On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Mathematical modeling for improved greenhouse gas balances, agro-ecosystems, and policy development: Lessons from the Australian experience

If the land sector is to make significant contributions to mitigating anthropogenic greenhouse gas (GHG) emissions in coming decades, it must do so while concurrently expanding production of food and fiber. In our view, mathematical modeling will be required to provide scientific guidance to meet this challenge. In order to be useful in GHG mitigation policy measures, models must simultaneously meet scientific, software engineering, and human capacity requirements. They can be used to understand GHG fluxes, to evaluate proposed GHG mitigation actions, and to predict and monitor the effects of specific actions; the latter applications require a change in mindset that has parallels with the shift from research modeling to decision support. We compare and contrast 6 agro-ecosystem models (FullCAM, DayCent, DNDC, APSIM, WNMM, and AgMod), chosen because they are used in Australian agriculture and forestry. Underlying structural similarities in the representations of carbon flows though plants and soils in these models are complemented by a diverse range of emphases and approaches to the subprocesses within the agro-ecosystem. None of these agro-ecosystem models handles all land sector GHG fluxes, and considerable model-based uncertainty exists for soil C fluxes and enteric methane emissions. The models also show diverse approaches to the initialisation of model simulations, software implementation, distribution, licensing, and software quality assurance; each of these will differentially affect their usefulness for policy-driven GHG mitigation prediction and monitoring. Specific requirements imposed on the use of models by Australian mitigation policy settings are discussed, and areas for further scientific development of agro-ecosystem models for use in GHG mitigation policy are proposed.

In vitro modeling of the prostate cancer microenvironment

Prostate cancer is the most commonly diagnosed malignancy in men and advanced disease is incurable. Model systems are a fundamental tool for research and many in vitro models of prostate cancer use cancer cell lines in monoculture. Although these have yielded significant insight they are inherently limited by virtue of their two-dimensional (2D) growth and inability to include the influence of tumour microenvironment. These major limitations can be overcome with the development of newer systems that more faithfully recreate and mimic the complex in vivo multi-cellular, three-dimensional (3D) microenvironment. This article presents the current state of in vitro models for prostate cancer, with particular emphasis on 3D systems and the challenges that remain before their potential to advance our understanding of prostate disease and aid in the development and testing of new therapeutic agents can be realised.

Data driven modeling for power transformer lifespan evaluation

Large sized power transformers are important parts of the power supply chain. These very critical networks of engineering assets are an essential base of a nation’s energy resource infrastructure. This research identifies the key factors influencing transformer normal operating conditions and predicts the asset management lifespan. Engineering asset research has developed few lifespan forecasting methods combining real-time monitoring solutions for transformer maintenance and replacement. Utilizing the rich data source from a remote terminal unit (RTU) system for sensor-data driven analysis, this research develops an innovative real-time lifespan forecasting approach applying logistic regression based on the Weibull distribution. The methodology and the implementation prototype are verified using a data series from 161 kV transformers to evaluate the efficiency and accuracy for energy sector applications. The asset stakeholders and suppliers significantly benefit from the real-time power transformer lifespan evaluation for maintenance and replacement decision support.

Bayesian predictive modeling and comparison of oil samples

Statistical comparison of oil samples is an integral part of oil spill identification, which deals with the process of linking an oil spill with its source of origin. In current practice, a frequentist hypothesis test is often used to evaluate evidence in support of a match between a spill and a source sample. As frequentist tests are only able to evaluate evidence against a hypothesis but not in support of it, we argue that this leads to unsound statistical reasoning. Moreover, currently only verbal conclusions on a very coarse scale can be made about the match between two samples, whereas a finer quantitative assessment would often be preferred. To address these issues, we propose a Bayesian predictive approach for evaluating the similarity between the chemical compositions of two oil samples. We derive the underlying statistical model from some basic assumptions on modeling assays in analytical chemistry, and to further facilitate and improve numerical evaluations, we develop analytical expressions for the key elements of Bayesian inference for this model. The approach is illustrated with both simulated and real data and is shown to have appealing properties in comparison with both standard frequentist and Bayesian approaches

Spatially explicit structural equation modeling

Structural equation modeling (SEM) is a powerful statistical approach for the testing of networks of direct and indirect theoretical causal relationships in complex data sets with intercorrelated dependent and independent variables. SEM is commonly applied in ecology, but the spatial information commonly found in ecological data remains difficult to model in a SEM framework. Here we propose a simple method for spatially explicit SEM (SE-SEM) based on the analysis of variance/covariance matrices calculated across a range of lag distances. This method provides readily interpretable plots of the change in path coefficients across scale and can be implemented using any standard SEM software package. We demonstrate the application of this method using three studies examining the relationships between environmental factors, plant community structure, nitrogen fixation, and plant competition. By design, these data sets had a spatial component, but were previously analyzed using standard SEM models. Using these data sets, we demonstrate the application of SE-SEM to regularly spaced, irregularly spaced, and ad hoc spatial sampling designs and discuss the increased inferential capability of this approach compared with standard SEM. We provide an R package, sesem, to easily implement spatial structural equation modeling.

Modeling meat yield based on measurements of body traits in genetically improved giant freshwater prawn (GFP) Macrobrachium rosenbergii

A single-generation dataset consisting of 1,730 records from a selection program for high growth rate in giant freshwater prawn (GFP, Macrobrachium rosenbergii) was used to derive prediction equations for meat weight and meat yield. Models were based on body traits [body weight, total length and abdominal width (AW)] and carcass measurements (tail weight and exoskeleton-off weight). Lengths and width were adjusted for the systematic effects of selection line, male morphotypes and female reproductive status, and for the covariables of age at slaughter within sex and body weight. Body and meat weights adjusted for the same effects (except body weight) were used to calculate meat yield (expressed as percentage of tail weight/body weight and exoskeleton-off weight/body weight). The edible meat weight and yield in this GFP population ranged from 12 to 15 g and 37 to 45 %, respectively. The simple (Pearson) correlation coefficients between body traits (body weight, total length and AW) and meat weight were moderate to very high and positive (0.75–0.94), but the correlations between body traits and meat yield were negative (−0.47 to −0.74). There were strong linear positive relationships between measurements of body traits and meat weight, whereas relationships of body traits with meat yield were moderate and negative. Step-wise multiple regression analysis showed that the best model to predict meat weight included all body traits, with a coefficient of determination (R 2) of 0.99 and a correlation between observed and predicted values of meat weight of 0.99. The corresponding figures for meat yield were 0.91 and 0.95, respectively. Body weight or length was the best predictor of meat weight, explaining 91–94 % of observed variance when it was fitted alone in the model. By contrast, tail width explained a lower proportion (69–82 %) of total variance in the single trait models. It is concluded that in practical breeding programs, improvement of meat weight can be easily made through indirect selection for body trait combinations. The improvement of meat yield, albeit being more difficult, is possible by genetic means, with 91 % of the variation in the trait explained by the body and carcass traits examined in this study.

Analysis of parameter uncertainty and sensitivity in PCPF-1 modeling for predicting concentrations of rice herbicides

This paper demonstrates the procedures for probabilistic assessment of a pesticide fate and transport model, PCPF-1, to elucidate the modeling uncertainty using the Monte Carlo technique. Sensitivity analyses are performed to investigate the influence of herbicide characteristics and related soil properties on model outputs using four popular rice herbicides: mefenacet, pretilachlor, bensulfuron-methyl and imazosulfuron. Uncertainty quantification showed that the simulated concentrations in paddy water varied more than those of paddy soil. This tendency decreased as the simulation proceeded to a later period but remained important for herbicides having either high solubility or a high 1st-order dissolution rate. The sensitivity analysis indicated that PCPF-1 parameters requiring careful determination are primarily those involve with herbicide adsorption (the organic carbon content, the bulk density and the volumetric saturated water content), secondary parameters related with herbicide mass distribution between paddy water and soil (1st-order desorption and dissolution rates) and lastly, those involving herbicide degradations. © Pesticide Science Society of Japan.

Modeling approaches for pesticide exposure assessment in rice paddies

Pesticide use in paddy rice production may contribute to adverse ecological effects in surface waters. Risk assessments conducted for regulatory purposes depend on the use of simulation models to determine predicted environment concentrations (PEC) of pesticides. Often tiered approaches are used, in which assessments at lower tiers are based on relatively simple models with conservative scenarios, while those at higher tiers have more realistic representations of physical and biochemical processes. This chapter reviews models commonly used for predicting the environmental fate of pesticides in rice paddies. Theoretical considerations, unique features, and applications are discussed. This review is expected to provide information to guide model selection for pesticide registration, regulation, and mitigation in rice production areas.

Cardiometabolic effects of genetic upregulation of the interleukin 1 receptor antagonist: A Mendelian randomisation analysis

Background To investigate potential cardiovascular and other effects of long-term pharmacological interleukin 1 (IL-1) inhibition, we studied genetic variants that produce inhibition of IL-1, a master regulator of inflammation. Methods We created a genetic score combining the effects of alleles of two common variants (rs6743376 and rs1542176) that are located upstream of IL1RN, the gene encoding the IL-1 receptor antagonist (IL-1Ra; an endogenous inhibitor of both IL-1α and IL-1β); both alleles increase soluble IL-1Ra protein concentration. We compared effects on inflammation biomarkers of this genetic score with those of anakinra, the recombinant form of IL-1Ra, which has previously been studied in randomised trials of rheumatoid arthritis and other inflammatory disorders. In primary analyses, we investigated the score in relation to rheumatoid arthritis and four cardiometabolic diseases (type 2 diabetes, coronary heart disease, ischaemic stroke, and abdominal aortic aneurysm; 453 411 total participants). In exploratory analyses, we studied the relation of the score to many disease traits and to 24 other disorders of proposed relevance to IL-1 signalling (746 171 total participants). Findings For each IL1RN minor allele inherited, serum concentrations of IL-1Ra increased by 0·22 SD (95% CI 0·18–0·25; 12·5%; p=9·3 × 10−33), concentrations of interleukin 6 decreased by 0·02 SD (−0·04 to −0·01; −1·7%; p=3·5 × 10−3), and concentrations of C-reactive protein decreased by 0·03 SD (−0·04 to −0·02; −3·4%; p=7·7 × 10−14). We noted the effects of the genetic score on these inflammation biomarkers to be directionally concordant with those of anakinra. The allele count of the genetic score had roughly log-linear, dose-dependent associations with both IL-1Ra concentration and risk of coronary heart disease. For people who carried four IL-1Ra-raising alleles, the odds ratio for coronary heart disease was 1·15 (1·08–1·22; p=1·8 × 10−6) compared with people who carried no IL-1Ra-raising alleles; the per-allele odds ratio for coronary heart disease was 1·03 (1·02–1·04; p=3·9 × 10−10). Per-allele odds ratios were 0·97 (0·95–0·99; p=9·9 × 10−4) for rheumatoid arthritis, 0·99 (0·97–1·01; p=0·47) for type 2 diabetes, 1·00 (0·98–1·02; p=0·92) for ischaemic stroke, and 1·08 (1·04–1·12; p=1·8 × 10−5) for abdominal aortic aneurysm. In exploratory analyses, we observed per-allele increases in concentrations of proatherogenic lipids, including LDL-cholesterol, but no clear evidence of association for blood pressure, glycaemic traits, or any of the 24 other disorders studied. Modelling suggested that the observed increase in LDL-cholesterol could account for about a third of the association observed between the genetic score and increased coronary risk. Interpretation Human genetic data suggest that long-term dual IL-1α/β inhibition could increase cardiovascular risk and, conversely, reduce the risk of development of rheumatoid arthritis. The cardiovascular risk might, in part, be mediated through an increase in proatherogenic lipid concentrations. Funding UK Medical Research Council, British Heart Foundation, UK National Institute for Health Research, National Institute for Health Research Cambridge Biomedical Research Centre, European Research Council, and European Commission Framework Programme 7.

A new regulatory variant in the interleukin-6 receptor gene associates with asthma risk

The main genetic determinant of soluble interleukin 6 receptor (sIL-6R) levels is the missense variant rs2228145 that maps to the cleavage site of IL-6R. For each Ala allele, sIL-6R serum levels increase by ∼20 ng ml -1 and asthma risk by 1.09-fold. However, this variant does not explain the total heritability for sIL-6R levels. Additional independent variants in IL6R may therefore contribute to variation in sIL-6R levels and influence asthma risk. We imputed 471 variants in IL6R and tested these for association with sIL-6R serum levels in 360 individuals. An intronic variant (rs12083537) was associated with sIL-6R levels independently of rs4129267 (P=0.0005), a proxy single-nucleotide polymorphism for rs2228145. A significant and consistent association for rs12083537 was observed in a replication panel of 354 individuals (P=0.033). Each rs12083537:A allele increased sIL-6R serum levels by 2.4 ng ml -1. Analysis of mRNA levels in two cohorts did not identify significant associations between rs12083537 and IL6R transcription levels. On the other hand, results from 16 705 asthmatics and 30 809 controls showed that the rs12083537:A allele increased asthma risk by 1.04-fold (P=0.0419). Genetic risk scores based on IL6R regulatory variants may prove useful in explaining variation in clinical response to tocilizumab, an anti-IL-6R monoclonal antibody.

Mapping the regulatory sequences controlling 93 breast cancer-associated miRNA genes leads to the identification of two functional promoters of the Hsa-mir-200b cluster, methylation of which is associated with metastasis or hormone receptor status in advanced breast cancer

MicroRNAs (miRNAs) are small non-coding RNAs of 20 nt in length that are capable of modulating gene expression post-transcriptionally. Although miRNAs have been implicated in cancer, including breast cancer, the regulation of miRNA transcription and the role of defects in this process in cancer is not well understood. In this study we have mapped the promoters of 93 breast cancer-associated miRNAs, and then looked for associations between DNA methylation of 15 of these promoters and miRNA expression in breast cancer cells. The miRNA promoters with clearest association between DNA methylation and expression included a previously described and a novel promoter of the Hsa-mir-200b cluster. The novel promoter of the Hsa-mir-200b cluster, denoted P2, is located 2 kb upstream of the 5′ stemloop and maps within a CpG island. P2 has comparable promoter activity to the previously reported promoter (P1), and is able to drive the expression of miR-200b in its endogenous genomic context. DNA methylation of both P1 and P2 was inversely associated with miR-200b expression in eight out of nine breast cancer cell lines, and in vitro methylation of both promoters repressed their activity in reporter assays. In clinical samples, P1 and P2 were differentially methylated with methylation inversely associated with miR-200b expression. P1 was hypermethylated in metastatic lymph nodes compared with matched primary breast tumours whereas P2 hypermethylation was associated with loss of either oestrogen receptor or progesterone receptor. Hypomethylation of P2 was associated with gain of HER2 and androgen receptor expression. These data suggest an association between miR-200b regulation and breast cancer subtype and a potential use of DNA methylation of miRNA promoters as a component of a suite of breast cancer biomarkers.

Association between the interleukin 23 receptor and ankylosing spondylitis is confirmed by a new UK case-control study and meta-analysis of published series

Objectives. It has been shown previously that IL-23R variants are associated with AS. We conducted an extended analysis in the UK population and a meta-analysis with the previously published studies, in order to refine these IL-23R associations with AS. Methods. The UK case-control study included 730 new cases and 1331 healthy controls. In the extended study, the 730 cases were combined with 1088 published cases. Allelic associations were analysed using contingency tables. In the meta-analysis, 3482 cases and 3150 controls from four different published studies and the new UK cases were combined. DerSimonian-Laird test was used to calculate random effects pooled odds ratios (ORs). Results. In the UK case-control study with new cases, four of the eight SNPs showed significant associations, whereas in the extended UK study, seven of the eight IL-23R SNPs showed significant associations (P < 0.05) with AS, maximal with rs11209032 (P < 10-5, OR 1.3), when cases with IBD and/or psoriasis were excluded. The meta-analysis showed significant associations with all eight SNPs; the strongest associations were again seen not only with rs11209032 (P = 4.06 × 10-9, OR ∼1.2) but also with rs11209026 (P < 10-10, OR ∼0.6). Conclusions. IL-23R polymorphisms are clearly associated with AS, but the primary causal association(s) is(are) still not established. These polymorphisms could contribute either increased or decreased susceptibility to AS; functional studies will be required for their full evaluation. Additionally, observed stronger associations with SNPs rs11209026 and rs11465804 upon exclusion of IBD and/or psoriasis cases may represent an independent association with AS. © The Author 2009. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved.

Toll-like receptor 4 and CD14 polymorphisms in ankylosing spondylitis: Evidence of a weak association in finns

Objective To investigate the association of CD14 and Toll-like receptor (TLR4) with ankylosing spondylitis (AS). Methods A promoter variant in CD14 and 2 coding polymorphisms in TLR4 were investigated in UK and Finnish families with AS and in a UK case-control study. A metaanalysis of published TLR4 and CD14 studies was performed. Results In the Finnish study the CD74-260bp T variant showed an association (p = 0.006), and the common 2-marker TLR4 haplotype showed a weak association (global p = 0.03), with AS. No associations were seen in the UK based studies or in the metaanalyses. Conclusion CD14 and TLR4 showed an association with AS in the Finns only.