Distribution of radial dose in water at nanometer scale for ions of the same linear energy transfer: benefits of the concept of annular dose

Abstract

Annular-dose AD is a new conception introduced, based on the radial dose distribution, RDD, introduced by the present work. AD is the integrated dose for many shells around the ions and it is defined as the dose deposited in the shell volume perpendicular to the ion path of width(r=0.1→R_min), length equal 2π and thickness equal unity (1nm). Thus, it integrates and maps the deposited dose due to ion in any medium at nanometer scale better than the ordinary radial dose. Katz and Awad radial dose formulae plus Butts-Katz and Tabata electron range-energy relations are composing three different approaches. These approaches were used for studying the AD for 30 ions forming 4 different equal LET and have energy at Bragg peak region from 1.5 to 24 MeV/n. The annual dose, AD as a function of the shell width for the ions under investigation showed that dose distributions around the ions of same LET are not the same and a clear peak at certain shell width called the ion’s maximum annular dose width, rMADW was determined for the first time. The rMADW is the position where the maximum reachable dose is delivered by secondary electrons around the ion. The ion’s rMADW showed an increasing function with Z*β within the same LET group. Interestingly, it was found that rMADW behaves as an increasing monotonic function of the relative ion velocity, β using the three approaches considered in this work.

Dual Nucleosomal Double-Strand Breaks Are the Key Effectors of Curative Radiation Therapy

“…Compared to DSBs, the much more severe dual DSBs (DDSBs) at the periphery of nucleosomes are truly the most common multiply damaged site, as seen in the lower right of Figures 3b, 6 and 7, and are much more lethal [1,[9][10][11][12][13][14]22,27]. In fact, the mean cellular lethal hit number of 0.69 at 2 Gy (Figure 5) is most likely related to the ≈1.5 δ-electron track ends (Figure 7) produced in the cell nucleus on average at this dose level and indicates that on average approximately half of them may hit nucleosomal DNA.…”

“…One may thus ask how cells are dying by radiation therapy if most and probably all simple DSBs are effectively being repaired by the cellular repair systems shown in some detail in the lower half of Figures 2a and 3a,b. This has been known for quite some time to be mainly due to so-called multiply damaged sites (MDSs, [10]) often caused by low-energy electrons (cf e.g., [11][12][13][14]) that have 10-30 nm ranges and by necessity are linked to all radiation beams as secondary so-called δ-rays or δ-electrons produced by the energy loss processes of the primary particle beam (cf Figure 1 inset and [1]: Figure 3). In fact, very low-energy electron and photon beams (1.5-0.2 keV) are linked to very high relative biological effectiveness (RBE > 3, cf Figure 1 [15,16]: Figure 8.7a), and the δ-electron fluence per unit dose in this energy range of the secondary electron slowing down spectrum largely determines the RBE as seen in Figure 1 [17][18][19][20][21].…”