Kellerer, Albrecht M.

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ICRU NEWS December 1990 Article 3 Rigour Within Uncertainty The Need for a Strict Definition of the Quality Factor A.M. Kellerer Ludwig-Maximilians-Universität Institut für Strahlenbiologie 8000 München, Federal Republic of Germany Dual Purpose of Radiation Protection Quantities Quantities for radiation protection serve a double purpose. They are used as indicators o f the potential harm produced by a radiation exposure, and they are employed as reference parameters in rules and regulations for radiation protection. A few years ago H.H.Rossi distin-guished between two applications by speaking o f the assessment system and the l imitation system. The limitation system used to be the basis of radiation protection: dose l imits were introduced that appeared to be practicable and entirely safe. When i t was realized that stochastic radiation effects can be produced with small but non-zero probability even by low doses, the assessment system was introduced. Its primary principle is to reduce exposures to levels o f acceptable risk. To judge the acceptability o f risks, one needs to know their magnitude, but the risk estimates are subject to considerable uncertainty. Wi th in the assessment system there is, accordingly, no point i n asking for precision i n dose determinations. However, the assessment system cannot stand by itself. To keep exposures as low as reasonably achievable is the primary aim o f radiation protection. But to enforce rules and regulations one needs also formal principles that permit an objective and quantifiable distinction between the pennissible and the unacceptable. The limitation system must, therefore, complement the assessment system, and it requires accuracy and precision in dose determinations. The magnitude o f the l imits that are adopted in radiation protection is largely arbitrary, but once a value is adopted, i t needs to be compared to measured or computed doses and there is a need for precise instrument calibrations. In a formal system, precision is required, even in the face o f uncertainty. The work o f the two International Radiological Commissions reflects the two complementary aspects o f radiation protection. Where there is complementarity, there is always the appearance, and sometimes the actual danger, o f incongruity. The revision o f the quality factor in radiation protection exemplifies this dilemma. Revision of the Quality Factor New radiobiological findings suggest a higher relative efficiency o f densely ionizing radiations, and especially o f neutrons, in comparison to 7 rays or χ rays, than had previously been assumed. This indicates the need for a revised quality factor. These matters have been treated i n ICRU Report 40, The Quality Factor in Radiation Protection, and more recently they have also been considered in the preparation o f the new recommendations o f the ICRP. There is considerable latitude in the choice o f the numerical values o f the quality factor, and any new convention that is in reasonable agreement w i th radiobiological data is, therefore, acceptable. Wi th in the framework o f the assessment system and in view of the uncertain risk estimates there is, as ICRP notes, no need for detail and precision, and this suggests the simplest possible approach to the definition o f the quality factor. Within the limitation system, simplicity is equally desirable, but i t cannot be attained by a loss o f rigour. ICRU prefaces its most recent summary o f "Quantities and Units for Use in Radiation Protection** by the statement: Quantities relevant to radiation protection must ofien be used with a variety of approximations. Although a comparatively wide margin for numerical uncertainties may be admissible in radiation protection, it is essential that the quantities employed be clearly defined, and the approximations clearly identified. The definition o f the quality factor and possible ramifications o f the concept need to be examined under this premise. Considerations on the Definition of the Quality Factor The Conventional Approach The current convention is based on the familiar concept o f the quality factor as a function o f the linear energy transfer (L), and a revision may merely replace the current convention Q(L) by a changed numerical relation. This is a matter o f taking into account new radiobiological information, i t does not change the concept. The approach remains consistent. 4 Article ICRU NEWS December 1990 The quality factor, β, and the dose equivalent, H, at a point: ß - / ß ( L ) d ( L > // - β * D are utilized to compute the dose equivalent, HT, i n an organ,T, or w the (mean) quality factor", β τ , for the organ: # T = £ Q ' D dm (mT : mass o f the organ) Qj = j Q' Dam IJ Dd/w ~ I Df The derivation o f Ηγ or β χ involves a double integration over the distribution, d(£), o f dose (at the point) in LET and over the tissue o f interest. This can be complex, but it is not, in principle, much more diff icult than the computation o f the organ absorbed dose, D T . I n most instances, i t is, o f course, unnecessary to perform the exact computations. Instead one can use approximations, such as the conventional values 10 and 20 for neutrons and α particles. The wide applicability o f approximations can, however, not remove the need for precise definitions, as they are required in standardization and calibration procedures. The actual dependence for the organ dose equivalent or for the "effective dose": Hc = £ β χ w T D x τ can, o f course, be replaced by an approximation. For example one can write: Τ where β is not obtained by the actual integration over the organs, but is an approximation for the mean quality factor of the radiation. In principle, however, Qj depends on the organ and, apart from the energy distribution o f the radiation, also on its directional distribution. In summary: one can use the familiar system o f the quality factor, Q(L), defined in terms o f the parameter L. This does not exclude the recommendation of approximations that disregard the dependence o f the quality factor on organs and on the directional distribution of the radiation (or position o f the body). The combination o f an exact definition w i th the use of acceptable approximations for typical radiations has been proposed in ICRU Report 40, The Quality Factor in Radia­tion Protection by a liaison committee o f ICRU and ICRP. Reasons for Seeking a Simpler System While the conventional system is, in itself, coherent and while i t has worked sufficiently well in the past, a simplified approach is now considered. I t aims at the introduction o f a "receptor free" quality factor, i.e., it postulates that the quality factor depends only on the characteristics o f a radiation field, without the need to consider the modified field that occurs when the human body is actually present. The simplification appears attractive, but whenever one computes effective doses, i t leads to a certain incongruity: the simplified quality factor that disregards the specific characteristics o f the exposed body is combined wi th the complexity o f computing actual absorbed doses within the different organs. There are, o f course, good reasons for seeking the simpler system. Computations o f absorbed dose can be complex, but they pose no problems in principle. For a specified radiation field and a specific orientation o f the body (or phantom) one obtains results that w i l l remain valid. Computations o f dose equivalents, on the other hand, are less permanent. New epidemiological findings or radiobiological results may, in the future, lead to changed conventions on the quality factors. This lack o f permanence suggests: • That there is l i tt le justification for detailed or accurate conventions on the quality factor. • That it is desirable to "uncouple" the computation of the organ (absorbed) doses, Dj, and their weighted sum, WjDj, from the further step that accounts for ; radiation quality. The uncoupling would obviate the need to perform the full computations de novo for any assumed or newly introduced set o f quality factors. These two aspects are, in fact, strong support for the : 1 idea to utilize "receptor free" quality factors that depend >j only on the type and energy o f the ionizing radiation. The'| approach appears, therefore, attractive. Unfortunately, it j leads to inconsistencies that make it usable only as aav| approximation. / ; | The Simpli f ied Approach ; | ν - If In the subsequent consideration of the simplified-! approach, we w i l l use the term "radiation Weighting|j factor" rather than the familiar term "quality factor". T h i r t ICRU NEWS December 1990 Article 5 reflects merely the terminology chosen in preliminary discussions by ICRP. The notation is irrelevant to the essence o f the discussion, it is adopted for the present considerations, and i t should not be seen as support for a changed terminology. I t has been recommended that the radiation weighting factors be defined i n a receptor free way, so that they w i l l depend only on the type and energy o f the radiation but not on the organ and the orientation o f the body or the directional distribution o f the field. I n a receptor free definition, i t is natural to abandon the L E T as the reference parameter and to use instead o f Q(L) a convention that links the weight, vvR(£), to the energy, £, o f a radiation (R) o f specified type (e.g., neutrons). Instead o f a continuous dependence, νν^(£)> a simple step function, i .e. , only a few discrete values for certain energy bands, have been considered. This is analogous to the initial convention on Q(L) which had also been formulated in terms o f discrete values for a few bands of LET-values. To choose between a continuous or discontinuous function w R ( £ ) is a secondary matter. We w i l l , in the fol lowing, consider the simplified approach in terms of discrete values, H ^ , for a number o f energy bins of a specified radiation, e.g., neutrons, i t would be straightforward to translate the formulae to the continuous ; case. Assume that one deals w i t h one "type o f radiation" (monoenergetic neutrons or neutrons i n the same energy ^bin), the dose equivalent i n an organ Τ is then: Hy ^ >VR ' Z?i» and the effective dose is; Τ where D e may be termed the "effective absorbed dose". Clearly the "organ radiation weighting factor", * % ^ R > a»d the "effective radiation weighting factor", , HJ®t> are equal to the value w R , and this is in line w i t h ^e^mipl i f i ed procedure. But the seeming simplicity disappears for an actual radiation field, e.g., a neutron field that consists o f several energy bins. The simplified approach would suggest that ; the overall radiation weighting factor, vvr, o f the field, i .e., the ratio o f the organ dose equivalent, // T , and the organ (mean) absorbed dose, Dr> be organ independent. But the formulae do not confirm this expectation. From: H<r * Σ W * D T , R R R one obtains: Σ WR D T , R ' DT R and this is, by no means, organ independent. Numerical examples show that the differences between the values w r for different organs can be large. For a frontal exposure to fission neutrons with accompanying γ rays, a large value >vr w i l l result for the breast, but a considerably smaller value for the bone marrow where the y rays may predominate. The appealing simplicity o f the approach is thus lost whenever one deals w i t h mixed radiations. There is no radiation weighting factor for a mixed field, and there is, accordingly, no direct way from the organ absorbed dose to the dose equivalent. M i x e d radiations are, however, the usual condition in radiation protection. One may seek a way out o f the dilemma. An earlier discussion o f the problem led to the recommendation of a "receptor free" radiation factor for a mixed radiation: >vr « £ >vR D R * / Z>* R where D R * the contribution o f the different radiation types to the ambient absorbed dose, D . Alternatively, one could, of course, sum over some other receptor free quantity, such as kerma. The added convention would reestablish the desired simplicity, and as an approximation it would certainly be adequate. As part o f a rigorous definition it introduces, however, a deeper inconsistency. The definition Fly — wt ' Dj provides a value o f // T that differs from the sum o f the organ dose equivalents due to the component radiations ("radiation types"), Ητ = ] T w R · / / T $ R R The same problem would, of course, arise for the effective dose. There is an unwelcome conclusion from these considerations. Either there is organ dependence o f the radiation weighting factors of a real field, or the added convention causes the effective dose to be different from the sum o f the effective doses due to the component radiations. Either conclusion is sufficiently unpalatable to make the simplified radiation weighting factors an unattractive tool for basic definitions. 6 Article ICRU NEWS December 1990 ICRU is, o f course, not merely concerned with rigour in the definition o f quantities. An equal concern is practicability, and this, too, may argue against the "s impl i f ied" definition o f the quality factor. To use energy of the ionizing radiation as the reference parameter would tend to replace the comparatively straightforward measurements o f L E T distributions - or rather o f y distributions - by more diff icult determinations o f the fluence spectra in energy. This would turn the intended simplicity into its opposite and produce needless complications. Conclusion The practice o f radiation protection can usually be based on simplifications and approximations. The present discussion may, therefore, appear as a fancy way to make plain things complicated. Conceptual clarity is, on the other hand, an essential ingredient o f simplicity, and simplicity must not be confused wi th looseness or w i th the approximations that are admissible under many circumstances. The rigour o f the underlying definitions may not become apparent in many applications o f radiation protection quantities, but i t is the necessary skeleton that supports the system o f radiation-protection measurements, computations and calibrations and that avoids conflicts of interpretation and needless discussions. Confusion in the basic definitions can never be a fair price for simplicity. But rigorous definitions do not exclude the use o f approximations, i f they are recognized as such. 

Rigour within uncertainty. The Need for a Strict Definition of the Quality Factor.

Universität München: Elektronischen Publikationen

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Rigour within uncertainty. The Need for a Strict Definition of the Quality Factor.

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