Effect of PM2.5 Levels on ED Visits for Respiratory Causes in a Greek Semi-Urban Area.

Fine particulate matter that have a diameter of <2.5 µm (PM2.5) are an important factor of anthropogenic pollution since they are associated with the development of acute respiratory illnesses. The aim of this prospective study is to examine the correlation between PM2.5 levels in the semi-urban city of Volos and Emergency Department (ED) visits for respiratory causes. ED visits from patients with asthma, pneumonia and upper respiratory infection (URI) were recorded during a one-year period. The 24 h PM2.5 pollution data were collected in a prospective manner by using twelve fully automated air quality monitoring stations. PM2.5 levels exceeded the daily limit during 48.6% of the study period, with the mean PM2.5 concentration being 30.03 ± 17.47 µg/m3. PM2.5 levels were significantly higher during winter. When PM2.5 levels were beyond the daily limit, there was a statistically significant increase in respiratory-related ED visits (1.77 vs. 2.22 visits per day; p: 0.018). PM2.5 levels were also statistically significantly related to the number of URI-related ED visits (0.71 vs. 0.99 visits/day; p = 0.01). The temperature was negatively correlated with ED visits (r: −0.21; p < 0.001) and age was found to be positively correlated with ED visits (r: 0.69; p < 0.001), while no statistically significant correlation was found concerning humidity (r: 0.03; p = 0.58). In conclusion, PM2.5 levels had a significant effect on ED visits for respiratory causes in the city of Volos.

Lessons We Have Learned Regarding Seroprevalence in High and Low SARS-CoV-2 Contexts in Greece before the Omicron Pandemic Wave.

BACKGROUND: Antibody seroprevalence in rural communities remains poorly investigated. We compared the SARS-CoV-2 seroprevalence in two Greek communities in June and July 2021 after the end of the Delta-driven pandemic wave that started in November 2020. One community was affected worse than the other. METHODS: The SARS-CoV-2 IgG II Quant method (Architect, Abbott, IL, USA) was used for antibody testing. RESULTS: We found a high rate of SARS-CoV-2 seropositivity in both communities, approaching 77.5%. In the area with a higher burden of COVID-19, Malesina, seropositivity was achieved with vaccine-acquired and naturally acquired immunity, whereas in the low-burden context of Domokos, the high rates of seropositivity were achieved mainly with vaccination. Previously infected individuals were less likely to be vaccinated than previously uninfected adults. The antibody titers were significantly higher in previously infected, vaccinated participants than in unvaccinated ones. In total, 4% and 10% of the unvaccinated population were diagnosed seropositive for the first time while not knowing about the previous infection. Age and gender did not impact antibody titers in high- or low-burden contexts. CONCLUSIONS: Before the Omicron pandemic wave, herd immunity was reached in different contexts in Greece. Higher antibody titers were measured in infected vaccinated individuals than in infected unvaccinated ones.

The Impact of the Lockdown Caused by the COVID-19 Pandemic on the Fine Particulate Matter (PM2.5) Air Pollution: The Greek Paradigm.

INTRODUCTION: Responding to the coronavirus pandemic, Greece implemented the largest quarantine in its history. No data exist regarding its impact on PM2.5 pollution. We aimed to assess PM2.5 levels before, during, and after lockdown (7 March 2020-16 May 2020) in Volos, one of Greece's most polluted industrialized cities, and compare PM2.5 levels with those obtained during the same period last year. Meteorological conditions were examined as confounders. METHODS: The study period was discriminated into three phases (pre-lockdown: 7 March-9 March, lockdown: 10 March-4 May, and post-lockdown period: 5 May-16 May). A wireless sensors network was used to collect PM2.5, temperature, relative humidity, rainfall, and wind speed data every 2 s. RESULTS: The lockdown resulted in a significant drop of PM2.5 by 37.4% in 2020, compared to 2019 levels. The mean daily concentrations of PM2.5 exceeded the WHO's guideline value for 24-h mean levels of PM2.5 35% of the study period. During the strictest lockdown (23 March to 4 May), the mean daily PM2.5 levels exceeded the standard 41% of the time. The transition from the pre-lockdown period into lockdown or post-lockdown periods was associated with lower PM2.5 concentrations. CONCLUSIONS: A reduction in the mean daily PM2.5 concentration was found compared to 2019. Lockdown was not enough to avoid severe exceedances of air pollution in Volos.

Effect of PM2.5 Levels on Respiratory Pediatric ED Visits in a Semi-Urban Greek Peninsula.

Ambient air pollution accounts for an estimated 4.2 million deaths worldwide. Particulate matter (PM)2.5 particles are believed to be the most harmful, as when inhaled they can penetrate deep into the lungs. The aim of this study was to examine the relationship between PM2.5 daily air concentrations and pediatric emergency department (ED) visits for respiratory diseases in a Greek suburban area. All pediatric ED visits for asthma-, pneumonia- and upper respiratory infection (URI)-related complaints were recorded during the one-year period. The 24-h PM2.5 air pollution data were prospectively collected from twelve fully automated air quality monitoring stations. The mean annual concentration of PM2.5 was 30.03 µg/m3 (World Health Organization (WHO) Air Quality Guidelines (AQG) Annual mean concentration: 10 µg/m3). PM2.5 levels rose above the WHO Air Quality Guidelines (AQG) 24-h concentrations (25 µg/m3)), 178 times (48.6% of the study period). When PM2.5 levels were above the daily limit, an increase of 32.44% (p < 0.001) was observed in daily pediatric ED visits for respiratory diseases and the increase was much higher during spring (21.19%, p = 0.018). A 32% (p < 0.001) increase was observed in URI-related visits, when PM2.5 levels were ≥25 µg/m3, compared to the mean daily visits when PM2.5 levels were <25 µg/m3. Air pollution levels were associated with increased pediatric ED visits for respiratory-related diseases.

Repeated Antigen-Based Rapid Diagnostic Testing for Estimating the Coronavirus Disease 2019 Prevalence from the Perspective of the Workers' Vulnerability before and during the Lockdown.

BACKGROUND: No previous study has investigated the SARS-CoV-2 prevalence and the changes in the proportion of positive results due to lockdown measures from the angle of workers' vulnerability to coronavirus in Greece. Two community-based programs were implemented to evaluate the SARS-CoV-2 prevalence and investigate if the prevalence changes were significant across various occupations before and one month after lockdown. METHODS: Following consent, sociodemographic, clinical, and job-related information were recorded. The VivaDiag™ SARS-CoV-2 Antigen Rapid Test was used. Positive results confirmed by a real-time Reverse Transcriptase Polymerase Chain Reaction for SARS-COV-2. RESULTS: Positive participants were more likely to work in the catering/food sector than negative participants before the lockdown. Lockdown restrictions halved the new cases. No significant differences in the likelihood of being SARS-CoV-2 positive for different job categories were detected during lockdown. The presence of respiratory symptoms was an independent predictor for rapid antigen test positivity; however, one-third of newly diagnosed patients were asymptomatic at both time points. CONCLUSIONS: The catering/food sector was the most vulnerable to COVID-19 at the pre-lockdown evaluation. We highlight the crucial role of community-based screening with rapid antigen testing to evaluate the potential modes of community transmission and the impact of infection control strategies.

Defining Antibody Seroprevalence and Duration of Humoral Responses to SARS-CoV-2 Infection and/or Vaccination in a Greek Community.

BACKGROUND: In this work, we aimed to evaluate antibody-response longevity to SARS-CoV-2 infection and/or vaccination in one of the Greek communities that was worst hit by the pandemic, Deskati, five months after a previous serosurveillance and nine months after the pandemic wave initiation (October 2020). METHODS: The SARS-CoV-2 IgG II Quant method (Architect, Abbott, IL, USA) was used for antibody testing. RESULTS: A total of 69 subjects, who previously tested positive or negative for COVID-19 antibodies, participated in the study. We found that 48% of participants turned positive due to vaccination. 27% of participants were both previously infected and vaccinated. However, all previously infected participants retained antibodies to the virus, irrespective of their vaccination status. The antibody titers were significantly higher in previously infected participants that had been vaccinated than those who were unvaccinated and in those that had been previously hospitalized for COVID-19 than those with mild disease. CONCLUSIONS: Antibody responses to SARS-CoV-2 infection were maintained nine months after the pandemic. Vaccination alone had generated an immune response in almost half of the population. Higher antibody titers were found in the case of vaccination in previously infected subjects and especially in those with severe disease leading to hospitalization.

Identity-by-descent detection across 487,409 British samples reveals fine scale population structure and ultra-rare variant associations.

Detection of Identical-By-Descent (IBD) segments provides a fundamental measure of genetic relatedness and plays a key role in a wide range of analyses. We develop FastSMC, an IBD detection algorithm that combines a fast heuristic search with accurate coalescent-based likelihood calculations. FastSMC enables biobank-scale detection and dating of IBD segments within several thousands of years in the past. We apply FastSMC to 487,409 UK Biobank samples and detect ~214 billion IBD segments transmitted by shared ancestors within the past 1500 years, obtaining a fine-grained picture of genetic relatedness in the UK. Sharing of common ancestors strongly correlates with geographic distance, enabling the use of genomic data to localize a sample's birth coordinates with a median error of 45 km. We seek evidence of recent positive selection by identifying loci with unusually strong shared ancestry and detect 12 genome-wide significant signals. We devise an IBD-based test for association between phenotype and ultra-rare loss-of-function variation, identifying 29 association signals in 7 blood-related traits.

Artifact from myomectomy/C-Section on MRI images - what does this mean for MR-guided focused ultrasound candidacy for uterine fibroids?

Background: Magnetic resonance-guided focused ultrasound (MRgFUS) is used for non-surgical treatment of uterine fibroids, often in patients who have had prior myomectomy or Cesarean section. The presence of post-surgical MRI artifacts along the beam path are a common contraindication to MRgFUS treatment. While potential problems arising from superficial cutaneous scars can be circumvented through scar patching and other techniques, deeper artifacts are difficult to bypass. Consequently, many patients with deeper artifacts are often excluded from treatment because of the assumption that these artifacts could deflect the ultrasound beam resulting in off target heating or perturb accurate MR thermometry. We sought to determine if these deep artifacts affect MRgFUS treatment efficacy or safety.Materials and Methods: A search of a MRgFUS center patient database yielded 19 patients with prior uterine surgery who had artifacts along the FUS beam path visible on MRI. Charts, operative reports (when available), screening MRI scans, and MRgFUS treatment scans were reviewed by an experienced MRgFUS treatment physician and artifacts were graded as mild, moderate, or severe.Results: One-way ANOVA showed no significant correlation between artifact severity and percent non-perfused volume (%NPV) (p = .41) or between fibroid size and % NPV (p = .49). There were no adverse events in this patient population except for one case of endometritis that occurred months after the operation, unlikely to be related to the MRgFUS treatments.Conclusion: Patients with uterine fibroids with post-operative susceptibility artifacts in the near-field can be successfully treated with MRgFUS.

Acute Pancreatitis Following Endoscopic Ampullary Biopsies without Attempted Cannulation of the Ampulla of Vater.

A 51-year-old man underwent diagnostic work-up for an abnormal-appearing ampulla of Vater. Three hours after biopsy of the ampulla, the patient presented with intense symptoms suggesting acute pancreatitis, which was later confirmed with laboratory and radiographic examinations. Other causes were excluded and the acute pancreatitis was considered a procedural complication. This is a rarely reported complication that must be taken into consideration when biopsies are performed in the ampulla of Vater.

Dosimetric and radiobiological comparison of CyberKnife M6™ InCise multileaf collimator over IRIS™ variable collimator in prostate stereotactic body radiation therapy.

The impetus behind our study was to establish a quantitative comparison between the IRIS collimator and the InCise multileaf collimator (MLC) (Accuray Inc. Synnyvale, CA) for prostate stereotactic body radiation therapy (SBRT). Treatment plans for ten prostate cancer patients were performed on MultiPlan™ 5.1.2 treatment planning system utilizing MLC and IRIS for 36.25 Gy in five fractions. To reduce the magnitude of variations between cases, the planning tumor volume (PTV) was defined and outlined for treating prostate gland only, assuming no seminal vesicle or ex-capsule involvement. Evaluation indices of each plan include PTV coverage, conformity index (CI), Paddick's new CI, homogeneity index, and gradient index. Organ at risk (OAR) dose sparing was analyzed by the bladder wall Dmax and V37Gy, rectum Dmax and V36Gy. The radiobiological response was evaluated by tumor control probability and normal tissue complication probability based on equivalent uniform dose. The dose delivery efficiency was evaluated on the basis of planned monitor units (MUs) and the reported treatment time per fraction. Statistical significance was tested using the Wilcoxon signed rank test. The studies indicated that CyberKnife M6™ IRIS and InCise™ MLC produce equivalent SBRT prostate treatment plans in terms of dosimetry, radiobiology, and OAR sparing, except that the MLC plans offer improvement of the dose fall-off gradient by 29% over IRIS. The main advantage of replacing the IRIS collimator with MLC is the improved efficiency, determined from the reduction of MUs by 42%, and a 36% faster delivery time.

A computational tool for patient specific dosimetry and radiobiological modeling of selective internal radiation therapy with (90)Y microspheres.

In recent years we have witnessed tremendous progress in selective internal radiation therapy. In clinical practice, quite often, radionuclide therapy is planned using simple models based on standard activity values or activity administered per unit body weight or surface area in spite of the admission that radiation-dose methods provide more accurate dosimetric results. To address that issue, the authors developed a Matlab-based computational software, named Patient Specific Yttrium-90 Dosimetry Toolkit (PSYDT). PSYDT was designed for patient specific voxel-based dosimetric calculations and radiobiological modeling of selective internal radiation therapy with (90)Y microspheres. The developed toolkit is composed of three dimensional dose calculations for both bremsstrahlung and beta emissions. Subsequently, radiobiological modeling is performed on a per-voxel basis and cumulative dose volume histograms (DVHs) are generated. In this report we describe the functionality and visualization features of PSYDT.

Posttraumatic Sphingomonas paucimobilis Endophthalmitis.

A rare case of Sphingomonas paucimobilis endophthalmitis secondary to a penetrating globe injury with a retained intraocular foreign body is presented. A 30-year-old man presented with severe pain following a penetrating left eye injury. Visual acuity (VA) was 6/120. Slit-lamp examination revealed perforation of the temporal cornea and iris, hypopyon, and a fibrinous membrane covering the pupil. Ultrasonography showed dense vitreous infiltration and an orbital CT-scan confirmed the presence of a metallic foreign body in the vitreous cavity. Topical and systemic therapy were initiated. Pars-plana vitrectomy combined with phacoemulsification was performed in order to remove the foreign body; vitreous samples were acquired and Sphingomonas paucimobilis, sensitive to ceftazidime, was identified. To the best of our knowledge, this is the first report of Sphingomonas paucimobilis endophthalmitis following penetrating ocular injury. In this case, Sphingomonas paucimobilis was not resistant to antibiotics. This allowed for a good healing response following vitrectomy despite the fact that long-term retinal complications resulted in low VA.

Safety and efficacy of combined immunosuppression and orbital radiotherapy in thyroid-related restrictive myopathy: two-center experience.

PURPOSE: To evaluate the safety and efficacy of oral steroids when combined with long-term oral azathioprine (AZA) and orbital radiotherapy in patients with active thyroid-related restrictive myopathy. METHODS: A total of 88 patients from adnexal outpatient clinics of Bristol Eye Hospital, UK, and 2nd Department of Ophthalmology at Aristotle University of Thessaloniki, Greece, were enrolled in a retrospective, twin-center study. All patients were diagnosed with active thyroid eye disease and concomitant restrictive myopathy. Treatment included oral AZA, low-dose steroids, and orbital radiotherapy (20 Gy). Clinical activity scores as well as orthoptic assessments were consistently evaluated. Clinical activity scores, improved levels of diplopia, and single muscle excursions were considered major criteria for treatment success. RESULTS: Clinical success was achieved in 54 (61.4%), 57 (64.8%), and 61 (69.3%) patients at 3-, 6-, and 12-month time points, respectively, after the initiation of the combined treatment. At 18 months following initiation of treatment, the percentage of treatment success reached 73.9% (n = 65). Nine patients developed AZA-related side effects. In 4 patients the drug had to be discontinued. CONCLUSIONS: Combined immunosuppression with orbital radiotherapy appears to reduce morbidity in patients with marked restrictive myopathy by improving major motility parameters such as diplopia and duction amplitude.

A novel reduced-order prioritized optimization method for radiation therapy treatment planning.

In this study, a novel reduced order prioritized algorithm is presented for optimization in radiation therapy treatment planning. The proposed method consists of three stages. In the first stage, the intensity space was sampled by solving a series of unconstrained optimization problems. The objective function of the first stage is expressed as a scalarized weighted sum of partial objectives for the target and organ at risk. Latin hypercube sampling was utilized to define the weights for each run of the unconstrained optimizations. In the second stage, principal component analysis is applied to the solutions determined in the first stage to identify the major eigen modes in the intensities space, significantly reducing the number of independent variables. In the third stage, treatment planning goals/objectives are prioritized, and the problem is solved in the reduced order space. After each objective is optimized, that objective function is converted into a constraint for the lower-priority objectives. In the current formulation, a slip factor is used to relax the hard constraints for planning target volume (PTV) coverage. The applicability of the proposed method is demonstrated for one prostate and one lung intensity-modulated radiation therapy treatment plan. Upon completion of the sequential prioritized optimization, the mean dose at the rectum and bladder was reduced by 21.3% and 22.4%, respectively. Additionally, we investigated the effect of the slip factor 's' on PTV coverage and we found minimal degradation of the tumor dose (∼4%). Finally, the speed up factors upon the dimensionality reduction were as high as 49.9 without compromising the quality of the results.

Accelerated event-by-event Monte Carlo microdosimetric calculations of electrons and protons tracks on a multi-core CPU and a CUDA-enabled GPU.

For microdosimetric calculations event-by-event Monte Carlo (MC) methods are considered the most accurate. The main shortcoming of those methods is the extensive requirement for computational time. In this work we present an event-by-event MC code of low projectile energy electron and proton tracks for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA in such a way that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC code on the CPU. Performance comparison was established on the speed-up for a set of benchmarking cases of electron and proton tracks. A maximum speedup of 67.2 was achieved for the GPU-based MC code, while a further improvement of the speedup up to 20% was achieved for the hybrid approach. The results indicate the capability of our CPU-GPU implementation for accelerated MC microdosimetric calculations of both electron and proton tracks without loss of accuracy.

Fidelity of dose delivery at high dose rate of volumetric modulated arc therapy in a truebeam linac with flattening filter free beams.

The purpose of this study is to assess fidelity of radiation delivery between high and low dose rates of the flattening filter free (FFF) modes of a new all-digital design medical linear accelerator (Varian TrueBeam™), particularly for plans optimized for volumetric modulated arc therapy (VMAT). Measurements were made for the two energies of flattening filter free photon beams with a Varian TrueBeam™ linac: 6 MV (6 XFFF) at 400 and 1400 MU/min, and 10 MV (10 XFFF) at 400 and 2400 MU/min. Data acquisition and analysis was performed with both ionization chambers and diode detector system Delta(4), for square radiation fields and for 8 VMAT treatment plans optimized for SBRT treatment of lung tumors. For the square fields, a percent dose difference between high and low dose rate of the order of 0.3-0.4% for both photon energies was seen with the ionization chambers, while the contribution to the difference from ion recombination was found to be negligible. For both the VMAT and square-field deliveries, the Delta(4) showed the same average percent dose difference between the two dose rates of ~0.8% and ~0.6% for 10 MV and 6 MV, respectively, with the lower dose rate values giving the greater measured dose compared to the high dose rate. Thus, the VMAT deliveries introduced negligible dose differences between high and low dose rate. Finally, reproducibility of dose measurements was good for both energies.

Toward IMRT 2D dose modeling using artificial neural networks: a feasibility study.

PURPOSE: To investigate the feasibility of artificial neural networks (ANN) to reconstruct dose maps for intensity modulated radiation treatment (IMRT) fields compared with those of the treatment planning system (TPS). METHODS: An artificial feed forward neural network and the back-propagation learning algorithm have been used to replicate dose calculations of IMRT fields obtained from PINNACLE(3) v9.0. The ANN was trained with fluence and dose maps of IMRT fields for 6 MV x-rays, which were obtained from the amorphous silicon (a-Si) electronic portal imaging device of Novalis TX. Those fluence distributions were imported to the TPS and the dose maps were calculated on the horizontal midpoint plane of a water equivalent homogeneous cylindrical virtual phantom. Each exported 2D dose distribution from the TPS was classified into two clusters of high and low dose regions, respectively, based on the K-means algorithm and the Euclidian metric in the fluence-dose domain. The data of each cluster were divided into two sets for the training and validation phase of the ANN, respectively. After the completion of the ANN training phase, 2D dose maps were reconstructed by the ANN and isodose distributions were created. The dose maps reconstructed by ANN were evaluated and compared with the TPS, where the mean absolute deviation of the dose and the γ-index were used. RESULTS: A good agreement between the doses calculated from the TPS and the trained ANN was achieved. In particular, an average relative dosimetric difference of 4.6% and an average γ-index passing rate of 93% were obtained for low dose regions, and a dosimetric difference of 2.3% and an average γ-index passing rate of 97% for high dose region. CONCLUSIONS: An artificial neural network has been developed to convert fluence maps to corresponding dose maps. The feasibility and potential of an artificial neural network to replicate complex convolution kernels in the TPS for IMRT dose calculations have been demonstrated.

Structural plasticity can produce metaplasticity.

BACKGROUND: Synaptic plasticity underlies many aspect of learning memory and development. The properties of synaptic plasticity can change as a function of previous plasticity and previous activation of synapses, a phenomenon called metaplasticity. Synaptic plasticity not only changes the functional connectivity between neurons but in some cases produces a structural change in synaptic spines; a change thought to form a basis for this observed plasticity. Here we examine to what extent structural plasticity of spines can be a cause for metaplasticity. This study is motivated by the observation that structural changes in spines are likely to affect the calcium dynamics in spines. Since calcium dynamics determine the sign and magnitude of synaptic plasticity, it is likely that structural plasticity will alter the properties of synaptic plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In this study we address the question how spine geometry and alterations of N-methyl-D-aspartic acid (NMDA) receptors conductance may affect plasticity. Based on a simplified model of the spine in combination with a calcium-dependent plasticity rule, we demonstrated that after the induction phase of plasticity a shift of the long term potentiation (LTP) or long term depression (LTD) threshold takes place. This induces a refractory period for further LTP induction and promotes depotentiation as observed experimentally. That resembles the BCM metaplasticity rule but specific for the individual synapse. In the second phase, alteration of the NMDA response may bring the synapse to a state such that further synaptic weight alterations are feasible. We show that if the enhancement of the NMDA response is proportional to the area of the post synaptic density (PSD) the plasticity curves most likely return to the initial state. CONCLUSIONS/SIGNIFICANCE: Using simulations of calcium dynamics in synaptic spines, coupled with a biophysically motivated calcium-dependent plasticity rule, we find under what conditions structural plasticity can form the basis of synapse specific metaplasticity.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.