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Submitted by Dietrich Harder, Medical Physics and Biophysics, University of Göttingen
   Commenting as an individual
Document Assessment of Radiation Exposure of Astronauts in Space

Comments concerning the draft ICRP Report on "Assessment of Radiation Exposure of Astronauts in Space" , ICRP ref 4819-7515-1888, 2012 July 03


Dear ICRP Secretary, dear Günther Dietze, dear collegues,


this draft report contains a treasure of valuable information, collected in a very commendable effort of your working group. However, there is a problem with quantities and units, which I will point out and for which I will propose a solution. This will perhaps lead to some further committee work towards an updated version of the report.


1) Concerns about the stability of the ICRP terminology on quantities and units

In the present, worldwide used ICRP terminology (ICRP 103) the equivalent dose in an organ or tissue due to radiation type R is defined as

HT = SR wR DT,R                                                                   (1)

where wR is the "radiation weighting factor". In accordance with this basic concept, the well-known values of wR for photons and other radiations including neutrons are cited in section 3.2.2 of the draft report. (In a correspondence with Günther Dietze, I have earlier taken part in establishing the three equations holding for the wR of neutrons.) The effective dose is then calculated from these HT values as the wT weighted sum.

However, in the corresponding definition of HT for high-energy ions such as protons or heavier nuclei in eq. 3.16, the report is switching to a different terminology by defining the dose equivalent in an organ or tissue by

HT, Q = QT DT                                                                                        (2)

where QT is the "quality factor" according to eq. (3.9) or (3.18). The effective dose is then calculated from the HT, Q values as the wT-weighted sum (eq. 3.20).

Sorry to say, but this means no less than a violation of the principle that the ICRP terminology should be stable over the years as far as possible. Firstly, since HT is a "protection quantity" defined by the ICRP, the correct term for it would be "equivalent dose", whereas "dose equivalent" is the term for an "operational quantity" defined by the ICRU. Of course it would be beneficial if ICRP and ICRU would succeed to make the duality of these terms disappear in the near future, but in an up-to-date special report on the radiation exposure of astronauts the present distinction between "dose equivalent" (ICRU) and "equivalent dose" (ICRP) should not be disregarded.

Secondly, the principle that the ICRP terminology should be stable over the years is also violated insofar as in eq. (2) ICRP's "radiation weighting factor" wR is abandoned and replaced by the "quality factor" which is normally restricted to ICRU's "operational quantities". In addition, the report is also somewhat ambiguous as it leaves it to the user whether the averaging process leading to QT (eqs. 3.17, 3.18a and 3.18b) shall be based upon function Q(L) from eq. (9) or on function Q(Z,E) from eq. (3.15).

To sum up, it must be criticised that this report, otherwise treating successfully a demanding subject, presents a confusing terminology and deviates from the worldwide accepted eq. (1).

2) A proposal for improvement

According to present knowledge, it should be possible to maintain the basic equation eq. (1) and to introduce wR values also for use in the case of high-energy ions. As in the case of neutrons, RBE data on radiation-induced carcinogenesis should be incorporated in the establishment of the wR values as far as possible, and - in analogy to the approach successfuly applied in the case of neutrons - the attempt should be made to describe wR(L) by a formula.

As shown in Fig. 3.14, NASA (Cuccinotta, 2011) have proposed continuous functions QS(L) and QL(L) which quantify the relative risks of getting solid tumors (S) respectively leukemia (L) from exposure to protons or carbon, silicon and iron nuclei in dependence of LET. (In order not to be misunderstood, I am using here Cuccinotta's symbol Q(L) notwithstanding my criticism of the terminology described in the previous section of my letter.) It would be a feasible task a) to combine the solid tumor and leukemia data, thereby constructing curves Q(L) for the overall risk of carcinogenesis and b) to adjust these values not as multiples of the Q(L) data asymptotically reached at low LET of these high-energy ions, but as wR values under consideration of the well established value wR = 1 for X- and gamma rays, c) to describe the resulting function wR(L) by a formula.

Steps a) and b) require the full knowledge of the data basis of Fig. 3.14. However I can supply a little contribution to step c). Based on well-known particle track structure and target conformation models let me suggest a formula whose core is the probability 1-e-m (1+m) for at least two hits in a target crossed by a particle producing, on the average , m hits per passage. The yield of two- or more hit events per unit dose is then proportional to [1-e-m (1+m)]/m, and the behavior of this formula for small, medium and large m is a linear increase with m, maximum at m = 1.75 and decay with 1/m.

I have tested the applicability of a variant of this formula to describe function Q(L) which I have simply obtained by adding the QS(L) and QL(L) functions in Figure 3.14 for each of the four types of ions dealt with in this figure. The formula which works almost perfectly is

Q(L) = 2 + a [1 - e-bL(1+bL)]c / bL                                                                 (3)

Here 2 is the asymptotic Q(L) value for L→0, factor a determines the amplitude of the variable term, factor b performs a shift along the L scale so that the maximum of the formula can be made to coincide with the maximum of the biological Q(L) data, exponent c serves to fit the steepness of the initial curve wing, which is (bL)2c-1, and the division by bL provides the decay at large values of L.

[The attached hand-drawn plots show that this simple formula is well suited to reproduce the Q(L) = QS(L) + QL(L) data (dark dots) from Fig. 3.14. The small open circle symbols have been calculated from the formula, and the lines are interpolated by hand.] The coefficients which I have found are shown in Tab. 1:

Tab.1. Coefficients for use with eq. (3)

High-energy ions

Coefficient   a

Coefficient   b [mm/keV]

Exponent   c





Carbon nuclei




Silicon nuclei




Iron nuclei




As said before in remarks a) and b), these Q(L) = QS(L) + QL(L) data are not the desired wR data, but the little study shows that the structure of eq. (3) is well suited to fit wR(L) data of a similar type.

Hoping that this letter may contribute to a turnover in this report of the Q(L) terminology to the wR(L) terminology of the ICRP, and that the steps a) to c) proposed above, including formula (3), may lead to a new, stringent formulation of the wR(L) values for high-energy ions,

I remain with kindest regards, Dietrich Harder.