Bacteria localization and chorion thinning among preterm premature rupture of membranes.

OBJECTIVE: Bacterial colonization of the fetal membranes and its role in pathogenesis of membrane rupture is poorly understood. Prior retrospective work revealed chorion layer thinning in preterm premature rupture of membranes (PPROM) subjects. Our objective was to prospectively examine fetal membrane chorion thinning and to correlate to bacterial presence in PPROM, preterm, and term subjects. STUDY DESIGN: Paired membrane samples (membrane rupture and membrane distant) were prospectively collected from: PPROM = 14, preterm labor (PTL = 8), preterm no labor (PTNL = 8), term labor (TL = 10), and term no labor (TNL = 8), subjects. Sections were probed with cytokeratin to identify fetal trophoblast layer of the chorion using immunohistochemistry. Fluorescence in situ hybridization was performed using broad range 16 s ribosomal RNA probe. Images were evaluated, chorion and choriodecidua were measured, and bacterial fluorescence scored. Chorion thinning and bacterial presence were compared among and between groups using Student's t-test, linear mixed effect model, and Poisson regression model (SAS Cary, NC). RESULTS: In all groups, the fetal chorion cellular layer was thinner at rupture compared to distant site (147.2 vs. 253.7 µm, p<0.0001). Further, chorion thinning was greatest among PPROM subjects compared to all other groups combined, regardless of site sampled [PPROM(114.9) vs. PTL(246.0) vs. PTNL(200.8) vs. TL(217.9) vs. TNL(246.5)]. Bacteria counts were highest among PPROM subjects compared to all other groups regardless of site sampled or histologic infection [PPROM(31) vs. PTL(9) vs. PTNL(7) vs. TL(7) vs. TNL(6)]. Among all subjects at both sites, bacterial counts were inversely correlated with chorion thinning, even excluding histologic chorioamnionitis (p<0.0001 and p = 0.05). CONCLUSIONS: Fetal chorion was uniformly thinner at rupture site compared to distant sites. In PPROM fetal chorion, we demonstrated pronounced global thinning. Although cause or consequence is uncertain, bacterial presence is greatest and inversely correlated with chorion thinning among PPROM subjects.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

On-board Robotic Multi-pinhole SPECT System for Region-of-interest (ROI) Imaging

On-board image guidance, such as cone-beam CT (CBCT) and kV/MV 2D imaging, is essential in many radiation therapy procedures, such as intensity modulated radiotherapy (IMRT) and stereotactic body radiation therapy (SBRT). These imaging techniques provide predominantly anatomical information for treatment planning and target localization. Recently, studies have shown that treatment planning based on functional and molecular information about the tumor and surrounding tissue could potentially improve the effectiveness of radiation therapy. However, current on-board imaging systems are limited in their functional and molecular imaging capability. Single Photon Emission Computed Tomography (SPECT) is a candidate to achieve on-board functional and molecular imaging. Traditional SPECT systems typically take 20 minutes or more for a scan, which is too long for on-board imaging. A robotic multi-pinhole SPECT system was proposed in this dissertation to provide shorter imaging time by using a robotic arm to maneuver the multi-pinhole SPECT system around the patient in position for radiation therapy.

A 49-pinhole collimated SPECT detector and its shielding were designed and simulated in this work using the computer-aided design (CAD) software. The trajectories of robotic arm about the patient, treatment table and gantry in the radiation therapy room and several detector assemblies such as parallel holes, single pinhole and 49 pinholes collimated detector were investigated. The rail mounted system was designed to enable a full range of detector positions and orientations to various crucial treatment sites including head and torso, while avoiding collision with linear accelerator (LINAC), patient table and patient.

An alignment method was developed in this work to calibrate the on-board robotic SPECT to the LINAC coordinate frame and to the coordinate frames of other on-board imaging systems such as CBCT. This alignment method utilizes line sources and one pinhole projection of these line sources. The model consists of multiple alignment parameters which maps line sources in 3-dimensional (3D) space to their 2-dimensional (2D) projections on the SPECT detector. Computer-simulation studies and experimental evaluations were performed as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise and acquisition geometry. In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, the six alignment parameters (3 translational and 3 rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by Radon transform, the estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution and detector acquisition geometry. The estimation accuracy was significantly improved by using 4 line sources rather than 3 and also by using thinner line-source projections (obtained by better intrinsic detector resolution). With 5 line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.

Simulation studies were performed to investigate the improvement of imaging sensitivity and accuracy of hot sphere localization for breast imaging of patients in prone position. A 3D XCAT phantom was simulated in the prone position with nine hot spheres of 10 mm diameter added in the left breast. A no-treatment-table case and two commercial prone breast boards, 7 and 24 cm thick, were simulated. Different pinhole focal lengths were assessed for root-mean-square-error (RMSE). The pinhole focal lengths resulting in the lowest RMSE values were 12 cm, 18 cm and 21 cm for no table, thin board, and thick board, respectively. In both no table and thin board cases, all 9 hot spheres were easily visualized above background with 4-minute scans utilizing the 49-pinhole SPECT system while seven of nine hot spheres were visible with the thick board. In comparison with parallel-hole system, our 49-pinhole system shows reduction in noise and bias under these simulation cases. These results correspond to smaller radii of rotation for no-table case and thinner prone board. Similarly, localization accuracy with the 49-pinhole system was significantly better than with the parallel-hole system for both the thin and thick prone boards. Median localization errors for the 49-pinhole system with the thin board were less than 3 mm for 5 of 9 hot spheres, and less than 6 mm for the other 4 hot spheres. Median localization errors of 49-pinhole system with the thick board were less than 4 mm for 5 of 9 hot spheres, and less than 8 mm for the other 4 hot spheres.

Besides prone breast imaging, respiratory-gated region-of-interest (ROI) imaging of lung tumor was also investigated. A simulation study was conducted on the potential of multi-pinhole, region-of-interest (ROI) SPECT to alleviate noise effects associated with respiratory-gated SPECT imaging of the thorax. Two 4D XCAT digital phantoms were constructed, with either a 10 mm or 20 mm diameter tumor added in the right lung. The maximum diaphragm motion was 2 cm (for 10 mm tumor) or 4 cm (for 20 mm tumor) in superior-inferior direction and 1.2 cm in anterior-posterior direction. Projections were simulated with a 4-minute acquisition time (40 seconds per each of 6 gates) using either the ROI SPECT system (49-pinhole) or reference single and dual conventional broad cross-section, parallel-hole collimated SPECT. The SPECT images were reconstructed using OSEM with up to 6 iterations. Images were evaluated as a function of gate by profiles, noise versus bias curves, and a numerical observer performing a forced-choice localization task. Even for the 20 mm tumor, the 49-pinhole imaging ROI was found sufficient to encompass fully usual clinical ranges of diaphragm motion. Averaged over the 6 gates, noise at iteration 6 of 49-pinhole ROI imaging (10.9 µCi/ml) was approximately comparable to noise at iteration 2 of the two dual and single parallel-hole, broad cross-section systems (12.4 µCi/ml and 13.8 µCi/ml, respectively). Corresponding biases were much lower for the 49-pinhole ROI system (3.8 µCi/ml), versus 6.2 µCi/ml and 6.5 µCi/ml for the dual and single parallel-hole systems, respectively. Median localization errors averaged over 6 gates, for the 10 mm and 20 mm tumors respectively, were 1.6 mm and 0.5 mm using the ROI imaging system and 6.6 mm and 2.3 mm using the dual parallel-hole, broad cross-section system. The results demonstrate substantially improved imaging via ROI methods. One important application may be gated imaging of patients in position for radiation therapy.

A robotic SPECT imaging system was constructed utilizing a gamma camera detector (Digirad 2020tc) and a robot (KUKA KR150-L110 robot). An imaging study was performed with a phantom (PET CT PhantomTM), which includes 5 spheres of 10, 13, 17, 22 and 28 mm in diameter. The phantom was placed on a flat-top couch. SPECT projections were acquired with a parallel-hole collimator and a single-pinhole collimator both without background in the phantom, and with background at 1/10th the sphere activity concentration. The imaging trajectories of parallel-hole and pinhole collimated detectors spanned 180 degrees and 228 degrees respectively. The pinhole detector viewed a 14.7 cm-diameter common volume which encompassed the 28 mm and 22 mm spheres. The common volume for parallel-hole was a 20.8-cm-diameter cylinder which encompassed all five spheres in the phantom. The maneuverability of the robotic system was tested by navigating the detector to trace the flat-top table while avoiding collision with the table and maintaining the closest possible proximity to the common volume. For image reconstruction, detector trajectories were described by radius-of-rotation and detector rotation angle θ. These reconstruction parameters were obtained from the robot base and tool coordinates. The robotic SPECT system was able to maneuver the parallel-hole and pinhole collimated SPECT detectors in close proximity to the phantom, minimizing impact of the flat-top couch on detector to center-of-rotation (COR) distance. In no background case, all five spheres were visible in the reconstructed parallel-hole and pinhole images. In with background case, three spheres of 17, 22 and 28 mm diameter were readily observed with the parallel-hole imaging, and the targeted spheres (22 and 28 mm diameter) were readily observed in the pinhole ROI imaging.

In conclusion, the proposed on-board robotic SPECT can be aligned to LINAC/CBCT with a single pinhole projection of the line-source phantom. Alignment parameters can be estimated using one pinhole projection of line sources. This alignment method may be important for multi-pinhole SPECT, where relative pinhole alignment may vary during rotation. For single pinhole and multi-pinhole SPECT imaging onboard radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC. In simulation studies of prone breast imaging and respiratory-gated lung imaging, the 49-pinhole detector showed better tumor contrast recovery and localization in a 4-minute scan compared to parallel-hole detector. On-board SPECT could be achieved by a robot maneuvering a SPECT detector about patients in position for radiation therapy on a flat-top couch. The robot inherent coordinate frames could be an effective means to estimate detector pose for use in SPECT image reconstruction.

Variation in Inpatient Rehabilitation Utilization After Hospitalization for Burn Injury in the United States.

Approximately 45,000 individuals are hospitalized annually for burn treatment. Rehabilitation after hospitalization can offer a significant improvement in functional outcomes. Very little is known nationally about rehabilitation for burns, and practices may vary substantially depending on the region based on observed Medicare post-hospitalization spending amounts. This study was designed to measure variation in rehabilitation utilization by state of hospitalization for patients hospitalized with burn injury. This retrospective cohort study used nationally collected data over a 10-year period (2001 to 2010), from the Healthcare Cost and Utilization Project (HCUP) State Inpatient Databases (SIDs). Patients hospitalized for burn injury (n = 57,968) were identified by ICD-9-CM codes and were examined to see specifically if they were discharged immediately to inpatient rehabilitation after hospitalization (primary endpoint). Both unadjusted and adjusted likelihoods were calculated for each state taking into account the effects of age, insurance status, hospitalization at a burn center, and extent of burn injury by TBSA. The relative risk of discharge to inpatient rehabilitation varied by as much as 6-fold among different states. Higher TBSA, having health insurance, higher age, and burn center hospitalization all increased the likelihood of discharge to inpatient rehabilitation following acute care hospitalization. There was significant variation between states in inpatient rehabilitation utilization after adjusting for variables known to affect each outcome. Future efforts should be focused on identifying the cause of this state-to-state variation, its relationship to patient outcome, and standardizing treatment across the United States.

Variation in pediatric traumatic brain injury outcomes in the United States.

OBJECTIVE: To ascertain the degree of variation, by state of hospitalization, in outcomes associated with traumatic brain injury (TBI) in a pediatric population. DESIGN: A retrospective cohort study of pediatric patients admitted to a hospital with a TBI. SETTING: Hospitals from states in the United States that voluntarily participate in the Agency for Healthcare Research and Quality's Healthcare Cost and Utilization Project. PARTICIPANTS: Pediatric (age ≤ 19 y) patients hospitalized for TBI (N=71,476) in the United States during 2001, 2004, 2007, and 2010. INTERVENTIONS: None. MAIN OUTCOME MEASURES: Primary outcome was proportion of patients discharged to rehabilitation after an acute care hospitalization among alive discharges. The secondary outcome was inpatient mortality. RESULTS: The relative risk of discharge to inpatient rehabilitation varied by as much as 3-fold among the states, and the relative risk of inpatient mortality varied by as much as nearly 2-fold. In the United States, approximately 1981 patients could be discharged to inpatient rehabilitation care if the observed variation in outcomes was eliminated. CONCLUSIONS: There was significant variation between states in both rehabilitation discharge and inpatient mortality after adjusting for variables known to affect each outcome. Future efforts should be focused on identifying the cause of this state-to-state variation, its relationship to patient outcome, and standardizing treatment across the United States.

Allopregnanolone Levels Are Inversely Associated with Self-Reported Pain Symptoms in U.S. Iraq and Afghanistan-Era Veterans: Implications for Biomarkers and Therapeutics.

BACKGROUND AND OBJECTIVES: Pain symptoms are common among Iraq/Afghanistan-era veterans, many of whom continue to experience persistent pain symptoms despite multiple pharmacological interventions. Preclinical data suggest that neurosteroids such as allopregnanolone demonstrate pronounced analgesic properties, and thus represent logical biomarker candidates and therapeutic targets for pain. Allopregnanolone is also a positive GABAA receptor modulator with anxiolytic, anticonvulsant, and neuroprotective actions in rodent models. We previously reported inverse associations between serum allopregnanolone levels and self-reported pain symptom severity in a pilot study of 82 male veterans. METHODS: The current study investigates allopregnanolone levels in a larger cohort of 485 male Iraq/Afghanistan-era veterans to attempt to replicate these initial findings. Pain symptoms were assessed by items from the Symptom Checklist-90-R (SCL-90-R) querying headache, chest pain, muscle soreness, and low back pain over the past 7 days. Allopregnanolone levels were quantified by gas chromatography/mass spectrometry. RESULTS: Associations between pain ratings and allopregnanolone levels were examined with Poisson regression analyses, controlling for age and smoking. Bivariate nonparametric Mann–Whitney analyses examining allopregnanolone levels across high and low levels of pain were also conducted. Allopregnanolone levels were inversely associated with muscle soreness [P = 0.0028], chest pain [P = 0.032], and aggregate total pain (sum of all four pain items) [P = 0.0001]. In the bivariate analyses, allopregnanolone levels were lower in the group reporting high levels of muscle soreness [P = 0.001]. CONCLUSIONS: These findings are generally consistent with our prior pilot study and suggest that allopregnanolone may function as an endogenous analgesic. Thus, exogenous supplementation with allopregnanolone could have therapeutic potential. The characterization of neurosteroid profiles may also have biomarker utility.

Differential developmental trajectories of magnetic susceptibility in human brain gray and white matter over the lifespan

As indicated by several recent studies, magnetic susceptibility of the brain is influenced mainly by myelin in the white matter and by iron deposits in the deep nuclei. Myelination and iron deposition in the brain evolve both spatially and temporally. This evolution reflects an important characteristic of normal brain development and ageing. In this study, we assessed the changes of regional susceptibility in the human brain in vivo by examining the developmental and ageing process from 1 to 83 years of age. The evolution of magnetic susceptibility over this lifespan was found to display differential trajectories between the gray and the white matter. In both cortical and subcortical white matter, an initial decrease followed by a subsequent increase in magnetic susceptibility was observed, which could be fitted by a Poisson curve. In the gray matter, including the cortical gray matter and the iron-rich deep nuclei, magnetic susceptibility displayed a monotonic increase that can be described by an exponential growth. The rate of change varied according to functional and anatomical regions of the brain. For the brain nuclei, the age-related changes of susceptibility were in good agreement with the findings from R2* measurement. Our results suggest that magnetic susceptibility may provide valuable information regarding the spatial and temporal patterns of brain myelination and iron deposition during brain maturation and ageing. © 2013 Wiley Periodicals, Inc.

Some models for discretized series of events

A discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals. Such data are common in environmental applications. We describe a class of models for them, based on an unobserved continuous-time discrete-state Markov process, which determines the rate of a doubly stochastic Poisson process, from which the binary time series is constructed by discretization. We discuss likelihood inference for these processes and their second-order properties and extend them to multiple series. An application involves modeling the times of exposures to air pollution at a number of receptors in Western Europe.

Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

A uniform, quality controlled Surface Ocean CO2 Atlas (SOCAT)

A well documented, publicly available, global data set of surface ocean carbon dioxide (CO2) parameters has been called for by international groups for nearly two decades. The Surface Ocean CO2 Atlas (SOCAT) project was initiated by the international marine carbon science community in 2007 with the aim of providing a comprehensive, publicly available, regularly updated, global data set of marine surface CO2, which had been subject to quality control (QC). Many additional CO2 data, not yet made public via the Carbon Dioxide Information Analysis Center (CDIAC), were retrieved from data originators, public websites and other data centres. All data were put in a uniform format following a strict protocol. Quality control was carried out according to clearly defined criteria. Regional specialists performed the quality control, using state-of-the-art web-based tools, specially developed for accomplishing this global team effort. SOCAT version 1.5 was made public in September 2011 and holds 6.3 million quality controlled surface CO2 data points from the global oceans and coastal seas, spanning four decades (1968–2007). Three types of data products are available: individual cruise files, a merged complete data set and gridded products. With the rapid expansion of marine CO2 data collection and the importance of quantifying net global oceanic CO2 uptake and its changes, sustained data synthesis and data access are priorities.

A uniform, quality controlled Surface Ocean CO2 Atlas (SOCAT)

A well-documented, publicly available, global data set of surface ocean carbon dioxide (CO2) parameters has been called for by international groups for nearly two decades. The Surface Ocean CO2 Atlas (SOCAT) project was initiated by the international marine carbon science community in 2007 with the aim of providing a comprehensive, publicly available, regularly updated, global data set of marine surface CO2, which had been subject to quality control (QC). Many additional CO2 data, not yet made public via the Carbon Dioxide Information Analysis Center (CDIAC), were retrieved from data originators, public websites and other data centres. All data were put in a uniform format following a strict protocol. Quality control was carried out according to clearly defined criteria. Regional specialists performed the quality control, using state-of-the-art web-based tools, specially developed for accomplishing this global team effort. SOCAT version 1.5 was made public in September 2011 and holds 6.3 million quality controlled surface CO2 data points from the global oceans and coastal seas, spanning four decades (1968–2007). Three types of data products are available: individual cruise files, a merged complete data set and gridded products. With the rapid expansion of marine CO2 data collection and the importance of quantifying net global oceanic CO2 uptake and its changes, sustained data synthesis and data access are priorities.

Surface Ocean CO2 Atlas (SOCAT) gridded data products

As a response to public demand for a well-documented, quality controlled, publically available, global surface ocean carbon dioxide (CO2) data set, the international marine carbon science community developed the Surface Ocean CO2 Atlas (SOCAT). The first SOCAT product is a collection of 6.3 million quality controlled surface CO2 data from the global oceans and coastal seas, spanning four decades (1968–2007). The SOCAT gridded data presented here is the second data product to come from the SOCAT project. Recognizing that some groups may have trouble working with millions of measurements, the SOCAT gridded product was generated to provide a robust, regularly spaced CO2 fugacity (fCO2) product with minimal spatial and temporal interpolation, which should be easier to work with for many applications. Gridded SOCAT is rich with information that has not been fully explored yet (e.g., regional differences in the seasonal cycles), but also contains biases and limitations that the user needs to recognize and address (e.g., local influences on values in some coastal regions).

Towards An Acoustic Model-Based Poroelastic Imaging Method: I. Theoretical Foundation

The ultrasonic measurement and imaging of tissue elasticity is currently under wide investigation and development as a clinical tool for the assessment of a broad range of diseases, but little account in this field has yet been taken of the fact that soft tissue is porous and contains mobile fluid. The ability to squeeze fluid out of tissue may have implications for conventional elasticity imaging, and may present opportunities for new investigative tools. When a homogeneous, isotropic, fluid-saturated poroelastic material with a linearly elastic solid phase and incompressible solid and fluid constituents is subjected to stress, the behaviour of the induced internal strain field is influenced by three material constants: the Young's modulus (E(s)) and Poisson's ratio (nu(s)) of the solid matrix and the permeability (k) of the solid matrix to the pore fluid. New analytical expressions were derived and used to model the time-dependent behaviour of the strain field inside simulated homogeneous cylindrical samples of such a poroelastic material undergoing sustained unconfined compression. A model-based reconstruction technique was developed to produce images of parameters related to the poroelastic material constants (E(s), nu(s), k) from a comparison of the measured and predicted time-dependent spatially varying radial strain. Tests of the method using simulated noisy strain data showed that it is capable of producing three unique parametric images: an image of the Poisson's ratio of the solid matrix, an image of the axial strain (which was not time-dependent subsequent to the application of the compression) and an image representing the product of the aggregate modulus E(s)(1-nu(s))/(1+nu(s))(1-2nu(s)) of the solid matrix and the permeability of the solid matrix to the pore fluid. The analytical expressions were further used to numerically validate a finite element model and to clarify previous work on poroelastography.

Higher incidence of childhood-onset type 1 diabetes mellitus in remote areas: a UK regional small-area analysis

Aims/hypothesis: We investigated the association between the incidence of type 1 diabetes mellitus and remoteness (a proxy measure for exposure to infections) using recently developed techniques for statistical analysis of small-area data.

Subjects, materials and methods: New cases in children aged 0 to 14 years in Northern Ireland were prospectively registered from 1989 to 2003. Ecological analysis was conducted using small geographical units (582 electoral wards) and area characteristics including remoteness, deprivation and child population density. Analysis was conducted using Poisson regression models and Bayesian
hierarchical models to allow for spatially correlated risks that were potentially caused by unmeasured explanatory variables.

Results: In Northern Ireland between 1989 and 2003, there were 1,433 new cases of type 1 diabetes, giving a directly standardised incidence rate of 24.7 per 100,000 personyears. Areas in the most remote fifth of all areas had a significantly (p=0.0006) higher incidence of type 1 diabetes mellitus (incidence rate ratio=1.27 [95% CI 1.07, 1.50]) than those in the most accessible fifth of all areas. There was also a higher incidence rate in areas that were less deprived (p<0.0001) and less densely populated (p=0.002). After adjustment for deprivation and additional adjustment for child population density the association between diabetes and remoteness remained significant (p=0.01 and p=0.03, respectively).

Conclusions/interpretation: In Northern Ireland, there is evidence that remote areas experience higher rates of type 1 diabetes mellitus. This could reflect a reduced or delayed exposure to infections, particularly early in life, in these areas.

A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.