An image-guided precision proton radiation platform for preclinical in vivo research.

There are many unknowns in the radiobiology of proton beams and other particle beams. We describe the development and testing of an image-guided low-energy proton system optimized for radiobiological research applications. A 50 MeV proton beam from an existing cyclotron was modified to produce collimated beams (as small as 2 mm in diameter). Ionization chamber and radiochromic film measurements were performed and benchmarked with Monte Carlo simulations (TOPAS). The proton beam was aligned with a commercially-available CT image-guided x-ray irradiator device (SARRP, Xstrahl Inc.). To examine the alternative possibility of adapting a clinical proton therapy system, we performed Monte Carlo simulations of a range-shifted 100 MeV clinical beam. The proton beam exhibits a pristine Bragg Peak at a depth of 21 mm in water with a dose rate of 8.4 Gy min-1 (3 mm depth). The energy of the incident beam can be modulated to lower energies while preserving the Bragg peak. The LET was: 2.0 keV µm-1 (water surface), 16 keV µm-1 (Bragg peak), 27 keV µm-1 (10% peak dose). Alignment of the proton beam with the SARRP system isocenter was measured at 0.24 mm agreement. The width of the beam changes very little with depth. Monte Carlo-based calculations of dose using the CT image data set as input demonstrate in vivo use. Monte Carlo simulations of the modulated 100 MeV clinical proton beam show a significantly reduced Bragg peak. We demonstrate the feasibility of a proton beam integrated with a commercial x-ray image-guidance system for preclinical in vivo studies. To our knowledge this is the first description of an experimental image-guided proton beam for preclinical radiobiology research. It will enable in vivo investigations of radiobiological effects in proton beams.

Imaging and dosimetric errors in 4D PET/CT-guided radiotherapy from patient-specific respiratory patterns: a dynamic motion phantom end-to-end study.

Effective positron emission tomography / computed tomography (PET/CT) guidance in radiotherapy of lung cancer requires estimation and mitigation of errors due to respiratory motion. An end-to-end workflow was developed to measure patient-specific motion-induced uncertainties in imaging, treatment planning, and radiation delivery with respiratory motion phantoms and dosimeters. A custom torso phantom with inserts mimicking normal lung tissue and lung lesion was filled with [(18)F]FDG. The lung lesion insert was driven by six different patient-specific respiratory patterns or kept stationary. PET/CT images were acquired under motionless ground truth, tidal breathing motion-averaged (3D), and respiratory phase-correlated (4D) conditions. Target volumes were estimated by standardized uptake value (SUV) thresholds that accurately defined the ground-truth lesion volume. Non-uniform dose-painting plans using volumetrically modulated arc therapy were optimized for fixed normal lung and spinal cord objectives and variable PET-based target objectives. Resulting plans were delivered to a cylindrical diode array at rest, in motion on a platform driven by the same respiratory patterns (3D), or motion-compensated by a robotic couch with an infrared camera tracking system (4D). Errors were estimated relative to the static ground truth condition for mean target-to-background (T/Bmean) ratios, target volumes, planned equivalent uniform target doses, and 2%-2 mm gamma delivery passing rates. Relative to motionless ground truth conditions, PET/CT imaging errors were on the order of 10-20%, treatment planning errors were 5-10%, and treatment delivery errors were 5-30% without motion compensation. Errors from residual motion following compensation methods were reduced to 5-10% in PET/CT imaging, <5% in treatment planning, and <2% in treatment delivery. We have demonstrated that estimation of respiratory motion uncertainty and its propagation from PET/CT imaging to RT planning, and RT delivery under a dose painting paradigm is feasible within an integrated respiratory motion phantom workflow. For a limited set of cases, the magnitude of errors was comparable during PET/CT imaging and treatment delivery without motion compensation. Errors were moderately mitigated during PET/CT imaging and significantly mitigated during RT delivery with motion compensation. This dynamic motion phantom end-to-end workflow provides a method for quality assurance of 4D PET/CT-guided radiotherapy, including evaluation of respiratory motion compensation methods during imaging and treatment delivery.

SU-E-T-239: In Vivo Dosimetry with Surface Diodes during Total Body Irradiation: A Patient Thickness Factor to Correct Midline Dose.

PURPOSE: In vivo dosimetry (IVD) assessment of treatment dose is important when delivering total body irradiation (TBI). One method is to average AP and PA surface diode measurements and compare them to prescribed midline doses. We designed phantom studies to examine the impact of patient thickness on surface IVD measurements under TBI conditions. METHODS: Phantom studies were designed to assess the effects of patient thickness on diode IVD. Sun Nuclear QED diodes with inherent buildup were placed on anterior and posterior surfaces of a solid water phantom. Phantom thickness was varied between 20 and 40 cm. A PTW farmer chamber was inserted in the center of the phantom at 425 SSD to reflect prescribed midline dose, and 50 cGy was delivered to midline with 18 MV photons. Averaged entrance and exit diode doses were then compared to farmer chamber measurements of phantom midline dose. RESULTS: A trend of increased deviation with increasing umbilicus thickness was observed between averaged surface diodes and midline farmer chamber measurements. Averaged surface diode dose ranged from 49.6 cGy (20 cm thickness) to 52.1 cGy (40 cm thickness). Interpolation of diode measurements to midline resulted in linear overestimation of delivered dose relative to farmer chamber measurements at midline, up to 6.8% at 40 cm umbilicus thickness. CONCLUSION: Accurate in vivo dosimetry at time of patient TBI is important to allow individual correction of MU exposure and tissue compensation. Without patient thickness correction, overresponse of surface diodes may lead to unnecessary clinical intervention to treatment MU or compensation and insufficient midline dose. Additionally, SAD setup is preferable to SSD setup to minimize thickness non-linearity. In conclusion, thickness correction factors should be used to generate expected diode readings for patients with thickness greater than 30 cm.

Patient-specific margins for proton therapy of lung.

Lung cancer treatment presents a greater treatment planning and treatment delivery challenge in proton beam therapy compared to conventional photon therapy due to the proton beam's energy deposition sensitivity to the breathing-induced dynamic tissue density variations along the beam path. Four-dimensional computed tomography (4D-CT) has been defined as the explicit inclusion of temporal changes of tumor and normal organ mobility into an image series. It allows more accurate delineation of lung cancer target volumes by suppression of any breathing motion artifacts present in the CT images. It also allows analysis of the tumor's 3D spatial movement within a breathing phase cycle. The motivation for this study was to investigate dosimetric errors caused by lung tumor motion in order to find an optimal method of design for patient compensators and apertures for a passive scattering beam delivery system and treatment of the patient under free breathing conditions. In this study, the maximum intensity projection (MIP) method was compared to patient-specific internal margin designs based on a single breathing phase at the end-of inhale (EOI) or middle-of-exhale (MOE). It was found that MIP method provides superior tumor dose distribution compared to patient-specific internal margin designs derived from 4D-CT.

Morphological study of endothelial cells during freezing.

Microvascular injury is recognized as a major tissue damage mechanism of ablative cryosurgery. Endothelial cells lining the vessel wall are thought to be the initial target of freezing. However, details of this injury mechanism are not yet completely understood. In this study, ECMatrix 625 was used to mimic the tumour environment and to allow the endothelial cells cultured in vitro to form the tube-like structure of the vasculature. The influence of water dehydration on the integrity of this structure was investigated. It was found that the initial cell shape change was mainly controlled by water dehydration, dependent on the cooling rate, resulting in the shrinkage of cells in the direction normal to the free surface. As the cooling was prolonged and temperature was lowered, further cell shape change could be induced by the chilling effects on intracellular proteins, and focal adhesions to the basement membrane. Quantitative analysis showed that the freezing induced dehydration greatly enhanced the cell surface stresses, especially in the axial direction. This could be one of the major causes of the final breaking of the cell junction and cell detachment.

A Monte Carlo based development of a cavity theory for solid state detectors irradiated in electron beams.

Recent Monte Carlo simulations have shown that the assumption in the small cavity theory (and the extension of the small cavity theory by Spencer-Attix) that the cavity does not perturb the electron fluence is seriously flawed. For depths beyond dmax not only is there a significant difference between the energy spectra in the medium and in the solid cavity material but there is also a significant difference in the number of low-energy electrons which cannot travel across the solid cavity and hence deposit their dose in it (i.e. stopper electrons whose residual range is less than the cavity thickness). The number of these low-energy electrons that are not able to travel across the solid state cavity increases with depth and effective thickness of the detector. This also invalidates the assumption in the small cavity theory that most of the dose deposited in a small cavity is delivered by crossers. Based on Monte Carlo simulations, a new cavity theory for solid state detectors irradiated in electron beams has been proposed as: Dmed(p) = meanDdet(p) x s(med,det)S-A x gamma(p)c x S(T) where Dmed(p) is the dose to the medium at point p. MeanDdet(p) is the average detector dose to the same point, s(med,det)S-A is the Spencer-Attix mass collision stopping power ratio of the medium to the detector material, gamma(P)c is the electron fluence perturbation correction factor and S(T) is a stopper-to-crosser correction factor to correct for the dependence of the stopper-to-crosser ratio on depth and the effective cavity size. Monte Carlo simulations have been computed for all the terms in this equation. The new cavity theory has been tested against the Spencer-Attix cavity equation as the small cavity limiting case and also Monte Carlo simulations.

Optimized treatment planning for prostate cancer comparing IMPT, VHEET and 15 MV IMXT.

The merits of intensity-modulated very-high energy electron therapy (VHEET) and intensity-modulated proton therapy (IMPT) in relation to intensity-modulated x-ray therapy (IMXT) with respect to the treatment of the prostate have been quantified. Optimized dose distributions were designed for 5-11 beams of 250 MeV VHEET and 15 MV IMXT as well as 1-9 beam ports of IMPT. In the case of the comparison between 250 MeV VHEET and 15 MV IMXT, it was found that the quality of target coverage achievable with VHEET was comparable to or sometimes better than that provided by IMXT. However, VHEET provided an improvement over IMXT in the dose sparing of the sensitive structures and normal tissues. Compared to IMXT, VHEET decreased the mean rectal dose and bladder dose by up to 10% of the prescribed target dose, while reducing by up to 12% of the prescribed target dose the integral dose to normal tissues. In quantifying the merits of IMPT relative to IMXT, it was found that using intensity-modulated proton beams for inverse planning instead of intensity-modulated photon beams improved target dose homogeneity by up to 1.3% of the prescribed target dose, while reducing the mean rectal dose, bladder dose, and normal tissue integral dose by up to 27%, 30% and 28% of the prescribed target dose respectively. The comparison of optimized planning for IMPT and VHEET showed that the quality of target coverage achievable with IMPT is comparable to or better (by up to 1.3% of the prescribed target dose) than that provided by VHEET. Compared to VHEET, IMPT delivered a mean rectal dose and a bladder dose that was lower by up to 17% and 23% of prescribed target dose respectively, and also reduced the integral dose to normal tissues by up to 17% of the prescribed target dose. These results indicate that of the three modalities the greatest dose escalation will be possible with IMPT, then VHEET, and then IMXT. It follows that IMPT will result in the highest probability of complication-free tumour control, while IMXT will provide the lowest probability.

Optimization of intensity-modulated very high energy (50-250 MeV) electron therapy.

This work evaluates the potential of very high energy (50-250 MeV) electron beams for dose conformation and identifies those variables that influence optimized dose distributions for this modality. Intensity-modulated plans for a prostate cancer model were optimized as a function of the importance factors, beam energy and number of energy bins, number of beams, and the beam orientations. A trial-and-error-derived constellation of importance factors for target and sensitive structures to achieve good conformal dose distributions was 500, 50, 10 and I for the target, rectum, bladder and normal tissues respectively. Electron energies greater than 100 MeV were found to be desirable for intensity-modulated very high energy electron therapy (VHEET) of prostate cancer. Plans generated for lower energy beams had relatively poor conformal dose distributions about the target region and delivered high doses to sensitive structures. Fixed angle beam treatments utilizing a large number of fields in the range 9-21 provided acceptable plans. Using more than 21 beams at fixed gantry angles had an insignificant effect on target coverage, but resulted in an increased dose to sensitive structures and an increased normal tissue integral dose. Minor improvements in VHEET plans utilizing a 'small' number (< or =9) of beams may be achieved if, in addition to intensity modulation, energy modulation is implemented using a small number (< or =3) of beam energies separated by 50 to 100 MeV. Rotation therapy provided better target dose homogeneity but unfortunately resulted in increased rectal dose, bladder dose and normal tissue integral dose relative to the 21-field fixed angle treatment plan. Modulation of the beam energy for rotation therapy had no beneficial consequences on the optimized dose distributions. Lastly, selection of beam orientations influenced the optimized treatment plan even when a large number of beams (approximately 15) were employed.

Flounder antifreeze peptides increase the efficacy of cryosurgery.

Type I antifreeze protein (AFP) from the winter flounder (Pseudopleuronectes americanus) was used as an adjuvant to cryosurgery of subcutaneous tumors of Dunning AT-1 rat prostate cells grown in Copenhagen rats. The cryosurgical procedure was performed with a commercially available cryosurgery device (CRYO-HIT, Galil Medical) with clinically relevant single- and double-freeze protocols. Injury was assessed with the alamar blue indicator of metabolic activity. The assay gave anomalous results when used to assess the extent of injury immediately following the procedure, underestimating the extent of injury. However, a double-freeze procedure with antifreeze protein present was found to give significantly better ablation than a double-freeze without AFP or a single-freeze with or without AFP.

Simultaneous optimization of cryoprobe placement and thermal protocol for cryosurgery.

We demonstrate that it is possible to simultaneously optimize multiple cryoprobe placements and their thermal protocol for one freeze-thaw cycle. A numerical optimization algorithm is used and three different forms of objective function are examined in terms of algorithm convergence rate, minimum value of the chosen objective function, temperature-volume histograms and isotherm distributions. The optimization results depend on the initial values of the variables, the form of the objective function, optimization goals and the mathematical method adopted for gradient calculation. The proposed optimization model offers significant advantages over the previously reported semi-empirical approach to conformal cryotherapy, such as the ability to handle an unlimited number of variables and eliminating the need for the user input between iterations, thereby reducing, if not removing, the subjectivity of cryosurgery treatment planning.

A model for the time dependent three-dimensional thermal distribution within iceballs surrounding multiple cryoprobes.

A time dependent three-dimensional finite difference model of iceball formation about multiple cryoprobes has been developed and compared to experimental data. Realistic three-dimensional probe geometry is specified and the number of cryoprobes, the cryoprobe cooling rates, and the locations of the probes are arbitrary inputs by the user. The simulation accounts for observed longitudinal thermal gradients along the cryoprobe tips. Thermal histories for several points around commercially available cryoprobes have been predicted within experimental error for one, three, and five probe configurations. The simulation can be used to generate isotherms within the iceball at arbitrary times. Volumes enclosed by the iceball and any isotherms may also be computed to give the ablative ratio, a measure of the iceball's killing efficiency. This ratio was calculated as the volume enclosed by a critical isotherm divided by the total volume of the iceball for assumed critical temperatures of -20 and -40 degrees C. The ablative ratio for a single probe is a continuously decreasing function of time but when multiple probe configurations are used the ablative ratio increases to a maximum and then essentially plateaus. Maximum values of 0.44 and 0.55 were observed for three and five probe configurations, respectively, with an assumed critical temperature of -20 degrees C. Assuming a critical temperature of -40 degrees C, maximum ablative ratios of 0.21 and 0.3 for three and five probe configurations, respectively, were observed.

The energy-dependent electron loss model for pencil beam dose kernels.

The 'monoenergetic' electron loss model was derived in a previous work to account for pathlength straggling in the Fermi-Eyges pencil beam problem. In this paper, we extend this model to account for energy-loss straggling and secondary knock-on electron transport in order to adequately predict a depth dose curve. To model energy-loss straggling, we use a weighted superposition of a discrete number of monoenergetic pencil beams with different initial energies where electrons travel along the depth-energy characteristics in the continuous slowing down approximation (CSDA). The energy straggling spectrum at depth determines the weighting assigned to each monoenergetic pencil beam. Supplemented by a simple transport model for the secondary knock-on electrons, the 'energy-dependent' electron loss model predicts both lateral and depth dose distributions from the electron pencil beams in good agreement with Monte Carlo calculations and measurements. The calculation of dose distribution from a pencil beam takes 0.2 s on a Pentium III 500 MHz computer. Being computationally fast, the 'energy-dependent' electron loss model can be used for the calculation of 3D energy deposition kernels in dose optimization schemes without using precalculated or measured data.

CPP calculation of multiple scattering distributions for charged particles penetrating compounds or mixtures.

Charged particle multiple scattering distributions may be constructed from individual atomic scattering events on the basis of compound Poisson process (CPP) theory. We present a CPP method for computing multiple scattering transition probability densities from charged particles penetrating compounds and mixtures. Water as a scattering medium provides here an example of the calculation method which is applicable to compounds or mixtures. Electrons are chosen as examples of charged particle beams. The Rutherford single scattering cross section and a partial wave analysis single scattering cross section are chosen as example cross sections. Transition probability densities predicted on the basis of CPP theory can be calculated with great accuracy for the improvement of radiation dose calculations. The advantages of the CPP method are (a) an effective atomic number need not be defined for the scattering medium, (b) it can be applied in both spherical and planar coordinate systems, and (c) it does not require any specific form for the single scattering cross section.

Shielding for neutron scattered dose to the fetus in patients treated with 18 MV x-ray beams.

Neutrons are associated with therapeutic high energy x-ray beams as a contaminant that contributes significant unwanted dose to the patient. Measurement of both photon and neutron scattered dose at the position of a fetus from chest irradiation by a large field 18 MV x-ray beam was performed using an ionization chamber and superheated drop detector, respectively. Shielding construction to reduce this scattered dose was investigated using both lead sheet and borated polyethylene slabs. A 7.35 cm lead shield reduced the scattered photon dose by 50% and the scattered neutron dose by 40%. Adding 10 cm of 5% borated polyethylene to this lead shield reduced the scattered neutron dose by a factor of 7.5 from the unshielded value. When the 5% borated polyethylene was replaced by the same thickness of 30% borated polyethylene there was no significant change in the reduction of neutron scatter dose. The most efficient shield studied reduced the neutron scatter dose by a factor of 10. The results indicate that most of the scattered neutrons present at the position of the fetus produced by an 18 MV x-ray beam are of low energy and in the thermal to 0.57 MeV range since lead is almost transparent to neutrons with energies lower than 0.57 MeV. This article constitutes the first report of an effective shield to reduce neutron dose at the fetus when treating a pregnant woman with a high energy x-ray beam.

Proton loss model for therapeutic beam dose calculations.

A transport algorithm called the proton loss (PL) model is developed for proton pencil beams of therapeutic energies. The PL model takes into account inelastic nuclear reactions, pathlength straggling, and energy-loss straggling and predicts the 3D dose distribution from a proton pencil beam. In proton beams, the multiple scattering and ionizational energy loss processes approach their diffusional limit where scattering and energy loss probability densities become Gaussian. Therefore we chose to derive the PL model from the Fermi-Eyges diffusional multiple scattering theory and the Gaussian theory of energy straggling. We first introduce a generalization of the Fermi-Eyges equation for proton pencil beams, labeled the proton loss (PL) transport equation. This new equation includes terms that model inelastic nuclear reactions as a depth-dependent absorption and pathlength straggling as a quasi-absorption. Then energy straggling is taken into account by using a weighted superposition of a discrete number of elementary pencil beams. These elementary pencil beams have different initial energies and lose energy according to the CSDA, thus they have different ranges of penetration. A final solution for the proton beam transport is obtained as a linear combination of elementary pencil beam solutions with weights defined by the Gaussian evolution of the proton energy spectrum with depth. A numerical comparison of the dose distribution predictions of the PL model with measurements and PTRAN Monte Carlo simulations indicates the model is both computational fast and accurate.

A semi-empirical treatment planning model for optimization of multiprobe cryosurgery.

A model is presented for treatment planning of multiprobe cryosurgery. In this model a thermal simulation algorithm is used to generate temperature distribution from cryoprobes, visualize isotherms in the anatomical region of interest (ROI) and provide tools to assist estimation of the amount of freezing damage to the target and surrounding normal structures. Calculations may be performed for any given freezing time for the selected set of operation parameters. The thermal simulation is based on solving the transient heat conduction equation using finite element methods for a multiprobe geometry. As an example, a semi-empirical optimization of 2D placement of six cryoprobes and their thermal protocol for the first freeze cycle is presented. The effectiveness of the optimized treatment protocol was estimated by generating temperature-volume histograms and calculating the objective function for the anatomy of interest. Two phantom experiments were performed to verify isotherm locations predicted by calculations. A comparison of the predicted 0 degrees C isotherm with the actual iceball boundary imaged by x-ray CT demonstrated a spatial agreement within +/-2 mm.

Suppression of high-density artefacts in x-ray CT images using temporal digital subtraction with application to cryotherapy.

Image guidance in cryotherapy is usually performed using ultrasound. Although not currently in routine clinical use, x-ray CT imaging is an alternative means of guidance that can display the full 3D structure of the iceball, including frozen and unfrozen regions. However, the quality of x-ray CT images is compromised by the presence of high-density streak artefacts. To suppress these artefacts we applied temporal digital subtraction (TDS). This TDS method has the added advantage of improving the grey scale contrast between frozen and unfrozen tissue in the CT images. Two sets of CT images were taken of a phantom material, cryoprobes and a urethral warmer (UW) before and during the cryoprobe freeze cycle. The high density artefacts persisted in both image sets. TDS was performed on these two image sets using the corresponding mask image of unfrozen material and the same geometrical configuration of the cryoprobes and the UW. The resultant difference image had a significantly reduced artefact content. Thus TDS can be used to significantly suppress or eliminate high-density CT streak artefacts without reducing the metallic content of the cryoprobes. In vivo study needs to be conducted to establish the utility of this TDS procedure for CT assisted prostate or liver cryotherapy. Applying TDS in x-ray CT guided cryotherapy will facilitate estimation of the number and location of all frozen and unfrozen regions, potentially making cryotherapy safer and less operator dependent.

Electron fluence perturbation correction factors for solid state detectors irradiated in megavoltage electron beams.

The perturbation correction factor gamma(p) is defined as the deviation of the absorbed dose in the medium from that predicted by the Spencer-Attix extension of the Bragg-Gray cavity theory where the medium occupies exactly the same volume as the solid state cavity and the electron fluence energy spectrum in the cavity is identical in shape, but not necessarily in magnitude, to that in the medium. The value of gamma(p) has been examined for TL detectors irradiated in megavoltage electron beams (5-20 MeV) using the EGS4 Monte Carlo code. LiF and CaF2 solid state detectors simulated were standard size discs of thickness 1 mm and diameter 3.61 mm irradiated in a water phantom with their centres at d(max) or close to it. Values of gamma(p) for LiF ranged from 0.998 +/- 0.005 to 0.994 +/- 0.005 for electron beams with initial energies of 5 and 20 MeV respectively. For CaF2 the corresponding values were 0.956 +/- 0.006 to 0.989 +/- 0.006 for the same size cavities irradiated at the same depth. EGS4 Monte Carlo simulations demonstrate that the total electron fluence (primary electrons and delta-rays) in these solid state detector materials is significantly different from that in water for the same incident electron energy and depth of irradiation. Thus the Spencer-Attix assumption that the electron fluence energy spectrum in the cavity is identical in shape to that in the medium is violated. Differences in the total electron fluence give rise to electron fluence perturbation correction factors which were up to 5% less than unity for CaF2, indicating a strong violation in this case, but were generally less than 1% for LiF. It is the density of the cavity which perturbs the electron fluence, but it is actually the atomic number differences between the medium and cavity that are responsible for the large electron fluence perturbation correction factors for detectors irradiated close to d(max) because the atomic number affects the change in stopping power with energy. When correction is made for the difference between the electron fluence spectrum in the uniform water phantom and the solid state cavity, the Spencer-Attix cavity equation predicts the dose to water within 0.3% in both clinical and monoenergetic electron beams. Harder's formulation for computing the average mass collision stopping power of water to calcium fluoride, surprisingly, requires perturbation correction factors that are closer to unity than those determined using the Spencer-Attix integrals at depths close to d(max).

Photon fluence perturbation correction factors for solid state detectors irradiated in kilovoltage photon beams.

Dose perturbation correction factors, gamma(p), for LiF, CaF2 and Li2B4O7 solid state detectors have been determined using the EGS4 Monte Carlo code. Each detector was simulated in the form of a disc of diameter 3.61 mm and thickness 1 mm irradiated in a clinical kilovoltage photon beam at a depth of 1 cm in a water phantom. The perturbation correction factor gamma(p) is defined as the deviation of the absorbed dose ratio from the average mass energy absorption coefficient ratio of water to the detector material, (mu(en)/rho)med,det, which is evaluated assuming that the photon fluence spectrum in the medium and in the detector material are identical. We define another mass energy absorption coefficient ratio, (kappa(en)/rho)med,det, which is evaluated using the actual photon fluence spectrum in the medium and detector for LiF and CaF2 rather than assuming they are identical. (kappa(en)/rho)med,det predicts the average absorbed dose ratio of the medium to the detector material within 0.3%. When the difference in atomic number between the cavity and the phantom material is large then their photon fluence spectra will differ substantially resulting in a difference between (kappa(en)/rho)med,det and (mu(en)/rho)med,det. The value of gamma(p) calculated using (mu(en)/rho)med,det is up to 27% greater than unity for a cavity of CaF2 in 50 kV x-rays. When the atomic number of the medium and detector are similar, their photon fluence spectra are similar, and the difference between (kappa(en)/rho)med,det and (mu(en)/rho)med,det is small. For instance their difference for LiF is less than 2%. The average mass energy absorption coefficient ratio, (mu(en)(E)/rho)w,LiF, evaluated using the mean or representative energy, E, is up to 8% different from (mu(en)/rho)w,LiF. For calcium fluoride the difference between (mu(en)/rho)w,CaF2 and (mu(en)(E)/rho)w,CaF2 is up to 42% in the energy range studied.

Depth ionization curves for an unmodulated proton beam measured with different ionization chambers.

Differences in depth dose curves for a 78 MeV unmodulated proton beam were measured with four commercially available ionization chambers. Measurements were performed both in water and in a commercially available solid water phantom. A depth scaling factor (Cpl) was determined from the ratio of depths distal to the Bragg peak where the dose is reduced to 80% of the maximum dose in water and in the solid water phantom. This scaling factor provides good agreement between the ionization curves at all depths in water and in this solid water phantom. There is no significant difference in the value of the depth scaling factor between the ratios (R80wat/R80med) and (R50wat/R50med), or (R100wat/R100med) for 78 MeV unmodulated proton beams. The depth scaling factor for this commercially available solid water phantom is 1.023. An effective point of measurement for a cylindrical ionization chamber was found to be slightly greater than the 50% of the cavity radius proposed by the AAPM-TG25 dosimetry protocol for electron beams and amounts to 62.5% of the cavity radius of cylindrical ionization chambers. The ion collection efficiency, Pion, and the polarity correction factor, Ppol, for all the ionization chambers studied are within 1% and 0.4% of unity, respectively. Absolute doses measured with a parallel plate ionization chamber in water and in the solid water phantom show that the doses measured in the solid water phantom are 1.4% +/- 0.5% lower than in water. The dose rate dependent response of the beam line monitor chamber was also investigated. Agreement between all the chambers was within 1.5% at the dose rates studied but the results showed that all four ionization chambers are less dose rate dependent than the monitor chamber.