New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Four-year results following treatment of intrabony periodontal defects with an enamel matrix derivative alone or combined with a biphasic calcium phosphate

The aim of this study was to evaluate the 4-year clinical outcomes following regenerative surgery in intrabony defects with either EMD + BCP or EMD. Twenty-four patients with advanced chronic periodontitis, displaying one-, two-, or three-walled intrabony defect with a probing depth of at least 6 mm, were randomly treated with either EMD + BCP (test) or EMD alone (control). The following clinical parameters were evaluated at baseline, at 1 year and at 4 years after regenerative surgery: plaque index, gingival index, bleeding on probing, probing depth, gingival recession, and clinical attachment level (CAL). The primary outcome variable was CAL. No differences in any of the investigated parameters were observed at baseline between the two groups. The test group demonstrated a mean CAL change from from 10.8 ± 1.6 mm to 7.4 ± 1.6 mm (p < 0.001) and to 7.6 ± 1.7 mm (p < 0.001) at 1 and 4 years, respectively. In the control group, mean CAL changed from 10.4 ± 1.3 at baseline to 6.9 ± 1.0 mm (p < 0.001) at 1 year and 7.2 ± 1.2 mm (p < 0.001) at 4 years. At 4 years, two defects in the test group and three defects in the control group have lost 1 mm of the CAL gained at 1 year. Compared to baseline, at 4 years, a CAL gain of ≥3 mm was measured in 67% of the defects (i.e., in 8 out of 12) in the test group and in 75% of the defects (i.e., in 9 out of 12) in the control group. There were no statistically significant differences in any of the investigated parameters at 1 and at 4 years between the two groups. Within their limits, the present results indicate that: (a) the clinical improvements obtained with both treatments can be maintained over a period of 4 years, and (b) in two- and three-walled intrabony defects, the addition of BCP did not additionally improve the outcomes obtained with EMD alone. In two- and three-walled intrabony defects, the combination of EMD + BCP did not show any advantage over the use of EMD alone.

Synchrotron X-ray interlaced microbeams suppress paroxysmal oscillations in neuronal networks initiating generalized epilepsy

Radiotherapy has shown some efficacy for epilepsies but the insufficient confinement of the radiation dose to the pathological target reduces its indications. Synchrotron-generated X-rays overcome this limitation and allow the delivery of focalized radiation doses to discrete brain volumes via interlaced arrays of microbeams (IntMRT). Here, we used IntMRT to target brain structures involved in seizure generation in a rat model of absence epilepsy (GAERS). We addressed the issue of whether and how synchrotron radiotherapeutic treatment suppresses epileptic activities in neuronal networks. IntMRT was used to target the somatosensory cortex (S1Cx), a region involved in seizure generation in the GAERS. The antiepileptic mechanisms were investigated by recording multisite local-field potentials and the intracellular activity of irradiated S1Cx pyramidal neurons in vivo. MRI and histopathological images displayed precise and sharp dose deposition and revealed no impairment of surrounding tissues. Local-field potentials from behaving animals demonstrated a quasi-total abolition of epileptiform activities within the target. The irradiated S1Cx was unable to initiate seizures, whereas neighboring non-irradiated cortical and thalamic regions could still produce pathological oscillations. In vivo intracellular recordings showed that irradiated pyramidal neurons were strongly hyperpolarized and displayed a decreased excitability and a reduction of spontaneous synaptic activities. These functional alterations explain the suppression of large-scale synchronization within irradiated cortical networks. Our work provides the first post-irradiation electrophysiological recordings of individual neurons. Altogether, our data are a critical step towards understanding how X-ray radiation impacts neuronal physiology and epileptogenic processes.

Generalized eMC implementation for Monte Carlo dose calculation of electron beams from different machine types

The electron Monte Carlo (eMC) dose calculation algorithm available in the Eclipse treatment planning system (Varian Medical Systems) is based on the macro MC method and uses a beam model applicable to Varian linear accelerators. This leads to limitations in accuracy if eMC is applied to non-Varian machines. In this work eMC is generalized to also allow accurate dose calculations for electron beams from Elekta and Siemens accelerators. First, changes made in the previous study to use eMC for low electron beam energies of Varian accelerators are applied. Then, a generalized beam model is developed using a main electron source and a main photon source representing electrons and photons from the scattering foil, respectively, an edge source of electrons, a transmission source of photons and a line source of electrons and photons representing the particles from the scrapers or inserts and head scatter radiation. Regarding the macro MC dose calculation algorithm, the transport code of the secondary particles is improved. The macro MC dose calculations are validated with corresponding dose calculations using EGSnrc in homogeneous and inhomogeneous phantoms. The validation of the generalized eMC is carried out by comparing calculated and measured dose distributions in water for Varian, Elekta and Siemens machines for a variety of beam energies, applicator sizes and SSDs. The comparisons are performed in units of cGy per MU. Overall, a general agreement between calculated and measured dose distributions for all machine types and all combinations of parameters investigated is found to be within 2% or 2 mm. The results of the dose comparisons suggest that the generalized eMC is now suitable to calculate dose distributions for Varian, Elekta and Siemens linear accelerators with sufficient accuracy in the range of the investigated combinations of beam energies, applicator sizes and SSDs.