an euler lagrange approach for studying blood flow in an aneurysmal geometry to numerically study blood flow in an aneurysm the development of an approach that tracks the moving tissue and accounts for its interaction with the fluid is required this study presents a mathe

trans dimensional geoacoustic inversion this paper develops a general trans dimensional bayesian methodology for geoacoustic inversion trans dimensional inverse problems are a generalization of fixed dimensional inversion that includes the number and type of model parameters as unknowns in the problem by extending the inversion state space to multiple subspaces of different dimensions the posterior probability density quantifies the state of knowledge regarding inversion parameters including effects due to limited knowledge about appropriate parametrization of the environment and error processes the inversion is implemented here using a reversible jump markov chain monte carlo algorithm and the seabed is parametrized using a partition model unknown data errors are addressed by including a data error model jumps between dimensions are implemented with a birth death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the markov chain trans dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self regularizing algorithm based on data information content not on subjective regularization functions together this results in environmental estimates that quantify appropriate seabed structure as supported by the data allowing sharp discontinuities while approximating smooth transitions where needed this approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection coefficient data

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

hierarchical bayesian inference for ill posed problems via variational method this paper investigates a novel approximate bayesian inference procedure for numerically solving inverse problems a hierarchical formulation which determines automatically the regularization parameter and the noise level together with the inverse solution is adopted the framework is of variational type and it can deliver the inverse solution and regularization parameter together with their uncertainties calibrated it approximates the posteriori probability distribution by separable distributions based on kullback leibler divergence two approximations are derived within the framework and some theoretical properties e g variance estimate and consistency are also provided algorithms for their efficient numerical realization are described and their convergence properties are also discussed extensions to nonquadratic regularization nonlinear forward models are also briefly studied numerical results for linear and nonlinear cauchy type problems arising in heat conduction with both smooth and nonsmooth solutions are presented for the proposed method and compared with that by markov chain monte carlo the results illustrate that the variational method can faithfully capture the posteriori distribution in a computationally efficient way

hopf algebra extensions arising from semi direct products of groups hopf algebra extensions arising from a matched pair of groups were intro duced by g i kac kac he established an exact sequence the kac sequence that connects group cohomology and hopf algebra extensions this was re cently considered and generalized by other authors for instance a masuoka in mal ma2

on the choice of outlet boundary conditions for patient specific analysis of aortic flow using computational fluid dynamics boundary conditions bcs are an essential part in computational fluid dynamics cfd simulations of blood flow in large arteries although several studies have investigated the influence of bcs on predicted flow patterns and hemodynamic wall parameters in various arterial models there is a lack of comprehensive assessment of outlet bcs for patient specific analysis of aortic flow in this study five different sets of outlet bcs were tested and compared using a subject specific model of a normal aorta phase contrast magnetic resonance imaging pc mri was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition computational results obtained with different outlet bcs were assessed in terms of their agreement with the pc mri velocity data and key hemodynamic parameters such as pressure and flow waveforms and wall shear stress related indices our results showed that the best overall performance was achieved by using a well tuned three element windkessel model at all model outlets which not only gave a good agreement with in vivo flow data but also produced physiological pressure waveforms and values on the other hand opening outlet bcs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

non planar curvature and branching of arteries and non planar type flow in this study magnetic resonance imaging techniques have been used to examine the geometry of arterial curvature and branching in casts and in vivo and to measure the distribution of axial velocity in the associated flow it is found contrary to a widely held view that the geometry is commonly non planar moreover relatively small values of the parameters which render the geometry non planar appear significantly to affect the velocity distribution the findings suggest that non planarity is an important factor influencing arterial flows including wall shear the implications are not restricted to vascular biology pathology and surgery but may extend to the design of general piping systems

expanded uncertainty quantification in inverse problems hierarchical bayes and empirical bayes a common way to account for uncertainty in inverse problems is to apply bayes rule and obtain a posterior distribution of the quantities of interest given a set of measurements a conventional bayesian treatment however requires assuming specific values for parameters of the prior distribution and of the distribution of the measurement errors e g the standard deviation of the errors in practice these parameters are often poorly known a priori and choosing a particular value is often problematic moreover the posterior uncertainty is computed assuming that these parameters are fixed if they are not well known a priori the posterior uncertainties have dubious value this paper describes extensions to the conventional bayesian treatment that assign uncertainty to the parameters defining the prior distribution and the distribution of the measurement errors these extensions are known in the statistical literature as empirical bayes and hierarchical bayes we demonstrate the practical applicati

a parametric model for studying the aorta hemodynamics by means of the computational fluid dynamics abstract perturbed aorta hemodynamics as for the carotid and the coronary artery has been identified as potential predicting factor for cardiovascular diseases in this study we propose a parametric study based on the computational fluid dynamics with the aim of providing information regarding aortic disease in particular the blood flow inside a parametrized aortic arch is computed as a function of morphological changes of baseline aorta geometry flow patterns wall shear stress time average wall shear stress and oscillatory shear index were calculated during the cardiac cycle the influence of geometrical changes on the hemodynamics and on these variables was evaluated the results suggest that the distance between inflow and aortic arch and the angle between aortic arch and descending trunk are the most influencing parameters regarding the wss related indices while the effect of the inlet diameter seems limited in particular an increase of the aforementioned distance produces a reduction of the spatial distribution of the higher values of the time average wall shear stress and of the oscillatory shear index independently on the other two parameters while an increase of the angle produce an opposite effect moreover as expected the analysis of the wall shear stress descriptors suggests that the inlet diameter influences only the flow intensity as conclusion the proposed parametric study can be used to evaluate the aorta hemodynamics and could be also applied in the future for analyzing pathological cases and virtual situations such as pre and or post operative cardiovascular surgical states that present enhanced changes in the aorta morphology yet promoting important variations on the considered indexes

dtn based mixed dimensional coupling using a boundary stress recovery technique abstract a new computational approach for the mixed dimensional modeling of time harmonic waves in elastic structures is proposed a two dimensional 2d structure is considered which includes a part that is assumed to behave in a one dimensional 1d way the 2d and 1d structural regions are discretized by using 2d and 1d finite element fe formulations the hybrid model if designed properly is much more efficient than the standard 2d model taken for the entire problem one important issue related to such hybrid 2d 1d models is the way the 2d 1d coupling is done and the coupling error generated here three closely related coupling methods are considered they are all based on the dirichlet to neumann dtn map associated with the 1d problem on the interface the first coupling method is the dtn method in its usual form where the dtn map is calculated numerically and where the 1d and 2d problems are solved separately the second coupling method is the one devised by carka mear and landis cml which is equivalent to the former one but in which the 2d and 1d interface solutions are solved for simultaneously in the third coupling method the dtn map is enforced on the interface iteratively direct application of these three methods results in low accuracy as a recent study shows therefore these methods are used here in conjunction with a boundary stress recovery bsr technique originally proposed by hughes which provides the same order of accuracy for the stress as for the primary variable the performance of the three methods is demonstrated and they are compared via numerical examples conclusions are drawn on their relative merit

numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques we consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary as a paradigm for such problems we simply refer to stokes flow after a brief review of the problem and of its well posedness we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints we exploit a penalty method to account for them we perform the analysis of the method in terms of consistency boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization since the additional terms introduced to account for the defective boundary conditions are non local we also analyze the spectral properties of the equivalent algebraic formulation and we exploit the analysis to set up an efficient solution strategy in contrast to alternative discretization methods based on lagrange multipliers accounting for the constraints on the boundary the present scheme is particularly effective because it only mildly affects the structure and the computational cost of the numerical approximation indeed it does not require neither multipliers nor sub iterations or additional adjoint problems with respect to the reference problem at hand

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

on the importance of blood rheology for bulk flow in hemodynamic models of the carotid bifurcation abstract here we present a study on the impact of assumptions on image based hemodynamic simulations of healthy carotid bifurcations in particular we evaluate to which extent assumptions on blood rheology influence bulk flow features driven by the fact that few studies have provided adequate insights into the influence of assumptions to confidently model the 4d hemodynamics within the bifurcation the final goal is to complement integrate and extend with a quantitative characterization of the bulk flow the description currently adopted to classify altered hemodynamics which is based on wall shear stress wss hemodynamic simulations of two image based carotid bifurcation geometries were carried out assuming a reference newtonian viscosity two non newtonian rheology models and newtonian viscosities based on characteristic shear rates wss based and lagrangian based metrics for helical flow quantification and for vorticity dynamics quantification were calculated our findings suggest that the assumption of newtonian rheology 1 could be reasonable for bulk flow metrics differences from non newtonian behavior are lower than 10 2 influences at different levels the wss based indicators depending on the bifurcation model even if in our study it is lower than the major source of uncertainty as recognized by the literature i e uncertainty on geometry reconstruction

a modular numerical method for implicit 0d 3d coupling in cardiovascular finite element simulations implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system the use of elaborate closed loop lumped parameter network lpn models of the heart and the circulatory system as boundary conditions for computational fluid dynamics cfd simulations can provide valuable global dynamic information particularly for patient specific simulations in this paper the necessary formulation for coupling an arbitrary lpn to a finite element navier stokes solver is presented a circuit analogy closed loop lpn is solved numerically and pressure and flow information is iteratively passed between the 0d and 3d domains at interface boundaries resulting in a time implicit scheme for neumann boundaries an implicit method regardless of the lpn is presented to achieve the desired stability and convergence properties numerical procedures for passing flow and pressure information between the 0d and 3d domains are described and implicit semi implicit and explicit quasi newton formulations are compared the issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation the requirements for coupling dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the neumann coupled boundaries having the option to select between dirichlet and neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3d 0d interface

a finite element solver and energy stable coupling for 3d and 1d fluid models the paper develops a solver based on conforming finite element method fem for a 3d 1d coupled incompressible flow problem new coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model we study the stability and the accuracy of the discretization method and the performance of some state of the art linear algebraic solvers for such flow configurations motivated by the simulation of the flow over inferior vena cava ivc filter we consider the coupling of a 1d fluid model and a 3d fluid model posed in a domain with anisotropic inclusions the relevance of our approach to realistic cardiovascular simulations is demonstrated by computing blood flows over a model ivc filter

least squares wave equation migration for avp ava inversion we present an acoustic migration inversion algorithm that uses extended double square root wave equation migration and modeling operators to minimize a constrained least squares data misfit function least squares migration we employ an imaging principle that allows for the extraction of ray parameter domain common image gathers cigs from the propagated seismic wavefield the cigs exhibit amplitude variations as a function of half offset ray parameter avp closely related to the amplitude variation with reflection angle ava our least squares wave equation migration inversion is constrained by a smoothing regularization along the ray parameter this approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise incomplete wavefield sampling and numerical operator artifacts these discontinuities should therefore be penalized in the inversion the performance of the proposed algorithm is examined with two synthetic examples in the first

controlling unstructured mesh partitions for massively parallel simulations parallel simulations at extreme scale require that the mesh is distributed across a large number of processors with equal work load and minimum interpart communications a number of algorithms have been developed to meet these goals e g graph hypergraph and coordinate based methods however the global implementation of current approaches can fail on very large core counts which is resolved by combining global and local partitioning using multiple parts per processor the other limitation of graph hypergraph based partitioning is that it uses one type of mesh entity as graph nodes thus the balance of other mesh entities may not be optimal in the case of three dimensional 3 d linear finite element analysis it is common to select mesh regions elements as partition objects in current examples the regions are well balanced up to 163 840 parts for a 1 07 billion element mesh while the vertices have an imbalance which is as high as 19 52 two methods are developed that work in conjunction with graph hypergraph based procedures to provide improved partitions example computations executed on an ibm blue gene p system using up to 163 840 cores demonstrate the usefulness of the procedures particularly for time critical calculations where individual cores may be lightly loaded in terms of the number of mesh entities per core the algorithms presented in this paper reduced the vertex imbalance from 17 8 to 4 97 for a partition with 131 072 parts and accelerated the equation solution phase of the finite element analysis by 10 4

cohomology of abelian matched pairs and the kac sequence the purpose of this paper is to introduce a cohomology theory for abelian matched pairs of hopf algebras and to explore its relationship to sweedler cohomology to singer cohomology and to extension theory an exact sequence connecting these cohomology theories is obtained for a general abelian matched pair of hopf algebras generalizing those of kac and masuoka for matched pairs of finite groups and finite dimensional lie algebras the morphisms in the low degree part of this sequence are given explicitly enabling concrete computations

the influence of the non newtonian properties of blood on the flow in large arteries unsteady flow in a 90 curved tube a numerical and experimental investigation of unsteady entry ow in a 903 curved tube is presented to study the impact of the non newtonian properties of blood on the velocity distribution the time dependent ow rate for the newtonian and the nonnewtonian blood analog uid were identical for the numerical computation a carreau yasuda model was employed to accommodate the shear thinning behavior of the xanthan gum solution the viscoelastic properties were not taken into account the experimental results indicate that signi cant di erences between the newtonian and non newtonian uid are present the numerical results for both the newtonian and the non newtonian uid agree well with the experimental results since viscoelasticity was not included in the numerical code shear thinning behavior of the blood analog uid seems to be the dominant non newtonian property even under unsteady ow conditions finally a comparison between the non newtonian uid model and a newtonian uid at a rescaled reynolds number is presented the rescaled reynolds number based on a characteristic rather than the high shear rate viscosity of the xanthan gum solution was about three times as low as the original reynolds number comparison reveals that the character of ow of the non newtonian uid is simulated quite well by using the appropriate reynolds number 1999 elsevier science ltd all rights reserved

uncertainty quantification in coronary blood flow simulations impact of geometry boundary conditions and blood viscosity computational fluid dynamic methods are currently being used clinically to simulate blood flow and pressure and predict the functional significance of atherosclerotic lesions in patient specific models of the coronary arteries extracted from noninvasive coronary computed tomography angiography ccta data one such technology ffrct or noninvasive fractional flow reserve derived from ct data has demonstrated high diagnostic accuracy as compared to invasively measured fractional flow reserve ffr obtained with a pressure wire inserted in the coronary arteries during diagnostic cardiac catheterization however uncertainties in modeling as well as measurement results in differences between these predicted and measured hemodynamic indices uncertainty in modeling can manifest in two forms anatomic uncertainty resulting in error of the reconstructed 3d model and physiologic uncertainty resulting in errors in boundary conditions or blood viscosity we present a data driven framework for modeling these uncertainties and study their impact on blood flow simulations the incompressible navier stokes equations are used to model blood flow and an adaptive stochastic collocation method is used to model uncertainty propagation in the navier stokes equations we perform uncertainty quantification in two geometries an idealized stenosis model and a patient specific model we show that uncertainty in minimum lumen diameter mld has the largest impact on hemodynamic simulations followed by boundary resistance viscosity and lesion length we show that near the diagnostic cutoff ffrct 0 8 the uncertainty due to the latter three variables are lower than measurement uncertainty while the uncertainty due to mld is only slightly higher than measurement uncertainty we also show that uncertainties are not additive but only slightly higher than the highest single parameter uncertainty the method presented here can be used to output interval estimates of hemodynamic indices and visualize patient specific maps of sensitivities

comparison between a generalized newtonian model and a network type multiscale model for hemodynamic behavior in the aortic arch validation with 4d mri data for a case study abstract blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties thus an appropriate non newtonian model is advisable and we choose a modified version of the rheological model of phan thien and tanner mptt the different parameters of this model derived from the rheology of polymers allow characterization of the non newtonian nature of blood taking into account the behavior of red blood cells in plasma using the mptt model that we implemented in the open access software openfoam numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient we started from a patient specific model which was constructed from medical images exiting flow boundary conditions have been developped based on a 3 element windkessel model to approximate physiological conditions the parameters of the windkessel model were calibrated with in vivo measurements of flow rate and pressure the influence of the selected viscosity of red blood cells on the flow and wall shear stress wss was investigated results obtained from this model were compared to those of the newtonian model and to those of a generalized newtonian model as well as to in vivo dynamic data from 4d mri during a cardiac cycle upon evaluating the results the mptt model shows better agreement with the mri data during the systolic and diastolic phases than the newtonian or generalized newtonian model which confirms our interest in using a complex viscoelastic model

velocity log upscaling based on reversible jump markov chain monte carlo simulated annealing abstractupscaling log measurements acquired at high frequencies and correlating them with corresponding low frequency values from surface seismic and vertical seismic profile data is a challenging task we have applied a sampling technique called the reversible jump markov chain monte carlo rjmcmc method to this problem a key property of our approach is that it treats the number of unknowns itself as a parameter to be determined specifically we have considered upscaling as an inverse problem in which we considered the number of coarse layers layer boundary depths and material properties as the unknowns the method applies bayesian inversion with rjmcmc sampling and uses simulated annealing to guide the optimization at each iteration the algorithm will randomly move a boundary in the current model add a new boundary or delete an existing boundary in each case a random perturbation is applied to backus average values we have developed examples showing that the mismatch between seismograms com

efficient anisotropic adaptive discretization of the cardiovascular system we present an anisotropic adaptive discretization method and demonstrate how computational efficiency can be increased when applying it to the simulation of cardiovascular flow we further propose a new adaptive approach which controls the mesh adaptation procedure to maintain structured and graded elements near the wall resulting in a more accurate wall shear stress computation to perform mesh adaptation for hemodynamic flows a single mesh metric field is constructed for the whole cardiac cycle two alternative approaches are applied one in which a metric field is constructed based on the average flow whereas in the other approach the metric field is obtained by intersecting metric fields computed at specified instants in the cycle we apply the method to the case of a 3d branching vessel model the efficiency of our approach is measured by analyzing the wall shear stress a challenging but important quantity in the understanding of cardiovascular disease the general anisotropic adaptivity based on metric intersection achieves over an order of magnitude reduction in terms of degrees of freedom when compared to uniform refinement for a given level of accuracy

analysis of a stabilized finite element method for stokes equations of velocity boundary condition and of pressure boundary condition abstract in this paper a new pressure stabilized finite element method is analyzed for solving the stokes equations the key feature of the method is using the curl integral instead of the standard dirichlet integral and using the pressure stabilization instead of the inf sup condition thus the method is very flexibly applicable to two problems of stokes equations in terms of velocity and pressure with either pressure dirichlet boundary condition or velocity dirichlet boundary condition for both stokes problems the finite element scheme and the finite element space of velocity are the same and one where only the finite element spaces of pressure have small differences a general analysis of stability and error estimates is developed and applications to both stokes problems are further analyzed the method covers the low regularity solution of very weak non h 1 space solution of stokes problem of pressure dirichlet boundary condition as well as higher regularity solutions of stokes problems of either pressure dirichlet boundary condition or velocity dirichlet boundary condition numerical results are presented to illustrate the performance of the method and to confirm the theoretical results

iterative asymptotic inversion in the acoustic approximation we propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation for this purpose we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods the different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image in the linearized inversion we use the background velocity model obtained by velocity analysis we determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model because the inverse operator is not exact and because the source and station distribution is limited the first iteration of our asymptotic inversion technique is not exact we improve the images by an iterative procedure since the background velocity does not change between iterations there is no need to retrace rays

a unified variational approach for coupling 3d 1d models and its blood flow applications in this work we propose an extended variational formulation in order to handle the problem of the flow of an incompressible fluid in compliant vessels with discontinuous fields this approach makes possible to tackle in a consistent variational manner problems like the coupling between models of different dimensionality the main ideas of the work are presented for a simple heat transfer problem and then are used in the context of modelling blood flow in large vessels a computational implementation of the proposed formulation is also shown and discussed by presenting examples of practical applications

numerical study of shear dependent non newtonian fluids in compliant vessels the aim of this contribution is to present recent results on numerical modelling of non newtonian flow in compliant stenosed vessels with application in hemodynamics we consider two models of shear thinning non newtonian fluids and compare them with the newtonian model for the structure problem the generalized string equation for radial symmetric tubes is used and extended to a stenosed vessel the global iterative approach to approximate the fluid structure interaction is used finally we present numerical experiments for some non newtonian models comparisons with the newtonian model and the results for hemodynamic wall parameters such as the wall shear stress and the oscillatory shear index

extensions of hopf algebras and lie bialgebras let f g be finite dimensional lie algebras over a field of characteristic zero regard f and g the dual lie coalgebra of g as lie bialgebras with zero cobracket and zero bracket respectively suppose that a matched pair f g of lie bialgebras is given which has structure maps then it induces a matched pair u f ug of hopf algebras where u f is the universal envelope of f and ug is the hopf dual of ug we show that the group opext u f ug of cleft hopf algebra extensions associated with u f ug is naturally isomorphic to the group opext f g of lie bialgebra extensions associated with f g an exact sequence involving either of these groups is obtained which is a variation of the exact sequence due to g i kac if g g g there follows a bijection between the set ext u f ug of all cleft hopf algebra extensions of u f by ug and the set ext f g of all lie bialgebra extensions of f by g

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

coupled fluid structure interaction hemodynamics in a zero pressure state corrected arterial geometry abstract hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall a numerical procedure for solving the fluid structure interaction problem encountered in cardiovascular flows is presented we consider a patient specific carotid bifurcation geometry obtained from 3d reconstruction of in vivo acquired tomography images which yields a geometrical representation of the artery corresponding to its pressurized state to recover the geometry of the artery in its zero pressure state which is required for a fluid structure interaction simulation we utilize inverse finite elastostatics time dependent flow simulations with in vivo measured inflow volume flow rate in the 3d undeformed artery are performed through the finite element method the coupled momentum method for fluid structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain to demonstrate the importance in recovering the zero pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero pressure state corrected geometric configurations of the carotid bifurcation the most important resulting effects in the hemodynamic environment are evaluated our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions

helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear abstract the main purpose of the study is to verify if helical flow might be a surrogate marker of the exposure to disturbed shear in normal carotid bifurcations based on hemodynamic simulations data of 50 carotid bifurcations we defined appropriate helicity based bulk flow descriptors and multivariate linear regression analysis was performed to assess the potential for a combination of helicity based indicators in describing the exposure to disturbed shear to select the optimal combination of helicity based descriptors in the regression model the akaike information criterion was applied the identified statistical model is composed of two bulk flow descriptors proposed here to quantify helicity intensity and the balance between counter rotating helical flow patterns in the flow field the model revealed the existence of a significant relationship with adjusted squared pearson s correlation coefficient in the range 0 4 0 7 p

adjoint based inverse analysis of windkessel parameters for patient specific vascular models a human circulatory system is composed of more than 50 000 miles of blood vessels such a huge network of vessels is responsible for the elevated pressure values within large arteries as such modeling of large blood arteries requires a full modeling of circulatory system this in turn is computationally not affordable thus a multiscale modeling of the arterial network is a necessity the multiscale approach is achieved through first modeling the arterial regions of interest with 3d models and the rest of the circulatory network with reduced dimensional reduced d models then coupling the multiscale domains together though reduced d models can well reproduce physiology calibrating them to fit 3d patient specific fluid structure interaction fsi geometries has received little attention for this reason this work develops calibration methods for reduced d models using adjoint based methods we also propose a reduced modeling complexity rmc approach that reduces the calibration cost of expensive fsi models using pure fluid modeling finally all of the developed calibration techniques are tested on patient specific arterial geometries showing the power and stability of the proposed calibration methods

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

a hyperbolic system of equations of blood flow in an arterial network we study a coupled system of the navier stokes equation and the equation of conservation of mass in a network the system models the blood circulation in arterial networks a special feature of the system is that the equations are coupled through boundary conditions at joints of the network we use a fixed point method to prove the existence and uniqueness of the classic solution to the initial boundary value problem and discuss the continuity of dependence of the solution and its derivatives on initial boundary and forcing functions and their derivatives we develop a numerical scheme that generates discretized solutions and we also prove the convergence of the scheme

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

bayesian linearized avo inversion a new linearized avo inversion technique is developed in a bayesian framework the objective is to obtain posterior distributions for p wave velocity s wave velocity and density distributions for other elastic parameters can also be assessed for example acoustic impedance shear impedance and p wave to s wave velocity ratio the inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the zoeppritz equation the solution is represented by a gaussian posterior distribution with explicit expressions for the posterior expectation and covariance hence exact prediction intervals for the inverted parameters can be computed under the specified model the explicit analytical form of the posterior distribution provides a computationally fast inversion method tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero with realistic noise levels acoustic impedance was the best determined parameter

augmented lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three dimensional finite element simulations of blood flow in three dimensional blood flow simulations of the cardiovascular system velocity and pressure fields in the computational domain are highly affected by outlet boundary conditions this fact has motivated the development of novel methods to couple three dimensional computational domains with one dimensional numerical models or alternatively with zero dimensional or one dimensional analytic models in all such methods described to date whether they are explicit or implicit the relationship between flow and pressure at the outlet boundary is enforced weakly this coupling does not include any constraints on the shape of the velocity profiles nor on the distribution of pressure at the interface as a result there remain some classes of problems that are at best difficult to solve and at worst intractable with current numerical methods for simulating blood flow these include problems with significant flow reversal during part of the cardiac cycle or geometric complexity in the proximity of the outlet of the computational domain we have implemented a novel method to resolve these challenging problems whereby an augmented lagrangian method is used to enforce constraints on the shape of the velocity profile at the interface between the upstream computational domain and the downstream analytic domain these constraints on the shape of the velocity profile are added to the coupled multidomain method in order to implicitly couple the computational domain with downstream analytic models in this study an axisymmetric profile is imposed after ensuring that each constrained outlet boundary is circular we demonstrate herein that including constraints on the shape of the velocity profile does not affect velocity and pressure fields except in the immediate vicinity of the constrained outlet boundaries furthermore this new method enables the solution of problems which diverged with an unconstrained method

finite element simulation of blood flow in the cerebral artery abstract the purpose of the paper is to develop a numerical simulation system for the clinical study of a cerebral aneurysm this paper presents the system which consists of three processes pre processing numerical simulation and post processing in the pre processing process the three dimensional solid model was constructed from the computed tomography ct angiography raw data the finite element method fem is used in order to simulate flow in a complicated geometry the simulation is conducted to investigate hemodynamics of blood flow in the carotid siphon under real flow conditions measured by doppler ultrasound velocimetry technique the results are visualized for a better understanding of the flow characteristics such as distributions of the flow pattern and the wall shear stress in the carotid siphon

two ways to quantify uncertainty in geophysical inverse problems we present two approaches to invert geophysical measurements and estimate subsurface properties and their uncertainties when little is known a priori about the size of the errors associated with the data we illustrate these approaches by inverting first arrival traveltimes of seismic waves measured in a vertical well to infer the variation of compressional slowness in depth first we describe a bayesian formulation based on probability distributions that define prior knowledge about the slowness and the data errors we use an empirical bayes approach where hyperparameters are not well known ahead of time e g the variance of the data errors and are estimated from their most probable value given the data the second approach is a non bayesian formulation that we call spectral in the sense that it uses the power spectral density of the traveltime data to constrain the inversion e g to estimate the variance of the data errors in the spectral approach we vary assumptions made about the characteristics of the slowness signal and evaluate the resulting slowness estimates and their uncertainties this approach is computationally simple and starts from a few assumptions these assumptions can be checked during the analysis on the other hand it requires evenly spaced traveltime measurements and it cannot be extended easily e g to data that have gaps in contrast the bayesian framework is based on a general theory that can be generalized immediately but it is more involved computationally despite the conceptual and practical differences we find that the two approaches give the same results when they start from the same assumptions the allegiance to a bayesian or non bayesian formulation matters less than what one is willing to assume when solving the inverse problem

calculations of some groups of hopf algebra extensions w let us recall the theory of group extensions with abelian kernels mc x chap iv let g be a group and m a g module the equivalence classes of group extensions m a e a g giving rise to the g module action on m form a group with respect to the baer sum furthermore this group is 2 isomorphic to the cohomology group h g m the theory is extended to the theory of hopf algebra extensions which w x are abelian in some sense h s we restrict our interests to hopf algebra extensions over a field k which are of the form

robust and accelerated bayesian inversion of marine controlled source electromagnetic data using parallel tempering bayesian methods can quantify the model uncertainty that is inherent in inversion of highly nonlinear geophysical problems in this approach a model likelihood function based on knowledge of the data noise statistics is used to sample the posterior model distribution which conveys information on the resolvability of the model parameters because these distributions are multidimensional and nonlinear we used markov chain monte carlo methods for highly efficient sampling because a single markov chain can become stuck in a local probability mode we run various randomized markov chains independently to some extent this problem can be mitigated by running independent markov chains but unless a very large number of chains are run biased results may be obtained we got around these limitations by running parallel interacting markov chains with annealed or tempered likelihoods which enable the whole system of chains to effectively escape local probability maxima we tested this approach using a transdimensional algorithm where the number of model parameters as well as the parameters themselves were treated as unknowns during the inversion this gave us a measure of uncertainty that was independent of any particular parameterization we then subset the ensemble of inversion models to either reduce uncertainty based on a priori constraints or to examine the probability of various geologic scenarios we demonstrated our algorithms fast convergence to the posterior model distribution with a synthetic 1d marine controlled source electromagnetic data example the speed up gained from this new approach will facilitate the practical implementation of future 2d and 3d bayesian inversions where the cost of each forward evaluation is significantly more expensive than for the 1d case

a bayesian inference approach to identify a robin coefficient in one dimensional parabolic problems this paper investigates a nonlinear inverse problem associated with the heat conduction problem of identifying a robin coefficient from boundary temperature measurement a bayesian inference approach is presented for the solution of this problem the prior modeling is achieved via the markov random field mrf the use of a hierarchical bayesian method for automatic selection of the regularization parameter in the function estimation inverse problem is discussed the markov chain monte carlo mcmc algorithm is used to explore the posterior state space numerical results indicate that mrf provides an effective prior regularization and the bayesian inference approach can provide accurate estimates as well as uncertainty quantification to the solution of the inverse problem

prior information and uncertainty in inverse problems solving any inverse problem requires understanding the uncertainties in the data to know what it means to fit the data we also need methods to incorporate data independent prior information to eliminate unreasonable models that fit the data both of these issues involve subtle choices that may significantly influence the results of inverse calculations the specification of prior information is especially controversial how does one quantify information what does it mean to know something about a parameter a priori in this tutorial we discuss bayesian and frequentist methodologies that can be used to incorporate information into inverse calculations in particular we show that apparently conservative bayesian choices such as representing interval constraints by uniform probabilities as is commonly done when using genetic algorithms for example may lead to artificially small uncertainties we also describe tools from statistical decision theory that can be used to characterize the performance of inv

iterative estimation of reflectivity and image texture least squares migration with an empirical bayes approach in many geophysical inverse problems smoothness assumptions on the underlying geology are used to mitigate the effects of nonuniqueness poor data coverage and noise in the data and to improve the quality of the inferred model parameters within a bayesian inference framework a priori assumptions about the probabilistic structure of the model parameters can impose such a smoothness constraint analogous to regularization in a deterministic inverse problem we have considered anempirical bayes generalization of the kirchhoff based least squares migration lsm problem we have developed a novel methodology for estimation ofthe reflectivitymodel andregularization parameters using a bayesian statistical framework that treats both of these as random variables to be inferred from the data hence rather than fixing the regularization parameters prior to inverting for the image we allow the data to dictate where to regularize estimating these regularization parameters givesusinformation about the degree of conditional correlation or lack thereof between neighboring image parameters and subsequently incorporating this information in the final model produces more clearly visible discontinuities in the estimated image the inference framework is verified on 2d synthetic data sets in which the empirical bayes imaging results significantly outperform standard lsm images we note that although we evaluated this method within the context of seismic imaging it is in fact a general methodology that can be applied to any linear inverse problem in which there are spatially varying correlations in the model parameter space

an iterative inversion of back scattered acoustic waves the application of the born approximation to the scattered wave field followed by a wkbj and far field approximation on the propagation green s function for a slowly varying background medium leads to a simple integral relation between the density and bulk modulus anomalies superimposed on the background medium and the scattered wave field an iterative inversion scheme based on successive back projections of the wave field is used to reconstruct the two acoustic parameters the scheme when applied to data generated using the direct integral relation shows that the variations of the parameters can be reconstructed the procedure is readily applicable to actual data since every iterative step is essentially a prestack kirchhoff migration followed by the application of the direct born approximation and far field operator

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100