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.

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.

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.

Universal characteristics of particle shape evolution by bed-load chipping.

River currents, wind, and waves drive bed-load transport, in which sediment particles collide with each other and Earth's surface. A generic consequence is impact attrition and rounding of particles as a result of chipping, often referred to in geological literature as abrasion. Recent studies have shown that the rounding of river pebbles can be modeled as diffusion of surface curvature, indicating that geometric aspects of impact attrition are insensitive to details of collisions and material properties. We present data from fluvial, aeolian, and coastal environments and laboratory experiments that suggest a common relation between circularity and mass attrition for particles transported as bed load. Theory and simulations demonstrate that universal characteristics of shape evolution arise because of three constraints: (i) Initial particles are mildly elongated fragments, (ii) particles collide with similarly-sized particles or the bed, and (iii) collision energy is small enough that chipping dominates over fragmentation but large enough that sliding friction is negligible. We show that bed-load transport selects these constraints, providing the foundation to estimate a particle's attrition rate from its shape alone in most sedimentary environments. These findings may be used to determine the contribution of attrition to downstream fining in rivers and deserts and to infer transport conditions using only images of sediment grains.

Author Correction: Shape evolution of ooids: a geometric model.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

Shape evolution of ooids: a geometric model.

Striking shapes in nature have been documented to result from chemical precipitation - such as terraced hot springs and stromatolites - which often proceeds via surface-normal growth. Another studied class of objects is those whose shape evolves by physical abrasion - the primary example being river and beach pebbles - which results in shape-dependent surface erosion. While shapes may evolve in a self-similar manner, in neither growth nor erosion can a surface remain invariant. Here we investigate a rare and beautiful geophysical problem that combines both of these processes; the shape evolution of carbonate particles known as ooids. We hypothesize that mineral precipitation, and erosion due to wave-current transport, compete to give rise to novel and invariant geometric forms. We show that a planar (2D) mathematical model built on this premise predicts time-invariant (equilibrium) shapes that result from a balance between precipitation and abrasion. These model results produce nontrivial shapes that are consistent with mature ooids found in nature.

Reconstructing the transport history of pebbles on Mars.

The discovery of remarkably rounded pebbles by the rover Curiosity, within an exhumed alluvial fan complex in Gale Crater, presents some of the most compelling evidence yet for sustained fluvial activity on Mars. While rounding is known to result from abrasion by inter-particle collisions, geologic interpretations of sediment shape have been qualitative. Here we show how quantitative information on the transport distance of river pebbles can be extracted from their shape alone, using a combination of theory, laboratory experiments and terrestrial field data. We determine that the Martian basalt pebbles have been carried tens of kilometres from their source, by bed-load transport on an alluvial fan. In contrast, angular clasts strewn about the surface of the Curiosity traverse are indicative of later emplacement by rock fragmentation processes. The proposed method for decoding transport history from particle shape provides a new tool for terrestrial and planetary sedimentology.

Universality of fragment shapes.

The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment shapes still remained a fundamental challenge. We performed a thorough experimental study of the problem fragmenting various types of materials by slowly proceeding weathering and by rapid breakup due to explosion and hammering. We demonstrate that the shape of fragments obeys an astonishing universality having the same generic evolution with the fragment size irrespective of materials details and loading conditions. There exists a cutoff size below which fragments have an isotropic shape, however, as the size increases an exponential convergence is obtained to a unique elongated form. We show that a discrete stochastic model of fragmentation reproduces both the size and shape of fragments tuning only a single parameter which strengthens the general validity of the scaling laws. The dependence of the probability of the crack plan orientation on the linear extension of fragments proved to be essential for the shape selection mechanism.

How river rocks round: resolving the shape-size paradox.

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.

Geographical variations in current clinical practice on transfusions and iron chelation therapy across various transfusion-dependent anaemias.

BACKGROUND AND OBJECTIVES: Many patients with chronic anaemia require blood transfusions as part of their treatment regimen. As a result, iron overload will inevitably develop if not adequately managed by iron chelation therapy. There are many guidelines relating to transfusion and chelation practices for patients with transfusion-dependent anaemia; however, there is a lack of information on how treatment practices differ around the world. The objective of this manuscript is to highlight key features of current transfusion and chelation management, including similarities and differences across various anaemias and between geographical regions worldwide. MATERIALS AND METHODS: Data collected at study entry to the multicentre Evaluation of Patients' Iron Chelation with Exjade (EPIC) study, which recruited 1,744 patients with a variety of transfusion-dependent anaemias across 23 countries from three geographic regions, were assessed. These analyses compared transfusion and chelation treatment prior to the start of study treatment, together with iron burden assessed at study entry by serum ferritin, liver iron concentration and labile plasma iron levels. RESULTS AND CONCLUSIONS: Data show that transfusion and iron chelation practices differ between anaemias and between geographical regions; this may be linked to availability and accessibility of transfusion and chelation therapy, patients' compliance, physicians' attitudes, costs and use of treatment guidelines. Approximately 60% of these transfusion-dependent patients were severely iron overloaded with a serum ferritin level over 2,500 ng/mL, indicating that the risks of iron burden may have been underestimated and current iron chelation therapy, if considered, may not have been adequate to control iron burden.

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.

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.

Clinical efficacy and safety evaluation of tailoring iron chelation practice in thalassaemia patients from Asia-Pacific: a subanalysis of the EPIC study of deferasirox.

Although thalassaemia is highly prevalent in the Asia-Pacific region, clinical data on efficacy and safety profiles of deferasirox in patients from this region are rather limited. Recently, data from the multicentre Evaluation of Patients' Iron Chelation with Exjade (EPIC) study in 1744 patients with different anaemias has provided an opportunity to analyse 1115 thalassaemia patients, of whom 444 patients were from five countries in the Asia-Pacific region (AP) for whom thalassaemia management and choice of iron chelators were similar. Compared to the rest of the world (ROW), baseline clinical data showed that the AP group appeared to be more loaded with iron (3745.0 vs. 2822.0 ng/ml) and had a higher proportion on deferoxamine monotherapy prior to the study (82.9 vs. 58.9%). Using a starting deferasirox dose based on transfusional iron intake and tailoring it to individual patient response, clinical efficacy based on serum ferritin reduction in AP and ROW thalassaemia patients was similar. Interestingly, the AP group developed a higher incidence of drug-related skin rash compared to ROW (18.0 vs. 7.2%), which may indicate different pharmacogenetic backgrounds in the two populations. Our analysis confirms that, with appropriate adjustment of dose, deferasirox can be clinically effective across different regions, with manageable side effects.

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).

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.

Deferasirox in iron-overloaded patients with transfusion-dependent myelodysplastic syndromes: Results from the large 1-year EPIC study.

The prospective 1-year EPIC study enrolled 341 patients with myelodysplastic syndromes (MDS); although baseline iron burden was >2500ng/mL, approximately 50% were chelation-naïve. Overall median serum ferritin decreased significantly at 1 year (p=0.002). Decreases occurred irrespective of whether patients were chelation-naïve or previously chelated; changes were dependent on dose adjustments and ongoing iron intake. Sustained reductions in labile plasma iron were observed. Discontinuation rate (48.7%) and adverse event profile were consistent with previously reported deferasirox data in MDS. Alanine aminotransferase levels decreased significantly; change correlated significantly with reduction in serum ferritin (p<0.0001). This large dataset prospectively confirms the efficacy and well characterizes the safety profile of deferasirox in MDS.

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).

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.

Geometry and self-righting of turtles.

Terrestrial animals with rigid shells face imminent danger when turned upside down. A rich variety of righting strategies of beetle and turtle species have been described, but the exact role of the shell's geometry in righting is so far unknown. These strategies are often based on active mechanisms, e.g. most beetles self-right via motion of their legs or wings; flat, aquatic turtles use their muscular neck to flip back. On the other hand, highly domed, terrestrial turtles with short limbs and necks have virtually no active control: here shape itself may serve as a fundamental tool. Based on field data gathered on a broad spectrum of aquatic and terrestrial turtle species we develop a geometric model of the shell. Inspired by recent mathematical results, we demonstrate that a simple mechanical classification of the model is closely linked to the animals' righting strategy. Specifically, we show that the exact geometry of highly domed terrestrial species is close to optimal for self-righting, and the shell's shape is the predominant factor of their ability to flip back. Our study illustrates how evolution solved a far-from-trivial geometrical problem and equipped some turtles with monostatic shells: beautiful forms, which rarely appear in nature otherwise.

Sturdy cycles in the chaotic Tribolium castaneum data series.

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).