Gaussian Fitting Research Articles

Variations in the Crystal Lattice of Tb-Dy-Fe Magnetostrictive Materials: The Lattice Constant Disturbance.

In Tb-Dy-Fe alloy systems, Tb0.29Dy0.71Fe1.95 alloy shows giant magnetostrictive properties under low magnetic fields, thus having great potential for transducers, microsensors, and other applications. The C15 cubic crystal structure of Tb-Dy-Fe has long been thought to be the source of giant magnetostriction. It is surprising that such a highly symmetrical crystal structure exhibits such a large magnetostrictive strain. In this work, the lattice parameters of Tb0.29Dy0.71Fe1.95 magnetostrictive materials were studied by processing atomic-resolution images. The selected area diffraction patterns show a face-centered cubic structure, but the fast Fourier transform diagram shows that the cubic structure has obvious distortion. The lattice parameters obtained by geometric phase analysis (GPA) and Gaussian model-based fitting and calculation show that the lattice constants a, b, and c are not strictly equal, and small disturbance of the lattice constants occurs based on the cubic structure. The actual crystal structure of the Tb-Dy-Fe material is a slightly disturbed cubic structure. This variation in the crystal lattice is mainly caused by the inhomogeneous composition and may be related to the giant magnetostrictive properties of Tb-Dy-Fe alloy.

Deep-UV Raman spectroscopy: A novel heuristic method to characterize volcanologically relevant glasses on Mars

Deep ultraviolet Raman spectroscopy is an essential component of the Perseverance rover operating on Mars. Here we propose a proof of concept of deep-UV Raman structural characterization of volcanologically relevant silicate glasses to provide a suitable analytical method of UV Raman spectra collected on Mars. The results show few but substantial spectral differences concerning those obtained by conventional Raman scattering using visible light laser sources. The evolution of the UV Raman spectra between 825 and 1300 cm−1 is confirmed to be more sensitive to the silica network's short-range structure than that below 700 cm−1 when compared to their visible counterpart. We adopted a Gaussian fitting model to parametrize the number of bridging oxygens resulting from the tetrahedral‑oxygens stretching vibrations along a sub-alkaline join of volcanic glasses. We used these parameters to empirically provide a relation with the glass silica content. The model was externally validated with glasses having different and known compositions (in particular different amounts of iron, alkali and alumina) extending the validation set also to other magmatic series (i.e. alkaline and shoshonitic). Our approach enables a fast screening of deep-UV Raman spectra collected on Mars to disentangle the glass structure and retrieve its silica content within a given magmatic series. This method is relevant for planetary exploration and applies both to microanalysis of dry or hydrate volcanologically relevant glasses and general technical glasses since deep-UV Raman spectroscopy is particularly effective in reducing the unwished photoluminescence and increasing the signal-to-noise ratio.

How does the precursor backbone length affect the grafting efficiency and kinetics for bottlebrush polystyrenes prepared by graft-onto Strategy?

The clarification of the potential dependence of grafting efficiency on the backbone length during the graft-onto reaction process is extremely important for subsequent structure–property study. In this work, by using alkyne-functional polypropargyne acrylate (PPANb, Mw/Mn < 1.10 and Nb = 960, 193, 35) and azide-functional polystyrene (PSNs, Mw/Mn < 1.15 and Ns = 54, 38, 22) as the backbone and sidechain precursors, we have investigated the Nb-dependence of the grafting reaction during the graft-onto click process. Specifically, the influence of solution concentration and feed ratio are investigated, and a combination of SEC characterization, Gaussian fitting and theoretical analysis is used to estimate the Nb-dependent grafting reaction for the bottlebrush product (PPANb-g-PSNs). The main findings include: 1) when the reaction time (t) is sufficient long (t = 24 h), the grafting efficiency is found to be nearly irrelevant with Nb, even if we consider 2 ∼ 5 times of difference in the diffusion coefficient (D) based the well-known scaling relation of D ∼ Nb1/2 in the semidilute reaction solution; 2) the time-dependent kinetics investigation further shows abnormal and different pathways for different backbone lengths when 0 min < t < 10 min, but the final grafting efficiency determined at t = 300 min shows no much difference, going back to the preliminary result of equilibrium state at t = 24 h; 3) the origin of abnormal pathways may be attributed to the relatively poor signal-to-noise ratio and potential dependence of dn/dC of PPANb-g-PSNs product on the composition at low grafting density range, which needs clarification in future. For the first time, our result has unambiguously demonstrated that, for a mixed solution of reaction system composed of backbone precursors with their lengths differing by hundreds of times, the polydispersity effect of the backbone length does not affect the final grafting efficiency during the process, no matter for long or short sidechain grafts. The result implies that it is the local dynamics of chain segments, instead of the overall translational diffusion dominates the graft-onto process in the concentration-regime studied.

A sub-millimetre two-wavelength EDM that compensates the air refractive index: uncertainty and measurements up to 5 km

Distance measurements over several kilometres with a sub-millimetre uncertainty are required for deformation monitoring in fields such as geodesy or civil engineering where well-controlled scale is critical. This paper presents a two-wavelength electro-optical distance meter (EDM) capable of such measurements and traceable to the SI (Système International d’unités). It is based on simultaneous measurements of optical path lengths, at two wavelengths, one at 780 nm and the other at 1560 nm, the dispersion between the two wavelengths allowing real-time compensation of the air refractive index along the optical paths. The uncertainty budget of this EDM has been established, taking into account both the telemetric and the mechanical contributions. One of the main sources of errors is crosstalk, which originates mainly from the optical splitters acting as circulators and becomes more pronounced for lower received powers over longer distances. For signal-to-crosstalk ratios (SCRs) higher than 60 dB, the instrumental uncertainty in the air-index compensated distance was assessed to be 320 µm (k = 1). In the field, two distance measurements, one over 2.6 km, the other over 5.4 km, were carried out over a period of up to 6 days, and for a temperature and pressure varying by as much as 10 °C and 17 hPa. For each distance, the standard deviation of the Gaussian fit of the experimental points was less than 250 µm. This level of refractivity compensation demonstrates that the developed instrument works properly. In addition, standard deviations lower than 140 µm were achieved for displacement measurements at distances around 2.6 km and 5.4 km. All these results were obtained for SCRs higher than 60 dB. Finally, solutions are proposed for mitigating the effect of high crosstalk values on instrumental uncertainty.

From medical strategy to foodborne prophylactic strategy: Stabilizing dental collagen with aloin.

Infectious oral diseases are longstanding global public health concerns. However, traditional medical approaches to address these diseases are costly, traumatic, and prone to relapse. Here, we propose a foodborne prophylactic strategy using aloin to safeguard dental collagen. The effect of aloin on the stability of dental collagen was evaluated by treating dentin with a solution containing aloin (0.1 mg/mL) for 2 min. This concentration is comparable to the natural aloin content of edible aloe. Furthermore, we investigated the mechanisms underlying the interactions between aloin and dentin collagen. Our findings, obtained through fluorescence spectroscopy, attenuated total reflection Fourier transform infrared spectroscopy, Gaussian peak fitting, circular dichroism spectroscopy, and X-ray diffraction, revealed that aloin interacts with dental collagen through noncovalent bonding, specifically hydrogen bonding insitu. This interaction leads to a reduction in the distance between molecules and an increase in the proportion of stable α-helical chains in the dental collagen. The ultimate tensile strength and thermogravimetric analysis demonstrated that dental collagen treated with aloin exhibited improved mechanical strength and thermostability. Additionally, the release of hydroxyproline, cross-linked carboxy-terminal telopeptide of type I collagen, and C-terminal cross-linked telopeptide of type I collagen, along with weight loss, indicated an enhancement in the enzymatic stability of dental collagen. These findings suggest that aloin administration could be a daily, nondestructive, and cost-effective strategy for managing infectious oral diseases.

The Discovery of the Zeeman Effect in 38 GHz Class II Methanol Masers

Magnetic fields likely play an important role in star formation, but the number of directly measured magnetic field strengths remains scarce. We observed the 38.3 and 38.5 GHz Class II methanol (CH3OH) maser lines toward the high-mass star-forming region NGC 6334 F for the Zeeman effect. The observed spectral profiles have two prominent velocity features that can be further decomposed through Gaussian component fitting. In several of these fitted Gaussian components we find significant Zeeman detections, with zB los in the range from 8 to 46 Hz. If the Zeeman splitting factor z for the 38 GHz transitions is of the order of ∼1 Hz mG−1, similar to that for several other CH3OH maser lines, then magnetic fields in the regions traced by these masers would be in the range of 8–46 mG. Such magnetic field values in high-mass star-forming regions agree with those detected in the better-known 6.7 GHz Class II CH3OH maser line. Since Class II CH3OH masers are radiatively pumped close to the protostar and likely occur in the accretion disk or the interface between the disk and outflow regions, such fields likely have significant impact on the dynamics of these disks.

Early Planet Formation in Embedded Disks (eDisk). VIII. A Small Protostellar Disk around the Extremely Low Mass and Young Class 0 Protostar IRAS 15398–3359

Protostellar disks are an ubiquitous part of the star formation process and the future sites of planet formation. As part of the Early Planet Formation in Embedded Disks large program, we present high angular resolution dust continuum (∼40 mas) and molecular line (∼150 mas) observations of the Class 0 protostar IRAS 15398–3359. The dust continuum is small, compact, and centrally peaked, while more extended dust structures are found in the outflow directions. We perform a 2D Gaussian fitting and find the deconvolved size and 2σ radius of the dust disk to be 4.5 × 2.8 au and 3.8 au, respectively. We estimate the gas+dust disk mass assuming optically thin continuum emission to be 0.6M J–1.8M J, indicating a very low mass disk. The CO isotopologues trace components of the outflows and inner envelope, while SO traces a compact, rotating disk-like component. Using several rotation curve fittings on the position–velocity diagram of the SO emission, the lower limits of the protostellar mass and gas disk radius are 0.022 M ⊙ and 31.2 au, respectively, from our Modified 2 single power-law fitting. A conservative upper limit of the protostellar mass is inferred to be 0.1 M ⊙. The protostellar mass accretion rate and the specific angular momentum at the protostellar disk edge are found to be in the range of (1.3–6.1) × 10−6 M ⊙ yr−1 and (1.2–3.8) × 10−4 km s−1 pc, respectively, with an age estimated between 0.4 × 104 yr and 7.5 × 104 yr. At this young age with no clear substructures in the disk, planet formation would likely not yet have started. This study highlights the importance of high-resolution observations and systematic fitting procedures when deriving dynamical properties of deeply embedded Class 0 protostars.

Extreme Red-wing Enhancements of UV Lines during the 2022 March 30 X1.3 Solar Flare

Here, we present the study of a compact emission source during an X1.3 flare on 2022 March 30. Within a ∼41 s period (17:34:48 UT to 17:35:29 UT), Interface Region Imaging Spectrograph observations show spectral lines of Mg ii, C ii, and Si iv with extremely broadened, asymmetric red wings. This source of interest (SOI) is compact, ∼1.″6, and is located in the wake of a passing ribbon. Two methods were applied to measure the Doppler velocities associated with these red wings: spectral moments and multi-Gaussian fits. The spectral-moments method considers the averaged shift of the lines, which are 85, 125, and 115 km s−1 for the Mg ii, C ii, and Si iv lines respectively. The red-most Gaussian fit suggests a Doppler velocity up to ∼160 km s−1 in all of the three lines. Downward mass motions with such high speeds are very atypical, with most chromospheric downflows in flares on the order 10–100 km s−1. Furthermore, extreme-UV (EUV) emission is strong within flaring loops connecting two flare ribbons located mainly to the east of the central flare region. The EUV loops that connect the SOI and its counterpart source in the opposite field are much less brightened, indicating that the density and/or temperature is comparatively low. These observations suggest a very fast downflowing plasma in the transition region and upper chromosphere, which decelerates rapidly since there is no equivalently strong shift of the O I chromospheric lines. This unusual observation presents a challenge that models of the solar atmosphere’s response to flares must be able to explain.

Low current driven bidirectional violet light emitting diode based on p-GaN/n-InN heterojunction

The fabrication of a low current bidirectional driven violet p-GaN/n-InN heterojunction light-emitting diode (LED) by the radio-frequency (RF) magnetron sputtering is reported in this paper. The indium nitride (InN) films grown at different substrate temperatures were characterized by X-ray diffraction (XRD), atomic force microscopy (AFM), UV-2600 spectrophotometer and Hall test system, and the optimum substrate temperature was found to be 250 °C. The bidirectional electroluminescence (EL) behavior and the luminescence mechanism of the diode have been investigated. Based on the above, the bidirectional EL and the effect of ambient temperature (room temperature (RT) to 80 °C) on the luminescence properties of the diode have been investigated. The diode can be driven bidirectionally at very low currents (0.03 mA under forward and 0.01 mA under reverse) and produce high-brightness violet light at forward currents of 1–5 mA and reverse currents of 1–3 mA. Finally, the EL spectra were subjected to the Gaussian peak fitting process combined with energy band diagrams to analysis the luminescence mechanism of the diode. The EL spectra all show predominantly violet emission and interface defects emissions under different polarity current drive. The proposed bidirectional violet LED based on p-GaN/n-InN heterojunction will be a potential commodity for the bidirectional driven LED market in the future.

A study on the method of analyzing the expressiveness of musical performance of flute based on steady-state stochastic process

Abstract In this paper, the performance data are processed using direct discretization in a steady-state stochastic process, and the flute performance white noise signal is transported through a linear transfer function to form a performance complex conjugate according to the indeterminate value of the power spectral density input music data. The envelope function is uniformly modulated to form a mixed Gaussian fit to the performance data to simulate the distribution of the performance frequency situation, combined with a closed-loop model to count the flute performance signal-to-noise ratio loss. The results show that the steady-state stochastic process reduces the time required for music performance classification by 1.18 seconds, and the pitch accuracy is 89%. Through the steady-state stochastic process, we can better understand performance, comprehend the integration of technique and emotion, and enhance our understanding of flute performance.

Solidification/stabilization and immobilization mechanism of Pb(II) and Zn(II) in ettringite

Ettringite, as the dominant hydration product in cement materials, plays a significant role in the solidification/stabilization of heavy metals. However, the combination and immobilization mechanism of heavy metal ions in ettringite crystals have yet to be fully understood. In this study, ettringite crystals were synthesized using the solution reaction method to investigate the adsorption and chemical encapsulation reactions of Pb2+ and Zn2+. In addition, the microstructures of the ettringite crystals doped with heavy metals were characterized by XRD, FTIR and SEM/EDS to elucidate the immobilization mechanism of Pb2+ and Zn2+ on ettringite crystals. The results indicated that ettringite has a high specific surface area of 64.456 m2/g and considerable mesopore and macropore volumers. The optimal adsorption efficiency of Pb2+ and Zn2+ in ettringite, accounting for 98.7 % and 99.9 %, respectively, was realized in an initial liquid with a pH of 10. The adsorption kinetics results showed that the equilibrium adsorption capacities of Pb2+ and Zn2+ were 196.04 and 185.57 mg/g, respectively. In addition, the adsorption reaction of Pb2+ in ettringite was predominantly characterized by a chemisorption process; whereas the adsorption reaction of Zn2+ in ettringite was characterized by the simultaneous action of physisorption and chemisorption. The multi-peaks Gaussian fitting curves of the FTIR patterns indicated that Pb2+ and Zn2+ promoted the formation of ettringite and induced more H-O-H groups. Moreover, this study proposed and confirmed that significant differences exist between the immobilization mechanisms of Pb2+ and Zn2+ in ettringite. The lattice constant and coordination chemistry analysis revealed that Pb2+ mainly substituted Ca2+ and Al3+ in ettringite via lattice substitution. In contrast, Zn2+ predominantly induced some lattice distortion in the ettringite crystal structure and formed a solid solution via interstitial doping. Furthermore, the micro channel architecture and hydrogen bond network significantly contributed to the adsorption and solidification of heavy metals. Overall, the chemical bonding mechanism was more prominent for the solidification of Pb2+ than that of Zn2+ in ettringite, and ettringite exhibited a superior adsorption capacity and stronger binding affinity for Pb2+.

Genesis of temperature-driven red-shift of charge transfer band edge for Sm3+-doped vanadate self-activated phosphor

The temperature-driven redshift of the charge transfer band (CTB) exhibits promising potential for optical temperature sensing as well as for the design of anti-thermal quenching phosphors. Therefore, it is essential to investigate the displacement mechanism in detail. In this contribution, we created LiCa2.95MV3O12:5%Sm3+ (M = Mg/Zn) phosphors with considerably red-shifted CTB edges upon temperature stimulation and outstanding anti-thermal quenching behavior. To investigate this unusual behavior, gaussian fitting was performed on the excitation spectra and emission spectra at different temperatures to investigate the redshift mechanism. By averaging the peak energy of the lowest excitation and emission peaks, the zero phonon line (Ezp) indicating the electronic energy level location of the charge transfer state (CTS) shows a downward trend is obtained. As well as the energy reduction of the 1A2(1T1)-1B1(1T2) and 1E(1T1)-1B1(1T2) absorption bands in the [VO4]3− group is observed. Therefore, the drop in the CTS electronic energy level is the dominant factor in the temperature-driven CTB redshift. Based on the redshift phenomenon and anti-thermal quenching phenomenon of CTB, the phosphor exhibited exceptional optical temperature measurement performance in all three thermometry modes of excitation intensity ratio (EIR), International Committee on Illumination (CIE) color coordinates, and fluorescence intensity ratio (FIR), demonstrating its broad application prospects in the field of optical temperature sensing as well as guiding the design of anti-thermal quenching phosphors.

Source function from two-particle correlation through deblurring

In heavy-ion collisions, low relative-velocity two-particle correlations have been a tool for assessing space-time characteristics of particle emission. Those characteristics may be cast in the form of a relative emission source related to the correlation function through the Koonin-Pratt (KP) convolution formula that involves the relative wave-function for the particles in its kernel. In the literature, the source has been most commonly sought by parametrizing it in a Gaussian form and fitting to the correlation function. At times the source was more broadly imaged from the function, still employing a fitting. Here, we propose the use of the Richardson-Lucy (RL) optical deblurring algorithm for deducing the source from a correlation function. The RL algorithm originally follows from probabilistic Bayesian considerations and relies on the intensity distributions for the optical object and its image, as well as the convolution kernel, being positive definite, which is the case for the corresponding quantities of interest within the KP formula.

132 W 132 μJ Femtosecond Pulses from a Coherently Combined System of Two Rod-Type Photonic Crystal Fibers

A coherent beam combination has the potential to revolutionize high-peak-power laser systems. However, achieving a high-average-power ultrashort pulse is difficult due to the accumulation of a nonlinear phase and gain narrowing. In this article, we demonstrate a coherent beam combination system that does not require pulse shaping or a spectral modulator. By optimizing the gain of each amplifier and using highly integrated optical components, we reduce the limitations caused by the accumulation of a nonlinear phase and gain narrowing. In our study, we used a polarization beam splitter to combine the pulses from two rod-type photonic crystal fibers (PCFs) in a Mach–Zehnder-type interferometer. A piezo-mounted mirror controlled with a Hänsch–Couillaud polarization detecting system was used to stabilize active phase locking. The system produces 165 W with a 91.6% combining efficiency compared to 90 W per amplifier. Compressed pulses with an energy of 132 µJ and Gaussian fitting pulse duration of 330 fs were achieved.

Noninvasive detection of diabetes mellitus based on skin fluorescence and diffuse reflectance spectroscopy.

There is an urgent need for a mass population screening tool for diabetes. Skin tissue contains a large number of endogenous fluorophores and physiological parameter markers related to diabetes. We built an excitation-emission spectrum measurement system with the excited light sources of 365, 395, 415, 430, and 455 nm to extract skin characteristics. The modeling experiment was carried out to design and verify the accuracy of the recovery of tissue intrinsic discrete three-dimensional fluorescence spectrum. Blood oxygen modeling experiment results indicated the accuracy of the physiological parameter extraction algorithm based on the diffuse reflectance spectrum. A community population cohort study was carried out. The tissue-reduced scattering coefficient and scattering power of the diabetes were significantly higher than normal control groups. The Gaussian multi-peak fitting was performed on each excitation-emission spectrum of the subject. A total of 63 fluorescence features containing information such as Gaussian spectral curve intensity, central wavelength position, and variance were obtained from each person. Logistic regression was used to construct the diabetes screening model. The results showed that the area under the receiver operating characteristic curve of the model for predicting diabetes was 0.816, indicating a high diagnostic value. As a rapid and non-invasive detection method, it is expected to have high clinical value.

Robustness of the Stochastic Parameterization of Subgrid-Scale Wind Variability in Sea Surface Fluxes

Abstract High-resolution numerical models have been used to develop statistical models of the enhancement of sea surface fluxes resulting from spatial variability of sea surface wind. In particular, studies have shown that flux enhancement is not a deterministic function of the resolved state. Previous studies focused on single geographical areas or used a single high-resolution numerical model. This study extends the development of such statistical models by considering six different high-resolution models, four different geographical regions, and three different 10-day periods, allowing for a systematic investigation of the robustness of both the deterministic and stochastic parts of the data-driven parameterization. Results indicate that the deterministic part, based on regressing the unresolved normalized flux onto resolved-scale normalized flux and precipitation, is broadly robust across different models, regions, and time periods. The statistical features of the stochastic part of the model (spatial and temporal autocorrelation and parameters of a Gaussian process fit to the regression residual) are also found to be robust and not strongly sensitive to the underlying model, modeled geographical region, or time period studied. Best-fit Gaussian process parameters display robust spatial heterogeneity across models, indicating potential for improvements to the statistical model. These results illustrate the potential for the development of a generic, explicitly stochastic parameterization of sea surface flux enhancements dependent on wind variability.

Applying fully convolutional networks for beam profile and emittance measurements

The transverse cross-sectional size and emittance are critical beam parameters that characterize the performance of the accelerator and assess the state of the beam. Inspired by the success of machine learning in image processing tasks, we have crafted a bespoke measurement system with a primary focus on accurately determine the transverse cross-sectional size and emittance of the beam. The system utilizes a beam spot detector to convert the beam spot to a light spot image, which is then projected onto the CCD camera through the telecentric lens for the acquisition. The image data collected by the camera is subsequently imported into the EPICS database developed based on ADAravis software. We employ the Gaussian fitting technique on the collected images to accurately calculate the cross-sectional size of the beam. Furthermore, by incorporating the four-level iron scanning method, the lateral emittance of the beam is calculated in a comprehensive manner. To suppress the salt and pepper noise introduced due to the presence of dark current and beam shooting phenomena on the transmission line, we propose a novel fully convolutional neural network (FCN) design with preactivated residual units. The test conducted at HLS-II confirms that the measurement uncertainty of this system is superior to 27.5 μm. Moreover, when operating at an electron beam energy of 800 MeV, the measured emittance of the accelerator is found to be 38.515 nm·rad, a value closely aligning with the theoretical value of 36.2 nm·rad. These compelling results provide strong evidence supporting the reliability of the emittance measurement algorithm, making it suitable for deployment in the forthcoming terahertz accelerator.

The dusty heart of Circinus

In this paper we present the first-ever L- and M-band interferometric observations of Circinus, building upon a recent N-band analysis. We used these observations to reconstruct images and fit Gaussian models to the L and M bands. Our findings reveal a thin edge-on disk whose width is marginally resolved and is the spectral continuation of the disk imaged in the N band to shorter wavelengths. Additionally, we find a point-like source in the L and M bands that, based on the LMN-band spectral energy distribution fit, corresponds to the N-band point source. We also demonstrate that there is no trace of direct sightlines to hot dust surfaces in the circumnuclear dust structure of Circinus. By assuming the dust is present, we find that obscuration of AV ≳ 250 mag is necessary to reproduce the measured fluxes. Hence, the imaged disk could play the role of the obscuring “torus” in the unified scheme of active galactic nuclei. Furthermore, we explored the parameter space of the disk + hyperbolic cone radiative transfer models and identify a simple modification at the base of the cone. Adding a cluster of clumps just above the disk and inside the base of the hyperbolic cone provides a much better match to the observed temperature distribution in the central aperture. This aligns well with the radiation-driven fountain models that have recently emerged. Only the unique combination of sensitivity and spatial resolution of the VLTI allows such models to be scrutinized and constrained in detail. We plan to test the applicability of this detailed dust structure to other MATISSE-observed active galactic nuclei in the future.

The VANDELS ESO public spectroscopic survey: The spectroscopic measurements catalogue

VANDELS is a deep spectroscopic survey, performed with the VIMOS instrument at VLT, aimed at studying in detail the physical properties of high-redshift galaxies. VANDELS targeted ~2100 sources at 1 &lt; z &lt; 6.5 in the CANDELS Chandra Deep-Field South (CDFS) and Ultra-Deep Survey (UDS) fields. In this paper, we present the public release of the spectroscopic measurement catalogues from this survey, featuring emission and absorption line centroids, fluxes, and rest-frame equivalent widths obtained through a Gaussian fit, as well as a number of atomic and molecular indices (e.g. Lick) and continuum breaks (e.g. D4000), and including a correction to be applied to the error spectra. We describe the measurement methods and the validation of the codes that were used.

Using Longitudinal MRI to Manage Proton Range Uncertainty for Pediatric Proton Craniospinal Irradiation

Clinical evidence has shown that proton therapy can effectively reduce side effects for pediatric patients undergoing vertebral body-sparing craniospinal irradiation (VBS CSI), compared to conventional photon treatment modalities. However, radiation-induced growth impairment remains challenging for VBS CSI due to proton range uncertainty, compromising vertebral body sparing for growing children. Previous studies have shown that fatty marrow replacement can be observed in vertebral bodies 4-48 weeks after treatment is complete. This study aims to detect and quantify the fatty marrow replacement in vertebral bodies using longitudinal magnetic resonance (MR) to manage proton range uncertainty. A prospective clinical trial of proton VBS CSI was designed, and ten pediatric patients were enrolled with prescribed doses of 15-36 Gy. The thecal sac and neural foramina were the clinical target volumes, and a Monte Carlo planning system was used to robustly optimize treatment plans with a 3.5% range margin. We analyzed patients' T1/T2 MR images acquired before, during, and after proton treatment to investigate the hematopoietic marrow transformation induced by irradiation. A metric was defined to calculate the ratio of fatty and hematopoietic marrow based on relative MR intensity histograms. We proposed a machine learning method via Gaussian fitting process (ML-GFP) to explore hidden correlations between marrow transition and radiation dose to 2 cm3 of the bone marrow (D2cc). We also leveraged this method to embed uncertainty to support potential proton range management for VBS enhancement. The results indicated that fatty marrow replacement could be observed during inter-fractional treatment. For instance, an individual patient showed that the fatty marrow generation ratios were 0.54, 0.74, and 0.45, corresponding to 11, 18, and 65 days after the treatment started. Using ML-GFP, the fatty marrow transition was found to be quadratically correlated to treatment fractions, and the maximum transformation ranged from 40 to 50 days. Then marrow regeneration was observed due to the decrease in fatty marrow ratios. The fatty marrow ratios were also positively correlated to the D2cc doses ranging from 10 Gy to 36 Gy. Limited by insufficient low-dose data, the ML-GFP model extrapolated the data to predict the marrow transformation below 10 Gy. We demonstrated the feasibility of using non-invasive longitudinal MR to quantify the fatty marrow transition from inter-fractional treatment. Based on this prospective study, the method can detect early fatty marrow generation in vertebrae caused by proton irradiation due to the conservative range margin used for robust optimization. The proposed method could be used to validate the actual proton range, allowing an accurate range margin to be defined to preserve bone marrow. Future investigation will likely focus on clinical implementation to improve life quality for pediatric CSI patients.