Finite element contact analysis as a critical technique in dental biomechanics: A review

PurposeNonlinear finite element contact analysis is used to mathematically estimate stress and strain in a time- and status-dependent mechanical model. However, the benefits and limitations of this method have not been thoroughly examined.Study selectionThe current review summarizes the utility of contact analysis in characterizing individual stressors: (1) tooth-to-tooth contact, (2) restorative interface, and (3) bone–implant integration.ResultsOpposing tooth contact, friction, and sliding phenomena were simulated to estimate stress distribution and assess the failure risk for tooth enamel, composite, and ceramic restorations. Mechanical tests such as the flexural tests were simulated with the contact analysis to determine the rationale underlying experimental findings. The tooth–restoration complex was modeled with interface contact elements that simulate imperfect bonding, and the normal and tangential stresses were calculated to predict failure progression. Previous studies have used a friction coefficient to represent osseointegration adjacent to dental implants, but the relationship between interface friction and the bone quality is unknown. An understanding of the local stress and strain may better predict loss of osseointegration, however, the effective stress as a critical contributor to bone degradation and formation has not been established.ConclusionsContact analysis provides numerous benefits for dental and oral health sciences, however, a fundamental understanding and improved methodology are necessary.     

Nonlinear viscoelastic behaviour of canine arterial walls

The nonlinear viscoelastic behaviour of arterial walls subjected to large deformation is studied theoretically and experimentally. It is assumed that the arterial walls are thick-walled cylindrical vessels composed of an incompressible, curvilinearly orthotropic and viscoelastic material. The radial displacement of vessel walls is simplified by superimposing a small time-dependent deformation due to pulse pressure on a large time-independent deformation. The radial and circumferential stresses are expressed as functions of the histories of strains in each direction. The functions are written in terms of a series of multiple integrals involving eight stress-relaxation functions. To determine these functions, experiments of stress relaxation were performed with common carotid and femoral arteries excised from mongrel dogs. For a strain imposition within 1–100 s, stress relaxation is expressed by a power-law function of time. On the basis of the theoretical equations, the vessel diameter and wall stresses are calculated as a function of time by assuming that a sinusoidal intraluminal pressure varying between 80 and 120 mm Hg is applied in the lumen. The creep phenomena are shown to be due to the viscoelasticity of the arterial walls. i.e. the deformation increases with elapsed time during pressure fluctuations.     

医院工作质量综合评价指标的非线性标准化

进行医院工作质量的多指标综合评价几乎无一例外地要涉及到指标值的标准化,以消除各评价指标量纲不同的影响,达到指标间的可加性或可乘性.目前指标值的标准化多使用线性方法.而事实上医院工作质量的指标值所反映的实际水平却极少为线性变化,故标准化值作为刻划原指标值实际水平的一个指标,采用原指标值的线性变换则具有明显的不合理性.本文引入了非线性变化的思想并提出一种幂转换的非线性标准化方法,结合一个实例运用非线性标准化方法进行了综合评价.     

Dissection of a nonlinear cascade model for sensory encoding

Action potential encoding in the cockroach tactile spine neuron may be treated as a single-input, single-output dynamic nonlinear process, where the input is the electric current flowing across the neuronal membrane and the output is the resultant train of action potentials. The nonlinear behavior of the system may be characterized by a functional expansion method which efficiently and accurately yields similar kernels to the Wiener method. A simple nonlinear cascade consisting of sequential dynamic linear, static nonlinear, and dynamic linear components was identified and gives a good approximation to the response of the neuron to random stimulation. Next, we attempted to study the components of the cascade by the use of a drug, phentolamine, which selectively modifies the dynamic behavior of the encoder. Application of phentolamine to the neuron caused a significant change in the first dynamic linear component of the cascade without affecting the other components. The change was much larger than the variability between results obtained from individual animals. This finding has implications for the biophysical processes which are involved in the components of the cascade.     

急性心肌梗塞后心肌酶代谢动力学二房室模型的理论研究

急性心肌梗塞后心肌酶的动态变化是估计梗塞面积的方法之一，本文在口服给药的二房室药物动力学数学模型的基础上设计了新的数学模型用以拟合急性心肌梗塞后心肌酶的时间－活性曲线，可望能够准确计算心肌酶释放总量，较好地估计梗塞面积。     

Use of pseudorandom noise in studies of auditory evoked potentials

The extent to which sensorineural systems such as the auditory system are nonlinear depends on the type of stimulus that is used, and the part of the system from which recordings are made. An estimate of the first-order Wiener kernel of the evoked response from the inferior colliculus to amplitude-modulated tones and noise was obtained by cross-correlating the response with the same pseudorandom noise as was used to amplitude modulate the sounds that were used as stimuli, in order to characterize the linear portion of the system. The shape of these cross-correlograms resembled the potentials evoked to short bursts of the unmodulated tones and noise. The degree of nonlinearity in the response to amplitude-modulated tones and noise was determined, and information about the type of nonlinearity was obtained using the inverse-repeat feature of the pseudorandom noise. Recordings both from the surface and from deep in the nucleus of the inferior colliculus revealed nonlinearities that were predominantly of an even order, but the magnitude of the nonlinearities depended on what stimulus was used, the stimulus intensity, and from which neural structure the recording was made.     

Identifying nonlinear difference equation and functional expansion representations: The fast orthogonal algorithm

A method is presented for identifying functional expansion and difference equation representations for nonlinear systems. The method relies on an orthogonal approach which does not require explicit creation of orthogonal functions. This greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique. In addition, storage requirements are considerably diminished. A wide variety of input excitation, both random and deterministic, can be used, and the method is not limited to inputs which are Gaussian, white or lengthy. A model of the peripheral auditory system is simulated to show kernel measurement is free of artifacts using the present method, in contrast to the crosscorrelation approach.     

药代动力学参数的计算机拟合及统计学评价

以残数法计算药代参数时,模型的选择可因主观影响,误差大,结果不恒定。我们在APPLEⅡ型微电脑上,采用非线性最小二乘法编程,大大提高了参数估计的精度,同时可对房室模型选择提供客观依据,并对参数作出统计学评价。程序采用菜单式结构,包括血管内、外各种模型,具有数据存取和较强的作图功能。     

Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction

This paper develops three high-order accurate discontinuous Galerkin (DG) methods for the one-dimensional (1D) and two-dimensional (2D) nonlinear Dirac (NLD) equations with a general scalar self-interaction. They are the Runge-Kutta DG (RKDG) method and the DG methods with the one-stage fourth-order Lax-Wendroff type time discretization (LWDG) and the two-stage fourth-order accurate time discretization (TSDG). The RKDG method uses the spatial DG approximation to discretize the NLD equations and then utilize the explicit multistage high-order Runge-Kutta time discretization for the first-order time derivatives, while the LWDG and TSDG methods, on the contrary, first give the one-stage fourth-order Lax-Wendroff type and the two-stage fourth-order time discretizations of the NLD equations, respectively, and then discretize the first- and higher-order spatial derivatives by using the spatial DG approximation. The $L^2$ stability of the 2D semi-discrete DG approximation is proved in the RKDG methods for a general triangulation, and the computational complexities of three 1D DG methods are estimated. Numerical experiments are conducted to validate the accuracy and the conservation properties of the proposed methods. The interactions of the solitary waves, the standing and travelling waves are investigated numerically and the 2D breathing pattern is observed.