EP1774445A2 - Procede de representation de donnees de flux et de sollicitations de la paroi en trois dimensions dans des vaisseaux conducteurs de fluide, en particulier des vaisseaux sanguins, a l'aide de la methode de boltzmann sur reseau - Google Patents

Procede de representation de donnees de flux et de sollicitations de la paroi en trois dimensions dans des vaisseaux conducteurs de fluide, en particulier des vaisseaux sanguins, a l'aide de la methode de boltzmann sur reseau

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Publication number
EP1774445A2
EP1774445A2 EP05774663A EP05774663A EP1774445A2 EP 1774445 A2 EP1774445 A2 EP 1774445A2 EP 05774663 A EP05774663 A EP 05774663A EP 05774663 A EP05774663 A EP 05774663A EP 1774445 A2 EP1774445 A2 EP 1774445A2
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European Patent Office
Prior art keywords
grid
vessel
flow
data
dimensional
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German (de)
English (en)
Inventor
Kamen Beronov
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Friedrich Alexander Univeritaet Erlangen Nuernberg FAU
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Friedrich Alexander Univeritaet Erlangen Nuernberg FAU
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders

Definitions

  • 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 is very expensive.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • LBM Lattice-Boltzmann method
  • the cells of such a grid can be processed comparatively quickly by means of high-performance computers.
  • 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.
  • the walls of the nasal cavity are recognized by segmentation techniques for coherent CT image elements up to the accuracy of the voxel geometry.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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
  • CT data 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 .
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • a linearization of the momentum Stokes instead Navier-Stokes equation
  • multigrid multigrid methods
  • the numeric iterations have the physical meaning of time steps.
  • 100 to 800 steps per pulse period are sufficient depending on accuracy requirements.
  • 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.
  • 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 ⁇ is unknown vessel walls, movement can be dispensed with the Mitbetician 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.
  • 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.
  • the walls must be rendered highly accurate, for which LBM second order boundary conditions known in the literature can be used.
  • LBM second order boundary conditions known in the literature can be used.
  • BBL bounce-back method
  • 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.
  • 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.
  • 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.
  • an adapted variant of the Lattice-Boltzmann method in which the computational grid is disassembled and the parts of the lattice are eliminated do not contain any perfused or infused voxels.
  • 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.
  • typical manifestations such as stenoses or aneurysms.
  • 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.
  • 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.
  • GDC an aneurysmal lumen as a result of implants
  • 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.
  • 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.
  • 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.
  • FVM field-to-elastomer
  • FEM field-effect transistor
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 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.
  • 3D tomography data that differentiates blood vessel tissue and time-dependent measurements of blood flow in veins proximal to the malformation under investigation.
  • 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.
  • 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.
  • 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.
  • 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 optimal temporal resolution which is required for the indication of the systolic pulse phase in the DNA, corresponds to a uniform time step of 4% of the total duration of a pulse period or even shorter, to 1%, in areas with very steep or complicated pulse progression, such as in the first aortic branches. In most practical cases, this accuracy is not achievable, especially with deep wires.
  • this problem is 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.
  • inlet and outflow boundary conditions 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.
  • 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.
  • 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.
  • 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.
  • 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 Er Siemens, 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).
  • 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.
  • 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 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.
  • 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).
  • the Ratio of lattice steps in adjacent blocks 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.
  • the wall layer must be stored and, if necessary, always again (eg in the case of the strong pulsations of an AAA).
  • 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).
  • 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.
  • 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.
  • a part of its points is selected interactively and then marked as elastically connected. Its Twila ⁇ 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 Tomographieamn.
  • the modern Tomogra ⁇ phietechnik allow recording of time-periodic movements of the heart or larger aneurysms.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 Maschinenmat ⁇ 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).
  • the vollexplic character of the LBM means that all calculations using this method require a sufficiently short time step (see above).
  • 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.
  • 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.
  • spatially averaged statistics such as e.g. the global mass flow through a certain cross section or effectively the residence time in a
  • 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).
  • 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
  • flow lines, scratch lines and LIC methods line integral folding
  • FIG. 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
  • FIG. 3 shows an example of a binary-segmented real brain vessel geometry, in which the aneurysm lying in the center is clearly recognizable
  • FIG. 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”).
  • FIG. 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. 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
  • FIG. 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.
  • FIG. 1 shows a schematic representation of the method according to the invention.
  • ID e.g., space curves
  • 2D e.g., vessel display
  • a brain aneurysm 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.
  • 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.
  • Ruds-boundary immersed, immersed-in, 'terface or similar methods also simulated.
  • 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.

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Abstract

Des données en valeurs de gris en trois dimensions (3D) fournies par l'imagerie par résonance magnétique ou la tomodensitométrie sont segmentées de manière binaire avec des variantes d'algorithmes adaptés à l'imagerie médicale et à l'imagerie en général. Les géométries de vaisseaux en 3D obtenues sont utilisées pour une simulation numérique à résolution de leur écoulement sur des grilles de calcul cubiques avec des résolveurs de flux selon la méthode Boltzmann en réseau. Les conditions secondaires nécessaires sont extraites de banques de données ou de mesures non invasives individuelles. Lorsque la dynamique de paroi est importante, elle est simulée en même temps. Les implants, l'angioplastie, les plaques présents dans le patient etc. sont identifiés et introduits dans la géométrie de simulation. De même, des modifications virtuelles (pas encore présentes chez le patient) de géométrie, par ex. des implants à poser, des parties de vaisseau à enlever etc. sont ajoutés à la description géométrique à calculer pour permettre, lors de la planification médicale d'opérations chirurgicales correspondantes, une évaluation préalable précise des effets desdites opérations. Les implants dont la structure fine ne peut être résolue sur la grille de calcul de la simulation de flux sont modélisés sous forme de corps poreux élastiques.
EP05774663A 2004-07-27 2005-07-27 Procede de representation de donnees de flux et de sollicitations de la paroi en trois dimensions dans des vaisseaux conducteurs de fluide, en particulier des vaisseaux sanguins, a l'aide de la methode de boltzmann sur reseau Withdrawn EP1774445A2 (fr)

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DE102007026519A1 (de) 2007-06-08 2008-12-18 Siemens Ag Verfahren zur Bestimmung eines Rupturrisikos wenigstens eines Aneurysmas eines Patienten und zugehöriges System
US10482215B2 (en) 2014-10-22 2019-11-19 Indiana University Research And Technology Corporation Unified computational method and system for patient-specific hemodynamics
DE102014226685A1 (de) 2014-12-19 2016-06-23 Siemens Healthcare Gmbh Verfahren zum Identifizieren von Versorgungsgebieten,Verfahren zur graphischen Darstellung von Versorgungsgebieten, Computerprogramm und maschinenlesbares Medium sowie bildgebendes Gerät
WO2019071249A1 (fr) * 2017-10-06 2019-04-11 Emory University Procédés et systèmes de détermination d'informations hémodynamiques pour un ou plusieurs segments artériels
US11037280B2 (en) 2019-03-12 2021-06-15 GE Precision Healthcare LLC System and method for simulating bilateral injection of contrast agent into a patient
CN111767683B (zh) * 2020-06-17 2023-06-06 北京理工大学 颈动脉弹性斑块流固耦合特性ib-lbm数值模拟方法

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