12. Comparison between Calculations and Experimental Data for a Microbeam Technique

Yukio Sato and Fuminori Soga

Keywords: cell killing, microbeam technique, quadratic dependence, high-LET, single track

Recent results on cell killing with a microbeam technique were analyzed using three parameters (k, L, L₁, where k is the mean number of lethal particles per cell nucleus, L [keV/m] is the track-average LET in cells, and L1 [keV/m] is a critical value for inducing lethal damage by a single track. Analysis showed that the model calculation {k(L/L₁)²=1} is consistent with two data sets from Pugliese and from Hei.

Findings obtained with the model are as follows: a quadratic dependence on the LET of the cellular effects (LET²) is clear in the high-LET region between 30-500 keVm; L1 of 152 ± 0 keV/m gives the best fit for the results of broad-beam experiments with light ion species from boron to neon, and the sensitive area of cell nucleus (A) is 49 ± 3 m² for Chinese hamster V79 cells; RBE reaches a maximum at around L=170 keV/m (1.12L¹), and the obtained A value agrees well with the Pugliese's result (49 ± 7 m²). In microbeam experiments on cell killing with several MeV particles, the relationship between k and L for V79 cells is expressed as L = 152(k)^-1/2 .

Under a given survival level (37%), we studied the difference in the required LET (L) between the microbeam and conventional broad-beam experiments. Results are shown in Fig.10. For Pugliese's data set, L of 4.3MeV particles was evaluated as 105 keV/m, under which we calculated the critical k-value as 2.1 ± 0.1. This value agrees well with his value of 2.2 ± 0.3 obtained for Chinese hamster V79 cells. Hei's result is 3.7 for human-hamster hybrid (A_L) cells using 5.5MeV particles with L of 90 keV/m. This value is somewhat larger than the value we calculated (2.9 ± 0.2). Taking account of the experimental variation in different cells (V79 and A_L cells), Hei's result is not far from our calculation. Using Maclaurin expansion L(n), expressed as L₁{-ln(1-1/n)}^1/2 for n > 1 in broad-beam experiments, we can rewrite the model as L(n) = L1(n^-1 + 1/2n^-2 + 1/3n^-3 + 1/4n^-4 + - - - - )^1/2. In microbeam experiments { L₁(1/k)^-1/2} corresponds to the first term of this expansion. We note that L(n) is always larger than L(k), suggesting that many over-killed cells with several traverses are involved in broad-beam experiments, particularly with high-LET region. Experimentally, both n and k are the effective (in average) numbers per cell nucleus, however their characteristics are quite different; n is mainly considered as the effect of a stochastic property in particle hits, while k is attributed to effects of the energy spread and fluctuation in radiosensitivity of individual cells.

In conclusion, the expression of L = 152(k)^-1/2 is applicable for analyzing single-track events of V79 cells under the conditions at high-LET and with light ion beams.

Fig.10. Calculated critical number of traversed heavy ions per cell nucleus of V79 cells vs. their track-average LET[keV/] in cells. The dotted line shows values calculated by L=152(k)^-1/2 for microbeam experiments (each symbol corresponds to an integer). The solid line shows values calculated by L=152{-ln(1-1/n)}^1/2 for broad-beam experiments.
The area above the curve is the lethal region. and are Pugliese's results (2.2 at 105 keV/m) and Hei's results (3.7 at 90 keV/m), obtained using Chinese hamster V79 cells and human-hamster hybrid (A_L) cells, respectively.

Publications:
[1] Sato Y. and Soga F.: Int. J. Radiat. Biol., 75, 1015-1019, 1999.