The microdosimetric variance-covariance method used for - DiVA

The microdosimetric variance-covariance method used for beam quality characterization

in radiation protection and radiation therapy

Jan Erik Lillhök

Stockholm University

The variance-covariance method used for beam quality characterization J. Lillhök

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© Jan Erik Lillhök, Stockholm 2007 ISBN (91-7155-391-6) Printed in Sweden by Universitetsservice AB, Stockholm 2007 Distributor: Medical Radiation Physics, Stockholm University, Karolinska Institutet


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Till Sofia, Gösta och den lillae

”Epäusko eilispäivän

tänään on totinen tieto,

tämän päivän taikausko

huomenna on huomenrusko.”

Eino Leino 1924


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Contents

ABSTRACT....................................................................................................................................7

1. INTRODUCTION .......................................................................................................................9

2. THEORY..................................................................................................................................11 2.1. The variance-covariance method ............................................................................................................ 11 2.2. The tissue-equivalent proportional counter.............................................................................................. 14 2.3. Nanodosimetry and radiation quality ....................................................................................................... 15

3. MATERIALS AND METHODS.................................................................................................19 3.1. Detector construction .............................................................................................................................. 19 3.2. Algorithms ............................................................................................................................................... 22 3.3. Separation of dose components.............................................................................................................. 27 3.4. Monte Carlo simulations.......................................................................................................................... 33

4. RESULTS ................................................................................................................................37 4.1. Instrument response................................................................................................................................ 37 4.2. Dose equivalent measurements .............................................................................................................. 45 4.3. Pulsed radiation fields ............................................................................................................................. 48 4.4. Separation of dose components.............................................................................................................. 50 4.5. A low-dose rate application ..................................................................................................................... 51 4.6. Uncertainties ........................................................................................................................................... 54 4.7. Nanodosimetry in radiation therapy ......................................................................................................... 57

5. CONCLUSION AND OUTLOOK .............................................................................................61

ACKNOWLEDGEMENTS............................................................................................................62

REFERENCES ............................................................................................................................64

APPENDIX...................................................................................................................................69


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PAPERS This thesis is based on the following papers. I. Kyllönen J-E, Lindborg L and Samuelson G, 2001. The response of the Sievert instrument in neutron beams up to 180 MeV. Radiation Protection Dosimetry 94 (3) 227 – 232 II. Kyllönen J-E and Lindborg L. Photon and neutron dose discrimination using low pressure proportional counters with graphite and A150 walls. Radiation Protection Dosimetry (2007) doi:10.1093/rpd/ncm162 III. Kyllönen J-E, Lindborg L and Samuelson G, 2001. Cosmic radiation measurements on-board aircraft with the variance method. Radiation Protection Dosimetry 93 (3) 197 – 205 IV. Lillhök J, Beck P, Bottolier-Depois J F, Latocha M, Lindborg L, Roos H, Roth J, Schraube H, Spurny F, Stehno G, Trompier F and Wissmann F. A comparison of ambient dose equivalent meters and dose calculations at constant flight conditions. Accepted 18 Dec 2006 for publication in Radiation Measurements V. Lillhök J E, Grindborg J E, Lindborg L, Gudowska I, Alm Carlsson G, Söderberg J, Kopeć M and Medin J. Nanodosimetry in a clinical neutron therapy beam using the variance-covariance method and Monte Carlo simulations. Submitted to Physics in Medicine and Biology 19 Feb 2007


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ABSTRACT Radiation quality is described by the RBE (relative biological effectiveness) that varies with the ionizing ability of the radiation. Microdosimetric quantities describe distributions of energy imparted to small volumes and can be related to RBE. This has made microdosimetry a powerful tool for radiation quality determinations in both radiation protection and radiation therapy. The variance-covariance method determines the dose-average of the distributions and has traditionally been used with two detectors to correct for beam intensity variations. Methods to separate dose components in mixed radiation fields and to correct for beam variations using only one detector have been developed in this thesis. Quality factor relations have been optimized for different neutron energies, and a new algorithm that takes single energy deposition events from densely ionizing radiation into account has been formulated. The variance-covariance technique and the new methodology have been shown to work well in the cosmic radiation field onboard aircraft, in the mixed photon and neutron fields in the nuclear industry and in pulsed fields around accelerators. The method has also been used for radiation quality characterization in therapy beams. The biological damage is related to track-structure and ionization clusters and requires descriptions of the energy depositions in nanometre sized volumes. It was shown that both measurements and Monte Carlo simulation (condensed history and track-structure) are needed for a reliable nanodosimetric beam characterization. The combined experimental and simulated results indicate that the dose-mean of the energy imparted to an object in the nanometre region is related to the clinical RBE in neutron, proton and photon beams. The results suggest that the variance-covariance technique and the dose-average of the microdosimetric quantities could be well suited for describing radiation quality also in therapy beams.


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1. INTRODUCTION A common device used to characterize radiation fields in terms of the linear energy transfer (LET) is the low-pressure proportional counter of tissue-equivalent material [ICRU 1984, Waker 1995, Gerdung et al 1995]. The measured quantity, lineal energy, can be used as a measure of the LET although the validity of the approximation depends on energy and type of particle, and on the size of the simulated volume [Kellerer and Chmelevsky 1975, Leuthold and Burger 1985]. Experimental microdosimetry has therefore been successful in radiation protection [Menzel et al 1989, Schmitz et al 1995, EURADOS 2004] and for beam characterization in radiation therapy [Menzel et al 1994, Tilikidis et al 1996, Wambersie et al 2002, Gerlach et al 2002, De Nardo et al 2004]. The linear energy transfer (LET) is a macroscopic quantity defined by the average energy lost by a particle while the lineal energy (y) is a stochastic quantity describing the energy distribution in small volumes. The microdosimetric quantities can therefore spot regions of concentrated ionizations, which is important since track-structure and electron clusters are crucial for describing the mechanisms of radiation damage [Goodhead 1994, Nikjoo et al 1997, Brahme et al 1997, Hill 1999]. If the probability of damage on the nanometre level is related to the energy imparted to a relevant volume, then it might be better described by the microdosimetric distribution for the same object size than by the LET. Measurements of the energy deposition from single events can be difficult at high dose rates and in pulsed radiation fields due to pile-up of several events. Experimental nanodosimetry with large gaseous detectors also faces the problem of a non-uniform gas multiplication region that distorts the measured spectrum [Ségur et al 1994]. Smaller detectors reduce this problem and single-event measurements have been reported for simulated objects in the nanometre region [Kliauga 1990, Anachkova et al 1997, Cesari et al 2002]. Some of these experimental limitations are also reduced when using the variance-covariance method in which the dose-average of the lineal energy (Dy ) is determined from the multiple-event energy distribution [Kellerer 1968, Bengtsson 1970, Lindborg and Bengtsson 1971, Lindborg et al 1988]. The measurements are based on charge measurements during specific time intervals and the method can be used in pulsed beams without pile-up effects. The technique can also be used without gas multiplication and is therefore suitable for measurements at low pressures and in high dose-rate applications [Goldhagen et al 1990, Grindborg et al 1995, Lindborg and Grindborg 1997]. The questions addressed in this thesis are how well the variance-covariance method can be used to determine ambient dose-equivalent in radiation protection, and if it can be used for beam quality characterization in radiation therapy. For this purpose an instrument based on the variance method was built [Paper I]. The method was further developed for some of the requirements in radiation protection applications. An algorithm correcting for beam intensity variations using one instead of the usual two detectors was formulated [summary]. An improved algorithm for the quality factor in mixed fields and methods to separate low- and high-LET dose components were developed [Paper II, III, summary]. The instrument and methods were evaluated in


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measurements onboard aircraft in the cosmic radiation field [Papers III, IV], in the nuclear industry [Paper II] and in pulsed fields around accelerators [summary]. Experiments and Monte Carlo simulations using both macroscopic (condensed history) and microscopic (track-structure) codes of the energy deposition in the nanometre region were compared and the relation between the dose-mean lineal energy (Dy ) and radiation quality in radiation therapy was investigated [Paper V, summary].


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2. THEORY The fundamental difference between quantities like absorbed dose and specific energy, or LET and lineal energy, is their relation to the stochastic nature of radiation interaction. Absorbed dose and LET are macroscopic quantities defined by average energy depositions, while specific and lineal energy are stochastic quantities described by distributions of energy deposition events (section 2.1). One of the important microdosimetric quantities is the dose-mean lineal energy Dy that can be determined

with the variance-covariance method (section 2.1) Experimentally Dy is measured using tissue-equivalent low-pressure proportional counters (TEPC) or ion chambers to simulate the energy deposition in small volumes (section 2.2). There are also nanodosimetric arguments for relating single-event spectra and Dy to the probability of biological damage and radiation quality (section 2.3). Comprehensive descriptions of microdosimetry are for the interested reader given by Kellerer [1975], ICRU [1984] and Rossi and Zaider [1995].

2.1. The variance-covariance method The fundamental dosimetric quantities absorbed dose (D) and linear energy transfer (L) are defined by

dm

dD

ε= (2.1)

and

dl

dEL = (2.2)

where εd is the average energy imparted to the small mass dm and dE is the mean energy lost by a particle traversing a distance dl [ICRU 1993a]. These quantities are sometimes referred to as macroscopic although they are point functions. The definitions in terms of the average energy imparted do not reflect the stochastic nature of radiation interaction with matter. The quantities can vary in a large volume but they do not fluctuate like the energy deposition from individual ionizing particles. The energy imparted (ε) to a slightly larger volume of mass m is described by the microdosimetric quantity specific energy (z)

mz

ε= (2.3)

The energy imparted in (2.3) varies with the absorbed dose, and can be due to interactions of several particles, or alternatively but not equivalently, several events. An


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event denotes the interaction of statistically correlated particles including also secondary particles such as delta-electrons [ICRU 1984, ICRU 1993a]. Both the number of events and the energy imparted in each event are described by Poisson statistics. The distribution of z-values at dose D is denoted f(z,D) and the average specific energy equals the absorbed dose in the limit

DzDzzfzm →= →

∞

∫ 00

d),( (2.4)

The lineal energy (y) is defined in terms of energy imparted in a single event and the mean chord-length of the object (l ).

ly

ε= (2.5)

The single-event frequency and dose distributions f1(z) and d1(z) (index 1 denotes it is a single event) are independent of the absorbed dose and they are characteristic of the radiation field itself. The average values for the lineal energy are defined by

∫∞

=0

1 d)( yyyfyF (2.6)

F

F

FD y

yyyfy

yyyydy

2

0

12

0

1 d)(1

d)( === ∫∫∞∞

(2.7)

Frequency and dose averages of the energy imparted (ε) and the specific energy (z) are defined analogously. The relative variance (V1) of a single-event distribution f1(z) can like any distribution be written in terms of its first and second moments.

112

2

2

22

2

2

2

2

1 −=−=−===F

D

F

F

F

FF

F

y

F

z

y

y

y

y

y

yy

yzV

σσ (2.8)

In a multiple-event spectrum there are several events that contribute to the energy imparted. For a Poisson distribution with n events on average, the relative variance in the event number is given by

nn

n

nV n

n

122

2

===σ

(2.9)

From statistical theory it is known that the variance of the average of independent stochastic variables decreases with the number of events [e.g. Rice 1995]. Since the events discussed here are independent by definition, the variance (V1) of the single-event spectrum has also decreased with a factor of n . The total relative variance in a multiple event spectrum is then according to (2.8) and (2.9) given by


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Dm

yl

zm

yl

znm

yl

yn

yV

n

VV DD

F

D

F

DnR ⋅

⋅=⋅

⋅=⋅⋅==+= 1 (2.10)

where m is the mass, l is the mean chord-length and D is the absorbed dose delivered by n events. The dose-mean lineal energy is then from (2.10) given by

−=== z

z

z

l

m

zl

mzV

l

my z

RD

22σ (2.11)

All variance sources such as the contribution from the chord-length distribution, energy straggling, electronic noise and varying beam intensity, contribute to the total variance. Kellerer and Rossi [1984] published a formulation of how to correct for a beam intensity variation by subtracting the relative covariance (CR) between two detectors (A and B) exposed in the same field. For detector A the expression is

( )

−=−=

B

BA

A

AARRD z

zz

z

z

l

mzCV

l

my

2

(2.12)

The purpose of the second detector is to monitor beam variations but the detectors do not necessarily have to be identical. Response differences might however influence the correction CR if the beam variations are not the same for different radiation components. For example a variation in a slow neutron component is not necessarily monitored correctly by a graphite-walled ionization chamber with low neutron sensitivity. The variance-covariance method was developed further by Kellerer [1996a–c] by including corrections also for slow spatial variations, i.e. changes in the signal ratio between two detectors. Slow means the influence of the spatial variation in successive measurement intervals is negligible. The dose-average lineal energy is expressed in terms of dose in two detectors A and B and the dose for the preceding measurement intervals denoted with indices A-1 and B-1. For detector A the expression is

( )

+⋅

−=−−

−

11

12 2

ABBAA

AABA

A

AD

zzzzz

zzzz

z

z

l

my (2.13)

An observed variation in the signal ratios between two detectors could be caused by detectors moving through an inhomogeneous field, spatial variations in the field itself or variations in the gas-gain of the proportional counter.


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2.2. The tissue-equivalent proportional counter An established method in microdosimetry is to use a low-pressure proportional counter to simulate the energy imparted to a microscopic tissue-volume [ICRU 1984, Rossi and Zaider 1995, Waker 1995, Gerdung et al 1995]. The detector is often spherical and made of tissue-equivalent A-150 plastic and filled with propane or methane based tissue-equivalent gas [ICRU 1989]. The mass stopping powers for charged particles in the detector gas and in a microscopic tissue object are equal if differences in density and atomic composition are neglected.

µdet

=

ρρSS

(2.14)

Consider a detector filled to a gas pressure corresponding to a density given by

det

µµ

det

µµdet r

r

l

lρρρ == (2.15)

where µl , detl , rµ, and rdet are the mean chord-lengths and the radii of the tissue object

and the detector, respectively. A particle passing the detector volume will then loose the same amount of energy as when passing the tissue object.

( ) ( ) µµµ

µ

lS

lS ερ

ρρ

ρε =

=

= detdet

det

det (2.16)

The cross sectional areas, the volumes and the masses of the detector and the tissue object are related as

2

2det

detµ

µ r

rAA = (2.17)

3

3det

det

µ

µr

rvv = (2.18)

2

2det

2

2det

3

3det

detdetdetdet

µ

µ

µ

µµ

µ

µµ

µr

rm

r

rv

r

rv

r

rvm ==== ρρρ (2.19)

For a constant particle fluence Φ in both volumes, a constant average stopping power S , and delta-particle equilibrium, the energy imparted to the detector is related to the energy imparted to the tissue volume as

2

2det

2

2det

detdetµ

µµ

µ r

rES

r

rASAE =Φ=Φ= (2.20)


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The absorbed doses in the two objects are then the same as seen from (2.1), (2.19) and (2.20)

µµ

µ

µµ

µµ

Dm

E

r

rm

r

rE

m

ED ====

2

2det

2

2det

det

detdet (2.21)

For a Poisson distributed random variable, like the number of particles crossing the detector volume, the relative variance decrease with the average number of particles according to (2.9). The relative variance in the detector and the micrometer volume are then given by

2det

2

detdetdet r

rV

A

AV

N

NVV µ

µµ

µµ

µ =ΦΦ

== (2.22)

Equations (2.11), (2.12), (2.13) and (2.14) then gives an expression for the dose-average lineal energy determined from the relative variance (Vdet) and the absorbed dose (Ddet) in repeated measurements.

µµ

µ

µ

µ

µµµD l

DVm

l

Dr

rV

r

rm

l

DVmy detdetdet

det2

2det

det2det

2

det ⋅⋅=⋅⋅

=⋅⋅

= (2.23)

It is also useful to express the total Dy -value of a radiation field in terms of the

absorbed dose fractions and Dy -values of its components, for example the photon and neutron component.

( ) nDnDnnDnDD ydydydyddyyydy ,,,, 1)( +−=+== ∫ γγγ (2.24)

2.3. Nanodosimetry and radiation quality One reason to study energy depositions in variable volume sizes is to see if a match between a measured quantity and some beam quality characteristics can be found for some specific size. The theory of dual radiation action [Kellerer and Rossi 1972] proposed that energy depositions in a micrometer sized object could account for the curvature of survival curves. The underlying assumption was that the damage was combined by two sublesions, which is equivalent with a damage probability proportional to the square of the energy imparted to the object (z2). Equation (2.11) gives that the average of z2 can be written


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222 Dm

yDlz

m

yzlz DD +=+= (2.25)

Since the probability of a damage was proportional to z2, the average biological effect due to this damage is at absorbed dose D given by the familiar linear-quadratic expression

+=+== 222)( DD

m

ylD

m

yDlzD DD ββββε (2.26)

Such a mechanistic derivation of a linear-quadratic dose-effect relation is not realistic [Kellerer and Rossi 1978, Goodhead 1987, Zaider 1998]. A therapeutic situation might well be described by a linear-quadratic model, but it is far too complex to be defined only by the first two moments of the energy imparted to a target volume of a few micrometer. However, it will be argued below that the concept of relating energy imparted to an object to the production of a biological damage can account for at least a part of empirical observations determined by damages on the nanometre level. Consider a number of very small objects inside a large macroscopic medium exposed to an absorbed dose D. The probability of having no interaction in one of the objects increases with decreasing D and with decreasing object size. Most of the nanometre sized objects do actually not receive any dose at all, while the affected volumes receive an extremely high dose on average. The absorbed dose to an affected volume is also most likely due to energy depositions from a single event, i.e. the frequency-mean specific energy Fz in microdosimetric terms. An increasing absorbed dose D is

therefore only related to an increasing number of affected volumes, while Fz in each

object remains the same. For example, Fy for 100 keV electrons in a 100 nm diameter volume is 1.6 keV/µm [Nikjoo et al 1994]. An absorbed dose D=2 Gy gives then

Fz =33 Gy to 6% of all 100 nm objects, while the remaining 94% are unaffected. At D=100 mGy, only 0.3% of the volumes are affected but they still recive 33 Gy. Assume that a biological effect (ε) is the result of damages on the nanometre level and that the production of damage is somehow related to the energy imparted to a corresponding volume. The damage probability (p) can then be expressed as a function of a microdosimetric quantity such as the lineal energy. As noted above the average number of affected nanometer volumes (n ) increases linearly with absorbed dose D, and the biological effect generated by damages on the nanometre scale can be written

+++=== ∫ ...)()()()( 21

0D

FF

ykky

kDdyypyf

y

DypnDε (2.27)

where ki are the constants of a serial expansion of p(y). If it is assumed that the damage frequency has a Poisson distribution, and that one damage is enough to give an effect, then the probability of no effect is P(ε=0) given by


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( )

+++−=−== ...)()0(ln 21

0D

F

ykky

kDDP εε (2.28)

As already mentioned it not realistic to understand an empirical survival relation only in terms of the initial damage probability like in (2.28). But a biological effect generated by initial damages on the nanometre level might however account for a part of the linear term in such a relation. Equation (2.28) would then be included in an exponential survival probability S(D) that expanded in a power series becomes

( )

++++

+++−= ...´...)(ln 32

210 DDDykk

y

kDDS D

F

γβα (2.29)

Another important nanodosimetric feature is that the relative dose contribution from delta-electrons increases at small object sizes [ICRU 1984, Leuthold and Burger 1988]. The energy distribution of delta-electrons is essentially determined by the velocity and not the LET of the primary particle. Low- and high-LET radiations become therefore more similar in terms of the energy imparted to small objects. The differences between the single-event distribution (and Dy ) decrease, and the shape of a biological weighting function RBE(L) must be different from a function RBE(Dy ). The maximum RBE occurs typically around and LET of 100–200 keV/µm, which with a mean-energy to produce an ion pair of W=30 eV corresponds to 30–80 ionizations in a 10 nm volume. For comparison the largest cluster sizes, i.e. the maximum number of ionizations, produced by a 4He ion travelling 10 nm is about 40 at 0.17 MeV/u [Grosswendt 2002]. If ionization clusters are assumed to never be larger than this, i.e. there is no saturation in the production of initial damage, and the probability of damage is proportional to the square of the lineal energy (or specific energy), then (2.27) and (2.28) gives

( ) DFF

ykDy

ykDdzkyyf

y

DP −=−=∫−==

22)()0(ln ε (2.30)

If for some reason the other contribution (α´) to the linear term in D in (2.29) can be disregarded in comparison with the initial damage probability (2.28), then a linear-quadratic expression considering only the first two terms in (2.29) becomes

( ) ( ) ( )22 (()(ln DDykDDDS D ββα +−=+−= (2.31)

In (2.26) the average energy imparted to the micrometre volume (2z ) defines both the first and second terms and relates them through

DDD z

mm

yl βεββα === (2.32)

Or in other words, the curvature (α/β) of the survival curve is defined by the dose-mean of one of the microdosimetric quantities in a micrometer sized volume. This is however


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fundamentally different from (2.31) where the linear and the quadratic terms are if not independent, at least not necessarily dependent. The linear term is defined by the initial damages on the nanometre volume only, while the quadratic term can account for other mechanisms (e.g. cell repair) of the complex biological system.


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3. MATERIALS AND METHODS Investigating the applicability of the variance-covariance method in radiation protection requires a reliable instrument for the measurements (Paper I). The method determines the dose mean of the lineal energy (Dy ), which can be used to determine a quality factor depending linearly on the lineal energy. This is inappropriate for high-LET radiation and an improved algorithm with dose rate limits for its application was formulated (Paper III and section 3.2). The low- and high-LET dose components are not directly accessible from a multiple-event spectrum and methods to separate the components were developed (Paper II and section 3.3). A practical instrument cannot be too large or heavy and using one detector instead of two is therefore attractive and a covariance correction for one detector was developed (section 3.2). Monte Carlo methods are useful not only for response simulations, but also for verification and extension of measurement results in difficult applications such as nanodosimetry (section 3.4).

3.1. Detector construction Two tissue-equivalent proportional counters (TEPC) and a graphite walled proportional counter (GPC) of identical design were constructed for the purpose of this investigation [Kyllönen et al 1997, Paper I, Paper II]. The TEPCs are made of A-150 plastic [ICRU 1989] with a wall-thickness of 5 mm. The sensitive volume of 1.2 dm3 is cylindrical with a height and a diameter of 11.5 cm. With a propane-based tissue-equivalent gas filling of 1.45 kPa it simulates a tissue-volume of 2 µm mean chord-length. The polarity effect, i.e. the difference in measured saturation current using positive or negative voltage, was determined to 0.2%. The A-150 plastic is hygroscopic due to its polyamide (nylon®) content and the detectors must be evacuated at an elevated temperature (baked) before gas-filling [Braby et al 1995, Gerdung et al 1995]. In a badly evacuated system the gas gain will decrease slowly with time due to an increasing pressure and the poor multiplication characteristics of the water vapour diffusing out from the walls. A proper baking is also of importance for the temperature dependence of the system since the water vapour content in the detector wall varies with temperature. An improved heating procedure for baking the tissue-equivalent material has been established and the long term stability is improved by refilling the detectors to their final working pressure after a few days when the diffusion rate back into the plastic has decreased. The saturation current of a sealed detector, i.e. the gas pressure with a constant We (mean energy to produce an ion pair), increased with 2% during 2 years. The gas multiplication at the same high-voltage decreased with -15% in the same time period. The temperature dependence of the detectors was determined to -0.4% per ºC. The baking procedure is not necessary for the graphite detector but it needs to be carefully evacuated at a low pressure.


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Figure 3.1. Cross-section of the low-pressure proportional counter with tissue-equivalent or graphite walls used in radiation protection applications.

The charge created in the detector volume is measured with capacitor feed-back electrometers developed by Combinova AB in cooperation with Göran Samuelson at the Swedish Radiation Protection Authority (SSI). The voltage over the 1000 pF capacitor is measured 10 times per second with a 24-bit analog-to-digital converter (ADS 1210U). One bit is used for polarity and the other 23 bits for dividing the maximum capacitor -voltage of 5V into steps of 0.6 µV. The electronic noise is dominated by the 0.6 µV (rms) contribution from the analog-to-digital-converter. The capacitor is reset with a current in the opposite direction, every 57 minutes at 1 pA. The highest reset frequency is about one reset every second, which with a gas multiplication of 1000 corresponds to a dose rate of about 10 mGy/h. This is of importance in e.g. cosmic radiation measurements where the atmospheric dose rates can suddenly increase in connection with strong solar eruptions and ground level events [Lantos 1993, Spurný and Daschev 2002]. Using a lower gas gain increases of course the maximum measurable dose rate correspondingly.


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The relative variance decrease with an integration time below 300 ms. The charge collection time in the detector is of the order of microseconds and the variance decrease is attributed to electronic time constants. The decrease is also independent of the radiation field (neutron, photon or mixed fields) and can be taken into account by applying a correction of 1.1 to measurements with 100 ms integration time. This is preferable for example in pulsed radiation fields where a high sampling frequency is desireable (section 4.3). The quantity of interrest in radiation protection is the ambient dose-equivalent H*(10), i.e. the dose-equivalent produced at 10 mm depth in the ICRU sphere in an expanded and aligned field [ICRU 1993]. The dose-equivalent (H) is given by the product of the absorbed dose and the quality factor and the measured dose-equivalent (Hm) is determined from a calibration factor (N), the absorbed dose to detector gas (Dgas) and the average quality factor (DQ )

),,,,,,,,( 2 Mmle

WbaqNfQNDH gasqDgasm σ== (3.1)

In practice Hm is calculated from a number of variables and coefficients. The average electric charge (q ) and its variance ( 2

qσ ) created during 100 ms in the detector volume

are measured with the electrometers described above and traceable to national standards. The parameters a and b were determined from H*(10)-response investigations in neutron fields of different energies [Paper I]. The gas mass (gasm ) and

mean chord-length (l ) are determined from the physical detector volume, a gas density of 1.798 kg.m-3 at 20°C and 100 kPa [ICRU 1984] and the gas pressure measured with a calibrated barometer traceable to national standards. The gas amplification (M) is determined as the current measured at the working voltage (typically -1000V) divided with the saturation current, i.e. with no gas gain and complete ion collection. The ambient dose-equivalent calibration factor relates the instrument reading to a reference ambient dose-equivalent value in a 137Cs-field.

m

ref

H

HN

)10(*

= (3.2)

This calibration factor is used in all applications but with different W/e-values, 26.8 J/C in low-LET fields and 31 J/C in high-LET fields [Lindborg 1985, IAEA 1995, Grosswendt 2002]. In mixed radiation fields the combined value 28 J/C is used. The detectors used in the nanodosimetric investigations (section 4.7) are described in detail in Paper V.


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3.2. Algorithms An important development of a practical instrument is the reduction of size and weight. The variance-covariance method would for example gain from using only one detector, which requires a different solution for the covariance correction. The method of using successive measurements in (2.13) is therefore reformulated for one detector. If the intensity changes are slow compared to the sampling time, it is possible to use the covariance between the data series formed by successive intervals in one detector. The expression for the dose-average lineal energy for detector A corrected for a covariance between two series (odd and even) becomes in analogy with (2.12)

− →

⋅−= ∞→

A

evenodd

A

An

evenodd

evenoddA

A

AD

z

zz

z

z

l

m

zz

zzz

z

z

l

my

22

(3.3)

A radiation protection instrument must also be able to determine the quality factor (Q) reasonably well. The average quality factor can be calculated from a single-event dose distribution d(y) by for example approximating L with y in the quality factor expression QICRP60(L) from ICRP60 [ICRP 1991].

( ) ∫∫∫

∫∫∞

∞∞

+++=

=≈≡

100

100

10

10

0

0

60

0

6060,

)(300

)(2.232.0)(

)()()()()(

dyydy

dyydydyyd

dyydyQdLLdLQLQ ICRPICRPICRPD

(3.4)

A first order linear approximation is given by

( ) DlinlinD ybadyydyQdyydbyayQ +==+= ∫∫∞∞

00

, )()()()( (3.5)

The linear approximation (3.5) will overestimate the average quality factor (3.4) in the high-LET region. This overestimation can be substantial in neutron radiation fields above a few MeV due to the contributions from secondary alpha particles and heavier recoils [Paper I]. The substitution L=y is also only approximate due to the differences between the two quantities [Kellerer and Chmelevsky 1975, Leuthold and Burger 1985]. This is however often acceptable since instrument characteristics can be taken into account when calibrating the quality factor expression for an optimal H*(10)-response.


23

0

1

10

100

1000

0 50 100 150 200

Energy deposition per mean chord-length [keV/µm]

Num

ber

of c

ount

s

Figure 3.2. A multiple-event spectrum in a mixed low- and high-LET radiation field with dose rate 11 µGy/h and Dy =5 keV/µm. The ordinate shows the number of measurements in 0.17 keV/µm bins. The abscissa shows the energy imparted in 100 ms divided by the mean chord-length.

A different formulation of the quality factor combines single- and multiple-events as described in Paper III. Figure 3.2 shows a typical multiple-event spectrum in a mixed photon and neutron field. The distribution is dominated by multiple events below 50 keV/µm, and single-events above 50 keV/µm. Energy depositon from high-LET particles can easily be distinguished in the spectrum and the probability of having more than one high-LET event in a 100 ms measurement is negligible. The quality factor for the spectrum can therefore be composed by one term for the multiple-events, and another for the single-events. The linear function (3.5) is used up to 150 keV/µm where (3.5) intersects with (3.4). For the events above 150 keV/µm the formulation in (3.4) is used (Figure 3.3).

( )

( ) ( )∑

∫∫∫

=<<

∞∞

−++=

=++==

n

kkyDy

combcombD

lGN

ybad

dyydy

dyydbyadyydyQQ

1150,150

150

150

00

,

)(300

)(300

)()()(

εεε

(3.6)


24

Here dy<150 and 150, <yDy are the absorbed dose fraction and dose-average lineal energy

below 150 keV/µm, εk is a measured single high-LET energy deposition, G(ε) is the average low-LET multiple-event energy deposition, n is the number of events above 150 keV/µm, N is the number of total measurements and l is the mean chord-length. The multiple-events are assumed to have a lognormal distribution and the most probable energy deposition is then given by the geometric average G(ε) [Paper II].

0.1

1

10

100

0.1 1 10 100 1000

Lineal energy [keVµm]

Qua

lity

fact

or

Figure 3.3. Different quality factor expressions as function of lineal energy. QICRP60(y):(––), Qlin(y)=0.52+0.28y: (----) and Qcomb(y) in (3.3) with a=0.73 and b=0.17 µm/keV:(●).

Figure 3.3 shows that the overestimation by Qlin(y) at high-LET has disappeared with Qcomb(y). The optimal values on the coefficients a and b depends on the dose distribution in y. A least square fit between QICRP60(y) and Qlin(y) gives a=0.61 and b=0.22 µm/keV for a rectangular dose distribution. In Paper I the values were determined to a = 0.52 and b = 0.28 µm/keV for low energy neutrons; a = 0.88 and b = 0.09 µm/keV for high energy neutrons; and a = 0.73 and b = 0.17 µm/keV for average neutron energies. The best values for the combined function (3.6) onboard aircraft were determined to a = 0.63 and b = 0.24 µm/keV from a single-event spectrum in Paper IV. The usefulness of Qcomb(y) is apparent for radiation fields with a high-LET component, but it requires that the high-LET events can be resolved. With a constant integration time the average energy imparted per integration increases and the relative variance decreases with increasing dose rate (2.10). This means that with increasing dose rate the multiple-event spectrum becomes narrower and is shifted towards higher values of


25

energy imparted (Figure 3.4). A larger detector that simulates the same mean chord-length will also shift the distribution towards higher values since it has a larger cross-sectional area and a larger energy imparted for the same particle fluence (2.20). With increasing radiation quality (Dy ) the variance increases (2.10), which broadens the spectrum.

0

20

40

60

80

100

120

10 100 1000

Energy deposition per mean chord-length [keV/µm]

Num

ber

of c

ount

s

yD=10 keV/µm

yD=2 keV/µm

5 cm detector

yD=2 keV/µm

230 µGy/h77 µGy/h230 µGy/h

10 cm detector

Figure 3.4. Shift of the multiple-event spectrum with different detector sizes, Dy -values and dose rates. The simulated mean chord-length is 2 µm. The ordinate shows the number of measurements in 1 keV/µm bins. The abscissa shows the energy imparted in 100 ms divided by the mean chord-length.

Assume that a high-LET event (yhigh) must be more than k standard deviations (

µlE /σ )

higher the average value to be clearly resolved.

µµ lEµ

lEµ

high kl

mDk

l

Ey

/det

/σσ +=+= (3.7)

Rewrite (2.23) in terms of the average energy per measurement interval.

E

l

l

E

lE

l

EV

l

DVmy

µlE

µ

µ

lE

µµD

µµ

2/

2

2/detdetdetdet

σσ=

=== (3.8)


26

Equations (3.7) and (3.8) gives a second order equation for µlE /

σ with the solution

DhighDD

lEyy

ykykµ

+

±−=

2

/ 22σ (3.9)

With (3.7) and (3.9) we can express the maximum dose-rate at which an event yhigh can be resolved, in terms of the detector gas density (ρdet) and measured total Dy for a detector with radius rdet.

det2

det

22

det

/

max

22

ρπσ

r

yyyk

kyk

y

m

kylD

DhighDD

highlEhigh µ

+

−+

=−

= (3.10)

Figure 3.5 shows Dmax for yhigh=150 keV/µm as a function of Dy of the radiation field for two detector sizes and for k=3. Equation (3.6) can for example with a 10 cm detector be used to correct for high-LET events above 150 keV/µm up to about 60 µGy/h in a radiation field with Dy = 5 keV/µm.

0

100

200

300

400

1 10 100

Dose-mean lineal energy of radiation field [keV/µm]

Max

imum

dos

e ra

te

[µG

y/h]

_

d=10 cm

d=5 cm

Figure 3.5. Maximum dose rate for resolving a high-LET event of 150 keV/µm in a multiple-event spectrum as a function of Dy of the radiation field. The limit is defined as 3 standard deviations (k=3) above the average energy imparted. Results for detectors with 10 cm diameter (––) and 5 cm diameter (----) are shown. A single high-LET event of 150 keV/µm or higher can be resolved below the lines.


27

Figure 3.6 shows (3.10) applied to multiple-event spectra measured in a 97 MeV neutron beam at the iThemba-lab (section 4.1). With k=4 the estimated lowest single-events that can be resolved at these dose rates are 174, 576 and 863 keV/µm, indicated by lines in the figure.

1

10

100

1000

1 10 100 1000 10000

Energy deposited per mean chord-length [keV/µm]

Num

ber

of c

ount

s 7 µGy/h80 keV/µm

50 µGy/h90 keV/µm 86 µGy/h

98 keV/µm

Figure 3.6. Measured multiple-event spectra in a 97 MeV neutron beam and estimated lowest LET-value (vertical lines) a single-event can have to be resolved in the spectra according to (3.10). The ordinate shows the number of measurements in energy bins between 0.5 and 1 keV/µm width (constant for each spectrum). The abscissa shows the energy imparted during 100 ms divided by the mean chord-length.

3.3. Separation of dose components Separation of single high-LET events with the variance method is typically possible only above a hundred keV/µm (Figure 3.2), which is not sufficient to separate photon and neutron absorbed dose fractions. The components are related via their Dy -values in

(2.24), which has as the consequence that the neutron dose-mean lineal energy (nDy , )

and the neutron quality factor ( nDQ , ) are very sensitive on the neutron absorbed dose

fraction dn, while the neutron dose-equivalent (Hn) is almost independent of dn.


28

{ } ( )

{ } { }n

nDnDn

nDn

nDD

nn

DnD

nnDn

n

nD

nDnD

nD

d

dyyd

yd

yy

dd

ydy

dyd

d

y

yy

y

∆−≈>>≈∆

−==

=∆

−−∂∂==∆

∂∂

=∆

γγ

γ

,,,

,,

,

,

,

,,

,

)24.2(

11)24.2(

1

(3.11)

{ } ( )( )

{ } ( ) { }n

nDnDn

n

nDD

nD

nn

nD

nDn

n

nD

nDnD

nD

d

dyyd

d

yy

yba

b

dd

yb

ybad

d

yba

QQ

Q

∆−≈>>≈∆

−+

==

=∆∂∂

+=∆

∂+∂

==∆

γγ

,,,,

,

,

,

,

,,

,

)11.3(

11)5.3(

(3.12)

{ } ( )

{ } 0)12.3(1

11)1.3(

,

,

,,

,

=

∆−

∆≈≈∆

∂∂

+=

=∆

∂∂

+=∆∂

∂==

∆

n

n

n

nn

nnD

nD

n

nn

nDnnD

nn

n

nDn

nn

n

d

d

d

dd

dQ

Q

d

dd

QDdQD

Hd

d

QDd

HH

H

(3.13)

If only the neutron dose-equivalent (Hn) is of interrest it is not very crucial that dn is determined with high accuracy. It is however important for example in comparisons that also the other quantities are determined with reasonable precision. A known method in mixed-field dosimetry is to use two detectors with different sensitivities for the different radiation components [Attix 1987, Bewley 1989]. Consider two low-pressure proportional counters, one with tissue-equivalent A-150 plastic walls (TEPC) and one with graphite walls (GPC) [Paper II]. The absorbed doses in the two detectors can be written

γγ

γ

DrDrD

DDD

nnGPC

nTEPC

+=+=

(3.14)

where rn and rγ are the neutron and photon absorbed dose ratios between the GPC and the TEPC. The relative neutron absorbed dose fraction (dn) in the TEPC is given by

( ) ( )n

TEPC

GPC

nTEPC

GPCTEPC

TEPC

nn rr

D

Dr

rrD

DDr

D

Dd

−

−=

−−

==γ

γ

γ

γ (3.15)


29

0

0.5

1

1.5

0.0001 0.001 0.01 0.1 1 10 100

Energy [MeV]

DG

PC/D

TE

PC

Figure 3.7. Ratio between dose to the GPC (graphite) and the TEPC detector as function of energy for neutrons (●) and photons (□).

Figure 3.7 shows rn and rγ as a function of photon and neutron energy. The results were simulated with the Monte Carlo code MCNP 4C as described in section 3.4. In photon fields the two detector responses are equal within ±20%. For neutrons rn increases above 5 MeV due to an increasing neutron non-elastic cross-section in graphite. At most workplaces the neutron fluence above 5 MeV is relatively low while the thermal fluence can be considerable and rn is typically 0.05. The two quantities nDy , and nDQ , are very sensitive on the uncertainty in rγ but not on

the uncertainty in rn, which is seen directly from differentiation of (3.15) and using that dn~0.1.

( ) ( ) { }

( ) ( )( )

( ) ( )( )( )n

n

n

nn

nn

nn

nn

n

rr

rr

rr

rrd

rr

dr

r

d

dd

d

−∆+∆

≈

−

∆+∆

−

=

==

∆

∂∂

+∆

∂∂

=∆

γ

γ

γ

γ

γγ

2/122

2/1

2

222

2/1

2

2

2

2

8111

)12.3(1

(3.16)


30

Typical values are rγ=1 and rn=0.05 (Figure 3.7) that with ∆rγ=0.05 results in a 50% uncertainty in dn, while ∆rn=0.05 results in only 5% uncertainty in dn. The same numbers apply for nDy , and nDQ , as seen from (3.11) and (3.12).

A second method to separate photon and neutron absorbed dose fractions was presented in Paper II. Specific Dy -values were assigned to the two components, which is

motivated by that the neutron Dy -value is essentially determined by the fast neutrons for many distribution. Both the absorbed dose to detector gas per unit neutron fluence δn(E) and the energy dependent neutron dose-mean lineal energy )(n, EyD decreases

strongly with decreasing energy (section 4.1). The total neutron nDy , given by

∫∫=

dEE

dEEyEy

nEn

nDnEn

nD)(

)()(

,

,,

, δφ

δφ (3.17)

decreases even more sharply. Here Φn,E is the neutron fluence differential in energy. Figure 3.9 shows )(Enδ , )(n, EyD and the product )()( n, EyE Dnδ as a function of

neutron energy. The functions have been normalized to unity at 2 MeV.

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10

Neutron energy [MeV]

Rel

ativ

e va

lues

_

Figure 3.9. The neutron energy dependence of the dose-average lineal energy

)(n, EyD (---), the dose to detector gas δn(E)(– – –), and the product δn(E)

)(n, EyD (–––). The functions are normalized to unity at 2 MeV.


31

The product δn(E) )(n, EyD decreases strongly below 1 MeV and the low energy

neutrons contribution to nDy , in (3.17) is small for most fluence distributions Φn,E. The

neutron dose fraction can according to (2.24) be determined from the measured Dy -value

( )( )γ

γ

,,

,

DnD

DDn yy

yyd

−−

= (3.18)

with typical values γ,Dy = 3 – 1.5 keV/µm and nDy , = 60 – 80 keV/µm (Figure 4.3).

At third (unpublished) method to separate low- and high-LET absorbed dose components is related to the observation that the peak in a multiple-event spectrum is mainly due to a large number of low-LET interactions if the dose rate is not too high and the high-LET component is not totally dominating. According to the Central limit theorem a sum of independent equally distributed variables will approach a normal distribution for a sufficient number of variables [e.g. Rice 1995]. The required number of variables depends on the symmetry of the original distribution. Energy depositions from single events are distributed on a logarithmic rather than on a linear scale and the sum distribution more likely to be well represented by a lognormal distribution. This is exemplified in Figure 3.10 with both a normal and a lognormal distribution fitted to a measured multiple-event distribution in a 137Cs field of 6 µSv/h.

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15

Energy per mean chord-length [keV/µm]

Num

ber

of c

ount

s [

a.u.

]

Figure 3.10. Multiple-event spectrum measured in a 6 µSv/h Cs-137 photon field (○) with fitted normal (---) and lognormal (––) distributions. The ordinate shows the number of measurements in 0.14 keV/µm bins. The abscissa shows the energy imparted during 100 ms divided by the mean chord-length.


32

A lognormal distribution fitted to the peak in a multiple-event distribution is used to estimate the absorbed dose fraction and the Dy -value of the low-LET component (Figure 3.11). Data on the high-LET (right) side of the peak, where high-LET events give a significant contribution, should not be included in the fit. The choice of what data to include is given by the best correlation between the fit and the measurements. A Dy -value for the peak that is higher than 1.5 – 3 keV/µm (Figure 4.3) indicates that the width of the fitted distribution is too large and includes a non-negligible number of high-LET events.

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300 350 400

Energy per mean chord-lenght [keV/µm]

Num

ber

of c

ount

s [a

.u.]

Figure 3.11. Separation of low-LET component using a lognormal distribution fitted to a multiple-event distribution. The absorbed dose rate is 47 µGy/h and the dose-mean lineal energy 9.2 keV/µm. The ordinate shows the number of counts in 1.4 keV/µm bins. The abscissa shows the energy imparted during 100 ms divided by the mean chord-length.


33

3.4. Monte Carlo simulations The Monte Carlo code MCNP version 4C [Briesmeister 2000] was used to simulate the absorbed dose responses of the tissue-equivalent (TEPC) and the graphite walled (GPC) detectors in photon and neutron fields. Simulated energies were 20 keV to 1 GeV for photons and thermal to 20 MeV for neutrons. In the photon simulations the absorbed dose to the detector gas was determined by scoring the energy imparted to the sensitive volume by secondary electrons. The neutron simulations were based on the kerma approximation, i.e. the absorbed dose was calculated from the neutron fluence and kerma coefficients under the assumption of charged particle equilibrium (CPE) [e.g. Attix 1987]. The solid materials in the detector geometry (Figure 3.12) have the same atomic composition as the physical detector (Figure 3.1), and the gas volumes are propane-based tissue-equivalent gas. The exception is the sensitive volume of the detector that in the neutron simulations was given the same atomic composition as the wall but with the same density as the other gas volumes. In this way the kerma of the wall material was determined with reasonable scattering properties retained. The simulated absorbed doses might be 2 – 3 % too low due to stopping power differences between A-150 plastic and the tissue-equivalent gas [ICRU 2005, ICRU 1993b].

Figure 3.12. Cross-section of the detector geometry used in the MCNP4C simulations.


34

Neutron interaction in the low pressure TE-gas cavity were hence neglected, which is reasonable at high energies [Newhauser and Brede 1997, Rubach and Bichsel 1982, Pszona and Makarewicz 1982]. At lower energies the neutron interaction in the gas increases and the detector is no longer a good Bragg-Gray cavity. However, the differences in stopping power and kerma coefficients between the gas and A150 are of the order of a few per cent for the neutron secondaries 1H and 4He [Chadwick et al 1999, ICRU 2005] and not corrected for here. The neutron interactions in the gas are not very important for the separation of the low-LET component using the TEPC+GPC detector combination either. The neutron absorbed dose fraction dn is not very sensitive to the uncertainty in the ratio of the GPC and TEPC neutron absorbed doses rn (3.16). Monte Carlo methods were also used in Paper V for verification and extrapolation of measured data to very small objects. The task was approached in two steps. The total

Dy -value of a radiation field can like in (2.24) be written in terms of the Dy -values and the absorbed dose fractions of its charged secondaries

...)( ,,,, HeDHeHDHDiDiD ydydydyddyyydy ++=== ∫ ∑ γγ (3.19)

The dose-mean lineal energy for the whole distribution of each particle type (iDy , ) was

calculated from the mass-stopping powers and energy dependent dose-mean lineal energies ( )(, Ey iD ).

∫

∫∞

∞

Φ

Φ=

0

,

0

,,

iD,)(

)()(

dEES

dEEyES

yi

iE

iDi

iE

ρ

ρ (3.20)

The code SHIELD-HIT [Gudowska et al 2004, Geithner et al 2006] was used to generate the dose fractions (di) and the fluence of the charged secondaries (ΦE,i). Corrections for material differences between the geometries in the simulation and the experiments were in Paper V introduced using Bragg-Gray cavity theory, i.e. with particle fluences and mass-stopping power ratios. The dose-mean lineal energy values

)(, Ey iD in (3.20) were taken from Kyllönen et al [2003] and Nikjoo et al [2001 and

2002]. These data were obtained from ion-track simulations in water vapor normalized to unit density using the Monte Carlo code PITS [Wilson and Nikjoo 1999] coupled with the electron transport code KURBUC [Uehara et al 1993]. Figure 3.13a shows the dose distributions in a volume with 100 nm diameter for 1H, 4He, 7Li and 12C ions of energy 5 MeV/u. Figure 3.13b shows the dose distributions in a volume with 100 nm for 1H in the energy range 0.3–30MeV. The frequency (Fy ) and dose average (Dy ) lineal energies are presented inside the figure. A selected data set from Kyllönen et al [2003],

Dy - and Fy -values for cylinders with equal diameter and length, are summarized in Appendix.


35

0

0.5

1

1.5

2

2.5

1 10 100 1000

Lineal energy [ev/nm]

yd(y

)12C yF=38 eV/nm

yD=250 eV/nm

7Li yF=24 eV/nm

yD=68 eV/nm4He yF=18 eV/nm

yD=35 eV/nm

1H yF=7 eV/nm

yD=12 eV/nm

Figure 3.13a. Simulated nanodosimetric distributions for ions with energy 5 MeV/u in a cylindrical volume with diameter and length 100 nm. 1H(×), 4He(●), 7Li(□) and 12C(◊).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.1 1 10 100 1000

Lineal energy [ev/nm]

yd(y

)

0.3 MeV 1H

yF=52 eV/nm

yD=77 eV/nm

1 MeV 1H

yF=23 eV/nm

yD=35 eV/nm

10MeV 1H

yF=4 eV/nm

yD=8 eV/nm 30MeV 1H

yF=2eV/nm

yD=7eV/nm

Figure 3.13b. Simulated nanodosimetric distributions for protons in a cylindrical volume with diameter and length 100 nm. Protons 0.3MeV (×), 1MeV(●), 10MeV(□) and 30MeV(◊).


36


37

4. RESULTS Section 4.1 presents the absorbed dose, dose-mean lineal energy, quality factor and dose-equivalent responses in neutron and photon fields for the TEPC detector described in section 3.1. Results from monoenergetic and quasi-monoenergetic neutron beams have been published in Paper I, Kyllönen and Mayer [2002] and Kyllönen et al [2002]. New results from defolding the peak responses, unpublished experimental data from iThemba-lab in Capetown, and unpublished Monte Carlo simulations are presented. In section 4.2 the results of using the variance-covariance method for radiation protection measurements in the cosmic radiation field and in the nuclear industry is evaluated. The performance of the different algorithms for covariance correction in pulsed fields is evaluated in section 4.3 and the different methods to separate low- and high-LET dose in section 4.4. In section 4.5 the instrument performance at extremely low levels of radiation is investigated, and in particular the influence on the result from a small radioactive content in the A-150 plastic wall discussed. Section 4.6 is devoted to an uncertainty analysis and the final section 4.7 is concerned with the variance-covariance method used for nanodosimetric investigations and beam quality characterization.

4.1. Instrument response The TEPC was in 2003 exposed in a 7Li(p,n)7Be neutron beam with 97 MeV peak energy at iThemba-lab outside Capetown, South Africa (unpublished). The neutron fluence was monitored with time-of-flight techniques and the characteristic low-energy (tail) contribution could be subtracted by using an additional measurement at 16º angle to the primary beam. Often the tail is not measured and the peak value δn(Epeak) must be defolded from the detector response and the fluence distribution.

∑−

=

∆Φ+∆Φ=1

1,, )()()()(

N

iiiniEnpeakpeaknpeakEn EEEEEED δδ (4.1)

Here δn(E) is the energy dependent conversion coefficient from neutron fluence to absorbed dose to detector gas, D is the measured total absorbed dose, Φn,E is the neutron fluence distribution differential in energy, ∆Ei the energy bins and N the total number of bins in the spectrum. The dose-mean lineal energy of the peak )(, peaknD Ey is

determined analogously from

∑

∑

=

−

=

∆Φ

∆Φ+∆Φ=

N

iiiniEn

N

iiiiniEnpeakpeakpeaknpeakEn

EEE

EEyEEEEyEEy

1,

1

1nD,,nD,,

D

)()(

)()()()()()(

δ

δδ (4.2)

where )(, Ey nD is the energy dependent dose-mean lineal energy function for the

detector.


38

Table 4.1 shows the results from iThemba and defolded results from measurements at UCL (Université catholique de Louvain) and TSL (The Svedberg Laboratory, Uppsala) [Paper I, Kyllönen et al 2002]. The neutron distributions at TSL were extrapolated to thermal energy using a constant distribution below the lowest calculated energy bin [Prokofiev 2001]. For the highest beam energy of 172 MeV there were no calculations available and the distribution was assumed to be the same as at 94 MeV, but shifted to higher energies.

Table 4.1. Defolded results for the peak in quasi-monoenergetic 7Li(p,n)7Be neutron beams (unpublished).

Laboratory

Epeak (MeV)

δn(Epeak) (pGy.cm2)

)(, peaknD Ey

(keV/µm) UCL 60 18.6 154

TSL 68 65.7 110

TSL 94 48.9 111

iThemba 97 92 106

TSL 172 9.1 40

Figure 4.1 shows the experimental δn(E) from Paper I, δn(Epeak) from Table 4.1 and MCNP simulations of the absorbed dose to TEPC gas (section 3.4), conversion coefficients to ambient absorbed dose D*(10) [Ferrari and Pelliccioni 1998, Leuthold et al 1992] and A-150 kerma [Chadwick et al 1999, Savitskaya and Sannikov 1995]. D*(10) is defined as the absorbed dose at 10 mm depth in the ICRU-sphere in an expanded and aligned field [ICRU 1993]. The D*(10) coefficients from Ferrari and Pelliccioni [1998] were derived as the ratio of the reported H*(10)-values and the effective quality factor ffeQ at 10 mm depth in the ICRU-sphere. The data of Ferrari and

Pelliccioni do not assume charge-particle equilibrium and the build-up layer consists only of the 10 mm ICRU-tissue in the definition of the quantities. The difference between the TEPC (MCNP simulations) and the ambient absorbed dose D*(10) at low energies is due to an increasing contribution from thermalized neutron interactions 14N(n,p)14C and 1H(n,γ)2H in the larger mass of the ICRU-sphere compared to the TEPC. Above 20 MeV the secondary proton ranges become comparable with the TEPC wall thickness and the condition of charged-particle equilibrium (CPE) fails. The TEPC absorbed dose is not expected to be a good measure of A150 kerma, but rather the D*(10) without CPE reported by Ferrari and Pelliccioni. The best estimate of the absorbed dose per unit neutron fluence δn(E) is hence using the experimental data between 71 keV and 19 MeV, MCNP simulations below 71 keV (normalized to the measurements) and the conversion coefficients to D*(10) above 19 MeV. The two experimental data points at 60 MeV (UCL) and 172 MeV (TSL) are significantly lower than expected. For the 172 MeV beam the energy distribution is uncertain and the results could be explained by the presence of low-energy neutrons with lower absorbed


39

dose conversion coefficients. For the 60 MeV beam the fluence distribution was however carefully measured and the low absorbed dose conversion coefficient is possibly related to an error in the absolute neutron fluence. These data points are not included in δn(E).

1E-03

1E-01

1E+01

1E+03

1E-08 1E-06 1E-04 1E-02 1E+00 1E+02 1E+04


Con

vers

ion

coef

ficie

nts

[fG

y.m

2]_

Figure 4.1. Conversion coefficients from neutron fluence to absorbed dose and kerma. Measured TEPC (♦), MCNP simulated TEPC (–––), ambient absorbed dose D*(10) (+) and A-150 kerma (- - -). See text for details.

The TEPC photon absorbed dose response was measured in gamma and x-ray beams between 15 keV and 7 MeV at SSI and at PTB (unpublished). Figure 4.2 shows the measured and MCNP simulated conversion coefficients from photon fluence to absorbed dose to detector gas. Included are coefficients for ambient dose-equivalent [ICRP 1996, Pelliccioni 2000] and tissue-kerma [ICRU 1992]. At low photon energies the absorbed dose and ambient dose-equivalent are lower than kerma due to attenuation. The dose to detector gas is lower than the ambient dose-equivalent due to higher attenuation in the detector. For example, using exponential attenuation and mass-attenuation coefficients [ICRU 1992] show that 0.2 cm Al + 0.5 cm A-150 plastic attenuates 36% more than 1 cm ICRU tissue, which is in good agreement with the 30% difference between the detector dose and ambient dose-equivalent in Figure 4.2. At high photon energies both the measured and the simulated TEPC absorbed dose is lower than kerma due to lack of build-up and charged-particle equilibrium. The ambient dose-equivalent conversion coefficients from ICRP74 are based on a CPE assumption and follow the kerma coefficient closely. Peliccioni [2000] does not presume external


40

CPE in his reported absorbed dose at 1 cm depth in the ICRU sphere and these values are consequently lower than the kerma coefficients. The TEPC absorbed dose is higher than H*(10) from Pelliccioni due a better build-up and the TEPC response should be reasonably well estimated by the MCNP simulated results for the whole energy range. The H*(10) response of the TEPC is within ±20% for photon energies usually encountered.

0.001

0.01

0.1

1

10

100

0.01 0.1 1 10 100

Photon energy [MeV]

Con

vers

ion

coef

ficie

nts

[fG

y.m

2 an

d fS

v.m

2]_

Figure 4.2. Photon fluence-to-dose, kerma and dose-equivalent conversion coefficients. Experimental dose to TEPC detector gas (♦), MCNP simulated dose to TEPC detector gas (—), ICRP74 ambient dose-equivalent (□), ambient dose-equivalent from Pelliccioni [2000] (---) and tissue kerma from ICRU46 (−−−).

The dose-mean lineal energy of this detector was not simulated and values at energies not covered by the experiments must be estimated by other means. A thermal neutron

thDy , -value of 46 keV/µm is calculated from the results of the non-moderated and

moderated 252Cf -field reported in Paper I using (2.24). At high neutron energies the simulations by Ferrari and Pelliccioni [1998] show relatively small (10%) variations in the effective quality factor ffeQ at 10 mm depth in the ICRU-sphere. It is assumed that

the relative variation in Dy above 100 MeV is the same as in ffeQ even though )(ff LQe

is not a linear function of L (or y). At intermediate neutron energies the dominating dose contribution comes from elastically scattered hydrogen recoils. Due to their short ranges most of these secondary protons deposit all their energy in the detector volume and their dose-mean lineal energy ( elpDy _, ) is approximately proportional to the neutron energy. The MCNP

simulations (Figure 4.1) show no gamma contribution generated by neutrons above 50


41

keV and Dy is determined by the protons only. The proton elpDy _, is therefore scaled in

proportion to neutron energy from the experimental Dy at the lowest neutron energy 71 keV. The MCNP simulations show also that for this particular detector the gamma contribution from 1H(n,γ)2H is about 60% of the total thermal neutron absorbed dose. It is assumed that the gamma dose at intermediate neutron energies is due to thermalized neutrons in the detector and then the MCNP simulated gamma dose gives directly the thermalized neutron dose fraction (dth) at different intermediate neutron energies. An estimation of the intermediate neutron Dy -value is then given by the contributions from elastic protons and thermalized neutrons according to

thDthelpDththDthelpDelpD ydydydydy ,_,,_,_ )1( +−=+= (4.3)

Figure 4.3 shows the estimated dose-mean lineal energy function )(, Ey nD for the TEPC

together with the measured data from the monoenergetic beams (Paper I, Kyllönen and Mayer 2002) and the defolded data from Table 4.1. The data from Paper I has been corrected for the W/e-difference between a pure neutron field (31 J/C) and a mixed radiation field (28 J/C). Included are also results reported by other groups [Rodgers and Gross 1981, Wissmann 2002, Nunomiya et al 2002, Nguyen et al 1980, Menzel and Schuhmacher 1981]. The data represent measured and simulated values for mean chord lengths between 1.3 and 2.7 µm, and all results are for spherical objects except for the variance-covariance TEPC. Included in Figure 4.3 are also experimental Dy -values from gamma and x-ray beams. The nuclei used were 238Pu, 241Am, 137Cs-137 and 60Co-60 with average gamma energies 15 keV, 60 keV, 662 keV and 1250 keV. The x-ray HVL-energies were between 32 keV and 242 keV.


42

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000

Energy [MeV]

Dos

e av

erag

e lin

eal e

nerg

y [

keV

/µm

]_

Photons

Neutrons

Figure 4.3. Experimental Dy for neutrons (■) and photons (□) for the variance-covariance instrument. Also shown is data from the literature [Rodgers and Gross 1981, Wissmann 2002, Nunomiya et al 2002, Nguyen et al 1980 and Menzel and Schuhmacher 1981]. The solid line represents the derived energy dependence of the neutron Dy -values for the variance-covariance instrument.

The defolded neutron Dy -values at 60 MeV and 172 MeV value (154 keV/µm and 40 keV/µm) deviate from the expected trend as they did also for the absorbed dose (Figure 4.1). As already mentioned the 172 MeV results could be explained by the presence of low-energy neutrons with lower absorbed dose conversion coefficients but also lower

Dy -values. For the 60 MeV beam there could be some problems with the absolute

neutron fluence, but since the Dy -value depends only on the fluence energy distribution the value 154 keV/µm may be fairly reliable. Partial A-150 kerma coefficients from Meulders et al [2000] show that the relative kerma contribution from secondary alpha-particles peaks around 30 MeV, which could result also in a maximum in the neutron

Dy -value due to the high-LET of the alpha-particles. This would imply that there is a

Dy -maximum between 19 MeV and 60 MeV, but the uncertainties are large and a constant value is assumed at energies in between. The measured neutron Dy -values are 20–30% higher than reported by the other groups,

and the photon Dy -values are 20% higher than reported in ICRU36 [ICRU 1984]. One

source of uncertainty is that the mean chord-length l is determined directly from the physical detector size and the gas pressure (section 3.1). Another is the variance contribution from the chord-length distribution, which however should be small [Kellerer 1975]. This difference require further investigations to be fully understood.


43

The neutron energy dependence of the linear quality factor Qlin(y) in (3.5) is given directly using )(, Ey nD . The combined quality factor Qcomb(y) in (3.6) requires however

that the high-LET events are considered. A correction is obtained from single-event measurements [Wissmann 2002] up to 19 MeV. At higher energies Dy was assumed not to vary much (Figure 4.3) and the correction obtained at 19 MeV is applied. Figure 4.4 shows the result together with the effective quality factor ffeQ at 10 mm depth in the

ICRU-sphere. The effective quality factor was derived from H*(10) and D*(10) conversion coefficients up to 20 MeV from ICRP [1996] and Leuthold et al [1992], and

ffeQ from Ferrari and Pelliccioni [1998] above 20 MeV.

1

10

100

0.00000001 0.000001 0.0001 0.01 1 100 10000


Qua

lity

fact

or

[Sv/

Gy]

Figure 4.4. Quality factors as a function of neutron energy. The effective quality

factor ffeQ at 10 mm depth in the ICRU-sphere (▬); Q(y) =0.52+0.28y (– –); Q(y)

=0.73+0.17y (––); Q(y) = 0.88+0.09y (---) and the Qcomb(y) relation that corrects for single-events above 150 keV/µm (○).

At high neutron energies Qlin(y) give very high values on the average quality factor due to the presence of high-LET secondaries (Figure 3.3). In the intermediate energy region the recoil protons are essentially stoppers in the detector cavity and their LET and quality factor are underestimated [Schuhmacher et al 1990, 1995]. In the thermal region the lower effective quality factor ffeQ is due to a larger photon contribution (low-LET)

from thermalized neutrons in the large mass of the ICRU-sphere.


44

Both the absorbed dose and quality factor responses are low in the intermediate energy region (Figures 4.1 and 4.4), and the effect is even more pronounced for the ambient dose-equivalent (Figure 4.5). The conversion coefficients from fluence to H*(10) are from ICRP74 below 20 MeV and from Ferrari and Pelliccioni [1998] for higher energies.

0.01

0.1

1

10

100

1000

1E-08 0.000001 0.0001 0.01 1 100 10000


H*

conv

ersi

on c

oeff

icie

nts

[fS

v.m

2]_

Figure 4.5. Fluence-to-dose-equivalent conversion coefficients as a function of neutron energy. The H*(10)/Φ-values for the ICRU-sphere are from ICRP74 below 20 MeV and from Ferrari and Pelliccioni [1997] at higher energies (▬). The other lines for Q(y) = 0.52+0.28y (– –); Q(y) = 0.73+0.17y (––); Q(y) = 0.88+0.09y (---) and Qcomb(y) in (3.6) (○).

The combined quality factor relation Qcomb(y) in (3.6) has improved the Q- and H*(10)- responses at high neutron energies compared to the linear relations Qlin(y) in (3.5). The large underestimation at intermediate energies however remains. It is a combination of scattering differences between the detector and the ICRU-sphere leading to a lower absorbed dose (Figure 4.1), and of an underestimation of the proton LET leading to a lower Q-value (Figure 4.4). The latter could be improved by reducing the gas pressure but the first is difficult since it is related to the physical size of the detector.


45

4.2. Dose equivalent measurements One of the most challenging applications for radiation protection dosimetry is aircrew exposure to cosmic radiation. The energetic cosmic radiation produces a wide range of secondary particles in the atmosphere with energies extending into the GeV-region. Contributions to the ambient dose-equivalent in the atmosphere at high latitudes are 50–60% from neutrons, 20–30% from electrons, 10% from protons and 10% from photons and muons [Roesler et al 2002, Ferrari et al 2002, EURADOS 2004]. The LET distribution in tissue-like media consists of both a low- and high-LET component, where the latter is mainly due to neutron secondaries such as alpha-particles, carbon, nitrogen and oxygen recoils. Instrument calibration and response characterization are consequently quite intricate, which can result in significant differences in the determined H*(10) [Paper IV]. The variance-covariance instrument was used in two research contracts for cosmic radiation dosimetry supported by the European Commission [European Commission 1995, 2000]. The results show that the method gives results in good agreement (±10%) with other active and passive instruments and calculations using Qlin(y) from high-energy neutron calibration, or Qcomb(y) [Paper III and IV, Bottollier-Depois et al 2004, EURADOS 2004]. A systematic difference is that combQ in (3.6) is 10% lower than

)(60, yQ ICRPD in (3.4), which is expected from the underestimation in the proton region

20–150 keV/µm (Figure 3.3). A corresponding underestimation would also be expected in the dose-equivalent, which was also observed in Paper III. During the devoted in-flight comparison in Paper IV such an effect related to the quality factor was hidden by other systematic differences related to calibration methods used by different groups. Calculations of the route doses are also extremely valuable as a complement in comparisons and for aircrew dose assessment. A number of codes have been developed for this application where one of the most well-established is EPCARD (European Program Package for the Calculation of Aviation Route Doses) [Schraube et al. 2000, Schraube et al. 2002]. Figure 4.6 shows the dose-equivalent measured with the variance-covariance instrument on flights between 1998 and 2003 as a function of the EPCARD calculated value. The average ratio between the measured and the calculated value is 0.99 ± 0.13 (1s), but despite this very good agreement there are some significant differences worth noting. The ratio varies with time from 0.80 ± 0.05 in 1998 (low solar activity) to 1.05 ± 0.07 in 2002/2003 (high solar activity). The same difference of 20% between low and high solar activity is also seen in published data compilations [EURADOS 2004]. Variations on a daily basis is also expected since EPCARD uses a monthly average of the signal from the ground-based neutron monitor CLIMAX in Colorado, and is therefore not sensitive to short-term variations in the cosmic radiation intensity. In Paper IV it was also noted that the measured altitude variation was stronger than calculated with EPCARD. The TEPC detectors measured an increase of 80% – 90% compared to 40 – 50 % for EPCARD in the high-LET (neutron) component of H* between flight levels FL400 (~12.2 km) and FL320 (~9.8 km).


46

1

10

100

1 10 100

H*EPCARD [µSv]

H* m

[µ

Sv]

Figure 4.6. Measured dose-equivalent as a function of the calculated value using EPCARD. Flights in 1998 from Paper III (□); flights in 2002 from Bottollier-Depois et al 2004 (×); flights between 2002 and 2003 (unpublished) (○) and in 2003 from Paper IV (∆).

Another high-energy comparison was done at the CERF facility, available at CERN (European Organization for Nuclear Research) until recently. The concrete moderated high-energy neutron field resembled the atmospheric neutron spectrum and was used for response studies, comparisons and calibrations of dose meters and instruments for aircrew dosimetry [Höfert and Stevenson 1994, Mitaroff and Silari 2002]. The CERF results obtained with the variance-covariance TEPC were in good agreement with other instruments and simulations [Paper I, Mayer 2003, Mayer et al 2004]. The dose-equivalent using a linear relation Q(y)=0.88+0.09y agreed with a single-event TEPC system (HANDI) within ± 5 %, which is well within the uncertainties. The measured

Dy -value of 37 ± 3 keV/µm is also in good agreement with the value 33 keV/µm derived from a single-event spectra measured by Höfert et al [1994]. The good response for the neutron dose-equivalent at high and thermal neutron energies is expected to get poorer with an increasing intermediate neutron contribution. Within the EVIDOS project (Evaluation of individual dosimetry in mixed neutron and photon radiation fields) a large number of measurements were made in simulated and real workplace fields [Paper II, d’Errico et al 2005, Schuhmacher et al 2005]. The neutron reference values were obtained by Bonner sphere spectrometry and the photon reference values evaluated from ion chamber measurements and from the variance-covariance instrument using the TEPC+GPC method (section 3.3). Figure 4.7 shows the ratio of the


47

TEPC neutron dose-equivalent (Hn) and the Bonne-sphere neutron dose-equivalent (H*n(10)) as a function of the intermediate neutron dose fraction for all the EVIDOS fields and confirms the dependence on the intermediate neutron component.

0

1

2

0.01 0.1 1

Intermediate neutron contribution to H *(10)

Hn/

H* n

(10)

Figure 4.7. Ratio of measured and reference neutron ambient dose-equivalent as a function of the intermediate neutron contribution. Intermediate neutrons are here defined by the energy interval 0.5 eV to 0.1 MeV. The quality factor was calculated according to (3.5) with a=0.52 and b=0.28 µm/keV.

It seems that H*n(10) is difficult to determine with better accuracy than 30–50% in unkown neutron radiation fields in the nuclear industry. But note that H*n(10) is usually only about half of the total ambient dose-equivalent, and the remaining photon component is determined correctly within 10–20% (Figure 4.2). The uncertainty (1s) in the total H*(10) in a typical radiation field in the nuclear industry then becomes ±20–25%. See section 4.6 for a detailed discussion about uncertainties.


48

4.3. Pulsed radiation fields The applicability of the different algorithms for calculating Dy (section 2.1) is investigated in an experimental comparison in beams with different time characteristics. The radiation field at the two facilities ISOLDE and CERF at CERN, are characterized by a synchrotron super cycle period of 16.8 seconds (Figure 4.8). At CERF the pulse length is about 5 seconds while at ISOLDE it is shorter and only seen in one or two of the 100 ms integrations.

0.1

1

10

100

1000

0 5 10 15 20 25 30 35 40

Time [s]

Abs

orbe

d do

se

[µG

y/h]

Figure 4.8. Time structure of the CERF (–) and the ISOLDE (◊) beams. Each point corresponds to a 100 ms measurement.

Figure 4.9 shows Dy calculated according to different algorithms: the variance alone (2.11), corrected for the covariance between detectors (2.12), correcting for time variations using one detector (3.3), and correcting for both time and spatial variations (2.13). The ratio (Vr-Cr)/Vr, where Vr is the relative variance and Cr is the relative covariance between the detectors, quantifies the time structure of the beam. In a strongly pulsed beam the covariance correction is large and (Vr-Cr)/Vr is small (ISOLDE and CERF S3), while in a beam of constant intensity the correction is small and the ratio close to one (PTB, iThemba and CANEL). For the two pulsed beams ISOLDE and CERF S3, the covariance correction is very large and any difference in the relative variance between the two detectors will be enlarged after subtraction of the relative


49

covariance (2.11). There can consequently be considerable differences in the Dy -values of the two detectors and therefore both are included in Figure 4.9. For ISOLDE and CERF the Dy -value was also calculated for the pulse peaks with the background between pulses subtracted (ISOLDE peak and CERF peak).

1

10

100

1000

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

(Vr-Cr)/Vr

Dos

e m

ean

linea

l ene

rgy

[ke

V/µ

m]_

ISOLDE CERF

ISOLDE peak

CERF peak

CANEL

PTB

iThemba

Figure 4.9. Dose-average lineal energy evaluated with four different algorithms in radiation fields with different pulse structures. Variance (×); Variance-covariance (□); Consecutive intervals from one detector (∆); Time and spatial correction (●). The ratio (Vr-Cr)/Vr has a low value in a strongly pulsed beam. For the two beams ISOLDE and CERF S3, the values of both detectors are included.

All algorithms are as expected in good agreement in the continuous or slowly varying beams. This is also the case for ISOLDE and CERF peaks, but the differences between the algorithms become apparent in the ISOLDE and CERF beams including the fast intensity changes shown in Figure 4.8. The variance method in its simplest form without covariance correction gives a very high value. Correcting for the covariance between successive samples using only one detector, works reasonably well at CERF where the pulse structure is slow compared to the sampling frequency (100 ms). When the pulse structure is extremely fast like at ISOLDE, this method fails since the pulse is not seen in two successive intervals and not interpreted as a beam variation.


50

4.4. Separation of dose components The performance of the three methods to separate dose components (section 3.3) was evaluated in the EVIDOS fields and in the cosmic radiation field. In the first the low-LET absorbed dose fraction dlow determined with the methods agreed within ±10% with the exception of three points that could not be directly related to a single property of the radiation field. As already mentioned and seen from (3.13) the precision of the neutron absorbed dose fraction dlow is not crucial for the neutron dose-equivalent that agreed within ±3%. A comparison is more illustrative in the cosmic radiation field. Table 4.1 shows the TEPC+GPC combination from an Icelandair flight between Stockholm and Baltimore, while the other three results are from flight level FL400 (12.2 km) at latitude 57° north and longitude 8° east (N57E08) described in Paper IV. The single-event results were derived from a spectrum measured with the HAWK system from ARC Seibersdorf research [Paper IV]. The dose components do not vary significantly at high latitudes [EURADOS 2004] and the flights should be comparable in this respect.

Table 4.1. Separation of low- and high-LET absorbed dose components with different methods on high-latitude flights. Method Single-event TEPC+GPC Constant- Dy Lognormal

dlow 0.89 0.9 0.88 0.92

lowDy , (keV/µm) 1.6 13 1.6 2.3

nDy , (keV/µm) 110 13 94 140

Using two detectors (TEPC+GPC) gives a low-LET dose fraction in agreement with the other methods, but this is only by coincidence. The absorbed dose contribution from high-energy neutrons in the GPC is considerable due to the increasing sensitivity above a few MeV (Figure 3.7) in combination with the atmospheric neutron energy distribution [Roesler et al 1998]. The GPC measures also the same Dy -value as the

TEPC since the contribution from low-energy neutrons to the total Dy is negligible for

both detectors (Figure 3.9). The high Dy -value measured by the GPC indicates the presence of high-energy neutrons, which in principle could be used for some characterization of the neutron energy distribution. The results from using constant Dy -values are in good agreement with the single-event

measurements. The nDy , -value of 94 keV/µm was derived from the )(, Ey nD -function in

Figure 4.3 and the neutron spectrum from Roesler et al [1998]. Contributions from other high-LET radiations than neutrons (or neutron secondaries) can account for the somewhat higher value (110 keV/µm) derived from the single-event spectrum.


51

A fast neutron nDy , -value as suggested in section 3.3 is not appropriate for this

application. The nDy , -value 73 keV/µm used in Paper IV and in particular the nDy , -

value 37 keV/µm from CERF used in Paper III are not representative for the atmospheric neutron field. The value in Paper IV was derived assuming an energy dependence of nDy , that differed from )(, Ey nD in Figure 4.3 at high neutron energies.

The CERF-value included a low-LET dose fraction that from a spectrum measured by Höfert et al [1994] is estimated to about 70% of the total absorbed dose. The reported neutron absorbed dose fractions in Paper IV and Paper III are therefore up to 20% too high, but the influence in the neutron dose-equivalent is much smaller (3.16), and it has no influence at all on the total dose-equivalent. The last method of using a lognormal low-LET approximation is also in good agreement with the other methods. All values are however slightly higher due to that some high-LET events are inevitably included in the fitted component (Figure 3.11). This increases lowDy , and hence also dlow and nDy , according to (2.24).

4.5. A low-dose rate application Of fundamental importance for a radiation protection instrument is the ability to measure H*(10) with good precision at low dose rates. The influence from leakage and noise sources increases at low doses and the (unpublished) results of this section describes a background source not usually associated with radiation detectors: small amounts of radioactive nuclei in the detector material. A chemical analysis of A150-plastic showed a low content of radioactive alpha emitting nuclei [Roos 2004] that could explain a significant contribution of high-LET events measured in a shielded whole-body laboratory at the Swedish Radiation Protection Authority. A devoted investigation was therefore performed at an underground laboratory for dosimetry and spectrometry (UDO) operated by Physikalisch-Technische Bundesanstalt in Braunschweig. The laboratory is situated in a salt mine at a depth of 490 m (1000 m water-equivalent) where the background is below 2 nSv/h, and that with an additional lead shield could be reduced below 1 nSv/h. Figure 4.10 shows the measured multiple-event distribution (charge created in 100 ms). The distribution is represented by a noise component and an alpha component from the radioactive elements. The non-symmetric alpha component corresponds to 10 nGy/h, or 200 nSv/h, due to events with an average Dy -value of 120 – 150 keV/µm.


52

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

-200 0 200 400 600 800 1000

Generated charge [fC]

Num

ber

of c

ount

s [

a.u.

]

Figure 4.10. Multiple-event distribution measured in a low-background laboratory. The distribution is shown as a noise component (–––) and a high-LET component (□). The ordinate shows the number of counts in 1 fC bins.

Figure 4.11 shows the sum-distribution of the alpha component, i.e. the frequency of events (per hour) above some value of y. Both TEPC detectors measure 13 – 15 events per hour, of which about 2 are larger than 150 keV/µm. A verification of these results was done with a track-etch measurement using poly allyl diglycol carbonate (PADC or CR-39®) films attached to the A-150 plastic. The measured alpha track density was 0.0159 ± 0.0013 (1s) cm-2 h-1, which corresponds to about 7 events per hour for the wall area 450 cm2 of the detector sensitive volume. This number is in good agreement with the results in Figure 4.11 considering that the track-distribution of the emitted alphas has not been taken into account.


53

0

5

10

15

10 100 1000

Lineal energy [keV/µm]

Sum

dis

trib

utio

n [

h-1]

_

Figure 4.11. Sum distribution of lineal energy, i.e. the number of events per hour above the lineal energy value y=E/l, measured with two tissue-equivalent proportional counters.

Measurements were also done in three 137Cs gamma fields of 35, 68 and 135 nSv/h in the low background environment at UDO. Figure 4.12 shows the reference values, the measured uncorrected values and corrected values where the high-LET dose contribution has been subtracted. A linear extrapolation of the uncorrected dose rates (leakage subtracted) resulted in a background level of 10 nGy/h, which is in good agreement with the high-LET dose contribution in Figure 4.10. If the proper corrections are included the variance-covariance instrument measures the ambient dose-equivalent with acceptable precision (40%) down to 35 nSv/h.


54

0.1

1

10

100

1000

0.1 1 10 100 1000

H*(10)ref [nSv/h]

Hex

p

[nS

v/h]

Figure 4.12. Reference H*(10)-values (–), experimental uncorrected (×) and corrected (□) dose-equivalent in three Cs-fields and in the low-background point of < 1 nSv/h. Events above 10 keV/µm from the internal radioactivity have been subtracted in the corrected data.

The UDO experiment together with the track-etch analysis have confirmed the presence of an internal background of about 10 events per hour that contribute with 0.2 µSv/h. The average Dy -value of these events is 120 – 150 keV/µm, and two events per hour are higher than 150 keV/µm. This means for example that the dose-equivalent measured onboard aircraft should be reduced with 5 – 10%.

4.6. Uncertainties Judging the relevance of a measurement requires knowledge about the uncertainties involved. The uncertainty analysis presented in this section is primarily for cosmic radiation measurements but it is also applicable to other situations. The analysis could in principle have been done for the dose-equivalent quantity directly, but it is more informative to discuss absorbed dose and quality factor separately. All uncertainties are given as one standard uncertainty in an one-hour measurement and the terminology follows the Guide to the Expression of Uncertainty in Measurement [ISO 1995].


55

The statistically determined Type A uncertainty in a one-hour absorbed dose measurement is typically less than 1 % (Table 4.2). The Type B uncertainty in absorbed dose is estimated to 3% from the difference between the dose to TEPC detector gas and the ambient absorbed dose D*(10) (Figure 4.1) weighted with the atmospheric neutron spectrum from Roesler et al [1998]. At intermediate neutron energies the difference between dose to detector gas and D*(10) is considerable due to scattering and thermalization. In a typical workplace field with 50% of H*(10) from photons the standard uncertainty is estimated to 20% (section 4.2). The dominating part of the underestimation of H*(10) at intermediate neutron energies is according to the MCNP simulations (Figure 4.1 and 4.4) due to the absorbed dose.

Table 4.2. Standard uncertainties for a one-hour TEPC measurement in mixed radiation field such as the atmospheric field onboard aircraft. The numbers in parenthesis correspond to a workplace field with a considerable fraction of intermediate neutrons. Type A (%) Type B (%) Type A&B (%) Dose 1 3 (20) Quality factor 4 10 Calibration 5 W/e 5 Temperature 2 Radioisotopes 2 TOTAL (H*) 5 13 (24) 14 (25)

The one-hour Type A uncertainty for the quality factor at high latitudes was estimated to 13% (1s) in Paper III. This is valid for the linear relation (3.5) with a=0.88 and b=0.09 µm/keV, but not for the combined relation (3.6) where the high-LET events are less influential. With the same assumptions as in Paper III (98% of the absorbed dose at 6 keV/µm and 2% at 300 keV/µm) the one-hour Type A uncertainty for combQ becomes

about 4%. The systematic difference between the Q(y)-relations (3.4) and (3.6) is 10% for cosmic radiation [Paper IV]. In principle this is an error that should be corrected for in aircraft measurements, but it is treated here as a Type B uncertainty to be used also in other applications. The Type B contributions from calibration, W/e and temperature dependence are taken from Paper III. The calibration uncertainty is independent on applications but the other two could be increased for a workplace application with low neutron energies (increasing W/e) and high temperatures. On the other hand the photon component is usually dominating and the measurements performed quickly in order to reduce the individual exposure, which keeps the temperature changes inside the detector small. Therefore these numbers are taken as valid estimates for all applications. A correction for the additional background from radioactive isotopes in the A-150 plastic introduces an uncertainty of about 2% at a dose-equivalent rate of 2–3 µSv/h.


56

On a long-haul flight the total combined uncertainty 14% in the dose-equivalent is dominated by the 13% of Type B (components added in quadrature). This is the same number as the standard deviation in H*(10) determined by different instruments and programs for different routes and dates reported by EURADOS [2004]. The Type B uncertainty is dominated by the 10 % from the different quality factor relation used by a variance instrument, but it has been shown that there are also systematic differences of the order of 10% for other systems [Paper IV]. If these differences were corrected for the combined Type A&B uncertainty would decrease from 14% to 10 %. For comparisons of experimental and simulated data in cosmic radiation applications there is an additional important uncertainty to consider. The ground-based neutron monitors around the world show daily intensity variations of the order of 10 – 20 % and these variations are correlated to the atmospheric dose and dose-equivalent rates. In Paper III it was found that a 10% change in the CLIMAX neutron monitor count corresponded to a 15–20% change in the atmospheric dose rate at high latitudes. A similar correlation was more recently also reported by Lantos [2005] and Wissmann [2006]. Figure 4.13 shows also roughly the same correlation in the measured absorbed dose rate on a route between Scandinavia and the Unites States in 2002 and 2003, and the Oulu neutron monitor (unpublished data). The result of each flight-level has been normalised to the average for that flight level.

0.9

0.95

1

1.05

1.1

5400 5500 5600 5700 5800 5900 6000

Oulu neutron monitor [min-1]

Abs

orbe

d do

se r

ate

[a.

u.]

Figure 4.13. Absorbed dose rates at different flight levels between Stockholm and Baltimore as a function of the ground-based neutron monitor count per minute in Oulu, Finland. The data has been normalised to the average for each flight-level. The lines serve only as eye-guides. Symbol key: ∆ FL330; ◊ FL340; ■ FL350; ♦ FL370; □ FL380; × FL390 ▲ FL400.


57

It is not a straightforward task to take these daily dose variations into account since the atmospheric dose rates are ruled by the complex dynamics of the earth magnetic field and it is obvious that the choice of monitor is crucial. The sensitivities and constructions of the neutron monitors vary, and not the same variation is seen in all monitors around the world. For example during the period shown in Figure 4.13, the Oulu monitor varied with ±10%, Climax with ±8% and two monitors on Hawaii with ±4%. However, the results suggest that there is a potential of improving the precision of cosmic radiation metrology and aircrew dose assessment.

4.7. Nanodosimetry in radiation therapy Track-structure and clustering of ionizations are considered to be of fundamental importance for describing radiation induced biological damage [Goodhead 1994, Brahme et al 1997]. In particular the ionizing ability of low-energy electrons seem to play a crucial role [Nikjoo and Goodhead 1991]. The range of a 500 eV energy electrons is only about 15 nm [Grosswendt 2002] and its radiobiological importance can not be reflected by the distribution of energy imparted to a micrometre sized object. In a nanometre volume this is obvious as seen in Figure 4.14 showing a single-event dose distributions in a cylindrical volume with 10 nm diameter and length, for a 5 MeV proton, a 500 eV electron and a 1MeV/u alpha-particle [Kyllönen et al 2003, Nikjoo et al 1994]. If RBE increases with lineal energy in a 10 nm volume, then clearly the RBE of the 500 eV electron is somewhere between the RBE of the proton and the alpha-particle. The variance method provides one experimental tool to obtain nanodosimetric data. The quantity Dy is a measure of the (dose) average energy imparted to the simulated sites and should somehow be related to the radiation quality if the biological effect is the result of damages on this level (section 2.3). In the nanometre region both measurements and simulations however face new difficulties and increasing uncertainties. Conversion from the measured ionizations to energy via the W/e-value becomes inappropriate [Kliauga 1990, Amols et al 1990, Bigildeev and Lappa 1994]. Variance measurements become more sensitive to noise and other variance sources as the detector pressure and signal level decreases with decreasing simulated object size.


58

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100 1000

Lineal energy [keV/µm]

yd(y

)

1H 5MeVyF=9 keV/µmyD=20 keV/µm

e- 500eV yF=24 keV/µmyD=39 keV/µm

4He 1MeV/uyF=34 keV/µmyD=87 keV/µm

Figure 4.14. Single-event dose distributions in a cylindrical volume with diameter and length 10 nm for 5 MeV protons (□), 500 eV electrons (×) and 1 MeV/u alpha particles (●). Data from Kyllönen et al [2003] and Nikjoo et al [1994].

In Paper IV the variance-covariance method and Monte Carlo simulations (section 3.4) were used to determine Dy in tissue-like media (A-150 plastic and tissue-equivalent gas) for object sizes between 3 nm and 15 µm in a p(65)+Be neutron therapy beam. The experimental Dy -values were 30% lower than the simulated at 100 nm (Figure 4.15) Using an experimentally determined absorbed dose fraction of 5% instead of the simulated 10% for ions (A>4) gave the same simulated and measured result within a few per cent. This is a reflection of the importance of these heavy recoils that give a relatively small contribution to absorbed dose but determine 50–70% of the total Dy . At smaller object sizes the difference between experimental and simulated data increases. The decreasing trend in the simulations is a reflection of that the secondaries heavier than protons generated in this neutron field are relatively slow with an amorphous track-structure [ICRU 1984, Leuthold and Burger 1988]. This is the part of the track defined by energy depositions close to the primary ion track, i.e. not energy depositions along single delta-electron tracks. The Dy -value for this component

decreases with decreasing object size, and so does the total Dy in the p(65)+Be beam since it is dominated by the 4He and ions (A>4) with an amorphous track-structures.


59

10

100

1000

1 10 100 1000

Simulated object diameter [nm]

Dos

e-m

ean

linea

l ene

rgy

[eV

/nm

]_

Figure 4.15. Measured (●) and calculated (–) Dy -value as a function of object diameter. The data is presented with two standard uncertainties (Type A and B). The values for the proton, helium and light ion (A>4) components are shown (---).

In section 2.3 it was argued that a biological effect generated by initial damages on the nanometre level can account for a part of the linear term in a linear-quadratic dose-effect relation (2.28). If the linear term was dominated by initial damages proportional to the square of the energy imparted, then a linear-quadratic model (2.31) gives for two different beams (n and γ)

γγαα

,

,

D

nDn

y

y= (4.4)

Figure 4.16 shows the measured and calculated Dy -ratios relative a 60Co beam, for the p(65)+Be neutron beam and for the spread-out Bragg-peak in a 175 MeV proton beam [Paper V]. The Dy -values at the smallest object sizes were determined from simulations using an experimentally determined absorbed dose fraction for ions (A>4). Equation (4.4) with ratios αn/αγ=3.8 and αp/αγ=1.1 derived from clinical RBE-values for early reacting tumours, is fulfilled with Dy determined in a region around 10 nm. The

calculations in the neutron beam were done using a dose per fraction of 2 Gy, an α/β-ratio of 10 Gy and an RBE of 3.2. These values can vary but the object size will remain in the nanometer region. For example varying the α/β-ratio between 5 and 15 Gy, the RBE between 1.5 and 5, gives object diameters between 3 and 30 nm.


60

0.1

1

10

100

1 10 100

Simulated object diameter [nm]

Rat

ios αn/αγ=3.8

yD,n/yD,γ

αn/αγ=1.1yD,p/yD,γ

Figure 4.16. Measured (■) and simulated (––) Dy -ratios for a p(65)+Be neutron

beam at Louvain-la-Nueve and a 60Co-γ beam. Also shown is simulated data for a spread-out Bragg-peak of a 175 MeV proton beam (– – –). The ratio of clinically determined α-values (---) equals the Dy -ratios in the region of 10 nm for both the neutron and proton beams.

The single-event spectrum and its dose-average value (Dy ) determined in the nanometre region seem to be correlated to the clinical RBE values, which opens for the possibility of comparing the radiation quality of different therapy beams using nanodosimetric methods. This is promising and further investigations of great importance. For future work it is proposed that comparison of experimental and Monte Carlo simulated results, as well as an evaluation of the radiobiological implications of the Dy -value in the nanometre region, should be done in monoenergetic neutron beams and ion beams of different RBE.


61

5. CONCLUSION AND OUTLOOK The variance-covariance method using one or two tissue-equivalent proportional counters (TEPC) was shown to be well-suited for radiation protection work. When known systematic differences were taken into account the measured dose-equivalent agreed within uncertainties (~10%) with other instruments, methods and calculations in high-energy neutron applications, such as aircrew exposure to cosmic radiation. The instrument response at intermediate neutron energies is poorer and the uncertainty in ambient dose-equivalent increases to about 25% in unkown radiation fields in the nuclear industry. The good agreement in high-energy neutron applications was obtained using a high-energy neutron calibration, or a new algorithm for the quality factor taking high-LET events into account. Experimental and Monte Carlo simulated response studies showed however that the uncertainties are large at neutron energies above 20 MeV and that further investigations are needed. Also the energy dependence of Dy is uncertain at high and intermediate neutron energies, and should be reduced by further investigations using Monte Carlo techniques. Methods of separating low- and high-LET components were developed for one detector and shown to work even better than if using a tissue-equivalent counter in combination with a graphite-walled low-LET monitor. The potential of using response differences between the tissue-equivalent and the graphite detector for energy spectrometry of neutron distributions should however be investigated further. A correction for beam intensity variations was derived for one detector and shown to work well in most applications, except in pulsed fields with pulses shorter than the charge integration time of the detector. The variance-covariance method was also shown to be a potential method for comparing radiation quality between different therapy beams. A Dy -value determined

in the nanometre region seems to correlate with α-coefficients of the linear-quadratic model used in fractionated therapy for early reacting tumours. The physical beam characteristics on the nanometre level are however difficult to determine and significant differences were observed between the measured and Monte Carlos simulated Dy -values due to uncertainties related to ions heavier than helium. The results reveal the need for improving both the particles transport and experimental techniques for nanodosimetric applications. The reported investigation was done in a high-energy neutron beam with a broad energy distribution, and further studies are suggested for monoenergetic neutron beams and ion beams of different relative biological effectiveness.


62

ACKNOWLEDGEMENTS To Lennart Lindborg for guiding and introducing me to the scientific world. To Jan-Erik Grindborg and Göran Samuelson for showing me your know-how. To Anders Brahme and colleagues at MSF for providing the necessary academic framework for this thesis. To my colleagues and friends at SSI for many stimulating discussions and for sharing your expertise in radiation protection. To Bo Nilsson at MSF for all valuable comments and support during these years. To my colleagues and friends in the field of dosimetry around the world for all scientific and non-scientific memories. Äitille ja isälle teidän loppumattomasta tuesta. Till min hustru Sofia, vår son Gösta och den lillae som vi väntar på. För att ni ställt upp, orkat med och för att ni finns. This work was partly funded by Swedish Radiation Protection Authority projects P1260 and P1395.02.


63

Related publications by the author Grindborg J E, Lillhök J E, Lindborg L, Gudowska I, Söderberg J, Alm Carlsson G, Nikjoo H 2006 Nanodosimetric measurements and calculations in beams for radiotherapy Submitted to Radiat. Prot. Dosim. (NEUDOS 10, Uppsala, June 2006) Lindborg L, Beck P, Bottolier-Depois J F, Latocha M, Lillhök J, Rollet S, Roos H, Roth J, Schraube H, Spurny F, Stehno G, Trompier F and Wissmann F 2006 Determination of H*(10) and its dose components onboard aircraft. Accepted in Radiat. Prot. Dosim. (NEUDOS 10, Uppsala, June 2006) Schuhmacher H, Bartlett D, Bolognese-Milsztajn T, Boschung M, Coeck M, Curzio G, d’Errico F, Fiechtner A, Kyllönen J-E, Lacoste V, Lindborg L, Luszik-Bhadra M, Reginatto M, Tanner R, Vanhavere F 2006 Evaluation of individual dosimetry in mixed neutron and photon radiation fields. PTB-N-49, (PTB Braunschweig) d’Errico F, Bartlett D, Bolognese-Milsztajn T, Boschung M, Coeck M, Curzio G, Fiechtner A, Kyllönen J-E, Lacoste V, Lindborg L, Luszik-Bhadra M, Reginatto M, Schuhmacher H, Tanner R, Vanhavere F 2005 Evaluation of individual dosimetry in mixed neutron and photon radiation fields (EVIDOS). Part I: Scope and mehtods of the project. Submitted to Radiat. Prot. Dosim. (IM2005, Wien, April 2005) Schuhmacher H, Bartlett D, Bolognese-Milsztajn T, Boschung M, Coeck M, Curzio G, d’Errico F, Fiechtner A, Kyllönen J-E, Lacoste V, Lindborg L, Luszik-Bhadra M, Reginatto M, Tanner R, Vanhavere 2005 Evaluation of individual dosimetry in mixed neutron and photon radiation fields (EVIDOS). Part II: Conclusions and recommendations Submitted to Radiat. Prot. Dosim. (IM2005, Wien, April 2005) Bolognese-Milsztajn T, Bartlett D, Boschung M, Coeck M, Curzio G, d'Errico D, Fiechtner A, Giusti V, Gressier V, Kyllönen J, Lacoste V, Lindborg L, Luszik-Bhadra M, Molinos C, Pelcot G, Reginatto M, Schuhmacher H, Tanner R, Vanhavere F and Derdau D 2004 Individual Monitoring in Workplaces with Mixed Neutron/Photon Radiation, Radiat. Prot. Dosim. 110 (1–4) 753–758 Mayer S, Golnik N, Kyllönen J E, Menzel H G and Otto Th 2004 Dose Equivalent Measurements in a Strongly Pulsed High-Energy Radiation Field Radiat. Prot. Dosim. 110 (1–4) 759–762 Kyllonen J-E, Girard P, Uehara S, Wilson W E, Lindborg L and Nikjoo H 2003 Energy Deposition by Monoenergetic Ions in Cylindrical Targets Monograph 2003 (MRC Radiation and Genome Stability Unit, Chilton, UK) Kyllönen J-E, Lindborg L and Grindborg J-E 2002 Response Investigations of a TEPC in High Energy Proton and Neutron Beams Using the Variance Method Radiat. Prot. Dosim 99 (1–4) 373–374 Kyllönen J E and Mayer S 2002 Response Investigations of the Sievert Instrument in Neutron Beams between 0.5 and 19 MeV at PTB CERN-TIS-2002-037-RP-IR (EDMS # 362983) Lindborg L, Kyllönen J-E, Beck P, Bottollier-Depois J F, Gerdung S, Grillmaier R E and Schrewe U 1999 The use of TEPC for reference dosimetry Radiat. Prot. Dosim. 61 (1–3) 119–124 Kyllönen J E, Lindborg L and Samuelson G 1997 Paired TEPCs for Variance Measurements In Microdosimetry: An Interdisciplinary Approach Eds Goodhead D, OŃeill P and Menzel H G, Special Publication No 204 (The Royal Society of Chemistry, Cambridge)


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APPENDIX

Simulated dose-mean lineal energy (Dy ) and frequency-mean lineal energy (Fy ) in unit density water vapor for ions up to oxygen of various energy. This is a selected data set for cylinders with equal diameter and length from Kyllonen J E, Girard P, Uehara S, Wilson, W E, Lindborg, L and Nikjoo, H, 2003. Energy Deposition by Monoenergetic Ions in Cylindrical Targets, Monograph 2003, MRC Radiation and Genome Stability Unit, Chilton, UK. The simulations were done using the Monte Carlo track-structure code PITS [Wilson and Nikjoo H 1999] coupled with the electron transport code KURBUC [Uehara et al 1993].

Table A1. Dose-mean lineal energy (Dy ) in ev/nm in cylindrical targets with equal diameter and length for 0.3–100 MeV 1H and 0.3–5 MeV/u 4He. E (MeV) d=3 nm d=10 nm d=30 nm d=100 nm 1H 0.3 52 69 76 77 0.5 42 49 54 57 1 33 34 34 35 2 28 26 23 22 5 26 20 16 12 10 24 18 13 8 30 22 17 12 7 100 21 18 12 6 4He 0.3 137 208 252 279 0.5 89 148 192 204 1 62 87 111 125 2 46 54 63 72 5 33 32 34 35


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Table A2. Frequency-mean lineal energy (Fy ) in ev/nm for 1H and 4He between 3 and 100 MeV in cylindrical targets with equal diameter and length. E (MeV) d=3 nm d=10 nm d=30 nm d=100 nm 1H 0.3 23 32 40 52 0.5 20 24 30 39 1 17 17 19 23 2 15 12 12 14 5 13 9 7 7 10 13 7 5 4 30 12 6 3 2 100 12 6 3 1 4He 0.3 31 39 53 74 0.5 29 41 59 71 1 25 34 48 62 2 22 23 30 40 5 16 15 17 18

Table A3. Dose-mean lineal energy (Dy ) in ev/nm for ions with A>4 between 1 and 5 MeV/u in cylindrical targets with equal diameter and length. E (MeV/u) d=3 nm d=10 nm d=30 nm d=100 nm Li 1 120 171 235 273 2 73 99 127 155 5 43 50 56 68 Be 2 108 162 221 270 5 55 79 99 118 B 2 158 248 333 408 5 83 118 151 183 C 2 220 351 490 548 5 100 158 200 250 N 5 128 200 272 337 O 5 166 245 344 419


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Table A4. Frequency-mean lineal energy (Fy ) in ev/nm for ions with A>4 between 1 and 5 MeV/u in cylindrical targets with equal diameter and length. E (MeV/u) d=3 nm d=10 nm d=30 nm d=100 nm Li 1 34 45 72 86 2 27 32 44 62 5 20 20 20 24 Be 2 30 39 56 86 5 22 23 26 31 B 2 34 45 66 100 5 26 28 32 37 C 2 37 54 73 101 5 27 28 30 38 N 5 28 31 35 43 O 5 30 32 36 44

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The microdosimetric variance-covariance method used for - DiVA