UNIVERSITY OF HELSINKI REPORT SERIES IN PHYSICS

HU-P-D102

Kinetic Mathematical Models for the 111In-labelled Bleomycin Complex

and 10B in Boron Neutron Capture Therapy

Päivi Ryynänen

Department of Physical Sciences

Faculty of Science

University of Helsinki

Helsinki, Finland

and

Department of Radiology

Helsinki University Central Hospital

Helsinki, Finland

ACADEMIC DISSERTATION

To be presented, with the permission of the Faculty of Science of the University of Helsinki, for

public criticism in the Small Auditorium (E204) of Physicum, on December 7th, 2002,

at 12 o’clock noon.

HELSINKI 2002

To András

ISSN 0356-0961Helsinki 2002Yliopistopaino

ISBN 952-10-0568-8 (pdf-version)http://ethesis.helsinki.fi/

Helsinki 2002Helsingin yliopiston verkkojulkaisut

ISBN 952-10-0567-X (printed version)

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P. Ryynänen: Kinetic mathematical models for the 111In-labelled bleomycin complexand 10B in boron neutron capture therapy, University of Helsinki, 2002, 65 p. +appendices, University of Helsinki Report Series in Physics, HU-P-D102, ISBN 952-10-0567-X (printed version), ISSN0356-0961, ISBN 952-10-0568-8 (pdf-version)

Classification (INSPEC): A8700, C7330Keywords: mathematical modelling, kinetics, 111In-bleomycin complex, BNCT, p-BPA

ABSTRACT

In this study, exponential function fittings, compartmental models, and numerical modelswere used to study and simulate the kinetics of an indium-111-labelled bleomycin complex(111In-BLMC) and of boron-10 (10B) atoms in boron neutron capture therapy (BNCT) afterinfusion of a p-boronophenylalanine fructose complex (BPA-F).

In twelve patients with a brain tumour the kinetics of 111In-BLMC after rapid intravenousinjection was quantified, using compartmental and non-compartmental modelling. Blood andurine samples were collected from 12 patients. In addition, tumour samples, obtained atsurgery, were available from three patients. Two-, three- and four-exponential functionfittings and open two-, three- and four-compartment models were applied to the data. Themost accurate models were a three-exponent function fitting and an open three-compartmentmodel. The biological mean half-lives of 111In-BLMC in blood obtained from the three-exponent model were 5.6±3.4 min for the fast, 1.7±0.4 h for the intermediate and 18±6 h forthe slow component. The biological mean half-life of 111In-BLMC in urine was 3.5±0.6 h andthe mean plasma clearance was 0.3±0.1 ml blood/min.

BNCT is radiotherapy, in which the patient is infused intravascularly with a 10B carrier,which accumulates in the tumour cells. External neutron beams are targeted on the tumour,resulting in neutron capture reactions in the 10B atoms. The energy released destroys thetumour tissue. The Finnish BNCT group uses BPA-F as a 10B carrier. Kinetic models for the10B time-concentration curves in the blood after BPA-F infusion were constructed for severalstudy assemblies: for an animal study and for four studies of patients. In the animal study ofnine dogs, 250 or 700 mg BPA/kg body weight was infused during 30 minutes or 1 hour, andblood samples from all dogs and urine samples from two dogs were collected. A bi-exponential model and an open three-compartment model were found to be the most accurate.There were 17 glioma patients from the Brookhaven National Laboratory (BNL), and twenty-one glioma patients and two volunteers from the Finnish BNCT trials. Fourteen patients andtwo volunteers received various amounts of infused BPA-F during variable times. Twenty-two patients received a 2-hr i.v. infusion of a BPA-fructose complex that delivered 290 mgBPA/kg body weight, which is the current treatment procedure in the Finnish BNCT trials.Data from the BNL BNCT trials were used to model construction and testing. All the datafrom the patients from the BNCT trials in Finland were fitted with the resulting fourmodelling tools, i.e. bi-exponent fitting, an open two-compartment model, and 3- and 4-

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parameter non-linear models. All these models were found to be suitable in the dose rangesused in this patient group, but the models had varying capabilities in the different phases ofthe BNCT. When considering the maximum error occurring in the models, the bi-exponentfunction fitting is the most accurate for both the first and the second irradiation field. The 3-parameter non-linear model provided mean absolute differences between the measured andthe estimated 10B concentrations in the blood that were less than 3.7 % when used to simulateirradiations of actual patients, which comprised two irradiation fields separated by a break forrepositioning the patient, and this model was found to be the most accurate, when consideringthe mean differences between the model and the measured data. In clinical practice, themodelling tool has to be simple to use, robust and rapid, and therefore, in these trials the two-compartment model will have a significant role. The future development of a user-friendlyversion of the 3-parameter model should be encouraged. As a result of this study, threemodelling tools, i.e. an open two-compartmental model, a bi-exponential fit and a 3-parameter non-linear model should be used in parallel to enhance the understanding of thekinetic aspects of this radiation therapy.

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CONTENTS

ABSTRACT 1

LIST OF ORIGINAL PUBLICATIONS 4

SYMBOLS AND ABBREVIATIONS 5

1. INTRODUCTION 61.1. The modelling process 61.2. Pharmacokinetics and brain tumours 71.3. 111In-labelled and unlabelled bleomycin and kinetic models 71.4. Kinetic models in BNCT 8

2. AIMS OF THE PRESENT STUDY 10

3. THEORY 113.1. Tracers in a biological system 113.2. Pharmacokinetics 123.3. Models 15

4. MATERIALS AND METHODS 194.1. Tracers 194.2. Materials 204.3. Models and computational methods 234.4. Statistical methods for models 25

5. RESULTS 265.1. 111In-BLMC 265.2. BPA-F and 10B 26

6. DISCUSSION 426.1. Models 426.2. Tracers 466.3. BNCT Studies 46

7. CONCLUSIONS 507.1. Conclusions from the study with 111In-BLMC and future prospects 507.2. Conclusions from the BNCT studies and future prospects 51

ACKNOWLEDGEMENTS 53

REFERENCES 55

ERRATA 65

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LIST OF ORIGINAL PUBLICATIONS

This thesis is based on the following publications, which are referred to in the text by Romannumerals. These publications have been examined by a referee and include three originalarticles and one manuscript on proceedings publication. This thesis also includes some datafrom the recent BNCT trials in Finland, which are to be published by Joensuu et al. (Joensuuet al 2002b).

I Ryynänen P, Savolainen S, Aronen HJ, Korppi-Tommola ET, Huhmar HM,Kallio ME and Hiltunen JV. Kinetics of 111In-labelled bleomycin in patients with braintumors: Compartmental vs. non-compartmental models. Annals of Nuclear Medicine 1998;12:313-321

II Ryynänen P, Savolainen S, Benczik J, Kulvik M, Vähätalo J and Snellman M.Compartmental and non-compartmental methods in studying the kinetics of boron-10 afterboronophenylalanine fructose complex (BPA-F)-infusion in dogs In: Frontiers in NeutronCapture Therapy, Eds. M. F. Hawthorne, K. Shelly and R. J. Wiersema, (New York: PlenumPub. Corp.), 2002, pp 959-963

III Ryynänen P, Kortesniemi M, Coderre J, Diaz A, Hiismäki P and Savolainen S.Models for estimation of the 10B concentration after BPA-Fructose complex infusion inpatients during epithermal neutron irradiation in BNCT. International Journal of RadiationOncology Biology Physics 2000; 48:1145-1154

IV Ryynänen P, Kangasmäki A, Hiismäki P, Coderre J, Diaz A, Kallio M, LaaksoJ, Kulvik M and Savolainen S. Non-linear models for kinetics of 10B in blood after BPA-fructose complex infusion in BNCT. Physics in Medicine and Biology 2002; 47:737-745

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SYMBOLS AND ABBREVIATIONS

In addition to the standard SI units, the following abbreviations and symbols are used in thetext. The subscripts and superscripts B, P, T, U, K and E refer to blood, plasma, tumour,urine, kidneys and excretion, respectively.

Ai constant of the exponential function10B boron-10 atomBBB blood-brain barrierBLM bleomycinBLMC bleomycin complexBNCT boron neutron capture therapyBNL Brookhaven National LaboratoryBPA p-boronophenylalanineBPA-F complex of p-boronophenylalanine and fructosec(t) concentration at time tCL clearanceCNS central nervous system (i.e. the brain and the spinal cord)gi coefficient of the exponent functionICP-AES inductively coupled plasma atomic emission spectrometryICP-MS inductively coupled plasma mass spectrometry111In-BLMC Indium-111-labelled bleomycin complexkij transfer (rate) coefficient, the amount of the tracer that leaves compartment j for

compartment i per unit time, i.e. �

2 chi-squared statistical testMTT mean transit time of a tracerPB-PK physiologically based pharmacokineticsPD pharmacodynamicsPK pharmacokineticspKa ionization constant, the pH value of a weak electrolyte, where 50 % of the

molecules are in the dissociated formS.D. standard deviationSPECT single photon emission computed tomographyt½ half-life of a tracert½

fast, t½slow half-lives of a bi-exponential blood clearance curve of a tracer

kij

i j

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1. INTRODUCTION

1.1. The modelling process

A mathematical model is a simplified expression of a system. Mathematical models arerepresented as equations, in which the most essential factors of the system (or its function)are expressed as variables, constants and parameters, and in which the relationships betweenthese factors are expressed in mathematical language. A system can be represented by asmany models as there are ways to study the form or function of the system. No final or“unique” model can be constructed.

In modelling the aim is to predict the behaviour of a system as precisely as possiblebeforehand knowing only the current state of the systems and the inputs to the system. Theform and structure of the model depend entirely on the specific aims and needs of themodeller. Figure 1 is a schematic diagram of the modelling process.

Figure 1. Schematic outline of the modelling process (Brownell et al 1968, Kuikka et al 1991).

When studying tracer kinetics in a biological system, and especially the various distributionphases and the clearance of a tracer, the use of simple (mathematical) models is worthwhile(Resigno and Segre 1966). Most of the modelling in the clinical sciences is related to fittingexponential curves (Savolainen 1992). Dividing the body into metabolic pools is useful whenstudying hormones, lipids, drugs, etc., especially when detailed knowledge of thebiochemical pathways is lacking (Feldman 1977a). This approach has led to the developmentof compartmental models, which have found widespread application in physiology andmedicine. Compartmental models have a practical relation to the actual physiological systemand its behaviour (Lassen and Perl 1979, Resigno and Segre 1966). Conventionally,compartmental models have been used in the definition of organ-specific residence times(ICRP 1987, Strand et al 1993). Modelling has also been used much in oncology, especially

Good

Bad

Aims and AssumptionsExperiment Model

Mathematical solutionResults

Comparison

CompetentModel

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in conjunction with chemotherapy, to determine the amounts of a chemotherapeutic agent indifferent parts of the body (van Osdol et al 1993) or in radiation dosimetry calculations, asfor the novel techniques with radiolabelled monoclonal antibodies (Strand et al 1993).

1.2. Pharmacokinetics and brain tumours

About 800 new cases of primary tumours of the central nervous system were diagnosed in the1999 in Finland (Organizations 2002). More than 350 of these are gliomas of the brain orspinal cord. Histologically, gliomas are devided into astrocytomas, oligodendrogliomas,ependymomas, etc, according to the predominant cell type, and are graded from I to IVaccording to the signs of anaplasia (Daumas-Duport et al 1988, Kleihues et al 1993). In spiteof aggressive treatment, which includes resection, surgery followed by chemotherapy andconventional radiotherapy, the median survival time after diagnosis of a high-grade glioma isonly about 12 months (Sandberg-Wollheim et al 1991).

In this study, exponential function fitting, compartmental models, and numerical models havebeen applied to the macropharmacokinetics of two different tracers that are used in braintumour treatment and research. These small–molecular tracers are an indium-111 labelledbleomycin complex (111In-BLMC), and boron-10 (10B) atoms in boron neutron capturetherapy (BNCT) after infusion of a p-boronophenylalanine fructose complex (BPA-F).

1.3. 111In-labelled and unlabelled bleomycin and kinetic models

Bleomycin (BLM) is a glycopeptide antibiotic originally isolated from Streptomycesverticillus (Umezawa et al 1966). The cytotoxic effect of BLM depends on the blocking ofDNA synthesis and, in he presence of iron, oxygen and a reducing agent BLM breaks theDNA chains (Barranco and Humphrey 1971). It is conventionally used for the treatment ofsquamous cell carcinomas, either combined with other chemotherapy or with radiationtherapy (Suntharalingam et al 2001) or as palliative treatment (Thigpen et al 1995), and alsoin the treatment of testicular cancers (Foster 2001) and lymphomas (Cohen and Scadden2001, Fung and Nademanee 2002).

Radiolabelling of BLM with 111In enables on line monitoring of the 111In-BLMC withSPECT, and is useful for the differentiation of high- and low-grade gliomas (Korppi-Tommola et al 1999); it may also improve the effectiveness of its cancer treatment propertiesif the 111In content is sufficient (Kairemo et al 1996a, Kairemo et al 1996b). Previously, 57Co-labelled BLM has been studied with single-photon positron emission computed tomography(Front et al 1988). According to one study, there is no significant difference in the serum t½or in the clearance rate between 111In-labelled- and un-labelled BLMC (Kairemo et al 1996a).In an animal study, the blood clearance of BLM after i.v. administration was reported to bebiphasic (Krohn et al 1977), and in a human study it was reported to be rapid (Crooke et al1977). BML is rapidly excreted into the urine (Dorr 1992); a large part is excreted during thefirst 24-48 h (ICRP 1987). According to previous studies (ICRP 1987), after injection, about10% of the injected activity is rapidly taken up by the kidneys, while the rest of the tracer is

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evenly distributed in the body, so that a large fraction (54%) is excreted with a half-time of10 h. Smaller fractions are translocated to the liver, bone marrow and spleen with a half-timeof 2 d (ICRP 1987).

1.4. Kinetic models in BNCT

Boron neutron capture therapy (BNCT) is an experimental radiation therapy so far mainlyused for treatment of malignant gliomas (Barth et al 1990, Ceberg et al 1995b, Chadha et al1998, Coderre et al 1998, Coderre et al 1997, Elowitz et al 1998). BNCT begins with aninfusion of a 10B-containing compound. One of the 10B carriers used is p-boronophenylalanine (BPA). Because of poor solubility in neutral conditions, BPA is givenas a fructose complex, (BPA-F) (Mori et al 1989, Yoshino et al 1989). The infusion isfollowed by local neutron irradiation(s) with low-energy neutrons, energy range of 0.5 eV to10 keV. Neutron capture reactions, mainly 10B(n,�)7Li, will occur and release their energywith high linear energy transfer. Radiation damage is dependent on the amount of 10B withinthe cells. The estimated minimum amount of evenly distributed 10B atoms to ensuretherapeutic success is at least 30 µg/g tissue (Coderre et al 1998), which is about 109 10Batoms per one cell (Fairchild and Bond 1985). Low-energy neutrons do not cause directionisation.

Clinical BNCT studies are underway at a number of centres in the USA, Europe and Japan.The boron carrier used has been BPA, with doses between 250-350 mg/kg body weightinfused over 1-2 hours, in the BNCT trials in the USA (Busse et al 2002). In Japan, theBNCT trials were initiated at the late 1960’s (Hatanaka 1975, Hatanaka and Sano 1973), andchildren have also been treated with BNCT (Uyama et al 2002). Both BSH and BPA havebeen used as boron carriers in the Japanese BNCT trials. BSH with a 1-hour infusion hasbeen used in the recent BNCT trials carried out in the Czech Republic (Burian et al 2002). InSweden BNCT has been administered with a 6-hour infusion of 900 mg BPA/kg body weight(Capala et al 2002). The first trial of using BNCT and BPA in the treatment of livermetastasis was recently performed in Italy and has aroused great interest (Pinelli et al 2002).

In order to calculate the radiation dose induced in the tumour and adjacent tissues, one shouldbe able to estimate the respective 10B concentration in the tumour on line for each patient.Positron emission tomography (PET) studies combined with compartmental models havebeen used to obtain in vivo information on the pharmacokinetics of the 18F-labeled analogueof BPA (Imahori et al 1998a) and BPA-F (Kabalka et al 1997a) in tumour and in brain tissue.Estimations of the uptake ratios between the tumour, the normal brain (Imahori et al 1998a,Imahori et al 1998b, Kabalka et al 1997a) and the plasma (Imahori et al 1998c) have beenascertained. Proton magnetic resonance spectroscopy for the direct detection of the 10B-carrier molecule BPA (Zuo et al 1999) and magnetic resonance spectroscopy to measure 11Bconcentrations (Bendel 1998, Kabalka et al 1991, Kabalka et al 1997b, Tang 1995) have alsobeen employed. Preliminary results of the use of prompt gamma spectroscopy for non-invasive in vivo determination of the boron uptake during the neutron irradiation haverecently been reported (Munck af Rosenschöld et al 2001). However, no in vivo measurementof 10B concentrations in the respective tissues after BPA-F infusions within the dose range

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used for therapy, are available. By utilising the values reported in these studies and bymeasurements on excised tissue samples (Coderre et al 1998), estimations of the 10Bconcentration in tumour and in the normal brain can be calculated from the 10B bloodconcentration values. For accurate neutron dosimetry, it is essential that the 10B time-concentration curves in the tumour tissue, the healthy brain tissue, and the blood are predictedreliably. The reported mean tumour-to-blood 10B ratio in human studies has varied from 1.4(Elowitz et al 1998) to 4 (Coderre et al 1998). Also a high variation in the tumour-to-bloodratio inside particular tumours has been reported (Elowitz et al 1998), which might be due tothe heterogeneity of the malignant tissue. The tissue-to-whole blood ratios used in the FinnishBNCT are as follows: brain-to-blood is 1:1 and tumour-to-blood is 3.5:1 (Coderre et al 1998).Furthermore, kinetic models are required for the 10B blood concentration curve, because ofthe limited availability of the blood samples during the neutron irradiations. Previously,simple compartmental models (Ceberg et al 1995a, Ceberg et al 1995b, Kiger III et al 2001)have been used to describe the kinetics of 10B after infusion of different boron compounds forBNCT in humans.

In order to obtain reliable estimates for the 10B concentration in blood during the subsequentclearance phase, blood samples are taken at regular intervals during and after the infusion.BPA-F has relatively rapid kinetics; thus, there is only a short time for taking and analysingblood samples between the end of the infusion and the start of the first irradiation. Therefore,it is desirable that the data points obtained during the infusion phase could also be used forestimating the 10B concentration in blood.

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2. AIMS OF THE PRESENT STUDY

The purposes of this study were:

1. To quantify the kinetics of an indium-111 labelled bleomycin complex after rapidintravenous injection into patients with a brain tumour and to compare compartmentmodelling and the inlet-outlet theorem in describing the distribution of the tracer. (StudyI)

2. To create models for the kinetics of 10B in dogs and in glioma patients after a singleinfusion of BPA-F in order to predict the 10B concentration in the whole blood during theneutron irradiations in BNCT. (Studies II, III and IV)

3. To gather all the data from the patients from the BNCT trials in Finland, and to compareand evaluate the suitability of the kinetic models created for the estimation of the 10Bconcentration after BPA-F infusion.

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3. THEORY

3.1. Tracers in a biological system

The life-cycle of a tracer in a physiological system can be said to consist of the followingsteps: entry to the system, absorption, distribution to different parts of the system (i.e. organs,tissues, cells), chemical transformation (i.e. metabolism) and elimination (Resigno and Segre1966). The aim of modelling a physiological system is to create a tool with which to predictand simulate the passage of the tracer through these steps. For this purpose, it is essential toknow the original state of the system and the characters of tracer inputs. The transportmechanisms of a tracer within the system depend on the physiological properties of both thetracer and the environment. The term pharmacokinetics includes studies of the time-dependent behaviour of the different tracers and their metabolites in a physiological system(Irwin and Nutt 1992). Pharmacodynamics depends on the correlation between theconcentration of a tracer and its biological effects. The term systemic steady state means the state of a system, in which all concentrations,flows, and masses of the substances of interest are constant during the experiment, althoughthe concentrations, flows and so forth, may vary in space (Lassen and Perl 1979). Whenintroducing a tracer into the system, it has to be assumed that the system is only minimallyperturbed. Infusing the indicator means that, with respect to the indicator, the system istemporarily in an unsteady state, but, after a transient period, the steady state is regained(Lassen and Perl 1979).

The transport of tracers in physiological systems may be a combination of passive diffusionand active, energy-demanding transport (Olkkola 1999). For 111In-BLMC and 10B, the mostusual form of transport is diffusion. The main factor restricting the passage of a tracer insidethe system is the cell membrane.

The term passive diffusion means random movement of molecules through membranes eithervia intercellular spaces (paracellular diffusion) or with the aid of a carrier protein, i.e.facilitated diffusion (transcellular diffusion), utilising only the energy of normal kineticmotion (Guyton and Hall 1996). The difference between paracellular diffusion and filtrationis that in filtration the tracer is transported by fluid flow (Marvola et al 1999). Lipid-solubletracers can diffuse directly through the capillary endothelium, whereas water-soluble tracers,with a mean width of 6-7 nm, can diffuse on through the intercellular pores, (Guyton and Hall1996). Paracellular diffusion is dependent on the size of the intercellular space and themolecular weight of the tracer, and is independent of the lipid-solubility of the tracer(Marvola et al 1999). The impact of tracer size is mainly to alter the rate of diffusion; ionsand suspended colloid particles diffuse in a similar manner (Guyton and Hall 1996). The rateof transcellular diffusion also correlates with the lipid solubility of the substance; the greaterthe lipid solubility, the faster the diffusion (Olkkola 1999). Tracers, which have freeelectrons, have poor lipid solubility (Olkkola 1999). Many of the tracers used to study aphysiological system are weak acids or weak bases, and the rate and efficiency of diffusion ofthese tracers thus depends on the pH of the surrounding environment (Olkkola 1999). Of thetracers used in this study, BPA-F is a weak acid and BLM is a base; however, BLM is used as

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a low pH solution (Hiltunen et al 1989). The degree of dissociation of a tracer is dependenton the pH of the environment and on the individual pKa and has a powerful impact on therate of excretion of the tracer through the kidneys (Olkkola 1999).

Active transport of a tracer is an energy-demanding activity, in which a tracer moves acrossthe membrane against the energy gradient, i.e. from a lower to a higher concentration(Guyton and Hall 1996). There are two types of active transfer. First, there is primary activetransport, where the source of the energy is the breakdown of a high-energy compound, e.g.adenosine triphosphate (Guyton and Hall 1996). Second, there is secondary active transport,where the energy is stored in the form of ionic concentration (Guyton and Hall 1996). Thesetransport mechanisms are highly specific.

3.2. Pharmacokinetics

It has been stated that “pharmacokinetics is what the body does to the drug andpharmacodynamics is what the drug does to the body” (Workman 1993). Especially, incancer chemotherapy pharmacokinetics plays a vital role both in preclinical research and indaily clinical practice, where, with the aid of kinetic studies, important questions, such as“how much, how often, how long and by what route?” can be rapidly answered (Workman1993). In pharmacodynamics, the phenomena under investigation are the effects of a traceron physiological functions (Irwin and Nutt 1992). In this study, no pharmacodynamic aspectswere considered.Pharmacokinetics comprises the different phases of a tracer in a system, i.e. absorption,distribution, biodistribution and elimination of the tracer (Irwin and Nutt 1992, Olkkola1999) (see Figure 2). After the different phases are resolved, a pharmacokinetic model can beconstructed, with which it is possible to predict the time-behaviour of a tracer (Olkkola1999). Micropharmacokinetics concerns the study of the distribution of the drug withintumour tissue, cells and subcellular components (Workman et al 1989).

Figure 2. Examples of the different phases, and basic relations of absorption, distribution, proteinbinding, biotransformation, elimination and responses of a tracer in a physiological system (Irwin andNutt 1992, Olkkola 1999). A, B and C represent the different metabolites of the tracer. The eliminationsite can be, for example, the kidneys, the liver or the lungs. The dotted area represents the part that iscommonly classified as pharmacodynamics.

DISTRIBUTION

Peripheralcompartment

Effectcompartment

EFFECT

PLASMA

EXCRETION

ELIMINATION SITE

AC

B

INPUT

Bound tracer Unbound tracer

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The term absorption includes the whole process by which a tracer enters the physiologicalsystem from the site of administration (Irwin and Nutt 1992). When a tracer is administeredvia the gastrointestinal tract, on by injection into subcutaneus tissue or muscle, its time-concentration behaviour is dependent on the absorption kinetics. Absorption is usually a first-order process, meaning that the rate of absorption is proportional to the amount of the drug atthe absorption site. The rate of absorption of a drug is influenced by its formulation, by theblood flow at the absorption site and by its biochemical properties, such as its water- andlipid solubility. Intravenous and intra-arterial routes of administration differ from other routesby circumventing absorption. Bioavailability is the amount and rate of the tracer available forsystemic circulation. It is affected by the same factors as the absorption (Irwin and Nutt1992).In the studies described here, the administration routes of the tracers to the systems wereintravenous injection (111In-BLMC) and infusion (BPA-F). The tracer concentrations andactivities were measured from the blood and urine, and in a few cases also from excisedtumour samples. Therefore, in these studies there is no need to model absorption mechanismsat the site of administration. Intravenous administration enables instant utilization of thetracer; therefore no bioavailability effects need be taken account.

The distribution of a drug in a physiological system is affected by many factors. The maincomponents are the vascularity, the blood flow to the tissues, the amount of unbound tracer inthe plasma, the tracer characteristics (for example the size, polarity, and solubility of thetracer) and tissue characteristics (for example the permeability barriers) (Irwin and Nutt1992). In a mammalian system, the main sites for distribution, are the plasma, theintracellular space and the extracellular space (Olkkola 1999). In the organs, for example,heart-muscle and the lungs are well perfused, whereas perfusion in the bone and the fattytissues is much less (Marvola et al 1999). In Figure 3 the different fluid compartments in thehuman body are schematically represented.

Figure 3. The physiological body fluid compartments and the membranes separating them, accordingto Guyton (Guyton and Hall 1996). The volumes correspond to an average man weighting 70 kg. Theoutput refers to the kidneys, lungs, faeces, sweat, etc.

Cell membrane

EXTRACELLULARFLUID(14 l)

Capillary membrane

INPUT OUTPUT

lymphatics

PLASMA(3 l)

INTERSTITIALFLUID(11 l)

INTRACELLULARFLUID(28 l)

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The volume of distribution (Vd) is a pharmacokinetic parameter that is defined as

Pd C

mV 0

� , (1)

where m0 is the total amount of tracer in the system and CP is the concentration of the tracerin the plasma (Irwin and Nutt 1992). This can be simplified by saying that tracers which havehigh lipid solubility have low plasma concentrations and therefore a high Vd (Irwin and Nutt1992). Tracers that have high solubility in water or strong binding to plasma proteins have alow Vd (Irwin and Nutt 1992).

Distribution of drugs to the central nervous system (CNS) is partly controlled by a specifictissue permeability barrier, the blood-brain barrier (BBB), which is a selective barrierbetween the intravascular and extravascular spaces. The BBB consists of three components;first there are tight junctions between the capillary endothelial cells; second, these endothelialcells have a low rate of endocytosis; and third, there are certain glial cell dendrites (footprocesses) around the blood vessels (Irwin and Nutt 1992). For survival and growth, a malignant tumour requires a good blood supply, which is achievedby angiogenesis (Folkman 1971, Neeman 2000) and vasculogenesis (Ribatti et al 2001). Theneoplastic growth of brain tumour tissue is often associated with a disrupted blood-brainbarrier (BBB), which allows intravascular tracers to leak into the extravascular space. Thischaracteristic can be utilized in diagnosis, and it has an effect on the transport of intravasculartracers to the tumour cells.In most parts of normal brain and areas of intact BBB, the capillaries are impermeable tointravascular contrast agents, i.e. iodinated agents used with CT scans and the gadoliniumcontrast chelates used with MRI (Atlas 1991, Kirkwood 1995). The presence of a disruptedBBB can be detected by contrast enhanced CT or MRI studies; in a neoplastic tissueintravascular contrast agents are able to leak through the defective BBB to the extravascular,interstitial space, which results in enhancement of the tumour on the images taken after theinjection of a contrast agent. The enhancement of a glioma on post-contrast MR images hasbeen reported to correlate with glioma grade, vascularity and proliferation activity (Tynninenet al 1999). By means of dynamic MRI studies, it is possible to quantitate the degree thepermeability defect of BBB. Generally, the more malignant the glioma, the more permeableare the vessels (Provenzale et al 2002, Roberts et al 2000).One of the main questions in treatment of tumours with chemotherapeutic agents, is thetransport of the tracers to the site of effect. There are published studies on a specificmembrane BLM-binding protein, which has an impact on the association between BLM andthe cells, and on its further internalization (Pron et al 1993). Little is known about thedetailed mechanism of this BLM internalization (Pron et al 1993), but it has been suggestedthat BLM is unable to diffuse through the cell membrane (Poddevin et al 1991). In an 111In-BLMC study with nineteen glioma patients, the uptake of 111In-BLMC, imaged with SPECT,was strongly associated with the BBB defect, evaluated on the post contrast T1-weighted MRimages, especially with high-grade glioma patients (Korppi-Tommola et al 1999). BPA isactively transported into tumour cells from the blood and is considered to be distributeduniformly in both the nucleus and the cytoplasm (Coderre et al 1998). It has been suggestedthat the 10B uptake is increased by the leakiness of the blood vessels (Clendenon et al 1990,Slatkin et al 1986, Soloway et al 1967).

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Elimination of a tracer occurs primarily by metabolism with excretion occurring via thekidneys (urinary excretion) and the bile (biliary excretion) (Irwin and Nutt 1992). Theprocesses of elimination and clearance of the tracer from a biological system involves twocomponents. First, there is a component of passive diffusion, which is independent of theconcentration of the tracer. Second, there is an active, energy demanding component, whichhas an enzymatic basis, and is thus dependent on the saturation level. When dealing with hightracer concentrations, the saturation limit of the tracer might be reached. In the glomerulae the contents (maximum size of 50 000 D (Marvola et al 1999)) of the bloodare filtered into the primary urine by the blood pressure. Depending on the chemicalcharacteristics of the substance and the prevailing circumstances, e.g. the electrolyte content,and the pH, the tracer can be further actively secreted into the urine, be taken up again fromthe urine or be unaffected. The elimination of a tracer is highly dependent on the functionalityof the organs of excretion and metabolism, for example renal failure, liver failure and cardiacdisease may have vast impacts on the rate and characteristics of elimination (Irwin and Nutt1992). The renal clearance of a substance is defined as the volume of plasma that iscompletely cleared of the substance by the kidneys per unit time (Guyton and Hall 1996).

3.3. Models

There has been a need to characterize the kinetics of the different tracers in a living systemand the first pharmacological models were available in the late 1930s. When modelling thebehaviour of a certain tracer in a living system, it is usually assumed that the tracer followsfirst order kinetics in the system (see equation 2) (Resigno and Segre 1966).

,dt

dC(t) )exp()0()()( gtCtCtgC ���� . (2)

In biological systems, zero-order and second-order kinetics are also common (Resigno andSegre 1966). For example, the clearance of ethanol form the blood obeys zero-order kinetics.Some tracers obey second order kinetics (Renner et al 2000) and some chemical reactionseven obey third-order kinetics (Davanloo and Crothers 1976, Resigno and Segre 1966).Enzymatic processes follow the more complicated Michaelis-Menten equation (Resigno andSegre 1966).

Most of the modelling in the area of clinical science is associated with exponential curvefitting. In the kinetic exponential function fitting method, a sum of the exponent functions isfitted to a time-concentration curve (Equation 3). The detected time-concentration curve inthe plasma, CP (t), can be represented as a sum of exponential functions;

� ��

iiiP tgAtC )exp()( , i = 1,2,3,… (3)

where Ai and gi are the constant and the coefficient, respectively. Usually, the time-concentration follows a descending curve. The solutions to this method are numerous, and themethods vary from curve peeling (Figure 4) to decomposition analysis. The curve peeling

16

technique is a classical method for bi-exponential analysis, which has been nowadays mainlydisplaced by more efficient computational methods.

(4)

Figure 4. An example of the curve peeling method for monoexponential function fitting, using afictional clearance curve (Lassen and Perl 1979).

In some cases it is difficult to decide the number of exponentials in the exponential function.This question is not mathematically unique; one has to decide on the criteria for the numberof exponentials that the fitting should include, and, furthermore the maximum error that canbe allowed in fitting. This question is related to error estimates. In most studies, backgroundand noise (i.e. total error estimates) cannot be separated objectively, and thus the question ofthe number of exponentials in the curves that are registered cannot be definitely solved.Moreover, it is difficult to define the optimal number of exponentials: exponents may be veryclose to each other, intensities of different decades or possible non-linear curve parts. Thetime-activity curves detected are affected by the study protocol. In Figure 5 schematicrepresentations of fitting sums of exponential functions to the same fictional data arerepresented.

Figure 5. Representations of fitting the sums of exponential functions to the same fictional data:mono-exponent function (a), bi-exponent function (b) and tri-exponent function (c).

(a) (b) (c)

time

1/g31/g1 1/g21/g1 1/g2

A2

A1

1/g1

A1

A3

A2

A1

Log

CB(t

)

t

Log

CB(t

)

t½

A1

(t)CB

t

A2

Log

CB(t

)

/t½gt)g(A(t)CB

2lnexp

1

11

�

��

17

From the exponential function fitting numerous transit times can be obtained, i.e. the meantransit time in the plasma pool (t1), the mean time of sojourn in the plasma pool, includingrecirculating concentration (t2) and the mean transit time in the total body pool (t3) (Lassenand Perl 1979), as represented in Study I. The half-life of a tracer in the urine can bedetermined by using the inverse of the regression coefficient of the semilogarithm of theurine time-concentration curve. The clearance (CL) can be obtained from the non-compartmental model (Lassen and Perl 1979), as represented in Study I.

Compartmental models are useful for describing a physiological system and its behaviour(Lassen and Perl 1979, Resigno and Segre 1966). In compartmental modelling, the mostimportant sites of the system, when regarding the aims of the modelling, are represented aspools or compartments. The definition of a compartment or pool is that it is a certain amountof material, the kinetic behaviour of which is homogeneously assigned (Lassen and Perl1979). In biological systems, the cells and the extracellular matrix can be divided intodifferent compartments, for example into plasma and blood cells, and it is common to dividethem into extra and intracellular fluids. Compartments can also be, for example, organs,tissues or even small groups of cells (Green 1992). Two types of compartmental models exist. In an open model there are interactions with theoutside world as opposed to the closed model, where no such interactions occur. An exampleof an open two-compartment model and the related equations is represented in Figure 6.

)()()(

)()()()(

2121212

101212121

tCktCkdt

tdC

tCkktCkdt

tdC

��

���� Input (5)

Figure 6. Schematic representation of an open two-compartmental model. C1 and C2 denote theconcentrations in the compartments, and kij are the transfer coefficients between the pools.

The compartment equations (see eq. 5) can be solved, either with a Laplace transformation(Resigno and Segre 1966) or by iterative computer methods (Feldman 1977a, Feldman1977b). There are certain restrictions to compartment modelling. The substance underinvestigation has to enter directly and rapidly into the intravascular plasma volume. Theflows between the compartments must be steady and the kinetics of the system have to belinear. The linear systems can be described by ordinary differential equations. It is alsoassumed that fluxes between compartments are linear and follow first-order kinetics and thatthe kinetic behaviour of every compartment is distinct and homogeneous.

Individual numerical models can be constructed when the existing models are not suitable ornot adequate. Certain precautions, however, should be taken into account. Firstly, the limitsand the circumstances within which the model is applicable should be predetermined.Secondly, careful proposals for the correspondence between the physiological properties ofthe system and different parameters of the model are desirable.

k01

k21

k12

1

Input

2

18

The concept of the uniqueness of a model has raised some debate (Berman 1963, Kuikka et al1991). On the other hand, it is possible to think that no perfectly unique model can ever beconstructed (Kuikka et al 1991), because it is always possible to construct an alternative,equally accurate or even more accurate than a previous model. The uniqueness of a model isdetermined by its degree of freedom, which depends on the number of parameters. If the totalnumber of parameters is n, then with the measured data it is possible to construct m�nindependent equations between the different parameters (Berman 1963). As a consequence,the degree of freedom is f=n-m, and a unique model is possible, when f=0. If m<n, theuniqueness of the model is possible only if new measured data are available or somepresumptions are made about the behaviour of the model, based on the simplicity anddeterministic behaviour of the system (Berman 1963). Even then, however, uniquenesscannot be guaranteed.

The aim has been to produce a simple and robust model tolerant to fault. No model can beunique, because it is always possible to create models that are more exact and more detailed(Berman 1963, Kuikka et al 1991) but the question of the limits to the complexity of themodel then arises. One of the goals in developing new models is the potential to providepathophysiological predictions. It is essential to have some insight into the physiology of thesystem under study in order to obtain appropriate data and choose appropriate models. Withthese considerations, one can make decisions regarding which parts of inaccessible data andwhether the complexity of the extraction and exchange routes can be ignored.

19

4. MATERIALS AND METHODS

4.1. Tracers

Bleomycin (BLM) is a chemotherapeutic agent that blocks DNA synthesis, and at highconcentrations destroys the cell by breaking DNA. The cells are most sensitive to bleomycinduring the G2 and M-phases of the cell cycle (Dorr 1992). BLM contains 13 basicglycopeptides, and is used as bleomycin sulphate, diluted with sodium chloride or glucose(Lääketietokeskus 2000). The molecular weight of BLM is about 1400 (Umezawa et al 1966)and there are three functional components in its molecule (Kairemo et al 1996b). Thegalactose and mannose derivatives may be responsible for tumour cell recognition (Kairemoet al 1996b), while the metal-chelating part could explain the anti-tumour activity of thisorganometallic compound. The terminal part of the molecule is probably responsible for theDNA cleavage in tumour cells (Kairemo et al 1996b). The structure of BLM is shown inFigure 7.

Figure 7. The structure of bleomycin (Dorr 1992). The double bonds are represented as bold lines.

In the case of normal kidney function, the biological half-life of BLM is 115 min(Lääketietokeskus 2000). About 60-70 % of the dose is excreted through the kidneys within24 hours of injection (Lääketietokeskus 2000). BLM binds to a slight extent to plasmaproteins. It has been suggested that the metabolism of BLM with inactive species involvescytosolic cysteine proteinase, the so-called bleomycin hydrolase (Dorr 1992). The dose-

20

limiting side-effects (10% of the patients) are seen in the lungs and include pneumonitis andeven lung fibrosis (Lääketietokeskus 2000). Indium-111 is a metal with a physical half-life of 67 hours (Mettler and Guiberteau 1998).The radiolabelling technique and formulation of the 111In-BLMC were performed by MAPMedical Technologies Ltd. (Tikkakoski, Finland) using a modification introduced by Hou etal. (Hou et al 1985). The labelled BLMC was found to be stable in vivo for up to 24 h(Hiltunen et al 1989). According to the literature, the clearance of 111In-BLMC is roughlysimilar to that of BLM; over 95% of the activity is excreted within 24 h (Kairemo et al1996b). 111In-BLMC accumulates in tumour tissue with an even higher uptake than theunlabelled form (Hou et al 1984), and a positive correlation has been found between theuptake and the frequency of mitoses and grade of proliferation (Kairemo et al 1996a).

Boronophenylalanine (BPA) is a boron containing amino acid. In the molecule, boron anddihydroxide groups are attached in the para position on a benzene ring (see Figure 8). BPAhas limited solubility in neutral (e.g. physiological) conditions, and thus it is used as BPA-F,a fructose complex (Mori et al 1989, Yoshino et al 1989). The molecular weight of BPA-F isabout 330. The BPA in the BNCT-trials in Finland was produced by Katchem s.r.o., CzeckRepublic and the final preparation was performed by HUCH Hospital Pharmacy. Theenrichment ratio 10B/11B was >99.7%.

Figure 8. The suggested structure of the BPA-fructose complex.

In Study II, with beagle dogs, the 10B concentrations in the respective blood samples weremeasured, using inductively coupled plasma-mass spectrometry, ICP-MS (Kulvik et al 2002).In Studies III and IV (BNL patients), the 10B concentrations in the respective blood sampleswere determined, using direct current plasma-mass spectrometry and/or prompt gammaneutron activation analysis (Chanana et al 1999, Elowitz et al 1998). In all the BNCT trials inFinland, the 10B concentrations in the whole blood samples were determined by inductivelycoupled plasma atomic emission spectroscopy (ICP-AES) (Laakso et al 2001). Thecomparison between these methods has been reported elsewhere (Laakso et al 2001). Thetime required for the 10B concentration to be determined from the blood samples by ICP-AESis about 10 minutes.

4.2. Materials

In Study I, there were 12 patients with a histologically verified tumour, 8 male and 2 femalepatients diagnosed with a glioma, one male patient with a meningioma, and one femalepatient diagnosed with adenocarcinoma metastatic to the brain. The age of the patients ranged

H

HO-CH2 CH2-O

H OH

OH H

O

O

B-

OH

CH-CH-COO-

NH3+

21

from 32 to 70 years at the time of the study; the mean age was 50 years. These patientsreceived from 2.0 to 3.3 mg of 111In-BLMC with a specific activity of 60 MBq/mg as a fastbolus injection. Blood samples were collected from each of the patients after varying timeintervals, with a mean of 12 samples per patient during 24 hours. Urine samples were alsocollected from every patient. The activities of the samples were determined with a gammacounter about 75 hours after the injection.

The beagle dogs studied were part of a study of the radiation tolerance reported elsewhere(Benczik 2000). From a total of 46 pure-bred beagle dogs, nine healthy individuals were usedas study objects in Study II. The beagles received various amounts of infused BPA during 30minutes or one hour. Blood samples were collected from every dog and urine samples werecollected from two dogs. The characteristics of the study objects are represented in Table 1 ofStudy II.

Ten histologically verified patients with glioblastoma multiforme and six additional patientswith glioma, formed the patient population of Study III. The first ten patients were part of thephase I BNCT clinical trial at Brookhaven National Laboratory (BNL); they received a two-hour infusion of BPA-F of 290 mg BPA/kg body weight (Chanana et al 1999). The age ofpatients varied from 40 to 81 years, and their mean age was 62 years. The weights of thepatients ranged from 65 kg to 104 kg, mean weight 82 kg. The six additional patients werefrom the BPA-F biodistribution studies conducted at BNL (Elowitz et al 1998). Thesepatients received one of the six different amounts of the compound studied (127 mg/kg, 170mg/kg, 210 mg/kg, 250 mg/kg, 290 mg/kg or 330 mg/kg); the infusion time was two hours.There were, further, two patients who received a one-hour infusion of 170 mg BPA/kg bodyweight. The weights of the patients ranged from 64 kg to 95 kg, mean weight 75 kg.

The patient group in Study IV consisted of the 10 patients with glioblastoma multiforme fromBNL (the patient population partly overlapping that of Study III), and a cohort of ten patientswith glioblastoma multiforme from the BNCT trial carried out in Finland (Kankaanranta et al2000, Laakso et al 2001). The ten glioblastoma multiforme patients who were part of theFinnish BNCT trial received a 2-hr infusion of 290 mg BPA/kg body weight. The weights ofthe patients varied from 53 kg to 89 kg, mean weight 72 kg. The flexibility of the models wastested using two additional Finnish volunteers, who participated in a biodistribution study:one volunteer received a 2-hr infusion of 330 mg BPA/kg body weight; the other received a3-hr infusion of 450 mg BPA/kg body weight. Since Study IV 11 further patients have been treated in the Finnish BNCT trials (Joensuu etal 2002b). Their weights varied from 64 to 105 kg, mean 82 kg. There were three females andeight males. All but three patients had previously unirradiated gliomas. Their detailedcharacteristics are presented in Table 1.

The purpose of this thesis, is to gather and analyse the kinetic data from all the patients in theBNCT trials in Finland. Ten patients were included in Study IV, and eight further patientswithout prior photon irradiation have been treated with BNCT in Finland (Joensuu et al2002b). Three patients with gliomas which progressed following surgery and conventionalradiotherapy, treated in another protocol, are also included (Joensuu et al 2002b).

22

Before injection of the tracers, written informed consent was obtained from every patient inStudy I and from all the patients who took part in the BNCT trials in Finland. The researchprotocols were approved by the Ethical Committee of the Helsinki University CentralHospital. In Study II the experimental protocols were reviewed and approved by theappropriate ethical committees of the respective Institutions (Benczik 2000). The dogs werepurchased from the National Laboratory Animal Centre, University of Kuopio; they werebred specifically for research purposes (Benczik 2000). In Study III the research protocol wasapproved by the Institutional Review Board of Brookhaven National Laboratory andinformed consent was obtained from every patient (Elowitz et al 1998).

Table 1. The characteristics of the series.

Dosage[mg BPA/kg]

Infusion time Characteristics

Study IIDog study (n=9)

250250700

1 hour (n=2)30 minutes (n=5)1 hour (n=2)

Group A in article IIGroup B in article IIGroup C in article II

Study IIIHuman study(n=15)

127170170250290330

2 hours (n=1)2 hours (n=1)1 hour (n=1)2 hours (n=1)2 hours (n=10)†

2 hours (n=1)

Study IVHuman study(n=20)

290290330450

2 hours (n=10)†

2 hours (n=10)¶‡2 hours (n=1)3 hours (n=1)

Protocol P01

Joensuu et al.�Human study(n=21)

290290330360400

2 hours (n=12)¶‡2 hours (n=3)¶

2 hours (n=1)¶

2 hours (n=3)¶

2 hours (n=2)¶

Protocol P01Protocol P03 ¦ Protocol P01Protocol P01Protocol P01

† The patient populations overlap.‡ The patient populations overlap.� Original patient series is to be published elsewhere (Joensuu et al 2002b).¶ BNCT trials in Finland.¦ Gliomas progressing following surgery and radiotherapy

23

4.3. Models and computational methods

The algorithms for the exponential function fitting programs are mostly modifications ofthose developed by Marquardt (Bard 1970, Lemaitre and Malengé 1971, Pitkänen et al 1982,Provencher 1976, Sperber et al 1990). One frequently used algorithm is based on the Nelder-Mead simplex algorithm for minimizing a nonlinear function of several variables. The use ofsuch programmes does not exclude the basic problem of curve fitting in nuclear medicine.

In Study I with 111In-BLMC, the fitting of the exponential functions to the observed plasmaactivity data was performed by the method described by Guardabasso et al (Guardabasso et al1989), using an MS-DOS-based Expfit programme (version 1.6). In this method, the dataobtained are fitted iteratively until the convergence criteria are met. The residual variance testand the runs test provide indices of the goodness of fit (Guardabasso et al 1989). The samemethod was used in Studies II and IV. In all the studies, the data were fitted without usingadjusted parameter estimations.

In Study III, an exponential fitting programme designed by Mika Kortesniemi, a physicist ofthe BNCT group in Finland, was introduced. In this thesis, the programme is called FinFit. InFinFit, an iterative gradient search algorithm was implemented for the bi-exponentialfunction fitting (Kortesniemi 2002). The code of the bi-exponential fitting application waswritten in Visual Basic to operate as a Microsoft Excel macro programme with a clinicalinterface (Kortesniemi 2002). When studying the kinetic data from all the patients in the BNCT trials in Finland, theexponential fittings were carried out with two programmes, with the Expfit programme andwith the Macro fitting programme designed by Mika Kortesniemi (Kortesniemi 2002).

Compartmental models were solved using the SAAM II (Simulation, Analysis and ModellingSoftware II)-program (Barret et al 1998, RFKA 1994). Computationally, the programmeforms a set of ordinary differential equations from the user’s specified compartmental modelstructure and simulates the solutions according to the given parameter values and theinformation from the input(s) (Barret et al 1998). In the fitting process, the iteration continuesuntil 1) the convergent criteria, adjusted by the user, are fulfilled, 2) the maximum number ofiterations is reached or 3) some of the parameters are outside its limits. These three items areall adjustable by the user. SAAM II provides a few integration methods, which do notinfluence the final result of the fit, but do influence the running time taken for the fit (Barretet al 1998). In these studies, the default integrator, i.e. the Rosenbrock integrator was chosen.The optimizer in SAAM II is a modification of the Gauss-Newton method, which deals withthe case of multiple datasets (Bell et al 1996).

The numerical model construction originated from the basic simplified assumptions of thebehaviour of BPA-F. For BPA-fructose molecules, the blood compartment is assumed to bewell mixed, connected with the body tissues through a diffusive membrane, and providedwith an excretion channel through the kidneys. Apart from the infusion input, the rate ofchange of the 10B concentration in the blood, must be a function of the 10B concentrationeverywhere in the body, � �C r t�, , written as

24

� � � �� � )(, tDtrCFtCdtd

B ���

� , (6)

where D(t) is the infusion input.

Obviously, a simplified expression is needed to substitute � �� �F C r t�, , which describes theresponse of CB(t) to all the 10B-transfer processes between the blood compartment and therest of the body. The first test is to replace � �� �F C r t�, by a polynomial expression of constantcoefficients. It is worth noting that the same expression must comply with the observationsboth during and after the infusion in order that the observations made during the infusion cancontribute fully to the forthcoming development. It should further be noted that there is nozero power term in this expression, since if the concentration itself is zero, the rate of changeof the 10B concentration in the blood must also be zero. From a trial comparison of thispolynomial model with the data, it is obvious that the first order term is not enough.When dealing with atypical kinetic behaviour of 10B in the blood, it was observed that asimple polynomial model was reasonable, but not reliable enough. Atypical kinetic behaviourhere refers to the vast variation in 10B-clearance between a patient and the patient populationused in the development of the model. For this reason, the model was further developed byaltering the form of the polynomial expression. A more complex model was created, based onthe findings in the previous models. A memory effect was introduced into the model. Thenew polynomial model has an analytical solution for the post-infusion times. The solution forall times can also be obtained by numerical integration according to the algorithm:

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

infm

02

11

infm

02

101

t> t when,)()(1

)()(

t t when,)()(1

)()(

3

3

amBm

mmB

mBmB

amBm

mmB

mBmB

tCtCa

atCtC

tCtCa

aDtCtC

(7)

where tm is the discrete time variable and tinf is the time of the infusion (in minutes). FromEquation 7 we know that, at time t=1 min, CB(t=1)=D0. This model is hereafter referred to asthe 4-parametric model. The model had only four parameters, an overall amplitude parameterD0, and parameters a1, a2 and a3. However, considering the small number of data points, thenumber of independent parameters was relatively high, which decreased the fitness of themodel. For this reason, a new, 3-parametric model was formed in which the number ofparameters was decreased by setting the value of parameter a1 at 1, as represented in StudyIV.

The Levenberg-Marquardt method is widely used and is efficient for solving non-linear least-squares problems (Marquardt 1963). When the results are not near the minimum, thealgorithm uses the steepest descent method in evaluating the size of the iteration step. As the

25

solution approaches the minimum, the Hessian matrix replaces the steepest descent methodfor determining the step size. As with any iterative fitting method, the impact of the initialparameter estimate is high.

4.4. Statistical methods for models

Statistical methods were used to test the models against the data, i.e. the goodness of fit, andto test the different models against each other. In all the statistical analyses, a p-value 0.05was considered statistically significant.

When testing a model versus data, the chi-squared test (�2 test) is widely used as thegoodness-of-fit test. With this test, the compatibility of the results obtained from the modeland the actual measured results and their dependence on the qualitative variables can bestudied (Vasama and Vartia 1980a). In the �2 test, the first quantity to be defined is

� � ,1

22��

�

�

k

i i

ii

eeoX (8)

where k is the number of data points, oi is the observed value (i.e. the result of the model) andei is the expected value (i.e. the actual result) (Vasama and Vartia 1980b). The high values ofthe X2-quantity may be due to the wide deviation between the observed and expected valuesand the large number of classes (Ranta et al 1999). From this, it follows that the number ofclasses, i.e. parameter k in Equation (8), has a marked impact on the distribution of the testquantity X2. The degree of freedom is a parameter that is now defined as df=k-1. The F test, known also as the variance ratio test, is useful and simple. The distribution of theF statistics has two values for degrees of freedom, one corresponding to each variance(Altman 1994).

When testing one model against another, it is necessary to compare the created models witheach other accurately, firstly to find out whether the new model is significantly better (orworse) than the previous one and secondly to place the different models in order.

whether the differences between the models are significant. It is a non-parametric form of

assumptions of a parametric method (Altman 1994). However, from Friedman’s two-way testof the analysis of variance it is not possible to discern the actual order; an overall significantP value does not indicate where the differences lie (Altman 1994). The Wilcoxon matched pair test is efficient for specifying the order of the models accordingto their mean absolute differences (Altman 1994). This test is a non-parametric analogue ofthe paired t-test (Ranta et al 1999). The Wilcoxon test is practical even when the paireddifferences do not follow a normal distribution (Ranta et al 1999), but it assumes that theobservations come from a population with a symmetrical distribution (Altman 1994).

Friedman’s two-way test of analysis of variance, is useful when it is necessary to know

two-way analysis of variance which can be used for data sets that do not fulfil the

26

5. RESULTS

5.1. 111In-BLMC

The mean transit time of 111In-BLMC in the plasma pool was 14�7 min without, and 1.8�0.6h when including recirculation, and 13�4 h in the total body pool. The mean plasmaclearance of 111In-BLMC was 0.3�0.1 ml blood/min and the mean half-life in urine was3.5�0.6 h.

An open three-compartmental model was found to be the most accurate (Figure 9). The meantransfer coefficients for the open three-compartmental model were: excretion from plasma =0.02�0.01, from depot to plasma = (12�9)�10-4, from plasma to depot = 0.01�0.01, fromtumour to plasma = 0.39�0.19 and from plasma to tumour = 1.11�0.57, all in units perminute-1. The mean turnover time from the tumour was 4.5�2.7 min and from the depot 20�8h.

Figure 9. An open three-compartmental model for the kinetics of 111In-BLMC.

5.2. BPA-F and 10B

In the animal study with beagle dogs, the bi-exponent function fit was found to be the most

using no initial parameter estimations.

In the dog study, data were available from the urine, and therefore more complexcompartmental models were constructed. The two main models are represented in Figure 10(a) and (b), and the corresponding transfer coefficients of the model in Figure 10 (b) aregiven in Table 2.

kEP

kPDkTP

kPT kDP

Tumour Plasma Depot

accurate of the exponential function fits. Fitting was performed with the Expfit programme,

27

10B after BPA-F infusion in the animal

studies.

In Study III, application of the bi-exponential fit used was FinFit (Kortesniemi 2002). Thefast and slow components of the mean half-lives of the 10B in the blood were 16�5 min and6.6�2.0 h, respectively. For the first irradiation field, starting about 180 minutes after thebeginning of the infusion and ending after about 210 minutes, the estimated boronconcentration, according to the pre-field situation, was 1.0 ppm (7%) higher than the value

about 240 minutes after the beginning of the infusion and ending after about 260 minutes, itwas 0.2 ppm (2%) lower, respectively.

In Study III, a two-compartmental open model (Fig. 11) was fitted to the 10B blood time-

were applied to the data from 10 patients who received a two-hour infusion of BPA-F of 290mg BPA/kg body weight. Distinct models were constructed for each of the ten patients. Theaccuracies of the two constructed models were tested with additional data from patients whowere part of the BPA-F biodistribution studies conducted at BNL (Elowitz et al 1998).

Figure 11. The compartmental model for the kinetics of 10B after BPA-F infusion in humans.

(a) (b)

kEK

kPT

kPK

kTP

Kidneys

Plasma Tumour

kKP

kPD

kUP

kDP

Urine

Plasma Depot

kEB

KBD

kDB

Blood Depot

concentration curve. The two compartments were blood and a depot. Compartmental models

from the final fit, including all the points measured. In the second irradiation field, starting

Figure 10. The compartmental models for the kinetics of

28

Table 2. The mean transfer coefficient (� 1 SD of the mean) for the BNCT trials, all transfercoefficients are in units of 10-3/min. The unit in dosage is mg BPA/kg. k = transfer coefficient;P=plasma; B=blood; D=depot; T=tumour; K=kidneys, U=urine, E=excretion, see Figs. 12-13.

Dosage Infusion time kPD kDP kUP

Study IIAnimalstudy (n=9)

250250700

1 hour (n=2)30 minutes (n=2)1 hour (n=5)

35±2014±7026±11

3700±41001130±126093±49

130±100170±19023±40

Dosage Infusion time kBD kDB kEB

Study IIIHuman study(n=18)†

127170170210250290290330

2 hours (n=1)2 hours (n=1)1 hour (n=2)2 hours (n=1)2 hours (n=1)2 hours (n=10)†�2 hours (n=1)*2 hours (n=1)

287737684264�476028

410681183410209325�208325111

513223172831�53117

Study IVHuman study(n=20)†‡

290290330450

2 hours (n=10)†2 hours (n=10)‡2 hours (n=1)3 hours (n=1)

60�3349�176316

325�207318�110402167

31�531�83115

Joensuu etal.Human study(n=21)‡

290290330360400

2 hours (n=12)‡2 hours (n=3)¦ 2 hours (n=1)2 hours (n=3)2 hours (n=2)

45±1856±296135±336±7

289±120378±155391235±51210±4

31±833±93129±334±12

† The patient populations overlap.‡ The patient populations overlap.� The data used for model construction.¦ Gliomas progressing following surgery and radiotherapy* Data used for testing the model.

In Study IV, the patient data were modelled with a bi-exponential fit, compartmental modelsand non-linear models. With BNL data, only four data points were available and fourparameters in the bi-exponential model to fit the data. Because of this, a perfect fit wasachieved. The mean absolute differences in the estimated 10B concentrations of the clearancephase for the Finnish patients were 0.28�0.20 ppm (2.1%), using all the available data points.The fast and slow components of the mean half-lives of the 10B clearance from blood were24�31 min and 5.4�2.6 h for the BNL study with all data points, respectively. For the BNL

provided mean absolute differences, which were about four times higher than the resultobtained with the 3-parametric non-linear model; however, for the second irradiation field theerror was only one and a half times as high. For the biodistribution study in Finland, with 330mg BPA/kg body weight, the mean absolute difference during the clearance phase for the

studies, during the clearance phase for the first irradiation field, the bi-exponential fit

29

second irradiation was 0.8 ppm, but, for the data available before the first irradiation field, noreasonable model could be fitted. For the study with 450 mg BPA/kg body weight, the meanabsolute differences during the clearance phases for the first and second irradiations wereabout 4 ppm and 2 ppm.

In Study IV, the mean absolute differences in the estimated 10B concentrations for theclearance phase in the BNL patients were 0.67�0.41 ppm (4.1%) for the open two-compartmental model, using all the available data points. For the open two-compartmentalmodel with the BNL patients, the error was about five and a half times higher than the errorusing the 3-parametric model for the first field, and for the second irradiation it was still threetimes as high. For the Finnish biodistribution study with 330 mg BPA/kg body weight, themean absolute differences during the clearance phase between the first and the secondirradiations were 3.5 ppm and about 2 ppm. For the study with 450 mg BPA/kg body weight,the mean absolute differences during the clearance phase for the first and second irradiationswere about 4 ppm and 1 ppm.

Non-linear models were introduced in Study IV. According to the results of Study IV, themean absolute differences in the estimated 10B concentrations for the clearance phase and forthe BNL patients were 0.11�0.06 (0.7%) for the 3-parametric non-linear model, using all theavailable data points. For the patients from the BNCT trials in Finland, the mean absolutedifferences in the estimated 10B concentrations were 0.38�0.30 (2.7%). For the BNL studies,the 3-parametric non-linear model provided the most accurate fits. The mean absolutedifference during the clearance phase for the first irradiation was 0.39 ppm and for the secondirradiation it was 0.27 ppm. For the BNCT trials in Finland the results were similar: the meanabsolute differences during the clearance phase for the first and second irradiation fields wereless than 0.5 ppm, and thus this was the most accurate model. For the 330 mg BPA/kg studyduring the infusion and clearance phases, the mean absolute differences obtained, using the 3-parametric non-linear model, were about 1 ppm for every treatment assembly; this wasclearly superior to the other models, especially when using the data available before the firstirradiation field. For the biodistribution study, with a three-hour infusion of 450 mg BPA/kgbody weight, the mean absolute difference of the 3-parametric non-linear model to the 10Bconcentration was 2.2 ppm for the first estimation and about 1 ppm for the second irradiationfield.

All the data on patients from the BNCT trials in Finland, i.e. part of Study IV (treated patientsfrom Finland) and from the more recent patients (Joensuu et al 2002b) were gathered and thesuitability of the kinetic models created for estimation of the 10B concentration after BPA-Finfusion was evaluated. The results of fitting the patient data with exponential function fitsare represented in Tables 3 and 4 for both the Expfit programme and FinFit programme.Table 3 gives the mean half-lives and Table 4 are the maximum and mean absolutedifferences between the measured and estimated 10B concentrations. The results imitating theactual treatment protocol are shown, i.e. first using the data points available before the firstirradiation field, then using the data points available before the second irradiation field, andfinally using all the available data points.

30

Table 3. The mean half-lives (� 1 SD of the mean) of the 10B after BPA-F infusion obtained from theExpfit and FinFit computer programmes using all the available data points for all the patients in theBNCT trials in Finland.

Dosage[mg BPA/kg]

Infusion time t½ fast[min]

t½ slow[h]

Expfit FinFit Expfit FinFit

290290330360400

2 hours (n=12)2 hours (n=3)¦ 2 hours (n=1)2 hours (n=3)2 hours (n=2)

18�1011�2�2518�79�3

16�79�32517�79�3

5.4�2.14.2�0.1�7.76.2�1.53.3�0.2

5.0�0.64.0�0.47.75.9�1.63.3�0.2

¦ Gliomas progressing following surgery and radiotherapy� The model was available for two patients only.

Table 4. The maximum and mean absolute differences between the measured and estimated 10Bconcentrations obtained from the biexponent function fits, using data available before the first and thesecond irradiations and using all the data points for the patients in the BNCT trials in Finland, all inppm.

Clearance phase First field Second field All data points

Dosage max mean max mean max mean

Expfit 50 4.58 (37 %) 2.08 0.30 (2.3 %) 0.56 0.17 (1.0 %)290 mg BPA/kg2 h infusion (n=12) FinFit 2.01 0.63 (4.5 %) 2.88 0.49 (3.3 %) 9.48 0.57 (3.3%)

Expfit † † 0.85 0.13 (1.0 %) 0.32 0.11 (0.8 %)290 mg BPA/kg2 h infusion (n=3)¦ FinFit 2.42 0.63 (4.16 %) 2.42 0.48 (3.1 %) 2.39 0.49 (3.2 %)

Expfit ‡ ‡ 2.34 0.75 (6.0 %) ‡ ‡330 mg BPA/kg2 h infusion (n=1) FinFit 1.51 0.58 (3.9 %) 2.27 0.73 (5.9 %) 0.90 0.37 (2.7 %)

Expfit 3.28 0.9 (5.3 %) 0.15 0.15 (0.9 %) 0.48 0.11 (0.5 %)360 mg BPA/kg2 h infusion (n=3) FinFit 28 1.19 (11 %) 9.69 0.65 (5.4 %) 9.75 0.74 (5.0 %)

Expfit 1.86 0.57 (2.8 %) 0.93 0.25 (1.5 %) 0.89 0.23 (1.2 %)400 mg BPA/kg2 h infusion (n=2) FinFit 1.86� 0.48 (2.8 %)� 0.92 0.24 (1.5 %) 0.89 0.23 (1.2 %)

¦ Gliomas progressing following surgery and radiotherapy†The model was not available for any of the three patients.‡The model was not available for the patient.�The model was available for one patient only.

31

Due to its limited calculation properties, the EXPIT programme was unable to perform thedesired bi-exponential model in all the cases. Figure 12 a, b, c presents the results of the twomodels for a patient who received 360 mg of BPA/kg body weight during two hours, usingthe data available before the first irradiation field and before the second irradiation field, andusing all the available data points, respectively. For the patient in Figure 12, the mean halflives obtained from the Expfit and FinFit using all the available data points were t½

fast=12 minand t½

slow=4.5 h, and t½fast =10 min and t½

slow=4.4 h, respectively. The initial parameter valuesused as the original parameter estimations for the iteration process in the FinFit weret½

fast=16 min and t½slow=5.2 h

The suitability of an open compartmental model for the kinetics of 10B after BPA-F infusionfor BNCT with patients from the BNCT trials in Finland was evaluated. The final meantransfer coefficients for the open two-compartmental models for all the BNCT-related studiesare represented in Table 5. Table 5 also presents the transfer coefficients that arerecommended for use as initial values in the Finnish BNCT trials with 290 mg BPA/kg bodyweight. Figure 13 depicts the final transfer coefficients for all the patients from the BNCTtrials in Finland, i.e. part of Study IV and the more recent patients (Joensuu et al 2002b), as afunction of increasing amounts of BPA.

Table 5. The initial transfer coefficient (� 1 SD of the mean) estimates for the BNCT trials carried outin Finland and the final results for all the patients from the BNCT trials in Finland, who received 290mg BPA/kg body weight (n=15), all in units 10-3/min. k = transfer coefficient; B=blood; D=depot;E=excretion, see Figure 11.

kBD kDB kEB

Initial estimate 60�33 325�207 31�5

All BNCT patients treated in Finlandwith 290 mg BPA/kg body weight

47�20 307�127 31�8

Table 6 shows the final parameters of the 3-parameter non-linear model applied to all thepatients from the BNCT trials in Finland who received 290 mg BPA/kg body weight,together with the initial parameter estimate obtained from fitting the averaged data fromStudy IV.

Table 6. The initial parameter estimations and final parameters (� 1 SD of the mean) for the 3-parameter model of the Finnish BNCT trials for patients who received 290 mg BPA/kg body weight.

a2 a3 D0

Initial estimate 10.94 2.82 0.65

BNCT trials in Finland (n=12), unirradiated glioblastomas 104�175 3.33�0.44 0.61�0.17

BNCT trials in Finland (n=3), irradiated glioblastomas 127�95 3.53�0.39 0.49�0.19

32

Figure 12. Results of the Expfit (solid line) and FinFit(broken line) exponential function fittingprogrammes for one patient who received 360 mg of BPA/kg body weight during two hours, using thedata available before the first irradiation field (a), before the second irradiation field (b) and all theavailable data points (c). The measured data points are expressed as circles, where full circlesrepresent the data available for the fit. Start and end indicators of the fields are presented as verticallines. The inserted figures represent the differences between the models and the measured data.

33

Figure 13. The transfer coefficients kDB (a), kBD (b) and kEB (c) from the open two-compartment modelfor all the patients from the BNCT trials in Finland as a function of increasing amounts of infused BPA.Closed and open diamonds represent the primary and recurrent gliomas, respectively. The regressionlines are represented as broken lines. The correlation coefficients are 0.68, 0.57 and 0.36 for kDB, kBD

and kEB, respectively. k=transfer coefficient, DB=to depot from blood, BD= to blood from depot, andEB=excretion from blood.

0

10

20

30

40

50

250 290 330 370 410

Amount of BPA [mg/kg body weight]

k EB[1

0-3 m

in-1

]

0

20

40

60

80

100

250 290 330 370 410

Amount of BPA [mg/kg body weight]

k BD

[10

-3 m

in-1

]

0

100

200

300

400

500

600

250 290 330 370 410

Amount of BPA [mg/kg body weight]

k DB [1

0-3 m

in-1

]

(c)

(a)

(b)

290 330 360 400

290 330 360 400

290 330 360 400

Amount of BPA [mg/kg body weight]

Amount of BPA [mg/kg body weight]

Amount of BPA [mg/kg body weight]

34

In Figure 14 the values for the 3-parameter non-linear model for all the patients from theBNCT trials of Finland as a function of increasing amount of infused BPA are presented.Figure 15 represents the results of all the models for one patient from the recent BNCT trialsin Finland given 290 mg BPA/kg body weight, and who had had prior cranial irradiations,using data available before the first irradiation field (a), using data available before thesecond irradiation field (b), and using all the available data points (c). The inserted figuresrepresent the difference between the model and measured data. Figure 16 shows thecorresponding results for one patient given 360 mg BPA/kg body weight, and Figure 17 forone patient infused with 400 mg BPA/kg body weight.

The maximum and the mean absolute differences between the measured and estimated 10Bconcentrations obtained from 3- and 4-parametric non-linear models, an open two-compartmental model and bi-exponential fit using the data points available before the firstirradiation and the second irradiation, and with all the data are represented in Tables 7(infusion and clearance phases) and 8 (clearance phase).

35

Figure 14. The parameters a2 (a), a3 (b) and D0 (c) from the 3-parameter non-linear model for all thepatients from the BNCT trials in Finland as a function of increasing amounts of BPA. Closed and opendiamonds represent the previously unirradiated and irradiated gliomas, respectively. The regressionlines are represented as broken lines. The correlation coefficients are 0.15, 0.49 and 0.95 for a2, a3

and D0, respectively.

0

0.3

0.6

0.9

1.2

D0

2

2.5

3

3.5

4

4.5

a 3

(b)

0

200

400

600

800

250 290 330 370 410

a 2

(a)

(c)

Amount of BPA [mg/kg body weight]

Amount of BPA [mg/kg body weight]

290 330 360 400

290 330 360 400

Amount of BPA [mg/kg body weight]

290 330 360 400

36

Figure 15. The results of the open two-compartment model (full curve), the bi-exponential fit (FinFit)(broken curve) and the 3-parameter non-linear model (chain curve) for one patient given 290 mg BPA/kgbody weight and a previously irradiated glioblastoma from the recent BNCT trials in Finland using dataavailable before the first irradiation field (a), data before the second irradiation field (b) and using all theavailable data points (c). The measured data points are expressed as circles, where full circles representthe data available for the fit. Start and end indicators of the fields are presented as vertical lines. Theinserted figures represent the difference between the model and measured data.

37

Figure 16. The results of the open two-compartment model (full curve), the bi-exponential fit (FinFit)(broken curve) and the 3-parameter non-linear model (chain curve) for one patient infused with 360mg BPA/kg body weight and a previously unirradiated glioblastoma from the recent BNCT trials inFinland using data available before the first irradiation field (a), data available before the secondirradiation field (b) and using all the available data points (c). The measured data points areexpressed as circles, where full circles represent the data available for the fit. Start and end indicatorsof the fields are presented as vertical lines. The inserted figures represent the difference between themodel and measured data.

38

Figure 17. The results of the open two-compartment model (full curve), the bi-exponential fit (FinFit)(broken curve) and the 3-parameter non-linear model (chain curve) for one patient from the recentBNCT trials in Finland infused with 400 mg BPA/kg body weight and a previously unirradiatedglioblastoma using the data available before the first irradiation field (a), and the second irradiation field(b) and using all the available data points (c). The measured data points are expressed as circles,where full circles represent the data available for the fit. Start and end indicators of the fields arepresented as vertical lines. The inserted figures represent the difference between the model andmeasured data.

Tab

le 7

. T

he m

axim

um a

nd m

ean

abso

lute

diff

eren

ces

betw

een

the

mea

sure

d an

d es

timat

ed 10

B c

once

ntra

tions

cal

cula

ted

for

the

infu

sion

and

clea

ranc

e ph

ases

, ob

tain

ed f

rom

the

mod

els,

usi

ng d

ata

avai

labl

e be

fore

the

firs

t an

d th

e se

cond

irra

diat

ions

, an

d us

ing

all t

he d

ata

poin

ts f

rom

all

the

patie

nts

trea

ted

in th

e B

NC

T tr

ials

in F

inla

nd, a

ll in

ppm

. Firs

t fie

ldSe

cond

fiel

dA

ll da

ta p

oint

s

Dos

age

max

mea

nm

ax m

ean

max

mea

n

4-pa

ram

eter

non

-line

ar m

odel

5.86

0.64

(4.8

%)

2.86

0.42

(3.0

%)

2.88

0.39

(2.6

%)

3-pa

ram

eter

non

-line

ar m

odel

3.36

0.51

(3.7

%)

3.36

0.46

(3.2

%)

3.34

0.46

(3.1

%)

290

mg

BPA

/kg

2 h

infu

sion

(n=

12)

2-co

mpa

rtmen

t mod

el6.

701.

34 (1

0 %

)5.

010.

73 (4

.9 %

)5.

450.

67 (4

.1 %

)

4-pa

ram

eter

non

-line

ar m

odel

3.51

0.66

(10

%)

2.18

0.58

(9.5

%)

2.73

0.49

(8.9

%)

3-pa

ram

eter

non

-line

ar m

odel

2.78

0.54

(9.3

%)

2.85

0.50

(9.1

%)

2.75

0.52

(9.1

%)

290

mg

BPA

/kg

2 h

infu

sion

(n=

3)¦

2-co

mpa

rtmen

t mod

el3.

570.

91 (1

2 %

)2.

430.

68 (1

0 %

)2.

530.

69 (1

0 %

)

4-pa

ram

eter

non

-line

ar m

odel

2.50

1.38

(17

%)

2.04

1.08

(16

%)

2.68

1.25

(14

%)

3-pa

ram

eter

non

-line

ar m

odel

2.76

1.03

(15

%)

3.03

0.86

(15

%)

2.90

0.85

(15

%)

330

mg

BPA

/kg

2 h

infu

sion

(n=

1)2-

com

partm

ent m

odel

7.60

3.18

(30

%)

2.99

1.69

(17

%)

3.07

1.48

(15

%)

4-pa

ram

eter

non

-line

ar m

odel

1.98

0.55

(3.0

%)

2.06

0.49

(2.7

%)

2.11

0.48

(2.6

%)

3-pa

ram

eter

non

-line

ar m

odel

2.41

0.54

(3.0

%)

2.40

0.51

(2.8

%)

2.40

0.51

(2.8

%)

360

mg

BPA

/kg

2 h

infu

sion

(n=

3)2-

com

partm

ent m

odel

5.60

1.14

(6.5

%)

2.39

0.78

(4.0

%)

2.33

0.77

(3.8

%)

4-pa

ram

eter

non

-line

ar m

odel

2.62

0.79

(3.9

%)

2.46

0.66

(2.9

%)

2.49

0.64

(2.8

%)

3-pa

ram

eter

non

-line

ar m

odel

2.67

0.72

(3.5

%)

2.52

0.66

(2.9

%)

2.56

0.64

(2.8

%)

400

mg

BPA

/kg

2 h

infu

sion

(n=

2)2-

com

partm

ent m

odel

4.50

1.39

(7.2

%)

3.20

0.77

(3.5

%)

3.27

0.76

(3.5

%)

¦ G

liom

as p

rogr

essi

ng f

ollo

win

g su

rger

y an

d ra

diot

hera

py

39

Tab

le 8

. T

he m

axim

um a

nd m

ean

abso

lute

diff

eren

ces

betw

een

the

mea

sure

d an

d es

timat

ed 10

B c

once

ntra

tions

cal

cula

ted

for

the

clea

ranc

eph

ase

obta

ined

fro

m f

our

mod

els,

usi

ng t

he d

ata

avai

labl

e be

fore

the

firs

t an

d th

e se

cond

irr

adia

tions

and

usi

ng a

ll th

e da

ta p

oint

s fr

om a

ll th

epa

tient

s tr

eate

d in

the

BN

CT

tria

ls in

Fin

land

, all

in p

pm.

Cle

aran

ce p

hase

Firs

t fie

ldSe

cond

fiel

dA

ll da

ta p

oint

s

Dos

age

max

mea

nm

ax m

ean

max

mea

n

4-pa

ram

eter

non

-line

ar m

odel

5.86

0.81

(6.3

%)

2.73

0.42

(2.8

%)

2.87

0.36

(2.2

%)

3-pa

ram

eter

non

-line

ar m

odel

3.04

0.51

(3.6

%)

3.05

0.42

(2.8

%)

3.02

0.41

(2.6

%)

2-co

mpa

rtmen

t mod

el6.

701.

20 (1

6 %

)5.

010.

58 (5

.9 %

)5.

450.

52 (4

.1 %

)

290

mg

BPA

/kg

2 h

infu

sion

(n=

12)

Bi-e

xpon

entia

l fit†

2.01

0.63

(4.5

%)

2.88

0.49

(3.3

%)

9.48

0.57

(3.3

%)

4-pa

ram

eter

non

-line

ar m

odel

2.52

0.52

(3.4

%)

2.18

0.55

(3.3

%)

1.44

0.41

(2.5

%)

3-pa

ram

eter

non

-line

ar m

odel

1.69

0.47

(2.9

%)

1.60

0.40

(2.4

%)

1.71

0.43

(2.6

%)

2-co

mpa

rtmen

t mod

el3.

571.

18 (8

.8 %

)2.

380.

62 (4

.3 %

)2.

140.

67 (4

.3 %

)

290

mg

BPA

/kg

2 h

infu

sion

(n=

3)¦

Bi-e

xpon

entia

l fit

2.42

0.63

(4.2

%)

2.42

0.48

(3.1

%)

2.39

0.49

(3.2

%)

4-pa

ram

eter

non

-line

ar m

odel

2.50

1.12

(7.5

%)

1.84

0.79

(5.3

%)

1.80

0.78

(5.2

%)

3-pa

ram

eter

non

-line

ar m

odel

2.21

1.01

(6.6

%)

1.58

0.72

(5.0

%)

1.50

0.71

(4.7

%)

2-co

mpa

rtmen

t mod

el7.

604.

52 (3

4 %

)2.

351.

40 (9

.4 %

)2.

230.

92 (5

.5 %

)

330

mg

BPA

/kg

2 h

infu

sion

(n=

1)B

i-exp

onen

tial f

it1.

510.

58 (3

.9%

)2.

270.

73 (5

.9 %

)0.

900.

37 (2

.7 %

)

4-pa

ram

eter

non

-line

ar m

odel

1.46

0.43

(2.2

%)

1.42

0.31

(1.5

%)

1.42

0.28

(1.3

%)

3-pa

ram

eter

non

-line

ar m

odel

1.41

0.36

(1.7

%)

1.34

0.30

(1.3

%)

1.38

0.30

(1.3

%)

2-co

mpa

rtmen

t mod

el5.

601.

70 (1

0 %

)2.

390.

79 (4

.0 %

)2.

270.

72 (3

.5 %

)

360

mg

BPA

/kg

2 h

infu

sion

(n=

3)B

i-exp

onen

tial f

it28

2.61

(11%

)9.

691.

16 (5

.4 %

)9.

751.

11 (5

.0 %

)

4-pa

ram

eter

non

-line

ar m

odel

2.26

0.81

(4.6

%)

1.42

0.58

(2.8

%)

1.44

0.55

(2.6

%)

3-pa

ram

eter

non

-line

ar m

odel

1.94

0.71

(4.0

%)

1.43

0.58

(2.8

%)

1.42

0.55

(2.6

%)

2-co

mpa

rtmen

t mod

el4.

501.

74 (1

0 %

)1.

620.

60 (3

.0 %

)1.

440.

59 (2

.8 %

)

400

mg

BPA

/kg

2 h

infu

sion

(n=

2)B

i-exp

onen

tial f

it1.

860.

48 (2

.8 %

)0.

920.

24 (1

.5 %

)0.

890.

23 (1

.2 %

)

¦ G

liom

as p

rogr

essi

ng f

ollo

win

g su

rger

y an

d ra

diot

hera

py†O

btai

ned

from

the

FinF

it-pr

ogra

mm

e.

40

41

According to Friedman’s two-way analysis of variance test, the fits of the different models(i.e. the 3-parametric non-linear model, the 4-parametric non-linear model, the open two-compartmental model and the two bi-exponential fits) for all the patient data obtained fromthe BNCT trials carried out in Finland differ significantly when the data available before thefirst field was used in the analyses (0.01<p<0.02), or when the data before the second field(0.02<p<0.05) or all the data points (0.01<p<0.02) were included in the analyses. Table 9shows the results when the Wilcoxon matched pair test was used for comparing the results ofthe models in pairs, and the rank of the models based on the mean rank from Friedman’s test.

Table 9. Crossed table showing the comparisons between the models based on data from all thepatients treated in the BNCT trials in Finland. Comparisons were performed with Wilcoxon’s matchedpair test to the mean absolute difference between the 10B-concentration obtained from the model andthe actual data. Ranking is based on the mean rank number obtained using Friedman’s test.

Before the 1st

irradiation3-parametermodel

4-parametermodel

Compartmentmodel

Expfit FinFit Rank

3-parameter model • – p<0.0001 p=0.0016 – 1.4-parameter model – • p=0.0002 p=0.0048 – 3.Compartment model p<0.0001 p=0.0002 • – p=0.0028 4.Expfit p=0.0016 p=0.0048 – • p=0.0166 4.FinFit – – p=0.0028 p=0.0166 • 2.

Before the 2nd

irradiation3-parametermodel

4-parametermodel

Compartmentmodel

Expfit FinFit

3-parameter model • – p<0.0001 p=0.0064 – 2.4-parameter model – • p=0.0001 p=0.0051 – 4.Compartment model p<0.0001 p=0.0001 • p=0.0001 p=0.001 5.Expfit p=0.0064 p=0.0051 p=0.0001 • p=0.0087 1.FinFit – – p=0.001 p=0.0087 • 3.

Using all the data 3-parametermodel

4-parametermodel

Compartmentmodel

Expfit FinFit

3-parameter model • p=0.0294 p<0.0001 p=0.0001 – 4.4-parameter model p=0.0294 • p<0.0001 p=0.0001 – 3.Compartment model p<0.0001 p<0.0001 • p=0.0001 p=0.0183 5.Expfit p=0.0001 p=0.0001 p=0.0001 • p=0.0207 1.FinFit – – p=0.0183 p=0.0207 • 2.

– = p>0.05

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6. DISCUSSION

6.1. Models

Comparison of compartmental and non-compartmental models has been the subject of severalearlier publications (Gambhir et al 1989, Kuikka et al 1991). The two model types wereinitially derived from the same concepts and, therefore the underlying mathematics isessentially similar, differences in interpretation lead to somewhat divergent descriptions ofthe underlying physiology. One model gives transfer coefficients between a chosen set ofcompartments and the other intercepts and decay constants of a multi-exponential equation.According to Gambhir et al (1989), it is basically possible to use both of these descriptivemethods but when in complicated systems, the correspondence between the models weakens.The difference between models also depends on their ability to characterize the modellinghypotheses quantitatively and occasionally there are problems with their computability(Kuikka et al 1991). A user-friendly interface, which allows the modeller to characterize thesystem graphically, is often available in the commercial compartmental model-fittingprogrammes. The two programs for fitting exponential function differ significantly in thiscontent: the older Expfit is somewhat difficult to use, while the newer FinFit (Kortesniemi2002) has a practical interface especially designed for the needs of BNCT. FinFit wasdeveloped for the specific needs of the Finnish BNCT project (Kortesniemi 2002).

All the data from the patients treated in the BNCT trials in Finland including the more recentdata (Joensuu et al 2002b) and part of the data from Study IV, were subjected tobiexponential function fitting with both the Expfit- and FinFit-exponential function fittingprograms, in order to study the differences in the accuracy and computational abilities ofthese programmes. In the FinFit bi-exponential function fitting programme the peak value ofthe 10B blood concentration at the end of the infusion and the fixed half-lives determinedfrom the Finnish BNCT trial data are used for a default fit. As the number of measured datapoints increases, another fit, called the iterated fit, is performed in addition to the default fit.The user is then able to decide which model is preferred. For some patients in cases wherethere were few data points available, and where the maximum concentration did not coincidewith the end of the infusion, the FinFit programme could not provide an accurate estimation.An example of this is presented in Figure 18. This was the factor that increased the meanabsolute differences between the measured and estimated 10B concentrations obtained fromthe FinFit.

For a few patients, the Expfit was not able to create a model that would fulfil the convergencecriteria. In further studies of these cases using the same initial half-lives as were used forFinFit programme, a good model could not be generated in half of the patients. It should benoted that, in fact, the actual clearance curves of the “unfittable” patient data wereanomalous. One example of the fit obtained with FinFit is presented in Figure 19.

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Figure 18. An example of the performance of the FinFit programme (a) as compared with the Expfitprogramme (b) for one patient treated with BNCT in Finland, using data available before the firstirradiation field (chain curve), before the second irradiation field (broken curve) and using all the datapoints (full curve). Start and end indicators of the fields are presented as vertical lines. The patientreceived 360 mg BPA/kg body weight.

Figure 19. An example of the unpredicted 10B concentration behaviour from one patient treated withBNCT. Note that the highest blood 10B concentration is obtained 20 minutes after discontinuation ofthe BPA-F infusion. The fits obtained using the FinFit programme, and the data available before thefirst irradiation field (chain curve), before the second irradiation field (broken curve) and with all thedata points (full curve) are shown. Start and end indicators of the fields are presented as vertical lines.The patient had glioblastoma that had recurred following photon irradiation, and received 290 mgBPA/kg body weight.

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On comparing the resulting mean half-lives of the 10B clearance from blood obtained fromthe two models, no clinically significant difference was observed. Using the Expfitprogramme, the fast and slow components of the mean half-lives were 18�10 min and5.4�2.1 h, whereas the corresponding results from the FinFit programme were 16�7 min and5.0�0.6 h for all the patients from the BNCT trials in Finland (n=15) who received 290 mgBPA/kg body weight.

Finally, it should be staed that especially when dealing with clinical experiments concerningpatient trials, the impact of a simple and reliable programme is significant. The clinicalinterface of FinFit is excellent.

In Study I, the concept of transit times was applied to 111In-labelled BLMC. When studyingthe kinetics of a small molecular substance in an animal model, these transit times can beapplied to the exponential function fitting of the clearance phase of the tracer, in a case of arapid injection. The actual meaning of these transit times and differences between them canbe, however, somewhat difficult to comprehend. The time t1 represents the “classic” transittime, i.e. the time required for one molecule to travel through the vascular system, assumingthat it is located intravascularly all the time. The mean sojourn time, i.e. t2, takes account ofthe fact that small molecules are able to travel through a capillary wall into the extravascularspace and back, and that there is thus a delay in the transit time. The ratio between the meantransit time and the mean sojourn time yields approximate value for the number of times thatthe molecule floats between the intra and the extravascular space (Lassen and Perl 1979). Thethird transit time, t3, is the mean transit time of the tracer in the total body tracer pool, andrepresents the final time that is required for the molecules to be cleared from the bloodstreamafter being taken up by some other organs. It should be noted that the term “total body tracerpool” means the space available for the tracer to enter. This is naturally dependent on thephysiological and chemical properties of the tracer molecules.

In an ideal compartmental model data on BPA-F, BPA and 10B distributions from allimportant body sites would be available. A schematic drawing of the suggested pathway of10B in a human system after BPA-F infusion is represented in Figure 20. The factors specifiedin Figure 20 are those which are important when considering the whole BNC treatment andespecially the safety of the treatment. The sizes of the organs are scaled to the estimatedmean 10B concentration ratio to that of the blood at the time of the irradiations, based onhuman (Chadha et al 1998, Coderre et al 1998, Coderre et al 1997, Kabalka et al 1997a) andanimal (Coderre et al 1994, Coderre et al 1999, Gregoire et al 1993a, Matalka et al 1994a,Matalka et al 1994b, Morris et al 1997, Smith et al 1996) studies. The kidney function has apowerful impact on the clearance of 10B from the blood. In most of the ongoing BNCT trialsaround the world, there is limit for the clearance value for a patient to be eligible for BNCT.BPA has been reported to accumulate in the proximal tubule area of the kidney (Pignol et al1998). There are few biodistribution studies with BPA, in which the liver has been taken intoaccount. According to a mouse study, after l-BPA i.p. injection, the 10B concentration in theliver was six times the concentration in the blood (Gregoire et al 1993a). The hypophysis is aspecial case of the normal brain tissue, because the blood-brain barrier does not exist around

45

the cells of the hypothalamus, resulting in high 10B concentrations during BNCT (Benczik2000). This is important when considering the safety of BNCT.

Figure 20. A multicompartmental model of the suggested kinetics of 10B after BPA-F infusion. Thesizes of the compartments reflect the concentration of 10B at the time of irradiation (references in thetext). The blood-brain barrier is described by enhanced borders around the tumour and the braincompartments. The broken line border around the tumour compartment represents the deficientblood-brain barrier.

When formulating the non-linear model, it was noticed that the results obtained from thepolynomial model were not good enough. The most straightforward alternative to developingthe model further was to couple a memory effect to the model. After entering this memoryeffect, the momentary rate of change of the 10B concentration is determined by the previousconcentration values of 10B in the blood. It was noticed that, for the 10B administrationprotocol adopted, the increase in the 10B concentration of the blood slowed down at the endof the infusion, implying an enhanced rate of transfer of 10B from the blood. Whether this wasdue to enhanced excretion via the kidneys or enhanced transfer to other tissues could bejudged by following the 10B concentration of the blood for a sufficiently long time after theend of the infusion. Fast decay, especially if the infusion time is extended markedly beyond 2hours, would point to enhanced excretion through the kidneys, and slow decay to temporarystorage of 10B in other tissues. The roles of the second and higher order terms are needed todescribe the transfer of 10B between the blood compartment and the surrounding tissues. Theparameters a2 and a3 do not have unambiguous physiological explanations. This is one reasonwhy part of the error evaluations are calculated for both the infusion phase and the clearancephase, thus resulting in higher error values than the actual errors during the two irradiationphases. This type of error evaluation was chosen, because there was no clear structuralcorrespondence between the non-linear models or parameters of the models and thephysiological system. There were variations between the final and initial parameter values ofthe 3-parametric non-linear model, and parameter a2, especially, varied considerably betweenthe patients, as can be seen from Figure 14. From Figure 14 it is also evident that parametersa2 and a3 are independent of the amount of infused BPA. However, there is a positivecorrelation between parameter D0 and BPA dose, with a correlation coefficient of 0.95.

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6.2. Tracers

The stability of the labelled BLM is a controversial issue. In Study I with 111In-BLMC, it wasassumed that labelled bleomycin is stable in in vivo conditions. Previously, it has beenreported that the kinetics of 111In-BLMC is uniform in patients with normal cardiovascularand renal function (Chabner 1990, Kairemo et al 1996a), but, according to this present studythe situation is more complicated. However, the third exponent accounted for less than 5% ofthe elimination and might actually be derived from either the free indium or the tissueretention of 111In-BLMC.

One might question the choice of 10B concentration measurements instead of the BPA-Fconcentration measurements. All the analyses and kinetic studies in this research are based onmeasurements of 10B concentrations in blood instead of the actual BPA-F concentrations. It ispossible that some of the 10B atoms are free from the carrier, while some are still attached tothe parent compound and some are attached to different metabolites of the parent compound,and that they might all have slightly differing kinetic properties, as previously suggested(Gregoire et al 1993a). However, the actual radiation dose is dependent only on the 10Bconcentration, and thus it is justifiable to use 10B concentration measurements in constructingmodels for the kinetic behaviour. In this study, we have modelled the kinetics of 10B in bloodusing measurement data obtained from whole blood samples. However, if thepharmacokinetics of 10B were of interest, it would be essential to measure the 10Bconcentrations from plasma, since the tissues are supplied with 10B from the plasma only(Kiger III et al 2000).

6.3. BNCT Studies A large animal model, a beagle dog, was chosen because of its capacity to provide thepossibility of studing both acute and late normal tissue effects when looking for an acceptablewhole body irradiation dose; further the life-span of a beagle dog allows the study of delayedradiation effects (Benczik 2000). The similarities between the pathological changes observedin the dog brain and in the human brain after irradiation led to the choice of dogs as an animalmodel (Benczik 2000). The size of a beagle dog’s head and the resulting dosimetriccalculation resemble those of man. Moreover, in the pharmacokinetics, the size of a beagledog makes it possible to match the administration and the blood sampling in humans(Benczik 2000).

An interesting issue is the different infusion schemes and protocols. In these studies, there hasbeen variation in the amount of BPA-F infused and in the duration of the infusion. All this isdue to the fact that the current BNCT trials in Finland are studies in dose escalation. The firstresults with a constant 2-hour infusion and 290 mg BPA/kg body weight have not been asdramatic as expected, either in Finland or in BNL. Therefore, for the trials to continue withenhanced effect, there have to be more trials with various amounts of 10B carrier(s).According to our studies, the maximum boron concentration in the blood at the end of aninfusion is approximately a linear function of the dose administrated to the patients (seeFigure 21). This is in good agreement with the literature (Coderre et al 1998).

47

There was no significant disparity in the forms of the 10B concentration curves in the blood.As can be seen from Figure 13, there is no correlation between the transfer coefficient kEP,which describes the excretion from plasma pool, and the BPA dose. However, the other twotransfer coefficients did correlate with the BPA dosage. There was no significant differencein the obtained transfer coefficients between the patients who had had prior cranialirradiations, and the patients diagnosed with previously untreated gliomas from the BNCTtrials in Finland. However, the group with prior cranial irradiations is too small for drawingdetailed statistical conclusions.

Figure 21. The maximum boron concentration (at the end of the infusion) as a function of theincreasing amount of infused BPA in all the patients of the BNCT trials carried out in Finland. Thediamonds represent the mean values of the maximum concentrations. All the values are containedinside the error bars. The regression line is represented as a broken line. The correlation coefficient is0.99. The numbers of patients are n=15, n=1, n=3 and n=2, for doses of 290, 330, 360 and 400 mgBPA/kg body weight, respectively.

The kinetic data from all the patients treated in the BNCT trials in Finland were modelledwith the four models, i.e. a bi-exponent function, an open two-compartment model, and 3-and 4-parameter non-linear models. On studying the percentage errors of the 10Bconcentrations with an increasing number of data points, it was observed that the fits of the 3-parametric non-linear model did not markedly improve when additional data points wereintroduced. In the case of the open two-compartmental model and especially for the bi-exponential fit, however, the impact of the number of data points was immense, and theaccuracy of the models increased as more data points became available. For the studies with290 mg BPA/kg body weight, the mean absolute difference during the clearance phase for the10B concentration in the 3-parameter non-linear model and the bi-exponent fit using the dataavailable before the first irradiation were about 0.5-0.6 ppm, whereas, for the 4-parametermodel, the error was about 1.6 times higher and, for the open two-compartment model, overtwice as high. When using the data available before the second irradiation field, the meanabsolute differences for the 3- and 4-parameter non-linear models and the bi-exponential fit

48

were about 0.40 ppm, but for the compartment model it was 50% higher. In the study ofpreviously irradiated glioblastomas with 290 mg BPA/kg body weight, the results weresimilar: the mean absolute difference during the clearance phase of the 10B concentrationfrom the 3-parametric non-linear model, using the data available before the first irradiation,was 0.47 ppm, and for the 4-parametric non-linear model the mean absolute difference wasabout the same, i.e. 0.52 ppm; whereas for the open two-compartmental model it was abouttwo and a half times higher and for the bi-exponential fit about 1.3 times higher. It shouldalso be noted that, owing to the small number of data points, the Expfit-version of the bi-exponential fit was not available for every patient. When using data available before thesecond irradiation field for the glioma patients with prior photon irradiation, the fits of theopen two-compartment model and the bi-exponential fit approached the results obtained forthe 3-and 4-parameter models. When using all the available data points, the mean errors forthe 3- and 4-parametric non-linear models and for the bi-exponential fit were between 0.41-0.49 ppm. The mean absolute difference for the open two-compartmental model was 0.67ppm. There was no difference between the fits for the patients in the group with previouslyirradiated glioblastomas compared with the patient group with previously unirradiatedglioma. The mean absolute difference for the 330 mg BPA/kg study group during theclearance phase using the data available before the first irradiation field obtained using a bi-exponential fit was 0.58 ppm. This was clearly superior to the other models, which all had anerror about twice as great (3- and 4-parameter model) or about eight times higher (two-compartment model). The mean errors of the 3- and 4-parameter models and the bi-exponential fit, were between 0.72-0.79 ppm for the second irradiation field, whereas themean error of the open two-compartment model was about twice as high. The mean absolute differences for the study of patients given 360 mg BPA/kg body weightbetween the 3- and 4-parametric non-linear models for the 10B concentration were about 0.4ppm for the first estimation, whereas the other models had an error of more than 1 ppm. Theabsolute difference for the second estimation, i.e. when using data available before the secondirradiation field, obtained when using the 3- or 4-parametric non-linear model was about 0.3ppm. The absolute differences for the other models were over twice as high (two-compartmental model) or almost four times as high (bi-exponential fit). The most accuratemodel for the studies with 400 mg BPA/kg body weight for the first irradiation field, was abi-exponential fit, which had a mean error of 0.48 ppm. The errors of the other models werealmost twice as high for the two non-linear models and over three times as high for the opencompartment model. The differences were smaller for the second irradiation field: the meanerror with a bi-exponential fit was 0.24 ppm, whereas the other models had errors between0.58 and 0.60 ppm.

Overall, the results of the 4-parameter model were about the same as those obtained using the3-parameter model. When using all the available data points, the 4-parameter model providedfits that were somewhat more accurate than those of the 3-parameter model. However, as themain purpose of the kinetic models for BNCT was to estimate the 10B concentration usingonly limited data the 3-parameter model, which also has a more favourable degree of freedomwould be more favourable.

The choice between the programmes fitting two exponential functions tends to favour FinFit.When using data before the first irradiation field, it was clearly superior to Expfit (see tables4 and 9). The fit with Expfit improved significantly when more data points were available,and therefore it was ranked as the most accurate model when using the data available before

49

the second field and when using all the data. However, the model should be robust andreliable, so the inability of Expfit to provide a fit, as was the case in some patients, is atroublesome point.

The two-compartment model provided mean differences between the data and the model thatresulted in its being ranked as the least accurate model.

The final choice is between the 3-parameter model and FinFit. As is evident from table 9,there is no statistical significance in favour of either of these models. We must look back tothe practical aspects of the models such as the finding that the clinical interface of FinFit ismore practical, though, the development of a user-friendly version of the 3-parameter fit is tobe encouraged.

It should be noted, however, that the mean differences obtained from the bi-exponential fit(FinFit), and the 3- and 4-parameter models were all under 1.2 ppm. For a BNCT trial patient,it can be estimated that if the 10B concentration in the blood is 1 ppm higher than that of theestimate obtained from a kinetic model, the calculated mean planning target volume dosewould be 3.4 Gy higher than originally intended. However, this inaccuracy in the calculatedradiation dose is typically less than 10% of the total dose and can be considered as acceptablein BNCT given the other certainties associated with the technique. The average planningtarget volume dose has been between 30 and 61 Gy(W) in this patient group (Joensuu et al2002a).

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7. CONCLUSIONS

7.1. Conclusions from the study with 111In-BLMC and future prospects

The following conclusions can be drawn from the study of kinetic models for 111In-BLMC:

1. The kinetics of 111In-BLMC in blood is broadly similar to that reported for unlabelledBLM. There is moderately fast clearance from the blood after a rapid injection.

2. The most accurate models were fitting of three exponentials and an open three-compartment model.

3. When comparing the accuracy of the compartmental model and non-compartmentalmodel for the kinetics of 111In-BLMC, no significant difference between the results ofthese models was found.

From Study I with 111In-BLMC, it is concluded that both compartmental and non-compartmental modelling are sufficient to describe the kinetics of the indium-111 labelledbleomycin complex. The non-compartmental model is more practical and to some extentmore efficient in providing the needed information from the in vivo behaviour of 111In-BLMCthan the compartmental model. The compartmental model used provides estimates for bothextraction and excretion of the compound from the plasma and the tumour.

No studies have been reported during the last few years on use of the 111In-labelledbleomycin complex. The combined use of a chemotherapeutic agent which both accumulatesin tumour and emits Auger-electrons is fascinating theoretically. Auger-electrons represent aform of high LET-like radiation: they deposit energy in DNA within an extremely short range(Jonsson et al 1996). There are several potential benefits of radiolabelling a chemotherapeuticagent: detailed study of the distribution of the chemotherapeutic agent becomes possible;diagnostics is facilitated and staging and grading of tumours is possible by imaging thetumour with SPECT; further there is the enhanced cytotoxic effect of the labelling (Jääskelä-Saari et al 1998). The labelling should be stable in vivo and should not worsen the affinity ofthe tumour for the chemotherapeutic agent. However, the side effects should also be takenaccount and for 111In-BLMC, the most vulnerable organs are the kidneys and bladder (ICRP1987).

Previously it has been suggested that labelling of BLM with 114mIn would achieve a higherAuger-electron emittance than labelling with 111In, thus resulting in greater destruction of thetumour cells (Kairemo et al 1997). There is still a need to carry out further studies of thebehaviour of 111In-BLMC in cell cultures due to the different mechanisms of radiationsensitivity and BLM sensitivity of the different cell types (Kairemo et al 1997).

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7.2. Conclusions from the BNCT studies and future prospects

The conclusions from the study of kinetic models for 10B in blood after BPA-F infusion are asfollows:

1. The kinetic behaviour of 10B in blood after a BPA-F infusion is quite independent of theinfused amount of BPA-F in the dose range of 290–400 mg BPA/kg body weight.

2. Several models were found to be accurate for the kinetics of 10B after a BPA-F infusion,bi-exponential fitting, an open two-compartment model, and 3- and 4-parameter non-linear models.

3. When regarding the maximum error in modelling, the bi-exponential fit is the mostprecise for both the first and the second irradiation field.

4. The 3-parameter non-linear model was found to be the most accurate, when consideringthe mean differences between the model and measured data.

5. The impact of a practical interface in BNCT studies is crucial as the modelling tool has tobe simple to use, robust and rapid, and therefore, in these trials the two-compartmentmodel will play a significant role. The future development of a user-friendly version ofthe 3-parameter model should be encouraged.

6. The recommendation of this study is the use of three modelling tools, i.e. an open two-compartmental model, a bi-exponential fit and a 3-parametric non-linear model in parallelto enhance the kinetic estimation of the radiation therapy.

At present the extant BNCT trials are safety-oriented dose-escalation studies. There havebeen changes in the amounts of 10B infused and in the duration of the infusion in order toenhance the radiation therapy. Kinetic studies are needed prior to the actual BNCT to findways of appling the changed circumstances to the model used for estimating 10B kineticbehaviour. Any changes in the treatment procedure could be applied to an ideal modelwithout comprehensive kinetic trials. At the moment, the Finnish BNCT group uses an opentwo-compartmental model and bi-exponential fitting to estimate the blood 10B concentrationduring the neutron irradiation(s) after BPA-F infusion. The compartmental model and bi-exponential fitting are flexible, but various kinetic studies are needed when certain trialcomponents are changed. These two modelling methods are robust and capable when usedtogether. However, they are fundamentally based on the same mathematical concepts (fittinga sum of exponential functions), and are thus not fully independent of each other. By creatingnew models, whose construction is based entirely on phenomenological findings, we wereable to increase the safety of our modelling phase in the BNCT procedure. According to thisstudy, the different models have different capabilities at different phases of the BNCT. Forthe first irradiation field, the 3-parameter non-linear model is the most accurate and, for thesecond irradiation field, the 4-parameter model is in the leading position with the 3-parametermodel, when taking into account the mean differences between the models and the measureddata and using 290 mg BPA/kg body weight. However, when considering the maximum error

52

provided by the models, the bi-exponential function fit is the most accurate for both the firstand the second irradiation field, with the same BPA dosage. In clinical practice, themodelling tool has to be simple to use, robust and fast, and therefore the two-compartmentmodel also has a role in these trials. The future development of a user-friendly version of the3-parameter model should be encouraged. The recommendation of this study is the use ofthree modelling tools, i.e. an open two-compartmental model, a bi-exponential fit (FinFit) anda 3-parametric non-linear model, to enhance the kinetic estimation of the radiation therapy.

The future of BNCT lies in the further development of the methods. The resources in theareas of animal models, dosimetry, dose planning and technological development havealready been exploited for the most part (Aschan 1999, Benczik 2000, Kortesniemi 2002,Kosunen 1999, Seppälä 2002). One area of further research and development could be asearch for the most optimal blood-tumour 10B-concentration ratio, which might lead to thedevelopment of new 10B carriers, or to the combined use of the old carriers, i.e. BPA-F andsodium mercapto-undecahydrodecarbonate (Na2B12H11SH, i.e. BSH) (Barth et al 2000).According to animal studies, the use of long BPA-F infusions might be beneficial forincreasing 10B uptake by the infiltrating tumour cells (Smith et al 2001). There have also beenstudies endeavouring to diminish the blood-brain barrier to achieve an increased 10Bconcentration with mannitol in animal models (Barth et al 2000, Yang et al 1997) and byexternal irradiation before BNCT (Gregoire et al 1993b), the latter with disappointing results.Artificial breakdown of the BBB could increase delivery of 10B into the near neighbourhoodof the tumour cells and thus enhance the radiation damage of BNCT. BNCT has also beenapplied to the treatment of various malignant tumours, for example liver tumours (Suzuki etal 2000).

World-wide there has been some interest in distribution studies with PET (Imahori et al1998a, Imahori et al 1998b). However, in these PET studies the input of the tracer is rapidinjection of fluorine-18-labeled fluoroboronophenylalanine, and therefore the results for theconcentration ratios are not directly applicable. Nevertheless, PET studies could possiblyserve as a method for excluding some patients from the actual BNCT due to abnormalities inthe boron uptake of the tumour tissue. As previously mentioned, proton magnetic resonancespectroscopy have been employed for directly detecting the 10B-carrier molecule BPA (Zuo etal 1999) and magnetic resonance spectroscopy for measuring 11B concentrations (Bendel1998, Kabalka et al 1991, Kabalka et al 1997b, Tang 1995). In the BNCT trials in Finland,the use of 1H magnetic resonance spectroscopy (MRS) (Heikkinen et al 2002) is underinvestigation. The Ethical Committee of the Department of Surgery, Helsinki UniversityCentral Hospital, has approved the in vivo MRS studies, and it is estimated that clinicalstudies with 1.5 T and 3.0 T will be initiated during the year 2002 (Heikkinen et al 2002).

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ACKNOWLEDGEMENTS

The main part of his thesis was carried out while I was a part-time research worker at theDepartment of Radiology at the Helsinki University Central Hospital and at the Departmentof Physical Sciences at the University of Helsinki, during the years 1997-2002. I wish tothank Jaakko Kinnunen, M.D., Ph.D., Head of Department of Radiology at HUS andProfessor Juhani Keinonen, Ph.D., Head of the Department of Physics, University ofHelsinki. I am very grateful to the Department of Radiology for providing the excellentworking conditions at Biomedicum Helsinki.

I am grateful to Docent Sauli Savolainen, Ph.D., and Professor Hannu J. Aronen, M.D, Ph.D.,for supervising of this work.

I am greatly indebted to Professor Heikki Joensuu, M.D, Ph.D, and Docent Matti Koskinen,Ph.D, for their professional reviews of the manuscript and the constructive comments thatmarkedly improved this thesis.

I thank all the co-authors of the original articles, especially Professor Pekka Hiismäki, Ph.D.,for his admirable intuition on modelling. I wish to thank Aki Kangasmäki, Ph.D. for valuablecomments and discussion while preparing the publications. I want to express my gratitude tothe whole BNCT group of Finland. Particularly, I want to thank Iiro Auterinen, M.Sc.Eng.,Mika Kortesniemi, Ph.D., Tiina Seppälä, M.Sc., Martti Kulvik, M.D and Merja Kallio, M.D,Ph.D. for their valuable advice. I am grateful to Jeffrey Coderre, M.D, Ph.D., for his valuablecomments on preparing the manuscripts.

I wish to thank Mrs. Jean Margaret Perttunen and Jan Dabek, M.D., Ph.D., for checking thelanguage of this thesis.

I thank my colleagues at the Department of Radiology, especially Soile Komssi, M.Sc., AnttiKorvenoja, M.D., and Jussi Perkiö, M.Sc. for making the long working hours a little morehuman. My warm thanks are offered to all my friends in the Medical School of the University ofHelsinki. Being a full-time medical student and a part-time research scientist is hard work.Especially I would like to thank Marja Nurmi, B.M., and Kristiina Santti, B.M., for theircheerful company.

Grateful thanks are also due to my mother, Leena Ryynänen, Ph.D., for her advice and herencouraging support and also my little brother, Juhana Ryynänen.

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Finally, I wish to express my warmest thanks to András Koroknay-Pál, M.Sc.Economics, forhis endless love and support.

Financial support from the State Subsidy for University Hospitals, the Radiology Society ofFinland, the Finnish Society of Nuclear Medicine, the Biomedicum Helsinki Foundation, theInstrumentarium Science Foundation, the University of Helsinki, the Nordic Cancer Union,the Ida Montin Foundation, the Emil Aaltonen Foundation, the Finnish Medical Foundation,the Saga and the Harry Korhonen Foundation from the Cancer Societies of Finland isgratefully acknowledged.

Helsinki, November 2002Päivi Ryynänen

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ERRATA

Paper Page Line Should be

I 321 7 Reference 27 should be as follows: Korppi-Tommola T, Huhmar H M,Aronen H J, Penttilä P I, Hiltunen J V, Savolainen S E, Kallio M E andLiewendahl B K 111In-labelled bleomycin complex for the differentiation ofhigh- and low-grade gliomas. Nuclear Medicine Communications 20: 145-152, 1999

II 961 3 The mean half lives of the fast component for groups A, B and C were 19�1minutes, 21�8 minutes and 14�4 minutes, respectively. The slowcomponents for the same groups were 12�8 hours, 9�2 hours and 4.0�1.9hours, respectively.

II 961 6 The example is from a dog from group B.