution in order to decide which the best acid for choice is. Once cerium could be separated by column chromatography according to the scheme shown in chapter 3.2.2, it was tested whether the RE resin could be re-used after several regeneration steps. It was reported that a mixture of 0.1 M HCl and 0.29 M HF could be a very effective removing agent for residual light rare earths (cerium) from the TRU resin (Pin and Bassin, 1992). As the RE resin is very similar to the TRU resin, the following regeneration experiments were performed. By using one RE resin column, an alternating solution of 100 ng of T-136 and of 100 ng T-138 (composition see Table 10) was loaded onto the resin. The isotopes 136 Ce and 138 Ce, respectively, were separated and collected in Teflon beakers, which contained a known amount of 142 Ce as the “spike”. After each elution step, a cleaning procedure of the resin by applying 10 ml 1 M HCl-0.29 M HF and 30 ml 1 M HCl was carried out. This procedure of alternating loading and cleaning was repeated ten times. Figure 8 shows the comparison of the expected ratio and the measured ratio of 136 Ce/ 140 Ce and of 138 Ce/ 140 Ce for both tracers. For tracer 136 Ce, the measured ratio of 136 Ce/ 140 Ce deviated about 1.36 % (mean, n = 5) from the expected value. For the ratio 138 Ce/ 140 Ce, the deviation was 3.0 % (mean, n = 5). For tracer 138 Ce, the measured ratio 136 Ce/ 140Ce varied about 1.43 % (mean, n = 4) and 138 Ce/ 140 Ce deviated about 0.5 % (mean, n = 4) from the expected value. Consequently, by cleaning the column resin with a sequence of 10 ml 1 M HCl followed by 30 ml 0.1 M HCl-0.29 M HF and finally 0.1. M HCl, nearly all remaining cerium could be removed, thus allowing a multiple use of the resin since no practically contamination is coming from the previously treated sample.

67 Results and discussions

0,50

0,48

Ce 0,46 140 T-138

Ce/ expected ratio

136 T-136 0,04 Ratio Ratio

0,02

0,00

0 1 2 3 4 5 6

0,80

0,76

Ce 0,72 140

Ce/ T-136

138 expected ratio T-138

Ratio Ratio 0,04

0,00 0 1 2 3 4 5 6 Sample number

Figure 8: Comparison of the expected and measured ratios of 136 Ce/ 140 Ce and 138 Ce/ 140 Ce for both of the tracer solutions T-136 and T-138 after the pre-concentration using Re resin-columns in successive loading and cleaning steps.

68 Development and optimization of sensitive Ce analytics

Subsequently, the microwave digestion method was optimized for destroying organic material from the biological samples in order to uncover cerium. The instructions from the microwave manufacturer for digestion, especially of blood plasma samples, could not be adopted as temperature and heating time (130 °C / 8 min, 155 °C / 5 min, 170°C / 12 min) were not sufficient to totally digest blood plasma samples. After evaporation to dryness, the sample residues were found not to be completely dissolvable. Therefore, tests with plasma samples were carried out in order to find the optimal temperature as well as the duration of the procedure. The temperature was increased stepwise to 230 °C and the digestion duration was also increased to a maximum 55 min. A further increase of temperature and time was not possible due to device limits of the microwave system. The residues after evaporation of the digestion solution to dryness seemed to be, at first, totally dissolvable. However, despite the modification of temperature and time, the measurement of plasma samples was not optimally reproducible (Figure 9).

1,0 T-136 T-138

0,8

0,6

0,4

0,2 amount of cerium tracer (ng/0.5 ml)

0,0 0 1 2 3 4 5 6 7 8 9 sample number

Figure 9: Measurement of eight aliquots of the same blood plasma sample before optimization of sample preparation.

69 Results and discussions

For this reason, the dried samples obtained after the first microwave procedure were redissolved again, and the new procedure of the microwave system was repeated in order to be sure that all organic compounds of the blood sample were destroyed. In order to test the new procedure, a tracer study with a volunteer was performed: onto the oral application and the intravenous injection of T-136 and T-138, respectively, 20 ml of blood was withdrawn and centrifuged to obtain the blood plasma. Then eight aliquots of 0.5 ml each were spiked with T-142. Finally, the sample digestion was performed with respect to the newly developed procedure as described in section 6.2. In Figure 10, the reproducibility of the data is shown for the oral tracer T-136 and the intravenous injected tracer T-138. The results of the repeated measurements were all in the same range and consistent with each other under consideration of the standard deviations. The arithmetic mean values ± standard deviation of T-136 was found to be about (0.075 ± 0.008) ng and for T-138 (0.49 ± 0.013) ng, respectively. Hence, the reproducibility for biological samples is warranted by the measurement method. The values lay within the confidence interval.

0,6

0,5

T-136 0,4 T-138 Mean

0,1 amount of cerium tracer (ng/0.5 ml)

0,0 0 1 2 3 4 5 6 7 8 9 sample number

Figure 10: Reproducibility of a blood plasma sample after optimization of the microwave system .

70 Sample measurements

After developing the measurement method it was possible to measure

- non biological samples with an uncertainty < 1 % - biological samples with an uncertainty < 11 %.

Having verified the reliability by the developed procedure, it was possible to proceed with the measurements of the samples collected in the tracer investigations.

4.2 Sample measurements

All measured data collected in this thesis are shown in the following two sections 4.2.1 and 4.2.2. Before the uncertain quantities are explained related to orally and intravenously administered tracers included isotope ratios, tracer concentrations and the amount of tracer solution applied during the investigations. Uncertainties are calculated according to chapter 3.5. The amount of tracer solution applied to test persons is dependent on the type of tracer application and the applied volume. Ampoules and drinking cups were weighted to measure the amount of solution injected or ingested. For intravenous injection, the measurement standard uncertainty of the tracer solution amount applied was determined by the weighting process and estimated to be ~ 0.2 % (relative uncertainty). The relative measurement standard uncertainty for oral application is larger, since multiple pipetting processes with up to three pipettes were involved. Its estimates range from 0.55 – 0.76 %, with a minimal absolute uncertainty of 0.08 ml. Both standard uncertainties are qualified as Type B, since they are based on manufacturer’s data. Input quantities relevant to sample drawing were estimated as (1.027 ± 0.006) g/ml, urine density as (1.02 ± 0.015) g/ml (ICRP, 2002). The collected amount of urine after weighting was measured initially with a standard uncertainty of 0.25 g. This corresponds to relative uncertainties in the range of 0.01 % to 8 %. An additional component of uncertainty concerning urine collection is associated with non-uniform urine production and the limited number of voids per day or sampling interval. In the current study, each concentration measurement in urine is attributed to a sampling period of fixed duration, usually 4 h, 12 h and 24 h. Usually, the start and end of each sampling period do not coincide with a urinary void; in contrast, a test person may delay a void over the end of a sampling period and thus shift a part of the produced urine amount from one sampling period to the next. A relative standard uncertainty of 17 % for this effect is adopted from the ICRP estimate of the number of

71 Results and discussions

voids per day of 6 (ICRP, 1995b). This uncertainty component is an exception to the “measurement” uncertainty concept. During sample preparation, volumes of 1 – 20 ml urine and 0.5 – 0.8 ml blood plasma were determined by pipetting from collected samples. The attributed relative uncertainties were 0.6 % and 1 % for urine and blood plasma volume, as long as completely fluid samples were processed.

4.2.1 Measurements in blood plasma samples

In the following Figures, the measurement results of investigated blood plasma samples are illustrated. In Figures 11 and 12 the intravenous tracer concentration in blood plasma is shown in a linear and in a log scale, respectively.

Volunteer 1 60 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 40 Volunteer 10 Volunteer 11 Volunteer 12

20 intravenous tracer concentration in plasma [%/kg]

0 0 10 20 30 40 50

time after administration [h]

Figure 11 : Time course of cerium T-138 concentration in blood plasma after intravenous injection for 12 different test persons.

72 Sample measurements

60 Volunteer 1 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 40 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12

20 intravenous tracer in plasma [%/kg]

0 0,1 1 10 100

time after administration [h]

Figure 12 : Time course of cerium T-138 concentration in blood plasma after intravenous injection for 12 different test persons in a log scale up to 48 h.

73 Results and discussions

0,014

Volunteer 1 0,012 Volunteer 2 Volunteer 3 Volunteer 4 0,010 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 0,008 Volunteer 9 Volunteer 10 Volunteer 11 0,006 Volunteer 12

0,004 oral tracer concentraion in plasma (%/kg) 0,002

0,000 0,1 1 10 100

time after administration [h]

Figure 13: Time-course of cerium T-136 concentration in blood plasma after ingestion up to 48 h after ingestion for all 12 test persons in a log scale.

74 Sample measurements

0,014

Volunteer 1 Volunteer 2 0,012 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 0,010 Volunteer 7 Volunteer 8 Volunteer 9 0,008 Volunteer 10 Volunteer 11 Volunteer 12 0,006

0,004

oral tracer concentration in plasma (%/kg) 0,002

0,000 0,0 0,5 1,0 1,5 2,0

time after administration [h]

Figure 14: Time-course of cerium T-136 concentration in blood plasma after ingestion within the first 2 h after ingestion for all 12 test persons .

In order to establish a comparison between experiments with different amounts of tracer, the tracer concentration values in plasma are given as % of the administered tracer per kg plasma. For most plasma samples, the relative uncertainty was 3.5 – 5 % (median 4.4 %). The amount of tracer solutions administered to test persons is dependent on the type of tracer application (oral or intravenous) and the applied volume. Ampoules were weighted to measure the amount of solutions injected. For intravenous injections the measurement standard uncertainty of the tracer solution amount applied was determined by weighting process and estimated to be around 0.2 % (standard uncertainty). Clearance of cerium from the investigated blood plasma was quite rapid in all subjects. This fast blood clearance can be based on two reasons: Firstly, the fast blood clearance can be explained through special mechanisms in the case of intravenous administration: Aeberhardt injected cerium colloids into rats and saw the same characteristic in blood

75 Results and discussions

clearance. 85 % of injected 144 Ce was excreted after 5 minutes and 88 % after 30 minutes after administration. The injected cerium can be in two states of art; it can stay “free” in the blood plasma and it can be fixed in the endothelial reticulum of different organs (Aeberhardt et al., 1962). From this it follows, that cerium may be transported partly bound to serum proteins and partly incorporated into phagocytes, which are taken mostly into the reticuloendothelial system by the phagocyte mechanism and deposited here. This phenomenon has been postulated by Nakamura in rats (Nakamura et al., 1997)and by Aeberhardt. (Aeberhardt et al., 1962), Sotogaku et al. (Sotogaku et al., 1999). The second effect can be that cerium ions are taken up into the human aortic endothelial cells (HAECs) vesicular pathways in a manner similar to Fe 2O3, Y 2O3, and ZnO particles. It is worthwhile to consider possible effects of intracellular solubility (Gojova et al., 2009). In Figures 13 and 14, the oral tracer concentrations in blood plasma for the whole sampling period and within the first two hours after injection are shown. Ten minutes after injection the cerium concentration in blood plasma reaches its maximum value, afterwards the plasma concentration of cerium rapidly declines similarly to the very fast clearance observed with the i.v. tracer.

4.2.2 Measurements in urine samples

In the following Figures 15 - 18 the cumulative urinary excretion for all data sets is shown. The highest proportion of urinary excretion of both tracers was in the first eight to twenty-four hours after administration, indicating that the excretion process is very fast. The broad range of excretion is an indicator for the individuality of humans, depending on the metabolism of each individual as well as his/her drinking behaviour. The uncertainty for urine samples also comprehends the combined measurements uncertainty and is for most samples around 19 %, including that the collected amount of urine gathered from the test person was weighed with a standard uncertainty of 0.2 g with a corresponding to a relative standard uncertainty of 0.05 – 10 %. Another aspect concerning the urine samples is the non-uniform production of urine and the individual and limited number of voids per day.

76 Sample measurements

120

100

80 Volunteer 1 Volunteer 2 Volunteer 3 Volunteer 4 60 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 40 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 20 cumulative tracer amount in urine (%)

0 0 20 40 60 80 100 120 140 160 time after administration (h)

Figure 15: Cumulative urinary excretion of cerium T-138 after intravenous injection for all 12 volunteers.

10

Volunteer 1 Volunteer 2 8 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 6 Volunteer 8 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 4

intravenous tracer excretion rate [%/h] 2

0 0 20 40 60 80 100 120 140 160

time after administration [h] Figure 16 : Urinary excretion rate of cerium T-138 after intravenous injection in urine for all 12 test persons.

77 Results and discussions

1

0,1 Volunteer 1 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 0,01 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 cumulative urinary excretion of oral tracer (%) 0,001 0 20 40 60 80 100 120 140 160 time after administration (h)

Figure 17: Cumulative urinary excretion rate of cerium T-136 after ingestion for different volunteers.

0,06

Volunteer 1 Volunteer 2 0,05 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 0,04 Volunteer 7 Volunteer 8 Volunteer 9 Volunteer 10 0,03 Volunteer 11

0,02 oral tracer urinary excretion (%)

0,01

0,00 0 20 40 60 80 100 120 140 160

time after administration [h] Figure 18: Urinary excretion rate of oral tracer T-136 after ingestion for 11 different volunteers.

78 Sample measurements

4.2.3 Comparison of the own newly measured human data with model predictions of the ICRP and of Taylor and Leggett

In the following Figures 20 – 23 the collected human data of this work and the model predictions of the current cerium model of the ICRP and from Taylor and Leggett are shown. A rapid clearance from plasma of the intravenously injected tracer (T-138) was observed in the data presented here, with a characteristic time of about 30 minutes. Figure 20 give the comparison of the whole data set with the curves obtained using the current ICRP model (red dashed line) and that one proposed by Taylor and Leggett (solid black line). For oral tracer administration T-136 in blood plasma the ICRP model overestimates the human data and the peak is out of alignment. In contrast to T-138 the Taylor and Leggett model underestimates the human data. For the urinary excretion the greatest deviations were observed. Indeed, the amount of systemic cerium (injected tracer) excreted over one week ranged from 50 – 90 % of the injected amount. In the current models only a minimal portion is excreted over such a short period of time. For the intravenous tracer administration T-138 and oral tracer administration T-136 in urine the ICRP and the Taylor and Leggett model underestimate the human data. Cuddihy (Cuddihy et al., 1975) reports for beagle dogs a similar plasma clearance course with a half-time of about 25 min like the human plasma clearance. But only 2 % of the initial amount of administered cerium amount goes to urine (Cuddihy et al., 1975) for beagle dogs. The high difference can only be explained that humans do not behave like beagle dogs in metabolism. Errors in measured or administered tracer concentration can be excluded. The concentrations were controlled via ICP-OES measurements in the institute of ecological chemistry, Helmholtz Zentrum München. These results were used for tracer amount concentrations. Furthering, errors in the measurement technique can be excluded like shown in Chapter 4.1. In addition two data sets, Ce 10 44 20 and Ce 10 45 21, of urine were also measured as control via ICP-OES in order to monitor the range of tracer amount in the samples (see Figure 19). In Table 16 the cerium concentration in urine measured for two data sets via ICP-OES and TIMS are shown. The resulting values were in the same magnitude. The quality check of tracer amounts in the cerium solutions and biological samples was successful.

79 Results and discussions

Table 16: Cerium concentration in urine measured via ICP-OES, split-up for tracer and natural cerium not possible, and measurement via TIMS for the urine samples taken after tracer administration.

Cerium concentration natural Cerium T-138 T-136 time (h) ICP-OES (ng/ml) TIMS (ng/ml) TIMS (ng/ml) TIMS (ng/ml)

Ce 10 44 20 0.965 0.2482 0.7310 0.0351 8 0.335 0.2591 0.3284 0.0095 12 0.187 0.3010 0.1912 0.0037 24 0.145 0.1988 0.0287 0.0029 48 0.1986 0.1901 0.0030 0.0001 72

Ce 10 45 21 0.814 0.2100 0.6302 0.0040 4 0.947 0.1400 0.8784 0.0046 8 0.625 0.1984 0.1638 0.0033 12 0.208 0.2141 0.0551 0.0078 24 0.158 0.1940 0.0100 0.0022 48 0.263 0.2310 0.0182 0.0004 72

1,2

1,0

0,8

0,6 ICP-OES

0,4

Ce 10 44 20 0,2

0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2

1,2

1,0

0,8

0,6 ICP-OES

0,4 Ce 10 45 21

0,2

0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2

TIMS

Figure 19: Correlation between cerium in urine samples measured with TIMS and ICP-OES for experiment Ce 10 45 21 and Ce 10 44 20.

80 Sample measurements

Volunteer 1 100 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 10 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 ICRP Taylor/Leggett

1

intravenous tracer concentration in plasmatracer (%/kg) intravenous 0,1 1 10 100

time after adminsitration (h)

Figure 20: Time-course of cerium T-138 concentration in blood plasma after ingestion for all 12 test persons, including prediction of the two current cerium models, ICRP and Taylor/Leggett for intravenous tracer.

0,030

Volunteer 1 0,025 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 0,020 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 Volunteer 10 0,015 Volunteer 11 Volunteer 12 ICRP Taylor/Leggett 0,010 tracer concentration (%/kg) concentration tracer

0,005

0,01 0,1 1 10 100

time after adminsitration (h) Figure 21: Time-course of cerium T-136 concentration in blood plasma after ingestion for all 12 test persons, including prediction of the two current cerium models, ICRP and Taylor/Leggett for oral applied tracer.

81 Results and discussions

100

10

Volunteer 1 1 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 0,1 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 Volunteer 10 0,01 Volunteer 11 Volunteer 12 ICRP Taylor/Leggett cumulate intravenous tracer concentration (%) concentration tracer intravenous cumulate 0,001 0 20 40 60 80 100 120 140 time after adminitration (h)

Figure 22: Cumulative urinary excretion rate of cerium T-138 after intravenous injection for all 12 different volunteers, including prediction of the two current cerium models, ICRP and Taylor/Leggett for intravenous tracer .

1e+1

1e+0 Volunteer 1 Volunteer 2 Volunteer 3 1e-1 Volunteer 4 Volunteer 5 Volunteer 6 1e-2 Volunteer 7 Volunteer 8 Volunteer 9 1e-3 Volunteer 10 Volunteer 11 Volunteer 12 1e-4 ICRP Taylor /Leggett

1e-5

cumulate oral tracer concentration (%) concentration tracer oral cumulate 1e-6

1e-7 0 20 40 60 80 100 120 140 160 time after administraion (h) Figure 23: Cumulative urinary excretion of cerium T-136 after oral administration for all 12 volunteer, including prediction of the two current cerium models, ICRP and Taylor/Leggett for oral tracer application.

82 Fractional absorption without compartment modelling

4.3 Fractional absorption without compartment modelling

Double tracer technique After detection of the biological sample through thermal ionisation mass spectrometry, a biokinetic parameter, e.g. fractional absorption, can be established without compartment modelling First the fractional absorption can be calculated with the double tracer technique. Ratios of oral tracer concentration over intravenous tracer concentration, each in %/kg are calculated. After the oral ingestion the tracer can be absorbed in the human body or be excreted directly in faeces. The resulting values of the 12 volunteer tests are shown in Table 16 together with those from the convolution integral technique. The assumption that both tracers have the same metabolic characteristics and are cleared similarly from blood plasma is strengthened by the small variation in tracer concentration ratios within each experiment.

Convolution integral technique For the convolution integral technique fitted functions, rather than stepwise linearly interpolated functions, were used for the description of the tracer concentration data. The reason for this was the noise in many data sets; large variations in oral and intravenous concentrations would likely yield absorption rate functions with several local maxima and minima, thus possibly obscuring the underlying trend of oral absorption into and clearance from blood. In contrast, short-term variations have little influence on the fitted functions and correspondingly also on the calculated absorption rate. The number of fitting points available for fitting a clearance curve to plasma data was limited to 10 – 14, which was depending on the amount of samples available. The fit functions used for intravenous tracer data are exponential decay functions with eight parameters as shown in Equation 31.

= + ⋅ −bt + ⋅ −dt + ⋅ −ht + ⋅ −nt tf )( y0 a e c e g e m e (31)

Oral tracer data were more difficult to fit, since the fitting function had to allow for an asymmetric peak. An inverse polynomial function was used as shown in Equation 32.

a b tf )( = y + + (32) 0 t t 2

Although the use of exponential decay functions bears resemblance to first-order kinetic compartment models, the approach is different and model-independent for the convolution integral technique:

83 Results and discussions

Functions are selected based on their number of free parameters and their ability to fit the data, rather than according to a specified (compartmental) model structure;
Parameters of i.v. and p.o. functions are not linked, thus negative absorption is possible. However, this effect on cumulative fractional absorption is limited, since tracer concentrations are not extrapolated beyond 50 h.

Fractional absorption values, as well as absorption rates, were calculated from the fitted functions explained in section 3.3.1. Figure 24 shows the time course of the resulting absorption rates. It can be seen that in all investigations the main absorption takes place within the first one and a half hours after injection, although the peak range of the absorption rate is highly variable in a range from ∼ 0.001 – 0.00043 %/min. Female test persons (1, 4, 5, 6 and 10) have higher peaks in the absorption rate (p ∼ 0.002 in a two- tailed t-test).

0,030 Volunteer 1 Volunteer 2 Volunteer 3 0,025 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 0,020 Volunteer 8 Volunteer 9 Volunteer 10 Volunteer 11 0,015 Volunteer 12

absorption rate (%/h) 0,010

0,005

0,000 0 5 10 15 20

time after injection (h)

Figure 24: Absorption rates of cerium tracers .

84 Fractional absorption without compartment modelling

The results on fractional absorption are shown in Table 17. They are in a good agreement with the results from the double tracer evaluation. The mean fractional absorption determined by the double tracer technique is (1.13·10 -3 ± 2.83·10 -4), thus only 4.4 % higher than with convolution integral technique (1.08·10 -3 ± 4.42·10 -4).

Table 17: Total fractional absorption of cerium, determined by double tracer technique and convolution integral technique.

Absorbed fraction Investigation Absorbed fraction Convolution integral Personal code Double tracer technique technique

Ce 07 24 04 9.59·10 -4 8.43·10 -4 Ce 07 29 05 9.22·10 -4 8.56·10 -4 Ce 07 30 06 9.54·10 -4 1.66·10 -3 Ce 10 35 10 1.10·10 -3 9.05·10 -4 Ce 10 36 12 1.45·10 -3 1.28·10 -4 Ce 10 38 14 1.77·10 -3 1.33·10 -3 Ce 10 39 15 1.46·10 -3 1.47·10 -3 Ce 10 40 16 9.99·10 -4 9.38·10 -4 Ce 10 41 17 1.06·10 -3 1.32·10 -3 Ce 10 42 18 9.07·10 -4 8.27·10 -4 Ce 10 44 20 8.36·10 -4 9.27·10 -4 Ce 10 45 21 1.13·10 -3 1.71·10 -3

Mean 1.13·10 -3 1.08·10 -3 Standard deviation ± 2.83 ± 4.42·10 -4

85 Results and discussions

4.4 Tracer kinetics and the corresponding development of a new compartmental model

From the total of 19 tests only those where both tracers T-136 and T-138 have been administered, were taken into account for compartment modelling with SAAM II. First the two already existing models from the ICRP and Taylor/Leggett were represented in SAAM II including the corresponding transfer coefficients given by literature. Figure 1 (Chapter 2.4) shows the simplified ICRP model combined with the ICRP GIT- model in a compartmental structure including transfer coefficients together with data points presented in Table 8. The model is a first-order kinetic model with constant transfer coefficients. The second model from Taylor and Leggett and its compartment structure as set up in SAAM II is shown in Figure 2 with the corresponding coefficients in Table 9. The two existing models of the ICRP and the TLM differ from each other. The model of the ICRP has been the official one for the biokinetics of cerium until now and so it has been used as a starting point for the analysis of the measured human data. The complex TLM model is for the amount of data in this work, that means only urine and plasma samples, not identifiable. As presented in the previous section, the intravenous tracer concentration in plasma is described well by a triple exponential decay. Data and the general fit curve of the ICRP prediction for intravenous administration of volunteer 5 are presented in Figure 25 as an example. Data from this investigation are similar to the general pattern of the other investigations. The figure clearly shows that the plasma clearance predicted by the current ICRP systemic model structure and plasma clearance half-life is not in accordance with the data. It overestimates the data. An initial distribution volume V D of 2.4 l can be estimated from the extrapolated tracer concentration cp,i.v. at the time of injection and the plasma density ρPlasma :

100 V = (33) D ⋅ ρ c vip .., Plasma

Data of volunteer 5 including the fit of the ICRP model for these data are shown in Figures 26 and 27. Here data were directly fitted with the model of the ICRP.

86 Tracer kinetics and the corresponding development of a new compartmental model

60

50

40

30

20

tracer concentration in plasma (%/kg) 10

0 0 10 20 30 40 50

time after administration (h)

ICRP model prediction , T 1/2 = 6 h, plasma volume 3.3 l

Fit of experimental data, triple exponential decay, T 1/2,a =3.72 min,

T1/2,b =2.41 h, T 1/2, c=66.97 h

● Experimentally m easured data (volunteer Ce 10 35 10)

Figure 25: Experimental data and prediction of the ICRP model for the time course of cerium after intravenous injection. Experimental data us given exemplarily for one volunteer 5 (Ce 10 35 10).

87 Results and discussions

1e+2 T-138 fit of ICRP model 1e+1 T-136 fit of ICRP model 1e+0

1e-1

1e-2

1e-3 tracer amount in plasma (%/kg) plasma in amount tracer 1e-4

1e-5 0,1 1 10 100 time after administration (h)

Figure 26: Human data from volunteer 5 of intravenous and oral tracer in plasma including the ICRP model prediction.

1e+2

1e+1

1e+0

1e-1

1e-2

1e-3

1e-4 T-138 fit of ICRP model

cumulative tracer amount in urine (%) urine in amount tracer cumulative 1e-5 T-136 fit of ICRP model

1e-6 0 20 40 60 80 100 120 140 time after administration (h)

Figure 27: Cumulative human data from volunteer 5 of intravenous and oral applied tracer in urine including the ICRP model prediction.

88 Tracer kinetics and the corresponding development of a new compartmental model

In contrast, the use of a triple exponential decay function similar to Equation 31 results in a good fit. In order to be able to describe this fit by a model, it is necessary to change the structure of the systemic model. This can be accomplished by adding at least one flux from the distribution compartment (skeleton, liver and other tissues) back to the transfer compartment. In an initial modelling attempt, two systematic models were proposed as modifications to the current ICRP model. Their structures are shown in Figure 28 and the intention of the individual changes is explained briefly. Black arrows symbolise transfers adopted from the ICRP and red arrows indicate newly introduced transfer chains. Both models were coupled to the new HAT model, which was introduced in ICRP publication 100 (ICRP, 2006).

89 Results and discussions

Tracer

Transfer

Other Skeleton Liver Tissues

Urinary bladder

Urine a)

Tracer Transfer

Other Skeleton Liver Tissues

Urinary bladder

b) Urine

Figure 28: a) Reflux-Model, including flux from Skeleton, Liver and other tissues back to the Transfer compartment. b) Excretion model based on the reflux model and adopts detailed urinary excretion pathway structures.

90 Tracer kinetics and the corresponding development of a new compartmental model

Both models as well as the ICRP model were fitted to the data sets of the 12 investigations using the “data relative” variance model. Apart from the subjective, optical comparison of the fitted curves to data, the resulting values of the objective function, the Akaike information criterion (AIC) and the Schwarz-Bayesian information criterion (BIC) were compared. The modelled absorption of the oral tracer into plasma was too slow for the reflux model. The transfer parameters kSI-colon (from small intestine

(SI) to upper large intestine or right colon) and kSI-transfer (from Si to the transfer compartment) are linked by the fractional absorption according to Equation 9. The fractional absorption is in turn influenced by the fitted ratio of oral intravenous plasma concentration, which is quite well defined due to a long period of measurements. The discrepancy between the measured data and the model arises because the fractional absorption is low, and the accordingly small value of kSI-transfer results in the assumption of a slow transfer of oral tracer into the transfer compartment. As an alternative, the possibility of substance transfers from the compartments of the alimentary tract to the transfer compartment, as implemented in the HAT model could be used. This option was tested by introducing additional transfer chains from oral cavity and stomach. The measured concentrations of the intravenously injected tracer cannot satisfactorily be modelled with the current ICRP model of cerium. It can be seen in Figure 26 exemplary on the experiment of volunteer 5 that the plasma clearance for both tracers, intravenously and orally applied, predicted by the current ICRP systematic model structure does not be in line with the human data, not even approximately. Also for urinary excretion the data and the ICRP model does not fit together. It is shown in Figure 27 that the model underestimates the data enormously.

Because of the disagreement between human data and the model prediction of the ICRP model it is necessary to improve the model for a better description of the cerium metabolism in humans.

It is required to change the structure of the systemic model. This can be accomplished by adding at least one flux from the distribution compartments (here centralised in organs) back to the transfer compartment blood (see Figure 28, Reflux Model). This model was coupled to the new HAT model, which was introduced in ICRP publication 100 (ICRP, 2006), by a direct transfer from the small intestine to the transfer compartment. In general the three compartments “skeleton”, “liver” and “other tissue” of the ICRP cerium model was deprived to their attribution and assigned to an abstract organ compartment. Furthermore a transfer coefficient between the transfer compartment blood and the urinary bladder was estimated, because of the existing artery vesicales superiors , which is in charge of the blood supply of the urinary bladder.

91 Results and discussions

In figure 29 the results for volunteer 5 are shown exemplarily for the intravenous and oral tracer in plasma and Figure 30 shows the urinary excretion for the experiment for volunteer 5 including the fit of the reflux model shown in Figure 28. For the intravenous tracer concentration in plasma the fit is quite suitable with the data points excepting the first data point, but for the oral tracer concentration in plasma the fit underestimates the data completely. For urinary excretion the modified model describes the model predictions very well. The modelled absorption of the oral tracer in plasma was too slow. The reason for this was later attributed to the choice of variable parameters modelling absorption, i.e. k Stomach →small intestine , kSmall intestine →colon . The effect of the choice of variable parameters can be seen in Figures 32 and 33. The transfer parameters ksmall intestine →colon (from small intestine (SI) to right colon or upper large intestine) and ksmall intestine →transfer (from SI to the transfer compartment) are linked by the fractional absorption according to Equation 9. The fractional absorption is in turn quite well-defined by a long period of investigation. The discrepancy between data and model arises because the fractional absorption is low, and the accordingly small value of ksmall intestine →transfer causes a slow transfer of oral tracer into the transfer compartment. As a consequence, the transfer parameter from stomach to SI is increased during fitting to unreasonable high values to speed up the absorption. This problem can be overcome to a large extent by fixing kStomach →small intestine and varying ksmall intestine →colon instead, which is related to ksmall intestine →transfer . As an alternative, the possibility of substance transfers from other compartments of the alimentary tract to the transfer compartment, as implemented in the HAT model, could be used. This option was tested by introducing an additional transfer chain from the stomach to the transfer compartment. The resulting fit was acceptable, but no physiological explanation is known for absorption already in the stomach. Similar to the fit results, the initial distribution volume is estimated by all models to be in the range of 1.4 – 3.5 l. This is consistent with the normal plasma volume of 3.0 l for a 70 kg adult person (Guyton and Hall, 2006), scaled to the test persons´ variation in the body weight and haematocrit, i.e. the fraction of blood volume composed of red blood cells. Thus, the transfer compartment can likely be identified with blood plasma; henceforth both being treated as synonyms. Summing up the following issues are essential for the model proposed in this work. The measured concentrations of intravenously injected and oral ingested tracer cannot satisfactory be modelled with the current ICRP biokinetic model of cerium. This issue is solved by introducing bidirectional transfer between the transfer compartment (blood plasma) and the organs compartment (skeleton, liver and other tissues). Furthermore, the selection of parameters for variation is crucial for a successful fitting of the absorption process from the alimentary tract. And last, due to the limited duration of the investigations, long-term whole-body retention can only be covered by assumptions and therefore it is based on the upper large intestine turnover rate adopted by ICRP publication 67.

92 Tracer kinetics and the corresponding development of a new compartmental model

1e+2

1e+1

1e+0

1e-1 T-138 reflux model prediction 1e-2 T-136 reflux model prediction

1e-3

(%/kg) plasma in amount tracer 1e-4

1e-5 0,1 1 10 100 time after administratrion (h)

Figure 29 : Human data of experiment 5 of intravenously and orally applied tracer in the blood plasma and the predicting fit of the model.

1e+3

1e+2

1e+1

1e+0

1e-1

1e-2

1e-3

1e-4

1e-5 T-138 reflux model prediction 1e-6 T-136 cumulative tracer amount in urine (%) urine in amount tracer cumulative reflux model prediction 1e-7

1e-8 20 40 60 80 100 time after administration (h) Figure 30: Cumulative urine excretion of experiment 5 of intravenously and orally applied tracer and the predicting fit of the model .

93 Results and discussions

4.5 Proposed new model

As a result of the model adoptions of the previous section the best correspondents to the measured data were achieved with the model presented in Figure 31. The new proposed more physiologic model was fitted individually to the data of each of the twelve studies, resulting in twelve parameter sets including the mean parameter set considered by modelling with SAAM II. Because of the underestimation of the oral tracer in blood in the current ICRP model, there must be a fast discharge flow through the stomach, indicated in the value of the transfer coefficient from the stomach to the small intestine. Also for calcium the flow through the stomach is very fast in order to get the quick absorption in the intestine. Because of the chemical similarity between cerium and calcium, as listed in Table 18, the same behaviour can be adopted.

Table 18: Chemical characertistics of calcium and cerium (Evans, 1990).

Characteristic calcium cerium

Coordination number 6 - 12 6 – 12 Coordination geometry highly flexible highly flexible Donor atom O>>N>>S O>>N>>S Ionic radius 1.00 – 1.18 0.86 – 1.22 Bond type ionic ionic Coefficient of diffusion 1.34 1.3

Because of the chemical similarities it is possible that cerium replaces calcium in a set of reactions (Birnbaum et al., 1970; Evans, 1990). The gastrointestinal absorption of trace elements, including calcium and magnesium is known to occur in different phases. First and for this work most important is the intraluminal phase with its chemical reaction and interaction with the contents of stomach and intestines (Abdulla and Chmielnicka, 1989). Cerium also can compete with calcium for binding sites on proteins and membrane, including intestine cell walls (Miller, 1994). Because of that it could be possible that cerium can resign very fast from the intestine and be in direct interaction with the blood circulation.

The estimates of the fractional absorption coefficient f, which were calculated from kSI- colon and kSI -transfer by Equation 9, can either be calculated as the weighted mean from individual investigations, or from the expected values of the parameters kSTO-transfer and kSTO-SI . The former alternative is preferred, since in the latter case, the resulting fA values

94 Proposed new model

have a greater significance than the above transfer rates for bioassay measurements of urine excretion, as well as for cerium retention in body beyond a few days and its consequences for dosimetry. Further on, a new compartment plasma diffusible was defined for the circulation with rapidly exchanging extravascuclar fluids. Soon after introduction of a cerium tracer into blood plasma, the tracer is largely available for diffusion into extravascuclar fluids (Heard and Chamberlain, 1984; Vander et al., 1977). Under steady-state conditions, however, most of the plasma cerium is bound to proteins, with α-globulin having a particularly high cerium-binding capacity (Griffin and Matson, 1971). Two plasma compartments are needed to depict a gradual shift of a large portion of plasma cerium to no diffusible plasma proteins. Cerium injected or absorbed from extravascuclar spaces is assigned to the diffusible compartment within plasma, from which it transfers rapidly to the extravascuclar spaces and red blood cells. Immediately after intravenous injection of cerium into adult humans, the cerium disappears into the second blood compartment within a half-life of 4.8 min and returns to the main blood compartment with a half-life of 12 h. For dosimetric calculation the plasma diffusible compartment was added to the remainder, because it is only a fast exchange within the blood circulation and has no ascendancy to organs and fit in the general structure given by the ICRP. The plasma diffusible compartment is a second blood compartment for fast interactions within the blood. The uncertainties for the model parameters were based on the standard deviation of the mean, according to Equation 26. The uncertainties of the 8 parameters of the new model to all investigations (n = 12) were as low as 2.4 – 7.9 % of the parameter value range if calculated according to Equation 26, but 10 -16 % if calculated according to Equation 28. The respective expected values of the standard deviation of the mean of 12 samples would be ~ 10 % of the range for a rectangular distribution, and ~ 6.5 % for a normal distribution cut off at 99 % coverage, according to the GUM. Thus, in order to avoid an underestimation of the uncertainty, the standard deviation of the mean was used as the parameter uncertainty.

95 Results and discussions

Figure 31: Proposed new HMGU biokinetic model of cerium, including the adopted human alimentary tract model from the ICRP publication 100 (ICRP, 2006). Blue arrows illustrate new defined transfer coefficients in comparison to the ICRP systematic model. Orange arrows illustrate new values of the transfer coefficients in comparison to the ICRP HAT model.

96 Proposed new model

Figures 32 and 33 show again exemplary the result for the new model for intravenous and oral applied tracer in blood plasma and urinary excretion for the investigation of volunteer 5. The model fit describes the data very well for both investigations, oral and intravenous, and blood plasma and urinary excretion. The underestimation of oral tracer in plasma is resolved by changing the value of the transfer coefficients kStomach-small intestine and ksmall intestine-right colon . The ICRP value for kStomach-small intestine is for all elements predicted as 2 h -1. In this work the ingested fluid is water with a small amount of cerium citrate, so no calorimetric liquid. The fasting test persons drank the solution and it can be estimated that the transfer from the stomach to the intestine is very fast. The resulting parameter set of test person 5 is shown in Table 19. Parameter and model fits of the remaining 11 volunteers are shown in Appendix II.

Table 19: Parameter estimation from fitted data of investigation volunteer 5.

Parameter Expected value absolute uncertainty (h -1) (h -1)

-01 -02 ksmall intestine-right colon 2.95·10 1.24·10 +01 +01 kStomach – Small intestine 40·10 1.50·10

kBlood-Plasma diffusible 9.22 1.55 -02 kPlasma diffusible-Blood 0.12 2.66·10

kBlood – Skeleton 0.69 0.14

kBlood – Liver 0.41 0.08

kBlood – other Tissues 0.28 0.06 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 0.56·10 1.03·10 -02 -03 kOrgans – Urinary bladder 1.81·10 9.15·10 -04 -05 ksmall intestine-blood 2.60·10 1.09·10 Plasma mass 2.20 0.19 -04 fA 0.00113 1.284·10

97 Results and discussions

100

T-138 10 HMGU model prediction T-136 HMGU model prediction 1

0,1

0,01 tracer amount in plasma (%/kg) plasma in amount tracer 0,001

0,0001 0,1 1 10 100 time after administration (h) Figure 32: Human data of experiment volunteer 5 of intravenously and orally applied tracer in blood plasma and the predicting fit of the new proposed model.

1e+3

1e+2

1e+1

1e+0

1e-1

1e-2

1e-3

cumulative tracer amount (%) amount tracer cumulative T-138 HMGU model prediction 1e-4 T-136 HMGU model prediction 1e-5 0 20 40 60 80 100 120 140 time after administration (h) Figure 33: Cumulative urine excretion of volunteer 5 of intravenously and orally applied tracer and the predicting fit of the new proposed model.

98 Proposed new model

In the following Figures 34 - 37 all data sets are shown with the mean parameter set of the new biokinetic cerium model. The comparison of the model and data for intravenously injected cerium in Figure 34 shows that the set of mean parameters presented in Table 20 yields an appropriate fit to the collected data. The uncertainties given are standard deviations of the mean for all investigations. The predicted cerium concentration in plasma can be described as a triple exponential decay function, with clearance half-lives of 4.14 min, 34.092 min, and 1.95 d for fractions of 75 %, 24 % and < 1 % of the injected cerium, respectively.

Table 20: Parameter estimates from fitted data for 12 investigations. * Fixed parameters adopted from ICRP .

Parameter, Expected value absolute uncertainty All investigations (h -1) (h -1)

KOesophagus fast – Stomach * 720

KOesophagus slow - Stomach * 120

kMouth – Oesophagus fast * 1620

kMouth – Oesophagus slow * 180

kBlood-Upper large intestine * 0.0574

-01 -02 ksmall intestine-right colon 5.42·10 1.24·10 +01 -01 kStomach – Small intestine 4.23·10 1.84·10

kBlood-Plasma diffusible 8.80 1.55 -02 kPlasma diffusible-Blood 0.06 2.66·10

kBlood – Skeleton 0.08 0.014

kBlood – Liver 0.05 0.01

kBlood – other Tissues 0.03 0.007 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 8.76·10 1.03·10 -02 -03 kOrgans – Urinary bladder 1.81·10 9.15·10 -04 -05 ksmall intestine-blood 2.60·10 1.09·10 Plasma mass 2.20 0.19 -03 -04 fA 1.18·10 0.04·10

99 Results and discussions

Volunteer 1 Volunteer 2 100 Volunteer 3 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 10 Volunteer 10 Volunteer 11 Volunteer 12 HMGU

1

intravenous tracer concentration in plasma tracer (%/kg) intravenous 0,1 0,1 1 10 100

time after adminsitration (h)

Figure 34: Intravenous tracer concentration data in plasma and the respective estimate of the proposed new HMGU cerium model with the set of mean parameters after eight hours of investigation.

0,014

Volunteer 1 0,012 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 0,010 Volunteer 6 Volunteer 7 Volunteer 8 0,008 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 0,006 HMGU

0,004 tracer concentration (%/kg) concentration tracer

0,002

0,01 0,1 1 10 100 time after adminsitration (h) Figure 35: Oral tracer concentration data in plasma and the respective estimate of the proposed new HMGU cerium model with the set of mean parameters after eight hours of investigation.

100 Proposed new model

e (%) 100

Volunteer 1 Volunteer 2 Volunteer 3 10 Volunteer 4 Volunteer 5 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 HMGU

1 0 20 40 60 80 100 120 140 cumulative intravenous tracer concentration in urin time after adminitration (h)

Figure 36: Cumulative intravenous tracer concentration in urine and the respective estimate of the new HMGU cerium model with the set of mean parameters.

1

0,1

Volunteer 1 Volunteer 2 Volunteer 3 Volunteer 4 Volunteer 5 0,01 Volunteer 6 Volunteer 7 Volunteer 8 Volunteer 9 Volunteer 10 Volunteer 11 Volunteer 12 HMGU

cumulative oral tracer concnentration0,001 in urine (%) 0 20 40 60 80 100 120 140

time after administraion (h)

Figure 37: Cumulative oral tracer concentration in urine and the respective estimate of the proposed new HMGU cerium model with the set of mean parameters.

101 Results and discussions

4.6 Implications of the new model for dosimetry

4.6.1 Dosimetry with the old ICRP model

The newly proposed cerium biokinetic model as presented in the section before shows differences in comparison to the current systematic model of the ICRP in the following points.
The structure of the systematic model has been changed with reference to the changes including recycling by bidirectional transfers to increase the cerium concentrations in blood plasma. Because of this radioisotopes of cerium will be continuously redistributed over the whole body. This results in a postponement in the number of transformations between the source region “other tissues” and “bone”.
Furthermore the new systematic model is coupled to the new human alimentary tract model (HATM) of ICRP publication 100 (ICRP, 2006) while the ingestion dose coefficients of the ICRP in ICRP publication 67 (ICRP, 1993) were calculated using the GI tract model. This change implies two new source organs, i.e. oral cavity and oesophagus for dose calculation.
The current ingestion of dose coefficients of 144 Ce was calculated for the ICRP reference man, neglecting gender differences. The radiation dose assessment of

incorporated radionuclide is based on the nuclear transformation number US over 50 y for adults and up to 70 y for children, calculated using biokinetic models and the specific absorbed fractions (SAFs). The current dose coefficients (ICRP, 1993; ICRP, 1995a) are derived on the basis of the SAFs calculated by using Medical Internal Radiation Dose (MIRD)-type mathematical phantoms developed by the Oak Ridge National Laboratory (ORNL) (Christy and Eckerman, 1987). With the publication of the human respiratory tract model (HRTM), SAFs for photons and absorbed fractions (Slutsky et al., 1999) for electrons were given in ICRP publication 66 (ICRP, 1994). Those photon SAFs were implemented into the used computer program SEECAL (Eckerman, 1993). The gastrointestinal (GI) tract model was updated in ICRP publication 100 (ICRP, 2006) with the new alimentary tract model (HATM), which also provides some AFs for electrons (ICRP, 2006).

102 Implications of the new model for dosimetry

Reproducibility of ICRP ingestion dose coefficients The reproducibility of the ICRP ingestion dose coefficients (ICRP, 1993) was tested by using the cerium ICRP model and the modelling procedure to ensure correct calculation procedures. The small deviation between the dose coefficients from ICRP publication 67 (ICRP, 1993) and the cerium biokinetic model (“Ce biokinetic”) are probably on account of rounding uncertainties either in the parameter sets or during numerical computation of the number of transformations in 50 y with SAAM II. By setting the model parameters to 2 digits instead of 4 digits accuracy changes dose coefficients by up to 1 %. A further verification was an independent recalculation with the same software and parameters performed by Dr. WeiBo Li (Li et al., 2010), who used a different numerical approach to calculate the number of transformations in 50 y, but the same SEE values. The resulting dose coefficients showed also only small deviations from the ICRP dose coefficients. This indicates that the general modelling and calculation procedure is assumed to be correct due to reproducibility of the published ingestion dose coefficients. The comparison of ingestion dose coefficients as calculated according to ICRP recommendations as of publication 67 is shown in Table 22. In Table 21 the number of nuclear transformations in source regions for 144 Ce and its decay product after acute ingestion using the ICRP models for the adult is shown, which are used in this work.

Table 21: Number of nuclear transformations in source regions for 144 Ce and its decay products after ingestion.

Source 144 Ce 144m Pr 144 Pr

UB_Cont 2.7·10 -2 4.8·10 -4 2.7·10 -2 C_Bone-S 2.5·10 3 44 2.5·10 3 T_Bone-S 2.5·10 3 44 2.5·10 3 ST_Cont 3.6·10 3 55 2.5·10 3 SI_Cont 1.4·10 4 2.5·10 2 1.4·10 4 ULI_Cont 4.8·10 4 8.5·10 2 4.8·10 4 LLI_Cont 8.6·10 4 1.5·10 3 8.6·10 4 Liver 8.2·10 3 1.5·10 2 8.2·10 3 Blood 16 0.28 16 Other 3.3·10 3 58 3.3·10 3

103 Results and discussions

Table 22: Comparison of ingestion dose coefficients (Sv/Bq), calculated according to the ICRP recommendations of publication 67 (ICRP, 1993) and calculated with SAAM II including deviation between both.

Target regions Published Modelled Deviation (% ICRP 67 Ce biokinetics ICRP 67) Adrenals 1.6·10 -11 1.6·10 -11 +1 Bladder wall 3·10 -11 3.0·10 -11 -1 Bone surface 3.3·10 -10 3.3·10 -10 +0 Brain 1.2·10 -11 1.2·10 -11 -2 Breast 1.2·10 -11 1.2·10 -11 +0 ST wall 1.1·10 -09 1.1·10 -09 +0 SI wall 3.7·10 -09 3.7·10 -09 +0 ULI wall 2.3·10 -08 2.3·10 -08 -2 LLI wall 6.7·10 -08 7.7·10 -08 +1 Kidneys 2·10 -11 2.0·10 -11 +0 Liver 9.6·10 -10 9.6·10 -10 +0 Lungs 1.3·10 -11 1.3·10 -11 +1 Muscle 1.8·10 -11 1.8·10 -11 -1 Pancreas 1.9·10 -11 1.9·10 -11 +2 Red marrow 1.9·10 -11 1.9·10 -10 +0 Skin 1.4·10 -11 1.4·10 -11 +0 Spleen 1.7·10 -11 1.7·10 -11 +0 Testes 1.7·10 -11 1.7·10 -11 +1 Thymus 1.2·10 -11 1.2·10 -11 +0 Thyroid 1.2·10 -11 1.2·10 -11 +0 Uterus 3.8·10 -11 3.8·10 -11 -1 Remainder 9.5·10 -11 9.5·10 -11 -1

Effective dose 5.2·10 -09 5.2·10 -09 +1

Gender differences due to SEE values The SEECAL software (Eckerman, 1993), which provides the standard reference man SEE values for the calculation of dose coefficients, includes also SEE values for a female standard person. In order to be able to distinguish between SEE-relate and model related differences in dose coefficients, it is suggestive to evaluate the differences in dose coefficients resulting from the use of these two sets of SEE values.

104 Implications of the new model for dosimetry

Table 23 shows the dose coefficients for sexes, male and female, calculated from identical numbers of transformations, which were obtained from the ICRP cerium model. Dose coefficients calculated with female SEEs are increased by 3 – 23 % over their respective male equivalents. For the most organs the masses are lower for the female reference person, but that is not in accordance with the increase of the SEE values.

Table 23: Dose coefficients (Sv/Bq) for male and female reference person calculated from the ICRP publication 67 cerium model including male and female specific SEEs.

Deviation of female dose coefficients from male dose coefficients (%)

Target regions Dose coefficients Dose coefficients Deviation with male SEEs with female SEEs

Adrenals 1.61·10 -11 1.81·10 -11 +11 Bladder wall 3.01·10 -11 3.33·10 -11 +9 Bone surface 3.32·10 -10 3.345·10-10 +0.7 Brain 1.20·10 -11 1.43·10 -11 +16 Breast 1.21·10 -11 1.31·10 -11 +7 ST wall 1.13·10 -09 1.46·10 -09 +22 SI wall 3.71·10 -09 3.89·10 -09 +5 ULI wall 2.34·10 -08 2.41·10 -08 +3 LLI wall 6.73·10 -08 7.77·10 -08 +13 Kidneys 2.03·10 -11 2.12·10 -11 +4 Liver 9.61·10 -10 9.99·10 -10 +4 Lungs 1.28·10 -11 1.68·10 -11 +23 Muscle 1.79·10 -11 1.93·10 -11 +7 Pancreas 1.91·10 -11 2.04·10 -11 +6 Red marrow 1.92·10 -11 2.11·10 -10 +9 Skin 1.37·10 -11 1.76·10 -11 +22 Spleen 1.71·10 -11 1.89·10 -11 +9 Testes 1.71·10 -11 1.99·10 -11 +14 Thymus 1.18·10 -11 1.12·10 -11 -5 Thyroid 1.21·10 -11 1.49·10 -11 +19 Uterus 3.79·10 -11 3.79·10 -11 +5 Remainder 9.51·10 -11 9.9·10 -11 +3

Effective dose 5.21·10 -09 6.02·10 -09 +14

105 Results and discussions

Differences due to alimentary tract model One objective of the new cerium biokinetic model proposal is to include the newest information on substance kinetics in the human alimentary tract (HAT) available through ICRP publication 100 (ICRP, 2006). This is important, because the double tracer method, as used in this work, do not contain detailed information about substance transfer within the alimentary tract. It is useful to use the revised, more detailed model and parameters from ICRP publication 100 (ICRP, 2006) instead of those in ICRP publication 30 (ICRP, 1979) in order to describe the substance transfer through the alimentary tract better. For the HAT model calculation, the default parameter values for non-caloric liquids and the calculated model parameters were used. The HAT model features a faster substance transfer through the body. The most extreme target organ is the stomach wall, which can be explained by the change on the transfer rate from the stomach to small intestine in the HAT model as compared to the GI tract model (Table 24). For radionuclides like cerium, with relatively short half-lives and small fractional absorption from intestine to the systemic circulation, the absorbed dose is prilimarly dependent on the radionuclide transformations in the alimentary tract. The HAT model features a slightly faster substance transfer through the body,; hence the calculated dose coefficients are generally lower than those associated to the older GI tract model. The most extreme target organ in this context is the stomach wall, which can be explained by the change in the transfer rate from the stomach to the small intestine in the HAT model compared to the GI tract model. In the HAT model, the transfer rate is a factor of 2 higher than in the GI tract model, hence in the stomach, content is substantially reduced in the HAT model.

106 Implications of the new model for dosimetry

Table 24: Dose coefficients (Sv/Bq) for transformations over 50 y, modelled with different alimentary tract models, ICRP 30 GI tract and ICRP 100 HAT model, for the current systemic model of the ICRP.

Target region ICRP 30 ICRP 100 Deviation of GI tract HAT HAT from GI (%)

Adrenals 1.61·10 -11 1.69·10 -11 -5 Bladder wall 3.01·10 -11 3.04·10 -11 -1 Bone surface 3.32·10 -10 3.32·10 -10 0 Brain 1.20·10 -11 1.30·10 -11 -8 Breast 1.21·10 -11 1.25·10 -11 -3 ST wall 1.13·10 -09 1.29·10 -09 -14 SI wall 3.71·10 -09 4.27·10 -09 -15 ULI wall 2.34·10 -08 2.50·10 -08 -7 LLI wall 6.73·10 -08 6.73·10 -08 0 Kidneys 2.03·10 -11 2.07·10 -11 -2 Liver 9.61·10 -10 9.90·10 -10 -3 Lungs 1.28·10 -11 1.30·10 -11 -1 Muscle 1.79·10 -11 1.97·10 -11 -10 Pancreas 1.91·10 -11 1.99·10 -11 -4 Red marrow 1.92·10 -11 1.98·10 -11 -3 Skin 1.37·10 -11 1.37·10 -11 0 Spleen 1.71·10 -11 1.73·10 -11 -1 Testes 1.71·10 -11 1.76·10 -11 -3 Thymus 1.18·10 -11 1.18·10 -11 0 Thyroid 1.21·10 -11 1.20·10 -11 1 Uterus 3.79·10 -11 3.87·10 -11 -2 Remainder 9.51·10 -11 9.51·10 -11 0

Effective dose 5.21·10 -09 5.47·10 -09 -5

107 Results and discussions

4.6.2 Dose coefficients of 144 Ce of the new cerium biokinetic model

The dose coefficients of 144 Ce for the new proposed cerium biokinetic model are presented in Table 25. The calculated ICRP dose coefficients and the dose coefficients of the new model are listed for both sexes. The relative differences of committed equivalent doses are shown in Table 26. Thus, the ingestion dose coefficients calculated for the new proposed cerium model are significantly different from the published ICRP dose coefficients, considering the estimated uncertainty of the numerical modelling process of ~ 2 % (see Table 21). One new feature of the HAT model is that the transfer rates between some compartments are material and gender specific. Within the current study only non- caloric liquids, i.e. solutions of cerium tracers, are used for investigations, thus no material specific parameters are yet introduced in the proposed model. Investigations of both genders are included and dose coefficients are derived for both genders individually by use of gender specific SEEs (see Table 23), and gender specific parameters from colon compartments. The ICRP also suggest a gender specific parameter from large intestine compartment to the colon compartment, but in the new proposed model this parameter is new defined and showed no significant difference between the two genders, male and female. In the HAT model the transfer rate kright- -d colon →left colon , kleft colon →rectosigmoid colon , and krectosigmoid colon →excreted faeces are 2 for men and 1.5 –d for women. Therefore ingested radionuclides stay longer in the female colon than in the men colon. Accordingly, the comparison in Table 25 shows that the dose coefficients for men are more elevated in the proposed new model than for women and both are higher than in the publication 67 (ICRP, 1993) models. In consideration of potential dose estimates after accidents, it is important to stress that the substantial gender differences observed in modelling are a consequence of different SEE values, and to a large extent, the transfer rates between the sections of the colon introduced by the HAT model.

108 Implications of the new model for dosimetry

Table 25: Dose coefficients (Sv/Bq) calculated for the ICRP model and for the new cerium biokinetic model for male and female.

Target region ICRP 67 modelled new cerium model Male female

Adrenals 1.6·10 -11 1.3·10 -11 7.1·10 -12 Bladder wall 3.0·10 -11 2.4·10 -7 3.3·10 -07 Bone surface 3.3·10 -10 3.5·10 -11 4.7·10 -09 Brain 1.2·10 -11 7.6·10 -11 8.8·10 -11 Breast 1.2·10 -11 8.3·10 -11 1.0·10 -10 Oesophagus 1.2·10 -11 8.6·10 -12 3.5·10 -12 ST wall 1.1·10 -09 4.5·10 -10 6.4·10 -10 SI wall 3.7·10 -09 2.0·10 -07 2.8·10 -07 ULI wall 2.3·10 -08 5.4·10 -09 7.2·10 -09 LLI wall 6.7·10 -08 6.8·10 -08 8.8·10 -08 Kidneys 2.0·10 -11 1.8·10 -10 2.4·10 -10 Liver 9.6·10 -10 3.7·10 -09 5.2·10 -09 Muscle 1.8·10 -11 3.0·10 -10 4.3·10 -10 Pancreas 1.9·10 -11 1.5·10 -10 1.8·10 -10 Red Marrow 1.9·10 -11 2.1·10 -09 2.9·10 -09 Skin 1.4·10-11 1.5·10 -10 1.9·10 -10 Spleen 1.7·10 -11 1.3·10 -10 1.5·10 -10 Testes 1.7·10 -11 6.1·10 -10 8.6·10 -10 Thymus 1.2·10 -11 8.2·10 -11 9.4·10 -11 Thyroid 1.2·10 -11 7.7·10 -11 8.7·10 -11 Uterus 3.8·10 -11 2.1·10 -09 2.3·10 -09 Remainder 9.5·10 -11 4.3·10 -09 5.2·10 -09

Effective Dose 5.2·10 -09 1.7·10 -08 2.0·10 -08

109 Results and discussions

Table 26: Deviations of female dose coefficients from male dose coefficients for the ICRP model, and the newly proposed model.

Deviation of female dose coefficients from male dose Coefficients in % Target region ICRP 67 new model (GI) (HAT)

Adrenals +11 +55 Bladder wall +9 +38 Bone surface +1 +33 Brain +16 +17 Breast +7 +26 ST wall +22 +41 SI wall +5 +47 ULI wall +3 +35 LLI wall +13 +31 Kidneys +4 +35 Liver +4 +41 Muscle +23 +44 Pancreas +7 +28 Red Marrow +6 +41 Skin +9 +28 Spleen +22 +24 Testes +9 +41 Thymus +14 +15 Thyroid -5 +14 Remainder +19 +23

Effective Dose +14 +15

110 Implications of the new model for dosimetry

Contribution of individual target tissues to effective dose In the following Figures 38 and 39 the composition of effective dose is presented for the ingestion dose coefficients of 144 Ce resulting from the proposed new biokinetic model of cerium. The effective dose is calculated from the individual target tissue dose coefficient and the appropriate weighting factors as described in paragraph 2.3 and 3.4. For each target tissue the percentage contribution of the weighted individual dose coefficients to the effective dose is noted next to the tissue name.

Colon:74.8 % Bladder:22.5 % Remaining target organs: 2.7 %

Remaining target organs:

Bone surface: 0.08 % Breast: 0.02 % Gonads: 0.17 % Kidney: 0.05 % Liver: 0.35 % Lungs: 0.004 % Red bone marrow: 0.084 % Remainder: 1.2 % Skin: 0.003 % Stomach: 0.13 % Thyroid: 0.007 %

Figure 38: Composition of the effective dose calculated from ingestion dose coefficients of the proposed male model.

111 Results and discussions

Colon: 75.2 % Bladder wall: 21.9 % Remaining target organs: 2.9 %

Remaining target organs:

Bone surface: 0.08 % Breast: 0.02 % Gonads: 0.46 % Kidneys: 0.016 % Liver: 1.03 % Lungs: 0.02 % Red Bone Marrow: 0.05 % Remainder: 1.03 % Skin: 0.04 % St Wall: 0.12 % Thyroid: 0.02 %

Figure 39: Composition of the effective dose calculated from ingestion dose coefficients of the proposed female model.

112 Implications of the new model for dosimetry

Summing up, the ingestion dose coefficients were calculated from radionuclide transformations over 50 y with the proposed new model for male and female reference persons.

The deviation of individual equivalent dose coefficients from the current values published by the ICRP publication 67 is in the range -45 % to -41 %, with a median deviation of – 3.3 %.
Ingestion equivalent dose coefficients are generally higher for women. Female effective doses are superior to male effective doses by 15 %. In comparison with the old model the dose coefficients are deviated of about 69 % higher for male and even 74 % higher for female persons calculated with the new model. Weighted contributions of individual target tissues to the effective dose coefficient are dominated by the colon dose with ∼ 75 %, the bladder wall with ∼ 22 % and doses to the remaining target tissues with ∼ 3 %.

In consideration of potential dose estimates after nuclear accidents, it is important that the substantial gender differences observed in modelling are a consequence of different SEE values and to a large extent the transfer rates between the sections of the colon introduced by the HAT model. Therefore it would be crucial for any individual dose estimate to accurately measure cerium clearance by faecal excretion and take into account the individual steric relations of radiosensitive tissues for the affected person.

113 Conclusions

5 Conclusions

In this work the development and optimization of thermal ionisation mass spectrometry for measurements of stable cerium isotopes in biological samples, i.e. urine and blood plasma, was established. With the developed method it is possible to accomplish tracerkinetic analysis for the cerium metabolism with stable cerium isotopes as tracers for the first time in humans and not anymore in animals. For this investigation important parameters for the cerium biokinetic in humans, like transport in the alimentary tract, absorption in the body, flux from the blood compartment as well as urinary excretion, were obtained, which were not known until now for humans. The method allowed evaluating 12 tracer kinetic investigations using the double tracer method with simultaneous oral and intravenous tracer administration. The results of this work improve the data on the biokinetic behaviour of tracer amounts of cerium in humans. For future work it would be necessary to collect blood plasma samples already every minute the first 15 minutes, to get a more detailed distribution. Furthermore, the biokinetic compartment model of cerium published by the International Commission on Radiological Protection (ICRP) was modified by including recycling processes and a physiological motivated direct excretion from blood to urine. Other paths of excretion were practically not identifiable and are not included in the model. The ingestion dose coefficients calculated with the new proposed model are on average not consistent with the current ingestion dose coefficients published in ICRP publication 67 (ICRP, 1993) and can vary significantly depending on gender. For the new male model the dose is about 69 % higher and for the new female model even about 74 % higher than predicted with the old model. Therefore it would be crucial for any individual dose estimate to accurately measure cerium clearance by faecal excretion and take into account the individual steric relations of radiosensitive tissues for the affected person.

114 Bibliography

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120 Determination of the fA value using the double tracer technique

Appendix

I. Determination of the fA value using the double tracer technique

The fA value is determined by the following equations:

z136 po m a (* h *k −k )+b 1(* −h *k )+h *k m *e f = * 138 iv = 136 140 136 138 140 138 136 * 138 138 iv (a) A − + − + − z138 iv m136 po a 1(* h136 *l140 ) b (* h138 *l140 l138 ) h136 *l138 h138 m136 *e136 po

where:

z z a = 138 ,b = 136 are the ratios of cerium isotopes in blood and urine, z140 z140 measured by TIMS;

z z = 138 nat = 136 nat 136 138 h138 ,h136 are the ratios of natural isotopes of Ce and Ce in z140 nat z140 nat relation to natural 140 Ce;

z z = 136 iv = 140 iv 136 140 k136 ,k140 are the ratios of isotopes of Ce and Ce in relation to z138 iv z138 iv the isotope of 138 Ce in the intravenous tracer;

z z = 138 po = 140 po 138 140 l138 ,l140 are the ratios of isotopes of Ce and Ce in relation to z136 po z136 po the isotope of 136 Ce in the oral tracer;

138 136 m138 and m136 : amounts of the isotopes of Ce and Ce as administered intravenously and orally;

138 136 e138 and e136 : enrichment factors of isotopes of Ce and Ce;

121 Appendix

The parameters of h138 , h 136 , k 136 , k 140 , l 140 , e 138 and e 136 can be obtained by abundances;

Derivation of the fA equation:

The compositions of the measured values at masses of z 136 , z138 and z 140 are the following: = + + z136 z136 nat z136 iv z136 po = + + z138 z138 nat z138 iv z138 po (b) = + + z140 z140 nat z140 iv z140 po

From Equation (b) one obtains: z z + z + z 138 = 138 nat 138 iv 138 po = a + + z140 z140 nat z140 iv z140 po (c) z z + z + z 136 = 136 nat 136 iv 136 po = b + + z140 z140 nat z140 iv z140 po and with Equation (c) and the following relationships

= z138 nat h138 * z140 nat = z136 nat h136 * z140 nat = z136 iv k136 * z138 iv = (d) z140 iv k140 * z138 iv = z138 po l138 * z136 po = z140 po l140 * z136 po

replacing z138nat by h138 *z 140nat and z136nat by h136 *z 140nat in Equation (c) one obtains:

(z + z ) − a (* z + z ) z = 138 iv 138 po 140 iv 140 po 140 nat a − h 138 (e) (z + z ) − b (* z + z ) z = 136 iv 136 po 140 iv 140 po 140 nat − b h136

Let z138p = l 138 *z 136po , z 136po = k 136 *z 138iv , z 140iv = k 140 *z 138iv and z 140po = l 140 *z 136po in

Equation (e) one obtains two equations for z140nat :

122 Data and resulting fits of the 12 data sets

(z + l * z ) − a (* k * z + l * z ) z = 138 iv 138 136 po 140 138 iv 140 136 po 140 naz a − h 138 (f) (k * z + z ) − b (* k * z + l * z ) z = 136 138 iv 136 po 140 138 iv 140 136 po 140 nat − b h136

Combining terms like for z136po and z138iv , one obtains: z 1( − a * k (*) b − h ) − (k − b * k (*) a − h ) 136 po = 140 136 136 140 138 − − − − − z138 iv 1( b *l140 (*) a h138 ) (l138 a *l140 (*) b h136 ) or (g) z a (* h * k − k ) + b 1(* − h * k ) + h * k − h 136 po = 136 140 136 138 140 138 136 136 − + − + − z138 iv a 1(* h136 *l140 ) b (* h138 *l140 l138 ) h136 *l138 h138

123 Appendix

II. Data and resulting fits of the 12 data sets

- Volunteer 1:

Ce 07 24 04

1e+3 1e+3

1e+2 1e+2 1e+1 1e+1 1e+0 1e+0 1e-1

1e-2 1e-1

1e-3 1e-2 i.v. tracer 1e-4 HMGU 1e-3 p.o. tracer

tracer amount in plasma (%/kg) 1e-5 HMGU cumulative tracer amount in urine (%) 1e-4 1e-6

1e-7 1e-5 0,1 1 10 100 0 20 40 60 80 100 120 140

time after administration (h) Figure 40: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 1.

Table 27: Parameter estimation (1/h) from fitted data of investigation volunteer 1.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 2.95·10 6.92·10 +01 +00 kStomach – Small intestine 4.07·10 5.0·10 +00 +00 kBlood-Plasma diffusible 7.26·10 1.55·10 -01 -02 kPlasma diffusible-Blood 3.42·10 2.66·10 -01 -01 kBlood – Skeleton 2.50·10 1.21·10 -01 -02 kBlood – Liver 1.52·10 8.24·10 -01 -02 kBlood – other Tissues 1.00·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 +00 -01 kBlood – Urinary bladder 1.84·10 1.72·10 -04 -05 ksmall intestine-blood 2.09·10 1.09·10 Plasma mass 2.20 0.19 -04 -05 fA 7.07·10 7.17·10

124 Data and resulting fits of the 12 data sets

- Volunteer 2 :

Ce 07 29 05

1e+3 1000

1e+2 100

1e+1 10

1e+0 1 1e-1 0,1 1e-2 i.v. tracer

0,01 HMGU 1e-3 p.o. tracer tracer amount in plasma (%/kg) HMGU 1e-4 cumulative trace amount in urine (%) 0,001

1e-5 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 41: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 2.

Table 28: Parameter estimation (1/h) from fitted data of investigation volunteer 2 .

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 3.69·10 2.73·10 +01 +00 kStomach – Small intestine 3.96·10 5.09·10 +01 +00 kBlood-Plasma diffusible 1.45·10 2.43·10 -01 -02 kPlasma diffusible-Blood 5.56·10 1.00·10 -01 -01 kBlood – Skeleton 2.50·10 1.21·10 -01 -02 kBlood – Liver 1.52·10 8.24·10 -01 -02 kBlood – other Tissues 1.00·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 +01 -00 kBlood – Urinary bladder 1.63·10 1.72·10 -03 -04 ksmall intestine-blood 1.68·10 2.17·10 Plasma mass 1.20 3.48·10 -02 -03 -04 fA 4.54·10 5.08·10

125 Appendix

- Volunteer 3:

Ce 07 30 06

100 1000

100 10

10 1

1 0,1 0,1 i.v. tracer 0,01 0,01 HMGU p.o. tracer cumulative trace amount (%) tracer amount in plasma (%/kg) 0,001 HMGU 0,001

0,0001 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 time after administration (h)

Figure 42: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 3.

Table 29: Parameter estimation (1/h) from fitted data of investigation volunteer 3.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 1.38·10 1.74·10 +01 +00 kStomach – Small intestine 4.28·10 5.53·10 +01 +00 kBlood-Plasma diffusible 1.45·10 2.43·10 +00 -01 kPlasma diffusible-Blood 1.64·10 2.90·10 -01 -01 kBlood – Skeleton 8.24·10 1.21·10 -01 -02 kBlood – Liver 4.94·10 8.24·10 -01 -02 kBlood – other Tissues 3.29·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 +00 -00 kBlood – Urinary bladder 3.20·10 1.72·10 -04 -05 ksmall intestine-blood 3.21·10 4.91·10 Plasma mass 1.16 1.31·10 -01 -03 -04 fA 2.31·10 3.76·10

126 Data and resulting fits of the 12 data sets

- Volunteer 4:

Ce 10 36 12

1e+2 100

1e+1 10

1e+0 1

1e-1 0,1 1e-2

0,01 i.v. tracer 1e-3 HMGU p.o. tracer tracer amount in plasma (%/kg) 0,001 1e-4 HMGU cumulative tracer amount in urine (%)

1e-5 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 43: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 4.

Table 30: Parameter estimation (1/h) from fitted data of investigation volunteer 4.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 3.03·10 3.53·10 +01 +00 kStomach – Small intestine 4.05·10 5.23·10 +00 -01 kBlood-Plasma diffusible 8.32·10 5.08·10 -02 -03 kPlasma diffusible-Blood 8.43·10 8.25·10 -01 -01 kBlood – Skeleton 8.24·10 1.21·10 -01 -02 kBlood – Liver 4.94·10 8.24·10 -01 -02 kBlood – other Tissues 3.29·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 +00 -01 kBlood – Urinary bladder 1.88·10 1.61·10 -04 -05 ksmall intestine-blood 3.75·10 4.58·10 Plasma mass 2.65 4.96·10 -01 -03 -04 fA 1.24·10 1.32·10

127 Appendix

- Volunteer 6:

Ce 10 38 14

100 100

10 10

1 1

0,1 0,1

i.v. tracer 0,01 0,01 HMGU p.o. tracer tracer amount in plasma (%/kg) 0,001 0,001 HMGU cumulative tracer amount in urine (%)

0,0001 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 44: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 6 .

Table 31: Parameter estimation (1/h) from fitted data of investigation volunteer 6.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 3.53·10 4.72·10 +01 +00 kStomach – Small intestine 4.27·10 5.54·10 +00 -01 kBlood-Plasma diffusible 6.06·10 3.99·10 -02 -03 kPlasma diffusible-Blood 9.56·10 9.52·10 -01 -01 kBlood – Skeleton 8.24·10 1.21·10 -01 -02 kBlood – Liver 4.94·10 8.24·10 -01 -02 kBlood – other Tissues 3.29·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 +00 -02 kBlood – Urinary bladder 1.05·10 5.15·10 -04 -05 ksmall intestine-blood 5.63·10 6.53·10 Plasma mass 1.15 5.42·10 -02 -03 -05 fA 1.59·10 7.74·10

128 Data and resulting fits of the 12 data sets

- Volunteer 7:

Ce 10 39 15

1e+2 100

1e+1 10 i.v. tracer HMGU 1e+0 1 p.o. tracer HMGU 1e-1 0,1 1e-2

0,01 1e-3

tracer amount in plasma (%/kg) 0,001 1e-4 cumulative tracer amount in urine (%)

1e-5 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 time after administration (h)

Figure 45: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 7.

Table 32: Parameter estimation (1/h) from fitted data of investigation volunteer 7.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 2.67·10 2.66·10 +01 +00 kStomach – Small intestine 4.14·10 5.56·10 +00 +00 kBlood-Plasma diffusible 7.84·10 1.34·10 -01 -02 kPlasma diffusible-Blood 1.89·10 2.25·10 -01 -01 kBlood – Skeleton 3.98·10 1.21·10 -01 -02 kBlood – Liver 2.39·10 8.24·10 -01 -02 kBlood – other Tissues 1.59·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 8.16·10 6.54·10 -04 -05 ksmall intestine-blood 1.72·10 1.87·10 Plasma mass 1.76 5.42·10 -01 -04 -05 fA 6.43·10 4.91·10

129 Appendix

- Volunteer 8:

Ce 10 40 16 100 100

10 10

1 1

0,1 0,1

0,01 0,01 i.v. tracer HMGU

tracer amount in plasma (%/kg) 0,001 0,001 p.o. tracer cumulative tracer amount in urine (%) HMGU

0,0001 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 46: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 8.

Table 33: Parameter estimation (1/h) from fitted data of investigation volunteer 8.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 3.66·10 5.48·10 +01 +00 kStomach – Small intestine 4.22·10 5.41·10 +00 +00 kBlood-Plasma diffusible 9.21·10 1.23·10 -01 -02 kPlasma diffusible-Blood 1.83·10 3.17·10 -01 -01 kBlood – Skeleton 3.45·10 1.21·10 -01 -02 kBlood – Liver 2.52·10 8.24·10 -01 -02 kBlood – other Tissues 1.89·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -01 kBlood – Urinary bladder 9.11·10 1.21·10 -04 -05 ksmall intestine-blood 2.63·10 4.57·10 Plasma mass 2.44 5.42·10 -01 -04 -04 fA 7.20·10 1.00·10

130 Data and resulting fits of the 12 data sets

- Volunteer 9:

Ce 10 41 17

100 1e+2

10 1e+1

1e+0 1

1e-1 0,1 1e-2

0,01 i.v. tracer 1e-3 HMGU

tracer amount in plasma (%/kg) 0,001 p.o. tracer 1e-4 cumulative tracer amount in urine (%) HMGU

0,0001 1e-5 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 47: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 9.

Table 34: Parameter estimation (1/h) from fitted data of investigation volunteer 9 .

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 2.97·10 6.17·10 +01 +00 kStomach – Small intestine 4.08·10 5.58·10 +00 +00 kBlood-Plasma diffusible 8.63·10 2.14·10 -01 -02 kPlasma diffusible-Blood 2.05·10 4.82·10 -01 -01 kBlood – Skeleton 2.88·10 1.21·10 -01 -02 kBlood – Liver 1.73·10 8.24·10 -01 -02 kBlood – other Tissues 1.15·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 7.89·10 7.11·10 -04 -05 ksmall intestine-blood 2.59·10 5.05·10 Plasma mass 2.01 4.42·10 -01 -04 -05 fA 8.73·10 8.15·10

131 Appendix

- Volunteer 10:

Ce 10 42 18 100 100

10 10 i.v. tracer HMGU 1 1 p.o. tracer HMGU

0,1 0,1

0,01 0,01

tracer amount in plamsa (%/kg) 0,001 0,001 cumulative tracer amount in urine (%)

0,0001 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 48: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 10.

Table 35: Parameter estimation (1/h) from fitted data of investigation volunteer 10.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 6.99·10 7.98·10 +01 +00 kStomach – Small intestine 4.47·10 5.34·10 +01 +00 kBlood-Plasma diffusible 1.37·10 1.54·10 -01 -02 kPlasma diffusible-Blood 2.08·10 2.88·10 -02 -03 kBlood – Skeleton 2.60·10 4.21·10 -02 -03 kBlood – Liver 1.56·10 8.24·10 -02 -03 kBlood – other Tissues 1.04·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 6.65·10 9.31·10 -04 -04 ksmall intestine-blood 6.60·10 1.02·10 Plasma mass 2.21 5.42·10 -01 -04 -04 fA 9.43·10 1.25·10

132 Data and resulting fits of the 12 data sets

- Volunteer 11:

Ce 10 44 20 100 100

10 10 i.v. tracer HMGU 1 1 p.o.tracer HMGU

0,1 0,1

0,01 0,01

tracer amount in plasma (%/kg) 0,001 0,001 cumulative tracer amount in urine (%)

0,0001 0,0001 0,1 1 10 100 0 20 40 60 80 100 120 140 time after administration (h)

Figure 49: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 11.

Table 36: Parameter estimation (1/h) from fitted data of investigation volunteer 11.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 2.83·10 5.09·10 +01 +00 kStomach – Small intestine 3.99·10 5.45·10 +00 -01 kBlood-Plasma diffusible 6.21·10 7.91·10 -01 -02 kPlasma diffusible-Blood 1.84·10 3.23·10 -02 -02 kBlood – Skeleton 8.69·10 1.21·10 -02 -02 kBlood – Liver 5.21·10 8.24·10 -02 -03 kBlood – other Tissues 4.46·10 6.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -02 kBlood – Urinary bladder 2.72·10 2.67·10 -04 -05 ksmall intestine-blood 1.94·10 3.11·10 Plasma mass 1.76 5.42·10 -01 -04 -05 fA 6.87·10 6.63·10

133

- Volunteer 12:

Ce 10 45 21

100 1e+3

1e+2 10 1e+1

1 1e+0

1e-1 0,1 1e-2

0,01 1e-3 i.v. tracer HMGU 1e-4 p.o. tracer 0,001

tracer concentration in plasma (%/kg) HMGU cumulative tracer amount in urine (%) 1e-5

0,0001 1e-6 0,1 1 10 100 0 10 20 30 40 50 60 time after administration (h)

Figure 50: Intravenous and oral applied cerium tracer (T-138 and T-136) in blood plasma (left) and cumulative urine (right) including model predictions of the new HMGU cerium model for volunteer 12.

Table 37: Parameter estimation (1/h) from fitted data of investigation volunteer 12.

Parameter Expected value Uncertainty, absolute (h -1) (h -1)

-01 -02 ksmall intestine-right colon 1.27·10 3.31·10 +01 +00 kStomach – Small intestine 3.99·10 5.59·10 +00 +00 kBlood-Plasma diffusible 7.35·10 1.25·10 -01 -02 kPlasma diffusible-Blood 1.98·10 4.77·10 -01 -02 kBlood – Skeleton 2.55·10 4.21·10 -01 -02 kBlood – Liver 1.53·10 4.24·10 -01 -02 kBlood – other Tissues 1.02·10 3.78·10 -05 -05 kSkeleton-Blood 9.90·10 1.98·10 -05 -06 kLiver-Blood 5.94·10 8.91·10 -05 -06 kother Tissues-Blood 3.96·10 7.92·10 -01 -01 kBlood – Urinary bladder 8.97·10 1.28·10 -04 -05 ksmall intestine-blood 1.91·10 3.59·10 Plasma mass 2.43 5.42·10 -01 -03 -04 fA 1.50·10 2.53·10

134 Acknowledgments

Acknowledgments

Many people have contributed to this work, and I am sincerely grateful for the time I was allowed to work for and with them.

First and foremost, I thank Prof. Dr. Dr. Herwig G. Paretzke for the possibility to work on this topic under his supervision. My thanks got to the staff of the Department of Medical Radiation Physics and Diagnostics of the Helmholtz Zentrum München. Many colleagues at the working group and beyond were involved in this work, but some than others, to whom my deepest gratitude is: Dr. Christoph Hoeschen, for his support as an excellent group leader; Dr. Uwe Oeh for making this work possible and for many inspiring discussions; Dr. Augusto Giussani for many fruitful discussions, explanations, nearly everything related to modelling and ongoing scientific mentorship; Dr. Vera Höllriegl for the grateful help in laboratory things and for support belonging to discussions; Dr. Weibo Li for the joint involvement in the biokinetics project; Florian Wagner for his effort and assistance in measurement; Monika Röhmuss and Nermin Hirlak for the grateful help in taking blood samples.

I am greatly indebted to all volunteers, without whom this work would not have been possible. Less painful of them, but nevertheless appreciated was the cooperation with Prof. Dr. T. Zilker, Dr. N. Felgenhauer, and Prof. Dr. M. Göttlicher.

I am deeply grateful for the support from my husband Markus and my parents, who helped me to keep up and finally finish this work.

This work is part of the project 02NUK002B and was funded by the Bundesministerium für Bildung und Forschung.

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„Das Leben ist wert gelebt zu werden, sagt die Kunst, die schönste Verführung; das Leben ist wert erkannt zu werden, sagt die Wissenschaft.“ (Friedrich Nietzsche)

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