Polygonal tessellations as predictive models of molecular monolayers.

Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by covalent, hydrogen or van der Waals interactions-self-assembly of alike molecules results in a large variety of complex patterns even in two dimensions (2D). Prediction of pattern formation for 2D molecular networks is extremely important, though very challenging, and so far, relied on computationally involved approaches such as density functional theory, classical molecular dynamics, Monte Carlo, or machine learning. Such methods, however, do not guarantee that all possible patterns will be considered and often rely on intuition. Here, we introduce a much simpler, though rigorous, hierarchical geometric model founded on the mean-field theory of 2D polygonal tessellations to predict extended network patterns based on molecular-level information. Based on graph theory, this approach yields pattern classification and pattern prediction within well-defined ranges. When applied to existing experimental data, our model provides a different view of self-assembled molecular patterns, leading to interesting predictions on admissible patterns and potential additional phases. While developed for hydrogen-bonded systems, an extension to covalently bonded graphene-derived materials or 3D structures such as fullerenes is possible, significantly opening the range of potential future applications.

Plato's cube and the natural geometry of fragmentation.

Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra-shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.

Soft cells and the geometry of seashells.

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes. Here, we solve this problem by introducing a new class of shapes, the soft cells, minimizing the number of sharp corners and filling space as soft tilings. We prove that an infinite class of polyhedral tilings can be smoothly deformed into soft tilings and we construct the soft versions of all Dirichlet-Voronoi cells associated with point lattices in two and three dimensions. Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells.

Iron chelation therapy with deferasirox in patients with aplastic anemia: a subgroup analysis of 116 patients from the EPIC trial.

The prospective 1-year Evaluation of Patients' Iron Chelation with Exjade (EPIC) study enrolled a large cohort of 116 patients with aplastic anemia; the present analyses evaluated the efficacy and safety of deferasirox in this patient population. After 1 year, median serum ferritin decreased significantly from 3254 ng/mL at baseline to 1854 ng/mL (P < .001). Decreases occurred in chelation-naive (3229-1520 ng/mL; P < .001, last-observation-carried-forward analysis), and previously chelated (3263-2585 ng/mL; P = .21, last-observation-carried-forward analysis) patients and were reflective of dose adjustments and ongoing iron intake. Baseline labile plasma iron levels were within normal range despite high serum ferritin levels. The most common drug-related adverse events were nausea (22%) and diarrhea (16%). Serum creatinine increases more than 33% above baseline and the upper limit of normal occurred in 29 patients (25%), but there were no progressive increases; concomitant use of cyclosporine had a significant impact on serum creatinine levels. The decrease in mean alanine aminotransferase levels at 1 year correlated significantly with reduction in serum ferritin (r = 0.40, P < .001). Mean absolute neutrophil and platelet counts remained stable during treatment, and there were no drug-related cytopenias. This prospective dataset confirms the efficacy and well characterizes the tolerability profile of deferasirox in a large population of patients with aplastic anemia. This study was registered at www.clinicaltrials.gov as #NCT00171821.

Efficacy of deferasirox in reducing and preventing cardiac iron overload in beta-thalassemia.

Cardiac iron overload causes most deaths in beta-thalassemia major. The efficacy of deferasirox in reducing or preventing cardiac iron overload was assessed in 192 patients with beta-thalassemia in a 1-year prospective, multicenter study. The cardiac iron reduction arm (n = 114) included patients with magnetic resonance myocardial T2* from 5 to 20 ms (indicating cardiac siderosis), left ventricular ejection fraction (LVEF) of 56% or more, serum ferritin more than 2500 ng/mL, liver iron concentration more than 10 mg Fe/g dry weight, and more than 50 transfused blood units. The prevention arm (n = 78) included otherwise eligible patients whose myocardial T2* was 20 ms or more. The primary end point was the change in myocardial T2* at 1 year. In the cardiac iron reduction arm, the mean deferasirox dose was 32.6 mg/kg per day. Myocardial T2* (geometric mean +/- coefficient of variation) improved from a baseline of 11.2 ms (+/- 40.5%) to 12.9 ms (+/- 49.5%) (+16%; P < .001). LVEF (mean +/- SD) was unchanged: 67.4 (+/- 5.7%) to 67.0 (+/- 6.0%) (-0.3%; P = .53). In the prevention arm, baseline myocardial T2* was unchanged from baseline of 32.0 ms (+/- 25.6%) to 32.5 ms (+/- 25.1%) (+2%; P = .57) and LVEF increased from baseline 67.7 (+/- 4.7%) to 69.6 (+/- 4.5%) (+1.8%; P < .001). This prospective study shows that deferasirox is effective in removing and preventing myocardial iron accumulation. This study is registered at http://clinicaltrials.gov as NCT00171821.

Deferasirox for up to 3 years leads to continued improvement of myocardial T2* in patients with ß-thalassemia major.

BACKGROUND: Prospective data on cardiac iron removal are limited beyond one year and longer-term studies are, therefore, important. DESIGN AND METHODS: Seventy-one patients in the EPIC cardiac substudy elected to continue into the 3(rd) year, allowing cardiac iron removal to be analyzed over three years. RESULTS: Mean deferasirox dose during year 3 was 33.6 ± 9.8 mg/kg per day. Myocardial T2*, assessed by cardiovascular magnetic resonance, significantly increased from 12.0 ms ± 39.1% at baseline to 17.1 ms ± 62.0% at end of study (P<0.001), corresponding to a decrease in cardiac iron concentration (based on ad hoc analysis of T2*) from 2.43 ± 1.2 mg Fe/g dry weight (dw) at baseline to 1.80 ± 1.4 mg Fe/g dw at end of study (P<0.001). After three years, 68.1% of patients with baseline T2* 10 to <20 ms normalized (≥ 20 ms) and 50.0% of patients with baseline T2* >5 to <10 ms improved to 10 to <20 ms. There was no significant variation in left ventricular ejection fraction over the three years. No deaths occurred and the most common investigator-assessed drug-related adverse event in year 3 was increased serum creatinine (n = 9, 12.7%). CONCLUSIONS: Three years of deferasirox treatment along with a clinically manageable safety profile significantly reduced cardiac iron overload versus baseline and normalized T2* in 68.1% (32 of 47) of patients with T2* 10 to <20 ms.

Continued improvement in myocardial T2* over two years of deferasirox therapy in ß-thalassemia major patients with cardiac iron overload.

BACKGROUND: The efficacy of cardiac iron chelation in transfusion-dependent patients has been demonstrated in one-year prospective trials. Since normalization of cardiac T2* takes several years, the efficacy and safety of deferasirox was assessed for two years in patients with ß-thalassemia major in the cardiac sub-study of the EPIC trial. DESIGN AND METHODS: Eligible patients with myocardial T2* greater than 5 to less than 20 ms received deferasirox, with the primary endpoint being the change in T2* from baseline to two years. RESULTS: Baseline myocardial T2* was severe (> 5 to < 10 ms) in 39 patients, and moderate-to-mild (10 to < 20 ms) in 62 patients. Mean deferasirox dose was 33.1 ± 3.7 mg/kg/d in the one-year core study increasing to 36.1 ± 7.7 mg/kg/d during the second year of treatment. Geometric mean myocardial T2* increased from a baseline of 11.2 to 14.8 ms at two years (P < 0.001). In patients with moderate-to-mild baseline T2*, an increase was seen from 14.7 to 20.1 ms, with normalization (≥ 20 ms) in 56.7% of patients. In those with severe cardiac iron overload at baseline, 42.9% improved to the moderate-to-mild group. The incidence of drug-related adverse events did not increase during the extension relative to the core study and included (≥ 5%) increased serum creatinine, rash and increased alanine aminotransferase. CONCLUSIONS: Continuous treatment with deferasirox for two years with a target dose of 40 mg/kg/d continued to remove iron from the heart in patients with ß-thalassemia major and mild, moderate and severe cardiac siderosis. (Clinicaltrials.gov identifier: NCT 00171821).

Response of iron overload to deferasirox in rare transfusion-dependent anaemias: equivalent effects on serum ferritin and labile plasma iron for haemolytic or production anaemias.

OBJECTIVES: It is widely assumed that, at matched transfusional iron-loading rates, responses to chelation therapy are similar, irrespective of the underlying condition. However, data are limited for rare transfusion-dependent anaemias, and it remains to be elucidated if response differs, depending on whether the anaemia has a primary haemolytic or production mechanism. METHODS: The efficacy and safety of deferasirox (Exjade®) in rare transfusion-dependent anaemias were evaluated over 1 yr, with change in serum ferritin as the primary efficacy endpoint. Initial deferasirox doses were 10-30 mg/kg/d, depending on transfusion requirements; 34 patients had production anaemias, and 23 had haemolytic anaemias. RESULTS: Patients with production anaemias or haemolytic anaemias had comparable transfusional iron-loading rates (0.31 vs. 0.30 mL red blood cells/kg/d), mean deferasirox dosing (19.3 vs. 19.0 mg/kg/d) and baseline median serum ferritin (2926 vs. 2682 ng/mL). Baseline labile plasma iron (LPI) levels correlated significantly with the transfusional iron-loading rates and with serum ferritin levels in both cohorts. Reductions in median serum ferritin levels were initially faster in the production than the haemolytic anaemias, but at 1 yr, similar significant reductions of 940 and 617 ng/mL were attained, respectively (-26.0% overall). Mean LPI decreased significantly in patients with production (P < 0.0001) and haemolytic (P = 0.037) anaemias after the first dose and was maintained at normal mean levels (< 0.4 µm) subsequently. The most common drug-related, investigator-assessed adverse events were diarrhoea (n = 16) and nausea (n = 12). CONCLUSIONS: At matched transfusional iron-loading rates, the responses of rare transfusion-dependent anaemias to deferasirox are similar at 1 yr, irrespective of the underlying pathogenic mechanism.

Curvature flows, scaling laws and the geometry of attrition under impacts.

Impact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. Here we establish the first link between microscopic, particle-based models and the mean field theory for these processes. Based on realistic computer simulations of particle-wall collision sequences we first identify the well-known damage and fragmentation energy phases, then we show that the former is split into the abrasion phase with infinite sample lifetime (analogous to Sternberg's Law) at finite asymptotic mass and the cleavage phase with finite sample lifetime, decreasing as a power law of the impact velocity (analogous to Basquin's Law). This splitting establishes the link between mean field models (curvature-driven partial differential equations) and particle-based models: only in the abrasion phase does shape evolution emerging in the latter reproduce with startling accuracy the spatio-temporal patterns (two geometric phases) predicted by the former.

Tailoring iron chelation by iron intake and serum ferritin: the prospective EPIC study of deferasirox in 1744 patients with transfusion-dependent anemias.

UNLABELLED: Background Following a clinical evaluation of deferasirox (Exjade) it was concluded that, in addition to baseline body iron burden, ongoing transfusional iron intake should be considered when selecting doses. The 1-year EPIC study, the largest ever investigation conducted for an iron chelator, is the first to evaluate whether fixed starting doses of deferasirox, based on transfusional iron intake, with dose titration guided by serum ferritin trends and safety markers, provides clinically acceptable chelation in patients (aged >or=2 years) with transfusional hemosiderosis from various types of anemia. DESIGN AND METHODS: The recommended initial dose was 20 mg/kg/day for patients receiving 2-4 packed red blood cell units/month and 10 or 30 mg/kg/day was recommended for patients receiving less or more frequent transfusions, respectively. Dose adjustments were based on 3-month serum ferritin trends and continuous assessment of safety markers. The primary efficacy end-point was change in serum ferritin after 52 weeks compared with baseline. RESULTS: The 1744 patients enrolled had the following conditions; thalassemia (n=1115), myelodysplastic syndromes (n=341), aplastic anemia (n=116), sickle cell disease (n=80), rare anemias (n=43) and other transfused anemias (n=49). Overall, there was a significant reduction in serum ferritin from baseline (-264 ng/mL; P<0.0001), reflecting dosage adjustments and ongoing iron intake. The most common (>5%) adverse events were gastrointestinal disturbances (28%) and skin rash (10%). Conclusions Analysis of this large, prospectively collected data set confirms the response to chelation therapy across various anemias, supporting initial deferasirox doses based on transfusional iron intake, with subsequent dose titration guided by trends in serum ferritin and safety markers (clinicaltrials.gov identifier: NCT00171821).