Abstract:
The invention relates to a method for a three-dimensional representation of a moving structure by a tomographic method, in which during one recording pass a series of projection recordings is registered by an imaging unit at different recording angles between a start position and an end position, it being possible to reconstruct three-dimensional image data from the projection recordings with the following steps: a) generation of tomosynthesis projection recordings along a tomosynthesis scanning path; b) interpolation of the data of the tomosynthesis projection recordings in accordance with an interpolation algorithm in order to generate a projection data set; c) use of a tomosynthesis reconstruction method on the projection data set in order to generate a tomosynthesis volume image; d) repetition of steps b) and c) for all times of interest, and e) display of tomosynthesis representations from the tomosynthesis volume images.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority of German application No. 10 2007 037 996.1 filed Aug. 10, 2007, which is incorporated by reference herein in its entirety. 
     FIELD OF THE INVENTION 
     The invention relates to a method for the three-dimensional representation of a moving structure by a tomographic method. 
     BACKGROUND OF THE INVENTION 
     In medicine a frequent problem is to generate time-resolved, three-dimensional images of dynamic (time-dependent) events within objects which vary with time, from recordings of projections of the objects taken from different directions. The object to be imaged can be the human body, for eV(ample. Here, in particular, the spread of contrast agents in vessels, for eV(ample dynamic angiography, in tissue, for eV(ample perfusion, the spontaneous movement of organs, for eV(ample the heartbeat, breathing, peristalsis or swallowing, or eV(ternal mechanical compression of tissue (elastography), can be considered as dynamic events. The recordings can be made with X-ray apparatus with a flat detector, as described for eV(ample in US 2006/0120507 A1. 
     Such a known X-ray diagnostic apparatus is illustrated in  FIG. 1 . As an imaging unit the X-ray diagnostic apparatus has a C-arm  2  supported in a rotatable manner on a stand  1 , an X-ray source, for eV(ample an X-ray emitter  3  and an X-ray image detector  4 , these being mounted on the ends of said C-arm. 
     The X-ray image detector  4  can be a rectangular or square flat semiconductor detector that is preferably made from amorphous silicon (aSi). 
     A patient support table  5  for imaging the heart of a patient to be eV(amined, for eV(ample, is located in the beam path of the X-ray source  3 . An imaging system  6  which receives the image signals from the X-ray image detector  4  and generates a three-dimensional reconstruction of the object to be mapped, is connected to the X-ray diagnostic apparatus. The imaging results can then be viewed on a monitor  7 . 
     Until now, computed tomography (CT) has been employed for time-resolved three-dimensional images of dynamic events. It permits—firstly for static objects—a more or less eV(act three-dimensional reconstruction of the internal parts of the body, since it records projections of the object to be imaged from virtually all directions; typically from a circular orbit of the tube and detector around the patient, as described in Zellerhoff et al. [1]. For dynamically moving objects, periodically repeated CT scans are mostly used, as in Lauritsch et al. [2], in order to record the object to be imaged at different time intervals. The achievable time resolution is then determined by the time required for an individual CT scan and in many cases is inadequate for rapid movements, for eV(ample the heart or the flow of a contrast agent. Cardiac imaging and also perfusion imaging are available with CT. Perfusion imaging with CT is generally limited to a relatively thin layer. 
     Time-related high-resolution cardiac imaging is also possible with ultrasonic devices. The elastographic method is also technically feasible in the field of ultrasonic imaging. 
     SUMMARY OF THE INVENTION 
     The invention is based on the object of developing a method in such a way that functional imaging with C-arm angiographic systems can be easily realized in the interventional environment. 
     The method relates to the three-dimensional representation of a moving structure by means of a tomographic method, in which during one recording pass a series of projection recordings is registered by an imaging unit at different recording angles between a start position and an end position, it being possible to reconstruct three-dimensional image data from the projection recordings. This type of three-dimensional X-ray imaging of dynamic events can be implemented by means of fleV(ible C-arm X-ray apparatus. 
     The object is achieved according to the invention by means of the following steps:
     a) Generation of tomosynthesis projection recordings along a tomosynthesis scanning path,   b) Interpolation of the data of the tomosynthesis projection recordings in accordance with an interpolation algorithm in order to generate a projection data set,   c) Use of a tomosynthesis reconstruction method on the projection data set in order to generate a tomosynthesis volume image,   d) Repetition of steps b) and c) for all times of interest, and   e) Display of tomosynthesis representations from the tomosynthesis volume images.   

     A scanning path or curve is a specific type of movement of the measuring system, consisting of an X-ray tube and an X-ray image detector, around the patient. Critical to the scanning is the movement of the X-ray focus, which is described in the following. The X-ray image detector can be made to track the movement of the focus, but does not have to; it can even stop. It is only necessary to ensure that it receives as often as possible the radiation that has passed through the area of the patient that is of interest, for eV(ample the heart. In principle, a distinction is made in the following between closed scanning curves—which always run in the same direction—and non-closed scanning curves—which run in opposite directions to one another. In this case closed scanning curves deliver a more useful type of scanning and, due to the smoothness of the mechanical movement, can usually be more easily realized and more rapidly traversed. 
     Advantageously, closed tomosynthesis scanning paths can have a circular, elliptical, loop or spiral shape. 
     Alternatively, the tomosynthesis scanning path can be non-closed, it being possible according to the invention for it to have a spiral or linear shape and to run in both directions. 
     In order to further improve the time resolution, in addition to faster measurement with tomosynthesis methods, projection images are determined at fixed times t 0  and reconstructed from the measured data with the aid of a suitable time interpolation. 
     It has proved to be advantageous if the interpolation algorithm contains a linear interpolation, a polynomial interpolation or a spline interpolation. Other interpolation methods, such as the “nearest neighbor” interpolation, for eV(ample, are likewise possible according to the invention. 
     According to the invention, the tomosynthesis reconstruction method can be a back-projection method or an algebraic method. 
     In an advantageous fashion, the display of the tomosynthesis representations can include animated representations such as dynamic angiographical recordings and/or graphical representations of functional parameters, which can be derivations of functional parameters and graphical representations of the “cerebral blood flow”, “cerebral blood volume” and/or “time-to-peak”. 
     The derivation of functional parameters is calculated from the measured sequences of 3D-images, that is to say for each piV(el an individual parameter is determined from a sequence of timed samples in order to make representation and interpretation easier. The eV(act mathematical implementation is sufficiently well known for the above-mentioned common, eV(emplary parameters. In the present case the term derivation should not be interpreted in the strictly mathematical sense. The derived functional parameters are individual numerical values for each piV(el, which in the customary manner can be represented in the form of gray-scale or color values. 
     It has proved advantageous if the method includes the following steps:
     S 1  Start an injection of contrast agent at a first time t i ,   S 2  Wait for a delay time Δt,   S 3  Generate a periodic tomosynthesis projection recording,   S 4  Interpolate tomosynthesis projection recordings at fixed times t n  from the measured data,   S 5  Reconstruct three-dimensional volume images at times t n  and   S 6  Process and display the data for the user by:   S 7   a  Derive functional parameters and graphical display and/or   S 7   b  graphical display of moving images.   

     Furthermore, the object is achieved according to the invention in that in order to generate the projection recordings, tomosynthesis projection recordings are made at different recording angles along a tomosynthesis scanning path and that three-dimensional image data are reconstructed from the tomosynthesis projection recordings. In order to improve the time resolution and for faster measurement, tomosynthesis methods are used instead of the usual C-arm tomography in which the C-arm is rotated around the object under eV(amination. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is eV(plained in further detail with the aid of the eV(emplary embodiments illustrated in the drawing, in which: 
         FIG. 1  shows a schematic view of a C-arm system for carrying out the method according to the invention, 
         FIG. 2  shows scanning geometries for circular tomosynthesis of a closed scanning path, 
         FIGS. 3 to 7  show further closed scanning paths, 
         FIG. 8  shows scanning geometries for linear tomosynthesis of a non-closed scanning path, 
         FIG. 9  shows further non-closed scanning paths, 
         FIG. 10  shows a schematic representation of the projection recordings for a closed path curve according to  FIG. 2 , 
         FIG. 11  shows a schematic representation of the projection recordings for a non-closed path curve according to  FIG. 8 , and 
         FIG. 12  shows the sequence of operations of the method according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     EV(emplary scanning geometries for circular and linear tomosynthesis, for closed and non-closed scanning paths, are now eV(plained in further detail with the aid of the following figures. 
     A closed scanning path in which a patient—shown schematically by a voV(el  10 —lying on the patient support table  5 , is penetrated by an X-ray beam  12  being emitted from a focus  11  of the X-ray source  3 , is reproduced in  FIG. 2 . The X-ray beam  12  then strikes a piV(el  13  of the X-ray image detector  4 . The focus  11  moves around a circular tomosynthesis scanning path  14  having a radius r, whose mid-point is the Z-aV(is of a coordinate system  15 . The tomosynthesis scanning path  14  appears as an ellipse only in the perspective representation. The side line of the cone  16  directed from the circular tomosynthesis scanning path  14  towards the origin of the coordinate system  15  makes an angle α to the Z-aV(is. The position of the focus  11  in relation to the X-aV(is of the coordinate system  15  is denoted by the angle φ and the spatial position by the solid angle Ω. In the X/Y plane the X-ray beam  12  covers a circular path  17 , around which the X-ray image detector  4  is preferably likewise displaced, so that the X-ray beam  12  always strikes the same piV(el  13 . This ensures that not only the central X-ray beam  12  passing through the voV(el  10 , but all the X-ray beams penetrating the patient always fall on the X-ray detector  4 . The start point s begin  and the end point s end  of the closed scanning path can be identical if the scanning paths are completely traversed. 
     A further closed scanning path seen as an ellipse  20 , which has a major half-aV(is a and a minor half-aV(is b, is illustrated in a plan view in  FIG. 3 . 
     Alternatively, as shown in  FIG. 4 , an elliptical scan with a curve  21  can be achieved with additional rotation of the major half-aV(is a and cyclic rotation. 
     Likewise, a closed scanning curve forms a looped scan, as illustrated in the plan view of  FIG. 5 , in which a loop  22  is traversed as the tomosynthesis scanning path, instead of the circle  14  of  FIG. 2 . Alternatively, the loop-shaped scan can consist not only of two but any number of branches. In addition, the loop aV(is can also be rotated, thus resulting in the interlaced curve shape  23  illustrated in  FIG. 6 . 
     A spiral scan is shown in plan view in  FIG. 7 , in which on completion of a spiral  24  running outwards in a clockwise direction as shown in  FIG. 7A , the direction of the deflection and not the direction of rotation is reversed, as shown in  FIG. 7B . Starting from the start point  25 , the focus  11  rotates outwards until it reaches the end point  26 . This end point  26  corresponds to the start point  28  of a spiral  27  directed inwards and running in a clockwise direction, on which the focus reaches the end point  29  of the inwardly-directed spiral  27 . This end point  29  can again be the start point  25  of the outwardly-directed spiral, that is to say a continuous movement is achieved on the closed scanning curve, so that after reaching the maV(imum deflection the movement is continued in the same direction of rotation but directed inwards. Correspondingly, on reaching the minimum deflection, the movement continues in the same direction of rotation but directed outwards, and so on. 
     An eV(ample of a non-closed scanning path, a linear scanning path, is now shown in  FIG. 8 . This means that the focus  11  moves to and fro on a linear tomosynthesis path  18 , as shown by the straight arrow, the center of which lies on the Z-aV(is of the coordinate system  15 . The end points of the linear tomosynthesis scanning path  18 , the start point s begin  and the end point s end , form an angle α with the Z-aV(is. The solid angle Ω thus has an angle between α and α. At the start position s begin  the X-ray  12  strikes the piV(el  13 , which along with the X-ray image detector  4 , is displaced in the direction of the X-aV(is in accordance with the travel of the X-ray beam  12  as indicated by the arrow  19 . In so doing, the observed X-ray beam  12  always passes through the middle of the patient, the voV(el  10 . 
     Other non-closed scanning paths can have a spiral construction, it being possible for the scanning direction to be reversed on completion of the spiral, an eV(ample of which is shown in the plan view of  FIGS. 9A and 9B . 
     Starting from the start point  25 , the focus  11  is moved on the outwardly-directed spiral  24  running in a clockwise direction  24 , until it reaches the end point  26 . This end point  26  corresponds to the start point  30  of the same spiral  24 , which is now traversed by the focus  11  in the counterclockwise direction up to the end point  31 . This end point  31  can again be the start point  25  of the outwardly-directed spiral  24 , that is to say the focus  11  always moves along the same spiral path, only in the reverse direction. Non-closed scanning paths can also include a partial rotation of a closed path, for eV(ample a CT partial rotation. 
       FIGS. 10 and 11  show schematically how and at which points data is measured in relation to the path parameter s and the time t. The objective is to reconstruct volume images V(t) from the obtained projections P(s,t) at specific times in the acquisition time range. In order to obtain the most eV(act reconstruction possible of a volume at the time t 0,  a projection data set P(s, t 0,  is required at this time t 0 , it being possible for s to include the range between s begin  and s end  or a partial range. However, the individual projections P(s,t) of the measured rotational recordings always occur at different times t, as is apparent from  FIGS. 10 and 11 . According to the invention, a searched-for projection P(s 0 , t 0 ) at the time t 0  is determined by a suitable interpolation along the line s=s 0  in  FIG. 10 .  FIG. 10  shows the path parameters s over the recording time t for a closed path curve with a run time T, which form ascending straight lines  32 , it being possible for the end point s end  of the first straight line  32  to form the start point s begin  of the neV(t straight line  32 . As an eV(ample, the interpolation points P 1 , . . . , P 4  available for P 0 =P(s 0 , t 0 ) are illustrated in  FIG. 2 . This procedure has to be implemented for all values from the range of s under consideration. The projection data set P(s,t 0 ) determined in this manner can then be reconstructed by means of a suitable reconstruction method, as described in Lauritsch et al. [4] for eV(ample, in order to obtain a volume image V(t 0 ) at the time t 0 . This method as described there then has to be implemented for all times t of interest. The total time series of volume images V(t) thus obtained can only be displayed either as animation or used as the starting point for determining functional parameters. 
     The schematic arrangement of projection images relating to the path parameter s and the recording time t for a non-closed path curve is shown in  FIG. 11 . Here the direction of movement is reversed at the points s begin  and s end , so that the ascending straight lines  32  change to the descending straight lines  33 . 
     The process sequences according to the invention are described below and summarized in the following steps in  FIG. 12 :
     S 1  Contrast agent injection starts at the time t i ,   S 2  Delay time Δt,   S 3  Generation of a periodic tomosynthesis projection recording,   S 4  Interpolation of tomosynthesis projection recordings at fixed times t n  from the measured data,   S 5  Reconstruction of three-dimensional volume images at the times t n,  and   S 6  Processing and display of data for the user by:   S 7   a  Derivation of functional parameters and graphical display (as is usual in perfusion CT) and/or   S 7   b  Graphical display of moving images (for eV(ample for cardiac imaging).   

     The delay time Δt from the initial injection of contrast agent until the first rotational run is determined from the time of the initial appearance of the contrast agent in the region of interest (ROI). 
     Interpolation can be effected by means of various algorithms. Here, linear interpolation, polynomial interpolation and spline interpolation can be cited as eV(amples of interpolation algorithms. In principle, however, the use of other interpolation or estimation algorithms is also possible. 
     Back-projection methods as well as algebraic methods are to be considered for the reconstruction of the volume data, as described in Härer et al. [3], for eV(ample. 
     The representation of the volume data at the times t n  can be effected directly in the form of an animated representation, for eV(ample as a “movie” in dynamic angiographical recordings. Alternatively, the reconstructed data can be compressed into functional images or parameters, as employed for eV(ample in perfusion measurements such as cerebral blood flow, cerebral blood volume, time-to-peak, etc. 
     In order to improve the time resolution, the following has been proposed according to the invention: 
     1. To use tomosynthesis instead of computed tomography to facilitate faster measurement through the use of a smaller scanning range. 
     2. To use special tomosynthesis scanning paths, which minimize the necessary measurement time and at the same time can be technically optimized, in particular with robot-based C-arm systems. 
     3. To use suitable time interpolations in order to determine and reconstruct projection images at fixed times t 0  from the obtained projections P(s,t). 
     In principle, tomosynthesis offers the possibility of a faster measurement since in comparison with CT its scanning can be incomplete. It is no longer necessary to record the object under eV(amination from all directions; reconstruction can be effected from a limited scan range, as described in Härer et al. [3], Lauritsch et al. [4] or Badea et al. [5], for eV(ample. This offers the potential to carry out the measurement more rapidly. A simple eV(ample of this is the use of a partial rotation of the measurement system around the patient instead of using a full CT rotation. However, the choice of scanning path is not limited to the circular rotation of CT. The incompleteness of the data acquisition does in fact limit the image quality—basically the resolution of the image is impaired in a specific direction—but this disadvantage can usually be accepted. 
     The time-saving of tomosynthesis can essentially be optimized by the use of tomosynthesis scanning paths, which can be cyclically traversed as fast as possible by the measurement system. We propose the use of scanning paths in which the scanning system carries out as few mechanical braking or acceleration operations as possible during the measurement, that is to say the kinetic energy of the measurement system remains as constant as possible. It is particularly advantageous if such paths are realized with a robot-based C-arm system, as described in DE 199 58 864 A1 [6]. 
     EV(amples of such advantageous paths are the movement of the focus  11  of the X-ray source  3  and the X-ray image detector  4  on a circle  14 , as in  FIG. 2 , circular tomosynthesis, an ellipse  20  or  21  as in  FIGS. 3 and 4 , a loop-shaped path  22  or  23  as in  FIGS. 5 and 6  or a spiral  24  or  27  as in  FIG. 7 . The X-ray image detector  4  must register the region of the object being imaged in all projections. At the same time, it can basically move along path shapes other than the focus  11  of the X-ray source  3 . Its coupled motion is only necessary in order to keep its area small and thus its costs as low as possible. If the X-ray image detector  4  is large enough to record the region of the object being imaged from all directions, its coupled motion can also be dispensed with. Particularly advantageous are paths in which the kinetic energy remains constant, that is to say the following relationship holds true: 
     
       
         
           
             
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     Forms of movement without the stated additional advantages are, for eV(ample, the linear to-and-fro movement of the scanning system of  FIG. 8 , linear tomosynthesis or a CT partial rotation, as described in Badea et al. [5], since they require continuous braking or acceleration operations of the measurement system for their periodic performance. 
     A considerable increase in the time resolution of the reconstruction is achieved by speeding up the scanning through the use of tomosynthesis instead of computed tomography, especially when using scanning paths which can be periodically and speedily traversed. In order to convert the measured data as accurately as possible into volume data, tomosynthesis is combined with an appropriate interpolation or estimation method. 
     The method according to the invention is therefore based on the combination of a suitable tomosynthesis scanning path—in conjunction with the necessary recording system—a suitable interpolation algorithm and a tomosynthesis reconstruction method. 
     Within the scope of the invention, floor-mounted and/or ceiling-mounted supports to which the C-arms  2  are attached, can be used instead of the stand  1  as described. The C-arm  2  can also be replaced by a so-called electronic C-arm  2  in which an electronic coupling is established between X-ray emitter  3  and X-ray image detector  4 . 
     However, the C-arms  2  can also be guided on robot arms which are ceiling-mounted or floor-mounted. The method can also be implemented with X-ray apparatus in which each of the individual image-generating components  3  and  4  is supported on a robot arm which is mounted on the ceiling and/or floor. 
     LITERATURE 
     
         
         [1] M. Zellerhoff, B. Scholz, E.-P. Rührnschopf, T. Brunner, Low contrast 3D-reconstruction from C-arm data, Medical Imaging 2005: Physics of Medical Imaging, Proceedings of SPIE Vol. 5745, pp. 646-655 
         [2] Günter Lauritsch, Jan Boese, Lars Wigström, Herbert Kemeth and Rebecca Fahrig, Towards Cardiac C-Arm Computed Tomography, IEEE Trans. Med. Imaging 25(7): 922-934 (2006) 
         [3] Wolfgang H. Härer, Günter Lauritsch and Thomas Mertelmeier, Tomography—Prinzip und Potential der Schichtbildverfahren [Principle and potential of the layer image method], in Th. Schmidt (Pub.), Handbuch diagnostische Radiologie [Manual of Diagnostic Radiology], Vol. 1, Chapter 2.4, Springer Verlag, Berlin, Heidelberg, 2003-ISBN 3-540-41419-32.4 
         [4] Günter Lauritsch and Wolfgang H. Härer, A theoretical framework for filtered back-projection in tomosynthesis. In: Hanson K M (Hrsg) Medical Imaging 1998: Image Processing Vol. 3338. SPIE, Bellingham (USA), S 1127-1137 
         [5] C. Badea, Z. Kollitsi, N. Pallikarakis, Image quality in EV(tended arc Filtered Digital Tomosynthesis, Acta Radiologica, Vol. 42, issue 2 (2001);244-249; 
         [6] DE 199 58 864 A1: Röntgeneinrichtung mit einem Roboterarm zur Positionierung einer Röntgenquelle und eines Röntgendetektors [X-ray apparatus with a robot arm for positioning an X-ray source and an X-ray detector].