Mammalian cell killing by ultrasoft X rays and high-energy radiation: an extension of the MK model

An alternate formulation of the microdosimetric-kinetic (MK) model is presented that applies to irradiation of mammalian cells with ultrasoft X rays as well as high-energy radiations of variable linear energy transfer (LET). Survival and DNA double-strand break measurements for V79 cells from the literature are examined to illustrate application of the model. It is demonstrated that the linear component of the linear-quadratic survival relationship (alpha) is enhanced because repairable potentially lethal lesions formed from a single ultrasoft X-ray energy deposition event, when closer on average than for a single high-energy radiation event, are more likely to combine to form a lethal lesion. The quadratic component (beta) of the linear-quadratic survival relationship is increased because the potentially lethal lesions formed by ultrasoft X rays are created with greater efficiency than those of high-energy radiation. In addition, potentially lethal lesions from very low-energy carbon K-shell X rays may be enriched in structural forms that favor combination to form lethal lesions instead of repair. These features account for the increased effectiveness of killing of V79 cells by ultrasoft X rays compared to cobalt-60 gamma radiation. The importance of pairwise combination of potentially lethal lesions to form exchange chromosome aberrations that become lethal lesions is discussed. The extended MK model explains and reconciles differences between the MK model and the theory of dual radiation action on the one hand, and on the other, the view that variation in the RBE with radiation quality is explained by differences in energy deposition in nanometer- rather than micrometer-size volumes.     

Distinct Roles of Ape1 Protein,an Enzyme Involved in DNA Repair,in High or Low Linear Energy Transfer Ionizing Radiation-induced Cell Killing

High linear energy transfer (LET) radiation from space heavy charged particles or a heavier ion radiotherapy machine kills more cells than low LET radiation, mainly because high LET radiation-induced DNA damage is more difficult to repair. Relative biological effectiveness (RBE) is the ratio of the effects generated by high LET radiation to low LET radiation. Previously, our group and others demonstrated that the cell-killing RBE is involved in the interference of high LET radiation with non-homologous end joining but not homologous recombination repair. This effect is attributable, in part, to the small DNA fragments (≤40 bp) directly produced by high LET radiation, the size of which prevents Ku protein from efficiently binding to the two ends of one fragment at the same time, thereby reducing non-homologous end joining efficiency. Here we demonstrate that Ape1, an enzyme required for processing apurinic/apyrimidinic (known as abasic) sites, is also involved in the generation of small DNA fragments during the repair of high LET radiation-induced base damage, which contributes to the higher RBE of high LET radiation-induced cell killing. This discovery opens a new direction to develop approaches for either protecting astronauts from exposure to space radiation or benefiting cancer patients by sensitizing tumor cells to high LET radiotherapy.     

Induction of gene and deletion mutations by accelerated heavy charged particles in Escherichia coli cells

The results of the induction of the point and the deletion mutations by the radiation with broad region of linear energy transfer (LET) ox Escherichia coli cells. The linear-quadratic function for point mutation induction was shown in comparison with linear dependence for deletion mutations. The relative biological effectiveness (RBE) is described as a function of LET by dependence with a local maximum. The greatest RBE coefficients for the lethal effects, gene and deletion mutation induction realize under different LET of heavy charged particles.     

Radioprotection by DMSO of mammalian cells exposed to X-rays and to heavy charged-particle beams

Populations of G1-phase Chinese hamster cells in stirred suspensions containing various concentrations of DMSO were irradiated with 250 kV X-rays or various heavy charged-particle beams. Chemical radioprotection of cell inactivation was observed for all LET values studied. When cell survival data were resolved into linear and quadratic components, the extent and concentration dependence of DMSO protection were found to be different for the two mechanisms. The chemical kinetics of radioprotection for single-events were similar for LET values up to those which gave the maximum RBE. DMSO protected to a lesser extent against energetic argon ions at an median LET of approximately 220 keV/micron. These data could indicate the contribution of indirect action by hydroxyl radicals and hydrogen atoms to cell inactivation by single-hit and double-hit mechanisms for various radiation qualities. The decrease in RBE observed at very high LET may result, in part, from reduced yields of water radicals at 10(-9)-10(-8) s resulting from radical recombination mechanisms within the charged particle tracks.     

The RBE-LET relationship for rodent intestinal crypt cell survival, testes weight loss, and multicellular spheroid cell survival after heavy-ion irradiation.

This report presents data for survival of mouse intestinal crypt cells, mouse testes weight loss as an indicator of survival of spermatogonial stem cells, and survival of rat 9L spheroid cells after irradiation in the plateau region of unmodified particle beams ranging in mass from 4He to 139La. The LET values range from 1.6 to 953 keV/microns. These studies examine the RBE-LET relationship for two normal tissues and for an in vitro tissue model, multicellular spheroids. When the RBE values are plotted as a function of LET, the resulting curve is characterized by a region in which RBE increases with LET, a peak RBE at an LET value of 100 keV/microns, and a region of decreasing RBE at LETs greater than 100 keV/microns. Inactivation cross sections (sigma) for these three biological systems have been calculated from the exponential terminal slope of the dose-response relationship for each ion. For this determination the dose is expressed as particle fluence and the parameter sigma indicates effect per particle. A plot of sigma versus LET shows that the curve for testes weight loss is shifted to the left, indicating greater radiosensitivity at lower LETs than for crypt cell and spheroid cell survival. The curves for cross section versus LET for all three model systems show similar characteristics with a relatively linear portion below 100 keV/microns and a region of lessened slope in the LET range above 100 keV/microns for testes and spheroids. The data indicate that the effectiveness per particle increases as a function of LET and, to a limited extent, Z, at LET values greater than 100 keV/microns. Previously published results for spread Bragg peaks are also summarized, and they suggest that RBE is dependent on both the LET and the Z of the particle.     

A Stochastic Model of DNA Fragments Rejoining

When cells are exposed to ionizing radiation, DNA damages in the form of single strand breaks (SSBs), double strand breaks (DSBs), base damage or their combinations are frequent events. It is known that the complexity and severity of DNA damage depends on the quality of radiation, and the microscopic dose deposited in small segments of DNA, which is often related to the linear transfer energy (LET) of the radiation. Experimental studies have suggested that under the same dose, high LET radiation induces more small DNA fragments than low-LET radiation, which affects Ku efficiently binding with DNA end and might be a main reason for high-LET radiation induced RBE [1] since DNA DSB is a major cause for radiation-induced cell death. In this work, we proposed a mathematical model of DNA fragments rejoining according to non-homologous end joining (NHEJ) mechanism. By conducting Gillespie''s stochastic simulation, we found several factors that impact the efficiency of DNA fragments rejoining. Our results demonstrated that aberrant DNA damage repair can result predominantly from the occurrence of a spatial distribution of DSBs leading to short DNA fragments. Because of the low efficiency that short DNA fragments recruit repair protein and release the protein residue after fragments rejoining, Ku-dependent NHEJ is significantly interfered with short fragments. Overall, our work suggests that inhibiting the Ku-dependent NHEJ may significantly contribute to the increased efficiency for cell death and mutation observed for high LET radiation.     

Protein synthesis modulates the biological effectiveness of the combined action of hyperthermia and high-LET radiation.

The combined effects of heavy-ion radiation and hyperthermia on the survival of CHO-SC1 cells and its temperature-sensitive (ts) mutant tsH1 cells were studied using accelerated neon ions followed by mild heating at 41.5 degrees C. The sequence of application of heat and high-LET radiation is significant to cell-killing effects. Heat applied to cells prior to irradiation with neon plateau ions (LET = 32 keV/microns) was less effective than heat applied immediately after irradiation. The ability of cells to synthesize new proteins plays a key role in this sequence-dependent thermal sensitization. When protein synthesis was shut down in tsH1 cells, the thermal enhancement of cell killing by high-LET radiation was the same regardless of the sequence. The thermal enhancement of radiation-induced cell killing was LET-dependent for the SC1 cells, but this was not clearly demonstrated in the tsH1 cells. Furthermore, the RBE of heated SC1 cells varied with LET and reached a maximum of greater than 3 at 80 keV/microns. In the absence of protein synthesis, the maximum RBE value was reduced to 2.6. These results suggest that the accumulation of cellular damage caused by exposure to densely ionizing particles with increasing LETs can be potentiated with active protein synthesis during postirradiation heat treatment.     

Inactivation of aerobic and hypoxic cells from three different cell lines by accelerated (3)He-, (12)C- and (20)Ne-ion beams

The LET-RBE spectra for cell killing for cultured mammalian cells exposed to accelerated heavy ions were investigated to design a spread-out Bragg peak beam for cancer therapy at HIMAC, National Institute of Radiological Sciences, Chiba, prior to clinical trials. Cells that originated from a human salivary gland tumor (HSG cells) as well as V79 and T1 cells were exposed to (3)He-, (12)C- and (20)Ne-ion beams with an LET ranging from approximately 20-600 keV/micrometer under both aerobic and hypoxic conditions. Cell survival curves were fitted by equations from the linear-quadratic model and the target model to obtain survival parameters. RBE, OER, alpha and D(0) were analyzed as a function of LET. The RBE increased with LET, reaching a maximum at around 200 keV/micrometer, then decreased with a further increase in LET. Clear splits of the LET-RBE or -OER spectra were found among ion species and/or cell lines. At a given LET, the RBE value for (3)He ions was higher than that for the other ions. The position of the maximum RBE shifts to higher LET values for heavier ions. The OER value was 3 for X rays but started to decrease at an LET of around 50 keV/micrometer, passed below 2 at around 100 keV/micrometer, and then reached a minimum above 300 keV/micrometer, but the values remained greater than 1. The OER was significantly lower for (3)He ions than the others.     

LET dependence of lethality in <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis> irradiated by heavy ions

To clarify the effect of heavy ions in plants, dry seeds of Arabidopsis were irradiated with carbon, neon, and argon ions with various linear energy transfer (LET) values. The relative biological effectiveness (RBE) for lethality peaked at LET values over 350 keV/microns for neon and argon ions. This LET giving the peak RBE was higher than the LET of 100-200 keV/microns which was reported to have a maximum RBE for other types of cells, such as mammalian cells. Furthermore, sterility showed a higher RBE at an LET of 354 keV/microns with neon ions than that at an LET of 113 keV/microns with carbon ions. Lethality and sterility are both considered to be caused by damage to DNA. The results indicate that the LET having a maximum of RBE for lethality is higher in Arabidopsis seeds than in other unicellular systems. The most likely explanation for this shift of LET is that the DNA in dry seeds has a different chemical environment and/or hydration state than the DNA in cells in culture.     

The relative biological effectiveness of 670 MeV/A neon as a function of depth in water for a tissue model

Linear energy transfer (LET infinity) spectra of identified charge fragments and primaries, produced by nuclear interactions of 670 MeV/A neon in water, were measured along the unmodulated Bragg curve of the neon beam. The relative biological effectiveness (RBE) values for spermatogonial cell killing, as reported on the basis of weight loss assay of mouse testes irradiated with beams of approximately constant single LET infinity, were summed over the particle LET infinity spectra to obtain an effective RBE for each charged-particle species, as a function of water absorber thickness. The resultant values of effective RBE were combined to obtain an effective RBE for the mixed radiation field. The RBE calculated in this way was compared with experimental RBEs obtained for spermatogonial cell killing in the mixed radiation field produced by neon ions traversing a thick water absorber. Discrepancies of 10-40% were observed between the calculated RBE and the RBE measured in the mixed radiation field. Part of this discrepancy can be attributed to undetected low-Z fragments, whose contribution is not included in the calculation, leading to an overestimated value for the calculated RBE. On the other hand, calculated values 10% greater than the measured RBE are explained as track structure effects due to the higher radial ionization density near neon tracks relative to the ionization density near the silicon tracks used to fit the RBE vs LET infinity data.     

Charged-particle mutagenesis. 1. Cytotoxic and mutagenic effects of high-LET charged iron particles on human skin fibroblasts.

Cytotoxic and mutagenic effects of high-LET charged iron (56Fe) particles were measured quantitatively using primary cultures of human skin fibroblasts. Argon and lanthanum particles and gamma rays were used in comparative studies. The span of LETs selected was from 150 keV/microns (330 MeV/u) to 920 keV/microns (600 MeV/u). Mutations were scored at the hypoxanthine guanine phosphoribosyl transferase (HPRT) locus using 6-thio-guanine (6-TG) for selection. Exposure to these high-LET charged particles resulted in exponential survival curves. Mutation induction, however, was fitted by the linear model. The relative biological effectiveness (RBE) for cell killing ranged from 3.7 to 1.3, while that for mutation induction ranged from 5.7 to 0.5. Both the RBE for cell killing and the RBE for mutagenesis decreased with increasing LET over the range of 1.50 to 920 keV/microns. The inactivation cross section (sigma i) and the action cross section for mutation induction (sigma m) ranged from 32.9 to 92.0 microns2 and 1.45 to 5.56 X 10(-3) microns2; the maximum values were obtained by 56Fe with an LET of 200 keV/microns. The mutagenicity (sigma m/sigma i) ranged from 2.05 to 7.99 X 10(-5) with an inverse relationship to LET.     

Response of colony-forming units-spleen to heavy charged particles

Survival of colony-forming units-spleen (CFU-S) was measured after single doses of photons or heavy charged particles from the BEVALAC. The purposes were to define the radiosensitivity to heavy ions used medically and to evaluate relationships between relative biological effectiveness (RBE) and dose-averaged linear energy transfer (LET infinity). In in vitro irradiation experiments. CFU-S suspensions were exposed to 220 kVp X rays or to 20Ne (372 MeV/micron) or 40Ar (447 MeV/micron) particles in the plateau portion of the Bragg curve. In in vivo irradiation experiments, donor mice from which CFU-S were harvested were exposed to 12C (400 MeV/micron). 20Ne (400 or 670 MeV/micron), or 40Ar (570 MeV/micron) particles in Bragg peaks spread to 4 or 10 cm by spiral ridge filters. Based on RBE at 10 survival, the maximum RBE of 2.1 was observed for 40Ar particles characterized by an LET infinity of approximately 100 keV/micron. Lower RBEs were determined at lower or higher estimated values of LET infinity and ranged from 1.1 for low energy 40Ar particles to 1.5-1.6 for low energy 12C and 20Ne. The responses of CFU-S are compared with responses of other model systems to heavy charged particles and with the reported sensitivity of CFU-S to neutrons of various energies. The maximum RBE reported here, 2.1 for high energy 40Ar particles, is somewhat lower than values reported for fission-spectrum neutrons, and is appreciably lower than values for monoenergetic 0.43-1.8 MeV neutrons. Low energy 12C and 20Ne particles have RBEs in the range of values reported for 14.7 MeV neutrons.     

Simulation of DNA damage after proton irradiation

The biophysical radiation track simulation model PARTRAC was improved by implementing new interaction cross sections for protons in water. Computer-simulated tracks of energy deposition events from protons and their secondary electrons were superimposed on a higher-order DNA target model describing the spatial coordinates of the whole genome inside a human cell. Induction of DNA double-strand breaks was simulated for proton irradiation with LET values between 1.6 and 70 keV/microm and various reference radiation qualities. The yield of DSBs after proton irradiation was found to rise continuously with increasing LET up to about 20 DSBs per Gbp and Gy, corresponding to an RBE up to 2.2. About half of this increase resulted from a higher yield of DSB clusters associated with small fragments below 10 kbp. Exclusion of experimentally unresolved multiple DSBs reduced the maximum DSB yield by 30% and shifted it to an LET of about 40 keV/microm. Simulated fragment size distributions deviated significantly from random breakage distributions over the whole size range after irradiation with protons with an LET above 10 keV/microm. Determination of DSB yields using equations derived for random breakage resulted in an underestimation by up to 20%. The inclusion of background fragments had only a minor influence on the distribution of the DNA fragments induced by radiation. Despite limited numerical agreement, the simulations reproduced the trends in proton-induced DNA DSBs and fragment induction found in recent experiments.     

Cell cycle delay in murine pre-osteoblasts is more pronounced after exposure to high-LET compared to low-LET radiation

Space radiation contains a complex mixture of particles comprised primarily of protons and high-energy heavy ions. Radiation risk is considered one of the major health risks for astronauts who embark on both orbital and interplanetary space missions. Ionizing radiation dose-dependently kills cells, damages genetic material, and disturbs cell differentiation and function. The immediate response to ionizing radiation-induced DNA damage is stimulation of DNA repair machinery and activation of cell cycle regulatory checkpoints. To date, little is known about cell cycle regulation after exposure to space-relevant radiation, especially regarding bone-forming osteoblasts. Here, we assessed cell cycle regulation in the osteoblastic cell line OCT-1 after exposure to various types of space-relevant radiation. The relative biological effectiveness (RBE) of ionizing radiation was investigated regarding the biological endpoint of cellular survival ability. Cell cycle progression was examined following radiation exposure resulting in different RBE values calculated for a cellular survival level of 1 %. Our findings indicate that radiation with a linear energy transfer (LET) of 150 keV/μm was most effective in inducing reproductive cell killing by causing cell cycle arrest. Expression analyses indicated that cells exposed to ionizing radiation exhibited significantly up-regulated p21(CDKN1A) gene expression. In conclusion, our findings suggest that cell cycle regulation is more sensitive to high-LET radiation than cell survival, which is not solely regulated through elevated CDKN1A expression.     

Dependence of the radiosensitivity of yeast cells on the LET of radiations. Experiments on haploid cells

The previously developed model was used to study the dependence of radiosensitivity (D0(-1) of Saccharomyces cerevisiae (the wild type and radiosensitive mutant) on linear energy transfer (LET) of ionizing radiation. D0(-1) (L) of haploid yeasts was shown to be associated, to a certain extent, with the capacity of radiation damages repair. As to the wild-type cells, the above function was represented by a curve showing a maximum, while a descending curve was characteristic of the radiosensitive mutant cells deficient in radiation damages repair. The influence of the repair processes on cell radiosensitivity decreased with increasing LET.     

RBE for carcinogenesis following exposure to high LET radiation

Stochastic radiation effects following exposure to heavy ions and other high linear energy transfer (LET) radiation in space are a matter of concern when the long-term consequences of space flights are considered. This paper is an overview of the relevant literature, emphasizing uncertainties entailed from estimates of relative biological effectiveness (RBE) for different experiment end-points, making the choice of a single weighting factor for the prediction of cancer risk in man extremely difficult. Life-span-shortening studies in mice exposed to heavy ions and ongoing large-scale experiments in monkeys exposed to protons suggest that RBEs for all cancers are lower than 5. This does not exclude a much higher RBE for rare tumors such as brain tumors in monkeys or promoted Harderian gland tumours in mice at LET >80 keV/µm. Skin cancer studies in rats exposed to neon or argon resulted in similar RBE. Exposure to fission neutrons led to high RBE in all species, not excluding values much higher than 20 for specific cancers such as lung tumors in mice and all cancers in rats. The estimate of maximal RBE is, however, extremely dependent on the hypothesis made on the shape of the dose-response curves in the lower range of doses. These results suggest that neutrons may be the most hazardous component of high-LET radiation. There is only limited evidence from cancer experiments that LET >150 keV/µm results in highly decreased efficiency, but this has been found for bone cancer induction following exposure to fission fragments.Invited paper presented at the International Symposium on Heavy Ion Research: Space, Radiation Protection and Therapy, Sophia-Antipolis, France, 21–24 March 1994     

Influence of radiation quality on the effectiveness of small doses for induction of reproductive death and chromosome aberrations in mammalian cells.

An analysis and interpretation is presented of published data concerning the dependence of radiobiological effectiveness on the radiation quality of photons, neutrons and heavy ions for the induction of these two effects in different types of mammalian cell. The results of this analysis suggest that chromosome aberrations observable at mitosis show a stronger dependence on YF or LET infinity than cell inactivation. At high YF, observable abberrations provide a major contribution to cell reproductive death induced by small doses. At low YF the effectiveness of small doses for cell death depends mainly on another type of damage, possibly also induced in the chromosomes, but not observable at mitosis. This type of damage depends less of YF or LET infinity than observable aberrations. The implications of these differences in damage in relation to radiation quality for the extrapolation of data on other types of damage to small doses of interest in radiation protection are discussed in relation to maximum r.b.e values observed.     

Responses of synchronous L5178Y S/S cells to heavy ions and their significance for radiobiological theory

Synchronous suspensions of the radiosensitive S/S variant of the L5178Y murine leukaemic lymphoblast at different positions in the cell cycle were exposed aerobically to segments of heavy-ion beams (20Ne, 28Si, 40Ar, 56Fe and 93Nb) in the Bragg plateau regions of energy deposition. The incident energies of the ion beams were in the range of 460 +/- 95 MeV u-1, and the calculated values of linear energy transfer (LET infinity) for the primary nuclei in the irradiated samples were 33 +/- 3, 60 +/- 3, 95 +/- 5, 213 +/- 21 and 478 +/- 36 keV microns-1, respectively; 280 kVp X-rays were used as the baseline radiation. Generally, the maxima or inflections in relations between relative biological effectiveness (RBE) and LET infinity were dependent upon the cycle position at which the cells were irradiated. Certain of those relations were influenced by post-irradiation hypothermia. Irradiation in the cell cycle at mid-G1 to mid-G1 + 3 h, henceforth called G1 to G1 + 3 h, resulted in survival curves that were close approximations to simple exponential functions. As the LET infinity was increased, the RBE did not exceed 1.0, and by 478 keV microns-1 it had fallen to 0.39. Although similar behaviour has been reported for inactivation of proteins and certain viruses by ionizing radiations, so far the response of the S/S variant is unique for mammalian cells. The slope of the survival curve for X-photons (D0: 0.27 Gy) is reduced in G1 to G1 + 3 h by post-irradiation incubation at hypothermic temperatures and reaches a minimum (Do: 0.51 Gy) at 25 degrees C. As the LET infinity was increased, however, the extent of hypothermic recovery was reduced progressively and essentially was eliminated at 478 keV microns-1. At the cycle position where the peak of radioresistance to X-photons occurs for S/S cells, G1 + 8 h, increases in LET infinity elicited only small increases in RBE (at 10% survival), until a maximum was reached around 200 keV microns-1. At 478 keV microns-1, what little remained of the variation in response through the cell cycle could be attributed to secondary radiations (delta rays) and smaller nuclei produced by fragmentation of the primary ions.     

High yields of isochromatid breaks and successive formation of chromosome exchanges may lead to reproductive cell death following high-LET irradiation

To clarify the relationship between cell death and chromosomal aberrations following exposure to heavy-charged ion particles beams, exponentially growing Human Salivary Gland Tumor cells (HSG cells) were irradiated with various kinds of high energy heavy ions; 13 keV/μm carbon ions as a low-LET charged particle radiation source, 120 keV/μm carbon ions and 440 keV/μm iron ions as high-LET charged particle radiation sources. X-rays (200 kVp) were used as a reference. Reproductive cell death was evaluated by clonogenic assays, and the chromatid aberrations in G2/M phase and their repairing kinetics were analyzed by the calyculin A induced premature chromosome condensation (PCC) method. High-LET heavy-ion beams introduced much more severe and un-repairable chromatid breaks and isochromatid breaks in HSG cells than low-LET irradiation. In addition, the continuous increase of exchange aberrations after irradiation occurred in the high-LET irradiated cells. The cell death, initial production of isochromatid breaks and subsequent formation of chromosome exchange seemed to be depend similarly on LET with a maximum RBE peak around 100–200 keV/μm of LET value. Conversely, un-rejoined isochromatid breaks or chromatid breaks/gaps seemed to be less effective in reproductive cell death. These results suggest that the continuous yield of chromosome exchange aberrations induced by high-LET ionizing particles is a possible reason for the high RBE for cell death following high-LET irradiation, alongside other chromosomal aberrations additively or synergistically.     

Development of modified microdosimetric kinetic model for relative biological effectiveness in proton therapy

To predict the biological effects of ionising radiation, the quantity of biological dose is introduced instead of the physical absorbed dose. In proton therapy, a constant relative biological effectiveness (RBE) of 1.1 is usually applied clinically as recommended by the International Commission of Radiation Units and Measurements. This study presents a new model, based on the modified microdosimetric kinetic model (MMKM), for calculating variable RBE values based on experimental data on the induction of DNA double-strand breaks (DSBs) within cells. The MMKM was proposed based on experimental data for the yield of DSBs in mammalian cells, which allows modification of the yield of primary lesions in the MKM. In this approach, a unique function named f(LET), which describes the relation between RBE and linear energy transfer (LET), was considered for charged particles. In the presented model (DMMKM), the MMKM approach was developed further by considering different f(LET)s for different relevant ions involved in energy deposition events in proton therapy. Although experimental data represent the dependence of the yield of primary lesions on the ion species, the DSB yield (assumed as the main primary lesion) is assumed independent of the ion species in the MMKM. In the DMMKM, by considering the yield of primary lesions as a function of the ion species, the α and β values are in better agreement with the experimental data as compared to those of the MKM and MMKM approaches. The biological dose in the DMMKM is predicted to be lower than that in the MMKM. Further, in the proposed model, the variation of the β parameter is higher than the constant value assumed in the MKM, at the distal end of the spread-out Bragg peak (SOBP). Moreover, the level of cell death estimated by the MMKM at the SOBP region is higher than that obtained based on the DMMKM. It is concluded that considering modified f(LET)s in the model developed here is more consistent with experimental results than when MMKM and MKM approaches are considered. The DMMKM examines the biological effects with full detail and will, therefore, be effective in improving proton therapy.