M3 Distribution Research Articles

Finite element analysis of different diameter prosthesis ball head in artificial femoral head replacement

In order to select the proper size of prosthesis ball head, the biomechanical changes of hip joint using different diameter prosthesis ball head was studied by three-dimensional finite element analysis. The thin-layer CT data and related parameters of artificial femoral head prosthesis were used to establish the finite element model of hip joint after artificial femoral head replacement with different ball diameter of prosthesis(M0:preoperative model;M1:ball head diameter=original femoral head diameter;M2:ball head diameter=original femoral head diameter+1 mm;M3:Ball head diameter= Original femoral head diameter -1 mm;M4:ball head diameter =original femoral head diameter -2 mm). Loading the joint forces and related muscle loads were loaded, and the stress distribution and change of bone and cartilage around acetabulum were analyzed by simulating the standing state of one foot when walking slowly. (1) In M1 to M4, the stress concentration in pelvis was different. The peak value of Von Mises stress in the pelvis of M3 was 44.8 MPa, which was the closest to that before operation, with an increment of 13.4%. The displacement of the pelvis of M3 was the smallest in the four groups after operation, with an increment of 1.40 mm. The next was M1, with a peak value of 47.3 MPa, with an increment of 19.7%, and a pelvic displacement of 1.59 mm. (2) In acetabulum area, the peak value of Von Mises stress in M3 was 23.3 MPa, which was the closest to that before operation, with an increment of about 6.3%, followed by M1, with a peak value of 24.0 MPa and an increment of about 8.1%. (3) On the acetabulum cartilage, the stress distribution of M1 and M3 was similar to that before operation, and the peak value of Von Mises stress of M3 was 18.5 MPa, which was the closest to that before operation, followed by M1, which was 22.5 MPa. (4) M1 to M4 showed different degree of stress concentration in the outer upper quadrant of the artificial femoral head, but showed stress shielding under it;among them, the von Mises stress distribution of M3 was more uniform than that of other models, and its peak value (70.8 MPa) was the lowest in each group, followed by M1 (80.7 MPa). When femoral head replacement is performed, it is suggested that the prosthesis ball head with the diameter less than 1 mm and the prosthesis ball head with the same diameter as the original femoral head should be used first, so as to obtain the closest natural mechanical characteristics of the hip joint before the replacement and reduce the risk of complications caused by size differences.

Sampled Trajectory Data-Driven Method of Cycle-Based Volume Estimation for Signalized Intersections by Hybridizing Shockwave Theory and Probability Distribution

The cycle-based volume is critical for traffic state estimation and signal control optimization at signalized intersections. Traditional volume estimation mainly depends on fixed detectors represented by loop detectors, but limited spatial coverage and detection failure are also prominent. With the development of vehicle positioning, smartphone-based navigation, and connected-vehicle technologies, massive high-resolution trajectory data have recently become available, which can provide rich and timely information on the traffic arrival and departure processes at signalized intersections. Hence, the studies utilizing trajectory data for estimating the queue length and traffic volume at intersections has received increasing attention in the past few years. However, the most existing studies have demanded a comparatively high penetration rate and adopted site-specific assumptions for unsteady arrival patterns. In contrast, this paper solely used trajectory data for cycle-based flow estimation through a generic hybrid method that combined a probabilistic model and shockwave theory to maximize the utilization of limited captured trajectories, especially under a low penetration rate. In this method, within each cycle, the volume of stopped vehicles is estimated based on the shockwave theory, while the volume of non-stopped vehicles is modeled as a parameter estimation problem of a time-dependent constrained Poisson distribution, where the time headway correspondingly obeys an M3 distribution. The cycle-based volume is solved by a maximum likelihood estimation using an expectation-maximization procedure. An empirical case study was conducted with various signal timing schemes and the results showed satisfactory robustness with an accuracy of more than 90% under a penetration rate of 7.6%.

Review of Roundabout Capacity Based on Gap Acceptance

Circulating vehicles have priority at modern roundabouts. Entrance vehicles can enter the roundabout when there is a time gap larger than the critical gap; otherwise, the vehicles need to wait until there is a large enough gap. The gap acceptance theory was used to analyze the entrance capacity of roundabouts, which can be derived by queuing theory involving two vehicle streams. The paper introduces the main styles of headway distribution, which are named as bunched exponential distribution or M3 distribution. The calculation model of free stream ratio is also introduced. The entrance capacity models can be classified by different entrance vehicle types, which are piecewise function or linear function, or by different critical gap types, which are constant or stochastic function. For each form, the typical capacity expressions are given. The calculation values show a very small difference between these kinds of models. The capacity value based on the critical gap of stochastic function is more realistic and more complex in function style. Some conclusions were derived that drivers’ nonhomogeneous and inconsistent character is more realistic than the fixed critical gap and following gap. The calculation results of capacity are similar to the field capacity under the assumption of homogeneity and continuance, with only a minor percent deviation. Finally, the paper points out additional problems and the suggested research in capacity of roundabouts.

Combined treatment with a β3 -adrenergic receptor agonist and a muscarinic receptor antagonist inhibits detrusor overactivity induced by cold stress in spontaneously hypertensive rats.

This study determined if combined treatment with the muscarinic receptor (MR) antagonist solifenacin and the β3 -adrenergic receptor (AR) agonist mirabegron could inhibit detrusor overactivity induced by cold stress in spontaneously hypertensive rats (SHRs). Thirty-two female 10-week-old SHRs were fed an 8% NaCl-supplemented diet for 4 weeks. Cystometric measurements of the unanesthetized, unrestricted rats were performed at room temperature (RT, 27 ± 2°C) for 20 min. The rats were then intravenously administered vehicle, 0.1 mg/kg solifenacin alone, 0.1 mg/kg mirabegron alone, or the combination of 0.1 mg/kg mirabegron and 0.1 mg/kg solifenacin (n = 8 each group). Five minutes later, the treated rats were exposed to low temperature (LT, 4 ± 2°C) for 40 min. Finally, the rats were returned to RT. After the cystometric investigations, the β3 -ARs and M3 -MRs expressed within the urinary bladders were analyzed. Just after transfer from RT to LT, vehicle-, solifenacin-, and mirabegron-treated SHRs exhibited detrusor overactivity that significantly decreased voiding interval and bladder capacity. However, treatment with the combination of solifenacin and mirabegron partially inhibited the cold stress-induced detrusor overactivity patterns. The decreases of voiding interval and bladder capacity in the combination-treated rats were significantly inhibited compared to other groups. Within the urinary bladders, there were no differences between expression levels of M3 -MR and β3 -AR mRNA. The tissue distribution of M3 -MRs was similar to that of the β3 -ARs. This study suggested that the combination of solifenacin and mirabegron act synergistically to inhibit the cold stress-induced detrusor overactivity in SHRs. Neurourol. Urodynam. 36:1026-1033, 2017. © 2016 The Authors. Neurourology and Urodynamics Published by Wiley Periodicals, Inc.

Lane by lane analysis of vehicle time headways — Case study of Izmir ring roads in Turkey

The studies on headway characteristics of traffic flow in Turkey are mainly dealing with signalized arterials, intersection approaches or roundabouts. Only a few studies can be found on headway characteristics of uninterrupted flow facilities and nearly none of them are on lane by lane basis. In this study, the authors are modeling headways of vehicles at zmir ring roads by lane by lane principle. The study demonstrates that lognormal distribution is an effective tool to define headways. In addition, the applicability of Cowan M3 distribution to time headways is investigated. Proportion of free vehicles is modeled for different lanes. The results show that traffic flow in the middle lane is highly affected by the vehicles in other lanes. Vehicles in the outer lane can be assumed to arrive randomly, but they are also disturbed by vehicles in other lanes. These results can be used in capacity and performance analysis of freeway segments, ramp junctions and weaving areas.

Perovskites in low dimensional multi-layer structure types

This study introduces examples of structure property relationships within the multi-layered Sillen-Aurivillius family (shown in Figure) and aims to investigate the effect of chemical doping and lattice matching effects. The first example involves doping 1/3 of the n = 3 ferroelectric perovskite layers with magnetic transition metal cations in Bi5PbTi3O14Cl [1] with charge balancing by removing Pb2+for Bi3+. A statistical 1:2 distribution of M3+and Ti4+across all three perovskite layers was found in Bi6Ti2MO14Cl, M = Cr3+, Mn3+, Fe3+, resulting in highly strained structures (enhancing the ferroelectricity compared to Bi5PbTi3O14Cl) and pronounced spin-glass behavior below Tirr(0) = 4.46 K. Ferroelectric transitions were observed at high temperature for each of the new compounds. Ferroelectric properties were also measured on Bi6Ti2FeO14Cl using piezoresponse force microscopy showing hysteretic phase behavior. A new n = 2 Sillen-Aurivillius compound Bi3Sr2Nb2O11Br, based on Bi3Pb2Nb2O11Cl [2], was synthesized by simultaneously replacing Pb2+with Sr2+and Cl-with Br-. Inter-layer mismatch prevented the formation of Bi3Sr2Nb2O11Cl and Bi3Pb2Nb2O11Br. Sr2+doping reduces the impact of the stereochemically active 6s2lone pair found on Pb2+and Bi3+, resulting in a stacking contraction in the lattice parameters by 1.22 % and an expansion of the a-b plane by 0.25 %, improving inter-layer compatibility with Br-. X-ray Absorption Near Edge Structure spectra analysis shows that the ferroelectric distortion of the B-site cation is less apparent in Bi3Sr2Nb2O11Br compared to Bi3Pb2Nb2O11Cl. Variable-temperature neutron diffraction data show no evidence for a ferroelectric distortion.

Estimation of Critical Gap Based on Raff’s Definition

Critical gap is an important parameter used to calculate the capacity and delay of minor road in gap acceptance theory of unsignalized intersections. At an unsignalized intersection with two one-way traffic flows, it is assumed that two events are independent between vehicles' arrival of major stream and vehicles' arrival of minor stream. The headways of major stream follow M3 distribution. Based on Raff's definition of critical gap, two calculation models are derived, which are named M3 definition model and revised Raff's model. Both models use total rejected coefficient. Different calculation models are compared by simulation and new models are found to be valid. The conclusion reveals that M3 definition model is simple and valid. Revised Raff's model strictly obeys the definition of Raff's critical gap and its application field is more extensive than Raff's model. It can get a more accurate result than the former Raff's model. The M3 definition model and revised Raff's model can derive accordant result.

Variation of Headways at Signalized Arterials with Respect to Distance and Cycle Times

In this study, the variation in the proportion of free vehicles at a signalized arterial is tried to be modeled with respect to distance and green/cycle time ratio. In the analysis, it is assumed that headways between vehicles can be defined with Cowan M3 distribution. From the analysis, proportion of free vehicles in the left lane of an arterial is lower than other lanes. This results indicates that, left lanes are occupied by higher vehicle volumes. The analysis also showed that, proportion free vehicles increase with respect to the distance to traffic signals as expected.

Estimation of major stream delays with a limited priority merge

The purpose of this paper is to develop an estimation model for major stream delays at an unsignalized intersection under limited priority conditions. The key idea of this paper is that, when the minor stream drivers accept smaller major stream gaps, some drivers on the major road have to slow down their speeds and adjust their relative positions to avoid traffic accidents, incurring some delays. Assuming that headways in the major stream follow the M3 distribution, the delay for the first major stream vehicle after a limited priority merge is presented using acceptance gap theory and probability theory, and then recursive models are developed for the following major stream vehicles before the next merge. Finally, the precision of the method proposed in this paper is calibrated using field survey data from Changchun city, China, and the results show that the maximum, minimum, and average relative error of the 12 samples are approximately 30.38%, 9.04%, and 18.97%, respectively.

Estimating the parameters of Cowan’s M3 headway distribution for roundabout capacity analyses

Capacity models based on the gap acceptance theory are widely used in unsignalised intersections and roundabout capacity analysis. These models are based on the statistical distribution of major vehicle headways. In this field, Cowan’s M3 distribution is usually recognized as the most adequate, but the estimation of its parameters is not trivial. In this paper, the main estimation methods are reviewed and a new method (Simultaneous Numerical Estimation – SNE) is proposed. The SNE method was used to develop a calibrated relation between parameters, using field data collected in Portuguese roads and roundabouts. It was determined that the new formula improves capacity estimates, either in one-lane or in two-lane roundabouts. The paper also addresses the importance of each input variable and parameter in the resulting capacity model, through a sensitivity analyses.

Minor Capacity Analysis of N Major Traffic Streams at Intersection

Based on the gap acceptance theory, this paper analyzed running state of the intersection streams about the main traffic priority controls. Theories were used in this paper, such as gap theory, the probability theory and the calculation methods of minor capacity under two vehicle streams. The calculating formula of minor capacity for n main vehicle streams was derived under the conditions of M3 distribution by the main stream headway at the uncontrolled intersection.

Travel Time Model of Left‐Turning Vehicles at Signalized Intersection

The travel time of left‐turning vehicles at signalized intersection was discussed. Under the assumption that the opposing through vehicles headway follows M3 distribution, the travel time model was established on the basis of gap theory and queue theory. Comparison was done with the common model based on the assumption that the opposing through vehicles headway follows negative exponential distribution. The results show that the model in this paper has stronger applicability and its most relative error is less than 15%. In addition, the sensitivity analysis was done. The results show that the opposing through flow rate has significant impact on travel time. The impact of left‐turning flow rate and following headway is light when the opposing through flow rate is small, the threshold is about 0.18 veh/s. The model established in this paper can well calculate travel time of left‐turning vehicles at intersection, and the methodology may provide reference to other occasions.

Distribution of muscarinic receptor subtype M3 in melanomas and their metastases

Muscarinic acetylcholine receptors (mR) are involved in the regulation of cancer cell motility and cancer progression. mR have been shown in melanoma cell lines and cryostat sections of melanomas. To substantiate the experimental data, here the correlation of mR-expression with invasive growth was studied on the cellular level by comparison with HMB-45 immunoreactivity. mR were detected by a M3 subtype-specific polyclonal antibody in normal skin, benign compound nevi, primary melanomas [nodular type, nodular malignant melanoma (NMM)] and metastases, and were compared with HMB-45 staining in parallel paraffin sections. The general staining pattern of anti-M3 and HMB-45 was similar with accentuation of zones with infiltrative growth. On the cellular level, only a subpopulation of the HMB-45 positive melanoma cells expressed mR. Immunoreactivity was encountered in 3 of 15 nevi, in 9 of 14 NMM and in 10 of 14 melanoma metastases. Polymorphonuclear granulocytes also exhibited strong reactivity for anti-M3. mR-expression is associated with invasive migration of melanomas.

Modeling Capacity Reliability of Minor Roads at At-Grade Un-Signalized Intersections for Potential Performance Evaluation

Given stochastic features of the demands on both the major road and the minor road at an at-grade un-signalized intersection, the capacity of the minor road is viewed as the vulnerable and critical part impacting on the overall capacity of the intersection. To facilitate the analysis of intersection performance reliability, the capacity reliability of the minor road is defined as the probability that the capacity of the minor road can accommodate a certain traffic demand at a certain degree of saturation. The headway distribution of traffic stream on major road is reflected by three types of distributions, namely, exponential distribution, shifted exponential distribution, and Cowan's M3 distribution. Based on field observations, the volumes on both major roads and minor roads are treated as correlated normal random variables. This paper presents the methods for modeling capacity reliability of the minor road at an at-grade un-signalized priority intersection. A method based on first-order reliability method is used to model the capacity reliability index. As important associated factors of capacity reliability analysis, the methods for modeling and analyzing capacity sensitivity of the minor road and reserve capacity of the priority intersection are also presented. A procedure for evaluating the intersection potential performance using capacity reliability, sensitivity and reserve capacity is developed and demonstrated with a numerical example. Finally, some new findings from the case studies are summarized.

Distribution of muscarinic receptor subtypes and interstitial cells of Cajal in the gastrointestinal tract of healthy dairy cows

To describe the distribution of muscarinic receptor subtypes M(1) to M(5) and interstitial cells of Cajal (ICCs) in the gastrointestinal tract of healthy dairy cows. Full-thickness samples were collected from the fundus, corpus, and pyloric part of the abomasum and from the duodenum, ileum, cecum, proximal loop of the ascending colon, and both external loops of the spiral colon of 5 healthy dairy cows after slaughter. Samples were fixed in paraformaldehyde and embedded in paraffin. Muscarinic receptor subtypes and ICCs were identified by immunohistochemical analysis. Staining for M(1) receptors was found in the submucosal plexus and myenteric plexus. Antibodies against M(2) receptors stained nuclei of smooth muscle cells only. Evidence of M(3) receptors was found in the lamina propria, in intramuscular neuronal terminals, on intermuscular nerve fibers, and on myocytes of microvessels. There was no staining for M(4) receptors. Staining for M(5) receptors was evident in the myocytes of microvessels and in smooth muscle cells. The ICCs were detected in the myenteric plexus and within smooth muscle layers. Distribution among locations of the bovine gastrointestinal tract did not differ for muscarinic receptor subtypes or ICCs. The broad distribution of M(1), M(3), M(5), and ICCs in the bovine gastrointestinal tract indicated that these components are likely to play an important role in the regulation of gastrointestinal tract motility in healthy dairy cows. Muscarinic receptors and ICCs may be implicated in the pathogenesis of motility disorders, such as abomasal displacement and cecal dilatation-dislocation.

Capacity of Unsignalized Intersections with Mixed Vehicle Flows

On the basis of gap-acceptance theory, mixed traffic flow composed of two representative vehicle types—heavy and light vehicles—is analyzed with probability theory. A capacity model is set up for an unsignalized intersection in which the minor-stream mixed traffic flows cross m major lanes and the traffic flow headways fit the M3 distribution; it is an extension of minor-lane capacity theory for one vehicle type and one major-stream traffic flow. A more complicated case with minor-stream flow composed of discretionary vehicle types is also considered, and the corresponding formula is given. After field testing in China, the conclusion is drawn that this model is better for analyzing Chinese traffic conditions than are other existing models.

Estimation of Parameters in Distribution of Headways in Roundabouts

Estimation of parameters in the distribution of headways in roundabouts is a cumbersome task. Inherent to data employed are temporal variation together with dependence between successive vehicles. This is a consequence of the sampling period and interactions in the roundabouts. The elimination of observations, so as to obtain trend-free samples of independent vehicles, removes too much information from the data. If all the observations are used, the results of the parameter estimations are affected by temporal variation and dependence between headways. In this paper, an analysis of the statistical properties of the headways between major stream vehicles in roundabouts is described. The properties investigated were the existence of temporal variation in the measured headways and independent and identically distributed successive headways, i.e., if the headways were from a random sample. More than 50% of the investigated subsets suffered from trends or other nonrandom variations. The question whether these subsets should be excluded or not is discussed. Three methods for the estimation of parameters in the M3 distribution were tested. For the two-lane subsets, it was possible to demonstrate a linear relationship between the proportion of free vehicles and the volume. For the one-lane subsets, the adjusted R-2 was low, and the linear constant was not significant. Nevertheless, the distributions estimated by use of the two-lane subsets did not provide a better fit to the observed data than the distributions estimated by the use of one-lane subsets. The predicted capacity for a minor lane, i.e., the capacity obtained by the fitted distribution, was close to the capacity obtained by the empirical distribution function (the estimated capacity).

A discussion on the parameters of Cowan M3 distribution for Turkey

In recent years, Cowan M3 distribution model started to be used widely around the world by traffic engineers and researchers for capacity and performance analysis of roundabouts and unsignalized intersections. However, some differences between the usage and application in different countries are observed. This is mainly because of the difference between drivers’ behaviors. In this study, the present applications of Cowan M3 distribution and its parameters are discussed and more appropriate parameters that will define Turkish drivers’ behavior are searched.

Properties of Cowan’s M3 Headway Distribution

Cowan’s M3 distribution has been used in several studies on unsignalized intersections, especially roundabouts. It allows separate analysis of follower and nonfollower headways, and it is simple enough for models of considerable complexity. Although M3 gives a simplistic model for short headways, it has many desirable properties as a headway distribution. It is possible to estimate its parameters with simple methods and with reasonable accuracy, and the estimated models give good results in the capacity analysis of unsignalized intersections. Described in this paper are the basic statistical properties of M3, and the accuracy of the method of moments and least-squares parameter estimators is evaluated. The validity of M3 in unsignalized intersection capacity analysis is evaluated by a Monte Carlo simulation with samples from M3 and semi-Poisson distributions.

A further generalization of Tanner’s formula

A general capacity formula for the case of more than one major lane is derived, using the M3 distribution and allowing the major lanes to differ in critical gaps and follow-up times. The derivation can be further extended to there being different minimum headways for the major lanes and to distributions other than the M3 distribution. It is shown that the resulting formulas provide more accurate capacity estimations.