Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery

The planning of refractive surgical interventions is a challenging task. Numerical modeling has been proposed as a solution to support surgical intervention and predict the visual acuity, but validation on patient specific intervention is missing. The purpose of this study was to validate the numerical predictions of the post-operative corneal topography induced by the incisions required for cataract surgery. The corneal topography of 13 patients was assessed preoperatively and postoperatively (1-day and 30-day follow-up) with a Pentacam tomography device. The preoperatively acquired geometric corneal topography – anterior, posterior and pachymetry data – was used to build patient-specific finite element models. For each patient, the effects of the cataract incisions were simulated numerically and the resulting corneal surfaces were compared to the clinical postoperative measurements at one day and at 30-days follow up. Results showed that the model was able to reproduce experimental measurements with an error on the surgically induced sphere of 0.38D one day postoperatively and 0.19D 30 days postoperatively. The standard deviation of the surgically induced cylinder was 0.54D at the first postoperative day and 0.38D 30 days postoperatively. The prediction errors in surface elevation and curvature were below the topography measurement device accuracy of ±5μm and ±0.25D after the 30-day follow-up. The results showed that finite element simulations of corneal biomechanics are able to predict post cataract surgery within topography measurement device accuracy. We can conclude that the numerical simulation can become a valuable tool to plan corneal incisions in cataract surgery and other ophthalmosurgical procedures in order to optimize patients' refractive outcome and visual function.

Combined effect of heterogeneity, anisotropy and saturation on steady state flow and transport: Structure recognition and numerical simulation

1 Natural soil profiles may be interpreted as an arrangement of parts which are characterized by properties like hydraulic conductivity and water retention function. These parts form a complicated structure. Characterizing the soil structure is fundamental in subsurface hydrology because it has a crucial influence on flow and transport and defines the patterns of many ecological processes. We applied an image analysis method for recognition and classification of visual soil attributes in order to model flow and transport through a man-made soil profile. Modeled and measured saturation-dependent effective parameters were compared. We found that characterizing and describing conductivity patterns in soils with sharp conductivity contrasts is feasible. Differently, solving flow and transport on the basis of these conductivity maps is difficult and, in general, requires special care for representation of small-scale processes.

Diagenesis of a light, tight-oil chert reservoir at the Ediacaran/Cambrian boundary, Sultanate of Oman

The Al Shomou Silicilyte Member (Athel Formation) in the South Oman Salt Basin shares many of the characteristics of a light, tight-oil (LTO) reservoir: it is a prolifi c source rock mature for light oil, it produces light oil from a very tight matrix and reservoir, and hydraulic fracking technology is required to produce the oil. What is intriguing about the Al Shomou Silicilyte, and different from other LTO reservoirs, is its position related to the Precambrian/Cambrian Boundary (PCB) and the fact that it is a ‘laminated chert‘ rather than a shale. In an integrated diagenetic study we applied microstructural analyses (SEM, BSE) combined with state-of-the-art stable isotope and trace element analysis of the silicilyte matrix and fractures. Fluid inclusion microthermometry was applied to record the salinity and minimum trapping temperatures. The microstructural investigations reveal a fi ne lamination of the silicilyte matrix with a mean lamina thickness of ca. 20 μm consisting of predominantly organic matter-rich and fi nely crystalline quartz-rich layers, respectively. Authigenic, micron-sized idiomorphic quartz crystals are the main matrix components of the silicilyte. Other diagenetic phases are pyrite, apatite, dolomite, magnesite and barite cements. Porosity values based on neutron density logs and core plug data indicate porosity in the silicilyte ranges from less than 2% to almost to 40%. The majority of the pore space in the silicilyte is related to (primary) inter-crystalline pores, with locally important oversized secondary pores. Pore casts of the silica matrix show that pores are extremely irregular in three dimensions, and are generally interconnected by a complex web or meshwork of fi ne elongate pore throats. Mercury injection capillary data are in line with the microstructural observations suggesting two populations of pore throats, with an effective average modal diameter of 0.4 μm. The acquired geochemical data support the interpretation that the primary source of the silica is the ambient seawater rather than hydrothermal or biogenic. A maximum temperature of ca. 45°C for the formation of microcrystalline quartz in the silicilyte is good evidence that the lithifi cation and crystallization of quartz occurred in the fi rst 5 Ma after deposition. Several phases of brittle fracturing and mineralization occurred in response to salt tectonics during burial. The sequences of fracture-fi lling mineral phases (dolomite - layered chalcedony – quartz – apatite - magnesite I+II - barite – halite) indicates a complex fl uid evolution after silicilyte lithifi cation. Primary, all-liquid fl uid inclusions in the fracturefi lling quartz are good evidence of growth beginning at low temperatures, i.e. ≤ 50ºC. Continuous precipitation during increasing temperature and burial is documented by primary two-phase fl uid inclusions in quartz cements that show brines at 50°C and fi rst hydrocarbons at ca. 70°C. The absolute timing of each mineral phase can be constrained based on U-Pb geochronometry, and basin modelling. Secondary fl uid inclusions in quartz, magnesite and barite indicate reactivation of the fracture system after peak burial temperature during the major cooling event, i.e. uplift, between 450 and 310 Ma. A number of fi rst-order trends in porosity and reservoir-quality distribution are observed which are strongly related to the diagenetic and fl uid history of the reservoir: the early in-situ generation of hydrocarbons and overpressure development arrests diagenesis and preserves matrix porosity. Chemical compaction by pressure dissolution in the fl ank areas could be a valid hypothesis to explain the porosity variations in the silicilitye slabs resulting in lower porosity and poorer connectivity on the fl anks of the reservoir. Most of the hydrocarbon storage and production comes from intervals characterized by Amthor et al. 114488 preserved micropores, not hydrocarbon storage in a fracture system. The absence of oil expulsion results in present-day high oil saturations. The main diagenetic modifi cations of the silicilyte occurred and were completed relatively early in its history, i.e. before 300 Ma. An instrumental factor for preserving matrix porosity is the diffi culty for a given slab to evacuate all the fl uids (water and hydrocarbons), or in other words, the very good sealing capacity of the salt embedding the slab.

Modeling of Heat Transfer in Microchannel Gas Flow

Due to the existence of a velocity slip and temperature jump on the solid walls, the heat transfer in microchannels significantly differs from the one in the macroscale. In our research, we have focused on the pressure driven gas flows in a simple finite microchannel geometry, with an entrance and an outlet, for low Reynolds (Re<200) and low Knudsen (Kn<0.01) numbers. For such a regime, the slip induced phenomena are strongly connected with the viscous effects. As a result, heat transfer is also significantly altered. For the optimization of flow conditions, we have investigated various temperature gradient configurations, additionally changing Reynolds and Knudsen numbers. The entrance effects, slip flow, and temperature jump lead to complex relations between flow behavior and heat transfer. We have shown that slip effects are generally insignificant for flow behavior. However, two configuration setups (hot wall cold gas and cold wall hot gas) are affected by slip in distinguishably different ways. For the first one, which concerns turbomachinery, the mass flow rate can increase by about 1% in relation to the no-slip case, depending on the wall-gas temperature difference. Heat transfer is more significantly altered. The Nusselt number between slip and no-slip cases at the outlet of the microchannel is increased by about 10%.

Modeling of temperature and turbidity in a natural lake and a reservoir connected by pumped-storage operations

Pumped-storage (PS) systems are used to store electric energy as potential energy for release during peak demand. We investigate the impacts of a planned 1000 MW PS scheme connecting Lago Bianco with Lago di Poschiavo (Switzerland) on temperature and particle mass concentration in both basins. The upper (turbid) basin is a reservoir receiving large amounts of fine particles from the partially glaciated watershed, while the lower basin is a much clearer natural lake. Stratification, temperature and particle concentrations in the two basins were simulated with and without PS for four different hydrological conditions and 27 years of meteorological forcing using the software CE-QUAL-W2. The simulations showed that the PS operations lead to an increase in temperature in both basins during most of the year. The increase is most pronounced (up to 4°C) in the upper hypolimnion of the natural lake toward the end of summer stratification and is partially due to frictional losses in the penstocks, pumps and turbines. The remainder of the warming is from intense coupling to the atmosphere while water resides in the shallower upper reservoir. These impacts are most pronounced during warm and dry years, when the upper reservoir is strongly heated and the effects are least concealed by floods. The exchange of water between the two basins relocates particles from the upper reservoir to the lower lake, where they accumulate during summer in the upper hypolimnion (10 to 20 mg L−1) but also to some extent decrease light availability in the trophic surface layer.

Modeling the heterogeneous ice and gas coma of Comet 103P/Hartley 2

The spectacular images of Comet 103P/Hartley 2 recorded by the Medium Resolution Instrument (MRI) and High Resolution Instrument (HRI) on board of the Extrasolar Planet Observation and Deep Impact Extended Investigation (EPOXI) spacecraft, as the Deep Impact extended mission, revealed that its bi-lobed very active nucleus outgasses volatiles heterogeneously. Indeed, CO2 is the primary driver of activity by dragging out chunks of pure ice out of the nucleus from the sub-solar lobe that appear to be the main source of water in Hartley 2's coma by sublimating slowly as they go away from the nucleus. However, water vapor is released by direct sublimation of the nucleus at the waist without any significant amount of either CO2 or icy grains. The coma structure for a comet with such areas of diverse chemistry differs from the usual models where gases are produced in a homogeneous way from the surface. We use the fully kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J. 685, 659-677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J. 732, 104-120) applied to Comet 103P/Hartley 2 including sublimating icy grains to reproduce the observations made by EPOXI and ground-based measurements. A realistic bi-lobed nucleus with a succession of active areas with different chemistry was included in the model enabling us to study in details the coma of Hartley 2. The different gas production rates from each area were found by fitting the spectra computed using a line-by-line non-LTE radiative transfer model to the HRI observations. The presence of icy grains with long lifetimes, which are pushed anti-sunward by radiation pressure, explains the observed OH asymmetry with enhancement on the night side of the coma.

Prediction of water–rock interaction and porosity evolution in a granitoid-hosted enhanced geothermal system, using constraints from the 5 km Basel-1 well

Numerical simulations based on plans for a deep geothermal system in Basel, Switzerland are used here to understand chemical processes that occur in an initially dry granitoid reservoir during hydraulic stimulation and long-term water circulation to extract heat. An important question regarding the sustainability of such enhanced geothermal systems (EGS), is whether water–rock reactions will eventually lead to clogging of flow paths in the reservoir and thereby reduce or even completely block fluid throughput. A reactive transport model allows the main chemical reactions to be predicted and the resulting evolution of porosity to be tracked over the expected 30-year operational lifetime of the system. The simulations show that injection of surface water to stimulate fracture permeability in the monzogranite reservoir at 190 °C and 5000 m depth induces redox reactions between the oxidised surface water and the reduced wall rock. Although new calcite, chlorite, hematite and other minerals precipitate near the injection well, their volumes are low and more than compensated by those of the dissolving wall-rock minerals. Thus, during stimulation, reduction of injectivity by mineral precipitation is unlikely. During the simulated long-term operation of the system, the main mineral reactions are the hydration and albitization of plagioclase, the alteration of hornblende to an assemblage of smectites and chlorites and of primary K-feldspar to muscovite and microcline. Within a closed-system doublet, the composition of the circulated fluid changes only slightly during its repeated passage through the reservoir, as the wall rock essentially undergoes isochemical recrystallization. Even after 30 years of circulation, the calculations show that porosity is reduced by only ∼0.2%, well below the expected fracture porosity induced by stimulation. This result suggests that permeability reduction owing to water–rock interaction is unlikely to jeopardize the long-term operation of deep, granitoid-hosted EGS systems. A peculiarity at Basel is the presence of anhydrite as fracture coatings at ∼5000 m depth. Simulated exposure of the circulating fluid to anhydrite induces a stronger redox disequilibrium in the reservoir, driving dissolution of ferrous minerals and precipitation of ferric smectites, hematite and pyrite. However, even in this scenario the porosity reduction is at most 0.5%, a value which is unproblematic for sustainable fluid circulation through the reservoir.

MODELING REACTIVE GAS UPTAKE, TRANSPORT, AND TRANSFORMATION IN AGGREGATED SOILS

Gas diffusion research in soils covers, to a large extent, the transport behavior of practically insoluble gases. We extend the mathematical description of gas transport to include reactive gaseous components that hydrolyze in water such as SO2 and CO2. The path between the free atmosphere and the microporous niches is modeled by assuming penetration through gas-filled macropores, air-water phase transfer, and diffusion and speciation in the liquid phase. For hydrolyzable gases, the rate of mass transfer into and the total absorption capacity of the soil solution may be high. Both the capacity and the transfer rate are influenced by the soil-solution pH; for high pH, they become extremely high for SO2. The soil absorption of such gases is also influenced by soil structure. Well-aerated, near-neutral soils are a potentially important sink for SO2.

P-T-t estimation of syn-kinematic strain in low-grade quartz-feldspar bearing rocks using thermodynamic modeling and 40Ar/39Ar dating techniques: example of the Plan-de-Phasy shear zone unit (Briançonnais Zone, Western Alps)

Pressure–Temperature–time (P–T–t) estimates of the syn-kinematic strain at the peak-pressure conditions reached during shallow underthrusting of the Briançonnais Zone in the Alpine subduction zone was made by thermodynamic modelling and 40Ar/39Ar dating in the Plan-de-Phasy unit (SE of the Pelvoux Massif, Western Alps). The dated phengite minerals crystallized syn-kinematically in a shear zone indicating top-to-the-N motion. By combining X-ray mapping with multi-equilibrium calculations, we estimate the phengite crystallization conditions at 270 ± 50 °C and 8.1 ± 2 kbar at an age of 45.9 ± 1.1 Ma. Combining this P–T–t estimate with data from the literature allows us to constrain the timing and geometry of Alpine continental subduction. We propose that the Briançonnais units were scalped on top of the slab during ongoing continental subduction and exhumed continuously until collision.

Benchmark problems for reactive transport modeling of the generation and attenuation of acid rock drainage

Acid rock drainage (ARD) is a problem of international relevance with substantial environmental and economic implications. Reactive transport modeling has proven a powerful tool for the process-based assessment of metal release and attenuation at ARD sites. Although a variety of models has been used to investigate ARD, a systematic model intercomparison has not been conducted to date. This contribution presents such a model intercomparison involving three synthetic benchmark problems designed to evaluate model results for the most relevant processes at ARD sites. The first benchmark (ARD-B1) focuses on the oxidation of sulfide minerals in an unsaturated tailing impoundment, affected by the ingress of atmospheric oxygen. ARD-B2 extends the first problem to include pH buffering by primary mineral dissolution and secondary mineral precipitation. The third problem (ARD-B3) in addition considers the kinetic and pH-dependent dissolution of silicate minerals under low pH conditions. The set of benchmarks was solved by four reactive transport codes, namely CrunchFlow, Flotran, HP1, and MIN3P. The results comparison focused on spatial profiles of dissolved concentrations, pH and pE, pore gas composition, and mineral assemblages. In addition, results of transient profiles for selected elements and cumulative mass loadings were considered in the intercomparison. Despite substantial differences in model formulations, very good agreement was obtained between the various codes. Residual deviations between the results are analyzed and discussed in terms of their implications for capturing system evolution and long-term mass loading predictions.