Convex polygons in Cartesian products

We study several problems concerning convex polygons whose vertices lie in aCartesian product of two sets of n real numbers (for short, grid). First, we prove that everysuch grid contains Ω(log n) points in convex position and that this bound is tight up to aconstant factor. We generalize this result to d dimensions (for a fixed d ∈ N), and obtaina tight lower bound of Ω(logd−1 n) for the maximum number of points in convex positionin a d-dimensional grid. Second, we present polynomial-time algorithms for computing thelongest x- or y-monotone convex polygonal chain in a grid that contains no two points withthe same x- or y-coordinate. We show that the maximum size of a convex polygon with suchunique coordinates can be efficiently approximated up to a factor of 2. Finally, we presentexponential bounds on the maximum number of point sets in convex position in such grids,and for some restricted variants. These bounds are tight up to polynomial factors

Convex Polygons in Cartesian Products

We study several problems concerning convex polygons whose vertices lie in a Cartesian product of two sets of n real numbers (for short, grid). First, we prove that every such grid contains a convex polygon with Omega(log n) vertices and that this bound is tight up to a constant factor. We generalize this result to d dimensions (for a fixed d in N), and obtain a tight lower bound of Omega(log^{d-1}n) for the maximum number of points in convex position in a d-dimensional grid. Second, we present polynomial-time algorithms for computing the longest convex polygonal chain in a grid that contains no two points with the same x- or y-coordinate. We show that the maximum size of such a convex polygon can be efficiently approximated up to a factor of 2. Finally, we present exponential bounds on the maximum number of convex polygons in these grids, and for some restricted variants. These bounds are tight up to polynomial factors

Mesenchymal Stem Cells Induce T-Cell Tolerance and Protect the Preterm Brain after Global Hypoxia-Ischemia

Hypoxic-ischemic encephalopathy (HIE) in preterm infants is a severe disease for which no curative treatment is available. Cerebral inflammation and invasion of activated peripheral immune cells have been shown to play a pivotal role in the etiology of white matter injury, which is the clinical hallmark of HIE in preterm infants. The objective of this study was to assess the neuroprotective and anti-inflammatory effects of intravenously delivered mesenchymal stem cells (MSC) in an ovine model of HIE. In this translational animal model, global hypoxia-ischemia (HI) was induced in instrumented preterm sheep by transient umbilical cord occlusion, which closely mimics the clinical insult. Intravenous administration of 2 x 106MSC/kg reduced microglial proliferation, diminished loss of oligodendrocytes and reduced demyelination, as determined by histology and Diffusion Tensor Imaging (DTI), in the preterm brain after global HI. These anti-inflammatory and neuroprotective effects of MSC were paralleled by reduced electrographic seizure activity in the ischemic preterm brain. Furthermore, we showed that MSC induced persistent peripheral T-cell tolerance in vivo and reduced invasion of T-cells into the preterm brain following global HI. These findings show in a preclinical animal model that intravenously administered MSC reduced cerebral inflammation, protected against white matter injury and established functional improvement in the preterm brain following global HI. Moreover, we provide evidence that induction of T-cell tolerance by MSC might play an important role in the neuroprotective effects of MSC in HIE. This is the first study to describe a marked neuroprotective effect of MSC in a translational animal model of HIE

Cerebral inflammation and mobilization of the peripheral immune system following global hypoxia-ischemia in preterm sheep

BACKGROUND: Hypoxic-ischemic encephalopathy (HIE) is one of the most important causes of brain injury in preterm infants. Preterm HIE is predominantly caused by global hypoxia-ischemia (HI). In contrast, focal ischemia is most common in the adult brain and known to result in cerebral inflammation and activation of the peripheral immune system. These inflammatory responses are considered to play an important role in the adverse outcomes following brain ischemia. In this study, we hypothesize that cerebral and peripheral immune activation is also involved in preterm brain injury after global HI. METHODS: Preterm instrumented fetal sheep were exposed to 25 minutes of umbilical cord occlusion (UCO) (n = 8) at 0.7 gestation. Sham-treated animals (n = 8) were used as a control group. Brain sections were stained for ionized calcium binding adaptor molecule 1 (IBA-1) to investigate microglial proliferation and activation. The peripheral immune system was studied by assessment of circulating white blood cell counts, cellular changes of the spleen and influx of peripheral immune cells (MPO-positive neutrophils) into the brain. Pre-oligodendrocytes (preOLs) and myelin basic protein (MBP) were detected to determine white matter injury. Electro-encephalography (EEG) was recorded to assess functional impairment by interburst interval (IBI) length analysis. RESULTS: Global HI resulted in profound activation and proliferation of microglia in the hippocampus, periventricular and subcortical white matter. In addition, non-preferential mobilization of white blood cells into the circulation was observed within 1 day after global HI and a significant influx of neutrophils into the brain was detected 7 days after the global HI insult. Furthermore, global HI resulted in marked involution of the spleen, which could not be explained by increased splenic apoptosis. In concordance with cerebral inflammation, global HI induced severe brain atrophy, region-specific preOL vulnerability, hypomyelination and persistent suppressed brain function. CONCLUSIONS: Our data provided evidence that global HI in preterm ovine fetuses resulted in profound cerebral inflammation and mobilization of the peripheral innate immune system. These inflammatory responses were paralleled by marked injury and functional loss of the preterm brain. Further understanding of the interplay between preterm brain inflammation and activation of the peripheral immune system following global HI will contribute to the development of future therapeutic interventions in preterm HIE

Comparison of ECG-based physiological markers for hypoxia in a preterm ovine model

BACKGROUND: Current methods for assessing perinatal hypoxic conditions did not improve infant outcomes. Various waveform-based and interval-based ECG markers have been suggested, but not directly compared. We compare performance of ECG markers in a standardized ovine model for fetal hypoxia. METHODS: Sixty-nine fetal sheep of 0.7 gestation had ECG recorded 4 h before, during, and 4 h after a 25-min period of umbilical cord occlusion (UCO), leading to severe hypoxia. Various ECG markers were calculated, among which were heart rate (HR), HR-corrected ventricular depolarization/repolarization interval (QTc), and ST-segment analysis (STAN) episodic and baseline rise markers, analogue to clinical STAN device alarms. Performance of interval- and waveform-based ECG markers was assessed by correlating predicted and actual hypoxic/normoxic state. RESULTS: Of the markers studied, HR and QTc demonstrated high sensitivity (≥86%), specificity (≥96%), and positive predictive value (PPV) (≥86%) and detected hypoxia in ≥90% of fetuses at 4 min after UCO. In contrast, STAN episodic and baseline rise markers displayed low sensitivity (≤20%) and could not detect severe fetal hypoxia in 65 and 28% of the animals, respectively. CONCLUSION: Interval-based HR and QTc markers could assess the presence of severe hypoxia. Waveform-based STAN episodic and baseline rise markers were ineffective as markers for hypoxia

Heart-rate mediated blood pressure control in preterm fetal sheep under normal and hypoxic-ischemic conditions

Background: The understanding of hypoxemia-induced changes in baroreflex function is limited and may be studied in a fetal sheep experiment before, during, and after standardized hypoxic conditions. Methods: Preterm fetal lambs were instrumented at 102 d gestation (term: 146 d). At 106 d, intrauterine hypoxia–­ischemia was induced by 25¿min of umbilical cord occlusion (UCO). Baroreflex-related fluctuations were calculated at 30-min intervals during the first week after UCO by transfer function (cross-spectral) analysis between systolic blood pressure (SBP) and R–R interval fluctuations, estimated in the low-frequency (LF, 0.04–0.15 Hz) band. LF transfer gain (baroreflex sensitivity) and delay (s) reflect the baroreflex function. Results: Baseline did not differ in LF transfer gain and delay between controls and the UCO group. In controls, LF gain showed postnatal increase. By contrast, LF gain gradually decreased in the UCO group, resulting in significantly lower values 4–7 d after UCO. In the UCO group, LF delay increased and differed significantly from controls. Conclusion: Our results show that intrauterine hypoxia–ischemia results in reduced baroreflex sensitivity over a period of 7 d, indicating limited efficacy to buffer BP changes by adapting heart rate. Cardiovascular dysregulation may augment already present cerebral damage after systemic hypoxia–ischemia in the reperfusion period