Heide, B.

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KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 1 | B. Heide | KIT - INE | 08.05.2014A Percolation Model for Calculating SSB- and DSB-yieldB. HeideKarlsruhe Institute for Technology (KIT), Institute for Nuclear Waste Disposal (INE), Radiation Research DepartmentKIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 2 | B. Heide | KIT - INE | 08.05.2014Motivation Problem: basic assumption in microdosimtery: Edeposited∝ (number of ionisations).… is violated in nanometre-sized volumes (number of ionisations is too small!). Way out (Bernd Grosswendt, RPD 115 (2005), pp. 1 – 9):Ionisation-cluster size “v“ (i. e. number of ionisations [in the volume] per primary particle) should be measured instead of Edeposited.[ ] ))(exp(!)();();(0*)1(11 QkkQkdQfdQPkkk〉−〈〉〈=∑∞=Probabil. to cause v = 1 at d  =[ ] ))(exp(!)();(0*)1(22 QkkQkdQfFkkkv 〉−〈〉〈= ∑∑∞=∞=νProbabil. to cause v ≥ 2 at d=KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 3 | B. Heide | KIT - INE | 08.05.2014Motivation Bernd Grosswendt‘s hypothesis (cf. B. Grosswendt, From Macro to Nanodosimetrylecture, Bad Honnef, 2008; B. Grosswendt, RPD 115(2005), pp. 1-9):P1F2single-strand break (SSB)double-strand break (DSB) However, an ionisation cluster with v ≥ 2 can also refer to single ionisations caused   Thus, an ionisation-cluster model would be of advantage!anywhere in the volume. KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 4 | B. Heide | KIT - INE | 08.05.2014Motivation In the following, I propose an alternative (percolati n) model which is There has been developed a highly sophisticated realistic DNA target modelby Friedland et al. (Radiat. Res. 150 (1998) pp. 170 – 182)up to now which can be used,→ very simple,→ very quick,→ and easy to use.be used (among others)→ to analyse the geometry dependence of the cluster di tribution.The model is by far not as powerful as the one of Friedland et al. (see above), but mayamong many others, for calculating the SSB- and DSB-yield.KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 5 | B. Heide | KIT - INE | 08.05.2014The Model General remarks about percolation models: (simple) statistical models percolation → percolare (Latin)  „to trickle through“E. g.: liquid trickles through sand  ( clusters arise). known in statistical/solid-state/nuclear/heavy basic idea:− site is occupied with occupation probability  „p“− occupied neighboured sites are connected withbound probability „q“ion physics, polymer chemistry, …KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 6 | B. Heide | KIT - INE | 08.05.2014The Model Model formulation : Scenario (cf. Bernd Grosswendt, RPD 115 (2005), pp. 1 – 9) :Electron beam(homogeneous,monoenergetic)Cylinder• Volume: Height as well as diameter:    2.0 nm.Liquid water, density:    0.998203 g/cm3Molar masses:    ma(H) = 1.00794 u     ma(O) = 15.9994 u     ⇒ Number of atoms within the cylinder:  ≈ 629KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 7 | B. Heide | KIT - INE | 08.05.2014The Model• Assumptions:    - triangular lattice structure … motivated by H2O molecule and DNA double helix.- Clustering is dominated by lattice structure → 3-dim. lattice can be approximated by a 2-dim. one (25x25 sites)- DNA molecule can be substituted by H2O molecules.KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 8 | B. Heide | KIT - INE | 08.05.2014The Model• Further assumptions:    - SSB if 1, 2, or 3 ionisations of the same H2O moleculeHHO- q = 1- p  ionisation probability W;   W = ω⋅σionnumber of atoms (sites) per areatook place.- DSB if ionisations belong to 2 or more moleculesKIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 9 | B. Heide | KIT - INE | 08.05.2014The Model• Cross section for single ionisation of molecules:Figure taken from Ch. Champion, GEANT4-DNA, New physics models, from cell to DNA, lecture, KIT - Basic Training CourseFor Micro‐ and Nanodosimetry, Oct. 2011.Kinetic energy[MeV]Occupation probability Cross section  [108 b]0.05 0.1711 2.00.10 0.1996 2.30.30 0.1800 2.10.50 0.1392 1.62.00 0.0365 0.44.00 0.0228 0.3KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 10 | B. Heide | KIT - INE | 08.05.2014The Model00,10,20,30,40,50,60,70,80,9110 100 1000 10000DSB/SSB Yield RatioKinetic Energy [eV]ElectronsPercolationExperimentGrosswendtFriedland et al. Result:Except for the percolation model, all values above were taken from Bernd Grosswendt, RPD 115 (2005), pp. 1 – 9).Experiment (irradiation of pBR322 plasmid DNA) was done by Folkard et al.,  Int. J. Radiat. Biol. 64 (1993), pp. 651 - 658.KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 11 | B. Heide | KIT - INE | 08.05.2014The Model00,10,20,30,40,50,60,70,80,9110 100 1000 10000DSB/SSB Yield RatioKinetic Energy [eV]ElectronsPercolationExperimentGrosswendtFriedland et al.Fit to exp. data Result :Except for the percolation model, all values above were taken from Bernd Grosswendt, RPD 115 (2005), pp. 1 – 9).Experiment (irradiation of pBR322 plasmid DNA) was done by Folkard et al.,  Int. J. Radiat. Biol. 64 (1993), pp. 651 - 658.KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 12 | B. Heide | KIT - INE | 08.05.2014The Model00,10,20,30,40,50,60,70,80,9110 100 1000 10000DSB/SSB Yield RatioKinetic Energy [eV]ElectronsPercolationExperimentGrosswendtFriedland et al.Fit to exp. data Result and Conclusion : Percolation model values agree similarly well with the experimental values like that of  Grosswendt or Friedland et al. Essential input of the percolation model only was: geometryand  p  σion .  CAUTION: Percolation model has not sufficiently been t sted up to now!  Except for the percolation model, allvalues above were taken from BerndGrosswendt, RPD 115 (2005), pp. 1 – 9).Int. J. Radiat. Biol. 64 (1993), pp. 651 - 658.Experiment (irradiation of pBR322plasmid DNA) was done by Folkard et al.,KIT – die Kooperation vonForschungszentrum Karlsruhe GmbHund Universität Karlsruhe (TH)No.: 13| B. Heide | KIT - INE | 08.05.2014Thank you!Ant Nebula (Mz 3)

A percolation model for Calculating SSB- and DSB-yield

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A percolation model for Calculating SSB- and DSB-yield

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