DE102005035181A1 - Blood flow representation method involves representing three dimensional flow data and wall loadings in blood vessels using lattice-Boltzmann method - Google Patents

Abstract

3D grey-value data from MRT or CT are binary segmented using suitable algorithms. 3D vessel shapes are then used for a resolved numeric simulation of the flow in cubic calculated grids with lattice Boltzmann resolution. The required boundary conditions are supplied from databases or individual non-invasive measurements. Wall dynamics can be simulated as required. Items, such as implants etc., can be identified. An independent claim is included for a system for use with the above method.

Description

The The invention relates to a method for displaying time-dependent, spatial three-dimensional flow data in fluid-carrying Vessels under Using the Lattice-Boltzmann method, in the three-dimensional Tissue structure data on regular data grids (Geometry voxel data) of the vascular area to be displayed including its Wall, i. their density data representing their geometric structure, are used and also regular isotropic computational grid (Voxel grid) for the vessel representation and for the determination of the flow pattern selected after which the course of the fluid flow in temporal steps is determined.

The Determination of a flow field, especially in a vascular system, is very expensive. For the hydrodynamic determination must be the Geometry of the perfused Area, the inlet and outlet boundary conditions and the conditions on its walls be given. The inlet and outlet boundary conditions include time-dependent Details of the pressure and, as far as known, the speeds and in the case of turbulent flows even to the tensions. This information must be the spatial and temporal dependence the flow contained in sufficient accuracy.

Bloodstreams through Veins, especially aortic branches and other larger arteries, are from one strong pulsating component and complex flow patterns near of bifurcations, curvatures as well as Malformationen (extensions or also constrictions) coined / shaped. The vessel walls are exposed to rapid elastic deformations in the cardiac pulse rhythm, what kind of hemodynamics depending on the position and condition of the vessels one play an essential role. The modeling of the mechanical Properties of these vessel walls is not unique and it is particularly difficult to individual and introduce site-specific corrections, since the coupled determination the wall and blood dynamics much more complex than the treatment of each of the two dynamic Process alone is and because of the nature of vessel walls generally difficult, yet open research area. The verification by direct measurements is also by the spatially and temporally very high required resolution difficult.

in the Computational Fluid Dynamics (CFD) available standard methods for the direct numerical simulation (DNS) of incompressible flows, mostly using finite volume method (FVM), as well CSM method (computational structure mechanics) under application of finite element method (FEM), where a discretization is performed with unstructured calculation grids of the flow volume and the vessel walls, enable the implementation resolved 3D simulations of the flow from larger blood vessels below Use of CT data in particular. The results of such simulations are detailed dynamic information about flow disturbances and wall loading, the in the medical data themselves are not included. The execution of such calculations with the named procedure places high demands on the examining Persons and is extraordinary time consuming, it may e.g. For a geometry take a week. A simplification of the simulation methods always remains due to the indispensable far-reaching model assumptions on specific vessels, simple Geometry of malformations and narrow parameter ranges severely limited.

With much more elaborate procedures based on the Doppler or the time-of-flight principle and at the same time on the general mathematical apparatus of tomography be based such as. Phase-contrast MRI or e.g. Doppler ultrasound velocimetry, can also individual speed components and average speeds, So a part of the relevant kinetic information, added become. The resolution is in most cases low, so that only the total volume that flows through a given lumen per unit time, with sufficient reliability can be measured. Local disturbances, strong Gradients and turbulence can not quantitatively reliable be identified, although their traces and influences with some methods can be discovered. However, limited 3D information with good resolution also provides the non-invasive DSA (Digital Substraction Angiography) method, a standard procedure for the determination of the kinetic blood flow information before and during the Vascular Surgery. In contrast, dynamic information, i. the time-dependent force balance, at Blood vessels either only indirectly or as with blood pressure also directly but then invasive and only for one Part of the forces be measured. No currently available measuring method, neither indirect still in situ, is able to perform 3D-resolved dynamic measurements too deliver.

In blood vessels, the main medical interest is not so much the velocity distribution as the associated distribution of pressure and shear stress on the vessel walls. It has become well known in the art that large variations in shear stresses lead to restructuring, remodeling, and possibly damage to the vessel walls, for example, in connection with sclerosis, stenosis, high blood pressure, and the like hamper the lives of those affected and threaten them directly. For the diagnosis of these types of health threats, however, the analysis of the velocity distributions themselves can be well used. More importantly, the role of pressure (eg in aneurysms obviously a major factor that can lead to rupture) and the vertebral field is little known and should therefore be easier and better to analyze than before.

Increasingly In fluid mechanics, the determination of complex flows is under Using the Lattice Boltzmann method (LBM) performed, the on a regular grid structure based. The cells of such a grid can by means of high performance computers be processed comparatively quickly. So for example by T. Zeiser in "Numerische Simulation of reactive flows in complex geometries with the Lattice Boltzmann method ", LSTM Annual Report, 2001 a geometry modeling presented on a picture of real samples from tube bundle reactors using 3D X-ray CT based on a Cartesian voxel grid.

In the DE 100 50 063 A1 For example, a method of the type mentioned above has been proposed for the computer-aided determination of a flow field in the respiratory tract of an animal in order to determine the flow properties of the inhaled and exhaled air through the nasal cavity of a patient and, in the case of a structural change in the airway, the expected flow characteristics within the altered one Airway to determine. The walls of the nasal cavity are recognized by segmentation techniques to coherent CT image elements to the accuracy of the voxel geometry. For each CT image, a Cartesian grid is formed, thus dividing the image into individual grid elements, distinguishing among these grid elements located within the interior space defined by the structure, ie in the airway, and determining a flow field for these grid elements. From the given description of the method it can be concluded that only a simple, voxel-based treatment of the adhesive edge conditions on the walls of the respiratory tract, for example with the bounce-back method, comes into question and the curvature of the walls only gradually, the resolution of the CT data can be displayed accordingly. Especially at higher flow rates, this becomes a major source of error. At any rate, in medical practice, the entire method for simulating the breathing process is currently not applicable, since the calculation times required for the reliable calculation of the relatively fast air flow (high Reynolds numbers) are still very great.

to Treatment of cerebral aneurysms with a porous stent is by B. Chopard, "A Lattice Boltzmann Study of Blood Flow in Stented Aneurysms ", SCS Seminar - Computational Hemodynamics, university Amsterdam, October 13, 2003 as a measure for the flow reduction a presentation the bloodstream been proposed by the Lattice-Boltzmann method. there but it was a two-dimensional simulation, the for none real clinical application a sufficient capture of the individual present vessel geometry allows and even fundamental ones Flow effects, that are related to the three-dimensional nature of blood flow, wrong estimates. So far, in applications of the Lattice-Boltzmann method on bloodstreams but only a single cuboid Grid and a simple calculation scheme used for the simulation of the flow processes Service.

The US 2003/0060988 A1 himself with the analysis of the filling in molds, the Lattice Boltzmann method due to the fast computation time and their suitability for a big Number of discretization points is applied. The one described therein Calculation method, however, is only for flows with relatively low Speeds well suited, e.g. due to the smaller number of Degrees of freedom and the derivation of the boundary conditions, it is very complicated and it is not suitable in itself, advanced To treat blood rheology models.

Especially Cardiac, vascular and neurosurgery makes of newer technical developments and ever more precise, more efficient, preferably minimally invasive, procedures, To evaluate and interpret three-dimensional (3D) medical data. At the moment for the clinical practice usual Tomo graphiedaten, which usually on ultrasound, magnetic field and X-ray measurements (However, the invention should not be limited to this). contain density information, which afterwards by so-called segmentation predominantly converted into geometric information. The resolution of this Procedure improves in the given order as the minimum resolvable Length proportional to the radiation wavelength is. At present an isotropic resolution of approx. 0.4 mm can be achieved with multilayer X-ray CT, a little coarser and yet comparable (about 1 mm) resolution with MRI. This means, that vessels with lumen diameters from at least 1-2 or 3-4 mm can be detected. The relationship between the resolution, the for the Detecting a vein is sufficient, and that necessary for a determination of the flow dynamics and especially the wall load (by measurements or simulations) is needed at least 1:10.

It is not possible yet detailed analyzes of the bloodstream and its relationship with the development of vascular anomalies only by medical measurement perform. On the other hand, has a variety of medical examinations Various aspects have been identified in which changes in the blood flow course the Provoke formation and development of vascular malformations. For understanding and for the treatment of vascular damage are detailed knowledge about the blood flow course and the influence of mechanical loads on the deformation is more important Blood vessels necessary. Desirable would be therefore a process that simultaneously efficient and easy flow conditions emulate and detailed hemodynamic information can create.

Around to successfully integrate individually specific features of the vessel geometry, is from Taylor, M.T. Draney, J.P. Ku, D. Parker, B.N. Steele, K. Wang, and C.K. Zarins, "Predictive medicine: computational techniques in therapeutic decision making ", Computer Aided Surgery 4, 231-247, 1999 a method has been proposed with the transverse diameter of the lumen of larger arteries using MRI tomography data automatically determines this information and for 1D model calculations of the Blood flow (only along the vessel axis) through These arteries are used even if implants (including bypasses) are present are. So far, this method is at AA (ascending aorta) in animals and humans have been tested, so in a jar, for once just and is long. Comparisons with MRI-based anemometry, published in B.N. Steele, J.Wan, J.P. Ku, T.J.R. Hughes, and C.A. Taylor, "In Vivo Validation of a one-dimensional finite element method for predicting blood flow in cardiovascular bypass grafts ", IEEE Trans. Biomed. Eng. 50 (6), 649 to 655, 2003 and with detailed 3D numerical simulations, released in V. Favier and C.A. Taylor, "Image-based modeling of blood flow in a procine aorta bypass graft ", Ann. Res. Briefs, Center for Turbulence Research, Stanford Univ., 2002 have shown that some averaged sizes good can be reproduced that the spatial Distribution of mechanical stresses and blood velocities however, can not be predicted.

The Simulation of blood flow with consideration real vessel geometries, including, for example of implants such as stents or aneurysms, and their networking See, for example, M.S. Juchems, D. Pless, T.R. Fleiter, A. Gabelmann, F. Liewald, H.J. Brambs, A.J. Aschpoff, "Blood Flow Simulations Using Computational Fluid Dynamics on aortic aneurysms reconstructed from CT data before and after Stent-Graft Implantation ", Fortschr. Röntgenstr. 176, 56 to 61, 2004) makes use of CT data of at least three different evaluation methods including visualization. The declared ultimate goal of developing a method for simulation-based medical Planning is hardly achievable in this way.

The Discretization of the perfused 3-D numerical simulation (3D DNS) volume for CFD applications finds either on structured or on unstructured grids instead of. The choice of the grid type has a great influence on the complexity, the accuracy and the efficiency of the simulations. Among other things, it means one Selection of consistent discrete representations for the volume on the one hand and for its Edge on the other hand, as well as the coupling of these representations. For blood vessels the geometry is relatively complicated and the ratio (in dynamically relevant measuring units) from wall surface to volume is relatively high, so that the need more efficient and more reliable Coupling method pronounced is.

creating structured Lattices based on, for example, the Lattice-Boltzmann method are created after a (coarse) a priori distribution of the total volume in neighboring or partially overlapping Individual areas, each one simple body, e.g. a cubic Cube, are diffeomorphic. This simple body comes with a regular, mostly orthogonal grid (3D spatial) covered. For such grids are highly accurate and highly efficient algorithms for Available, like e.g. FFT, compact finite differences, and polynomial decompositions high order, e.g. in the construction of p-FEM or spectral element method be used. Therefore but is the structure of structured computing grids for complex Geometries very complicated or even impossible without simplifying assumptions. On unstructured grids, however, is the structure of the grid largely automatable, since the restrictive distribution of the 3D space can be avoided. Thereby can Even very complex geometries are treated. However, this leads in the end, to higher Cost (partly because of low accuracy, because of higher algorithmic Complexity, etc.) during the simulation.

The identification of the flow area in hemodynamic simulations in blood vessels is based on an identification of the vessel walls, in particular CT data, which represent gray value data on a simple structured grid and whose processing is based on the assumption of their sufficient resolution and in most cases also of their spatial smoothness , Standard methods of imaging, such as the marching cubes algorithm, can very quickly create a discretized, approximate representation of the wall geometry, for example as unstructured 2D grids, from these data. The Qua This representation is necessarily a function of the CT data quality, eg a bias in the CT scan will require a local adaptive thresholding method such as RC Gonzalez and RE Woods, Digital Image Processing, Prentice Hall, 2002. The resulting 2D triangulation of the wall surfaces can already be used directly on DNA on unstructured grids for automatic 3D mesh generation. For structured 3D grids, triangulation is a stand-alone object whose relationship to the 3D computational grid can be shaped by coupling schemes of various types, accuracy, complexity, and efficiency. Unstructured grids are adapted to the edge geometry and therefore have to change with a movement of the walls, resulting in complex global 3D calculations, the need to control the degree of deformation, possibly for the generation and deletion of grid elements and the emergence of multiple sources of error with these Operation connected leads.

It But there is also a practical way to use the 2D grid a Lagrangian To change the process at each time step, without the 3D computational grid to have to modify. It is noteworthy that one such kind of coupling between a fixed (Eulerian) 3D grid and a Lagrangian "wall grid" originally in an early one Peskin's attempt in 1974 to numerically record cardiac dynamics emerged, in which he called the moving walls of the heart as internal Limits used. Nevertheless, almost all previous CFD applications are in the field of hemodynamics, with the exception of the works of Peskin and his school, far from this efficient and natural Approach stayed away. Such approaches bring with it a high Potential for simplification, accuracy improvement and acceleration the calculation method, especially with structured computing grids, because the coupling of the two coupled grids is easier to calculate is.

Of the mentioned above 3D Euler-2D Lagrange approach was named "immersed boundary method "technical versatile. In particular, the original was theoretical limitation accuracy to first order through improvements to the algorithm solved from a practical point of view, so that entire process achieves effective second-order convergence (Lai & Peskin (1999)). A systematic Approach for coupling the two types of grids (fixed 3D computational grid for the Flow solver and 2D grid for moving or stationary surfaces complex shape, which can also be applied to blood vessel walls) has been developed and tested in recent years under the name "immersed interface method". It is based on a precise as possible and sharp representation of the boundary between the fluid and the surrounding Medium. By contrast, the limit is the immersed boundary method deliberately and controlled on a "thin layer smeared. "Algorithms Both types are related to different discretization procedures (Finite differences, FVM, FEM) for The 3D computing grid has been developed and tested, but not with the Lattice-Boltzmann method. Your stability and efficiency, in particular even on parallel computers, has already been demonstrated in the literature Service.

The Determining the sizes that it from the pressure and velocity fields calculated by the simulation to calculate and then visualizing and evaluating is mostly easy and fast, although it is useful in calculating spatial derivatives (e.g. needed in the representation of tensions and vortices) insufficient resolution to instabilities can come. To suppress these problems, are temporal and spatial Averaging or smoothing (Filtering) used. Although there are a variety of visualization software tools, which allow to represent 3D flows stands rarely, at least as far as commercial simulation software is concerned, also the possibility to disposal, smoothing operations to perform with a mouse click.

More difficult is the transmission and multiple visualizations (from different angles) the big Datasets of DNA. As with the visualization Often practiced by turbulence, the overhead in visualization can be be reduced to a technically meaningful level by the already calculated sizes the visualization is reduced (projected, averaged, strobed, etc.). In the literature about Hemodynamic CFD are such considerations unfortunately not yet known.

Of the Invention is based on the object, a method for representation of three-dimensional, time-dependent or time-averaged medically usable data, the detailed analysis of the bloodstream even in vascular anomalies as well as considering the pulsations - both the entire blood stream as well as possibly the affected vessel parts themselves - allows and also with complex geometry is efficient feasible. This task is by the invention in a method having the features of the claim 1 solved. Advantageous process variants are the subject of the dependent claims.

In the method according to the invention for the representation of three-dimensional flow data in fluid-carrying vessels using the Lattice-Boltzmann method, three-dimensional geometric data (geometry-voxel data) of the vascular area to be displayed, including its wall, generated using a regular, isotropic grid are thus used. The same data grid or fully automatically generated regular isotropic computing grid (voxel grid) will be selected for the vessel representation and for the determination of the flow pattern and the course of the fluid flow is determined in temporal steps. One or more vessel sections to be examined are selected, further a region of the vessel is selected from the three-dimensional geometric data containing the vessel section (s) and in which the flow conditions are to be displayed. The three-dimensional geometric data representing the vessel walls are segmented, the inlet and outflow edge surfaces of the vessel region are determined, and the screen grid size of the computing grid is selected depending on the dimensions of the selected vessel region and the parameters of the flow therein. The computational grid is disassembled and the parts of the grid are eliminated that do not contain any traversed or incoming voxels. The time determination of the fluid flow is carried out until the flow representation is sufficiently accurate. The presentation, ie, the intersecting characteristics of the flow and the mechanical loading of the vessel walls are determined from the flow solution and the results in data structures optimized for imaging or archiving are transmitted and stored.

The Intersection of the vessel volume with the edge of the chosen one Area is divided into inlet and outlet edge areas and for every one of them single, uninterrupted surface section appropriate types of constraints are set. These need temporally and spatially resolution Edge data. Corresponding information can be obtained from individual measurements calculated on the patient or even existing databases be removed. There are a variety of published procedures for the determination, signal-technical and statistical post-processing, Modeling and application of such data. It will also be suitable body forces assumed that determine the pulsating nature of the bloodstreams studied and based on physiological measurements.

The Grid grid size of the grid becomes dependent from the dimensions of the selected vessel area selected and is not necessarily to the size of the geometry data bound. In the method according to the invention are the possibility the local refinement as well as the coarsening of the lattice step based on automatic area decomposition and geometry analysis as well an indication of the expected flow rates provided.

For the temporal Determination of fluid flow is a stationary (time independent) solution for some applications Flow task sufficient, to influence diagnostic statements. Such a solution is easier and faster than a time-periodic (pulsating) solution. The complex boundary of the flow area affected decisively the entire pressure and mass flow distribution and is so in all cases determined first. To speed up this simulation phase become a linearization of dynamics (Stokessche rather than Navier-Stokes equation) and, if appropriate, one for LBM specialized multigrid method (Multigrid) used. If desired, it then becomes a time-dependent one solution calculated by specified, synchronized time-periodic Pressure differences at the inlet and outlet edges and volumetric forces in the Interior of the flow area is driven. In this simulation phase, the numeric Iterations the physical meaning of time steps. For LBM are 100 to 800 steps per pulse period depending on accuracy requirements sufficient. For the Circulation of an adult human is the average duration a pulse period of about 0.8 seconds, so that each (explicit) time step of the LBM solver about 1 to 10 milliseconds. The convergence of all those interested Sizes up a time-periodic course is always measured and the simulation then interrupted, if a sufficient approximation to a periodic Behavior is received or a time limit is exceeded. Still at Simulation start is automatically announced to the user, which Number of simulated pulse periods corresponding to this time limit and whether this is sufficient according to existing rules and heuristics, to the desired Sizes with the desired Accuracy calculated. Thus, an optimization of the computational effort before the possibly elaborate simulation allows.

The inventive method can according to different Alternatives can be done either fast or with high precision. It can, for example moving walls be simulated, the process more accurate, but much more complicated than when assuming rigid walls. For smaller and especially in intracranial (located within the cranial cavity) Vessels as well For example, if the nature of the vessel walls is unknown, may the computation of the wall movement be dispensed with.

An alternative deployment scenario is vascular movement, including, but not only determined by the wall pulsation, to determine from multiple and thus time-resolved tomographic images, rather than having to recalculate them as part of the modeled and simulated dynamics at each time step of the simulation. In this scenario, therefore, the coupling between the fluid and the wall is one-sided: The wall movement induces a flow from which the wall load can then be calculated, but this load is not considered to drive the further wall movement and no wall movement is simulated since it is off the recording sequences is already known.

If Wall shearing stresses must be determined, the walls must be displayed with high accuracy become, for what Second-order LBM boundary conditions known from the literature can be used. These and other, alternative calculation methods in the wall area are more complicated as the simple bounce-back method (BBL) and perform in the Contrary to him to a small "mass loss" during the simulation. But with sufficient resolution, neither this loss nor the error in the discretized variant of the incompressibility of the flow of concern. at certain issues, e.g. Treatments of intracranial Aneurysms or in analyzes of the flowability of whole branches the vascular system, can resort to the BBL become.

Mostly become the illustrated vessel sections a vessel structure part contain. This is understood to mean in particular deformations and impurities For example, implants or geometry changes such as aneurysms and Stenoses. these can spatial be present or synthesized based on stored data records and into the vessel representation be installed to the corresponding resulting flow and / or pressure conditions to determine. Conversely, you can also in reality existing vascular deformations virtually from the vessel representation be removed, for example, the efficiency and the long-term To investigate effects of an extension of the flow-through lumen. The latter is suitable, e.g. in wreath vessel operations for relief of stenosis or "clipping" of aneurysms and of arterial branches in neurosurgery.

The Use only of regular 3D data grids in the method according to the invention leads to a leap in the efficiency and standardization of simulation-based investigations. This is based on the following characteristics: the same and as sufficiently fine-meshed raster grid directly or after a fully automatic and very fast mapping or interpolation in the coordinate direction, which is the main thing of the recording device, on collinear, partially overlapping lattices used with cubic voxels. These voxel meshes can then for the Determination of the course of the flow be used immediately. A specification of the figure in dependence from the size, curvature and Branching of the considered vessel structure is part of the process. It is not a complex geometry-adapted generation of unstructured 3D computing grids required to get all the details the vessel geometry with good resolution display. This has dramatic reductions in complexity and the Total duration of the simulation result.

The Reconstruction of the vessel geometry refers to several parts of the room, which are in their distance from each other the examined vascular malformation as well also in each required resolution and modeling precision differ. The reconstruction is fast on current computers, but can only be partially automated. The dimension of the to be examined vessel section, e.g. the extent of a malformation itself and the space parts of Clinical interest in its environment is due to individual differences in the vessel geometry and the type and cause of the disease codetermined and can be determined interactively.

Around a robust flow simulation with the described kind of regular grids at all too will allow for expected geometries an adapted one Variant of the Lattice Boltzmann method used, at the computational grid is disassembled and eliminates the parts of the grid which do not contain any perfused or infused voxels. Compared On the one hand, with CFD standard methods, this also results in a high level of efficiency on highly parallel computer architectures and on the other hand less dependence from the complexity achieved the geometry and the computing grid.

Of the entire work process can be performed on the basis of measurement data, the exclusively with Minimally invasive and non-invasive procedures are detectable.

The Method provides four-dimensional (temporal and 3D spatial) resolution Predictions about the Course of blood flow through arteries nearby of typical malformations such as stenoses or aneurysms. Thereby can occurring mechanical loads and the relationship between Vessel geometry, hemodynamics and wall load, in turn, through physiological wall modeling the vessel geometry affected examined and better predicted.

The inventive method can at the individualized investigation of possible mechanical causes, which are connected to the exact spatial structure of the blood vessels of a patient, for the development of vascular malformations and its further development. Because of its high efficiency, diagnostics and prognosis can be individually supported for multiple patients on a single day of hemodynamic data, which is significantly more extensive and detailed compared to direct measurements and, moreover, does not require additional manipulation of the patient. It is a regular clinical use of the flow studies and also subsequent checks of examination data possible.

The direct use of tomography data in regular voxel format allows a simple and reliable investigation of the effect already in the body implants (stents, coils, etc.). Because models for the biomechanical Reaction of blood (such as coagulation or dilution) and from vessel walls mechanical stresses available can stand, the likelihood of clinically important consequences the introduction of implants can be individually assessed through a series of simulations. Examples of such consequences are hyperplasia and restenosis, which Weeks after a stent implantation can occur, the desired compression of an aneurysmal lumen as a result of implants (e.g., GDC) caused blood coagulation or the later possible unwanted recanalization of the aneurysm lumen, and in any case a risk of embolism downstream from the location of the implant.

A Another important application is the "virtual angioplasty", which is a detailed Predicting the clinical consequences of planned but not yet operative conducted inserts of implants or vasoplastic surgery. The tomographically recorded vessel geometry can after software-supported Detection of spatial Structure of the vessels virtually changed be, e.g. by closing vessels or with implants. The resulting new vessel geometry then does not correspond to the current condition of the patient, but the presentation of the doctor as the patient's blood vessels after a procedure should look like. This virtual vessel geometry can be used as a basis for numeric Simulations and on its basis for quantitative statements about the hemodynamics and wall load serve as well as the original, geometry information obtained directly from tomographic data.

The restrictions in the scope of possible applications are essentially limited in the reception and registration procedures. The heart and lung area is subject a non-suppressible strong movement. The invention makes it possible, when using the process options, in particular the dynamic coupling of blood flow and wall movement, also the blood flow in the heart and / or the wreaths. Veins are difficult to model and often difficult with tomography exactly to locate. Small vessels (stenoses under 2 mm in diameter and aneurysms below 4 mm) are due limited CT resolution (about 0.5 mm) at the moment not reliably predictable.

The fluid Dynamics is currently the most time-consuming element of the process. With the Use of the Lattice-Boltzmann method and smaller high-performance computers (2 to 8 processors), only for a fraction of the cost of a tomograph (e.g., CT or MRI) To acquire the duration of a typical simulation can be simpler Neurosurgical applications are already reduced to 1 hour. The preparation of the simulation including segmentation, 3D computational grid, Refinement, specification of boundary conditions, etc. should be on average 5 to 10 minutes and the evaluation of the simulation results 5 to 20 minutes, including archiving of used vessel geometry, Boundary data, the converged flow state, the for further simulations, e.g. For a "virtual Angioplasty "used can be, as well as selected, over the Time integrated simulation results. The procedure is with it not for Emergency treatment suitable, but in therapy planning and the subsequent Control can be used as a standard agent for clinical support.

The Method can also be used as an upgrade for built-in tomography equipment installed become. requires become current powerful computer clusters and proprietary interface software, the one connection with the measuring apparatus allows the manufacturer. For specific applications such as. Neurosurgery is for the reliable Simulation a scanner resolution in Submillimeter range necessary, which in some tomography devices not is reachable.

The main advantage of the inventive method for simulation-based therapy planning and control is the automation, standardization and acceleration of blood flow simulations in veins. A segmentation of the three-dimensional geometric data allows the representation of the vessel walls. Of crucial importance is the use of regular data grids in all stages of computational processing and in particular in the Lattice-Boltzmann (LBM) method for flow simulation. All previously published simulations based on individual tomography data of patients, have been performed by other methods (FVM, FEM). Only a few experiments are known to use LBM for blood flow simulation, the structure of the flow-through geometry has always not been related to data from individual patients. Even with the simulations with conventional methods (FVM, FEM), the influence of the flow area circumference has not been investigated. The influence of boundary conditions at the inlet and outlet and the spatial resolution has been rarely and then only empirically investigated without a reliability rule (eg in the form of an error interval) would have been set. Virtual surgery has already been discussed as a promising means of simulation-based therapy planning, but only in connection with coronary arteries and aortic segments. The present feasibility of 3D simulations for clinical practice has been negatively assessed.

First the inventive method with spatial resolved three-dimensionally Bloodstream simulation provides an implementable with existing hardware Option for simulation-based Diagnosis and treatment planning of vascular malformations. Important is the definition of the required scope (one sufficient wide environment of malformation, depending on the type, complexity of the vessel structure in the area, and according to individual characteristics) and the required (spatial and temporal) resolution the bloodstream simulation and, accordingly, those obtained using tomographic methods Output data. Furthermore, the decisive factor is the continuous use only from regular data grids, what both the efficiency and the accuracy of the individual Steps of the procedure improved.

For the implementation of the Procedures will not be experts in the field of fluid mechanics more needed. There will be interfaces for the introduction of biomechanical, cytological and other (for the representation of the normal and pathological remodeling of Vessels relevant) Models provided. Thereby can additional important influences on the hemodynamics and Vessel wall load, e.g. through wall pulsation, blood rheology and coagulation, transient and systematic changes in the biochemical behavior of wall cells, etc. also calculated become.

The inventive method is the standard method for simulation-based diagnostics, Therapy and control of blood vessel malformations, thus for Diagnosis, treatment planning and control of many symptoms in cardiology, neurology and vascular surgery is common and is in contrast to the previous 3D blood flow simulation method in every currently equipped Clinic usable.

The method according to the invention is based on the following prerequisites:
There must be spatially resolved tomography data (3D of approximately stationary parts of the body, or 4D, that is, including time dependence, on the heart and lungs). The possibilities of existing tomography hardware thereby limit the number and location of the treatable vessels.

At all proximal end cross-sections (with respect to the existing spatially limited imaging, as the geometry specification for the numerical simulation is to be used) of arteries must be an independent temporal resolution Measurement information about the Volume flow or blood pressure. blood flow information can e.g. by ultrasonic measurements with Doppler analysis (a fast Method used as standard in sufficiently large vessels ) or obtained by MRI Doppler techniques. To the dimension of Pressure curve in larger veins There are a number of mostly non-invasive procedures available.

models for the mechanical behavior of healthy and damaged vessel walls, as well as for spatial Course of the lumen cross-sectional area smaller Become a vessel for one complete modeling and simulation needed. Corresponding information is available in the specialist literature, see e.g. G. A. Holzapfel and R.W. Ogden, eds., "Biomechanics of soft tissue in cardiovascular systems ", CISM courses and lectures 441, Springer, Wien, 2003. For some applications it is but not enough and then either 4D recordings or the adoption of rigid walls used in conjunction with 3D shooting.

in the The following will be the method according to the invention explained in more detail. The core of the procedure is a direct numerical simulation (DNS) of the Bloodstream nearby of arterial malformations, using standard methods of angiography individually and reliable can be detected in patients. The procedure is based in three main steps, essentially in every application performed by CFD software Need to become.

Pre-processing: The geometry of the flowed through area (vascular system) and the appropriate boundary conditions are determined. Accordingly, a system of computing grids is designed, which together cover the entire volume flowed through and the required spatial Auf locally, each individual grid having only cubic voxels of a corresponding size, and the minimum and maximum grid sizes being optimally adapted to the architecture of the computer used when installing the software.

Processing: A numerical simulation of the pulsating blood flow through the specified geometry is carried out until a reliable evaluation the flow parameter of interest possible is (numerically converged solution present in the sense described above), including spatial or maybe also time-averaged statistics.

Post-Processing: The simulation data are evaluated and visualized. Spatially distributed fields, e.g. Varying amplitudes of the shear stresses at selected sections the vessel walls or "turbulence intensity" after time averaging in the Inside of a vessel lumen, as well as simple time series, e.g. The pressure curve at control points within aneurysms, and characteristic single values, such as e.g. spatial averaged oscillation indices or mass flow distributions on vascular bifurcations, are calculated and for the estimate the influence of hemodynamic factors, but also from inaccuracies in modeling and numerical Approximation of the calculated dynamics provided.

at Each of these three main steps in the work process is subject to the following new measures that increase the efficiency and accuracy and the standardization facilitate: The management of all data grids is fully automated. All three-dimensional (3D) data is exclusively based on regular, rectangular and as often as possible shown on isotropic lattices. This allows the fastest and most accurate versions the respective algorithms for numerical smoothing, differentiation, integration, etc. are used.

For the DNS the Navier-Stokes fluid mechanics a lattice Boltzmann method is used. This will also in very complicated vessel geometries On the one hand, optimal computing power, even on parallel computers secured and on the other hand a reliable determination of all hemodynamic Ensures parameters, in particular the pressure in manifolded vascular systems and viscous tensions near vessel walls. So is from our own research known that it to the DNS resolution also the strongest fluctuating modes (Womersley numbers up to about 20) that are realistic Representation of a pulsating flow especially near the wall is still important are, a moderate spatial resolution from 15 to 25 grid points in the vessel diameter when used of LBM is sufficient, with the wall layers containing the highest modes locate with only 3 to 5 grid points. An appropriate grid size in the "Region of Interest" can (automatically) and should while ensured by the preprocessing be and can afterwards during the solution step easily be processed by the LBM.

It Comparisons between LBM and FVM are known to provide significant benefits the LBM, e.g. These show that in flow areas with more complex Geometry LBM a much smaller number of grid points needs to have comparable accuracy in determining the stationary To achieve pressure loss. For turbulent flows has a comparison with Pseudo-spectral methods that are of the highest accuracy, one comparable accuracy of the calculated statistics as well as speed advantages at grid sizes above about 100 points in one coordinate direction. Because quite a few spectral methods are very difficult to use in complex geometries, competes LBM in such cases with FEM and FVM. From the literature it is known that FEM very time consuming and quite complicated to apply to blood vessel flow. Own comparisons with commercial FVM-based CFD software have shown that the Calculation of a stationary solution with the FVM software, the use of advanced multi-grid methods (Multigrid, MG), a computation time comparable to LBM without MG takes up. By using MG for LBM can be up to an order of magnitude to be achieved in acceleration. The basic description of the LBM-MG can already be found on the internet together with a well-founded selection a particular course of action from a number of theoretically offering alternatives. When simulating pulsating flows, it has the same Compare a lead of LBM (without MG) of at least one Magnitude already shown in the calculation time. By means of such a multi-grid process can the stationary one Scalar and vector sizes faster for the Lattice-Boltzmann method be determined.

By these and other features described below is the inventive method much easier, largely automatable and much more precise and faster in determining clinically relevant flow patterns and hemodynamic Charges.

Pre-processing requires two types of input from the method described here: 3D tomography data that differentiates blood vessel tissue and time-dependent measurements of blood flow in veins proximal to the malformation being studied the. In order to ensure a reliable geometry recognition and then flow simulation, requirements are placed on the resolution of the input data: A pulse cycle must be at least 8 in the systole and 8 in. By specifying at least 16 independent data acquisitions corresponding to different time phases in one cycle Diastole in a healthy heart cycle, be defined with sufficient time resolution. The spatial resolution of velocity profiles must not be more than 3 times coarser (the ratio for a coarsening / refinement transition on adjacent mesh blocks) than that of the computational mesh that is to receive the edge data. On the contrary, it is necessary to make use of the CFD software's usual global constraint type, where a total mass flow through a selected cross-section is indicated.

The tomography data typically used to generate input data (CT, MRI, etc.) are used as a 3D dataset of gray values that appear on a regular grid in physical space (and not in frequency space), expected, in conjunction with corresponding gray value intervals and filter functions similar to those used in medical imaging Segmentation used to specify the discrimination thresholds. The preparation phase, in which this information is first determined by the user Need to become, can do so with existing, manufacturer-specific medical software carried out become. Usually lie in the clinic such gray value data in a variant of DICOM format, typically as a variety of 2D shots specified in parallel layers. The nominal resolution (the spatial grid step to be read from the DICOM file) within a layer may thereby in a ratio of the grid step sizes of not less than 1: 3 for dissolution in the third, axial coordinate direction stand. (The ideal and so far maximum ratio from 1: 1 is only in the latest devices and then not at all measurement methods achieved.) The check whether the so specified resolution the actual technical resolution while The data recording can not always be automatic and if necessary be performed by the user. It is therefore assumed that the axial resolution not much worse than the one along the cutting planes. The coarser from the two resolutions must reach out be to all the diameter of vessels in the area of Interest (Region of Interest) should be included (ie in the segmented geometry description) with at least 4 voxels appear in the input file. For example, one has a vein of 10 mm diameter, which has a section with 75% stenosis. If this section is within the area of interest, the resolution not grosser than 0.6 mm per pixel. In aneurysms, her neck must be at least 4 and the shortest Diameter of her bag to be represented with at least 6 voxels. At an isotropic resolution of 0.4 mm, as they are currently available with the new 64-line CT from Siemens can be Aneurysms up to 3 mm and veins of 1.5 to 2 mm are treated.

The second type of expected information is pulse, blood pressure, and blood flow volume data, which allow the determination of inflow boundary conditions for the DNA with sufficient precision. A number of non-invasive and minimally-invasive, largely standardized procedures are available for the independent design of these parameters. In G. Pedrizzetti and K. Perktold, eds., Cardiovascular fluid mechanics, CISM courses and 1ectures 446, Springer, Vienna, 2003, for example, an overview of existing ultrasonic measuring method for determining speeds and shear stresses can be found. The spatial distribution of blood flow velocity in cross-sections of medium and smaller veins, which is needed for indication of inlet and outflow boundary conditions, is not to be considered measurable for standardized clinical applications even in the foreseeable future, with the possible exception of large ones Veins that lie close to the skin and are not supported by hard tissue, which is also the case for the carotid artery beyond its bifurcation. For the most common cases of deeper-lying veins, a database has to be created which calculates a plausible velocity profile from the local Reynolds number (from ultrasound or sine-contrast MRI or even estimates) and vessel curvature (from CT, MRI). This requires a series of systematic hydrodynamic calculations and subsequent medical verification tests. These data should show a spatial resolution of at least 20 voxels in the lumen diameter. The optimal temporal resolution, which is required for the indication of the systolic pulse phase in the DNA, corresponds to a uniform time step of 4% of the total duration of a pulse period or even shorter, to 1%, in areas with very steep or complicated pulse progression, such as in the first aortic branches. In most practical cases, this accuracy is not achievable, especially with deep wires. This problem is also to be solved by a database of pulse patterns which allows simple pressure curve measurements (see above for details of minimum time resolutions) with inclusion of further information such as age, gender and general health of the patient, position of the vessel etc. to calculate a plausible pulse course in the vicinity of the investigated malformation. It remains unclear whether correlations and TFM (transfer function method) for certain body parts can be used reliably.

Geometry determination: To the influence of inevitable Errors when specifying in and out boundary conditions (EARB) too diminish, these constraints are only far enough from the be reported malformation. It is expected that swirling Features of the vessel geometry (like bifurcations and strong bends) the local structure of the flow strongly influence and thus the influence of details in the indication reduce the EARB. Both up as well as down the main direction of blood flow should the input or Outflow edge surfaces continue as the first two bends and the first bifurcation away from the location of the malformation lie. In cases, if the anatomy or the extent of the present tomography data this excludes (typically in the inflow area), will be an investigation of the influence of EARB on the flow structure the corresponding numerical solution recommended, compared to at least two variants of the simulation, that differ only by the profile or type (pressure or mass flow) of the inflow boundary condition, consists. The automatic verification of EARB conditions is possible, however, requires a (again automatic) topological vascular structure recognition and therefor also a good spatial resolution the tomography data far distal from the malformation. If one such resolution is unreachable, or the vascular structure extraordinary complicated, the must Selection of border areas from an operator, e.g. a doctor, to be taken. These Need is signaled automatically. It is additionally required that all larger vessels (in contrast to "smaller vessels", see below) with presented with the location of the deformation (stenosis, aneurysm, Stent, bypass, etc.) within a sphere of diameter 3 L directly are associated with the deformation, where L is the length (den largest diameter) of the examined deformation. This ball must be for the most part in the interest and for the flow determination was taken into account Be contained in one area, vessels with one Diameter less than 30% of the effective diameter of the largest wire, which passes directly by the deformation are called "smaller vessels". Such Become a vessel automatically removed from the geometry description if they are not lead directly into or past the deformation. from the remaining ones Vessels "ends" the majority of edge surfaces, and those inlet or outlet boundary conditions must be prescribed although they are unknown. These surfaces become synthetic boundary conditions given that proportional to the mass flow to the cross-sectional area of respective vessel (in with respect to its axis, that of the above-mentioned recognition method for the topological Structure of the existing binary segmented vessel geometry already calculated automatically or with decision of a supervising Physician has been established) and the dynamic mass conservation law be determined accordingly. Important vessels can be far downstream (distal) after deformation from physiological or technical establish become poorly recognizable. In these cases, an operator, e.g. the doctor, only in determining the course of the vessel axis asked and supports, during the Vessel diameter based on known approximation formulas extrapolated exponentially. To a plausible course to calculate the axis of such vessels local threshold adjustments, regularization e.g. with non-linear Diffusion, adapted Inclusion of the gray scale gradient in the location of the vessel wall, as well included other well-known advanced segmentation techniques.

simulations of vessels with Implants (stents, coils, but also bypasses) are using the new procedure also individually patient-dependent possible. The Geometry and mechanical properties of the implant should known for that be and be sufficiently resolved 3D tomography image with the already placed, clearly recognizable Implant be present. As with the representation of the walls (as curved surfaces without thickness) and the axes (as curved lines in 3D space) of modeled blood vessels, will the actual position of the implant by curved geometric objects without Thick "registered" (in the jargon of the medical Imaging). These are preceded by deformations corresponding to prepared geometric models of the implant in a reference position (e.g., a stent that is in a straight or plain (with constant Radius of curvature) curved tube with a constant, circular cross-section disposed is), the present tomography record in a suitable standard on next come, first determined automatically and then with the support of imaging and simulation of their mechanical (hyperelastic, plastic, or else, e.g. in natural implants, viscoelastic) movements between the vessel walls, its rheology as modeled in the calculation of the dynamic coupling of wall and flow becomes. After the current spatial Location of the implant is determined by its known mechanical properties or even by simple "curvature experiments" with spatial Deviations indicated by the recognition software, the mechanical stresses within the implant as well as between determined it and the vessel walls become.

Of the missing, hemodynamic Proportion of these burdens is then estimated by DNS. there be, with sufficient resolution the DNS, coils with simple geometry in the current state as well Stents as a 3D body represented in which their adapted "skeletons" to a width is spread, the actual thickness of the wire cross-sections preferably exactly corresponds, but not thinner than 3 voxels on the grid is. At low resolution the Need DNS Coil bundle as a porous medium be modeled, with the porosity from the tomographic images (if already present in the body Implants) or from the experience of an operator, e.g. the doctor (in medical planning), be appreciated have to.

finer Coils and gels, Verklottungen, soft plaques and the like be as homogeneous-porous body modeled. Not only the porosity, but also the stiffness, Solubility, Diffusion properties, the proportion of chemically unstable substances and other parameters need be known to model the clinically relevant effects of such To be able to completely determine implants or deformations. Appropriate Mass transfer simulations, according to the state of the art, including Diploma thesis at the LSTM Erlangen, with finite difference method on the same computational grid as LBM and with the LBM solver directly, at coupled to each time step, using simulation schemes and boundary conditions of second order (ie coordinated with the LBM) carried out.

For each of these Therefore, types of objects should already have records in advance representative Values exist. Its development is not part of the present description. Also the selection of optimal models for porous media let yourself not clearly described and should be determined during the generation of the records. You need to but the structure of Navier-Stokes's equations essentially keep so that theirs Calculation with LBM by means of an introduction of correspondingly calculated "model forces" and "model stresses" remains possible. The required information of diffusion properties should be a Calculation of fluctuations in temperature and concentration of important substances and blood components. Appropriate Diffusion convection equations are related to LBM simulations best by means of adapted Finite difference method calculated.

Grid computing: Even if the original grayscale file is not isotropic, i. if the step in the axial direction is not equal to that in the cutting planes, the binary is segmented Geometry can be represented on an isotropic grid. An advantage of which is that numeric Errors due to lattice anisotropies at all Computing occur and at low resolution than prove essential. Another, closely related advantage is that easier and more precise variants of the Lattice-Boltzmann method used become. The transfer An isotropic grid can be very efficiently linked to filtering and refining become. At the strongly curved and branched vessel geometry, in most cases should be treated, these benefits are of great importance. When filtering significant changes the topology, this is signaled to the user (e.g., the supervising Doctor) becomes an easy way given to modify the filter properties or one of the resulting Select topologies as "right". The filtering should be location-dependent and in the area of the investigated vessel deformation one (non-isotropic, local adapted) smoothing operator correspond, usually with a filter width of at least 3 and a maximum of 12 voxels of the original Grid to non-physical "waves" of the vessel wall in the area to avoid the deformation. The spatial resolution of the resulting isotropic data grid is there at least 15 to 20 voxels along the shortest Dimension of "normal" vessels near the examined vessel deformation guarantee.

the same minimal resolution also applies to smaller ones important vessels and even especially in stenoses, because in the narrowed lumen higher speeds and gradients occur. Only for smaller vessels with automatically determined and typically low outflow, the resolution can go up to 6 to 12 grid points (depending on the variant of the used Lattice Boltzmann schemes) are reduced in diameter. Yet smaller vessels (diameter below 30% of 18 voxels) are modeled and not simulated. there it assumes a pulsating laminar flow and a third database put to use, which calculated a detailed amount of short-term influence currents in Vessels with different curvature contains. The velocity profile at the inflow edge can be used in these calculations be given only with 2D polynomials of low order, since the The object is to provide low-speed velocity data, made of surfaces with Diameters below 5 voxels stem from "extrapolating" into the modeled vessel.

A grating decomposition with subsequent elimination of the parts in which there are no voxels traversed, and a refinement (or coarsening to avoid unnecessarily high resolution) should take place after the creation of the isotropic grating. Each grid part should be a cuboid networked by its own isotropic grid whose minimal size is dependent on the technical specification of the particular computer, but should not be less than 12 voxels in each coordinate direction, which is associated with the efficiency of cache architectures, but also with the resolution in the cross-section of most treated vessels. The original subdivision is roughly equal to (plus / minus one voxel in each direction) blocks that overlap one voxel (the original isotropic lattice). After refinement or coarsening, the ratio of the lattice steps in adjacent blocks may only be 1: 1 or 2: 1 or 3: 1. This simplifies communication and allows accurate and efficient interpolation between neighboring parts. Refined blocks are automatically subdivided into a corresponding number of new blocks if the grid size recommended for the existing computing system is significantly exceeded. The refinement procedure thus described is then repeated recursively in blocks where necessary until all vessels are well resolved. Descriptions of all original blocks and all intermediate blocks are also stored in the refinement. This is necessary both in the visualization and archiving of the simulation results in general as well as in the simulation itself, if LBM-MG are used.

presentation the vessel walls: The Identification of the location of vessel walls The 3D tomography data has already been described. This situation must be for the DNS be kept in an easy-to-handle data structure. The only exception occurs when using the bounce-back method will, as an approximation the adhesive boundary conditions on vessel walls, the are assumed to be fixed and immovable and only vaguely known may be. This is a fast, simple and robust variant of the method, which also guarantees an exact mass conservation. It is only conditionally applicable, for example, in relatively well-resolved vessels, but almost immobile are (as in the brain, for example) or in vessels whose movement is unimportant for the Dynamics in the area of interest. The wall information will open mapped the rigid computing grid and coupled with this. In in all other cases, the wall layer stored and, if necessary, always again (for example, the strong Pulsations of an AAA). When the wall dynamics are calculated should, must mechanical model of nonlinear elasticity and (in the case of large deviations or heavy loads, e.g. in larger aneurysms) of plasticity become. An example of such models is in Holzapfel & Ogden (supra). 2003).

It be two ways covered for displaying the wall position. Both are an "exact" or "sharp" representation of what the unambiguous calculation of the wall load allowed and the efficient Simulation of wall dynamics facilitates, but also communication Dynamic information between the "wall grid" and suitable for the flow simulation 3D computing grid caused. This communication can be done by means of the known "immersed-boundary" method or one of its newer variants such as the "immersed-interface" method (see above).

The First wall rendering method is always small wall deviations easier to handle: the connections between adjacent grid points in the 3D isotropic computational grid are marked, if they have a Overlap vessel wall, whereby also the position of the cut is stored on the 3D-Rechengitter becomes. Cases, in which a lattice point overlaps (almost) with an overlap point, be through "generic small deformations ", which can be installed locally, systematically avoided.

The second method of presentation is classic: it becomes an unstructured grid (see 4 ) automatically, eg with the marching cubes method or other standard methods of image processing and imaging. CAD representations are also possible, but usually too expensive to produce. For example, they can be used meaningfully when generating test geometries. For this reason, standard formats of the largest CAD software manufacturers as well as other standard formats such as STL will be readable and automatically converted into an internal representation of the surface geometry. The ratio of each point of this representation to the 3D computational grid is easy to determine due to the maximum simplified structure of the isotropic computational grid, even if the wall grid has moved after each time step. This method is well suited for larger wall deviations, such as a large aneurysm or parts of the aorta.

In the "virtual operation" of vascular deformations, the spatial progression of the vascular walls is changed with respect to the 3D arithmetic grid and implants are also added to the geometry description by their "skeletons" (see geometry determination) first adapted to the wall and then prepared (see above) or by interactively selected portions of the flowed-through vessel volume is no longer characterized as blood, but as a porous medium (see above). In any case, an unstructured 2D grid is manipulated to change the wall geometry. Optionally, the final result of the geometry change from the shape of a deformed 2D grating to a new designation of the wall penetrating grating point connections on the 3D fixed grating is converted. For the Ma nipulation of the unstructured 2D grid, some of its points are interactively selected and then marked as elastically connected. Its starting position is considered as a reference configuration in which there are no unbalanced voltages. The rest of the points remain fixed.

The Possibility, Trace wall movements and with pulsating flow to Considering the Lattice-Boltzmann method (LBM) coupled a decisive advantage of the invention Wall movements synthetically from 2D representations, especially as lattices, also be determined from several tomographic images. The modern ones tomography devices leave a recording of time-periodic movements of the heart or of larger aneurysms too. About the Coupling with the flow The mechanical load of the wall can be determined without any invasive intervention must be made. This procedure is more accurate and cheaper as direct recording methods (ultrasound, Sine Contrast MRI) for acquisition the bloodstream and allows a reliable assessment the wall tensions. When editing a time series of recordings becomes a condition similar to that found at the end of diastole is created as a reference configuration.

By graphically interactive movement of individual "elastic" points in the independent wall display the position of all other points can be changed. After every movement are combined very close points in one point and then it will be given the opportunity an automatic optimization of the number and location of the "elastic" points on the 2D grid too cause. changes in the topology of the entire vessel geometry are based on the already existing axis structure automatically after each movement detected and signaled the same.

method to "inflate" the implants, under Incorporating their elastic properties until they are against the Vascular walls firmly depressed are not, adequately reported in the literature to be. Its principle is the numerical calculation of the displacement and Deformation of the implant to be from an initial state, the determined by the reference shape of the implant and a starting position being interactively activated by an operator, e.g. from the doctor, is given. Once the implant is in the direction of movement a vessel wall she reached at one point, it is called hyperelastic or elasto-plastic Object (as a 3D body, as a shell or as interconnected "wires"). During the further adjustment of the position of the implant, the vessel wall is at typical applications immovable and rigid. In the spread the "balloon" becomes the needed force (against the resistance of the implant) and it will be a maximum (adjustable) force and minimum vessel diameter not exceeded in the balloon area. In the end, the "virtual Balloon "removed entire procedure of placement of an implant does not exclude consideration of the vessel present Blood. The resulting geometry will continue to be treated exactly the same way as already actually placed in the patient implants, their location as described above has been registered.

Flow simulation: The blood flow is modeled as incompressible. The determination of the pressure is nevertheless complicated by two factors: On the one hand, the elasticity of the vessel walls allows the spread of pressure waves incompressible in the standard formulation Flow solver algorithms can not be treated. On the other hand, every very complex geometry is a prerequisite for difficulties at the solution the Poisson task for the instantaneous pressure distribution. is the pressure on Areas with "holes" not unique Are defined. This problem is avoided with the use of Lattice Boltzmann solvers, because the pressure thereby by means of numerical "pressure waves", thus qualitatively according to the actual Physics, and is not calculated by means of Poisson solvers. comparisons between LBM and FVM in solving laminar flows in a "generic porous medium" (see above) shown that the LBM solution for the Pressure converges much better. The "incompressible" variants have the best known LBM technical and other benefits. The problem of elastic Walls became already discussed.

Furthermore The non-Newtonian rheology of the blood can also be a decisive one Have influence, especially in flow areas with very low blood velocity, e.g. within large aneurysms or in capillaries. In big Veining, on the other hand, is an assumption of Newtonian rheology almost without problems. An exception are cases in which the wall tension is to be examined. An established Model for Blood rheology is not yet known, although several measurements have been made have been. Especially in the modeling of partially through-flow parts of the vessel lumen as porous Media is emerging the need for tensor models for viscosity (as well as the diffusion of different blood components and entrained substances) apply.

Previous LBM applications have always used scalar (also non-Newtonian, eg turbulent) viscosity models. Nevertheless, there are still few tried-and-tested approaches that allow the use of tensor models, eg in which the stress tensor is included in the definition of the LBM equation weight function is included. If flow modeling requires the use of complicated voltage sensors, it may also be necessary to use information from adjacent voxels and calculate finite differences.

The perfect locality leads to all LBM algorithms to an excellent scaling on parallel computers. The number of operations and degrees of freedom per grid point is moderate, so that on Processors with sufficient "fast Memory "(Vector Register or cache levels) a high computing speed is achieved. The locality even allows the calculation of a good approximation of the total stress tensor only from data that exists locally on the respective grid point are. Especially near the wall is this an advantage over FVM or finite difference methods (FDM), because the genaen position and movement of the wall is not directly in the Voltage calculation needed becomes. It also provides an efficiency advantage in the calculation of tension. If the FDM approximation Nevertheless, it can be calculated by comparing it with the result the "local" calculation of the voltages a sensitive test of accuracy in the LBM calculation higher Reynolds numbers deliver. The vollexplic character of the LBM means that all Calculations with this method require a sufficiently small time step (see above). On the other hand, the need to adjust the pulse history reliable too discretize, a similar one Requirement. The comparison of both limitations is by the inventor as a confirmation felt for it been that the explicit character of the calculations in blood vessels is not essential plays. The resolution, the at the steep time gradients of the pressure curve at different Places with appropriate delay is required, requires the selection of the time step to a constant and small value. This allows pulsating flows, where the pressure fluctuations have a complex time course, be presented and in particular fine and fast movements also included in the fluid become. Implicit procedures based on LBM (but mostly with a spatial Discretization by FEM or FVM and not, as with the standard LBM, that too in the method according to the invention provided by FDM) are designed for static problems Service. In the case considered here, these have no advantages. Instead, LBM-MG is used here for stationary tasks.

Post-Processing: The most important sizes in the assessment The mechanical loading of vessel walls is that transmitted by the bloodstream Tensions. All components of the stress tensor, differentiated in a viscous and a pressure component, in DNS with LBM at each grid point within the area through which it flows at each time step as part of the simulation process and not as additional Independent load calculated from other points and times, what the creation of Facilitates time series at checkpoints determined by the physician. Based on this data can after completion of the simulation statistics such. an oscillation index for the Shear stress (as a vector tangential to the wall) calculated very quickly and be presented. A calculation of statistics during the Simulation causes a significant amount of time and should only then turned on when spatially averaged statistics, such as. the global mass flow through a certain cross-section or effectively the residence time in a selected volume portion of the area through which it has passed required become.

Next the tensions can Also, other hydrodynamic fields, such as the 3D vector fields of Speed or vortex (calculated as the application of a Finite difference approximation the rotation operator to the velocity field), important information deliver. Because the structures of these fields are a fluid mechanic familiar and for this meaningful are, but a doctor with great Probability of little importance will have to be theirs Effects on the wall stresses, residence time, etc. the doctor be made available on request with simple and readily available explanations can. For example, are said to be strong vortexes as areas of low relative pressure within the lumen and potentially high wall shear rates be or should the length of streamlines as an indicator of possible fouling or plaque formation, etc. Adjustable thresholds and facilitate the automatic numeric indication of the assessable loads or even allow only for a doctor's identification and evaluation of the risk of individual Vessel deformations.

In addition, should also for CFD and visualization software common presentation modalities available such as. the 3D isosurfaces of an example presented by Speed (or other vector fields such as the pressure gradient and scalar fields such as the concentration of a preparation in the blood), flow lines, Streaks and LIC (line integral folding). Local spatial and time-averaged (in-phase) averaged data can easily match the original one DICOM grid can be projected. The pulsating part of the speed and the vortex in selected Can cuts without big ones Effort during The simulation can be calculated and then visualized.

Representations of the results are always stored in a standard format (DICOM) to support automatic documentation, but also the To facilitate 3D visualization (through rotation, zooming, etc.) with pre-existing and familiar software for medical imaging. The resolution of the result data must be chosen before the simulation and should not be coarser than that of the original 3D tomography data set. The fields actually moving in time during the simulation are much too large and are not directly usable in medical practice to justify their storage.

The Invention will be further on the basis of examples and the Drawing explained. In the drawing show:

1 a schematic representation of the method according to the invention,

2 3 is a schematic representation of the automated 3D data flow taking place exclusively on rectangular grids and in the form of voxel information in the method according to the invention;

3 an example of a binary-segmented real brain vessel geometry in which the aneurysm in the center is clearly visible,

4 an automatic networking of the surface of the 2 geometry with an unstructured 2D file using a marching cubes algorithm implemented in commercial software,

5 a snapshot of the magnitude of a velocity component for an illustrated vessel, represented as isosurfaces that correspond to a positive ("light gray"), a negative ("dark gray"), and zero ("dotted gray").

6 a representation of an instantaneous flow state in which the tinted lines tangentially along the velocity vector field and the size of the velocity vector is locally encoded by the tint,

7 Stowage areas, fluidization areas, and a laminar area of a vessel structure represented by a LIC method implemented in commercial software;

8th the time course of velocity components along the three fixed in space and in time coordinate directions of the Cartesian computational grid at a control point within an aneurysm and

9 the time course of shear stress components at a control point within an aneurysm, as in FIG 9 showing the non-diagonal elements of the hydrodynamic stress tensor.

1 shows a schematic representation of the method according to the invention. One of the main requirements for the higher efficiency of the method in comparison with previous approaches is the limitation of all occurring 3D data structures to rectangular uniform grids, what in 2 is shown schematically. For 1D (eg space curves) and 2D (eg vascular wall representations) data, no such restrictions apply. As a result, the efficiency is hardly affected because the low-dimension data in fast memory types can be stored on current computers, and therefore, especially with larger overall computing grids, take up a negligible amount of access and computation time.

When Application example is illustrated by a brain aneurysm that has a sufficiently complex geometry. The results of Steps of the inventive method are represented here uniformly.

3 shows a binary-segmented brain-vessel geometry with aneurysm in the center that is clearly visible. 4 shows the surface of in 3 appeared vascular structure, in a network with an unstructured 2-D file.

At the in 5 shown snapshot of a velocity component is to see the entire surface of the walls in dotted gray given the conditions of adhesion to the vessel walls. The inside of the vessel is shown in dark gray. Immediately before the large arc of the main vessel, part of the flow is diverted into the pathological structure. As expected, this is only a very small part of the total electricity volume. As 6 As can be seen, within the aneurysm the velocities are very low and a stagnation area can be detected in the sharpened part of the bag.

7 Figure 11 illustrates a LIC-based representation on a surface within the vessel structure whose distance from the vessel wall is regularly small. The damming areas (with increased pressure loads), fluidization areas (where a relatively higher shear stress ensures better expansion of the wall) and the laminar area are very clearly visible.

In 8th and 9 the time course of hydrodynamic quantities at a control point within the aneurysm is shown. 8th shows Ge speed components and 9 Shear stress components. The pulse progression is clearly recognizable. Because of the very low speeds within the aneurysmal sac, a precise periodicity is not reached even after 10 pulse periods. The change of sign of one of the voltage components, which can also be represented by a standardized scalar index, indicates increased mechanical load.

Of the biggest effort in the application of the method according to the invention is not the Segmentation and (unlike some of the known approaches to numerical blood flow simulation) also not the cross-linking of the vessel geometry, but the purely computational power for the solved numerical simulation. The resulting big ones Data volumes are only after essential processing and reduction for one practical decision making process, but then the good one leaves resolution extensive conclusions about the Relationship between the condition of the vessel walls and the hemodynamic Loads too.

The Invention can be summarized as follows: Three-dimensional (3-D) grayscale data from tomographic scans (MRI or X-ray CT) with variants of suitable known algorithms for medical and general Imaging binary segmented. Be created 3-D vessel geometries for one resolution numerical simulation of their flow on cubic computing grids used with Lattice Boltzmann flow solvers. needed Boundary conditions are derived from specifically developed databases or, insofar feasible, extracted from individual noninvasive measurements. Just where and if the wall dynamics is important, it is using immersed-boundary, immersed-interface or similar Method mitsimuliert. Alternatively, it can be made from time-resolved (4-D) Tomography data are created using the same segmentation methods, which requires less computation and no modeling The wall condition also causes a lower calculation error. In the patient existing implants, vasoplasty, plaques and the like are identified and incorporated into the simulation geometry, as well as virtual (in the patient not yet created) geometry changes, Implants and the like with mathematically unresolved Fine structure modeled as an elastic, porous body. Exclusive use find rectangular Cartesian grids for 3D data and the Lattice Boltzmann method Experience ensures efficiency (just a few hours, a maximum of 1 hour) Physician use per patient), standardization (use does not require non-medical education, inputs and results in DICOM format) and accuracy.

Though the invention is described above in connection with blood vessels However, it should not be limited to this, in particular also other fluid-carrying Include vessels.

Claims (32)

Method for displaying three-dimensional flow data in fluid-conducting vessels of the human or animal body using the Lattice-Boltzmann method, in which three-dimensional tissue structure data are used on regular data lattices (geometry voxel data) of the vascular area to be displayed, including the wall, the same data lattice or generated fully automatically regular isotropic computing grid (voxel grid) are selected for the vessel representation and for the determination of the flow path and the course of the fluid flow is determined in temporal steps, characterized in that one or more to be examined vessel sections are selected, an area of the vessel from the three-dimensional geometric data is selected containing the vessel sections or in which the flow conditions are to be displayed, the three-dimensional geometric data for representation segmenting the vessel walls, defining the inlet and outflow edge areas of the vascular area, selecting the mesh grid size of the computational grid depending on the dimensions of the selected vascular area and the parameters of the flow therein, dissecting the computational grid, and eliminating those parts of the grid that do not or flowed voxels, the timing of the fluid flow is performed until the flow representation is sufficiently accurate, the presentation characteristics of the flow and mechanical loading of the vessel walls from the flow solution are determined and the results in for imaging or archiving optimized data structures are transmitted and stored. Method according to claim 1, characterized in that that the resolution of the computing grid in areas is increased (refinement), in which a larger number needed from grid points and a re-segmentation is performed. Method according to Claim 1, characterized in that the resolution of the computing grid in Ge is reduced (coarsening), in which a smaller number of grid points is needed. Method according to one of claims 1 to 3, characterized the existence for three-dimensional Lattice-Boltzmann calculations developed multigrid method (Multigrid) is used for acceleration. Method according to one of claims 1 to 4, characterized the existence block-structured grid is used whose blocks overlap, being in adjacent blocks the lattice steps in proportion 1: 1, 2: 1 or 3: 1. Method according to one of claims 2 to 5, characterized that the Refinement recursively and if necessary repeatedly performed in blocks, until all vessels are well dissolved. Method according to one of claims 1 to 6, characterized the existence Vessel section is selected a vessel structure part be added should. Method according to claim 7, characterized in that that information on the geometry of the vascular struc- ture, e.g. from tomography or CAD data, as voxel data or as an independent data structure being transformed. Method according to claim 7, characterized in that that the three-dimensional geometric data of the vessel structure part from a stored Vascular structure table or database selected become. Method according to one of claims 7 to 9, characterized that the Location of the vessel structure part to be examined is determined and its three - dimensional geometric data in the structural data of the vascular area to be displayed are inserted. Method according to one of claims 7 to 10, characterized that the three-dimensional geometric data of the vessel structure part or a part from this as porous Structure (s) have been modeled. Method according to one of claims 7 to 10, characterized that the Vascular structure part an artificial, natural or by bioengineering generated implant or a vasoplasty. Method according to one of claims 7 to 11, characterized that the Vascular structure part a vascular malformation (e.g., dilation, narrowing). Method according to one of claims 1 to 13, characterized that for the inflow and outflow boundary conditions from a stored table or database based on the measured or estimated local Reynolds number and vascular curvature Speed profile is determined. Method according to one of claims 1 to 13, characterized that for the inflow and outflow boundary conditions from a stored table, in particular database, based on anatomical and physiological indications, e.g. the position of the vessel in the body, pressure history measurements, Body condition data one or more pulse patterns are determined and from these the pulse progression near of the vessel structure part to be examined is determined. Method according to one of claims 1 to 6, characterized that for the presentation which may be changing over time Wall geometry an unstructured two-dimensional grid is used and before a change in position of points of the two-dimensional Grid the location of the intersections of the wall penetrating grid point joints stored in the computational grid. Method according to claim 16, characterized in that that this two-dimensional grids using known algorithms of imaging and image processing, e.g. of the marching cubes algorithm becomes. Method according to claim 16, characterized in that that the Wall of the vessel area separately from the vessel interior, in particular as a two-dimensional grid, in particular unstructured Lattice, displayed and used with that for flow simulation three-dimensional computational grid coupled by dynamic equations becomes. Method according to claims 16 to 18, characterized that this two-dimensional grids and the computational grid through the immersed interface method be coupled and the two-dimensional grid independent of Computational grid is changed at every time step and the computational grid is not modified. Method according to one of Claims 16 to 18, characterized that the Wall of the vessel area is represented by connecting the neighboring grid points, which cut through the wall (wall penetrating lattice point connections), where the location of the intersections is stored in the computational grid. Process according to claim 20, characterized that, while one Part of the points of the two-dimensional grid remains fixed, the Connection of the other points is defined as hyperelastic and from these points the position of selected points is changed, with which the position of the points elastically connected with these points also changed becomes. Method according to one of Claims 16 to 19, characterized that the Vascular wall off several tomographic images (e.g., X-ray, MRI, Doppler) are reconstructed, each coupled to the computational grid. 23, procedures according to claim 1, characterized in that the transport of substances and / or the diffusion of different blood parts through the same computational grid associated scalar values in the temporal steps of the determination the fluid flow coupled with determined. Method according to claims 1 to 23, characterized that the Distribution of the voltage, the velocity and the pressure in the flowing fluid will be shown. Method according to Claim 24, characterized that for everyone Point of the grid of the stress tensor, divided into one viscous and a pressure component, is determined, without numerical differentiation to use. Method according to Claim 24, characterized that the Whirl and the dissipation are shown in the flowing fluid. Method according to one of claims 24 to 26, characterized that the pulsating portion of the shown sizes directly, but also by calculation from characteristic numbers over a pulse period is displayed. Process according to Claims 24 and 27, characterized that the Shear stresses and pressure, their mean and fluctuation characteristics shown on the vessel walls become. Method according to one of claims 1 to 28, characterized that before the determination of the fluid flow the resolution the representation of the flow which is at least the resolution of the three-dimensional Structure data is. Computer program product for implementing a method according to one of the claims 1 to 29. Application of the method according to one of claims 1 to 29 on blood vessels. Application of the method according to one of claims 1 to 29, in particular 16 to 23, on elastic blood or fluid-carrying vessels with moving walls. System for displaying three-dimensional flow data in fluid-carrying Vessels of the human or animal body using the Lattice-Boltzmann method, in which three-dimensional Fabric structure data on regular data grids (Geometry voxel data) of the vascular area to be displayed including its wall be used and the same data grid or fully automatic produced regular isotropic Computational grid (voxel grid) for the vessel representation and for the determination of the flow path is selected and the course of the fluid flow in Time steps is determined, in particular for carrying out the Method according to one of the claims 1 to 29, characterized in that Means for selecting one or more vessel sections to be examined are provided, medium to choose a portion of the vessel the three-dimensional geometric data are provided, the or contains the vessel sections and in the flow conditions shown should be Means for segmenting the three-dimensional geometric data are provided for the representation of the vessel walls, medium for defining the inlet and outlet edge surfaces of the vessel area are provided Means for selecting the mesh grid size of the computational grid dependent from the dimensions of the selected vascular area and the parameters of the flow taking place therein, a Device is provided which decomposes the computational grid and the Eliminates parts of the grid that do not contain voxels through or a Device is provided, the timing of the fluid flow so long performed until the flow representation is sufficiently accurate a device is provided which the for the representation provided characteristics of the flow and determines the mechanical load on the vessel walls from the flow solution, and a facility for the transfer and storing the results in for imaging or archiving optimized data structures is provided.