Time-dependent density-functional-theory calculations of the nonlocal electron stopping range for inertial confinement fusion applications.

Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. We utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code lilac to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. Results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.

Proton stopping measurements at low velocity in warm dense carbon.

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Physical health, behavioral and emotional functioning in children of gulf war veterans.

OBJECTIVE: We examined whether the prevalence of medical and behavioral conditions is higher in children of deployed veterans (DVs) versus non-deployed veterans (NDVs) after the 1991 Gulf War. METHODS: We examined 1387 children of 737 veterans. Children ages 2-18 had physical exams and parental reports of physical history and behavior. RESULTS: Physical health was analyzed using GEE models. Behavioral health [total, internalizing, and externalizing behavior problems (TBP, IBP, EBP)] was analyzed with mixed-effects regression models. Analyses were conducted by age group (2-3, 4-11, 12-18), and gender (ages 4-11, 12-18). Children of DVs ages 2-3 had significantly worse dentition (13.9% vs. 4.8%, P = 0.03) and more EBP {least square means (lsmeans) 54.31 vs. 47.59, P = 0.02}. Children of DVs ages 4-11 had significantly more obesity (18.8% vs. 12.7%, P = 0.02). Among children 4-11, male children of DVs had significantly more TBP (lsmeans 70.68 vs. 57.34, P = 0.003), IBP (lsmeans 63.59 vs. 56.16, P = 0.002) and EBP (lsmeans 61.60 vs. 52.93, P = 0.03), but female children did not. For children ages 12-18, male children of DVs had more EBP (lsmeans 63.73 vs. 43.51, P = 0.008), while female children of DVs had fewer EBP (lsmeans 45.50 vs. 50.48, P = 0.02). Veteran military characteristics and mental health, and children's social status and health, including obesity, predicted children's TBP for one or more age groups. CONCLUSIONS: Children of DVs experienced worse dentition, greater obesity, and more behavioral problems compared to NDV children, suggesting adverse health effects associated with parental deployment in need of further exploration.

Perceived usefulness and ease of use of fundoscopy by medical students: a randomised crossover trial of six technologies (eFOCUS 1).

BACKGROUND: Fundoscopy outside ophthalmology is in decline, and the technical demands of the traditional direct ophthalmoscope examination are likely contributing. Alternative fundoscopy technologies are increasingly available, yet valid comparisons between fundoscopy technologies are lacking. We aimed to assess medical students' perceptions of usefulness and ease of use of traditional and contemporary fundus-viewing technologies including smartphone fundoscopy. METHODS: One hundred forty-six second-year medical students participated in a cross-sectional, randomised, cross-over study of fundoscopy methods. Medical students completed small group training sessions using six current fundoscopy technologies including: a non-mydriatic fundus camera; two types of direct fundoscopy; and three types of smartphone fundoscopy. A novel survey of perceived usefulness and ease of use was then completed by students. RESULTS: Repeated-measures ANOVA found students rated both the perceived usefulness (p< 0.001) and ease of use (p< 0.001) of smartphone fundoscopy significantly higher than both the non-mydriatic camera and direct fundoscopy. CONCLUSIONS: Smartphone fundoscopy was found to be significantly more useful and easier to use than other modalities. Educators should optimise student access to novel fundoscopy technologies such as smartphone fundoscopy which may mitigate the technical challenges of fundoscopy and reinvigorate use of this valuable clinical examination.

Second international guidelines for the diagnosis and management of hereditary hemorrhagic telangiectasia

Hereditary hemorrhagic telangiectasia (HHT) is an autosomal dominant disease with an estimated prevalence of 1 in 5000 that is characterized by the presence of vascular malformations (VMs). These result in chronic bleeding, acute hemorrhage, and complications from shunting through VMs. The goal of the Second International HHT Guidelines process was to develop evidence-based consensus guidelines for the management and prevention of HHT-related symptoms and complications. The guidelines were developed using the AGREE II (Appraisal of Guidelines for Research and Evaluation II) framework and GRADE (Grading of Recommendations Assessment, Development and Evaluation) methodology. The guidelines expert panel included expert physicians (clinical and genetic) in HHT from 15 countries, guidelines methodologists, health care workers, health care administrators, patient advocacy representatives, and persons with HHT. During the preconference process, the expert panel generated clinically relevant questions in 6 priority topic areas. A systematic literature search was done in June 2019, and articles meeting a priori criteria were included to generate evidence tables, which were used as the basis for recommendation development. The expert panel subsequently convened during a guidelines conference to conduct a structured consensus process, during which recommendations reaching at least 80% consensus were discussed and approved. The expert panel generated and approved 6 new recommendations for each of the following 6 priority topic areas: epistaxis, gastrointestinal bleeding, anemia and iron deficiency, liver VMs, pediatric care, and pregnancy and delivery (36 total). The recommendations highlight new evidence in existing topics from the first International HHT Guidelines and provide guidance in 3 new areas: anemia, pediatrics, and pregnancy and delivery. These recommendations should facilitate implementation of key components of HHT care into clinical practice.

Mixed quantum-classical approach to model non-adiabatic electron-nuclear dynamics: Detailed balance and improved surface hopping method.

We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional "virtual" nuclear wave packets whose interference with the "real" (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma.

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

Multicomponent mutual diffusion in the warm, dense matter regime.

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Fine-grained Material Associated with a Large Sulfide returned from Comet 81P/Wild 2.

In a consortium analysis of a large particle captured from the coma of comet 81P/Wild 2 by the Stardust spacecraft, we report the discovery of a field of fine-grained material (FGM) in contact with a large sulfide particle. The FGM was partially located in an embayment in the sulfide. As a consequence, some of the FGM appears to have been protected from damage during hypervelocity capture in aerogel. Some of the FGM particles are indistinguishable in their characteristics from common components of chondritic-porous interplanetary dust particles (CP-IDPs), including glass with embedded metals and sulfides (GEMS) and equilibrated aggregates (EAs). The sulfide exhibits surprising Ni-rich lamellae, which may indicate that this particle experienced a long-duration heating event after its formation but before incorporation into Wild 2.

Fecal stanols show simultaneous flooding and seasonal precipitation change correlate with Cahokia's population decline.

A number of competing hypotheses, including hydroclimatic variations, environmental degradation and disturbance, and sociopolitical disintegration, have emerged to explain the dissolution of Cahokia, the largest prehistoric population center in the United States. Because it is likely that Cahokia's decline was precipitated by multiple factors, some environmental and some societal, a robust understanding of this phenomenon will require multiple lines of evidence along with a refined chronology. Here, we use fecal stanol data from Horseshoe Lake, Illinois, as a population proxy for Cahokia and the broader Horseshoe Lake watershed. We directly compare the fecal stanol data with oxygen stable-isotope and paleoenvironmental data from the same sediment cores to evaluate the role of flooding, drought, and environmental degradation in Cahokia's demographic decline and sociopolitical reorganization. We find that Mississippi River flooding and warm season droughts detrimental to agriculture occurred circa (ca.) 1150 CE and possibly generated significant stress for Cahokia's inhabitants. Our findings implicate climate change during the Medieval Climatic Anomaly to Little Ice Age transition as an important component of population and sociopolitical transformations at Cahokia, and demonstrate how climate transitions can simultaneously influence multiple environmental processes to produce significant challenges to society.

Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory.

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.

Highly active aluminium catalysts for room temperature ring-opening polymerisation of rac-lactide.

A new series of aluminium complexes bearing 'catam' ligands has been synthesised and fully characterised. They were found to exhibit high activity at room temperature for rac-lactide ring-opening polymerisation, a rather rare feature for aluminium-based catalysts.

Maternal vitamin D, DNA methylation at imprint regulatory regions and offspring weight at birth, 1 year and 3 years.

BACKGROUND/OBJECTIVE: Vitamin D deficiency during pregnancy is associated with poor birth outcomes in some studies, but few have examined weight beyond birth. In addition, little is known about how vitamin D influences DNA methylation of regulatory regions known to be involved in growth, as possible mediators to weight status in offspring. SUBJECTS/METHODS: We conducted linear regressions to assess maternal plasma 25-hydroxyvitamin D (25(OH)D) by quartile and birth weight for gestational age z-score, 1-year weight-for-length z-score and 3-year body mass index (BMI) z-score among 476 mother/infant dyads from a prospective cohort. We assessed maternal 25(OH)D and infant DNA methylation at nine differentially methylated regions (DMRs) of genomically imprinted genes with known functions in fetal growth, including H19, IGF2, MEG3, MEG3-IG, MEST, NNAT, PEG3, PLAGL1 and SGCE/PEG10. RESULTS: Mean (standard deviation, s.d.) maternal 25(OH)D was 41.1 (14.2) nmol l-m at a mean (s.d.) of 13.2 (5.5) weeks gestation. After adjustment for potential confounders, the first (Q1) and second (Q2) quartiles of 25(OH)D, compared to the fourth (Q4), were associated with lower birth weight for gestational age z-scores (-0.43 units; CI: -0.79, -0.07; P=0.02 for Q1 and -0.56 units; CI: -0.89, -0.23; P=0.001 for Q2). Q1 compared to Q4 was associated with higher 1-year weight-for-length z-scores (0.78 units; 0.08, 1.54; P=0.04) and higher 3-year BMI z-scores (0.83 units; 0.11, 0.93; P=0.02). We did not observe associations between maternal 25(OH)D and methylation for any of the nine DMRs after correcting for multiple testing. CONCLUSIONS: Reduced maternal 25(OH)D was associated with lower birth weight for gestational age z-scores but higher 1-year weight-for-length and 3-year BMI z-scores in offspring. However, 25(OH)D does not appear to be operating through the regulatory sequences of the genomically imprinted genes we examined.

The impact of ionic liquids on the coordination of anions with solvatochromic copper complexes.

Solvatochromic transition metal (TM)-complexes with weakly associating counter-anions are often used to evaluate traditional neutral solvent and anion coordination ability. However, when employed in ionic liquids (IL) many of the common assumptions made are no longer reliable. This study investigates the coordinating ability of weakly coordinating IL anions in traditional solvents and within IL solvents employing a range of solvatochromic copper complexes. Complexes of the form [Cu(acac)(tmen)][X] (acac = acetylacetonate, tmen = tetramethylethylenediamine) where [X]- = [ClO4]-, Cl-, [NO3]-, [SCN]-, [OTf]-, [NTf2]- and [PF6]- have been synthesised and characterised both experimentally and computationally. ILs based on these anions and imidazolium and pyrrolidinium cations, some of which are functionalised with hydroxyl and nitrile groups, have been examined. IL-anion coordination has been investigated and compared to typical weakly coordinating anions. We have found there is potential for competition at the Cu-centre and cases of anions traditionally assigned as weakly associating that demonstrate a stronger than expected level of coordinating ability within ILs. [Cu(acac)(tmen)][PF6] is shown to contain the least coordinating anion and is established as the most sensitive probe studied here. Using this probe, the donor numbers (DNs) of ILs have been determined. Relative donor ability is further confirmed based on the UV-Vis of a neutral complex, [Cu(sacsac)2] (sacsac = dithioacetylacetone), and DNs evaluated via23Na NMR spectroscopy. We demonstrate that ILs can span a wide donor range, similar in breadth to conventional solvents.

Single operation palladium catalysed C(sp3)-H functionalisation of tertiary aldehydes: investigations into transient imine directing groups.

Simple amine and diamine derivatives can promote the palladium catalysed direct ß-C-H arylation of aliphatic aldehydes via transient imine formation. Trifluoroacetate was shown to be crucial in promoting the reaction. Sub-stoichiometric quantities of simple N-tosylethylenediamine was shown to form a bidentate directing group with an imine linkage. Isolation of an unsymmetrical palladacycle has shown different potential binding modes of the secondary NTs coordinating group by single crystal X-ray diffraction analysis, suggestive of a hemilabile ligand.

The Prevalence of Malformations of Cortical Development in a Pediatric Hereditary Hemorrhagic Telangiectasia Population.

BACKGROUND AND PURPOSE: Brain AVM, cerebral abscess, and ischemic stroke are among the well known neurologic manifestations of hereditary hemorrhagic telangiectasia. However, recently reported data suggest an additional association with malformations of cortical development. The purpose of this study was to determine the prevalence of malformations of cortical development in a population of pediatric patients with hereditary hemorrhagic telangiectasia. MATERIALS AND METHODS: A retrospective review of brain MRIs from 116 pediatric patients was performed. Each patient was referred from our institution's Hereditary Hemorrhagic Telangiectasia Clinic. Each MRI included a 3D sequence, most frequently MPRAGE. The 3D sequence was evaluated by a neuroradiology fellow, with specific attention to the presence or absence of malformations of cortical development. Positive studies were subsequently reviewed by 2 attending neuroradiologists, who rendered a final diagnosis. RESULTS: Fourteen of 116 (12.1%) patients were found to have a malformation of cortical development. Among these 14, there were 12 cases of polymicrogyria and 2 cases of bifrontal periventricular nodular heterotopia. CONCLUSIONS: Pediatric patients with hereditary hemorrhagic telangiectasia have a relatively high prevalence of malformations of cortical development, typically perisylvian polymicrogyria.

Hypogammaglobulinemia in pediatric systemic lupus erythematosus.

OBJECTIVE: Systemic lupus erythematosus (SLE) is a systemic autoimmune disease typically associated with elevated serum immunoglobulin G (IgG). Hypogammaglobulinemia in SLE patients has been attributed to immunosuppressive treatment or a transient effect associated with nephrotic syndrome. We retrospectively reviewed pediatric SLE patients from a single institution to identify patients with hypogammaglobulinemia and risk factors for hypogammaglobulinemia. METHODS: A total of 116 pediatric SLE cases from 1997 to 2011 were reviewed and patients with hypogammaglobulinemia (IgG < 500 mg/dl) were identified. The two cohorts were evaluated for association with age, sex, presence of lupus nephritis at SLE diagnosis, disease activity at diagnosis, initial IgG level, and drug treatment. RESULTS: Eighty-six patients were included in our study, with a median age of 15 years and a median follow-up of 39.5 months. Seven percent (six of 86) of patients had hypogammaglobulinemia with a median onset of 27 months (0-72 months) after SLE diagnosis. Significant associations were noted for white race (p value 0.029), male sex (p value 0.009), and the presence of lupus nephritis at SLE diagnosis (p value 0.004). Use of immunosuppressive treatment did not show a statistical association with hypogammaglobulinemia, although two of the patients with hypogammaglobulinemia did receive rituximab. Most patients with hypogammaglobulinemia received intravenous immunoglobulin (IVIG) replacement therapy because of infections and/or concern for infection. CONCLUSION: Measurement of immunoglobulin levels during treatment in SLE could help identify patients with hypogammaglobulinemia who might require more aggressive follow-up to monitor for increased risk of infection and need for IVIG treatment. A prospective study is needed to validate associated risk factors identified in this study.

The use of electroconvulsive therapy in a patient with juvenile systemic lupus erythematosus and catatonia.

Catatonia is a rare manifestation in patients with systemic lupus erythematosus (SLE). As catatonia can be associated with both psychiatric and organic conditions, this could create a diagnostic dilemma once this occurs in SLE patients. The report describes a 15-year-old female with SLE who developed catatonia three days after the diagnosis of SLE was made. Her catatonia was refractory to the treatment with immunosuppressive therapy, which included pulse methylprednisolone, intravenous cyclophosphamide, rituximab, intravenous immunoglobulin (IVIG) and plasmapheresis. Given her persistent catatonia, electroconvulsive therapy (ECT) was initiated three months after the onset of her symptoms. After the third ECT treatment, her mental status dramatically improved and returned nearly to baseline while she was continued on the immunosuppression. This is the first report of a successful ECT therapy in catatonic lupus in children.

Inhibition of erosive dissolution by sodium fluoride: evidence for a dose-response.

OBJECTIVES: The aim of this study was to investigate the protective effects of sodium fluoride solutions and commercial mouthrinses on hydroxyapatite (HA) dissolution in citric acid in vitro, with and without a salivary pellicle. METHODS: A rapid-throughput HA solubility-reduction model was employed in which HA dissolution was quantified using ion chromatography. Two HA substrates were selected, a high-resolution powder and 80 µm diameter beads, and studied in the presence and absence of a salivary pellicle (pooled human saliva, 2 h). Immediately prior to acid exposure, substrates were exposed to one of a number of pre-treatments that included aqueous fluoride (F(-)) solutions and commercially available mouthrinses with F(-) concentrations of 0-450 µg/g (as NaF). Dissolution reduction was calculated relative to a deionised water negative control. RESULTS: For aqueous solutions and mouthrinses, a fluoride dose-response was observed with a plateau around 100 µg/g F(-) for both HA substrates, with or without pellicle. Concentrations as low as 10 µg/g F(-) significantly reduced HA dissolution. The HA substrate had little impact on the fluoride dose-response, and the fluoride was equally effective in the presence of a pellicle as in its absence. CONCLUSIONS: Fluoride significantly reduced HA dissolution at concentrations of 10 µg/g and higher. A fluoride dose-response was seen at low concentrations. This study illustrates the use of a powerful rapid-throughput HA solubility-reduction model for investigating HA dissolution in citric acid in the presence of dissolution inhibitors. CLINICAL SIGNIFICANCE: A single exposure to fluoride solutions with fluoride concentrations and exposure time representative of brushing or rinsing with mainstream oral care products was shown to significantly inhibit HA dissolution under conditions relevant to dental erosion. A similar efficacy was observed in the presence and absence of salivary pellicle.

Inhibition of dental erosion by casein and casein-derived proteins.

The application of milk-derived proteins such as casein as anti-erosion agents in oral healthcare products is of current interest. The aim of this study was to investigate the potential of 3 commercially available, milk-derived proteins as agents to inhibit enamel erosion. Aqueous solutions of 0.5% w/v casein, casein phosphopeptide (CPP) or glycomacropeptide (GMP) with and without 300 ppm fluoride (F, as NaF) were investigated with regard to enamel softening and tissue loss, in comparison with a deionised water (DIW) negative control and 300 ppm F positive control. Casein and F reduced enamel surface softening compared to DIW, but CPP and GMP did not (DIW: 58.2% reduction in hardness; F: 13.3%; casein: 21.8%; CPP: 50.8%; GMP: 62.4%). Similar results were obtained with solutions containing protein and F, and the effects were statistically indistinguishable from protein alone (casein + F: 19.1%; CPP + F: 48.2%; GMP + F: 66.1%). By contrast, all protein solutions and F significantly reduced tissue loss (p < 0.050; DIW: 25.8 µm tissue loss; F: 21.6 µm; casein: 20.3 µm; CPP: 20.5 µm; GMP: 20.0 µm). Solutions containing protein and F reduced erosion more than protein alone, but this difference was only significant from protein alone for casein (casein + F: 12.2 µm; CPP + F: 17.3 µm; GMP + F: 18.2 µm). Casein and casein-derived proteins may therefore have the potential to act as agents to reduce or prevent enamel erosion. Furthermore, the erosion-reducing efficacy is not reduced by F, and is in some cases enhanced.