A 3d-fem Simulation of Highest Stress Lines in Mandible Fractures by Elastic Impact

Abstract

In this article, the more usual mandible fracture areas are located by identifying the highest stress lines using a three-dimensional (tetrahedral) finite element method. By taking into account the temporomandibular contact and the inertia effects, the mathematical model is considered to be a dynamic Signorini's problem, that is, a dynamic variational inequality which is discretized in time following Newmark's method. So, in each time step a stationary variational inequality is solved by a penalty-duality algorithm. Finally, some numerical results obtained by simulating the more usual fractures in the human mandible are presented and compared with clinical experimental information.     

具有约束条件的变分不等式的可行的增广拉格朗日方法

采用增广拉格朗日方法求解了具有约束条件的变分不等式问题,并证明了这一方法的全局收敛性．运用增广拉格朗日方法和非精确的半光滑牛顿法求解了具有约束条件的变分不等式的一类子问题．我们给出了四个数值算例以说明这一方法的可行性．     

Optimal feed policy for fed-batch fermentation of ethanol production by Zymomous mobilis

Optimal feed control for the fed-batch fermentation process of ethanol production is studied. Additional inequality constraints are introduced in this optimization problem to assure the optimal solution in a reality region. Introducing an updating rule of augmented Lagrange multipliers to handle these inequality constraints, iterative dynamic programming can be used in a straightforward manner for the optimization of fed-batch fermentors. To obtain more accurate solution a method of sequential quadratic programming can be used to solve this problem again. As a result of this optimal control, the maximum production at final time is very close to the theoretical yield. Although sequential quadratic programming can be rapid convergence to the optimal solution, but very good initial starting points has to be used to ensure obtaining the global optimum. Experimental works were used to validate this study. The simulated results could fit the experiments satisfactorily.     

Dynamic analysis of leaflet stresses and application to heart valve design

The problem is approached using an approximate and simple variational procedure. A comparison with results obtained by means of the finite element method reveals that the analytical solution is convenient from a practical engineering viewpoint. It is hoped that biomedical researchers and designers will find the present approach useful when dealing with more complex structural dynamic situations.     

A new approach of fitting biomass dynamics models to data

A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The data assimilation method provides a novel and computationally efficient procedure for combining all available information, i.e., the data and the model in the analysis of a resource system. This technique will be used to analyze data for the North-east Arctic cod stock. Two alternative population growth models: the logistic and the Gompertz model are used for estimating parameters of simple bioeconomic models by the method of constrained least squares. Estimates of the parameters of the models dynamics are reasonable and can be accepted. The main inference from the work is that the average fishing mortality is found to be significantly above the maximum sustainable yield value.     

Dynamic vaccination games and variational inequalities on time-dependent sets

This paper presents a model of a dynamic vaccination game in a population consisting of a collection of groups, each of which holds distinct perceptions of vaccinating versus non-vaccinating risks. Vaccination is regarded here as a game due to the fact that the payoff to each population group depends on the so-called perceived probability of getting infected given a certain level of the vaccine coverage in the population, a level that is generally obtained by the vaccinating decisions of other members of a population. The novelty of this model resides in the fact that it describes a repeated vaccination game (over a finite time horizon) of population groups whose sizes vary with time. In particular, the dynamic game is proven to have solutions using a parametric variational inequality approach often employed in optimization and network equilibrium problems. Moreover, the model does not make any assumptions upon the level of the vaccine coverage in the population, but rather computes this level as a final result. This model could then be used to compute possible vaccine coverage scenarios in a population, given information about its heterogeneity with respect to perceived vaccine risks. In support of the model, some theoretical results were advanced (presented in the appendix) to ensure that computation of optimal vaccination strategies can take place; this means, the theory states the existence, uniqueness and regularity (in our case piecewise continuity) of the solution curves representing the evolution of optimal vaccination strategies of each population group.     

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

In biology, many quantitative traits are dynamic in nature. They can often be described by some smooth functions or curves. A joint analysis of all the repeated measurements of the dynamic traits by functional quantitative trait loci (QTL) mapping methods has the benefits to (1) understand the genetic control of the whole dynamic process of the quantitative traits and (2) improve the statistical power to detect QTL. One crucial issue in functional QTL mapping is how to correctly describe the smoothness of trajectories of functional valued traits. We develop an efficient Bayesian nonparametric multiple-loci procedure for mapping dynamic traits. The method uses the Bayesian P-splines with (nonparametric) B-spline bases to specify the functional form of a QTL trajectory and a random walk prior to automatically determine its degree of smoothness. An efficient deterministic variational Bayes algorithm is used to implement both (1) the search of an optimal subset of QTL among large marker panels and (2) estimation of the genetic effects of the selected QTL changing over time. Our method can be fast even on some large-scale data sets. The advantages of our method are illustrated on both simulated and real data sets.     

Dynamic vaccination games and variational inequalities on time-dependent sets

This paper presents a model of a dynamic vaccination game in a population consisting of a collection of groups, each of which holds distinct perceptions of vaccinating versus non-vaccinating risks. Vaccination is regarded here as a game due to the fact that the payoff to each population group depends on the so-called perceived probability of getting infected given a certain level of the vaccine coverage in the population, a level that is generally obtained by the vaccinating decisions of other members of a population. The novelty of this model resides in the fact that it describes a repeated vaccination game (over a finite time horizon) of population groups whose sizes vary with time. In particular, the dynamic game is proven to have solutions using a parametric variational inequality approach often employed in optimization and network equilibrium problems. Moreover, the model does not make any assumptions upon the level of the vaccine coverage in the population, but rather computes this level as a final result. This model could then be used to compute possible vaccine coverage scenarios in a population, given information about its heterogeneity with respect to perceived vaccine risks. In support of the model, some theoretical results were advanced (presented in the appendix) to ensure that computation of optimal vaccination strategies can take place; this means, the theory states the existence, uniqueness and regularity (in our case piecewise continuity) of the solution curves representing the evolution of optimal vaccination strategies of each population group.     

A sharp incisor tool for predator house mice back to the wild

The house mouse (Mus musculus domesticus), as a successful invasive species worldwide, has to forage a variety of resources. Subantarctic mice display among the most notable diet shift from the usual omnivorous–granivorous diet, relying on a larger proportion of terrestrial animal prey. In agreement, a recent study of their mandible morphology evidenced an evolution of their mandible shape to optimize incisor biting and hence seize preys. Here, the incisors themselves are the focus of a morphometric analysis combined with a 3D study of their internal structure, aiming at a comparison between subantarctic populations (Guillou island, Kerguelen archipelago) with a range of western European continental, commensal mice. The predatory foraging behavior of Guillou mice was indeed associated with a sharper bevel of the lower incisor, which appears as an efficient morphology for piercing prey. The incisor of these mice also displays a reduced pulp cavity, suggesting slower eruption counterbalancing a reduced abrasion on such soft food material. The dynamics of the ever‐growing incisor may thus allow adaptive incisor sculpting and participate to the success of mice in foraging diverse resources.     

Size variation and mating success in the stag beetle, Lucanus cervus

Abstract.  The stag beetle, Lucanus cervus , is Britain's largest beetle, with a patchy distribution in southern England. The literature suggests that it displays exceptional size variation, particularly in the males, but no analysis of size inequality has ever been conducted. In the present study, stag beetle adults are measured and allometric relationships derived between various parameters and total body length. Most of the specimens found each year are fragments and head width can be used as a good predictor of total body length in each sex. Body size differs between years and between localities and male beetles show a greater degree of size inequality than females. However, L. cervus does not show greater inequality in size than many other beetle species and populations of males are composed of a relatively large number of small individuals. These males are not at a disadvantage in mating because it is the ratio of male : female size that determines mating success. Very large males are less successful in mating and it is suggested that lack of mating success may act as an additional constraint on mandible size in this species. Size variation is most likely caused by variation in larval food resources, coupled with variation in local climatic conditions.     

Theoretical considerations of the Tsou plot

A graphical method was proposed by Tsou in 1962 for interpreting the data obtained by chemical modification of proteins and determining the number of essential groups involved. A strict mathematical proof and the estimation of deviation probability for this method are presented here. From the well-known Chebyshev's inequality, it has been shown that the possible error which could be derived from the Tsou plot will be much smaller than the usual experimental error obtainable. Some problems related to experiment and to application of Tsou plot in oligomeric enzymes have been discussed. Some analysis of experimental data taken from the literature are presented.     

A simple and inexpensive system for monitoring jaw movements in ambulatory humans

A simple and inexpensive method for recording vertical movements of the human mandible relative to the maxilla is presented. Measurements are made from accelerometers and a Hall-effect device temporarily glued to the upper and lower anterior teeth. The accelerometer signals are integrated once to give velocity and a second time to give position. Movements of the mandible relative to the maxilla are obtained by integrating the difference between the two accelerometer signals. The (relative) velocity and position records derived in this way are linear, but subject to drift when the jaw is stationary. Steady mandibular position is obtained from the Hall-effect system, but this signal must be corrected for its inherent non-linearity. This device can record rapid movements of the mandible even when the head is unrestrained, and interferes minimally with normal jaw movements.     

A variational Bayesian mixture modelling framework for cluster analysis of gene-expression data

MOTIVATION: Accurate subcategorization of tumour types through gene-expression profiling requires analytical techniques that estimate the number of categories or clusters rigorously and reliably. Parametric mixture modelling provides a natural setting to address this problem. RESULTS: We compare a criterion for model selection that is derived from a variational Bayesian framework with a popular alternative based on the Bayesian information criterion. Using simulated data, we show that the variational Bayesian method is more accurate in finding the true number of clusters in situations that are relevant to current and future microarray studies. We also compare the two criteria using freely available tumour microarray datasets and show that the variational Bayesian method is more sensitive to capturing biologically relevant structure.     

Injuries associated with mandible fractures sustained in motor vehicle collisions

Motor vehicle collisions are second only to altercations as the most common cause of mandible fractures. This article details in a retrospectively studied group the incidence of isolated mandible fractures and associated injuries in patients who were involved in motor vehicle collisions. This group consisted of 148 patients with mandible fractures listed in the University of Mississippi's trauma registry during the past 5 years. In almost all patients, associated injuries occurred with mandible fractures that were caused by motor vehicle collisions, with an incidence of 99.3 percent. Facial and head lacerations and facial fractures were the leading associated injuries, occurring in more than half of the patients who had a mandible fracture. Closed head injury is the major life-threatening associated injury and cause of mortality. The life-threatening injuries occurred in 64.8 percent of patients in this study. The mortality rate in this group of patients was 8.1 percent. These data suggest that mandible fractures from motor vehicle collisions should never be viewed as an isolated injury but rather as part of a spectrum of significant and sometimes life-threatening injuries that require thorough trauma evaluation at the time of presentation.     

Note on the hamiltonian principle in biology and in physics

A suggestion is made to establish a general variational principle of which the recently discussed principle of maximum energy exchange in biology and the usual Hamiltonian principle in physics would be particular cases.     

Analysis and treatment of hemifacial microsomia

Our experience over the past 25 years leads us to conclude that hemifacial microsomia is a progressive skeletal and soft-tissue deformity with the earliest skeletal manifestations in the mandible. We find that not only does the mandibular asymmetry become worse with time, but as the contralateral side grows, the deformed mandible also increases ipsilateral secondary deformation of the maxilla, nose, and orbit. We also find that there is virtually no "catch up" growth on the affected side of the face and that these patients always become more deformed with age. The psychological problems also increase with time and progression of the facial deformity. Based on our experience with correction of end-stage deformities, we now treat these patients at the earliest possible age, as determined by the patient's skeletal classification. We treat the mandible first in the hope that this repositioning in a more physiologic position will unlock the growth potential of the adjacent structures, minimize secondary deformity, and improve function and appearance to the greater benefit of the skeletal and psychological growth of the patient.     

Variational data assimilation with epidemic models

Mathematical modelling is playing an increasing role in developing an understanding of the dynamics of communicable disease and assisting the construction and implementation of intervention strategies. The threat of novel emergent pathogens in human and animal hosts implies the requirement for methods that can robustly estimate epidemiological parameters and provide forecasts. Here, a technique called variational data assimilation is introduced as a means of optimally melding dynamic epidemic models with epidemiological observations and data to provide forecasts and parameter estimates. Using data from a simulated epidemic process the method is used to estimate the start time of an epidemic, to provide a forecast of future epidemic behaviour and estimate the basic reproductive ratio. A feature of the method is that it uses a basic continuous-time SIR model, which is often the first point of departure for epidemiological modelling during the early stages of an outbreak. The method is illustrated by application to data gathered during an outbreak of influenza in a school environment.     

The Inequality Footprints of Nations: A Novel Approach to Quantitative Accounting of Income Inequality

In this study we use economic input-output analysis to calculate the inequality footprint of nations. An inequality footprint shows the link that each country''s domestic economic activity has to income distribution elsewhere in the world. To this end we use employment and household income accounts for 187 countries and an historical time series dating back to 1990. Our results show that in 2010, most developed countries had an inequality footprint that was higher than their within-country inequality, meaning that in order to support domestic lifestyles, these countries source imports from more unequal economies. Amongst exceptions are the United States and United Kingdom, which placed them on a par with many developing countries. Russia has a high within-country inequality nevertheless it has the lowest inequality footprint in the world, which is because of its trade connections with the Commonwealth of Independent States and Europe. Our findings show that the commodities that are inequality-intensive, such as electronic components, chemicals, fertilizers, minerals, and agricultural products often originate in developing countries characterized by high levels of inequality. Consumption of these commodities may implicate within-country inequality in both developing and developed countries.     

Predicting the folding pathway of engrailed homeodomain with a probabilistic roadmap enhanced reaction-path algorithm

To predict a protein-folding pathway, we present an alternative to the time-consuming dynamic simulation of atomistic models. We replace the actual dynamic simulation with variational optimization of a reaction path connecting known initial and final protein conformations in such a way as to maximize an estimate of the reactive flux or minimize the mean first passage time at a given temperature, referred to as MaxFlux. We solve the MaxFlux global optimization problem with an efficient graph-theoretic approach, the probabilistic roadmap method (PRM). We employed CHARMM19 and the EEF1 implicit solvation model to describe the protein solution. The effectiveness of our MaxFlux-PRM is demonstrated in our promising simulation results on the folding pathway of the engrailed homeodomain. Our MaxFlux-PRM approach provides the direct evidence to support that the previously reported intermediate state is a genuine on-pathway intermediate, and the demand of CPU power is moderate.     

Computational geometry assessment for morphometric analysis of the mandible

This paper presents a fully automated algorithm for geometry assessment of the mandible. Anatomical landmarks could be reliably detected and distances were statistically evaluated with principal component analysis. The method allows for the first time to generate a mean mandible shape with statistically valid geometrical variations based on a large set of 497 CT-scans of human mandibles. The data may be used in bioengineering for designing novel oral implants, for planning of computer-guided surgery, and for the improvement of biomechanical models, as it is shown that commercially available mandible replicas differ significantly from the mean of the investigated population.