Stochastic mathematical models for the spread of COVID-19: a novel epidemiological approach.

In this paper, three stochastic mathematical models are developed for the spread of the coronavirus disease (COVID-19). These models take into account the known special characteristics of this disease such as the existence of infectious undetected cases and the different social and infectiousness conditions of infected people. In particular, they include a novel approach that considers the social structure, the fraction of detected cases over the real total infected cases, the influx of undetected infected people from outside the borders, as well as contact-tracing and quarantine period for travellers. Two of these models are discrete time-discrete state space models (one is simplified and the other is complete) while the third one is a continuous time-continuous state space stochastic integro-differential model obtained by a formal passing to the limit from the proposed simplified discrete model. From a numerical point of view, the particular case of Lebanon has been studied and its reported data have been used to estimate the complete discrete model parameters, which can be of interest in estimating the spread of COVID-19 in other countries. The obtained simulation results have shown a good agreement with the reported data. Moreover, a parameters' analysis is presented in order to better understand the role of some of the parameters. This may help policy makers in deciding on different social distancing measures.

Alveolar Bone and Epithelial Attachment Status following Two Different Closed-eruption Surgical Techniques for Impacted Maxillary Central Incisors.

AIM: Two eruption surgical techniques are commonly described for the treatment of upper impacted central incisors (ICIs): Open and closed. Currently, the closed-eruption surgical technique (CEST) is the most commonly used, as it allows for the best esthetic and periodontal results.The aim of this study was to determine the effect of traction discontinuation on maxillary central incisor sulcal depth and alveolar bone ridge levels compared with contralateral incisors, when CEST is used. MATERIALS AND METHODS: Our study involved 28 unilateral impacted maxillary central incisors treated by CEST. Thirteen teeth were subjected to traction interruption for a month at the time of emergence of the crown, while 15 teeth underwent continuous traction. One year after treatment, periapical digital X-rays, anterosuperior cone beam computerized tomography (CBCT) scanning, and periodontal probing of the ICIs and contralateral central incisors (CCIs) were performed. Student's t-test was used to study whether a statistically significant difference between continuous and interrupted tractions takes place while using the CCI measurements as reference. RESULTS: There was a statistically significant difference between the two techniques only for the following measurements: Mesial probing (p-value 0.039352), labial bone level (p-value 2.58E-08), and palatal bone level (p-value 2.56E-06). LIMITATIONS: A larger sample size and longer term follow-up are needed to draw more robust conclusions. CONCLUSION: A temporary discontinuation during traction of the tooth appears to positively impact treatment outcome on ICIs. CLINICAL SIGNIFICANCE: • The CEST leads to the best periodontal status for ICIs.• The discontinuation of traction at the emergence of the tooth allows the supracrestal fibers to insert into the cement in a proper way.How to cite this article: Sfeir E, Gholmieh M, Skaf Z, Mourad A. Alveolar Bone and Epithelial Attachment Status following Two Different Closed-eruption Surgical Techniques for Impacted Maxillary Central Incisors. Int J Clin Pediatr Dent 2018;11(4):317-322.

Evaluation of Masticatory Stimulation Effect on the Maxillary Transversal Growth in Ectodermal Dysplasia Children.

AIMS: Severe oligodontia is one of the most important symptoms in children with hypohidrotic ectodermal dysplasia (HED). The growth of the maxilla is a key consideration in restoring their mouth. The aim of this study was to evaluate the transversal maxillary sutural growth, after passive masticatory stimulation, in HED children. We also thought to assess the efficiency and functional outcome of the proposed propriocep-tive passive expansion (PPE) prosthetic device. MATERIALS AND METHODS: We studied 13 children (age 6-11 years) suffering from HED with severe oligodontia. Their maxilla was restored by a PPE device formed from two parts and joined by a passive slide system. Distance between the two parts was noted at the anterior and posterior regions at each control visit over an average of 23 months. We also conducted and filled a satisfaction questionnaire over the same period. We tested the hypothesis that the posterior expansion is greater than the anterior expansion (one-tailed Student's t-test with p-value <0.05). Best-fit linear and quadratic models were used to explore the relationship between age, duration of observation, and the rate of growth. RESULTS: The average opening of the device was 2.27 mm in the anterior region and 2.96 mm in the posterior region. The questionnaire response was positive for all children. There are no significant linear or quadratic relationships between the data at the 5% significance level. The posterior expansion is greater than the anterior expansion at the 5% significance level (p-value 0.000394). LIMITATIONS: Further studies are mandatory to assess the reliability of our particular intervention and treatment modalities for these cases. CONCLUSION: The PPE device, we propose, assures function and esthetics in the long- term. It enhances stimulation by a passive way that leads to physiological growth of the palatal suture. CLINICAL SIGNIFICANCE: Using this PPE device to restore the maxilla in children with HED promotes physiological growth. The passive nature of this prosthesis helps by eliminating the need for any changes or replacement over time. HOW TO CITE THIS ARTICLE: Sfeir E, Nahass MG, Mourad A. Evaluation of Masticatory Stimulation Effect on the Maxillary Transversal Growth in Ectodermal Dysplasia Children. Int J Clin Pediatr Dent 2017;10(1):55-61.

In vitro Macro-qualitative Comparison of Three Enamel Stripping Procedures: What is the Best Shape We can get?

AIM: Interdental stripping is a common clinical procedure in orthodontic therapy, by reshaping the proximal contacts. Handheld abrasive strips have been criticized as time-consuming process. Metallic strip system, diamond disk, or segment disks have become increasingly popular. The aim of this study is to evaluate the morphological aspects of remodeled dental surfaces so as to conclude which of the different techniques (disk, bur, or strip) used to reduce the mesiodistal diameter is the best to reproduce the initial contour of the proximal surface of the tooth. MATERIALS AND METHODS: Seventy-nine pieces ("teeth") were prepared from permanent healthy teeth (premolars and molars) extracted for orthodontic reasons. They were mounted on a stand resembling the position of the natural teeth in a mild crowded dentition. The "teeth" are divided into three groups as follows: group S (strip): 26 "teeth," group D (disk): 25 "teeth," group B (bur): 28 "teeth." In order to study the changes, these prepared "teeth" are macro-photographed in groups of 5 before and after proximal grinding. RESULTS: The "teeth" contours have been identified using piecewise cubic Hermit polynomials. The change in the contour has been traduced in terms of the change of curvature in the "teeth" contours. We used the z-test in order to find the confidence interval for the proportion of the class "+" for each of the techniques B, S, and D. With confidence level of 95%, we obtained the following confidence intervals:B = (0.6943; 0.9057); S = (0.9093; 1.0138); D = (0.6184; 0.8616)These results can be interpreted, as the technique S is significantly much better than the other two techniques if we aim at conserving the shape of the teeth before and after treatment. CONCLUSION: We conclude that the use of a strip for remodeling the proximal surface of a tooth is an optimal technique to preserve the proximal shape of the tooth although it requires more time. CLINICAL SIGNIFICANCE: The use of abrasive strip preserves the best shape of the proximal side. Abrasive strip could be the last step of any proximal reshaping technique.How to cite this article: Nassif N, Gholmieh MN, Sfeir E, Mourad A. In vitro Macro-qualitative Comparison of Three Enamel Stripping Procedures: What is the Best Shape We can get? Int J Clin Pediatr Dent 2017;10(4):358-362.

Human ventricular fibrillation during global ischemia and reperfusion: paradoxical changes in activation rate and wavefront complexity.

BACKGROUND: Ischemic ventricular fibrillation in experimental models has been shown to progress through a series of stages. Progression of ischemic VF in the in vivo human heart has not been determined. METHODS AND RESULTS: We studied 10 patients undergoing cardiac surgery. Ventricular fibrillation was induced by burst pacing. After 30 seconds, global myocardial ischemia was induced by aortic cross-clamp and maintained for 2.5 minutes, followed by coronary reflow. Epicardial activity was sampled (1 kHz) with a sock that contained 256 unipolar contact electrodes. Dominant frequencies were calculated with a fast Fourier transform with a moving window. The locations of phase singularities and activation wavefronts were identified at 10-ms intervals. Preischemic (perfused) ventricular fibrillation was maintained by a disorganized mix of large and small wavefronts. During global myocardial ischemia, mean dominant frequencies decreased from 6.4 to 4.7 Hz at a rate of -0.011±0.002 Hz s(-1) (P<0.001) and then increased rapidly to 7.4 Hz within 30 seconds of reflow. In contrast, the average number of epicardial phase singularities increased during ischemia from 7.7 to 9.7 at a rate of 0.013±0.005 phase singularities per second (P<0.01) and remained unchanged during reflow, at 10.3. The number of wavefronts showed a similar time course to the number of phase singularities. CONCLUSIONS: In human ventricular fibrillation, we found an increase in complexity of electric activation patterns during global myocardial ischemia, and this was not reversed during reflow despite an increase in activation rate.

Analysis of the fiber architecture of the heart by quantitative polarized light microscopy. Accuracy, limitations and contribution to the study of the fiber architecture of the ventricles during fetal and neonatal life.

OBJECTIVE: To address the advantages and drawbacks of quantitative polarized light microscopy for the study of myocardial cell orientation and to identify its contribution in the field. METHODS: Quantitative polarized light microscopy allows to measure the orientation of myocardial fibers into the ventricular mass. For each pixel of a horizontal section, this orientation is the mean value of the directions of all myosin filaments contained in the thickness of the section for each pixel of the section and is accounted for by two angles, the azimuth angle, which is the angle of the fiber in the plane of the section, and the elevation angle, which measures the way the fiber escapes from the section. The azimuth is accurately measured, and its range of definition is complete from 0 degrees to 180 degrees . The elevation angle can be defined only in the range 0 degrees to 90 degrees . It is accurately measured between 20 degrees and 70 degrees . From 0 degrees to 20 degrees , there is a systematic bias raising the measured values, and from 70 degrees to 90 degrees , the angle is not accurately measured. RESULTS: With this method, we validated Streeter's conjecture concerning the architecture of the left ventricle. We formulated a pretzel conjecture about the fiber architecture of the whole ventricular mass during fetal period. In our model, elaborated by visual analysis of registered maps of orientation, the fibers run like geodesics on a nested set of 'pretzels'. Next, the validity of the helical ventricular myocardial band model of Torrent-Guasp has been examined. It appears that the band model does not account for the patterns observed in our data during the fetal period. However, after the major events of postnatal cardiovascular adaptation, our data can neither discard nor confirm Torrent-Guasp's model. CONCLUSIONS: Present limitations of quantitative polarized light analysis can neither confirm nor discard the existing models of fiber orientation in the whole ventricular mass after the neonatal period. However, the problems of mathematical and experimental validation of these two models have been posed in a rigorous manner. Non-ambiguous fiber tracking and demonstration of these models will require significant improvement of the definition range of the elevation angle that should be extended to 180 degrees .

Method for quantifiying conduction velocity during ventricular fibrillation.

Velocity of propagation of electrical excitation in the heart is important for the understanding of complex arrhythmias such as ventricular fibrillation (VF). In this paper, we present a method to estimate the conduction velocity of electrical activation wavefronts that are defined to be a particular isovalue of any scalar field, such as electrical activation times, electrical phase, or indeed any other quantity that can be used to determine excitation wavefronts. This general method is based on tracking trajectories of material points that are assumed to be embedded within the wavefronts, whilst the direction of propagation is assumed to be perpendicular to the wavefront. We have derived an explicit expression for the conduction velocity in terms of the spatiotemporal gradients of the scalar field used to define wavefronts. Moreover, although it is often difficult to use activation times to compute conduction velocities during complex VF, we show that other scalar fields such as detrended voltage or electrical phase, which can faithfully represent the electrical activity during fibrillatory conduction, can be used to determine conduction velocities. We demonstrate the application of our method to determine conduction velocities from contact mapping recordings over the entire epicardial surface of the fibrillating pig heart.

Evidence for multiple mechanisms in human ventricular fibrillation.

BACKGROUND: The mechanisms that sustain ventricular fibrillation (VF) in the human heart remain unclear. Experimental models have demonstrated either a periodic source (mother rotor) or multiple wavelets as the mechanism underlying VF. The aim of this study was to map electrical activity from the entire ventricular epicardium of human hearts to establish the relative roles of these mechanisms in sustaining early human VF. METHODS AND RESULTS: In 10 patients undergoing cardiac surgery, VF was induced by burst pacing, and 20 to 40 seconds of epicardial activity was sampled (1 kHz) with a sock containing 256 unipolar contact electrodes connected to a UnEmap system. Signals were interpolated from the electrode sites to a fine regular grid (100x100 points), and dominant frequencies (DFs) were calculated with a fast Fourier transform with a moving 4096-ms window (10-ms increments). Epicardial phase was calculated at each grid point with the Hilbert transform, and phase singularities and activation wavefronts were identified at 10-ms intervals. Early human VF was sustained by large coherent wavefronts punctuated by periods of disorganized wavelet behavior. The initial fitted DF intercept was 5.11 +/- 0.25 (mean +/- SE) Hz (P < 0.0001), and DF increased at a rate of 0.018 +/- 0.005 Hz/s (P < 0.01) during VF, whereas combinations of homogeneous, heterogeneous, static, and mobile DF domains were observed for each of the patients. Epicardial reentry was present in all fibrillating hearts, typically with low numbers of phase singularities. In some cases, persistent phase singularities interacted with multiple complex wavelets; in other cases, VF was driven at times by a single reentrant wave that swept the entire epicardium for several cycles. CONCLUSIONS: Our data support both the mother rotor and multiple wavelet mechanisms of VF, which do not appear to be mutually exclusive in the human heart.