Differences In Relative Biological Effectiveness Research Articles

Biological Characterization of the Effects of Filtration on the Xoft Axxent® Electronic Brachytherapy Source for Cervical Cancer Applications.

Low-energy X-ray sources that operate in the kilovoltage energy range have been shown to induce more cellular damage when compared to their megavoltage counterparts. However, low-energy X-ray sources are more susceptible to the effects of filtration on the beam spectrum. This work sought to characterize the biological effects of the Xoft Axxent® source, a low-energy therapeutic X-ray source, both with and without the titanium vaginal applicator in place. It was hypothesized that there would be an increase in relative biological effectiveness (RBE) of the Axxent® source compared to 60Co and that the source in the titanium vaginal applicator (SIA) would have decreased biological effects compared to the bare source (BS). This hypothesis was drawn from linear energy transfer (LET) simulations performed using the TOPAS Monte Carlo user code as well a reduction in dose rate of the SIA compared to the BS. A HeLa cell line was maintained and used to evaluate these effects. Clonogenic survival assays were performed to evaluate differences in the RBE between the BS and SIA using 60Co as the reference beam quality. Neutral comet assay was used to assess induction of DNA strand damage by each beam to estimate differences in RBE. Quantification of mitotic errors was used to evaluate differences in chromosomal instability (CIN) induced by the three beam qualities. The BS was responsible for the greatest quantity of cell death due to a greater number of DNA double strand breaks (DSB) and CIN observed in the cells. The differences observed in the BS and SIA surviving fractions and RBE values were consistent with the 13% difference in LET as well as the factor of 3.5 reduction in dose rate of the SIA. Results from the comet and CIN assays were consistent with these results as well. The use of the titanium applicator results in a reduction in the biological effects observed with these sources, but still provides an advantage over megavoltage beam qualities. © 2023 by Radiation Research Society.

A Nucleoside Anticancer Drug, 1-(3-C-Ethynyl-β-D-Ribo-Pentofuranosyl)Cytosine, Induces Depth-Dependent Enhancement of Tumor Cell Death in Spread-Out Bragg Peak (SOBP) of Proton Beam.

The effect of 1-(3-C-ethynyl-β-D-ribo-pentofuranosyl)cytosine (ECyd) on proton-induced cell death was evaluated in human lung carcinoma cell line A549 and Chinese hamster fibroblast cell line V79 to enhance relative biological effectiveness (RBE) within the spread-out Bragg peak (SOBP) of proton beams. Treatment with ECyd significantly enhanced the proton-induced loss of clonogenicity and increased senescence at the center, but not at the distal edge of SOBP. The p53-binding protein 1 foci formation assay showed that ECyd decelerated the rate of DNA double-strand break (DSB) repair at the center, but not the distal region of SOBP, suggesting that the ECyd-induced enhancement of proton-induced cell death is partially associated with the inhibition of DSB repair. This study demonstrated that ECyd enhances proton-induced cell killing at all positions of SOBP, except for the distal region and minimizes the site-dependent differences in RBE within SOBP. Thus, ECyd is a unique radiosensitizer for proton therapy that may be useful because it levels the biological dose within SOBP, which improves tumor control and reduces the risk of adverse effects at the distal edge of SOBP.

TU-AB-BRC-02: Accuracy Evaluation of GPU-Based OpenCL Carbon Monte Carlo Package (goCMC) in Biological Dose and Microdosimetry in Comparison to FLUKA Simulations

Purpose: One of the most accurate methods for radiation transport is Monte Carlo (MC) simulation. Long computation time prevents its wide applications in clinic. We have recently developed a fast MC code for carbon ion therapy called GPU-based OpenCL Carbon Monte Carlo (goCMC) and its accuracy in physical dose has been established. Since radiobiology is an indispensible aspect of carbon ion therapy, this study evaluates accuracy of goCMC in biological dose and microdosimetry by benchmarking it with FLUKA. Methods: We performed simulations of a carbon pencil beam with 150, 300 and 450 MeV/u in a homogeneous water phantom using goCMC and FLUKA. Dose and energy spectra for primary and secondary ions on the central beam axis were recorded. Repair-misrepair-fixation model was employed to calculate Relative Biological Effectiveness (RBE). Monte Carlo Damage Simulation (MCDS) tool was used to calculate microdosimetry parameters. Results: Physical dose differences on the central axis were <1.6% of the maximum value. Before the Bragg peak, differences in RBE and RBE-weighted dose were <2% and <1%. At the Bragg peak, the differences were 12.5% caused by small range discrepancy and sensitivity of RBE to beam spectra. Consequently, RBE-weighted dose difference was 11%. Beyond the peak, RBE differences were <20% and primarily caused by differences in the Helium-4 spectrum. However, the RBE-weighted dose agreed within 1% due to the low physical dose. Differences in microdosimetric quantities were small except at the Bragg peak. The simulation time per source particle with FLUKA was 0.08 sec, while goCMC was approximately 1000 times faster. Conclusion: Physical doses computed by FLUKA and goCMC were in good agreement. Although relatively large RBE differences were observed at and beyond the Bragg peak, the RBE-weighted dose differences were considered to be acceptable.

Comparative Risk Predictions of Second Cancers After Carbon-Ion Therapy Versus Proton Therapy

This work proposes a theoretical framework that enables comparative risk predictions for second cancer incidence after particle beam therapy for different ion species for individual patients, accounting for differences in relative biological effectiveness (RBE) for the competing processes of tumor initiation and cell inactivation. Our working hypothesis was that use of carbon-ion therapy instead of proton therapy would show a difference in the predicted risk of second cancer incidence in the breast for a sample of Hodgkin lymphoma (HL) patients. We generated biologic treatment plans and calculated relative predicted risks of second cancer in the breast by using two proposed methods: a full model derived from the linear quadratic model and a simpler linear-no-threshold model. For our reference calculation, we found the predicted risk of breast cancer incidence for carbon-ion plans-to-proton plan ratio, <Rc/Rp>, to be 0.75 ± 0.07 but not significantly smaller than 1 (P=.180). Our findings suggest that second cancer risks are, on average, comparable between proton therapy and carbon-ion therapy.

Microdosimetric and Biological Effects of Photon Irradiation at Different Energies in Bone Marrow.

To ensure reliability and reproducibility of radiobiological data, it is necessary to standardize dosimetry practices across all research institutions. The photoelectric effect predominates over other interactions at low energy and in high atomic number materials such as bone, which can lead to increased dose deposition in soft tissue adjacent to mineral bone due to secondary radiation particles. This may produce radiation effects that deviate from higher energy photon irradiation that best model exposure from clinical radiotherapy or nuclear incidences. Past theoretical considerations have indicated that this process should affect radiation exposure of neighboring bone marrow (BM) and account for reported differences in relative biological effectiveness (RBE) for hematopoietic failure in rodents. The studies described herein definitively estimate spatial dose distribution and biological effectiveness within the BM compartment for (137)Cs gamma rays and 320 kVp X rays at two levels of filtration: 1 and 4 mm Cu half-value layer (HVL). In these studies, we performed: 1. Monte Carlo simulations on a 5 μm resolution model of mouse vertebrae and femur derived from micro-CT images; 2. In vitro biological experiments irradiating BM cells plated directly on the surface of a bone-equivalent material (BEM); and 3. An in vivo study on BM cell survival in irradiated live mice. Simulation results showed that the relative dose increased in proximity to bone at the lower radiation energies and produced averaged values of relative dose over the entire BM volume within imaged trabecular bone of 1.17, 1.08 and 1.01 for beam qualities of 1 mm Cu HVL, 4 mm Cu HVL and (137)Cs, respectively. In accordance with Monte Carlo simulations, in vitro irradiation of BM cells located on BEM and in vivo whole-body irradiation at a prescribed dose to soft tissue of 6 Gy produced relative cell killing of hematopoietic progenitors (CFU-C) that significantly increased for the 1 mm Cu HVL X rays compared to radiation exposures of higher photon energies. Thus, we propose that X rays of the highest possible kVp and filtration be used to investigate radiation effects on the hematopoietic system, as this will allow for better comparisons with high-energy photon exposures applied in radiotherapy or as anticipated in a nuclear event.

SU‐E‐T‐494: Influence of Proton Track‐Cell Nucleus Incidence Angle On Relative Biological Effectiveness

Purpose:To explain a Monte Carlo (MC) simulation artifact whereby differences in relative biological effectiveness (RBE) in the induction of initial double strand breaks are observed as a function of the proton track incidence angles in a geometric cell nucleus model. Secondly, to offer an alternative isotropic irradiation procedure to mitigate this effect.Methods:MC tracks of 1 MeV protons were generated in an event‐by‐event mode. They were overlaid on a cylindrical model of a cell nucleus containing 6×109 nucleotide base pairs. The tracks incidence angle θ with respect to the cell nucleus's axis was varied in 10 degrees intervals, each time generating one hundred fractions of ∼2 Gy. Strand breaks were scored in the modeled DNA sugar‐phosphate groups and further sub‐classified into single or double strand breaks (ssbs or dsbs). For each angle, an RBE for the induction of initial dsbs with reference to Co‐60 was calculated.Results:Our results show significant angular dependencies of RBE, with maximum values for incidence angles parallel to the nucleus central axis. Further examination shows that the higher cross‐sections for the creation of dsbs is due to the preferential alignment of tracks with geometrical sub‐parts of the cell nucleus model, especially the nucleosomes containing the sugar‐phosphate groups. To alleviate the impact of this simulation artifact, an average RBE was calculated with a procedure based on a weighted sampling of the angular data.Conclusion:This work demonstrates a possible numerical artifact in estimated RBE if the influence of the particle incidence angle is not correctly taken into account. A correction procedure is presented to better conform the simulations to real‐life experimental conditions.We would like to acknowledge support from the Fonds de recherche du Quebec Sante (FRQS), from the CREATE Medical Physics Research Training Network grant (number 432290) of NSERC, support from NSERC under grants RGPIN 397711‐11 and RGPIN‐2014‐06475 and support from the CIHR under grants MOP‐114910, MOP‐136774 and MOP‐102550.

Quality factors for space radiation: A new approach

NASA has derived new models for radiological risk assessment based on epidemiological data and radiation biology including differences in Relative Biological Effectiveness for leukemia and solid tumors. Comprehensive approaches were used to develop new risk cross sections and the extension of these into recommendations for risk assessment during space missions. The methodology relies on published data generated and the extensive research initiative managed by the NASA Human Research Program (HRP) and reviewed by the National Academy of Sciences. This resulted in recommendations for revised specifications of quality factors, QNASA(Z,β) in terms of track structure concepts that extend beyond LET alone. The new paradigm for quality factors placed demands on radiation monitoring procedures that are not satisfied by existing dosimetry systems or particle spectrometers that are practical for space exploration where mass, volume, band width and power consumption are highly constrained. We have proposed a new definition of quality factors that relaxes the requirements for identifying charge, Z, and velocity, β, of the incident radiation while still preserving the functional form of the inherent risk functions. The departure from the exact description of QNASA(Z,β) is that the revised values are new functions of LET for solid cancers and leukemia. We present the motivation and process for developing the revised quality factors. We describe results of extensive simulations using GCR distributions in free space as well as the resulting spectra of primary and secondary particles behind aluminum shields and penetration through water. In all cases the revised dose averaged quality factors agreed with those based on the values obtained using QNASA(Z,β). This provides confidence that emerging technologies for space radiation dosimetry can provide real time measurements of dose and dose equivalent while satisfying constraints on size, mass, power and bandwidth. The revised quality factors are sufficiently generalized to be applicable to radiation protection practices beyond space exploration.

Dilemmas concerning dose distribution and the influence of relative biological effect in proton beam therapy of medulloblastoma

To improve medulloblastoma proton therapy. Although considered ideal for proton therapy, there are potential disadvantages. Expected benefits include reduced radiation-induced cancer and circulatory complications, while avoiding small brain volumes of dose in-homogeneity when compared with conventional X-rays. Several aspects of proton therapy might contribute to reduced tumour control due to (a) the use of more homogenous dose levels which can result in under-dosage, (b) differences in relative biological effectiveness (RBE) between that prescription RBE of 1.1 and the RBE of brain and spinal cord (likely to exceed 1.1) and in medulloblastoma cells (where RBE is likely to be below 1.1). Such changes, although speculative for RBE, might result in potential underdosage of tumour cells and a higher bio-effect in brain tissue. Dose distributions for X-ray and proton treatment are compared, with allocation of likely RBE values for fast growing medullolastoma cells and stable central nervous system tissue. These physical and radiobiological factors are shown to combine to give a higher risk of tumour recurrence with further risks on tumour control when dose reduction schedules used for X-ray therapy are replicated for proton therapy for "low-risk" patients. The dose distributions and prescribed doses of proton therapy, taking into account RBE, in children and adults with medulloblastoma, need to be reconsidered.

Induction and repair of DNA double-strand breaks assessed by gamma-H2AX foci after irradiation with pulsed or continuous proton beams

In particle tumor therapy including beam scanning at accelerators, the dose per voxel is delivered within about 100ms. In contrast, the new technology of laser plasma acceleration will produce ultimately shorter particle packages that deliver the dose within a nanosecond. Here, possible differences for relative biological effectiveness in creating DNA double-strand breaks in pulsed or continuous irradiation mode are studied. HeLa cells were irradiated with 1or 5Gy of 20-MeV protons at the Munich tandem accelerator, either at continuous mode (100ms), or applying a single pulse of 1-ns duration. Cells were fixed 1h after 1-Gy irradiation and 24h after 5-Gy irradiation, respectively. A dose-effect curve based on five doses of X-rays was taken as reference. The total number of phosphorylated histone H2AX (gamma-H2AX) foci per cell was determined using a custom-made software macro for gamma-H2AX foci counting. For 1h after 1-Gy 20-MeV proton exposures, values for the relative biological effectiveness (RBE) of 0.97±0.19 for pulsed and 1.13±0.21 for continuous irradiations were obtained in the first experiment 1.13±0.09 and 1.16±0.09 in the second experiment. After 5Gy and 24h, RBE values of 0.99±0.29 and 0.91±0.23 were calculated, respectively. Based on the gamma-H2AX foci numbers obtained, no significant differences in RBE between pulsed and continuous proton irradiation in HeLa cells were detected. These results are well in line with our data on micronucleus induction in HeLa cells.

The potential impact of relative biological effectiveness uncertainty on charged particle treatment prescriptions

There continues to be uncertainty regarding the relative biological effectiveness (RBE) values that should be used in charged particle radiotherapy (CPT) prescriptions using protons and heavier ions. This uncertainty could potentially offset the physical dose advantage gained by exploiting the Bragg peak effect and it needs to be clearly understood by clinicians and physicists. This paper introduces a combined radiobiological and physical sparing factor (S). This factor includes the ratio of the most relevant physical doses in tumour and normal tissues in combination with their respective RBE values and can be extended to contain the uncertainties in RBE. S factors can be used to study, in a simplified way for tentative modelling, those clinical situations in which high-linear energy transfer (LET) irradiations are likely to prove preferable over their low-LET counterparts for a matched tumour iso-effect. In cases where CPT achieves an excellent degree of normal tissue sparing, the radiobiological factors become less important and any uncertainties in the tumour and healthy tissue RBE values are correspondingly less problematic. When less normal tissue sparing can be achieved, however, the RBE uncertainties assume greater relevance and will affect the reliability of the dose-prescription methodology. More research is required to provide accurate RBE estimation, focusing attention on the associated statistical uncertainties and potential differences in RBE between different tissue types.

Apparent absence of a proton beam dose rate effect and possible differences in RBE between Bragg peak and plateau

Respiration-gated irradiation for a moving target requires a longer time to deliver single fraction in proton radiotherapy (PRT). Ultrahigh dose rate (UDR) proton beam, which is 10-100 times higher than that is used in current clinical practice, has been investigated to deliver daily dose in single breath hold duration. The purpose of this study is to investigate the survival curve and relative biological effectiveness (RBE) of such an ultrahigh dose rate proton beam and their linear energy transfer (LET) dependence. HSG cells were irradiated by a spatially and temporally uniform proton beam at two different dose rates: 8 Gy/min (CDR, clinical dose rate) and 325 Gy/min (UDR, ultrahigh dose rate) at the Bragg peak and 1.75 (CDR) and 114 Gy/min (UDR) at the plateau. To study LET dependence, the cells were positioned at the Bragg peak, where the absorbed dose-averaged LET was 3.19 keV/microm, and at the plateau, where it was 0.56 keV/microm. After the cell exposure and colony assay, the measured data were fitted by the linear quadratic (LQ) model and the survival curves and RBE at 10% survival were compared. No significant difference was observed in the survival curves between the two proton dose rates. The ratio of the RBE for CDR/UDR was 0.98 +/- 0.04 at the Bragg peak and 0.96 +/- 0.06 at the plateau. On the other hand, Bragg peak/plateau RBE ratio was 1.15 +/- 0.05 for UDR and 1.18 +/- 0.07 for CDR. Present RBE can be consistently used in treatment planning of PRT using ultrahigh dose rate radiation. Because a significant increase in RBE toward the Bragg peak was observed for both UDR and CDR, further evaluation of RBE enhancement toward the Bragg peak and beyond is required.

MO‐SAM‐BRB‐01: Biological Aspects of Heavy Charged Particle Radiation Therapy

The relative biological effectiveness (RBE) is defined as the ratio of the doses required by two radiations to cause the same level of effect. Thus, the RBE depends on the dose and the biological endpoint.Proton therapy has been based on the use of a generic RBE of 1.1, which is applied to all treatments independent of dose/fraction, position in the irradiated volume, initial beam energy or the particular tissue. The variability of RBE in clinical situations is believed to be within 10% but quantitative dependencies of the RBE on various physical and biological properties are disregarded. The magnitude of RBE values and their variations is significantly larger for Carbon ion therapy. Studies have demonstrated significant RBE values of more than 3 in clinically relevant scenarios for Carbon ions. Further, there might be considerable variations in RBE within the irradiated volume that are being considered in treatment planning and delivery.Heavy ions have a potential advantage compared to protons when it comes to their therapeutic ratio due to an elevated RBE in the tumor (based on the oxygen enhancement ratio and higher average LET values) compared to the surrounding tissue. However, on the other hand, at present there are still considerable uncertainties in heavy ion RBE values. Elevated RBE values (even for protons) might be expected particularly near the edges of the high‐dose volume because doses may be deposited by high‐LET particles. The increase in RBE as a function of depth in the patient results in an extension of the bio‐effective range of the beam. Further, because RBE values may increase with deceasing dose causing elevated RBE values for organs at risk compared to the target area. In order to incorporate detailed RBE modeling in treatment planning as a function of LET, dose and endpoint, two aspects have to be considered. Firstly, the available information from experimental studies and secondly, our ability to calculate RBE values for a given treatment plan based on parameters extracted from such experiments. RBE values are often based on cell survival data because this is the main endpoint of interest in radiation therapy. However, one migt expect differences in RBE for cell survival compared to cell mutation, the latter being an important endpoint for late effects.This educational session will focus on summarizing the mechanisms behind RBE variations among treatment modalities. Further, RBE variations as a function of LET, tissue and dose will be presented based on experimental and simulated data for proton and Carbon ion beams. Finally, different approaches for theoretical modeling of RBE values for treatment planning purposes will be discussed briefly.Learning Objectives:1. Understand the mechanisms behind heavy charged particle RBE values2. Understand the variations of RBE as a function of physical and biological parameters3. Understand the clinical implication of RBE values in proton and Carbon ion therapy

Relative biological effectiveness of fast neutrons in a multiorgan assay for apoptosis in mouse

This study compared the effects of high linear energy transfer (LET) fast neutrons on the induction of apoptosis in several tissue types (hair follicle, intestine crypt, testis) of ICR mouse exposed to low LET 60Co gamma-rays. The changes that occurred from 0 to 24 h after exposing the mice to either 2 Gy of gamma-rays (2 Gy/min) or 0.8 Gy of neutrons (94 mGy/min, 35 MeV) were examined. The maximum frequency of apoptosis was observed at 8 or 12 h after irradiation. The mice that had received 0-8 Gy of gamma-rays or 0-1.6 Gy of neutrons were examined 8 h after irradiation. The best-fitting dose-response curves were linear-quadratic, and there was a significant relationship between the number of apoptotic cells and the dose. The stained products in the TUNEL-positive cells or bodies correlated with the typical morphologic characteristics of apoptosis observed by optical microscopy. In the follicles showing an apoptosis frequency between 2 and 14 per hair follicle, the relative biological effectiveness (RBE) of the neutrons in the small and large follicles was 2.09 +/- 0.31 and 2.15 +/- 0.18, respectively. In the intestine crypts showing an apoptosis frequency between 1 and 3 per crypt, the RBE of the neutrons was 4.03 +/- 0.06 and 3.87 +/- 0.04 in the base and total crypts, respectively. The RBE of the neutrons in the seminiferous tubule showing an apoptosis frequency between 0.5 and 2 per tubule was 5.18 +/- 0.06. The results determined the time-response relations and the RBE for fast neutron-induced apoptosis in several organs at the same time. The differences in RBE observed between the high and low LET radiation and it is believed that the difference in the DSB repair capacity in hair follicle, intestine crypt, and seminiferous tubule cells plays a role in determining the RBE of the high-LET radiation for the induced apoptotic cell formation.

Analysis of secondary electron emission spectra of equal-LET protons and α particles for purposes of radiation quality and spaceflight hazard assessment

Amongst the great variety of heavy particles present in the galactic and solar cosmic ray spectra, hydrogen and helium nuclei are significantly more abundant than all other heavier ions and, as such, represent a major radiation hazard to humans in space. Experimental data have suggested that differences in relative biological effectiveness (RBE) exist between the two species at the same value of linear energy transfer (LET). This has consequences for heavily ionising radiation protection procedures, which currently still assume a simple dependence of radiation quality on LET. By analysing the secondary electron (δ-ray) emission spectra of protons and α particles, in terms of the spatial characteristics of energy deposition in cellular targets and the likelihood of complex lesion formation, a numerical quantity representing biological effectiveness is generated. When expressed relative to a reference radiation, this quantity is found to differ for protons and α particles of the same LET, demonstrating not only the ion-specific nature of RBE but also the inadequacy of specifying radiation quality as a function of LET only. Such a method for numerically assessing radiation quality may have implications for procedures for heavy ion protection in space at low doses and for understanding the initial mechanisms of radiation action.

Relative biological effectiveness (RBE) of 0·43-MeV neutrons and 250-kVp X-rays for somatic aberrations in Tradescantia subacaulis Bush

The RBE of 0·43-MeV monoenergetic neutrons and 250-kVp X-rays for somatic cell aberrations or mutations in the heterozygous Tradescantia subacaulis Bush (clone 4405) was determined and compared with known RBE values for similar end points in Tradescantia clone 02. Young inflorescences were irradiated with 0·04–15 rad of 0·43-MeV neutrons and with 6·25–150 rad of 250-kVp X-rays. Stamen hairs were scored daily over the peak response period from day 11–15 postirradiation. Data were recorded for cell color changes from normal blue to pink, plum and colorless and for changes in cell size from normal to dwarf and giant. Dose-response curves based on 5-day mean numbers of aberrant events were plotted for the various end points and their natural slopes computed. The slopes of the dose-response curves for each aberrant cell type resulting from X irradiation were higher than +1 but in 5 out of 6 cases significantly less than +1 for neutron irradiation. RBE values increased with decreasing doses, at least over the dose range investigated. Maximum RBE values for plum, dwarf, colorless, pink and giant were 124, 110, 99, 93 and 57 respectively. The RBE values were higher for color changes but lower for cell size aberrations in T. subacaulis than in clone 02. The reasons for these differences in RBE are not known. The possible dependence of RBE on interphase chromosome volume (ICV) is discussed.

A device for the measurement of dose as a function of specific ionization.

The physical parameters influencing the biological effect of ionizing radiation are the energy delivered to the tissues affected and the ion density along the paths of the charged particles producing the ions. Variations of the latter quantity are believed to be responsible for differences in relative biological effectiveness (R.B.E.). Zirkle has suggested the use of the concept of “linear energy transfer” (L.E.T.) in tissue. This is more fundamental than specific ionization in a gas, but the latter, which may be measured much more readily, may be presumed to be proportional to the former within about 10 per cent in most cases. At present there are several methods by which the total energy imparted to tissue by ionizing radiations can be determined. In this laboratory, tissue-equivalent ionization chambers (1) have been developed on the basis of the Bragg-Gray principle. Employing these chambers, one can obtain a measure of the total energy delivered per gram of tissue by particles of any specific ionization. Since these chambers, when exposed to the same radiation field, are traversed by ionizing particles of the same type, energy, and direction as is tissue, it appeared feasible to develop a method whereby the specific ionization of individual particles crossing the cavity might be determined. Since the ionization produced by individual particles will often be too small to be detected directly, recourse must be taken to gas multiplication. Hence the chamber must operate as a proportional counter. In this case the pulse obtained will be proportional to the ionization produced by the particle traversing the counter. The total ionization will be the product of specific ionization and path length in the gas volume. Discrimination on the basis of pulse height alone cannot lead to a clear distinction between particles of different specific ionization, since the pulse produced by a lightly ionizing particle having a long trajectory may be equally as large as that produced by a heavily ionizing particle having a short path. If the particles involved are of greatly different specific ionization, e.g., electrons and protons, a reasonably satisfactory separation of pulses produced by either type can be achieved, and it is upon this basis that Hurst and Ritchie (2) developed their neutron dosimeter. If, however, detailed information on specific ionization is required, allowance must be made for the distribution of geometric path lengths. This may be done most easily for the simplest kind of cavity, which is a sphere. This shape has the additional advantage of being isotropic and directional response is thus absent. Formula 1 in the Appendix gives a general expression for the distribution of path lengths intercepted by a spherical cavity at any distance from a point source. The most important practical case is the one where the source is effectively at infinity (i.e., many sphere radii away).