A two-dimensional mathematical model of percutaneous drug absorption

Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1) the flow rate of the drug, (2) the flux and the cumulative amount of drug eliminated into the receptor cell, (3) the steady-state value of the flux, (4) the time to reach the steady-state value of the flux and (5) the optimal value of r, which gives the maximum absorption of the drug. The paper gives valuable information which can be obtained by this two-dimensional model, that cannot be obtained with one-dimensional models. Thus this model improves upon the much simpler one-dimensional models. Some future directions of the work based on this model and the one-dimensional non-linear models that exist in the literature, are also discussed

Prospective surveillance of multivariate spatial disease data

Surveillance systems are often focused on more than one disease within a predefined area. On those occasions when outbreaks of disease are likely to be correlated, the use of multivariate surveillance techniques integrating information from multiple diseases allows us to improve the sensitivity and timeliness of outbreak detection. In this article, we present an extension of the surveillance conditional predictive ordinate to monitor multivariate spatial disease data. The proposed surveillance technique, which is defined for each small area and time period as the conditional predictive distribution of those counts of disease higher than expected given the data observed up to the previous time period, alerts us to both small areas of increased disease incidence and the diseases causing the alarm within each area. We investigate its performance within the framework of Bayesian hierarchical Poisson models using a simulation study. An application to diseases of the respiratory system in South Carolina is finally presented

Author Correction: Modelling and predicting the spatio‑temporal spread of COVID‑19, associated deaths and impact of key risk factors in England

The original version of this Article contained an error in the Introduction where, “We utilise weekly MSOA level population mobility data against observed confirmed COVID-19 case data to assess the impact mobility reduction at small-area scale has had on case transmission, and counterfactually what the magnitude may have been under the scenario of no mobility loss.” now reads: “We utilise weekly Clinical Commission Group (CCG) level population mobility data against observed confirmed COVID-19 case data to assess the impact mobility reduction at small-area scale has had on case transmission, and counterfactually what the magnitude may have been under the scenario of no mobility loss.” In addition, in Table 2, the Spatial resolution was incorrectly given in the column “Model component”, rows “Covariate (daily varying)” and “Covariates (annual estimates, weekly fixed), Elderly population proportion living in deprivation”. The correct and incorrect values appear below. Incorrect: (Table presented.) Correct: (Table presented.) Finally, in the Methods section, under the subheadings ‘Data’, and ‘Data analysis”, “Daily population movement data by MSOA was extracted from the COVID-19 Impact monitor (https:// www. oxford- covid- 19. com/).” now reads: “Daily population movement data by Clinical Commission Group (CCG) was extracted from the COVID-19 Impact monitor (https:// www. oxford- covid- 19. com/). Weekly mobility in a given MSOA where assumed to be the same as the weekly mobility in the higher level CCG containing most of that MSOA.” “Here b = (b0, b1, b2) is the vector of regression coefficients for the intercept (representing the log-transformed baseline transmission rate across all locations), mobility represents the observed weekly mobility by MSOA;” now reads: “Here b = (b0, b1, b2) is the vector of regression coefficients for the intercept (representing the log-transformed baseline transmission rate across all locations), mobility represents the observed weekly mobility in a given MSOA based on the mobility in the CCG containing most of that MSOA;” The original Article has been corrected

Modelling and predicting the spatio-temporal spread of COVID-19, associated deaths and impact of key risk factors in England.

COVID-19 caseloads in England have passed through a first peak, and at the time of this analysis appeared to be gradually increasing, potentially signalling the emergence of a second wave. To ensure continued response to the epidemic is most effective, it is imperative to better understand both retrospectively and prospectively the geographical evolution of COVID-19 caseloads and deaths at small-area resolution, identify localised areas in space-time at significantly higher risk, quantify the impact of changes in localised population mobility (or movement) on caseloads, identify localised risk factors for increased mortality and project the likely course of the epidemic at high spatial resolution in coming weeks. We applied a Bayesian hierarchical space-time SEIR model to assess the spatiotemporal variability of COVID-19 caseloads (transmission) and deaths at small-area scale in England [Middle Layer Super Output Area (MSOA), 6791 units] and by week (using observed data from week 5 to 34 of 2020), including key determinants, the modelled transmission dynamics and spatial-temporal random effects. We also estimate the number of cases and deaths at small-area resolution with uncertainty projected forward in time by MSOA (up to week 51 of 2020), the impact mobility reductions (and subsequent easing) have had on COVID-19 caseloads and quantify the impact of key socio-demographic risk factors on COVID-19 related mortality risk by MSOA. Reductions in population mobility during the course of the first lockdown had a significant impact on the reduction of COVID-19 caseloads across England, however local authorities have had a varied rate of reduction in population movement which our model suggest has substantially impacted the geographic heterogeneity in caseloads at small-area scale. The steady gain in population mobility, observed from late April, appears to have contributed to a slowdown in caseload reductions towards late June and subsequent start of the second wave. MSOA with higher proportions of elderly (70+ years of age) and elderly living in deprivation, both with very distinct geographic distributions, have a significantly elevated COVID-19 mortality rates. While non-pharmaceutical interventions (that is, reductions in population mobility and social distancing) had a profound impact on the trajectory of the first wave of the COVID-19 outbreak in England, increased population mobility appears to have significantly contributed to the second wave. A number of contiguous small-areas appear to be at a significant elevated risk of high COVID-19 transmission, many of which are also at increased risk for higher mortality rates. A geographically staggered re-introduction of intensified social distancing measures is advised and limited cross MSOA movement if the magnitude and geographic extent of the second wave is to be reduced

Disappeared persons and homicide in El Salvador

During 2012–2013, the homicide rate in El Salvador came down from 69.9 to 42.2 per 100,000 population following a government brokered truce between the leaders of the two major gangs, Mara Salvatrucha and Barrio 18. But despite the apparent successes of the truce, it was speculated that the drop in murders could have been due to the killers simply hid the bodies of their victims. This paper aims at determining whether gangs effectively disappeared their victims to cut down the official counts of murders, or they committed these crimes for other reasons. The results from this study suggest that Salvadoran gangs had been using disappearance as a method to gain sustained social control among residents of already gang-dominated areas, that together with homicide, disappearance is part of a process of territorial spread and strategic strengthening by which these groups are enhancing their capabilities to interfere in the alliances of Mexican drug trafficking organizations with Central American criminal organizations specializing in the trans-shipment of drugs and in providing access to local markets to distribute and sell drugs. Our findings show that the risk for disappearance has been large even before the truce was in place and that actually, it continues as such and going through a process of geographic expansion

Black carbon as an additional indicator of the adverse health effects of airborne particles compared with PM10 and PM2.5.

Current air quality standards for particulate matter (PM) use the PM mass concentration [PM with aerodynamic diameters ≤ 10 μm (PM(10)) or ≤ 2.5 μm (PM(2.5))] as a metric. It has been suggested that particles from combustion sources are more relevant to human health than are particles from other sources, but the impact of policies directed at reducing PM from combustion processes is usually relatively small when effects are estimated for a reduction in the total mass concentration

The strategy and clinical relevance of in vitro models of MAP resistance in osteosarcoma: a systematic review

Over the last 40 years osteosarcoma (OS) survival has stagnated with patients commonly resistant to neoadjuvant MAP chemotherapy involving high dose methotrexate, adriamycin (doxorubicin) and platinum (cisplatin). Due to the rarity of OS, the generation of relevant cell models as tools for drug discovery is paramount to tackling this issue. Four literature databases were systematically searched using pre-determined search terms to identify MAP resistant OS cell lines and patients. Drug exposure strategies used to develop cell models of resistance and the impact of these on the differential expression of resistance associated genes, proteins and non-coding RNAs are reported. A comparison to clinical studies in relation to chemotherapy response, relapse and metastasis was then made. The search retrieved 1891 papers of which 52 were relevant. Commonly, cell lines were derived from Caucasian patients with epithelial or fibroblastic subtypes. The strategy for model development varied with most opting for continuous over pulsed chemotherapy exposure. A diverse resistance level was observed between models (2.2–338 fold) with 63% of models exceeding clinically reported resistance levels which may affect the expression of chemoresistance factors. In vitro p-glycoprotein overexpression is a key resistance mechanism; however, from the available literature to date this does not translate to innate resistance in patients. The selection of models with a lower fold resistance may better reflect the clinical situation. A comparison of standardised strategies in models and variants should be performed to determine their impact on resistance markers. Clinical studies are required to determine the impact of resistance markers identified in vitro in poor responders to MAP treatment, specifically with respect to innate and acquired resistance. A shift from seeking disputed and undruggable mechanisms to clinically relevant resistance mechanisms may identify key resistance markers that can be targeted for patient benefit after a 40-year wait

Dry weather induces outbreaks of human West Nile virus infections

<p>Abstract</p> <p>Background</p> <p>Since its first occurrence in the New York City area during 1999, West Nile virus (WNV) has spread rapidly across North America and has become a major public health concern in North America. By 2002, WNV was reported in 40 states and the District of Columbia with 4,156 human and 14,539 equine cases of infection. Mississippi had the highest human incidence rate of WNV during the 2002 epidemic in the United States. Epidemics of WNV can impose enormous impacts on local economies. Therefore, it is advantageous to predict human WNV risks for cost-effective controls of the disease and optimal allocations of limited resources. Understanding relationships between precipitation and WNV transmission is crucial for predicting the risk of the human WNV disease outbreaks under predicted global climate change scenarios.</p> <p>Methods</p> <p>We analyzed data on the human WNV incidences in the 82 counties of Mississippi in 2002, using standard morbidity ratio (SMR) and Bayesian hierarchical models, to determine relationships between precipitation and human WNV risks. We also entertained spatial autocorrelations of human WNV risks with conditional autocorrelative (CAR) models, implemented in WinBUGS 1.4.3.</p> <p>Results</p> <p>We observed an inverse relationship between county-level human WNV incidence risk and total annual rainfall during the previous year. Parameters representing spatial heterogeneity in the risk of human exposure to WNV improved model fit. Annual precipitation of the previous year was a predictor of spatial variation of WNV risk.</p> <p>Conclusions</p> <p>Our results have broad implications for risk assessment of WNV and forecasting WNV outbreaks. Assessing risk of vector-born infectious diseases will require understanding of complex ecological relationships. Based on the climatologically characteristic drought occurrence in the past and on climate model predictions for climate change and potentially greater drought occurrence in the future, we suggest that the frequency and relative risk of WNV outbreaks could increase.</p

Current estimates of biogenic emissions from Eucalypts uncertain for Southeast Australia

The biogenic emissions of isoprene and monoterpenes are one of the main drivers of atmospheric photochemistry, including oxidant and secondary organic aerosol production. In this paper, the emission rates of isoprene and monoterpenes from Australian vegetation are investigated for the first time using the Model of Emissions of Gases and Aerosols from Nature version 2.1 (MEGANv2.1); the CSIRO chemical transport model; and atmospheric observations of isoprene, monoterpenes and isoprene oxidation products (methacrolein and methyl vinyl ketone). Observations from four field campaigns during three different seasons are used, covering urban, coastal suburban and inland forest areas. The observed concentrations of isoprene and monoterpenes were of a broadly similar magnitude, which may indicate that southeast Australia holds an unusual position where neither chemical species dominates. The model results overestimate the observed atmospheric concentrations of isoprene (up to a factor of 6) and underestimate the monoterpene concentrations (up to a factor of 4). This may occur because the emission rates currently used in MEGANv2.1 for Australia are drawn mainly from young eucalypt trees (\u3c 7 years), which may emit more isoprene than adult trees. There is no single increase/decrease factor for the emissions which suits all seasons and conditions studied. There is a need for further field measurements of in situ isoprene and monoterpene emission fluxes in Australia

Enhanced external counter pulsation in treatment of refractory angina pectoris: two year outcome and baseline factors associated with treatment failure

<p>Abstract</p> <p>Background</p> <p>Enhanced external counter pulsation (EECP) is a non-invasive treatment option for patients with refractory angina pectoris ineligible to further traditional treatment. The aim of this study was to evaluate the effect of EECP on patients at a Scandinavian medical centre and to investigate if outcome can be predicted by analysing baseline factors.</p> <p>Methods</p> <p>86 consecutive patients (70 male, 16 female) were treated with EECP and followed for two years post treatment. Canadian cardiovascular society (CCS) class was analysed, and medication and adverse clinical events were researched prior to EECP, at the end of the treatment, and at six, 12 and 24 months thereafter. Patients responding to therapy by improving at least one CCS class were compared with those who failed to respond. Any differences in background factors were recorded and analysed.</p> <p>Results</p> <p>79% of the patients responded to therapy by improving at least one CCS class. In general, the CCS class improved by one class after EECP treatment (3.05 before versus 2.14 after treatment). A total of 61.5% of the initial responders showed sustained improvement at the 12 month follow-up while 29% presented sustained improvement after 24 months. Treatment was most effective among patients suffering from CCS class III-IV angina pectoris, while patients suffering from CCS class II angina pectoris improved transiently but failed to show sustained improvement after the 12 month follow-up. Diabetes mellitus and calcium channel antagonists were more common among the non-responders (<it>p </it>< 0.05).</p> <p>Conclusion</p> <p>This study confirms the safety and efficiency of EECP as a treatment option for patients suffering from refractory angina pectoris. The therapy is most beneficial in patients suffering from severe angina (CCS III-IV) while sustained response to therapy could not be verified among patients suffering from CCS class II angina pectoris.</p