WO2006010609A2

WO2006010609A2 - Method for the representation of three-dimensional flow data and wall loadings in fluid-channeling vessels, in particular, blood vessels using the lattice-boltzmann method

Info

Publication number: WO2006010609A2
Application number: PCT/EP2005/008155
Authority: WO
Inventors: Kamen Beronov
Original assignee: Friedrich-Alexander- Universität Erlangen- Nürnberg
Priority date: 2004-07-27
Filing date: 2005-07-27
Publication date: 2006-02-02
Also published as: WO2006010609A3; EP1774445A2

Abstract

Three-dimensional (3D) grey-value data from MRT or CT (X-ray tomography) are binary segmented with versions of suitable algorithms for medicinal and general imagery. 3D vessel shapes produced are used for a resolved numeric simulation of flow in cubic calculated grids with lattice-Boltzmann flow resolution. The required boundary conditions are taken from data banks or individual non-invasive measurements. When wall dynamics are important these are also simulated. Implants, vasal grafts extant plaques etc. are identified in patients and included in the simulation geometry. In addition virtual geometry changes (not yet present in patients), for example, implants for introduction, vessel parts of removal etc. are also included in the geometry description for calculation, in order to permit a prior precise estimation of the effects thereof for the medical planning of the relevant operative procedures. Implants, the fine structure of which cannot be resolved on the calculated grid, are modelled as elastic porous bodies.

Description

METHOD FOR THE PRESENTATION OF THREE-DIMENSIONAL ELECTRICITY DATA AND WALL LOADS IN FLUID-LEADING VESSELS, IN PARTICULAR BLOOD VESSELS, USING THE LATTICE BOLTZMANN METHOD

The invention relates to a method for displaying time-dependent, spatially three-dimensional flow data in fluid-carrying vessels using the Lattice-Boltzmann method, in which three-dimensional tissue structure data on regular data lattices (geometry voxel data) of the vessel region to be displayed including its wall, ie Density data representing their geometric structure are also used, and regular isotropic computing grids (voxel gratings) are likewise selected for the vessel representation and for the determination of the flow profile, after which the course of the fluid flow is determined in temporal steps.

The determination of a flow field, in particular in a vascular system, is very expensive. For the hydrodynamic determination, the geometry of the area through which it flows, the inlet and outflow boundary conditions and the conditions on the walls thereof must be given. The inflow and outflow boundary conditions comprise time-dependent information on the pressure and, insofar as known, on the velocities and in the case of turbulent flows also on the stresses. This information must include the spatial and temporal dependence of the flow in a sufficient accuracy.

Blood flows through veins, especially aortic branches and other larger arteries, are characterized by a strong pulsating coma component and complicated flow patterns near bifurcations, curvatures, as well as deformations (enlargements or narrowing). The vascular walls are exposed to rapid elastic deformations in the cardiac pulse rhythm, which can play an essential role in hemodynamics depending on the position and condition of the vessels. The modeling of the mechanical properties of these vessel walls is not unambiguous and it is particularly difficult to introduce individual and site-specific corrections, since the coupled determination of the wall and blood dynamics is much more complicated than the treatment of each of the two dynamic processes alone and because the Be¬ creation of vascular walls is a generally difficult, yet open field of research. The verification by direct measurements is also complicated by the spatially and temporally very high required resolution.

In the field of Computational Fluid Dynamics (CFD) available standard methods for direct numerical simulation (DNS) incompressible flows, mostly using Fi- nite Volume Method (FVM), as well as CSM (computational structure mechanics) method using Finite-Blemen- te-method (FEM), in which a discretization is performed with unstruk¬ tured computing grids of the flow volume and the Gefäßwän¬ de, allow the implementation of resolved 3D simulations of the flow through larger blood vessels un¬ use especially of CT Dates. The results of such simulations are detailed dynamic information on flow disturbances and wall load not included in the medical measurement data itself. Carrying out such calculations with the named methods places great demands on the persons to be examined and is extremely time-consuming; for example, it can last a week for one geometry. Simplification of the simulation methods is always kept in mind by the essential extensive assumptions of the model zifische vessels, simple geometry of MaIformationen and narrow parameter areas severely limited. With much more elaborate methods that are based on the Doppler or the time-of-flight principle and may be based on the general mathematical apparatus of tomography, such as phase-contrast MRI or Doppler ultrasound anemometry, for example also individual speed components and average speeds, ie a part of the relevant kinetic information, are recorded. The resolution is low in most cases, so that only the total volume which flows through a specific lumen per unit of time can be measured with sufficient reliability. Local disturbances, strong gradients and turbulence can not be reliably quantified reliably, although their traces and influences can be detected with some methods. However, a limited 3D information with good resolution also provides the non-invasive DSA (digital subtraction angiography) method, a standard method for the determination of the kinetic blood flow information before and during the vascular surgery. By contrast, dynamic information, ie the time-dependent force balance, can be measured either only indirectly or, as in the case of blood pressure, directly but then invasively and only for part of the forces in blood vessels. No currently available measuring method, either indirect or in situ, is able to provide 3D-resolved dynamic measurements.

In the case of blood vessels, the main medical interest is not so much the velocity distribution as the distribution of pressure and shear stress on the vessel walls associated therewith. It has become well known in the medical arts 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 related disorders that hinder the lives of those affected also threaten directly. However, the analysis of the velocity distributions themselves can be used well for the diagnosis of this type of health threat. More importantly, the role of pressure (eg in aneurysms obviously a major factor leading to rupture can lead) and the field of vertebrae is little known and therefore should be easier and better to analyze than before.

In fluid mechanics, the determination of complex flows is increasingly carried out using the Lattice-Boltzmann method (LBM), which is based on a regular lattice structure. The cells of such a grid can be processed comparatively quickly by means of high-performance computers. For example, T. Zeiser presented in "Numerical Simulation of Reactive Flows in Complex Geometries with the Lattice Boltzmann Method", LSTM Annual Report, 2001 'Geometry Modeling' based on a mapping of real samples from tube bundle reactors using 3D X-ray CT a Cartesian voxel grid is based.

DE 100 50 063 A1 has proposed a method of the type mentioned at the outset for computer-assisted 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 a patient Structural change in the airway to determine the likely emerging flow characteristics within the altered airway. In this case, the walls of the nasal cavity are recognized by segmentation techniques for coherent CT image elements up to the accuracy of the voxel geometry. For each CT image, a Cartesian grid is formed so that the image is subdivided into individual grid elements, whereby these grid elements are distinguished, which are located within the interior defined by the structure, ie in the airway, and for these grid elements Flow field determined. It can be concluded from the given description of the method 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, is possible and only grades the curvature of the walls ¬ example, the resolution of the CT data can wer¬ displayed accordingly. Especially at higher flow rates, this becomes a major source of error. In medical practice In any case, the entire method for simulating the breathing process is currently not applicable, since the calculation times required for reliably calculating the relatively fast air flow (high Reynolds numbers) are still very great.

For the treatment of cerebral aneurysms with a porous stent by B. Chopard, "A Lattice Boltzmann Study of Blood Flow in Stented Aneurysms", SCS Seminar - Computational Hemodynamics, University of Amsterdam, October 13, 2003 as a measure for the flow reduction a representation of the blood flow by The Lattice-Boltzmann method has been proposed. However, this was a two-dimensional simulation which, for no real clinical application, enables sufficient detection of the individual vessel geometry and evenly estimates basic flow effects that are connected with the three-dimensional nature of the blood flow , So far, however, only a single cuboid grid and a simple calculation scheme for the simulation of the flow processes have been used in applications of the Lattice-Boltzmann method on bloodstreams.

US 2003/0060988 A1 deals with the analysis of filling in casting molds, the Lattice-Boltzmann method being used on account of the fast computing time and its suitability for a large number of discretization points. However, the computational method described therein is well suited only for flows at relatively low speeds, e.g. Due to the lower number of degrees of freedom and the derivation of the boundary conditions, it is very complicated and it is not suitable per se to deal with advanced blood rheology models.

In particular, cardiac, vascular and neurosurgery makes use of newer technical developments and ever more precise, efficient, preferably minimally invasive methods for evaluating and interpreting three-dimensional (3D) medical data. The tomo- graphing data, which are usually based on ultrasound, magnetic field and X-ray measurements (the invention should not be limited to this.), Density Informatio¬ contain NEN, which is then converted by so-called segmentation predominantly in geometric information. The resolution of these methods improves in the given order because the minimum resolvable length is proportional to the radiation wavelength. At present, an isotropic resolution of about 0.4 mm can be achieved with multilayer X-ray CT, a somewhat coarser and still comparable (about 1 mm) resolution with MRI. This means that vessels with lumen diameters of at least 1-2 or 3-4 mm can be detected. The ratio between the resolution, which is sufficient for the detection of a vein, and that which is at least needed for a determination of the flow dynamics and especially the wall load (by measurements or simulations), is about 1:10.

It is therefore not yet possible to carry out detailed analyzes of the course of blood flow and of its relationship with the development of vascular anomalies only by means of medical measuring methods. On the other hand, a variety of medical investigations have discovered various aspects in which changes in the course of the blood flow provoke the formation and further development of vascular malformations. To understand and treat vascular damage requires detailed knowledge of the blood flow and the impact of mechanical stress on the deformation of important blood vessels. It would therefore be desirable to have a method which simultaneously simulates flow conditions efficiently and can easily generate detailed hemodynamic information.

In order to successfully incorporate individually specific features of the vessel geometry, A. Taylor, M. T Draney, JP Ku, D. Parker, BN Steele, K. Wang, and CK Zarins, "Predictive medicine: computational techniques in therapeutic decision- Making ", Computer Aided Surgery 4, 231 to 247, 1999, a method has been proposed, with the transverse diameter of the Lumens larger arteries on the basis of MRI tomography data au¬ automatically determined and this information for 1D model calculations of the blood stream (only along the vessel axis) is used by these arteries, even if implants (including bypasses) are present. So far, this method has been tested in AA (ascending aorta) in animals and humans, so in a vessel that is exceptionally straight and long. Comparisons with MRI-based anemometry published in BN Steele, J. Wan, JP Ku, TJR Hughes, and CA Taylor, "In Vivo Validation of a One-Dimensional Finite Element Method for Predicting Blood Flow in Cardiovascular Bypass Grafts ", IEEE Trans. Biomed. Closely. 50 (6), 649-655, 2003 and with detailed 3D numerical simulations published in V. Favier and CA Taylor, "Image-based modeling of blood flow in a procine aorta bypass graft", Ann. Res. Briefs, Center for Turbulence Research, Stanford Univ., 2002 has shown that some averaged quantities can be well reproduced, but that the spatial distribution of the mechanical stresses and blood velocities can not be predicted.

The simulation of blood flow, taking into account real vessel geometries, including, for example, implants such as stents or aneurysms, and their cross-linking (see eg MS Juchems, D. Pless, TR Fleiter, A. Gabelmann, F. Liewald, HJ Brambs, AJ Aschpoff, "Blutflußsimulationen using computational fluid dynamics on aortic aneurysms reconstructed from CT data before and after stent-graft implantation ", Fortschr. Röntgenstraße 176, 56 to 61, 2004) makes use of CT data using at least three different Aus¬ Value 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 volume flowed through in three-dimensional numerical simulation (3D DNS) for CFD applications takes place either on structured or on unstructured grids. The selection of the grid type has a large flow on the complexity, accuracy and efficiency of the simulations. Among other things, it also means a 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. In the case of blood vessels, the geometry is relatively complicated and the ratio (in dynamically relevant measuring units) of the wall surface to the volume is relatively high, so that the necessity of efficient and reliable coupling methods is pronounced.

Structured gratings, on which, for example, the Lattice-Boltzmann method is based, arise after a (coarse) a priori distribution of the total volume into adjacent or partially overlapping individual areas, each of which is a simple body, e.g. a cubic cube, are diffeomorphic. This simple body is covered with a regular, mostly orthogonal grid (3D spatial). For such gratings, highly accurate and highly efficient algorithms are available, e.g. FFT, compact finite differences, and high order polynomial decompositions, e.g. be used in the construction of p-FEM or spectral element method. However, the construction of structured computing grids for complex geometries is very complicated or even impossible without simplifying assumptions. On the other hand, the structure of the grid can largely be automated on unstructured gratings since the restrictive distribution of the 3D space can be avoided. As a result, even very complex geometries can be handled. However, this ultimately leads to higher costs (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 The methods of imaging such as the marching cubes algorithm can very quickly create from these data a discretized, approximating representation of the wall geometry, for example as unstructured 2D grids. The quality of this representation is necessarily a function of the CT data quality, for example, in the case of a bias in the CT recording, a locally adaptive threshold value method as described in RC Gonzalez and RE Woods, "Digital Image Processing". , Prentice Hall, 2002 necessary. The resulting 2D triangulation of the wall surfaces can already be used directly on DNA on unstructured grids for automatic 3D mesh generation. In structured 3D gratings, triangulation is a standalone object whose relationship to the 3D computing grid can be shaped by coupling schemes of various types, accuracy, complexity and effi ciency. Unstructured gratings are adapted to the edge geometry and therefore have to change with a movement of the walls, resulting in complex global SD calculations, the need to control the degree of deformation, possibly the generation and deletion of grid elements and the emergence of several sources of error associated with this operation leads.

But there is also a convenient way to change the 2D grid with a Lagrange method at each time step without having to modify the 3D computational grid. It is noteworthy that such a kind of coupling between a fixed (Eulerian) 3D lattice and a Lagrangian "wall lattice" was originally created in an early attempt by Peskin 1974 to numerically capture the heart dynamics, in which he identified himself used moving walls of the heart as internal boundaries. However, almost all previous CFD applications in the field of hemodynamics, with the exception of the work of Peskin and his school, have been far removed from this efficient and natural approach. Such approaches bring with them a high potential for simplification, accuracy improvement and acceleration of the computation methods, in particular in the case of structured computing grids, since the coupling of the both coupled grids is easier to calculate.

The above-mentioned 3D-Euler-2D-Lagrangian approach was developed in a technically versatile manner under the name "immersed boundary method". In particular, the original theoretical limitation of the accuracy to the first order was solved by improvements on the algorithm from a practical point of view, so that the entire method achieves an effective "second-order" convergence (Lai & Peskin (1999)). A systematic approach for the coupling of the two types of grids (fixed 3D computational grid for the flow solver and 2D grids for moving or stationary surfaces of complex shape, which can also be used on blood vessel walls) has been immersed in recent years under the name "immersed Interface method "developed and tested. It is based on a precise and sharp representation of the boundary between the fluid and the surrounding medium. In contrast, in the immersed boundary method, the boundary is deliberately and con trolled to a "thin layer smeared". Algorithms of both types have been developed and tested in connection with various discretization methods (finite differences, FVM, FEM) for the 3D mesh grid, but not with the Lattice-Boltzmann method. Their stability and efficiency, in particular also on parallel computers, has already been demonstrated in the literature.

The determination of the quantities which it has to calculate from the pressure and velocity fields calculated by the simulation and then to visualize and evaluate is most simple and fast, although it is of great importance in the calculation of spatial derivatives (eg in the representation of Spann¬ voltages and vortices would be needed) can lead to instabilities inadequate resolution. To suppress these problems, temporal and spatial averaging or smoothing (filtering) are used. Although there are a variety of visualization software tools that allow to represent 3D flows, is also rare, at least as far as commercial simulation software is concerned, also the possibility for Available to perform smoothing operations by mouse click.

More difficult is the transmission and multiple visualization (from different angles of view) of the large amounts of data that arise in DNS. As is often practiced in the visualization of turbulence, the effort in visualization can be reduced to a technically meaningful level by reducing (projecting, averaging, strobing, etc.) the quantities already calculated before the visualization. Unfortunately, such considerations are not yet known in the literature on hemodynamic CFD.

The invention has for its object to provide a method for the display of three-dimensional, time-dependent or time-averaged medically useful data, the detailed analyzes of the bloodstream even in Gefäßano¬ malals and taking into account the pulsations - both the total blood flow and possibly the affected Gefäßtei¬ le itself - allows and effi¬ zient feasible even with complex geometry. This object is achieved by the invention in a method having the features of claim 1. Advantageous process variants are the subject of Unteran¬ claims.

In the method according to the invention for displaying three-dimensional flow data in fluid-carrying vessels using the Lattice-Boltzmann method, three-dimensional geometric data (geometry voxel data) of the vessel region to be displayed, including its wall, generated using a regular, isotropic grid are used , The same data grid or regular isotropic computing grids (voxel gratings) generated therefrom fully automatically are selected for the vessel representation and for determining the course of the flow, 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 becomes the three-dimensional geometric one Data selected containing the vessel sections or in which the flow conditions should be displayed. The three-dimensional geometric data for representing the vessel walls are segmented, the inlet and outflow edge areas of the vessel area are determined, and the grid size of the computer grid is selected depending on the dimensions of the selected vessel area and the parameters of the flow taking place therein. The computational grid is disassembled and the parts of the grid are eliminated that do not contain any traversed or incoming voxels. The temporal determination of the fluid flow is carried out until the flow representation is sufficiently accurate. The characteristics of the flow and the mechanical loading of the vessel walls, which are provided for the representation, 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 selected area is divided into inflow and outflow edge areas and corresponding types of boundary conditions are defined for each individual, uninterrupted area intersection thereof. These require temporally and spatially resolved edge data. Corresponding details can be calculated from individual measurements on the patient or can also be taken from existing databases. There are a variety of published methods for the determination, signal-technical and statistical post-processing, modeling and application of such data. Also suitable volume forces are assumed which determine the pul¬ sierenden character of the bloodstreams investigated and are based on physiological measurements.

The grid size of the computational grid is selected depending on the dimensions of the selected vessel area and is not necessarily tied to the size of the geometry data. In the method according to the invention, the possibility of local refinement as well as the coarsening of the lattice Step based on an automatic area decomposition and geometry analysis and an indication of the expected flow quantities provided.

For the temporal determination of the fluid flow, in some applications a stationary (time-independent) solution of the flow task is sufficient to influence diagnostic statements. Such a solution is simpler and faster than a time-periodic (pulsating) solution. The complex boundary of the flow area decisively influences the entire pressure and mass flow distribution and is thus determined first in all cases. To accelerate these simulations ^'■ tion phase are a linearization of the momentum (Stokes instead Navier-Stokes equation) and, if appropriate, one ^for' specialized LBM multigrid methods (multigrid) used. If desired, a time-dependent solution is then calculated therefrom, which is driven by specified, synchronized time-periodic pressure differences at the inlet and outlet edges and volume forces in the interior of the flow region. In this simulation phase, the numeric iterations have the physical meaning of time steps. For LBM, 100 to 800 steps per pulse period are sufficient depending on accuracy requirements. For the adult human adult, the average duration of a pulse period is about 0.8 seconds, so that each (explicit) time step of the LBM solver is about 1 to 10 milliseconds. The convergence of all variables of interest on a time-periodic profile is always measured and the simulation is interrupted when a sufficient approximation to a periodic behavior is obtained or a time limit is exceeded. Even at the beginning of the simulation, the user is automatically informed as to which number of simulated pulse periods corresponds to this time limit and whether this is sufficient according to existing rules and heuristics in order to be able to calculate the desired quantities with the desired accuracy. Thus, an optimization of the computational effort is already possible before the potentially expensive simulation. The process according to the invention can be carried out either rapidly or with high precision according to various alternatives. It can for example be simulated moving walls, the method in more detail, but much more complex than in the _A n¬ exception of rigid walls. For smaller, and particularly in intracranial (located within the cranial cavity) vessels and, for example, if the nature of the _G È¬ is unknown vessel walls, movement can be dispensed with the Mitberechnung the Wandbe¬.

An alternative deployment scenario is to determine the vessel motion, including but not limited to wall pulsation, from multiple and thus time-resolved tomographic images rather than as part of the modeled and simulated dynamics at each time step to recalculate 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 then not considered to drive the further wall movement and no wall movement is simulated it is already known from the recording sequences.

If wall shear stresses are to be determined, the walls must be rendered highly accurate, for which LBM second order boundary conditions known in the literature can be used. These and other, alternative calculation methods in the wall area are more complicated than the simple bounce-back method (BBL) and, in contrast to it, lead 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 is questionable. For certain questions, eg treatments of intracranial aneurysms or analyzes of flowability of entire branches of the vascular system, the BBL can be used. In most cases, the illustrated vessel sections will contain a vessel structural part. These are to be understood in particular as deformations and impurities, for example implants or geometry changes such as aneurysms and stenoses. These can be spatially available or synthesized on the basis of stored data sets and incorporated into the vessel representation in order to determine the correspondingly resulting flow and / or pressure conditions. Conversely, even existing vascular deformations in reality can be virtually removed from the vascular presentation in order, for example, to investigate the efficiency and the long-term effects of expanding the lumen that can be flowed through. The latter is suitable, for example, for coronary artery surgery for the relief of stenoses or for "clipping" of aneurysms and arterial branches in neurosurgery.

The use of only regular 3D data gratings in the method according to the invention leads to a leap in the efficiency and standardization of simulation-based examinations. This is based on the following features:

The same raster gratings, which are assumed to be sufficiently fine-meshed, are used directly or after a fully automatic and very fast imaging or interpolation in the coordinate direction, which corresponds to the main thing of the recording device, to collinear, partially overlapping gratings with cubic voxels. These voxel gratings can then be used directly for determining the flow profile. A specification of the image as a function of the size, curvature and branching of the vessel structure considered is part of the process. No elaborate geometry-adapted generation of unstructured 3D computing grids is required in order to present all details of the vessel geometry with good resolution. This results in dramatic reductions in the complexity and overall duration of the simulation.

The reconstruction of the vessel geometry refers to several Space parts that differ in their distance from the examined Gefäß¬ malformation as well as in the respectively required resolution and modeling precision. The reconstruction is fast on current computers, but can only be partially automated. The dimension of the vessel section to be examined, for example the extent of a malformation itself and the spatial parts of clinical interest in its surroundings, is determined by individual differences in the vessel geometry and the type and cause of the complaints and can be determined interac¬ tively.

In order to enable a robust flow simulation with the described type of regular lattice in all expected geometries, an adapted variant of the Lattice-Boltzmann method is used, in which the computational grid is disassembled and the parts of the lattice are eliminated do not contain any perfused or infused voxels. In comparison with standard CFD methods, on the one hand high efficiency is thus achieved on highly parallel computer architectures and, on the other hand, less dependence on the complexity of the geometry and the computing grid.

The entire operation can be performed on the basis of measurement data that can be detected only with minimally invasive and non-invasive methods.

The method provides four-dimensional (temporally and 3D spatially resolved) predictions of the course of blood flow through arteries in the vicinity of typical manifestations such as stenoses or aneurysms. As a result, occurring mechanical stresses and the relationship between vessel geometry, hemodynamics and wall load, which in turn influences the vessel geometry by physiological wall modeling, are investigated and better predicted.

The method according to the invention can be used in the individualized examination of possible mechanical causes which are associated with the nauen spatial structure of the blood vessels of a patient, are used for the development of vascular malformations and its further development. Due to the high effi ciency so diagnosis and prognosis can be supported individually for several patients in a day with hemodynamic data, which are much more extensive and detailed in comparison to direct measurements and beyond requiring no additional manipulations on the patient. It is a regular clinical use of the flow studies and also subsequent checks of examination data possible.

The direct use of tomographic data in regular voxel format allows a simple and at the same time reliable investigation of the effect of implants already in the body (stents, coils, etc.). Since models for the bipmechanical reaction of blood (for example by coagulation or dilution) and vessel walls for mechanical stresses are available, the likelihood of clinically important consequences of the introduction of implants can be assessed individually by means of a series of simulations. Examples of such consequences are hyperplasia and restenosis, which can occur weeks after a stent implantation, the desired densification of an aneurysmal lumen as a result of implants (eg GDC) caused blood coagulation or the later possible unwanted recanalization of the aneurysm lumen, and in each case one Risk of emboli downstream from the site of the implant.

Another important application is the "virtual angioplage", which will allow a detailed prediction of the clinical consequences of planned but not yet surgically performed use of implants or vasoplastic surgery. The tomographically recorded vessel geometry can be virtually changed after software-supported recognition of the spatial structure of the vessels, for example by closing vessels or providing them with implants. The resulting new vessel geometry does not correspond to the current condition of the patient, but to the physician's idea of how the blood vessels of the patient are Patients after an intervention should look like. This virtual vessel geometry can serve as a basis for numerical simulations and on its basis for quantitative statements about the hemodynamics and wall load, just as well as the original geometry information obtained directly from tomographic data.

The limitations in the scope of possible applications are essentially due to restrictions in the admission and registration procedures. The heart and lung area is subject to a strong movement that can not be suppressed. By using the method possibilities, in particular the dynamic coupling of blood flow and wall movement, it is also possible by means of the invention to calculate the blood flow in the heart and / or the coronary vessels. Veins are difficult to model and often hard to pinpoint with tomography. Small vessels (stenoses less than 2 mm in diameter and aneurysms of less than 4 mm) are currently not reliably assessable due to limited CT resolution (about 0.5 mm).

The flow simulation is currently the most time-consuming element of the process. With the use of the Lattice-Boltzmann method and of smaller high-performance computers (2 to 8 processors), which can only be acquired for a fraction of the cost of a tomograph (eg CT or MRI), the duration of a typical Simulation in simpler neurosurgical applications already reduced to 1 hour. The preparation of the simulation including segmentation, 3D calculation grid, refinement, indication of boundary conditions, etc. should amount to on average 5 to 10 minutes and the evaluation of the simulation results 5 to 20 minutes, including archiving the used vessel geometry, Edge data, the converged flow state, which can be used for further simulations, eg for a "virtual angioplasty", as well as selected simulation results integrated over time. The procedure is therefore not suitable for emergency treatment, but in the therapy planning and the subsequent control as Standard agent for clinical support.

The method can also be installed as an upgrade for tomography apparatuses already in use. What is needed are current high-performance computer clusters and manufacturer's own interface software, which enables a connection with the measuring equipment of the manufacturer. For specific applications such as e.g. Neurosurgery requires scanner resolution in the sub-millimeter range, which is not achievable with some tomography devices, for reliable simulation.

The main advantage of the method according to the invention 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 especially in the Lattice-Boltzmann method

(LBM) for the flow simulation. All previously published simulations, which are based on individual tomography data of patients, have been carried out using 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 point of inflow and outflow and from the spatial resolution has been investigated only rarely and then only empirically without any reliability rule

(eg in the form of an error interval). Virtual surgery has already been discussed as a promising means of simulation-based therapy planning, albeit only in connection with coronary arteries and aortic segments. Here is the current feasibility of 3D simulations for clinical practice have been assessed negatively.

Only the method according to the invention with spatially three-dimensionally resolved blood flow simulation represents an option that can be implemented with existing hardware for simulation-based diagnosis and therapy planning of vascular malformations. It is important to determine the required scope (a sufficiently wide environment of malformation, depending on the type, according to the complexity of the vascular structure in the environment, and according to individual features) and the required (spatial and temporal) resolution of the blood flow simulation and, accordingly, the output data obtained with tomography methods. Furthermore, the continuous use of only regular data grids is crucial, which improves both the efficiency and the accuracy in the individual steps of the method.

For the implementation of the method, no expert in the field of fluid mechanics longer needed. Interfaces are provided for the introduction of biomechanical, cytological and other models (relevant for the depiction of normal and pathological remodeling of vessels). This can add additional important influences on hemodynamics and vascular wall loading, e.g. By Wandpulsa¬ tion, blood rheology and coagulation, transient and systemati¬ cal changes in the biochemical behavior of wall cells, etc. are included.

The method according to the invention is suitable as standard method for simulation-based diagnostics, therapy and control of blood vessel malformations, thus for diagnostics, therapy planning and control of many symptoms in cardiology, neurology and vascular surgery in general and in contrast to the previous 3D blood flow simulation methods in each case ¬ currently equipped clinic usable.

The method according to the invention is based on the following prerequisites: tongues:

Spatially resolved tomography data (3D of approximately stationary body parts or 4D, ie including time dependence, in the heart and lungs) must be present. The possibilities of the available tomography hardware limit the number and position of the treatable vessels.

At all proximal end cross-sections (with respect to the existing spatially limited imaging, which is to be used as a geometry for the numerical simulation) of arteries, independent time-resolved measurement information about the volume flow or the blood pressure must be present. Blood flow information may e.g. by ultrasound measurements with Doppler analysis (a fast procedure that is used as standard in sufficiently large vessels) or by MRI Doppler techniques. A number of mostly non-invasive methods are available for measuring the pressure in larger veins.

Models for the mechanical behavior of healthy and damaged vessel walls, as well as for the spatial progression of the lumen cross-sectional area of smaller vessels are required for complete modeling and simulation. Corresponding information is available in the specialist literature, see e.g. G.A. Holz- apple and R.W. Ogden, eds. "Biomechanics of soft tissue in cardiovascular systems", CISM courses and lectures 441, Springer, Vienna, 2003. However, for some applications it is not yet sufficient and then either 4D images or the assumption of rigid walls are related used with 3D recordings.

In the following, the method according to the invention will be explained more in detail. The core of the method is a direct numerical simulation (DNA) of the bloodstream in the vicinity of arterial malformations, which are determined individually and reliably in patients by standard methods of angiography can. The process is based on three main steps, which must be performed essentially with each application of CFD software.

Pre-processing: The geometry of the flowed-through space (vascular system) and the appropriate boundary conditions are festge¬ sets. Accordingly, a system is designed by computer grids, which together cover the entire volume flowed through and ensure the required spatial resolution locally, each grid has only cubic voxels of a corresponding size and the minimum and maximum grid size to the Ar¬ architecture of the computer used in the Installation of the software can be optimally adapted.

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

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

For each of these three main steps in the working process, the following new measures take effect:. increase efficiency and accuracy and facilitate standardization: The management of all data grids is fully automated. All three-dimensional (3D) data are displayed exclusively on regular, rectangular and as often as possible on isotropic gratings. As a result, the fastest and highest-precision versions of the respective algorithms for numerical smoothing, differentiation, integration, etc. can be used.

For the DNA of Navier-Stokes' fluid mechanics, a Lattice-Boltzmann method is used. As a result, optimum computing performance on parallel computers is ensured on the one hand even with very complicated vessel geometries and on the other hand a reliable determination of all hemodynamic parameters is ensured, in particular the pressure in many branched vessel systems and the viscous stresses in the vicinity of vessel walls. It is known from our own research that for the DNS resolution even the most fluctuating modes (Womersley numbers up to about 20), which are still important for the realistic representation of a pulsating flow, especially near the wall, a moderate spatial resolution of 15 to 25 Gitterpunk¬ sufficient in the vessel diameter when using LBM, wherein the wall layers, in which the highest modes lokalisie¬ ren, are represented with only 3 to 5 grid points. A corresponding grid size in the "region of interest" can (au¬ automatically) and should be ensured during preprocessing and can then be easily edited by the LBM during the solution step.

Comparisons between LBM and FVM are known, which show significant advantages of the LBM, eg. These show that in flow areas with complex geometry, the LBM needs a considerably smaller number of grid effects, in order to achieve comparable accuracy in determining the steady state To achieve pressure loss. For turbulent flows, a comparison with pseudo-spectral methods that are of the highest accuracy has a comparable accuracy of the calculated statistics as well as speed advantages for grid sizes over about 100 points in a coordinate direction. Since several spectral methods are very difficult to use for complex geometries, LBM competes with FEM and FVM in such cases. It is known from the literature that FEM are very time-consuming and rather complicated in their application to blood vessel flow. Own comparisons with commercial FVM-based CFD software have shown that the calculation of a stationary solution using the FVM software, which makes use of advanced multigrid methods (Multigrid, MG), results in a computing time comparable to LBM without MG takes up. Through the use of MG for LBM can be up to an order of magnitude. acceleration can be achieved. The basic description of the LBM-MG can already be found on the Internet together with a well-founded selection of a specific procedure from a number of theoretically offering alternatives. In the simulation of pulsating flows, the same comparison has already shown a projection of the LBM (without MG) of at least one order of magnitude in the computing time. By means of such a multigrid method, the stationary scalar and vector quantities for the Lattice-Boltzmann method can be determined more quickly.

By means of these and other features described below, the method according to the invention is much simpler, largely automatable and substantially more precise and faster in the determination of clinically relevant flow patterns and hemodynamic loads.

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 under investigation. In order to ensure reliable geometry recognition and then also flow simulation, requirements are made of the resolution of the input data: A pulse cycle must be determined by specifying at least 16 independent data recordings, which at least 8 in the systole and 8 in the diastole in a healthy Herz¬ 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 lattice blocks) than that of the raster that is to receive the edge data. On the contrary, it is necessary to make use of the global boundary condition which is usual in CFD software, in which a total mass flow is indicated by a selected cross-section.

The tomography data (CT, MRT, etc.) typically used to generate input data is expected to be a 3D data set of gray values given on a regular grid in physical space (and not in frequency space), in conjunction with FIG corresponding Grauwertintervallen and Filter¬ functions, which are used as in the conventional imaging in medical imaging to specify the discrimination thresholds. The preparation phase, in which this information must first be determined by the user, can thus be carried out with existing, manufacturer-specific medical software. Such gray scale data are usually present in the clinic in a variant of the DICOM format, typically given as a multiplicity of 2D images in parallel layers. The nominal resolution (the spatial grid step to be read from the DICOM file) within a slice may be in a ratio of the grid step sizes of not less than 1: 3 to the resolution in the third, axial coordinate direction. (The ideal and so far maximum ratio of 1: 1 is reached only in the latest devices and then not in all measuring methods.) The check whether the resolution thus indicated corresponds to the actual technical Auf¬ solution during data acquisition, can not always be done automatically and may need to be performed by the user. It is therefore assumed that the axial resolution is not significantly worse than that along the cutting planes. The coarser of the two resolutions must be be sufficient to let appear all the diameter of vessels that are in the region of interest (ie in the segmented geometry description) with at least 4 voxels 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 region of interest, the resolution must not be greater than 0.6 mm per pixel. In aneurysms, their neck must be at least 4 and the shortest diameter of their sac with at least 6 voxels. With an isotropic resolution of 0.4 mm, as is currently the case with the new '64rZeiler CT device from Siemens, aneurysms up to 3 mm and 1.5 to 2 mm can be treated.

The second type of expected information is pulse, blood pressure, and blood flow volume data, which allow in-flow marginal conditions for the strain gauges to be determined 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. Perk-told, eds. Cardiovascular fluid mechanics, CISM courses and lectures 446, Springer, Vienna, 2003 For example, an overview of existing ultrasound measuring methods for determining speeds and shear stresses can be found. The spatial distribution of the blood flow velocity in cross sections of medium and smaller arteries, which is required for the indication of inflow 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 veins that are close to the skin and not supported by hard tissue, which is also the case with the carotid artery beyond its bifurcation. For the most common cases of deeper-lying veins, a database must be created that can calculate 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 are intended to provide 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. Also, this problem is to be solved by a database of pulse, pattern, which allows, from simple Druckver¬ running measurements (see above details minimum Zeitauflö¬ solutions) with inclusion of other information, such as age, Ge and bad general state of health of the patient, position of the vessel, etc., to calculate a plausible pulse progression in the vicinity of the investigated malformation. It remains undecided as to whether correlations and TFM (transfer function method) for certain body parts can be used reliably for this purpose.

Geometry determination: In order to reduce the influence of unavoidable errors in the specification of inlet and outflow boundary conditions (EARB), these boundary conditions should be given only far enough from the investigated malformation. It is anticipated that vortex-producing features of the vessel geometry (such as bifurcations and high curvatures) will strongly influence the local structure of the flow and thus reduce the influence of details in the indication of the EARB. Both upstream and downstream of the main direction of the blood flow, the inflow or outflow edge surfaces should be further away from the location of the malformation than the first two curvatures and the first bifurcation. In cases where the anatomy or the circumference of the present tomography data preclude this (typically in the inflow region), an investigation of the influence of the EARB on the flow structure of the corresponding numerical solution is recommended, which compares to less at least two variants of the simulation, which differ only by the profile or the type (pressure or mass flow) of the inflow boundary condition exists. The automatic verification of the EARB conditions is possible, but requires a (again automatic) topological vessel structure recognition and therefore also a good spatial resolution of the tomographic data far distal from the malformation. If such a resolution is not achievable, or the vessel structure is extremely complicated, the selection of the peripheral surfaces must be made by an operator, for example a doctor. This need is automatically signaled. It is additionally required that all larger vessels (in contrast to "smaller vessels", see below) be represented with those with the location of the deformation (stenosis, aneurysm, stent, bypass, etc.) within a sphere with diameter 3 L directly connected to the deformation, where L denotes the length (the largest diameter) of the investigated deformation. This sphere must, for the most part, be included in the region of interest and flow determination.

Vessels with a diameter of less than 30% of the effective diameter of the largest vein that passes directly by the deformation are referred to as "smaller vessels". Such vessels are automatically removed from the geometry description if they do not lead directly into or past the deformation. Of the remaining vessels, the majority of marginal areas "finish", and inlet or outflow boundary conditions must be prescribed, although they are unknown. At these surfaces, synthetic boundary conditions are specified, which are already calculated automatically by the mass flow proportional to the cross-sectional area of the respective vessel (with respect to its axis, which is automatically calculated by the above-mentioned recognition method for the topological structure of the existing binary segmented vessel geometry or with Decision of a supervising physician has been determined) and the dynamic mass maintenance law accordingly be determined. Important vessels can be far strom¬ downward (distal) after the deformation of physiological or even for technical reasons are difficult to see. In these cases, an operator, for example the doctor, is asked and supported only when determining the course of the vessel axis, while the vessel diameter is extrapolated on the basis of known proximity formulas of an exponential type. In order to calculate a plausible course of the axis of such vessels, the local threshold value adjustments, regularization eg with non-linear diffusion, adapted inclusion of the gray-scale gradient into the location of the vessel wall, as well as further known advanced segmentation methods are included.

Simulations of vessels with implants (stents, coils, but also bypasses) are also possible individually with the new procedure. The geometry and the mechanical properties of the implant should be known and a sufficiently resolved 3D tomography image with the already placed, clearly recognizable implant should 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, the actual position of the implant is "registered" by curved geometric objects without thickness (in jargon medical imaging). These are the deformations of corresponding, previously prepared geo¬ metric models of the implant in a reference position (eg, a stent, which is in a straight or simply curved (with constant radius of curvature) tube with a constant, circular cross-section disposed), the present tomography - Coming closest to data set in a suitable standard, first determined automatically and then with the support of bildge¬ benden method and by simulating their mechanical (hy-perelastischen, plastic, or even, for example, in natural implants, viscoelastic) movements between the Gefäß¬ walls , whose rheology is modeled as in the calculation of the dynamic coupling of wall and flow. After the current spatial position of the implant has been determined, it can be determined by its known mechanical properties or by simple "warping experiments" with spatial deviations. The detection software identifies the mechanical stresses within the implant as well as between it and the vessel walls.

The missing hemodynamic part of these strains is then estimated by DNA. In this case, with sufficient resolution of the DNA, coils with simple geometry in the current state and stents shown as a 3D body, in which their adapted "skeletons" is spread to a width that corresponds to the actual thickness of the wire cross sections as closely as possible ent, but not thinner than 3 voxels. is on the grid. With low resolution of the DNA coil bundles must be modeled as porous medium, - where the porosity from the tomography recordings (in implant already present in the body) or from personal experience of an operator, e.g. of the physician (in medical planning), must be appreciated.

Finer coils as well as gels, verklottungen, soft plaques and the like are modeled as a homogeneous-porous body. Not only the porosity, but also the rigidity, solubility, diffusion properties, the proportion of chemically unstable substances and other parameters must be known in order to be able to completely determine the clinically relevant effects of such modeled implants or deformations. Corresponding mass transfer simulations are, according to the latest state of the art, including diploma theses at LSTM Erlangen, coupled with finite difference methods on the same computational grid as LBM and with the LBM solver directly coupled with each time step, with use of simulation schemes and boundary conditions of second order (that is, matched with the LBM).

For each of these types of objects, records with representative values should therefore already exist in advance. Its development is not part of the present description. Also, the selection of optimal models for porous media can not be clearly described and should be used during the Generation of records are determined. However, they must essentially retain the structure of the Navier-Stokes equations, so that their calculation with LBM remains possible by means of an introduction of correspondingly calculated "model forces" and "model stresses ^1. " The required indications of diffusion properties are to be calculated of fluctuations in the temperature and in the concentration of important substances and blood constituents, and corresponding diffusion-convection equations are best calculated in the context of LBM simulations by means of adapted finite difference methods.

Computational grid: 'Even if the original gray-scale file is not isotropic, ie if the step in the axial direction is not equal to that in the section planes, the binary-segmented geometry should be displayed on an isotropic grid. An advantage of this is that numerical errors are avoided which occur due to grid anisotropies in all Rechen¬ methods and turn out to be wesent¬ Lich at low resolution. Another closely related advantage is that simpler and more accurate variants of the Lattice-Boltzmann method are used. The transfer to an isotropic grid can very efficiently be combined with filtering and refining. With the highly curved and branched vessel geometry that is to be treated in most cases, these benefits are of great importance. If the filtering results in significant changes to the topology, this is signaled and the user (eg the supervising physician) is given a simple possibility to modify the filter properties or to select one of the resulting topologies as "correct". The filtering should be location-dependent and correspond to a (non-isotropic, locally adapted) smoothing operator, usually with a filter width of at least 3 and a maximum of 12 voxels of the original lattice, to avoid non-physical "waves" of the vessel wall in the region of the vessel wall To avoid deformation. The spatial resolution of the resulting isotropic data grid should be ensure at least 15 to 20 voxels along the shortest dimension of "normal" vessels in the vicinity of the investigated vessel deformation.

The same minimum resolution also applies to smaller, important vessels, and even more so to stenoses, as higher velocities and gradients occur in the narrowed lumen. Only in smaller vessels with automatically determined and typically low outflow can the resolution be reduced to 6 to 12 grid points (depending on the variant of the Lattice-Boltzmann scheme used) in diameter. Even smaller vessels (diameter less than 30% of 18 voxels) are modeled and not simulated. In this case, a pulsating laminar flow is assumed and a third database is used, which contains a detailed amount of calculated short-term inflow flows in vessels with different curvature. The velocity profile at the inflow edge can be given in these calculations only with low-order 2D polynomials, since the task is to extrapolate velocity data of small gradient originating from areas of diameter less than 5 voxels into the modeled vessel.

A lattice decomposition with subsequent elimination of the parts in which there are no voxels traversed, and a refinement (or even coarsening to avoid unnecessarily high resolution) should ensue after the creation of the isotropic lattice. Each grid part should be a cuboid, networked by its own isotropic grid, whose minimum size depends on the technical specification of the particular computer, but should not fall below 12 voxels in each coordinate direction, which with the efficiency of cache architectures, but also with the Resolution in cross-section of most treated Gefä¬ Shen is connected. 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 lattice steps in adjacent blocks to be only 1: 1 or 2: 1 or 3: 1. This simplifies communication and permits 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 substantially exceeded. The refinement procedure thus described is then repeated recursively in blocks where necessary until all vessels are well resolved. The descriptions of all the original blocks and all the intermediate blocks are also stored during the refinement or coarsening. 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.

Representation of the vessel walls: The identification of the position of vessel walls from the 3D tomography data has already been described. This location must be kept for the DNS in an easy-to-handle data structure. The only exception is when the bounce-back method is used, as an approximation of the sticking boundary conditions on vessel walls, which are assumed to be fixed and immobile and may only be known inaccurately. This is a fast, simple and robust variant of the method, which also guarantees exact mass conservation. However, it is of limited use, for example, in relatively well-resolved vessels, but they are almost immobile (as in the brain) or in vessels whose movement is unimportant for the dynamics in the area of interest. The wall information is mapped onto the rigid computing grid and coupled with it. In all other cases, the wall layer must be stored and, if necessary, always again (eg in the case of the strong pulsations of an AAA). If the wall dynamics is to be calculated, a mechanical model of nonlinear elasticity and (in case of large deviations or heavy loads, such as in larger aneurysms) of plasticity must be given. An example of such models is given in Holzapfel & Ogden (loc. Cit., 2003). There are two options for displaying the wall position. Both are an "exact" or "sharp" representation, which allows the clear calculation of Wand¬ load and facilitates the efficient simulation of the wall dynamics, but also a communication dynamic information tion between the "wall grid" and the for the Flow simulation causes suitable 3D computational grid. 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 imaging method is easier to handle with always small deviations from the wall: the connections between adjacent grid points in the isotropic 3D computational grid are characterized when they intersect a vessel wall, whereby the position of the section is also stored on the 3D computation grid. Cases in which a lattice point overlaps (almost) with an overlap point are systematically avoided by "generic small deformations" which can be applied locally.

The second method of presentation is classical: An unstructured grid (see FIG. 4) is automatically constructed, 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. Standard formats of the largest CAD software manufacturers as well as other standard formats such as STL will therefore be readable and automatically converted into an internal representation of the surface geometry. The ratio of each point of this representation to the 3D computing grid can be easily determined on the basis of the maximally simplified structure of the isotropic computing 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 course of the vascular walls is changed with respect to the 3D arithmetic grid and, if necessary, implants are also added to the description of the geometry by matching their "skeletons" (see geometry determination) to the course of the wall and then preparing them (see above) or in which interactively selected subareas of the vessel volume flowed through are 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. If appropriate, the final result of the change in geometry is converted from the shape of a deformed 2D grating into a new designation of the wall-penetrating grid point connections on the fixed 3D computation grid. For the manipulation of the unstructured 2D grating, a part of its points is selected interactively and then marked as elastically connected. Its Ausgangsla¬ ge is considered as a reference configuration in which there are no unbalanced voltages. The rest of the points remain fixed.

The possibility of simulating wall movements and coupled with pulsating flow in accordance with the Lattice-Boltzmann method (LBM) represents a decisive advantage of the invention. The wall movements can be synthesized from 2D representations, in particular as grids, as well be determined from several Tomographieaufnahmen. The modern Tomogra¬ phiegeräte allow recording of time-periodic movements of the heart or larger aneurysms. By coupling with the flow, the mechanical load on the wall can be determined without any invasive intervention having to be made. This procedure is more accurate and less expensive than direct recording methods (ultrasound, sine contrast-MRI) for the detection of the blood flow and allows a reliable estimation of the wall stresses. When processing a time series of shots, a condition close to that found at the end of diastole is generated 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 each movement, the points which have come very close to each other are unified in one point and thereafter the possibility is given to initiate an automatic optimization of the number and position of the "elastic" points on the 2D grid. Changes in the topology of the entire vessel geometry are automatically detected after each movement on the basis of the already existing axis structure and signaled the same.

Methods of "inflating" the implants, including their elastic properties, until firmly pressed against the vessel walls, do not appear to be adequately reported in the literature. Its principle is to be the numerical calculation of the displacement and deformation of the implant from an initial state, which is determined by the reference shape of the implant and a starting position interactively selected by an operator, e.g. prescribed by the doctor. As soon as the implant has reached it at one point after a movement in the direction of a vessel wall, it is represented as a hyper-elastic or elasto-plastic object (as a 3D body, as a sheath or as a network of linked "wires"). During the further adaptation of the position of the implant, the vessel wall is held immobile and rigid in typical applications. When the "balloon" spreads, the required force (against the resistance of the implant) is determined and a maximum (adjustable) force and the minimum vessel diameter in the balloon area are not exceeded. In the end, the "virtual balloon" is removed. The entire method of placing an implant does not include consideration of the blood present in the vessel. The resulting geometry is further treated exactly as in the case of implants already placed in the patient whose position has been registered as described above.

Flow Simulation: Blood flow becomes incompressible modeled. The determination of the pressure is nevertheless complicated by two factors: On the one hand, the elasticity of the vessel walls allows the propagation of pressure waves, which can not be treated in the standard formulation of incompressible flow solver algorithms. On the other hand, any very complex geometry is a prerequisite for difficulties in solving the Poisson task for the instantaneous pressure distribution. For example, the pressure on areas with "holes" is not unambiguously defined. This problem is avoided with the use of lat- tice Boltzmann solvers because the pressure is calculated by means of numerical "pressure waves", ie qualitatively according to the actual physics, and not by means of Poisson solvers. Comparisons between LBM and FVM in the solution of laminar flows in a "generic porous medium" (see above) have shown that the LBM solution converges much better for the pressure. The "incompressible" variants of the well-known LBM have technical and other advantages. The problem of elastic walls has already been discussed.

In addition, the non-Newtonian rheology of the blood may also have a significant influence, especially in flow areas with very low blood velocity, e.g. within large aneurysms or in capillaries. In large veins, on the other hand, an assumption of Newtonian rheology is almost problematic. 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 taken. Particularly in the modeling of partially durch¬ flowable parts of the vessel lumen as a porous media, the need is apparent to apply tensor models for the viscosity (and the diffusion of different blood components and mitge¬ contributed substances).

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 tensor is included in the definition of the LBM equilibrium function. If it is necessary for flow simulation to resort to complicated voltage sensors, it may also be necessary to use information from adjacent voxels and to calculate finite differences.

The perfect locality of all LBM algorithms leads to excellent scaling on parallel computers. The number of operations and degrees of freedom per grid point is moderate, so that a high computing speed is achieved on processors with sufficient "fast memory" (vector registers or cache levels). The locality even allows the calculation of a good approximation of the entire voltage tensors only from data that are locally present on the respective grid point. Especially near the wall, this is an advantage over FVM or finite difference methods (FDM), since the proper position and movement of the wall is not needed directly in the stress calculation. It also provides an efficiency advantage in calculating stress. If the FDM approximation is still computed, it can provide a sensitive test of accuracy in the LBM calculation at higher Reynolds numbers by comparing it to the result of "local" stress calculation. The vollexplic character of the LBM means that all calculations using this method require a sufficiently short time step (see above). On the other hand, the need to reliably discretize the pulse history poses a similar requirement. The comparison of both restrictions has been accepted by the inventor as confirmation that the explicit character of the calculations does not play a significant role in blood vessels. The resolution, which is required at the steep time gradients of the pressure curve at various locations with a corresponding delay, necessitates the selection of the time step to a constant and small value. Thus, pulsating flows, in which the pressure fluctuations have a complex time course, can be represented, and in particular fine and fast movements in the fluid can be detected. Implicit procedure on the base LBM (but mostly with a spatial discretization by FEM or FVM and not, as in the standard LBM that is also provided in the inventive method, by FDM) have been developed for static problems. In the case considered here, these have no advantages. Instead, LBM-MG is used here for stationary tasks.

Post-processing: The most important variables in estimating the mechanical loading of vessel walls are the stresses transmitted by the blood stream. All components of the stress tensor, differentiated into a viscous and a pressure component, are calculated at each lattice point within the area through which flow occurs at each time step as part of the simulation method and not as additional computational load independently of other points and times which facilitates the production of time series at check points determined by the physician. On the basis of these data, after the simulation has been completed, statistics such as e.g. An oscillation index for the shear stress (as a vector tangential to the wall) can be calculated and displayed very quickly. Computation of statistics during the simulation causes a significant amount of time and should only be turned on when spatially averaged statistics, such as e.g. the global mass flow through a certain cross section or effectively the residence time in a selected volume part of the area through which it flows must be desired.

In addition to the stresses, other hydrodynamic fields, such as the 3D vector terms of velocity or of the vortex (calculated as the application of a finite difference approximation of the rotation operator to the velocity field), can also provide important information. Since the structures of these fields are familiar and meaningful to a fluid mechanic, but are unlikely to be of much concern to a physician, their effects on wall tensions, dwell time, etc. must be made available to the physician on request with simple and readily available explanations can be. For example, strong vortices should be referred to as regions of low relative pressure within the lumen and potentially high wall shear rates, or the length of streamlines should be used as an indicator of potential fouling or pilling, etc. Adjustable thresholds and the automatic numerical indication of To facilitate assessable burdens or even allow for a doctor to identify and evaluate the risk of individual Gefäß¬ deformations.

In addition, the display modalities customary for CFD and visualization software should also be available, such as e.g. the 3D isoflachen of velocity (or other vector fields such as the pressure gradients and scalar fields such as the concentration of a preparation in the blood) presented by way of example, flow lines, scratch lines and LIC methods (line integral folding). Local spatially and temporally (in-phase) averaged data can easily be projected onto the original DICOM raster. The pulsating portion of the speed and the vortex in selected sections can be calculated without great expense during the simulation and then visualized.

Representations of the results are always stored in a standard format (DICOM) in order to facilitate automatic documentation, but also the 3D visualization (by rotation, zooming, etc.) with already existing and familiar software for medical imaging. The resolution of the result data must be selected 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 also not directly usable in medical practice in order to justify their storage.

The invention will be further explained below with reference to examples and drawings. In the drawing show: 1 is a schematic representation of the method according to the invention,

2 shows a schematic representation of the automated SD data flow taking place exclusively on rectangular grids and in the form of x-ray information in the case of the method according to the invention,

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

4 shows an automatic cross-linking of the surface of the geometry shown in FIG. 2 with an unstructured 2D file by means of a marching cubes algorithm implemented in commercial software, FIG.

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

6 shows a representation of an instantaneous flow state, in which the toned lines extend tangentially along the velocity vector field and the size of the velocity vector is locally coded by the tone,

FIG. 7 shows accumulation areas, fluidization areas and a laminar area of a vessel structure, represented by a LIC method implemented in commercial software, FIG.

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

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

1 shows a schematic representation of the method according to the invention. One of the main requirements for the higher efficiency of the method compared to previous approaches is the limitation of all occurring 3D data structures on rectangular uniform grating, which is shown schematically in FIG. For ID (e.g., space curves) and 2D (e.g., vessel display) data, no such limitations apply. As a result, the efficiency is hardly impaired since the data of lower dimension can be stored in fast memory types on current computers, and therefore, especially with larger overall computer grids, take up an insignificant proportion of the access and computation time.

As an example of use, a brain aneurysm is illustrated which has a sufficiently complex geometry. The results of the steps of the method according to the invention are represented uniformly here.

Fig. 3 shows a binary segmented brain vessel geometry with aneurysm in the center, which is clearly visible. FIG. 4 shows the surface of the vessel structure appearing in FIG. 3, in a cross-linking with an unstructured 2-D file.

In the snapshot of a speed component shown in FIG. 5, given the conditions of adhesion to the barrel walls to see the entire surface of the walls in dotted gray. 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 FIG. 6 illustrates, within the aneurysm the speeds are very low and a congestion area can be recognized in the pointed part of the bag.

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

FIGS. 8 and 9 show the time course of hydrodynamic variables at a control point within the aneurysm. FIG. 8 shows velocity components and FIG. 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.

The greatest expense in the application of the Ver¬ process according to the invention is not the segmentation and (unlike some of the known approaches to numerical blood flow simulation) nor the networking of the vessel geometry, but the purely computational power for resolved numerical simulation. The resulting large amounts of data can be used only after substantial processing and reduction for a practical decision-making process, but then the good resolution permits extensive conclusions about the relationship between the condition of the vessel walls and the hemodynamic loads. The invention can be summarized as follows: Three-dimensional (3-D) gray scale data from tomographic images (MRI or X-ray CT) are binary-segmented with variants of suitable known algorithms for medical and general imaging. Arisen 3-D vessel geometries are used for a solved numerical simulation of their flow on cubic computing grids with Lattice-Boltzmann flow solvers. Required boundary conditions are extracted from specifically developed databases or, insofar as feasible, from individual non-invasive measurements. Just where and when the wall dynamics is important is sie.mittels-boundary immersed, immersed-in, _'terface or similar methods also simulated. Alternatively, it can be created from time-resolved (4-D) tomography data using the same segmentation methods, which results in lower computation effort and, by dispensing with a modeling of the wall condition, also a lower computation error. Implants, vasoplastics, plaques and the like present in the patient are identified and introduced into the simulation geometry as well as virtual (not yet developed in the patient) geometry changes, implants and the like with computationally unresolved fine structure modeled as an elastic, porous body. Rectangular Cartesian grids for 3D data are used exclusively and the Lattice-Boltzmann method ensures efficiency (a few hours calculation, a maximum of 1 hour use per patient), standardization (use requires no non-medical training , Inputs and results in DICOM format) and accuracy.

Although the invention has been described above in connection with blood vessels, it should not be limited thereto, in particular also encompass other fluid-carrying vessels.

Claims

Expectations

1. Method 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 tissue structure data is used on regular data grids (geometry voxel data) of the vessel area to be represented, including its wall, the same data grids or regular isotropic computational grids (voxel grids) generated from them are selected for the vessel representation and for determining the flow course and the course of the fluid flow is determined in time steps, characterized in that one or more vessel sections to be examined are selected , an area of the vessel is selected from the three-dimensional geometric data, which contains the vessel section(s) and in which the flow conditions are to be represented, the three-dimensional geometric data are segmented to represent the vessel walls, the inflow and outflow edge surfaces of the vessel area are determined, the grid size of the computing grid is selected depending on the dimensions of the selected vessel area and the parameters of the flow taking place therein, the computing grid is dismantled and the parts of the grid are eliminated that do not contain any voxels through which flow or flow occurs, the time determination The fluid flow is carried out until the flow representation is sufficiently accurate, the characteristics of the flow and the mechanical load on the vessel walls intended for the representation of the flow solution and the results are transferred and stored in data structures optimized for imaging or archiving.

2. The method according to claim 1, characterized in that the resolution of the computational grid is increased (refinement) in areas in which a larger number of grid points are required and renewed segmentation is carried out.

3. • Method according to claim 1, thereby g e k e n. n - . This means that the resolution of the computational grid is reduced (coarsening) in areas in which a smaller number of grid points is required.

4. Method according to one of claims 1 to 3, characterized in that a multigrid method developed for three-dimensional Lattice Boltzmann calculations (Multigrid) is used for acceleration.

5. Method according to one of claims 1 to 4, characterized in that a block-structured grid is used, the blocks of which overlap, with the grid steps in adjacent blocks being in a ratio of 1:1, 2:1 or 3:1.

6. The method according to one of claims 2 to 5, characterized in that the refinement is carried out recursively and, if necessary, repeatedly in blocks until all vessels are well resolved.

7. The method according to one of claims 1 to 6, characterized in that a vessel section is selected to which a vessel structural part is to be added.

8. The method according to claim 7, characterized in that information on the geometry of the vascular structure ture, e.g. from tomography or CAD data, can be converted as voxel data or as an independent data structure.

9. The method according to claim 7, characterized in that the three-dimensional geometric data of the vascular structure part are selected from a stored vascular structure table or database.

10. The method according to one of claims 7 to 9, characterized in that the position of the vascular structural part to be examined is determined and its three-dimensional geometric data is inserted into the structural data of the vascular area to be represented.

11. The method according to one of claims 7 to 10, characterized in that the three-dimensional geometric data of the vascular structural part or a part of it have been modeled as a porous structure (s).

12. The method according to any one of claims 7 to 10, characterized in that the vascular structural part is an artificial, natural or bioengineered implant or a vasoplasty.

13. The method according to any one of claims 7 to 11, characterized in that the vascular structural part is a vascular malformation (e.g. dilation, narrowing).

14. The method according to one of claims 1 to 13, characterized in that a velocity profile is determined for the inflow and outflow boundary conditions from a stored table or database based on the measured or estimated local Reynolds number and the vessel curvature.

15. The method according to one of claims 1 to 13, characterized in that for the inflow and outflow flow boundary conditions from a stored table, in particular a database, based on anatomical and physiological information, e.g. the position of the vessel in the body, pressure curve measurements, body condition data, one or more pulse patterns are determined and from these the pulse curve in the vicinity of the vascular structural part to be examined is determined.

16. The method according to one of claims 1 to '6, characterized in that an unstructured two-dimensional grid is used to represent the wall geometry that may change over time and, before a change in the position of points of the two-dimensional grid, the position of the intersection points of the wall-penetrating grid is used Grid point connections are stored in the computational grid.

17. The method according to claim 16, characterized in that the two-dimensional grid is created using known imaging and image processing algorithms, e.g. the marching cubes algorithm.

18. The method according to claim 16, characterized in that the wall of the vessel area is represented separately from the interior of the vessel, in particular as a two-dimensional grid, in particular an unstructured grid, and is coupled to the three-dimensional computational grid used for the flow simulation by dynamic equations.

19. The method according to claims 16 to 18, characterized in that the two-dimensional grid and the computational grid are coupled by the immersed interface method and the two-dimensional grid is changed independently of the computational grid at each time step and the computational grid is not modified becomes.

20. The method according to one of claims 16 to 18, characterized in that the wall of the vessel area is represented by connecting the adjacent ones Grid points that intersect the wall (wall-penetrating grid point connections), with the position of the intersection points being saved in the computational grid.

21. The method according to claim 20, characterized in that, while some of the points of the two-dimensional grid remain fixed, the connection of the other points is defined as hyperelastic and the position of selected points is changed by these points, with which the position of the points elastically connected to these points is also changed.

22. Method according to one of claims 16 to 19, characterized in that the vessel wall is reconstructed from several tomography images (e.g. from X-rays, MRI, Doppler methods), each of which is coupled to the computing grid.

23. The method according to claim 1, characterized in that the transport of substances and / or the diffusion of different blood components is determined coupled with scalar values assigned to the same computing grid in the temporal steps of determining the fluid flow.

24. The method according to claims 1 to 23, characterized in that the distribution of the tension, the speed and the pressure in the flowing fluid is shown.

25. The method according to claim 24, characterized in that the stress tensor, divided into a viscous and a pressure component, is determined for each point of the computational grid without using numerical differentiation.

26. The method according to claim 24, characterized in that the vortex and the dissipation in flowing fluid can be shown.

27. The method according to one of claims 24 to 26, characterized in that the pulsating portion of the variables shown is displayed directly, but also by calculating characteristic numbers over a pulse period.

28. Method according to claims 24 and 27, characterized in that the shear stresses and the pressure, their mean values and fluctuation characteristics are shown on the vessel walls.

29.. Method according to one of claims 1 to 28, characterized in that before the fluid flow is determined, the resolution of the representation of the flow is determined, which is at least the resolution of the three-dimensional structural data.

30. Computer program product for implementing a method according to one of claims 1 to 29.

31. Application of the method according to one of claims 1 to 29 on blood vessels.

32. Application of the method according to one of claims 1 to

29. especially 16 to 23, on elastic blood or fluid-carrying vessels with moving walls.

33. 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 tissue structure data is used on regular data grids (geometry voxel data) of the vessel area to be represented, including its wall and the same data grids or regular isotropic computational grids (voxel grids) generated from them fully automatically for vessel representation and for determining the flow profile selected and the course of the fluid flow is determined in time steps, in particular for carrying out the method according to one of claims 1 to 29, characterized in that

Means are provided for selecting one or more vessel sections to be examined,

Means are provided for selecting an area of the vessel from the three-dimensional geometric data, which contains the vessel section(s) and in which the flow conditions are to be represented,

Means are provided for segmenting the three-dimensional, geometric data to display the vessel walls,

Means are provided for determining the inflow and outflow edge surfaces of the vessel area,

Means for selecting the grid size of the computing grid are provided depending on the dimensions of the selected vessel area and the parameters of the flow taking place therein, a device is provided which dismantles the computing grid and eliminates the parts of the grid that have no flow through or on it Voxels are included, a device is provided which carries out the temporal determination of the fluid flow until the flow representation is sufficiently accurate, a device is provided which determines the characteristics of the flow and the mechanical load on the vessel walls intended for the representation the flow solution is determined, and a device is provided for the transmission and storage of the results in data structures optimized for imaging or archiving.