Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Polygonal cracks in the seasonal semi-translucent CO2 ice layer in Martian polar areas

In this paper, we use morphological and numerical methods to test the hypothesis that seasonally formed fracture patterns in the Martian polar regions result from the brittle failure of seasonal CO2 slab ice. The observations by the High Resolution Imaging Science Experiment (HiRISE) of polar regions of Mars show very narrow dark elongated linear patterns that are observed during some periods of time in spring, disappear in summer and re-appear again in the following spring. They are repeatedly formed in the same areas but they do not repeat the exact pattern from year to year. This leads to the conclusion that they are cracks formed in the seasonal ice layer. Some of models of seasonal surface processes rely on the existence of a transparent form of CO2 ice, so-called slab ice. For the creation of the observed cracks the ice is required to be a continuous media, not an agglomeration of relatively separate particles like a firn. The best explanation for our observations is a slab ice with relatively high transparency in the visible wavelength range. This transparency allows a solid state green-house effect to act underneath the ice sheet raising the pressure by sublimation from below. The trapped gas creates overpressure and the ice sheet breaks at some point creating the observed cracks. We show that the times when the cracks appear are in agreement with the model calculation, providing one more piece of evidence that CO2 slab ice covers polar areas in spring.

Modeling of ore-forming and geoenvironmental systems: Roles of fluid flow and chemical reaction processes

Ore-forming and geoenviromental systems commonly involve coupled fluid flowand chemical reaction processes. The advanced numerical methods and computational modeling have become indispensable tools for simulating such processes in recent years. This enables many hitherto unsolvable geoscience problems to be addressed using numerical methods and computational modeling approaches. For example, computational modeling has been successfully used to solve ore-forming and mine site contamination/remediation problems, in which fluid flow and geochemical processes play important roles in the controlling dynamic mechanisms. The main purpose of this paper is to present a generalized overview of: (1) the various classes and models associated with fluid flow/chemically reacting systems in order to highlight possible opportunities and developments for the future; (2) some more general issues that need attention in the development of computational models and codes for simulating ore-forming and geoenviromental systems; (3) the related progresses achieved on the geochemical modeling over the past 50 years or so; (4) the general methodology for modeling of oreforming and geoenvironmental systems; and (5) the future development directions associated with modeling of ore-forming and geoenviromental systems.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Modeling asteroid collisions and impact processes

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

Systematic review of medication safety assessment methods

Purpose The accuracy, efficiency, and efficacy of four commonly recommended medication safety assessment methodologies were systematically reviewed. Methods Medical literature databases were systematically searched for any comparative study conducted between January 2000 and October 2009 in which at least two of the four methodologies—incident report review, direct observation, chart review, and trigger tool—were compared with one another. Any study that compared two or more methodologies for quantitative accuracy (adequacy of the assessment of medication errors and adverse drug events) efficiency (effort and cost), and efficacy and that provided numerical data was included in the analysis. Results Twenty-eight studies were included in this review. Of these, 22 compared two of the methodologies, and 6 compared three methods. Direct observation identified the greatest number of reports of drug-related problems (DRPs), while incident report review identified the fewest. However, incident report review generally showed a higher specificity compared to the other methods and most effectively captured severe DRPs. In contrast, the sensitivity of incident report review was lower when compared with trigger tool. While trigger tool was the least labor-intensive of the four methodologies, incident report review appeared to be the least expensive, but only when linked with concomitant automated reporting systems and targeted follow-up. Conclusion All four medication safety assessment techniques—incident report review, chart review, direct observation, and trigger tool—have different strengths and weaknesses. Overlap between different methods in identifying DRPs is minimal. While trigger tool appeared to be the most effective and labor-efficient method, incident report review best identified high-severity DRPs.

Stochastic amplitude-modulated stretching of Rabbit flexor digitorum profundus tendons reduces stiffness compared to Cyclic Loading but does not affect Tenocyte Metabolism

Background It has been demonstrated that frequency modulation of loading influences cellular response and metabolism in 3D tissues such as cartilage, bone and intervertebral disc. However, the mechano-sensitivity of cells in linear tissues such as tendons or ligaments might be more sensitive to changes in strain amplitude than frequency. Here, we hypothesized that tenocytes in situ are mechano-responsive to random amplitude modulation of strain. Methods We compared stochastic amplitude-modulated versus sinusoidal cyclic stretching. Rabbit tendon were kept in tissue-culture medium for twelve days and were loaded for 1h/day for six of the total twelve culture days. The tendons were randomly subjected to one of three different loading regimes: i) stochastic (2 – 7% random strain amplitudes), ii) cyclic_RMS (2–4.42% strain) and iii) cyclic_high (2 - 7% strain), all at 1 Hz and for 3,600 cycles, and one unloaded control. Results At the end of the culture period, the stiffness of the “stochastic” group was significantly lower than that of the cyclic_RMS and cyclic_high groups (both, p < 0.0001). Gene expression of eleven anabolic, catabolic and inflammatory genes revealed no significant differences between the loading groups. Conclusions We conclude that, despite an equivalent metabolic response, stochastically stretched tendons suffer most likely from increased mechanical microdamage, relative to cyclically loaded ones, which is relevant for tendon regeneration therapies in clinical practice.

Percutaneous coronary interventions in Europe: prevalence, numerical estimates, and projections based on data up to 2004

AIMS: A registry mandated by the European Society of Cardiology collects data on trends in interventional cardiology within Europe. Special interest focuses on relative increases and ratios in new techniques and their distributions across Europe. We report the data through 2004 and give an overview of the development of coronary interventions since the first data collection in 1992. METHODS AND RESULTS: Questionnaires were distributed yearly to delegates of all national societies of cardiology represented in the European Society of Cardiology. The goal was to collect the case numbers of all local institutions and operators. The overall numbers of coronary angiographies increased from 1992 to 2004 from 684 000 to 2 238 000 (from 1250 to 3930 per million inhabitants). The respective numbers for percutaneous coronary interventions (PCIs) and coronary stenting procedures increased from 184 000 to 885 000 (from 335 to 1550) and from 3000 to 770 000 (from 5 to 1350), respectively. Germany was the most active country with 712 000 angiographies (8600), 249 000 angioplasties (3000), and 200 000 stenting procedures (2400) in 2004. The indication has shifted towards acute coronary syndromes, as demonstrated by rising rates of interventions for acute myocardial infarction over the last decade. The procedures are more readily performed and perceived safer, as shown by increasing rate of "ad hoc" PCIs and decreasing need for emergency coronary artery bypass grafting (CABG). In 2004, the use of drug-eluting stents continued to rise. However, an enormous variability is reported with the highest rate in Switzerland (70%). If the rate of progression remains constant until 2010 the projected number of coronary angiographies will be over three million, and the number of PCIs about 1.5 million with a stenting rate of almost 100%. CONCLUSION: Interventional cardiology in Europe is ever expanding. New coronary revascularization procedures, alternative or complementary to balloon angioplasty, have come and gone. Only stenting has stood the test of time and matured to the default technique. Facilitated access to PCI, more complete and earlier detection of coronary artery disease promise continued growth of the procedure despite the uncontested success of prevention.

Pregnancy induces numerical and functional changes of CD4+CD25 high regulatory T cells in patients with rheumatoid arthritis

OBJECTIVE: In a prospective study we investigated whether numerical and functional changes of CD4+CD25(high) regulatory T cells (Treg) were associated with changes of disease activity observed during pregnancy and post partum in patients with rheumatoid arthritis (RA). METHODS: The frequency of CD4+CD25(high) T cells was determined by flow cytometry in 12 patients with RA and 14 healthy women during and after pregnancy. Fluorescence-activated cell sorting (FACS) was used to sort CD4+CD25(high) T cells and CD4+CD25- T cells were stimulated with anti-CD3 and anti-CD28 monoclonal antibodies alone or in co-culture to investigate proliferation and cytokine secretion. RESULTS: Frequencies of CD4+CD25(high) Treg were significantly higher in the third trimester compared to 8 weeks post partum in patients and controls. Numbers of CD4+CD25(high) Treg inversely correlated with disease activity in the third trimester and post partum. In co-culture experiments significantly higher amounts of IL10 and lowered levels of tumour necrosis factor (TNF)alpha and interferon (IFN)gamma were found in supernatants of the third trimester compared to postpartum samples. These findings were independent from health or disease in pregnancy, however postpartum TNFalpha and IFN gamma levels were higher in patients with disease flares. CONCLUSION: The amelioration of disease activity in the third trimester corresponded to the increased number of Treg that induced a pronounced anti-inflammatory cytokine milieu. The pregnancy related quantitative and qualitative changes of Treg suggest a beneficial effect of Treg on disease activity.

Stochastic rank correlation: a robust merit function for 2D/3D registration of image data obtained at different energies

In this article, the authors evaluate a merit function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type merit functions with the flexibility of mutual-information-type merit functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman's rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another merit function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other merit functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.

Age modeling of young non-varved lake sediments: methods and limits. Examples from two lakes in Central Chile

High-resolution and highly precise age models for recent lake sediments (last 100–150 years) are essential for quantitative paleoclimate research. These are particularly important for sedimentological and geochemical proxies, where transfer functions cannot be established and calibration must be based upon the relation of sedimentary records to instrumental data. High-precision dating for the calibration period is most critical as it determines directly the quality of the calibration statistics. Here, as an example, we compare radionuclide age models obtained on two high-elevation glacial lakes in the Central Chilean Andes (Laguna Negra: 33°38′S/70°08′W, 2,680 m a.s.l. and Laguna El Ocho: 34°02′S/70°19′W, 3,250 m a.s.l.). We show the different numerical models that produce accurate age-depth chronologies based on 210Pb profiles, and we explain how to obtain reduced age-error bars at the bottom part of the profiles, i.e., typically around the end of the 19th century. In order to constrain the age models, we propose a method with five steps: (i) sampling at irregularly-spaced intervals for 226Ra, 210Pb and 137Cs depending on the stratigraphy and microfacies, (ii) a systematic comparison of numerical models for the calculation of 210Pb-based age models: constant flux constant sedimentation (CFCS), constant initial concentration (CIC), constant rate of supply (CRS) and sediment isotope tomography (SIT), (iii) numerical constraining of the CRS and SIT models with the 137Cs chronomarker of AD 1964 and, (iv) step-wise cross-validation with independent diagnostic environmental stratigraphic markers of known age (e.g., volcanic ash layer, historical flood and earthquakes). In both examples, we also use airborne pollutants such as spheroidal carbonaceous particles (reflecting the history of fossil fuel emissions), excess atmospheric Cu deposition (reflecting the production history of a large local Cu mine), and turbidites related to historical earthquakes. Our results show that the SIT model constrained with the 137Cs AD 1964 peak performs best over the entire chronological profile (last 100–150 years) and yields the smallest standard deviations for the sediment ages. Such precision is critical for the calibration statistics, and ultimately, for the quality of the quantitative paleoclimate reconstruction. The systematic comparison of CRS and SIT models also helps to validate the robustness of the chronologies in different sections of the profile. Although surprisingly poorly known and under-explored in paleolimnological research, the SIT model has a great potential in paleoclimatological reconstructions based on lake sediments