Mean Excitation Energy Research Articles

Derived properties from the dipole and generalized oscillator strength distributions of an endohedral confined hydrogen atom

We report the electronic properties of a hydrogen atom confined by a fullerene molecule by obtaining the eigenvalues and eigenfunctions of the time-independent Schrödinger equation by means of a finite-differences approach. The hydrogen atom confinement by a C60 fullerene cavity is accounted for by two model potentials: a square-well and a Woods–Saxon. The Woods–Saxon potential is implemented to study the role of a smooth cavity on the hydrogen atom generalized oscillator strength distribution. Both models characterize the cavity by an inner radius R0, thickness Δ, and well depth V0. We use two different values for R0 and Δ, found in the literature, that characterize H@C60 to analyze the role of the fullerene cage size and width. The electronic properties of the confined hydrogen atom are reported as a function of the well depth V0, emulating different electronic configurations of the endohedral cavity. We report results for the hyper-fine splitting, nuclear magnetic screening, dipole oscillator strength, the static and dynamic polarizability, mean excitation energy, photo-ionization, and stopping cross section for the confined hydrogen atom. We find that there is a critical potential well depth value around V0 = 0.7 a.u. for the first set of parameters and around V0 = 0.9 a.u. for the second set of parameters, which produce a drastic change in the electronic properties of the endohedral hydrogen system. These values correspond to the first avoided crossing on the energy levels. Furthermore, a clear discrepancy is found between the square-well and Woods–Saxon model potential results on the hydrogen atom generalized oscillator strength due to the square-well discontinuity. These differences are reflected in the stopping cross section for protons colliding with H@C60.

Extracting Wair from the electron beam measurements of Domen and Lamperti.

The average energy expended by an energetic electron to create an ion pair in dry air, Wair , is a key quantity in radiation dosimetry. Although Wair is well established for electron energies up to about 3MeV, there is limited data for higher energies. The measurements by Domen and Lamperti [Med. Phys. 3, 294-301 (1976)] using electron beams in the energy range from 15 to 50MeV can, in principle, be used to deduce values for Wair , if the electron stopping power of graphite and air are known. A previous analysis of these data revealed an anomalous variation of 2% in Wair as a function of the electron energy. We use Monte Carlo simulation techniques to reanalyze the original data and obtain new estimates for Wair , and to investigate the source of the reported anomaly. Domen and Lamperti (DL) reported the ratio of the response of a graphite calorimeter to that of a graphite ionization chamber for broad beams of electrons with energies between 15 and 50MeV and at different depths in graphite (including depths well beyond the range of the primary electrons, i.e., in the bremsstrahlung photon regime). Using a detailed EGSnrc model of the DL apparatus, as well as up-to-date stopping powers, we compute the dose ratio between the ionization chamber cavity and the calorimeter core, for plane-parallel electron beams. This dose ratio, multiplied by the DL measured ratio, provides a direct estimate for Wair . Despite an improved analysis of the original work, the extracted values of Wair still exhibit an increase as the mean electron energy at the point of measurement decreases below about 15MeV. This anomalous trend is dubious physically, and inconsistent with extensive data for Wair obtained at lower energies. A thorough sensitivity analysis indicates that this trend is unlikely to stem from errors in extrapolation and correction procedures, uncertainties in electron stopping powers, or bias in calorimetry or ionization chamber measurements. However, we find that results are quite sensitive to the intrinsic graphite mass thickness of the detectors and to the incident beam energy. The DL experiment provides data in an energy regime where the electron stopping power is insensitive to the mean excitation energy of graphite - an issue plaguing Wair experiments at lower energies. Unfortunately, state-of-the-art scrutiny of the original data cannot explain the anomalous trend in terms of perturbation effects or extrapolation bias. It can only be understood in terms of speculative offsets in graphite mass thickness or beam energy. Therefore higher accuracy measurements for electron energies above 15MeV are recommended to further resolve the value of Wair .

Electron impact secondary electron emissions from atomic and molecular solid targets

SynopsisThe Sternglass theory [Sternglass, Phys. Rev. 108, (1957) 1] for fast-ion-induced secondary electron emission, which is proportional to the stopping powers, has been modified to calculate the electron impact secondary electron yield from both elemental and compound targets with atomic number Z = 4 - 92 for incident energy range 5 ≤ Ei ≤ 105 eV. This modification includes the use of a realistic stopping power expression that involves calculations of the effective atomic electron number, effective mean excitation energies and realistic electron density distribution of the target atoms along with the effective charge of incident electron.

Simplified derivation of stopping power ratio in the human body from dual-energy CT data.

The main objective of this study is to propose an alternative parameterization for the empirical relation between mean excitation energies (I-value) and effective atomic numbers (Zeff ) of human tissues, and to present a simplified formulation (which we called DEEDZ-SPR) for deriving the stopping power ratio (SPR) from dual-energy (DE) CT data via electron density (ρe ) and Zeff calibration. We performed a numerical analysis of this DEEDZ-SPR method for the human-body-equivalent tissues of ICRU Report 46, as objects of interest with unknown SPR and ρe . The attenuation coefficients of these materials were calculated using the XCOM photon cross-sections database. We also applied the DEEDZ-SPR conversion to experimental DECT data available in the literature, which was measured for the tissue-characterization phantom using a dual-source CT scanner at 80kV and 140kV/Sn. It was found that the DEEDZ-SPR conversion enables the calculation of SPR simply by means of the weighted subtraction of an electron-density image and a low- or high-kV CT image. The simulated SPRs were in excellent agreement with the reference values over the SPR range from 0.258 (lung) to 3.638 (bone mineral-hydroxyapatite). The relative deviations from the reference SPR were within ±0.6% for all ICRU-46 human tissues, except for the thyroid that presented a -1.1% deviation. The overall root-mean-square error was 0.21%. Application to experimental DECT data confirmed this agreement within the experimental accuracy, which demonstrates the practical feasibility of the method. The DEEDZ-SPR conversion method could facilitate the construction of SPR images as accurately as a recent DECT-based calibration procedure of SPR parameterization based directly on the CT numbers in a DECT data set.

Pressure effects on the dipole oscillator strength, polarizability, and mean excitation energy of a hydrogen impurity under cylindrical confinement: off-center axis effect

We study the electronic properties of a hydrogen atom under cylindrical confinement as obtained by a numerical solution to the Schrödinger equation by means of a finite-differences approach. In particular we calculate the dipole oscillator strength, static and dynamic dipole polarizabilities, as well as the mean excitation energy as a function of the position of the hydrogen impurity along the symmetry axis for the case of a ‘standard’ cylindrical confinement cavity and several confinement conditions. The effect of the displacement on the electronic properties is reflected in the change of the wave-function as the impurity approaches the cylinder potential lid produced by the surrounding confinement environment. We find that the intensity of the main dipole transition, , is reduced as the atom is displaced off-center along the symmetry axis, reaching a minimum half-way between the center of the cylinder and the lid and then increasing when at the cylinder lid. In the process some other transition lines become more intense with a maximum also at half-way between the center and the cylinder lid. We find that the label assignment on the excitation transitions changes as the impurity is displaced along the symmetry axis due to the polarizability of the impurity electronic cloud. Results for the static and dynamic polarizability for the confined impurity as well as the mean excitation energy for the cases of penetrable and impenetrable confinement are presented. We find that the static polarizability increases as the impurity approaches the cylinder lid meanwhile the mean excitation energy is reduced.

Electron impact secondary electron emissions from elemental and compound solids

The Sternglass theory [Sternglass, Phys. Rev. 108, (1957) 1] for fast-ion-induced secondary-electron emission, which is proportional to the stopping powers, from metals has been modified to calculate the electron impact secondary electron yield from both elemental and compound targets with atomic number Z = 4–92 for incident energy range 5 ≤Ei≤105eV. This modification includes the use of a realistic stopping power expression that involves calculations of the effective atomic electron number, effective mean excitation energies and realistic electron density distribution of the target atoms along with the effective charge of incident electron. Throughout the studied energy range, the predictions of our proposed theory are in reasonable agreement with the experimental data for Be to U elemental and six important compound targets.

Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions

The object of this work is to present the consequences for the stopping power and range values of some human tissues at energies ranging from 1MeV to 1GeV and 1–500MeV, respectively. The considered human tissues are lung, intestine, skin, larynx, breast, bladder, prostate and ovary. In this work, the stopping power is calculated by considering the number of velocity-dependent effective charge and effective mean excitation energies of the target material. We used the Hartree-Fock-Roothaan (HFR) atomic wave function to determine the charge density and the continuous slowing down approximation (CSDA) method for the calculation of the proton range. Electronic stopping power values of tissues results have been compared with the ICRU 44, 46 reports, SRIM, Janni and CasP data over the percent error rate. Range values relate to tissues have compared the range results with the SRIM, FLUKA and Geant4 data. For electronic stopping power results, ICRU, SRIM and Janni's data indicated the best fit with our values at 1–50, 50–250MeV and 250MeV–1GeV, respectively. For range results, the best accordance with the calculated values have been found the SRIM data and the error level is less than 10% in proton therapy. However, greater 30% errors were observed in the 250MeV and over energies.

Spectral distribution of particle fluence in small field detectors and its implication on small field dosimetry.

Correction factors for the relative dosimetry of narrow megavoltage photon beams have recently been determined in several publications. These corrections are required because of the several small-field effects generally thought to be caused by the lack of lateral charged particle equilibrium (LCPE) in narrow beams. Correction factors for relative dosimetry are ultimately necessary to account for the fluence perturbation caused by the detector. For most small field detectors the perturbation depends on field size, resulting in large correction factors when the field size is decreased. In this work, electron and photon fluence differential in energy will be calculated within the radiation sensitive volume of a number of small field detectors for 6 MV linear accelerator beams. The calculated electron spectra will be used to determine electron fluence perturbation as a function of field size and its implication on small field dosimetry analyzed. Fluence spectra were calculated with the user code PenEasy, based on the PENELOPE Monte Carlo system. The detectors simulated were one liquid ionization chamber, two air ionization chambers, one diamond detector, and six silicon diodes, all manufactured either by PTW or IBA. The spectra were calculated for broad (10 cm × 10 cm) and narrow (0.5 cm × 0.5 cm) photon beams in order to investigate the field size influence on the fluence spectra and its resulting perturbation. The photon fluence spectra were used to analyze the impact of absorption and generation of photons. These will have a direct influence on the electrons generated in the detector radiation sensitive volume. The electron fluence spectra were used to quantify the perturbation effects and their relation to output correction factors. The photon fluence spectra obtained for all detectors were similar to the spectrum in water except for the shielded silicon diodes. The photon fluence in the latter group was strongly influenced, mostly in the low-energy region, by photoabsorption in the high-Z shielding material. For the ionization chambers and the diamond detector, the electron fluence spectra were found to be similar to that in water, for both field sizes. In contrast, electron spectra in the silicon diodes were much higher than that in water for both field sizes. The estimated perturbations of the fluence spectra for the silicon diodes were 11-21% for the large fields and 14-27% for the small fields. These perturbations are related to the atomic number, density and mean excitation energy (I-value) of silicon, as well as to the influence of the "extracameral"' components surrounding the detector sensitive volume. For most detectors the fluence perturbation was also found to increase when the field size was decreased, in consistency with the increased small-field effects observed for the smallest field sizes. The present work improves the understanding of small-field effects by relating output correction factors to spectral fluence perturbations in small field detectors. It is shown that the main reasons for the well-known small-field effects in silicon diodes are the high-Z and density of the "extracameral" detector components and the high I-value of silicon relative to that of water and diamond. Compared to these parameters, the density and atomic number of the radiation sensitive volume material play a less significant role.

Role of the density, density effect and mean excitation energy in solid-state detectors for small photon fields

A number of recent publications on small photon beam dosimetry aim at contributing to the understanding of the response of solid-state detectors in small fields. Some of them assign the difference in response to the mass density, or to the electron density, of the sensitive detector material relative to that of water. This work analyses the role of the mass and electron density (), density effect (δ) and mean excitation energy (I-value) of some detector materials in a 6 MV photon beam of 0.5 cm radius, its rationale being that the response of a detector depends critically on the stopping-power ratio detector-to-water. The influence on the detector response of volume scaling by electron density, and of electron single and multiple scattering, is also investigated. Detector materials are water, diamond and silicon, and additional materials are included for consistency in the analysis. A detailed analysis on the () dependence of stopping-power ratios shows that the density effect δ depends both on the electron density and on the I-value of the medium, but not on the mass density ρ alone as is usually assumed. This leads to a double dependence of stopping-power ratios on the I-value and questions the adequacy of a ‘density perturbation factor’ or of common interpretations of detector response in terms of ρ alone. Differences in response can be described in terms of the variation of stopping power ratios detector-to-water, mainly due to different I-values and to a lesser extent to different values of electron density. It is found that at low energies the trend of Monte Carlo-calculated electron fluence spectra inside the detector materials depends solely on their I-values. No dependence on mass density or density effect alone is observed at any energy. The trend of restricted-cema ratios to water (as a substitute of absorbed dose ratios) follows that of stopping-power ratios at 1 MeV, the most probable energy of differential restricted-cema distributions in this study. It is concluded that the combined effect of the I-value and the dependence of δ on governs the restricted-cema values, and that neither ρ or a alone explain the different response of diverse detector materials. The results show that, for the small non-scaled and scaled volumes in this work, is practically constant and that in both cases the contribution of electron scattering to the restricted-cema values is about 2%.

Mean excitation energies for molecular ions

The essential material constant that determines the bulk of the stopping power of high energy projectiles, the mean excitation energy, is calculated for a range of smaller molecular ions using the RPA method. It is demonstrated that the mean excitation energy of both molecules and atoms increase with ionic charge. However, while the mean excitation energies of atoms also increase with atomic number, the opposite is the case for mean excitation energies for molecules and molecular ions. The origin of these effects is explained by considering the spectral representation of the excited state contributing to the mean excitation energy.

Proton Impact of Bimolecular Targets

For a better control and understanding of the effects of radiation damage in living tissues by using the irradiation of biological systems by energetic ion beams have multiple applications in medical physics and space radiation health, such as hadron therapy for cancer treatment and it is necessary to advance an accurate description of the energy loss from the ion beam to the target. In the present work the dielectric formalism like Drude has been used to calculate the probability for an energetic proton and to produce electronic excitations in five targets of high biological interest, namely, liquid water, DNA, PMMA, Adenine and Guanine. Also, the effects of ionization fraction on the mean excitation energy, average energy and Inelastic mean free path studied taking in to consideration electronic excitation in the target. Good agreement achieved with previous work.

A robust empirical parametrization of proton stopping power using dual energy CT.

In this study the authors present a new method for estimation of proton stopping power ratios (SPRs) using dual energy CT (DECT), which is robust toward CT noise. The authors propose a parametrization for SPR based directly on the CT numbers in a DECT image set, whereby the intermediate steps of estimating the relative electron density, ρe, and mean excitation energy, I, are avoided. The SPR parametrization proposed in this study is a purely empirical fit based on the theoretical SPR values for a list of 34 reference human tissues. To investigate the SPR estimation made with this new method the authors performed a calibration and an evaluation with the method. The authors initially calculated CT numbers using CT energy spectrum characterization parameters obtained from calibration based on a Gammex 467 electron density calibration phantom. These CT numbers were fitted to the theoretical SPR for the reference human tissues using the new SPR parametrization presented in this study. The method was evaluated based on theoretical CT numbers for the reference human tissues. The root-mean-square error (RMSE) of the SPR and the proton range error from the continuous slowing down approximation were calculated for the reference human tissues. To test the stability of the parametrization the authors varied the density and elemental composition of the reference human tissues and calculated their new SPR estimates. Further, clinically realistic noise values were added to the theoretical CT numbers to investigate how CT noise affected the estimated water equivalent range through 10 cm of the reference human tissues. All results for the new SPR parametrization were compared to the results obtained using two previously published DECT methods for SPR estimation. Comparisons were also made to a single energy CT (SECT) SPR estimation method, the stoichiometric method, which is commonly used in clinical practise for proton therapy treatment planning. The RMSE for the SPR of the 34 reference human tissues using the new SPR parametrization was 0.12%, compared to 0.19% and 0.28% for the two previously published DECT methods. The SPR parametrization was more stable toward variations of the calcium content in the reference human tissues, but less stable toward density variations and changes to the hydrogen content than the two other DECT methods. When adding noise to the theoretical CT numbers the SPR parametrization gave the lowest water equivalent range errors of all four tested SPR estimation methods (maximum error reduced to 0.4 mm). In all cases tested, the new SPR parametrization outperformed the SECT stoichiometric method. The new SPR parametrization gave lower RMSEs than the two other published DECT methods, and was in particular more robust against added noise. The method has potential for reducing range uncertainty margins in treatment planning of proton therapy.

Electron impact stopping powers for elemental and compound media

A semi-analytical model is proposed for evaluating the electron stopping powers (ESPs) of material media including both elements and compounds in the energy range 1.0 eV–100 MeV. This paper reports details of our calculations using the effective atomic electron number, effective mean excitation energies of target atoms and realistic electron density distribution of the target atoms. This simple formula is capable of generating accurate cross-section for diverse systems. We present here only few simple cases. In comparison with other theoretical predictions, our calculated ESPs for elemental [C, Al, Cu, Pt, Au and Pb] and compound [H2O, C5H5N5O, GaAs, Bi2Sr2CaCu2O8, SiO2 and ZnTe] media agree reasonably well with the experimental findings.

TU-FG-BRB-03: Basis Vector Model Based Method for Proton Stopping Power Estimation From Experimental Dual Energy CT Data

Purpose: This work aims at reducing the uncertainty in proton stopping power (SP) estimation by a novel combination of a linear, separable basis vector model (BVM) for stopping power calculation (Med Phys 43:600) and a statistical, model-based dual-energy CT (DECT) image reconstruction algorithm (TMI 35:685). The method was applied to experimental data. Methods: BVM assumes the photon attenuation coefficients, electron densities, and mean excitation energies (I-values) of unknown materials can be approximated by a combination of the corresponding quantities of two reference materials. The DECT projection data for a phantom with 5 different known materials was collected on a Philips Brilliance scanner using two scans at 90 kVp and 140 kVp. The line integral alternating minimization (LIAM) algorithm was used to recover the two BVM coefficient images using the measured source spectra. The proton stopping powers are then estimated from the Bethe-Bloch equation using electron densities and I-values derived from the BVM coefficients. The proton stopping powers and proton ranges for the phantom materials estimated via our BVM based DECT method are compared to ICRU reference values and a post-processing DECT analysis (Yang PMB 55:1343) applied to vendorreconstructed images using the Torikoshi parametric fit model (tPFM). Results: For the phantom materials, the average stopping power estimations for 175 MeV protons derived from our method are within 1% of the ICRU reference values (except for Teflon with a 1.48% error), with an average standard deviation of 0.46% over pixels. The resultant proton ranges agree with the reference values within 2 mm. Conclusion: Our principled DECT iterative reconstruction algorithm, incorporating optimal beam hardening and scatter corrections, in conjunction with a simple linear BVM model, achieves more accurate and robust proton stopping power maps than the post-processing, nonlinear tPFM based DECT analysis applied to conventional reconstructions of low and high energy scans. Funding Support: NIH R01CA 75371; NCI grant R01 CA 149305.

Stopping power of a heterogeneous warm dense matter

AbstractThe stopping power of warm dense matter (WDM) is estimated by means of the individual contributions of free electrons and bound electrons existing in this special kind of matter, located between classical and degenerate plasmas. For free electrons, the dielectric formalism, well described in our studies, is used to estimate the free electron stopping power. For bound electrons, the mean excitation energy of ions is used. Excitation energies are obtained through atomic calculations of the whole atom or, shell by shell in order to estimate their stopping power. Influence of temperature and density is analyzed in case of an impinging projectile. This influence becomes important for low projectile velocities and is negligible for high ones. Using free and bound electron analysis, the stopping power of an extended WDM is inferred from a dynamical calculation of energy transferred from the projectile to the plasma, where the stopping range is calculated. Finally, this theoretical framework is used to study a typical plasma density profile of a WDM heated by lasers.

Monte Carlo calculation of beam quality correction factors in proton beams using detailed simulation of ionization chambers

This work calculates beam quality correction factors (kQ) in monoenergetic proton beams using detailed Monte Carlo simulation of ionization chambers. It uses the Monte Carlo code penh and the electronic stopping powers resulting from the adoption of two different sets of mean excitation energy values for water and graphite: (i) the currently ICRU 37 and ICRU 49 recommended and and (ii) the recently proposed and . Twelve different ionization chambers were studied. The kQ factors calculated using the two different sets of I-values were found to agree with each other within 1.6% or better. kQ factors calculated using current ICRU I-values were found to agree within 2.3% or better with the kQ factors tabulated in IAEA TRS-398, and within 1% or better with experimental values published in the literature. kQ factors calculated using the new I-values were also found to agree within 1.1% or better with the experimental values. This work concludes that perturbation correction factors in proton beams—currently assumed to be equal to unity—are in fact significantly different from unity for some of the ionization chambers studied.

On the universal scaling in the electronic stopping cross section for heavy ion projectiles

ABSTRACTEnergy deposition of heavy ions when penetrating a material is of crucial importance in determining the damage to materials with implications in areas such as material science, plasma physics, radiotherapy and dosimetry. Due to the N-body electron problem, it has been thought that the electronic stopping cross section is unique for a given projectile–target combination and differs from system to system. In this work, we show that within the Bethe theory, there is a universal scaling when the electronic stopping cross sections and projectile kinetic energy are scaled properly in terms of the target mean excitation energy, , for all projectile–target combinations. We show that the scaling is given by as a function of , thus showing the importance of the characterization of the mean excitation energy. The scaling law expresses a systematic and universal behavior among complex projectile–target systems in the energy deposition, characterized by the minimum momentum transfer during the slowing down process. We provide an analytic expression for the universal scaling law for the stopping cross section of any projectile–target combination valid at high collision energies. Finally, we verify the universal scaling law by comparison to atomic and molecular experimental data available in the literature. We expect our findings will motivate further experimental work to verify our universal scaling for more complex systems in the absence of experimental data.

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation.

To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl2 aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe-Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. ["Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues," Phys. Med. Biol. 55, 1343-1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Based on the authors' idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

SU‐E‐J‐136: Investigation Into Robustness of Stopping Power Calculated by DECT and SECT for Proton Therapy Treatment Planning

Purpose:To investigate the robustness of dual energy CT (DECT) and single energy CT (SECT) proton stopping power calibration techniques and quantify the associated errors when imaging a phantom differing in chemical composition to that used during stopping power calibration.Methods:The CIRS tissue substitute phantom was scanned in a CT‐simulator at 90kV and 140kV. This image set was used to generate a DECT proton SPR calibration based on a relationship between effective atomic number and mean excitation energy. A SECT proton SPR calibration based only on Hounsfield units (HUs) was also generated. DECT and SECT scans of a second phantom of known density and chemical composition were performed. The SPR of the second phantom was calculated with the DECT approach (SPR_DECT),the SECT approach (SPR_SECT) and finally the known density and chemical composition of the phantom (SPR_ref). The DECT and SECT image sets were imported into the Pinnacle3 research release of proton therapy treatment planning. The difference in dose when exposed to a common pencil beam distribution was investigated.Results:SPR_DECT was found to be in better agreement with SPR_ref than SPR_ SECT. The mean difference in SPR for all materials was 0.51% for DECT and 6.89% for SECT. With the exception of Teflon, SPR_DECT was found to agree with SPR_ref to within 1%. Significant differences in calculated dose were found when using the DECT image set or the SECT image set.Conclusion:The DECT calibration technique was found to be more robust to situations in which the physical properties of the test materials differed from the materials used during SPR calibration. Furthermore, it was demonstrated that the DECT and SECT SPR calibration techniques can Result in significantly different calculated dose distributions.

Excitation migration in fluctuating light-harvesting antenna systems.

Complex multi-exponential fluorescence decay kinetics observed in various photosynthetic systems like photosystem II (PSII) have often been explained by the reversible quenching mechanism of the charge separation taking place in the reaction center (RC) of PSII. However, this description does not account for the intrinsic dynamic disorder of the light-harvesting proteins as well as their fluctuating dislocations within the antenna, which also facilitate the repair of RCs, state transitions, and the process of non-photochemical quenching. Since dynamic fluctuations result in varying connectivity between pigment-protein complexes, they can also lead to non-exponential excitation decay kinetics. Based on this presumption, we have recently proposed a simple conceptual model describing excitation diffusion in a continuous medium and accounting for possible variations of the excitation transfer pathways. In the current work, this model is further developed and then applied to describe fluorescence kinetics originating from very diverse antenna systems, ranging from PSII of various sizes to LHCII aggregates and even the entire thylakoid membrane. In all cases, complex multi-exponential fluorescence kinetics are perfectly reproduced on the entire relevant time scale without assuming any radical pair equilibration at the side of the excitation quencher, but using just a few parameters reflecting the mean excitation energy transfer rate as well as the overall average organization of the photosynthetic antenna.