Register for Updates | Search | Contacts | Site Map | Member Login

news

View Comment

Submitted by Harry Slaper, The National Institute for Public Health and the Environment (RIVM)
   Commenting on behalf of the organisation
Document Operational Quantities for External Radiation Exposure
 

The following commnets with full equations are availalbe from 
https://goo.gl/jqYvpB

RIVM’s comments on the joint ICRU/ICRP Report on


“Operational Quantities for External Radiation Exposure” 


Authors: Teun van Dillen*, Arjan van Dijk*, and Puck Brandhoff*


With input and coordination by Harry Slaper*


The National Institute for Public Health and the Environment (RIVM), Bilthoven, The Netherlands.


With input and support from: Majid Farahmand** and Frans van de Put** on behalf of the


**The Authority for Nuclear Safety and Radiation Protection (ANVS) in the Netherlands


Introduction


In the joint ICRP/ICRU report, new operational quantities are defined, which – by construction – provide a more direct and thus better estimate of the protection quantities (like effective dose), and cover a larger range of particle energies and more particle types, than the current set of operational quantities. In this way, the new operational protection quantities also cover a larger field of applications. Thus, the report provides scientific improvements. However, the new proposed approach has potentially also large implications in everyday operational dosimetry for external exposures (environmental monitoring). Many of these situations don’t require an extension of the energy range. Thus, we have some questions on the reasonability and justification of the investments that might be necessary in instrumentation, calibration, new normalization documents, legislation, regulation, training, etc. to replace the presently used concepts. Also, the new concept H* could be over-conservative for situations with specifically known exposure geometries. The report lacks information on correction factors for other irradiation geometries than the geometry with maximum effective doses. A further report on the implications of the conversion from present operational quantities to the new set of quantities is highly recommended.


We acknowledge that the current set of operational quantities suffers from several limitations and therefore we appreciate a new set of operational values with an extended scope. The proposed discontinuation of the use of operational quantities based on the ‘(directional) dose equivalent’ at a certain point in a well-defined phantom (ICRU sphere or slab) and its replacement by new operational quantities that are directly related to the protection quantities, effective dose or (directional) absorbed dose (lens of the eye, local skin), clearly has several advantages. One of them is that the unit sievert (Sv) will then only be used for the effective dose.


However, we also have several concerns related to the proposed quantities and to the equations and parameter descriptions. In this communication, we give our suggestions for improvement of the report. We start with our general remarks on the proposed quantities, followed by more detailed comments.


Major remark


This report presents a major change in the operational quantities that are used for estimating the Effective and tissue doses following external radiation exposure. A major question that arises from a regulatory and policy perspective, is why ICRU / ICRP proposes to replace the old operation radiation protection quantities? (See also general remarks point 2 and 3). This proposal will have a major impact on many levels of the radiation protection system, also including the dose limits for tissue effects (as mentioned in the general remarks). The consequences of these changes are, however, difficult to oversee, and deserve to be addressed further in the report. Do the advances of the new approach outweigh the costs for all applications?


General remarks:


1.


The report is a rather technical and mathematical description of the proposed operational quantities without elaborating on (1) the underlying choices and assumptions, (2) uncertainties (with exception of the uncertainties of the Monte-Carlo calculations), and (3) the impact on radiation protection in practice. As it stands, it is probably not suited to broad readership, which is unfortunate since the scope of this report in principle affects the entire radiation-protection community. As becomes clear from the following points, practical guidance, examples and context are missing throughout the report.


2.


The report lacks a clear explanation and argumentation for the replacement of the old operational quantities by the new operational quantities (from H*(10) to H* etc.). ICRP’s choice to discontinue the use of equivalent tissue or organ dose (using the radiation weighting factors ) as a separate protection quantity, in order to avoid confusion with the effective dose has important implications, also for the protection against tissue-reaction effects. The document lacks a thorough discussion on this issue (see also next point).


3.


Protection of the lens and skin against tissue reactions require, in addition to the calculation of absorbed doses, a weighting with the relative biological effectiveness for these deterministic effects. One of the reasons leading to the proposal of the new operational quantities is the abandonment of the use of the equivalent dose in a tissue or organ ( in Sv) to protect against deterministic effects (tissue reactions), as mentioned in the above point. Instead, the absorbed dose is now used as the underlying protection quantity. As a consequence, should these operational quantities be implemented in future practice, the relevant deterministic limits (lens of the eye, local skin, extremities) are then to be expressed in units of absorbed dose, i.e., in Gy (Harrison et al, 2016). Obviously, the absorbed dose limits should then take into account the relative biological effectiveness (RBE) related to the deterministic effects in order to guarantee a sufficient level of protection for all particle types and energies against these tissue reactions. These issues need to be addressed as well, inasmuch as they require significant changes in standards, regulations and legislation.


4.


For area monitoring, the new operational quantity replacing the ambient dose equivalent is the ambient dose . Values of are now often used as an estimate of the effective dose . When additional information is known on the irradiation geometry, conversion constants can be used to arrive at a more accurate estimate of the effective dose.


As presented in the report, the ambient dose provides a better and more direct estimate of the effective dose for protection purposes. Even though this is in principle correct, it should be stated that is an estimate of the maximum possible value of the effective dose, over all possible irradiation geometries. However, if more information is known on the actual irradiation geometry, the value of may in certain cases considerably overestimate the effective dose. For instance, for photons the largest overestimation could occur in the low- or high-energy spectral range, say < 0.1 MeV and > 100 MeV as seen from Fig. 2 in Ref. Endo, 2016a.


The use of as an operational quantity for radiation-protection purposes may therefore certainly be appropriate, but for more precise dose calculations ( e.g. after exposure during an incident), correction factors should be provided to convert (or better, ) to the effective dose in the actual irradiation geometry.


5.


For personal monitoring, the personal dose – defined by Eq. (3.25) – now includes incident radiation from all angles, as seen from the integration over the solid angle . Theoretically, this can of course be defined as such, implying or suggesting that the effective dose in complicated radiation fields with different irradiation angles can be determined accurately. However, from a practical point of view this is virtually impossible, since the direction (or the angular distribution) of the radiation with respect to the dosimeter’s position on the body is unknown. In fact, at certain angles (part of) the radiation might not even reach the detector as it is shielded by the body, thus not registering any dose at all, whereas at the same time this person does receive a dose. The theoretical construction of thus suggests an accuracy that will in practice never be obtained due to the abovementioned uncertainties, which should be discussed in the document. In this respect, guidance should be given on how to deal with these uncertainties and their impact on calibration procedures.


6.


Currently, the protection quantities ambient dose equivalent and personal dose equivalent are related to a physical point quantity, i.e. the dose equivalent at a depth of 10 mm in a tissue-substitute phantom (ICRU tissue-equivalent sphere or slab, respectively). However, these quantities would be replaced by the operational quantities (ambient dose) and (personal dose), which are - by definition - directly related to (maximum) effective dose, which is a non-physical and non-measurable protection quantity. Since these operational quantities lose their direct physical meaning, this should be carefully explained in the report.


7.


With new operational quantities based on the effective dose (see point 6 above), the values of the new conversion coefficients may change if the tissue weighting factors change in value. This implies that measuring equipment and dosimeters may require recalibration every time the ICRP updates the tissue weighting factors in the future. This is an undesired side effect associated with the use of the new operational quantities which raises great concerns. This report should highlight and elaborate on these issues and concerns.


8.


RIVM is greatly concerned with the costs associated with the switch to proposed operational quantities, as well as the efforts to practically implement them, both issues not addressed in this report. This is why the report should also emphasize the benefits of the proposed operational quantities over the current ones, in order to assess whether such a switch can actually be justified, and if so, whether it would indeed lead to an optimized level of radiation protection.


9.


The preface, abstract, executive summary and introduction are not easy to read and should better summarize the main conclusions of this report. The report would benefit from several schematic illustrations in Section 3, indicating the reference phantom in the coordinate system together with the incident radiation. The results presented in Section 4 are merely presented as such without a description or explanation of the observed features and trends (example: what happens around 2 MeV in Fig. 4.6 for electrons?). Sections 5 and 6 are of great importance when it comes to radiation protection in practice. However, these sections are surprisingly short. Finally, the report consists of many long sentences, some of them rather cryptic and thereby ambiguous. We suggest a serious further editing of the concept-report.


Specific and detailed remarks:


Below we present a list of specific remarks and findings, some of which are rather technical, but, to our opinion, necessary for a better understanding of the introduced quantities.


The detailed comments and remarks are found below, and in addition the full detailed comments with an improved layout can be found as pdf-document on the RIVM-website (copy paste link to browser):
http://www.rivm.nl/en/Documents_and_publications/Scientific/Scientific_Articles/2017/November/
RIVM_s_comments_on_the_joint_ICRU_ICRP_Report_on_Operational_Quantities_for_External_Radiation_Exposure


1. Lines 333 335 ( Section 1, Introduction):


“ Although the conversion coefficients from fluence or air kerma are to values of protection quantities that are not point quantities but are averaged over an organ or tissue, or the sum of these averages, the operational quantities that are recommended are point quantities ”


We do agree with this statement, although it should be explained in more detail. To our understanding the following would explain it:


The radiation field at a specific point in space is characterized by the type (or distribution) of particles, their energies (in MeV), directions and fluences (in m-2) or fluence-rates (in m-2 s-1). The operational quantity that is associated with (or assigned to) that specific radiation field at that point in space is found by imagining a phantom externally irradiated by an extended, broad-beam radiation field characterized by the same properties (particles, energies, directions, fluences or fluence-rates). The dose-related operational quantity calculated for the phantom may indeed be an average (and sum) over tissues and organs, but its value is dependent on the governing external-radiation field at that point in space, which served as input for the phantom-related dose calculation. A change in radiation field at that point thus leads to a change in the associated operational quantities, from which we conclude that the operational quantities themselves are a point quantities as well.


2. Line 373 (Sect. 2.6):


The irradiation geometries SS-ISO and IS-ISO are not explicitly explained in the main text (i.e., Sect. 3.2 concerning the irradiation geometries) of ICRP-116 (2010). They are only mentioned in Annex H of that publication regarding aircraft-crew dosimetry. This should be mentioned more explicitly in the current report, or even better, these radiation geometries should be explained in a footnote.


3. Lines 385 403 (Section 3.1.1):


In line 393 we read “in the volume ”, whereas the volume has not yet been defined explicitly. This leads us to believe that this refers to the volume of the sphere of cross-sectional area .


Actually, if we define the small sphere of radius and volume , we have: as the volume, as its cross-sectional area. Furthermore, for the sphere we have as its surface area. If we look at Eq. (3.2), , we can now arrive to Eq. (3.1) in the following way: = sum of lengths of particle trajectories in = average chord length * number of particles incident on the sphere: . With (Kruijf and Kloosterman, 2003), we have: . Since for the sphere we have , we can write , and thus Eq. (3.2) is in agreement with Eq. (3.1). Hence, with being the volume of the sphere, Eq. (3.2) and Eq. (3.1) are identical, but this does not mean that should always be the volume of the sphere. Eq. (3.2) is valid for any small volume element and not just the small sampling sphere on which Eq. (3.1) is based. Said differently, the track length-definition Eq. (3.2) of fluence in any small volume is a generalization of the small sampling-sphere definition Eq. (3.1) introduced by the ICRU. This is shown and explained in Ref. Papiez and Battista, Phys. Med. Biol. 39, p. 1053-1064 (1994) and should be clarified in this report to avoid any confusion.


In addition, the symbol in the ‘particle number density’, , used in Eq. (3.3) for fluence, is different from the used in Eq. (3.1). The definition of has changed, which is not clear from the brief description. We suggest to either explicitly mention this in the report, or to use different symbols to avoid confusion.


4. Lines 385 403 and 409 422 (Section 3.1.1 and 3.1.3):




  • Lines 399-400: the unit of is missing. It should be m-2 MeV-1 or m-2 J-1;




  • Line 403: the unit of is missing. It should be m-2 MeV-1 sr-1or m-2 J-1 sr -1;


    We also recommend to write down the double differential explicitly: ;




  • Line 415: in Sect. 3.1.3 the quantity is defined in formula 3.7, but it should read ;




  • If we understand correctly, from line 415 (see previous bullet) is the time-derivative of from line 403, but this is not explicitly mentioned. We recommend to mention this and to use the same order of the two indices/subscripts.




5. Lines 424 452 (Section 3.2.1 on Kerma):


Eq. (3.10) is not completely clear from Eq. (3.8) and Eq. (3.9). To our opinion, an extra quantity, the distribution of Kerma , should be defined first as:


 


Here the distribution of kerma is defined such that is the kerma contribution (in Gy) of particles with energies between and and whose total fluence contribution equals . In that case, we can write:


 


Comparing this result with Eq. (3.10) gives us:


 


We then indeed see that is the mean value of averaged over the distribution of kerma. Without the above additions, this remains unclear.


6. Lines 470 – 478 (Section 3.3.1 on the mean absorbed dose in an organ or tissue):
Line 471: There is no Section 3.3.3.


In Section 3.3.1 on the mean absorbed dose in an organ or tissue, the local skin is defined as well. However, since this is not defined as the mean absorbed dose in the entire skin tissue, we suggest treating it in a separate section.


7. Lines 490 – 505 (Sections 3.4.1 on ambient dose):


From the definition of in lines 491-493 it is not clear that is actually a maximum of the effective dose over the set of selected irradiation geometries at a fixed energy Ep . In the next sentence (lines 494 – 499) it is said that and thus is calculated for whole-body, broad-beam irradiation of the phantoms in various irradiation geometries, but this could in principle mean that is calculated for each irradiation geometry separately. However, what is of course meant here, is that it is the maximum value of the effective dose among the selected irradiation geometries (AP, PA, etc…), i.e.,


 


where is the effective dose related to irradiation with particles of energy under a specific irradiation geometry. Said differently, as a function of , one regards the enveloping curve of the separate curves of for all irradiation geometries.


In addition, it would be helpful to explicitly write the following equation defining the operational dose quantity :


 


with . We emphasize that is not necessarily the same as :


is the fluence of the radiation field at a specific point in space, whereas


is the fluence used for the Monte-Carlo calculation of phantom-related value of .


To our opinion, this distinction should be made clear to avoid confusion. The same then holds for Eq. (3.16).


Below Eq. (3.16), it is stated that is the fluence of particles with kinetic energies in the interval around (line 502). This is incorrect and should be: is the fluence of particles with kinetic energies in the interval around . The distribution is the fluence of particles per unit (kinetic) energy of those particles with (kinetic) energies in the interval around . Note that similar arguments hold for the sentence under Eq. (3.19), line 523, under Eq. (3.22), line 557, under Eq. (3.25), line 586, under Eq. (3.27), line 601 and under Eq. (3.29), line 630.


Another suggestion would be to write as based on Eq. 3.4. In that way, one makes efficient use of the radiometric quantities defined earlier in Section 3.1. Based on the remark above, we also recommend to add the subscript “field”. Altogether, Eq. (3.16) then reads:


 


with the fluence of particles with kinetic energies in the interval around .


Finally, the summation in Eq. (3.17) is over all contributing particles, so we would prefer . The same argument holds for Eq. (3.20) on line 526, Eq. (3.23) on line 560, Eq. (3.26) on line 589, Eq. (3.28) on line 604, and Eq. (3.30) on line 632.


8. Lines 512 – 534 (Sections 3.4.3 on directional absorbed dose in the lens of the eye):


Similar findings as previous point, briefly summarized below.


We recommend adding the following equation partly replacing lines 517 – 519:


 


with . Here is the calculated directional absorbed dose in the phantom-related stylized eye model at a fluence for irradiation with broad parallel beams. Then, is the operational quantity (directional absorbed dose in the lens of the eye) associated with the radiation field defined/characterized by fluence .


Equation (3.19) can be written as (“field” added in the subscript):


 


Or alternatively as:


 


in which we make use of Eq. (3.4), but with an extra angular dependence. Here is the field’s fluence of particles (at that point) with direction of incidence and with kinetic energies in the interval around . lines 523 –524.


Line 526, Eq. (3.20): summation over particles i.


Lines 529 – 534: a schematic illustration indicating the directions , and would be helpful.


9. Lines 542 – 569 (Sections 3.4.5 on directional absorbed dose in local skin):


Findings similar to those discussed in the previous point, so here this would become as follows:


We recommend adding the following equation partly replacing lines 547 – 549:


 


with . Here is the calculated directional absorbed dose in the specified, skin-related phantom (ICRU 4-element tissue slab of dimensions 300x300x150 mm3) at a fluence . Then, is the operational quantity (directional absorbed dose in local skin) associated with the radiation field defined/characterized by fluence .


Equation (3.22) on line 556 can be written as (“field” added in the subscript):


 


Or alternatively as:


 


in which we make use of Eq. (3.4), but with an extra angular dependence. Here is the field’s fluence (at that point) of particles with direction of incidence and with kinetic energies in the interval around . lines 557 – 558.


Line 560, Eq. (3.23): summation over particles i.


10. Lines 577 – 590 (Sections 3.4.7 on the personal dose):


Findings similar to those discussed in the previous points, so here this would become as follows:


We recommend adding the following equation partly replacing lines 580 – 582:


 


with . Here, is the calculated effective dose in the ICRP/ICRU reference phantoms at a fluence . Then, is the personal directional dose associated with the radiation field defined/characterized by fluence .


Note: to obtain the (full) operational quantity “personal dose”, an integration is required over all angles (and particle energies), as shown below.


Equation (3.25) on line 585 can be written as (“field” added in the subscript and differential d changed to d2):


 


Or alternatively as:


 


in which we make use of the quantity defined in Sect. 3.1.1 in line 403.


Here, is the field’s fluence of particles at that point, with kinetic energies in the interval around and directions of incidence in the interval around . lines 586 – 588.


Line 589, Eq. (3.26): summation over particles i.


11. Lines 591 – 606 (Sections 3.4.8 on the personal absorbed dose in the lens of the eye):


Findings similar to those discussed in the previous points, so here this would become as follows:


We recommend adding the following equation partly replacing lines 595 – 597:


 


with . Here is the calculated absorbed directional dose in the phantom-related stylized eye model at a fluence for broad, parallel-beam irradiation. Then, is the personal, directional absorbed dose in the lens of the eye associated with the radiation field defined/characterized by fluence .


A few extra notes here:



  • is not yet the full operational quantity. Integration over all directions (and energies) is required before arriving at the actual operational quantity (personal absorbed dose in the lens of the eye), in contrast to the “directional absorbed dose in the lens of the eye”, which does not require integration over all directions. Similar to remark for personal dose .




  • To our understanding: in both conversion coefficients (see above, point 8). Therefore, we see that both conversion coefficients must be equal: . This is mentioned in Appendix A.3 of the report, but we recommend mentioning this in Section 3.4.8 as well.



  • Equation (3.27) on line 600 can be written as (“field” added in the subscript and differential d changed to d2):


     


    Or alternatively as:


     


    in which we make use of the quantity defined in Sect. 3.1.1 in line 403.


    Here is the field’s fluence of particles at that point, with kinetic energies in the interval around and directions of incidence in the interval around . lines 601 – 603.


    Line 604, Eq. (3.28): summation over particles i.


    Furthermore, it is worth mentioning the differences between the operational quantities and .


    12. Lines 607 – 635 (Sections 3.4.9 on the personal absorbed dose in local skin):


    Findings similar to those discussed in the previous points, so here this would become as follows:


    We recommend adding the following equation partly replacing lines 611 – 613:


     


    with . Here is the calculated directional absorbed dose in the various specified skin-related phantoms at a fluence for broad, parallel-beam irradiation. Then, is the personal, directional absorbed dose in local skin associated with the radiation field defined/characterized by fluence .


    A few extra notes here:



  • is not yet the full operational quantity. Integration over all directions (and energies) is required before arriving at the operational quantity (personal absorbed dose in local skin), in contrast to the “directional absorbed dose in local skin”, which does not require integration over all directions. Similar to remark for personal dose .




  • To our understanding: in both skin-related conversion coefficients. Therefore, we see that both conversion coefficients must be equal: . This is mentioned in Appendix A.4, but we recommend mentioning this in Section 3.4.9 as well.



  • Equation (3.29) on line 629 can be written as (“field” added in the subscript and differential d changed to d2):


     


    Or alternatively as:


     


    in which we make use of the quantity defined in Sect. 3.1.1 in line 403.


    Here is the field’s fluence of particles at that point, with kinetic energies in the interval around and directions of incidence in the interval around . lines 630 – 631.


    Line 632, Eq. (3.30): summation over particles i.


    Furthermore, it is worth mentioning the differences between the operational quantities and .


    Finally, the description of the various phantoms in lines 614 – 627 would greatly benefit from a few schematic illustrations.


    13. Lines 636 – 1151 (several remarks for Section 4 on conversion coefficients):


    Lines 665 – 668 and 672 – 675 should already be mentioned in the relevant subsections in Section 3, i.e., Sect. 3.4.8 and 3.4.9, respectively.


    Lines 681 – 684. Here it is mentioned that calibration should be performed under the condition of full charged-particle equilibrium (CPE). However, in ICRP Publication 116 (2010) it is shown that CPE is not fulfilled in many of the irradiated phantom organs (at high energy irradiations). Though maybe logical and understandable from an experimental-calibration point of view, this apparent discrepancy should at least be mentioned and explained further. In this context, it is also important to specify what is meant with “sufficient material”.


    Lines 691 – 696. This interpolation procedure is not mentioned in ICRP Publication 116 (actually, the same sentences are included in ICRP Publication 116). Instead, we suggest to refer to ICRP publication 74.


    Line 707: “Above these energies”: what is meant is “above energies of about 2 MeV ”, since CPE still seems to hold for energies of 65 keV and 740 keV.


    Line 718. Change to and to .


    Line 720 –721. Change to .


    Also change to and to .


    Lines 714 – 723. If the slightly revised notation is used from the aforementioned points above, some symbols need to be modified here. Then, and in line 719 should be changed to and , respectively. Also, and in line 722 should then be changed to and , respectively.


    Lines 795 – 804. This description is very unclear and should be explained in detail. Is the overestimation at low energies caused by a lack of secondary charged-particle equilibrium (CPE) in the endosteal layer, as suggested by ICRP Publication 116 (see page 46, Sect. 3.1)?


    Lines 801 – 804: what is exactly meant here?


    To our understanding, the main reason for deviances in the low and high-energy regions of Fig. 4.1 and 4.2 is the lack of CPE (for low energies CPE is not fulfilled in the endosteal layer, for the high energy range there is a lack of CPE in several organs).


    Lines 843 – 884: what exactly happens between 1 and 3 MeV? This should be explained in the text.


    Lines 885 – 886: between 1 and 10 MeV, should be: between 3 and 10 MeV.


    Lines 992 – 1009, Figure 4.14: we suggest to change the energy axis to MeV (total energy of the ions) instead of MeV u-1.


    Line 1014: and should be: and .


    Line 1092 (and 1138): and should be: and .


    Lines 1137 – 1140. The overestimation for photon energies above 65 keV is not clearly visible in Figs. 4.18 and 4.19. From these figures an overestimation occurs > 300 keV.


    14. Lines 1152 – 1209 (Section 5 on the applications of the operational quantities):


    Lines 1176 – 1189. This part deals with calibration and could be moved to Sect. 6.


    Lines 1206 – 1208. “It is important … ,2012)”: this sentence is not clear and should be changed.


    15. Lines 1210–1251 (Sect. 6 on calibration of area monitoring instruments and personal dosimeters):


    Lines 1223 – 1227. In this part, a discussion should be included on the uncertainties with respect to the incident angle of the radiation. (See general comment # 4). Moreover, although personal dosimeters could be calibrated for ROT or ISO exposure geometries, its use in other exposure geometries may result in an underestimation of the incurred effective dose from external radiation.


    16. Lines 1252–1300 (Sect. 7, Conclusions):


    Lines 1274 – 1277. “The values of these … method”.


    What is meant by ‘including the contributions to the quantities from electron conversion coefficients’?


    To our understanding from ICRP Publication 116 (Section 5.2, pages 117 and 118), for photon energies > 2 or 3 MeV, there is an increasing deviation from the kerma approximation, i.e., the approximation based on secondary charged particle equilibrium. This follows from Monte-Carlo calculations where secondary electrons are tracked and their dose contributions at the point of interest of the ICRU sphere are taken into account. This deviation is the reason why the revised, Monte-Carlo calculated value of (i.e., not calculated using the kerma approximation) then becomes an underestimate of the effective dose for energies > 3 MeV, as seen in Fig. 5.2 of ICRP-116 (2010). At 10 MeV, the ratio attains values between 2 and 3, instead of values < 1 (about 0.8 - 0.9) under the kerma approximation (see Fig. 5.1). Note, with thus having a value of about 2.5 at 10 MeV photons, the value of becomes about 0.4, which is in agreement with the value observed in Fig. 4.1.


    If this is indeed what is meant by the sentence on lines 1274 to 1277, it should be explained in some more detail, not just in Sect. 7, but also in Sect. 4.


    Bilthoven, November 2, 2017.