An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Statistical model-based segmentation of the proximal femur in digital antero-posterior (AP) pelvic radiographs.

PURPOSE    Segmentation of the proximal femur in digital antero-posterior (AP) pelvic radiographs is required to create a three-dimensional model of the hip joint for use in planning and treatment. However, manually extracting the femoral contour is tedious and prone to subjective bias, while automatic segmentation must accommodate poor image quality, anatomical structure overlap, and femur deformity. A new method was developed for femur segmentation in AP pelvic radiographs. METHODS    Using manual annotations on 100 AP pelvic radiographs, a statistical shape model (SSM) and a statistical appearance model (SAM) of the femur contour were constructed. The SSM and SAM were used to segment new AP pelvic radiographs with a three-stage approach. At initialization, the mean SSM model is coarsely registered to the femur in the AP radiograph through a scaled rigid registration. Mahalanobis distance defined on the SAM is employed as the search criteria for each annotated suggested landmark location. Dynamic programming was used to eliminate ambiguities. After all landmarks are assigned, a regularized non-rigid registration method deforms the current mean shape of SSM to produce a new segmentation of proximal femur. The second and third stages are iteratively executed to convergence. RESULTS    A set of 100 clinical AP pelvic radiographs (not used for training) were evaluated. The mean segmentation error was [Formula: see text], requiring [Formula: see text] s per case when implemented with Matlab. The influence of the initialization on segmentation results was tested by six clinicians, demonstrating no significance difference. CONCLUSIONS    A fast, robust and accurate method for femur segmentation in digital AP pelvic radiographs was developed by combining SSM and SAM with dynamic programming. This method can be extended to segmentation of other bony structures such as the pelvis.

A model of the roles of essential kinases in the induction and expression of late long-term potentiation.

The induction of late long-term potentiation (L-LTP) involves complex interactions among second-messenger cascades. To gain insights into these interactions, a mathematical model was developed for L-LTP induction in the CA1 region of the hippocampus. The differential equation-based model represents actions of protein kinase A (PKA), MAP kinase (MAPK), and CaM kinase II (CAMKII) in the vicinity of the synapse, and activation of transcription by CaM kinase IV (CAMKIV) and MAPK. L-LTP is represented by increases in a synaptic weight. Simulations suggest that steep, supralinear stimulus-response relationships between stimuli (e.g., elevations in [Ca(2+)]) and kinase activation are essential for translating brief stimuli into long-lasting gene activation and synaptic weight increases. Convergence of multiple kinase activities to induce L-LTP helps to generate a threshold whereby the amount of L-LTP varies steeply with the number of brief (tetanic) electrical stimuli. The model simulates tetanic, -burst, pairing-induced, and chemical L-LTP, as well as L-LTP due to synaptic tagging. The model also simulates inhibition of L-LTP by inhibition of MAPK, CAMKII, PKA, or CAMKIV. The model predicts results of experiments to delineate mechanisms underlying L-LTP induction and expression. For example, the cAMP antagonist RpcAMPs, which inhibits L-LTP induction, is predicted to inhibit ERK activation. The model also appears useful to clarify similarities and differences between hippocampal L-LTP and long-term synaptic strengthening in other systems.

Three-Dimensional Mechanics of Yakutat Convergence in the Southern Alaskan Plate Corner

Three-dimensional numerical models are used to investigate the mechanical evolution of the southern Alaskan plate corner where the Yakutat and the Pacific plates converge on the North American plate. The evolving model plate boundary consists of Convergent, Lateral, and Subduction subboundaries with flow separation of incoming material into upward or downward trajectories forming dual, nonlinear advective thermal/mechanical anomalies that fix the position of major subaerial mountain belts. The model convergent subboundary evolves into two teleconnected orogens: Inlet and Outlet orogens form at locations that correspond with the St. Elias and the Central Alaska Range, respectively, linked to the East by the Lateral boundary. Basins form parallel to the orogens in response to the downward component of velocity associated with subduction. Strain along the Lateral subboundary varies as a function of orogen rheology and magnitude and distribution of erosion. Strain-dependent shear resistance of the plate boundary associated with the shallow subduction zone controls the position of the Inlet orogen. The linkages among these plate boundaries display maximum shear strain rates in the horizontal and vertical planes where the Lateral subboundary joins the Inlet and Outlet orogens. The location of the strain maxima shifts with time as the separation of the Inlet and Outlet orogens increases. The spatiotemporal predictions of the model are consistent with observed exhumation histories deduced from thermochronology, as well as stratigraphic studies of synorogenic deposits. In addition, the complex structural evolution of the St Elias region is broadly consistent with the predicted strain field evolution. Citation: Koons, P. O., B. P. Hooks, T. Pavlis, P. Upton, and A. D. Barker (2010), Three-dimensional mechanics of Yakutat convergence in the southern Alaskan plate corner, Tectonics, 29, TC4008, doi: 10.1029/2009TC002463.

A Model Study of the Circulation in the Pearl River Estuary (PRE) and Its Adjacent Coastal Waters: 2. Sensitivity Experiments

The Princeton Ocean Model is used to study the circulation in the Pear River Estuary (PRE) and the adjacent coastal waters in the winter and summer seasons. Wong et al. [2003] compares the simulation results with the in situ measurements collected during the Pearl River Estuary Pollution Project (PREPP). In this paper, sensitivity experiments are carried out to examine the plume and the associated frontal dynamics in response to seasonal discharges and monsoon winds. During the winter, convergence between the seaward spreading plume water and the saline coastal water sets up a salinity front that aligns from the northeast to the southwest inside the PRE. During the summer the plume water fills the PRE at the surface and spreads eastward in the coastal waters in response to the prevailing southwesterly monsoon. The overall alignment of the plume is from the northwest to the southeast. The subsurface front is similar to that in the winter and summer except that the summer front is closer to the mouth and the winter front closer to the head of the estuary. Inside the PRE, bottom flows are always toward the head of the estuary, attributed to the density gradient associated with the plume front. In contrast, bottom flows in the shelf change from offshore in winter to onshore in summer, reflecting respectively the wintertime downwelling and summertime upwelling. Wind also plays an essential role in controlling the plume at the surface. An easterly wind drives the plume westward regardless winter or summer. The eastward spreading of the plume during the summer can be attributed to the southerly component of the wind. On the other hand, the surface area of the plume is positively proportional to the amount of discharge.

Simulation study of joint transition and Weibull survival model with shared parameters

This study investigates a theoretical model where a longitudinal process, that is a stationary Markov-Chain, and a Weibull survival process share a bivariate random effect. Furthermore, a Quality-of-Life adjusted survival is calculated as the weighted sum of survival time. Theoretical values of population mean adjusted survival of the described model are computed numerically. The parameters of the bivariate random effect do significantly affect theoretical values of population mean. Maximum-Likelihood and Bayesian methods are applied on simulated data to estimate the model parameters. Based on the parameter estimates, predicated population mean adjusted survival can then be calculated numerically and compared with the theoretical values. Bayesian method and Maximum-Likelihood method provide parameter estimations and population mean prediction with comparable accuracy; however Bayesian method suffers from poor convergence due to autocorrelation and inter-variable correlation. ^

Microcharcoal concentration and elongation, and age model of sediment core MD96-2098

Although grassland and savanna occupy only a quarter of the world's vegetation, burning in these ecosystems accounts for roughly half the global carbon emissions from fire. However, the processes that govern changes in grassland burning are poorly understood, particularly on time scales beyond satellite records. We analyzed microcharcoal, sediments, and geochemistry in a high-resolution marine sediment core off Namibia to identify the processes that have controlled biomass burning in southern African grassland ecosystems under large, multimillennial-scale climate changes. Six fire cycles occurred during the past 170,000 y in southern Africa that correspond both in timing and magnitude to the precessional forcing of north-south shifts in the Intertropical Convergence Zone. Contrary to the conventional expectation that fire increases with higher temperatures and increased drought, we found that wetter and cooler climates cause increased burning in the study region, owing to a shift in rainfall amount and seasonality (and thus vegetation flammability). We also show that charcoal morphology (i.e., the particle's length-to-width ratio) can be used to reconstruct changes in fire activity as well as biome shifts over time. Our results provide essential context for understanding current and future grassland-fire dynamics and their associated carbon emissions.

Trace metal concentration and age model of ODP Hole 165-1002C sediments

Titanium and iron concentration data from the anoxic Cariaco Basin, off the Venezuelan coast, can be used to infer variations in the hydrological cycle over northern South America during the past 14,000 years with subdecadal resolution. Following a dry Younger Dryas, a period of increased precipitation and riverine discharge occurred during the Holocene 'thermal maximum'. Since ~5400 years ago, a trend toward drier conditions is evident from the data, with high-amplitude fluctuations and precipitation minima during the time interval 3800 to 2800 years ago and during the 'Little Ice Age'. These regional changes in precipitation are best explained by shifts in the mean latitude of the Atlantic Intertropical Convergence Zone (ITCZ), potentially driven by Pacific-based climate variability. The Cariaco Basin record exhibits strong correlations with climate records from distant regions, including the high-latitude Northern Hemisphere, providing evidence for global teleconnections among regional climates.

Age model, stable isotopes, major element proportions and endmember unmixing results from four western tropical Atlantic cores

We investigate changes in the delivery and oceanic transport of Amazon sediments related to terrestrial climate variations over the last 250 ka. We present high-resolution geochemical records from four marine sediment cores located between 5 and 12° N along the northern South American margin. The Amazon River is the sole source of terrigenous material for sites at 5 and 9° N, while the core at 12° N receives a mixture of Amazon and Orinoco detrital particles. Using an endmember unmixing model, we estimated the relative proportions of Amazon Andean material ("%-Andes", at 5 and 9° N) and of Amazon material ("%-Amazon", at 12° N) within the terrigenous fraction. The %-Andes and %-Amazon records exhibit significant precessional variations over the last 250 ka that are more pronounced during interglacials in comparison to glacial periods. High %-Andes values observed during periods of high austral summer insolation reflect the increased delivery of suspended sediments by Andean tributaries and enhanced Amazonian precipitation, in agreement with western Amazonian speleothem records. Increased Amazonian rainfall reflects the intensification of the South American monsoon in response to enhanced land-ocean thermal gradient and moisture convergence. However, low %-Amazon values obtained at 12° N during the same periods seem to contradict the increased delivery of Amazon sediments. We propose that reorganizations in surface ocean currents modulate the northwestward transport of Amazon material. In agreement with published records, the seasonal North Brazil Current retroflection is intensified (or prolonged in duration) during cold substages of the last 250 ka (which correspond to intervals of high DJF or low JJA insolation) and deflects eastward the Amazon sediment and freshwater plume.

Age model, lipids, and iron/calcium-ratios of sediment core GeoB9307-3

Hide Intense debate persists about the climatic mechanisms governing hydrologic changes in tropical and subtropical southeast Africa since the Last Glacial Maximum, about 20,000 years ago. In particular, the relative importance of atmospheric and oceanic processes is not firmly established. Southward shifts of the intertropical convergence zone (ITCZ) driven by high-latitude climate changes have been suggested as a primary forcing, whereas other studies infer a predominant influence of Indian Ocean sea surface temperatures on regional rainfall changes. To address this question, a continuous record representing an integrated signal of regional climate variability is required, but has until now been missing. Here we show that remote atmospheric forcing by cold events in the northern high latitudes appears to have been the main driver of hydro-climatology in southeast Africa during rapid climate changes over the past 17,000 years. Our results are based on a reconstruction of precipitation and river discharge changes, as recorded in a marine sediment core off the mouth of the Zambezi River, near the southern boundary of the modern seasonal ITCZ migration. Indian Ocean sea surface temperatures did not exert a primary control over southeast African hydrologic variability. Instead, phases of high precipitation and terrestrial discharge occurred when the ITCZ was forced southwards during Northern Hemisphere cold events, such as Heinrich stadial 1 (around 16,000 years ago) and the Younger Dryas (around 12,000 years ago), or when local summer insolation was high in the late Holocene, i.e., during the last 4,000 years.

Efficient Model-based 3D Tracking by Using Direct Image Registration

This thesis deals with the problem of efficiently tracking 3D objects in sequences of images. We tackle the efficient 3D tracking problem by using direct image registration. This problem is posed as an iterative optimization procedure that minimizes a brightness error norm. We review the most popular iterative methods for image registration in the literature, turning our attention to those algorithms that use efficient optimization techniques. Two forms of efficient registration algorithms are investigated. The first type comprises the additive registration algorithms: these algorithms incrementally compute the motion parameters by linearly approximating the brightness error function. We centre our attention on Hager and Belhumeur’s factorization-based algorithm for image registration. We propose a fundamental requirement that factorization-based algorithms must satisfy to guarantee good convergence, and introduce a systematic procedure that automatically computes the factorization. Finally, we also bring out two warp functions to register rigid and nonrigid 3D targets that satisfy the requirement. The second type comprises the compositional registration algorithms, where the brightness function error is written by using function composition. We study the current approaches to compositional image alignment, and we emphasize the importance of the Inverse Compositional method, which is known to be the most efficient image registration algorithm. We introduce a new algorithm, the Efficient Forward Compositional image registration: this algorithm avoids the necessity of inverting the warping function, and provides a new interpretation of the working mechanisms of the inverse compositional alignment. By using this information, we propose two fundamental requirements that guarantee the convergence of compositional image registration methods. Finally, we support our claims by using extensive experimental testing with synthetic and real-world data. We propose a distinction between image registration and tracking when using efficient algorithms. We show that, depending whether the fundamental requirements are hold, some efficient algorithms are eligible for image registration but not for tracking.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

Techniques to accelerate convergence of stress-controlled molecular dynamics simulations of dislocation motion

Dislocation mobility —the relation between applied stress and dislocation velocity—is an important property to model the mechanical behavior of structural materials. These mobilities reflect the interaction between the dislocation core and the host lattice and, thus, atomistic resolution is required to capture its details. Because the mobility function is multiparametric, its computation is often highly demanding in terms of computational requirements. Optimizing how tractions are applied can be greatly advantageous in accelerating convergence and reducing the overall computational cost of the simulations. In this paper we perform molecular dynamics simulations of ½ 〈1 1 1〉 screw dislocation motion in tungsten using step and linear time functions for applying external stress. We find that linear functions over time scales of the order of 10–20 ps reduce fluctuations and speed up convergence to the steady-state velocity value by up to a factor of two.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.