Biexponential Function Research Articles

Comparative investigation of structural, morphological and temperature-dependent photoluminescence characteristics of trivalent rare-earth-activated NaCaPO4 phosphors for solid-state lighting applications

This study explores the synthesis, structure, morphology, and photoluminescence features of trivalent RE3+-activated NaCaPO4 phosphors, aiming to develop phosphor materials for white-light-emitting diode (WLED) applications. Single-phase polycrystalline NaCa(1-x) REx3+ PO4 (REx3+ = Sm, Eu, Dy, and Tb) phosphor materials with various REx3+-doping percentiles were produced by a solid-state reaction process, which were analyzed using various characterization techniques. The FullProf Suite software program was used for phase evidence and crystalline structure analysis, confirming the composition of orthorhombic materials as a single phase. FE-SEM micrographs revealed asymmetrically stacked morphologies across all the compositions. This study reveals that trivalent RE3+-activated phosphors produced exceptional PL outcomes. Dexter's and Blasse's approaches were used to establish the interaction mechanisms and critical energy transfer ranges as dipole-dipole. Lifetime decay patterns were used to fit a bi-exponential function and the resulting values were approximated in milliseconds. This study reveals that trivalent RE3+-activated NaCaPO4 phosphors, with their thermal resilience and color integrity, have potential applications in solid-state lighting (SSL) technology.

Exploring single rare earth doped nanophosphor for efficient white emission through codoping of Na+ and Bi3+ ions into Dy3+ activated LaPO4

Using the simple hydrothermal technique, high-purity nanocrystalline Na+ and Bi3+ co-doped Dy3+ activated LaPO4 was effectively prepared. The structural characterisation of the prepared samples was carried out using XRD, EDS, SEM and FTIR analysis. The existence of Na+, Dy3+, La3+, P5+, O2– and Bi3+ was demonstrated using EDS analysis. The direct band gap value of 4.72 eV is obtained from UV visible absorption spectrum and infer that the doped samples are suitable for optical applications. The photoluminescence excitation spectrum monitored at 474 nm and 570 nm emission, the Na+ and Bi3+ co-doped Dy3+ activated LaPO4 exhibit narrow, and intense characteristics f-f peak of Dy3+ ion at 349 nm, 363 nm, 386 nm and 452 nm. Photoluminescence emission spectrum, monitored under 349 nm, 363 nm and 386 nm shows high intense sharp blue emission peaks of Dy3+ with stark splitting at 475 nm, 478 nm, and 486 nm, yellow emission at 571 nm and 580 nm and a very feeble peak at 658 nm in the red region. When the sample is excited at 452 nm only a yellow band is present. Since the intensity of blue and yellow emission in this host matrix is so high and nearly equal, it is appropriate for cool white emission under 350 nm, 363 nm and 386 nm (near UV) excitation and under 452 nm (blue LED) excitation the prepared phosphor may emerge as highly efficient warm white light emitter suitable for general solid-state lighting applications, which can be further confirmed by CIE chromaticity analysis of the prepared sample. In photoluminescence excitation and emission spectra intensities of peaks of the samples with Bi3+ are more intense, this confirms the positive impact of co-doping of Bi3+ into the sample. The Q value from the Dexter’s formula is calculated as an average of 6.4 and is very close to 6 indicates that the interaction is dipole − dipole, which causes the non-radiative energy migration among the Dy3+ ions in the sample. The lifetime of characteristic yellow emission of Dy3+ in the Na+ and Bi3+ co-doped Dy3+ activated LaPO4 host matrix monitored under 350 nm is calculated as 0.642 ms from decay analysis, fitted by a bi-exponential function. The results support the idea that co-doping of Bi3+ and Na+ into the LaPO4:Dy3+ matrix could emerge as a potential white light emitting phosphor for phosphor-converted white LED application.

Bi-exponential description for different forms of refractive development.

It was recently established that the axial power, the refractive power required by the eye for a sharp retinal image in an eye of a certain axial length, and the total refractive power of the eye may both be described by a bi-exponential function as a function of age (Rozema, 2023). Inspired by this result, this work explores whether these bi-exponential functions are able to simulate the various known courses of refractive development described in the literature, such as instant emmetropization, persistent hypermetropia, developing hypermetropia, myopia, instant homeostasis, modulated development, or emmetropizing hypermetropes. Moreover, the equations can be adjusted to match the refractive development of school-age myopia and pseudophakia up to the age of 20 years. All of these courses closely resemble those reported in the previous literature while simultaneously providing estimates for the underlying changes in axial and whole eye power.

Impact of the Reference Multiple-Time-Point Dosimetry Protocol on the Validity of Single-Time-Point Dosimetry for [177Lu]Lu-PSMA-I&T Therapy.

Internal dosimetry supports safe and effective patient management during radionuclide therapy. Yet, it is associated with high clinical workload, costs, and patient burden, as patient scans at multiple time points (MTPs) must be acquired. Dosimetry based on imaging at a single time point (STP) has continuously gained popularity. However, MTP protocols, used as a reference to judge the validity of STP dosimetry, differ depending on local requirements and deviate from the unknown patient-specific ground truth pharmacokinetics. The aim of this study was to compare the error and optimum time point for different STP approaches using different reference MTP protocols. Methods: Whole-body SPECT/CT scans of 7 patients (7.4-8.9 GBq of [177Lu]Lu-PSMA-I&T) were scheduled at 24, 48, 72, and 168 h after injection. Sixty lesions, 14 kidneys, and 10 submandibular glands were delineated in the SPECT/CT data. Two curve models, that is, a mono- and a biexponential model, were fitted to the MTP data, in accordance with goodness-of-fit analysis (coefficients of variation, sum of squared errors). Three population-based STP approaches were compared: one method published by Hänscheid etal., one by Jackson etal., and one using population-based effective half-lives in the mono- or biexponential curve models. Percentage differences between STP and MTP dosimetry were evaluated. Results: Goodness-of-fit parameters show that a monoexponential function and a biexponential function with shared population-based parameters and physical tail are reasonable reference models. When comparing both reference models, we observed maximum differences of -44%, -19%, and -28% in the estimated absorbed doses for lesions, kidneys, and salivary glands, respectively. STP dosimetry with an average deviation of less than 10% from MTP dosimetry may be feasible; however, this deviation and the optimum imaging time point showed a dependence on the chosen reference protocol. Conclusion: STP dosimetry for [177Lu]Lu-PSMA therapy is promising to boost the integration of dosimetry into clinical routine. According to our patient cohort, 48 h after injection may be regarded as a compromise for STP dosimetry for lesions and at-risk organs. The results from this analysis show that a common gold standard for dosimetry is desirable to allow for reliable and comparable STP dosimetry.

Dynamic Observation of the Membrane Interaction Processes of β-Lactoglobulin by Time-Resolved Vacuum-Ultraviolet Circular Dichroism.

The elucidation of protein-membrane interactions is pivotal for comprehending the mechanisms underlying diverse biological phenomena and membrane-related diseases. In this investigation, vacuum-ultraviolet circular dichroism (VUVCD) spectroscopy, utilizing synchrotron radiation (SR), was employed to dynamically observe membrane interaction processes involving water-soluble proteins at the secondary-structure level. The study utilized a time-resolved (TR) T-shaped microfluidic cell, facilitating the rapid and efficient mixing of protein and membrane solutions. This system was instrumental in acquiring measurements of the time-resolved circular dichroism (TRCD) spectra of β-lactoglobulin (bLG) during its interaction with lysoDMPG micelles. The results indicate that bLG undergoes a β-α conformation change, leading to the formation of the membrane-interacting state (M-state), with structural alterations occurring in more than two steps. Global fitting analysis, employing biexponential functions with all of the TRCD spectral data sets, yielded two distinct rate constants (0.18 ± 0.01 and 0.06 ± 0.003/s) and revealed a unique spectrum corresponding to an intermediate state (I-state). Secondary-structure analysis of bLG in its native (N-, I-, and M-states) highlighted that structural changes from the N- to I-states predominantly occurred in the N- and C-terminal regions, which were prominently exposed to the membrane. Meanwhile, transitions from the I- to M-states extended into the inner barrel regions of bLG. Further examination of the physical properties of α-helical segments, such as effective charge and hydrophobicity, revealed that the N- to I- and I- to M-state transitions, which are ascribed to first- and second-rate constants, respectively, are primarily driven by electrostatic and hydrophobic interactions, respectively. These findings underscore the capability of the TR-VUVCD system as a robust tool for characterizing protein-membrane interactions at the molecular level.

Time distribution of stimulated transition probabilities

In recent years, an increasing number of experimental results have been published for a wide variety of systems in which high-precision, ultra-fast, and ultra-short laser pulses techniques have been used to study time-resolved dynamical processes. In the absence of a theoretical prediction of the time distribution of the transition probabilities, the lifetimes τ are generally extracted by fitting the decay time with an exponential, bi-exponential or three-exponential function. In fitting the data, the short-time behavior is generally neglected. The purpose of this study is to show that an explicit formula for the time distribution of the transition probability can be determined rigorously using time-dependent perturbation theory. A formula that perfectly fits an important subset of the experimental results from t = 0 to t=∞ . We show that by following a route different from the usual procedure for deriving transition amplitudes and Einstein coefficients in time-dependent perturbation theory, one ends up with a time-dependent factor, that is, a temporal distribution function of the transition probabilities, and for the Einstein coefficients. The time distribution reported here looks in the time domain similar to the Planck distribution in the frequency domain. In fact, the behavior of the time distribution, with a maximum at 2τln⁡2 , and with τ playing the role of temperature, resembles the behavior of the Planck frequency distribution. We present several examples to demonstrate that the theoretical formula allows for easier fitting of the experimental results reported in the literature. We also show that the time distribution explains the difference in resonance heights between the experimental and theoretical blue laser spectra.

Identifying physiological determinants of 800 m running performance using post-exercise blood lactate kinetics

PurposeThe aims of the present study were to investigate blood lactate kinetics following high intensity exercise and identify the physiological determinants of 800 m running performance.MethodsFourteen competitive 800 m runners performed two running tests. First, participants performed a multistage graded exercise test to determine physiological indicators related to endurance performance. Second, participants performed four to six 30-s high intensity running bouts to determine post-exercise blood lactate kinetics. Using a biexponential time function, lactate exchange ability (γ1), lactate removal ability (γ2), and the quantity of lactate accumulated (QLaA) were calculated from individual blood lactate recovery data.Results800 m running performance was significantly correlated with peak oxygen consumption (r = −0.794), γ1 and γ2 at 800 m race pace (r = −0.604 and −0.845, respectively), and QLaA at maximal running speed (r = −0.657). V˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{\ ext{V}}}$$\\end{document}O2peak and γ2 at 800 m race pace explained 83% of the variance in 800 m running performance.ConclusionOur results indicate that (1) a high capacity to exchange and remove lactate, (2) a high capacity for short-term lactate accumulation and, (3) peak oxygen consumption, are critical elements of 800 m running performance. Accordingly, while lactate has primarily been utilized as a performance indicator for long-distance running, post-exercise lactate kinetics may also prove valuable as a performance determinant in middle-distance running.

Differences in lactate metabolism between middle- and long-distance runners

It is important for runners and coaches to figure out the characteristics of lactate metabolism in terms of planning the proper training. This study investigated the differences in lactate production and oxidation capacities between middle- and long-distance runners by using blood lactate concentration. We hypothesized that long-distance runners have greater capacity to oxidize lactate and middle-distance runners have greater capacity to produce lactate. In this study, 14 middle- and 14 long-distance male runners performed a multi-stage incremental test until exhaustion. Each running stage was 3-minute with 1-minute rest between stages. Blood lactate concentration was measured at rest and after each stage, and some metrics associated with runner’s capacity to oxidative lactate during moderate intensity exercise were calculated. The changes in blood lactate concentration measured after the final state of the test were modeled as a biexponential time function to evaluate lactate productive and oxidative capacities after high-intensity exercise. During moderate-intensity exercise, long-distance runners showed significant decrease in blood lactate concentrations during the first few stages of the test compared to rest, indicating greater oxidation of lactate than production of lactate during moderate intensity exercise (p<0.05), while middle distance runners showed slight increase in blood lactate concentrations even for the first several stages. Middle-distance runners showed significantly higher amount of lactate produced (p<0.05) and greater lactate oxidation during high-intensity exercise than those in long-distance runners (p<0.01), suggesting that both lactate production and oxidation of middle-distance runners were greater than those of long-distance runners during high-intensity exercise. These results suggest that characteristics of lactate metabolism in middle- and long-distance runners depend partly on exercise intensity. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

An Explicit Form of Ramp Function

In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, the ramp function is performed in a simple manner as the pointwise limit of a sequence of real and continuous functions with pointwise convergence. This limit is zero for strictly negative values of the real variable x, whereas it coincides with the independent variable x for strictly positive values of the variable x. Here, one may elucidate beforehand that the pointwise limit of a sequence of continuous functions can constitute a discontinuous function, on the condition that the convergence is not uniform. The novelty of this work, when compared to other research studies concerning analytical expressions of the ramp function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g., gamma function, biexponential function, or any other special functions, such as error function, hyperbolic function, orthogonal polynomials, etc. Hence, this formula may be much more practical, flexible, and useful in the computational procedures, which are inserted into digital signal processing techniques and other engineering practices.

Fluorescent Carbon Dots: Aggregation-Induced Emission Enhancement, Application as Probe for CN- and Cr2O7-2, Sensing Strips and Bio-imaging Agent.

Fluorescent carbon dots (Trp-CDs) were prepared using tryptophan as precursor and were characterized on the basis of elemental analysis, powder-XRD, IR, Raman spectroscopy, 13C-NMR, UV-Vis, fluorescence and TEM. Trp-CDs exhibit poor fluorescence in 100% water but showed strong Aggregation Induced Emission (AIE) in ethanol and higher alcohols. The anion sensing study of Trp-CD revealed that it selectively detects CN- and Cr2O7-2 and from fluorescence quenching titration study, quenching constant, LOD and range of detection were evaluated. The emission life-time of Trp-CD before and after addition of CN- and Cr2O7-2 were measured, the decay curve before addition of anion was best fitted with a bi-exponential function with life-time of τ1 2.79ns (10.74%) and τ2 18.93ns (89.26%). The mechanistic study revealed that for CN-, the fluorescence quenching is due to its interaction with protons attached to surface functional groups and for Cr2O7-2, it is due to inner filter effect (IFE). Sensing strips were prepared by coating Trp-CDs onto various solid surfaces including agarose films and were used for detection of CN- and Cr2O7-. Trp-CD was found to be nontoxic and biocompatible and used as staining agent for Artemia and Bacteria (Bacillus Subtilis, Pseudomonas) and detection of CN- and Cr2O7-.

Structural, photoluminescence and energy transfer investigations of novel Dy3+ → Sm3+ co-doped NaCaPO4 phosphors for white-light-emitting diode applications.

In this study, Dy3+-doped and Dy3+/Sm3+ co-doped NaCaPO4 white-emitting polycrystalline phosphor samples were synthesized using a solid-state reaction method. The samples were characterized by powder X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Field-emission scanning electron microscopy (FE-SEM), and Photoluminescence (PL) analysis. The phase purity characterization and crystal structural analysis were done using the Rietveld refinement-based FullProf Suite software. The Rietveld refinement result confirms single-phase formation for both Sm3+ and Dy3+/Sm3+ co-doped NaCaPO4 samples with an orthorhombic structure and with a monotonic change in lattice parameters with doping. The PL studies of the Dy3+-doped samples revealed two emission bands. However, at 352 nm, the Dy3+/Sm3+-co-doped samples revealed distinctive emission bands for both ions. The emission peaks at 480 nm (blue) and 573 nm (yellow) are related to the 4F9/2 → 6H15/2 and 4F9/2 → 6H13/2 transitions of Dy3+ ions; however, the emission peaks at 600 nm and 647 nm are attributed to the 4G5/2 → 6H7/2 and 4G5/2 → 6H7/2 transitions of Sm3+ ions. The intensity of the Dy3+ emissions decreased as the Sm3+ levels increased but the emission intensity of the Sm3+ ions increased. The co-doping of Sm3+ ions in Dy3+-doped phosphors results in unique characteristics due to the energy transfer (ET) from Dy3+ → Sm3+ ions. The effectiveness of this ET from Dy3+ → Sm3+ ions is positively correlated with the dopant amounts of the Sm3+ ions. The interaction mechanisms have been identified as dipole-dipole based on Dexter's energy transfer and Readfield's approaches. All decay curves can be adequately fitted via bi-exponential functions, suggesting the movement of energy between Dy3+ → Sm3+ ions. Temperature-dependent PL measurements and CIE color coordinate analysis reveal excellent luminescent properties, making these Dy3+/Sm3+ co-doped phosphors advantageous for white light-emitting diode (WLED) technologies.

Cool green-emissive Y2Si2O7:Tb3+ nanophosphor: auto-combustion synthesis and structural and photoluminescence characteristics with good thermal stability for lighting applications.

A cheap, versatile, sustainable and energy-efficient gel-combustion method was applied to develop a series of green-emitting down-converted Y2Si2O7:Tb3+ (YPS:Tb3+) nanophosphors. Employing XRD-based Rietveld refinement approach, the phase purity and crystallographic evaluation of the produced phosphor were conducted, revealing a triclinic crystal with P1̄ space group. EDX and TEM analyses were performed on the synthesized samples to determine their elemental composition and morphological properties. Diffuse reflectance spectra yielded 5.61 eV and 5.79 eV optical energy band gaps for the host and the optimized (0.04 mole of Tb3+) sample, respectively. UV light has the ability to excite the nanocrystalline phosphor in an efficient manner, leading to significant luminosity qualities attributed to the radiative relaxation of 5D4 → 7FJ (J = 6, 5, 4, 3). The bi-exponential decay function was derived by the PL decay curves. With an activation energy of 0.2206 eV, the Y1.96Si2O7:0.04Tb3+ phosphor exhibits good thermal quenching capabilities. Improved photometric attributes including CIE coordinates, CCT and color purity confirmed the green glow, indicating a strong competitor for cool-green emission in lighting applications.

A generalized functions based approach for stress-driven nanobeam bending problems subjected to point loads

The research community has widely accepted the stress-driven nonlocal integral model to study static and dynamic characteristics of nanostructures. Although closed-form solutions for stress-driven point-loaded nanobeam bending problems that find potential for applications in the design of real-world MEMS/NEMS-based sensors have been explored recently, the static bending behavior of stress-driven Bernoulli-Euler and Timoshenko nanobeams subjected to point-loading conditions in various end configurations are studied in the present work wherein, analytical solutions for the same are arrived at by expressing the input bending and shear fields in terms of generalized functions for the first time. Equipped with the Helmholtz bi-exponential kernel function to model the nonlocality, the obtained solutions have demonstrated their ability to capture size-effects consistently. An overall stiffening effect on the nanobeam is observed as a consequence of these size-effects.

The Surprising Dynamics of the McLafferty Rearrangement.

We report femtosecond time-resolved measurements of the McLafferty rearrangement following the strong-field tunnel ionization of 2-pentanone, 4-methyl-2-pentanone, and 4,4-dimethyl-2-pentanone. The pump-probe-dependent yields of the McLafferty product ion are fit to a biexponential function with fast (∼100 fs) and slow (∼10 ps) time constants, the latter of which is faster for the latter two compounds. Following nearly instantaneous ionization, the fast time scale is associated with rotation of the molecule to a six-membered cyclic intermediate that facilitates transfer of the γ-hydrogen, while the ∼50-100 times longer time scale is associated with a π-bond rearrangement and bond cleavage between the α- and β-carbons to produce the enol cation. These experimental measurements are supported by ab initio molecular dynamics trajectories, which further confirm the time scale of this important stepwise reaction in mass spectrometry.

Photophysical studies of a coumarin derivative in the aqueous solution of three different classes of copolymers

In this article we have reported the modulation of spectral behavior of a hydrophilic coumarin based molecule 7-(diethylamino) coumarin-3-carboxylic acid (7-DCCA) in aqueous solution of polyethylene oxide (PEO)-polypropylene oxide (PPO) block copolymers with different structures and hydrophobicity. Linear triblock copolymer namely Pluronic (F-98, F-38, P-84), its X-shaped counterpart namely Tetronic (T-1304, T-1307) along with a reverse Pluronic (17-R4) were utilised with a temperature variation from 10 °C to 50°C and 7-DCCA was used as the probe to observe the changes in photophysical aspect. Of the studied copolymers, 10 wt% T-1307 and F-38 face difficulty in micelle formation owing to their hydrophilic nature and lower molecular weight PPO blocks. Also, 0.1 wt% 17-R4 remains as single-coils in the studied temperature range. Hence, these copolymers induce a different environment on the photophysics in 7-DCCA as compared to copolymers that form usual micelles (10 wt% T-1304, P-84, F-98). With increasing temperature, a persistent blue-shift in absorption and excitation spectra of the probe could be noticed upon addition of 10 wt% T-1304, T-1307, F-98, P-84, as well as 0.1 wt% 17-R4. The fluorescence emission maximum of the probe blue-shifted in T-1304, T-1307, F-98 and P-84 solutions whereas a red-shift was noticed in 17-R4. The fluorescence emission decays collected in the presence of T-1304, T-1307, F-38, F-98 and P-84 were fitted using tri-exponential functions while bi-exponential functions were used in the presence of 17-R4. A dip-rise-dip anisotropy decay pattern was observed for T-1307, F-38, and 17-R4 whereas, bi-exponential functions were used for T-1304, F-98 and P-84. The constitution of the copolymer along with its molecular properties helped us to correlate the obtained data.

Time-resolved fluorescence anisotropy with Atto 488-labeled phytochrome Agp1 from Agrobacterium fabrum.

Phytochromes are photoreceptor proteins with a bilin chromophore that undergo photoconversion between two spectrally different forms, Pr and Pfr. Three domains, termed PAS, GAF, and PHY domains, constitute the N-terminal photosensory chromophore module (PCM); the C-terminus is often a histidine kinase module. In the Agrobacterium fabrum phytochrome Agp1, the autophosphorylation activity of the histidine kinase is high in the Pr and low in the Pfr form. Crystal structure analyses of PCMs suggest flexibility around position 308 in the Pr but not in the Pfr form. Here, we performed time-resolved fluorescence anisotropy measurements with different Agp1 mutants, each with a single cysteine residue at various positions. The fluorophore label Atto-488 was attached to each mutant, and time-resolved fluorescence anisotropy was measured in the Pr and Pfr forms. Fluorescence anisotropy curves were fitted with biexponential functions. Differences in the amplitude A2 of the second component between the PCM and the full-length variant indicate a mechanical coupling between position 362 and the histidine kinase. Pr-to-Pfr photoconversion induced no significant changes in the time constant t2 at any position. An intermediate t2 value at position 295, which is located in a compact environment, suggests flexibility around the nearby position 308 in Pr and in Pfr.

Electron-stimulated desorption kinetics of ultra-thin LiCl films on graphene

Ultra-thin alkali halide films are an important substrate for studying single quantum objects at the atomic scale, as they serve as decoupling scaffolds. However, their stability upon exposure to electrons and photons, the most common probes used to study nanomaterials, is not fully understood. Here we present a study of the evolution of the structure of ultra-thin LiCl films, grown on graphene, upon low-energy electron irradiation by means of microspot-low-energy electron diffraction and microscopy. We find that the intensity of the LiCl diffraction spots irradiated at various electron energies follows a bi-exponential decay function, which can be rationalized by two different desorption regimes. In addition, we detect a change in the work function caused by the electron irradiation, confirming desorption of the LiCl film from the graphene layer. We understand the underlying mechanisms for the electron-induced desorption of the salt film in terms of the evolution of the elementary quasiparticles involved in the process: holes, excitons and F and H center pairs. Moreover, a direct comparison of the electron-induced and the soft X-ray photon-induced processes reveal that, in addition to LiCl desorption, the intercalation of lithium into graphene reported for X-ray induced desorption does not take place in electron-stimulated desorption.

Tri- and bi-exponential diffusion analyses of the kidney: effect of respiratory-controlled acquisition on diffusion parameters.

This study examined whether respiratory-controlled acquisition influences diffusion parameters obtained with intravoxel incoherent motion (IVIM) analysis using tri-exponential and bi-exponential models. Ten healthy volunteers were examined on a 3.0T MRI system to obtain coronal diffusion-weighted images of both kidneys. The participants were scanned twice using respiratory-triggering (RT) and free-breathing (FB) acquisition to assess the repeatability of the measurements. We determined mean signal intensities in the renal cortex at each b value. Then, perfusion-related diffusion coefficient (Dp), fast-free diffusion coefficient (Df), slow-restricted diffusion coefficient (Ds), and their corresponding fractions (Fp, Ff, and Fs, respectively) were calculated using tri-exponential function. Moreover, perfusion-related diffusion coefficient (D*), the fraction (F), and perfusion-independent diffusion coefficient (D) were calculated using bi-exponential function. Normalized root-mean-square errors for the tri- and bi-exponential analyses (nRMSEtri and nRMSEbi, respectively) were determined to assess the deviation of the fitted to measured data, i.e., the fitting accuracy. Additionally, repeatability coefficients (RCs) were calculated from Bland-Altman plots to evaluate the repeatability of each diffusion parameter. These values were compared between the RT and FB groups. Dp and D* in the RT group were significantly lower than those in the FB group (P < 0.05). In addition, the RT group showed significantly lower nRMSEtri and nRMSEbi values than those in the FB group (P < 0.05). Moreover, Dp, Ds, Fs, and D* at RT showed lower RC values than those at FB. Respiratory-controlled acquisition affects perfusion-related diffusion parameters of the kidney obtained using tri-exponential and bi-exponential analyses.

Dosimetric analysis of a compartmental model for radioligand uptake in tumor lesions

Radioligand therapy is a targeted cancer therapy that delivers radiation to tumor cells based on the expression of specific markers on the cell surface. It has become an important treatment option in metastasized neuroendocrine tumors and advanced prostate cancer. The analysis of absorbed doses in radioligand therapies has gained much attention and remains a challenging task due to individual pharmacokinetics. As an alternative to the often used sum of exponential functions in intra-therapeutic dosimetry, a basic compartmental model for the pharmacokinetics of radioligands is described and analyzed in this paper. In its simplest version, the model behavior is determined by the uptake capacity and the association constant and can be solved analytically. The model is extended with rates for excretion from the source compartment and externalization from the lesion compartment. Numerical calculations offer an insight into the quantitative effects of the model parameters on the absorbed dose in the tumor lesion. This analysis helps understanding the importance of clinically relevant factors, e.g. the effect on absorbed doses of modified radioligands that bind to albumin. Using clinical data, the potential application in intra-therapeutic dosimetry is illustrated and compared to the bi-exponential function which lacks a mechanistical basis. While the compartmental model is found to constitute a feasible alternative in these examples, this has to be confirmed by further clinical studies.

Accuracy and uncertainty analysis of reduced time point imaging effect on time-integrated activity for 177Lu-DOTATATE PRRT in patients and clinically realistic simulations

BackgroundDosimetry promises many advantages for radiopharmaceutical therapies but repeat post-therapy imaging for dosimetry can burden both patients and clinics. Recent applications of reduced time point imaging for time-integrated activity (TIA) determination for internal dosimetry following 177Lu-DOTATATE peptide receptor radionuclide therapy have shown promising results that allow for the simplification of patient-specific dosimetry. However, factors such as scheduling can lead to sub-optimal imaging time points, but the resulting impact on dosimetry accuracy is still under investigation. We use four-time point 177Lu SPECT/CT data for a cohort of patients treated at our clinic to perform a comprehensive analysis of the error and variability in time-integrated activity when reduced time point methods with various combinations of sampling points are employed.MethodsThe study includes 28 patients with gastroenteropancreatic neuroendocrine tumors who underwent post-therapy SPECT/CT imaging at approximately 4, 24, 96, and 168 h post-therapy (p.t.) following the first cycle of 177Lu-DOTATATE. The healthy liver, left/right kidney, spleen and up to 5 index tumors were delineated for each patient. Time-activity curves were fit with either monoexponential or biexponential functions for each structure, based on the Akaike information criterion. This fitting was performed using all 4 time points as a reference and various combinations of 2 and 3 time points to determine optimal imaging schedules and associated errors. 2 commonly used methods of single time point (STP) TIA estimation are also evaluated. A simulation study was also performed with data generated by sampling curve fit parameters from log-normal distributions derived from the clinical data and adding realistic measurement noise to sampled activities. For both clinical and simulation studies, error and variability in TIA estimates were estimated with various sampling schedules.ResultsThe optimal post-therapy imaging time period for STP estimates of TIA was found to be 3–5 days (71–126 h) p.t. for tumor and organs, with one exception of 6–8 days (144–194 h) p.t. for spleen with one STP approach. At the optimal time point, STP estimates give mean percent errors (MPE) within ± 5% and SD < 9% across all structures with largest magnitude error for kidney TIA (MPE = − 4.1%) and highest variability also for kidney TIA (SD = 8.4%). The optimal sampling schedule for 2TP estimates of TIA is 1–2 days (21–52 h) p.t. followed by 3–5 days (71–126 h) p.t. for kidney, tumor, and spleen. Using the optimal sampling schedule, the largest magnitude MPE for 2TP estimates is 1.2% for spleen and highest variability is in tumor with SD = 5.8%. The optimal sampling schedule for 3TP estimates of TIA is 1–2 days (21–52 h) p.t. followed by 3–5 days (71–126 h) p.t. and 6–8 days (144–194 h) p.t. for all structures. Using the optimal sampling schedule, the largest magnitude MPE for 3TP estimates is 2.5% for spleen and highest variability is in tumor with SD = 2.1%. Simulated patient results corroborate these findings with similar optimal sampling schedules and errors. Many sub-optimal reduced time point sampling schedules also exhibit low error and variability.ConclusionsWe show that reduced time point methods can be used to achieve acceptable average TIA errors over a wide range of imaging time points and sampling schedules while maintaining low uncertainty. This information can improve the feasibility of dosimetry for 177Lu-DOTATATE and elucidate the uncertainty associated with non-ideal conditions.