Three-dimensional localisation based on projectional and tomographic image correlation: an application for digital tomosynthesis

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1 Medical Engineering & Physics 21 (1999) Three-dimensional localisation based on projectional and tomographic image correlation: an application for digital tomosynthesis G. Messaris, Z. Kolitsi, C. Badea, N. Pallikarakis * Dept of Medical Physics, Faculty of Medicine, University of Patras, , Patras, Greece Received 16 July 1998; received in revised form 5 January 1999; accepted 5 January 1999 Abstract Accurate three-dimensional tumor localisation in Radiotherapy, is critical to the treatment outcome, particularly when high dose gradients are present. A number of techniques have been proposed for the localisation of anatomical structures or markers. The present study proposes an approach to a concurrent maximisation of localisation accuracy and efficiency by correlation of tomographic and projectional images. The method introduces an element of direct verification and interactive optimisation of the process. Tomographic images are used for the identification of a point of interest. Its position is computed within the treatment co-ordinate system and verification of this position is achieved by obtaining the beam s eye view of the identified point on two projection radiographs. The key element of the approach is that all images used should be part of one single image data set. The implementation of this localisation method, as part of the functionality of a Digital Tomosynthesis prototype, has provided an integrated facility for localisation, of optimised accuracy and precision, while easy and efficient to use. The considerations are general and apply in principle to any imaging system that can augment tomographic images with projections IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: Localisation; Digital tomosynthesis; 3D reconstruction 1. Introduction Accurate three-dimensional tumor localisation in Radiotherapy, is critical to the treatment outcome, particularly when high dose gradients are present, as in brachytherapy or conformal treatments with dose escalation. Several techniques have been proposed for localisation of brachytherapy sources, anatomical structures or markers, which are based either on tomographic or on projectional imaging techniques [1 17]. Tomographic images from CT can be used either alone or in correlation, to provide a three-dimensional display representation of body structures and objects of interest. The accuracy of localisation is subject to a fine spacing between consecutive slices and for 2 mm slice thickness an accuracy of mm has been reported [18]; nevertheless, when complex arrangements are presented as in the case * Corresponding author. Tel: ; fax: ; nipa@bit.med.upatras.gr of interweaved vascular structures or wire sources, identification of these structures on consecutive tomograms, using CT data is not always feasible. Projectional techniques, on the other hand, utilize two or three film radiographs [7 17] and when suitable small x-ray opaque markers are used, so that loci positions can be measured with less than 0.15 mm accuracy, the marker point position vector can be determined with an rms error of magnitude of approximately 0.25 mm [7]. These techniques maintain a relevant simplicity, while they remain most appropriate for special applications, such as the localisation of Arteriovenous Malformations (AVMs) where accuracies of mm and mm, for localization of discrete targets, have been reported for film and digital images respectively [18]. In principle, the orthogonal reconstruction method, based on two radiographs obtained at 0 and 90, provides the highest degree of localisation accuracy [6,7,12]; however, matching markers or structures on the two images is often difficult and some times impossible, mainly due to overlapping of the structures on the projection radio /99/$ - see front matter IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S (99)

2 102 G. Messaris et al./ Medical Engineering & Physics 21 (1999) graphs, introducing localisation errors of the order of a few millimeters [6,13]. The implementation of matching algorithms has improved accuracy in ribbon type arrangements to approximately 1 mm [16,17]. Alternatively, isocentric reconstruction from two symmetrically acquired projections, selected on the criterion of good visualization of the points of interest on both projections, may improve the efficiency of matching, however at a cost of introducing localisation uncertainties. The technique of variable angle reconstruction constitutes a compromise between a high degree of localisation accuracy and unambiguous matching. In such approaches, localisation accuracy may be further improved by minimization of the length of the common vertical to the two rays that correspond to the point in each of the two projections [7,12]. Techniques that do not require prior knowledge of the relative acquisition geometry between the projection images have also been reported. This information may be obtained by the use of a calibration object, or alternatively, by identifying characteristic structures on both images [14]. The mean absolute error in the relative position of points depends on input image data error and was found equal to 1.5 mm for a 0.7 mm input error. The present study proposes a novel approach to maximisation of localisation accuracy and efficiency, based on the utilization of both a tomographic and projectional images in order to localise points, verify positions and interactively optimize localisation. Tomographic images are used for the identification of a point of interest. Its position is computed within the treatment co-ordinate system and verification of this position is achieved by obtaining the beam s eye view of the identified point on two projection radiographs. The key element in this approach, is that both cross-sectional and projection images should be part of one single image data set. The methodology described in the following sections and its implementation into a clinical application have been developed on the basis of Digital Tomosynthesis (DTS); however, the technique can be readily adapted to any system that fulfill the above stated requirement. retrospectively, on the basis of appropriately processed digitized projection data. The reconstruction of horizontal planes in DTS as in conventional tomography, consists of shifting each discrete projections image, by a specific amount, and subsequently adding them together. The amount of shifting of each projection image determines which projected structure will be made to appear sharp in focus and which will be blurred in a certain reconstructed plane. In its generalized form, for planes of arbitrary orientations, the reconstruction process becomes equivalent to a backprojection method for transferring and depositing data at the intersection of the respective rays with the plane of reconstruction. During DTS imaging, all originally acquired projection data is retained [19 22], and is associated to the gantry orientation at which it was acquired. The localisation method involves the identification of a point of interest on a DTS reconstructed anatomical cross-section of arbitrary orientation, the calculation of its position within the treatment co-ordinate system, the verification of this position on two selected projection radiographs and the system feedback on the necessary corrective actions if this trial has been unsuccessful. The steps involved in the localisation procedure are shown in the flow chart of Fig Coordinate calculation An anatomical plane appropriately focused at the point or structure of interest is identified and reconstructed. A point of interest P, is then identified and marked at P i on the image of this anatomical plane (Fig. 2). The latter is formed at the image formation plane, which is parallel to the anatomical plane and may or not coincide with it, depending of the reconstruction algorithm [19]. The position of point P i on the image is given 2. Materials and methods 2.1. Theoretical considerations DTS can be regarded as the digital analogue of classical tomography; it involves the reconstruction of the volume of interest in its planar sections from one single set of digitized projection images acquired over a limited arc. In isocentric systems, such as angiography units or radiotherapy simulators, projection images are acquired during isocentric rotation of the x-ray tube-detector system, around the patient. Horizontal as well as tilted planes of arbitrary orientations can be then reconstructed Fig. 1. Flow chart illustrating the successive steps of the localisation method of a point of interest (POI).

3 G. Messaris et al./ Medical Engineering & Physics 21 (1999) y R x a cos sin y a cos rsin sin z R x a sin rcos where x a x i /M, y a y i /M and M is the magnification factor. It can be readily seen that the last terms of each of these expressions correspond to the co-ordinates of the transferred origin I A in the reference system Coordinate verification In order to verify the user s perception of the location of point P, one can inspect the position of the point s projection on two appropriately selected projection images. In Fig. 3, point P(x R, y R, z R ) is projected on the projection radiograph obtained at a gantry angle at P p (x p, y p ) The co-ordinates of P p are obtained by means of a transformation involving a rotation of the reference system by an angle around Y R axis and a subsequent projection on the image intensifier plane. That is V R V R, where: Fig. 2. Correlation between the 2-D image coordinate system x i y i and the 3-D reference coordinate system x R y R z R. by its co-ordinates (x i, y i ) defined on the respective 2D co-ordinate system x i y i. The position of this point is then computed in a reference system x R y R z R which is an orthogonal right-handed co-ordinate system with its origin at the isocenter. Any arbitrary anatomical plane x a - y a can thus be defined within this reference system. The co-ordinates of P in the reference system can therefore be computed by applying a transformation V R, involving a rotation R of the reference system by an angle around the z R axis, a subsequent rotation R by an angle around the resultant y axis, followed by a translation T r of the origin by r along the z axis and a demagnification of x i and y i to their actual size (x a, y a ) at the anatomical plane:v R R R T r, where: V x y cos 0 and R z sin 0 sin cos which leads to the following system of equations: x x R cos z R sin (1) V R x R y R R cos sin 0 R sin cos 0 z cos 0 sin R T sin 0 cos xa r y a r. Therefore, the co-ordinates (x R, y R, z R ) of point P, in the reference system are related to its co-ordinates on the anatomical plane by the following equations: x R x a cos cos y a sin rsin cos Fig. 3. Projection of a point P on fluoroscopic radiographs.

4 104 G. Messaris et al./ Medical Engineering & Physics 21 (1999) y y R (2) z x R sin z R cos (3) The co-ordinates (x p, y p ) are then derived using simple magnification geometry considerations: x P x d (b z ) (4) x p (x Rcos z R sin d ) b x R sin z R cos y P y R d b x R sin z R cos (6) (7) If is the marking error on the tomogram, equal in all directions, then the respective displacements are given by: y P y d (b z ) (5) x(x R,z R,, ) x P (x R,z R, ) (8) x P (x R,z R, ) where d is the source-to-detector distance and b is the source-to-axis distance System feedback on corrective actions The first localisation trial, even if unsuccessful to produce a coincidence of the displayed position with the actual projected image P p of P, will as a minimum provide useful clues for its identification. If the user marks the correct loci of P on the two radiographs, the system will provide feedback as to the height, relative to the isocenter, of the coronal tomogram that contains point P. The user may then choose to reconstruct the suggested tomogram and repeat the localisation trial, until verification has shown a satisfactory result. Several approaches to identifying the position in space of a point from its locus on two radiographs have been proposed [12,14]. For our DTS implementation we have based our approach on the Multiple Projection Algorithm (MPA) used for image reconstruction [19]. A detailed description of the calculation method is presented in the Appendix Error detection sensitivity The choice of radiographs to be used for verification and optimization is based primarily on considerations that relate to the detectability of the structures of interest on the selected radiographs. Such radiographs, however, should be within an acceptable range of angular positions, for which the method ensures sensitivity in the detection of localization errors. Based on the following considerations, a set of selection criteria can be deduced. Errors occur when (i) selecting the tomograms that are perceived to be best focused on the structures of interest (error z) and (ii) when marking on these tomograms the position of structures (errors x, y). Errors x, z manifest themselves as x-displacements of the respective loci from their true positions on the projection radiographs. Errors y are projected as y-displacements. These errors will be detected if their corresponding displacement are of detectable magnitude. The position P P of a point P on the projected image can be readily deduced from Eqs. (1) (5) as follows: y(x R,y R,z R,, ) y P (x R,y R,z R, ) (9) y P (x R,y R,z R, ) Hence, the error detection sensitivity of the method is expressed by the magnification of the projected marking errors. If we consider that an acceptable condition for system sensitivity is that marking errors should be projected at least with a magnification equal to 1: x(x R,z R,, ) (10) y(x R,y R,z R,, ) (11) Eq. (11), as can be easily seen in Eq. (7), is always satisfied for the imaging geometries used, i.e. d 130 cm and b 100 cm. The solutions of the equation x(x R,z R,, ) constitute surfaces representing projected marking errors equal to the input marking error. Fig. 4 shows two separate sets of data for errors z and x 0, respectively. It is therefore possible to quantify criteria, for selection of projection radiographs, to be used for verification, according to the level of sensitivity demanded by the clinical application at hand. Fig. 4 displays in a 3D graph the surfaces corresponding to 1 mm. Therefore projections placed under the surface in 4(a) and above the surface in 4(b) will ensure sensitivity in marking errors along the x and z-axis respectively. As seen, any point within a volume cm 3, centered at the isocenter and delimitated by the size of the 9 in. image intensifier, used in our application, can be effectively localized, provided that the two projections used for verification are taken at angles in the range of 30 to 30 and 60 to 120 respectively, relative to the plane used for localization. Obviously the supplementary ranges may also be used Implementation The above described localisation method together with a set of navigation facilities and guided selection of projections have been implemented on a DTS clinical

5 G. Messaris et al./ Medical Engineering & Physics 21 (1999) thus allowing for real time tomographic scanning through the anatomical volume under consideration. In practical terms, once the patient has been set-up for simulator imaging, the acquisition of projection data involves an automated sampling process, during which projections are collected at 2 intervals while the gantry is rotated around a predefined arc. Projection data is corrected for distortion prior to being used for reconstruction using a local correction technique, which provides a table of correction coefficients for images acquired at any arbitrary angle about the patient [23,24]. The entire process chain, from patient data acquisition to determination of the location of sources, structures or points of interest, can be performed within a few minutes. The user interface permits visualization and manipulation of tomographic and projectional images. One single active window for localisation and verification is used, shown in Fig. 5 displaying images from a brachytherapy application. The tip of a source is marked on a tomographic image (top left) and its corresponding projection is concurrently displayed on two selected projection images (bottom). The top left window is updated when a new anatomical plane is selected, or a new marking trial, is performed. Alternatively the user may mark the perceived loci of the source edge on the two radiographs and receive the systems suggestion as to the level of the tomographic plane containing the tip. This type of interaction with simultaneous reference to projection and tomographic data allows the user to verify his perception of spatial relationships and ensures a high degree of localisation accuracy. Eventually, it is possible to produce a 3-D reconstruction of the sources by interpolating between marked points and using Geomview a shareware application that makes it possible to display in real time geometric arrangements in 3D space. 3. Experimental evaluation Fig. 4. A 3D representation of the surfaces delimiting the suitable projection radiographs to be used for verification of localization for 1 mm when (a) z 0, (b) x 0. prototype imaging system [20]. The system comprises a digital chain interfaced with an isocentric fluoroscopic unit to form an integrated DTS facility. The system presently interfaces to a radiotherapy simulator unit while the acquisition of projection images is computer controlled. The analogue signal from the TV camera is digitized to a pixel size of 0.60 mm. Image reconstruction is performed on a UNIX workstation. Reconstruction times are influenced by the hardware platform used, however they are typically of a few seconds per plane, The localisation accuracy and precision of the localisation tool were assessed with the use of a cm, plexi-glass phantom containing 25 pellets of 1 mm diameter at a known fixed arrangement, shown in Fig. 6(a). The pellets were localized on horizontal tomograms, while two sets of projection images corresponding to (i) 0 and 90 and (ii) 30 and 60 were used for verification. A total of 7 observers participated in an experiment, involving the identification of the location of the pellets using the above described application. The co-ordinates of the pellets with respect to the isocenter were calculated and the mean of all measured positions for each pellet was compared to a reference value, representing its actual position, as this was determined using two orthogonal film radiographs. The overall accuracy r i of the DTS-based localisation procedure is reflected

6 106 G. Messaris et al./ Medical Engineering & Physics 21 (1999) Fig. 5. Illustration of the interactive localisation using the implemented application. A tip of a brachytherapy source is marked on a cross-sectional image (top left) and its projection is concurrently identified on two selected projections (bottom). 3-D reconstruction of the sources through interpolation between marked points is displayed using the Geomview shareware. by the mean of all displacement errors r i (x t x i ) 2 (y t y i ) 2 (z t z i ) 2 between the actual x t, y t, z t and measured x i, y i, z i co-ordinates of the pellets. The precision of the procedure is reflected by the standard deviation of the mean of all displacement errors S r. Fig. 6(b) shows the frequency distribution of the calculated differences between the displacement errors of the measured and the actual positions of the pellets for both sets of projection data used (i.e. 0, 90 and 30, 60 ). The proposed method presented an overall localisation accuracy of 1.2 mm and a precision of 0.4 mm. The systematic uncertainty r, on the other hand, is reflected by the length of the mean of all vectorial displacements in space between the actual and measured co-ordinates and is calculated using the following analytical expression: r i 1 7 (x t x i ) 2 i 1 7 (y t y i ) 2 i 1 (z t z i ) 2 This was found for both cases to be approximately equal to 1.1 mm. 4. Discussion The problem of accurate localization in space has been subject of a great number of investigations and solutions have been proposed, each presenting specific advantages and limitations associated with their clinical applications. Such limitations relate to either the quality of input data used for localization or to the capability of the methods to yield accurate results under all possible situations. The method proposed here has been shown to be capable of overcoming such obstacles, by exploiting an element of verification and feed-back in combination with the use of an extended sample of projectional images which significantly increases the probability of adequate visualization of the structures of interest. The theoretical study of sensitivity of the verification method, to errors introduced during localisation, has indicated that it is possible to utilize projections within a broad range of angular orientations, without any loss in accuracy and precision. This has been also verified experimentally in Fig. 6, where the frequency distribution of localization errors is shown for two sets of data, representing conditions for maximized (0, 90 ) and marginal (30, 60 ) sensitivity, respectively. The

7 G. Messaris et al./ Medical Engineering & Physics 21 (1999) Fig. 6. (a) Schematic representation of the phantom used in the evaluation of the localisation method. (b) Frequency distribution of the displacement errors between the actual and the measured positions in the two cases when, 0, 90 and 30, 60 projection images were used. marginal arc, on the other hand, does not represent an absolute condition, but rather a consequence of the requirements for sensitivity. Accuracy and precision are also subject to the limitations imposed by the resolution of the imaging chain, the type and magnitude of distortions, as well as gantry alignment errors present. The confinement of usable projections within the ranges 30 and 60 and their supplementary range has been found necessary in order to fulfil the requirement for detectability of an 1mm marking error projected at unit magnification, corresponding to 1 pixel on the image matrices used in our application. The precision of the method was found to be comparable to the pixel size. The systematic uncertainty of 1.2 mm found, on the other hand is comparable to the systematic error of the order of 1mm of the isocenter position during rotation around 360. The implementation of this localisation method, as part of the functionality of the DTS prototype, has provided an integrated facility for localisation, with optimised accuracy and precision while easy and efficient in use. The treatment of the subject in this paper has been specifically referenced to Digital Tomosynthesis used in conjunction with fluoroscopic isocentric imaging which also presents the advantge of low dose for patient. In principle, the considerations presented in section II of this article are general and apply in principle to any imaging system, which can augment tomographic images with projections. The method has been readily transferred to an experimental cone beam CT (CBCT) application on the radiotherapy application [24]. Localisation precision is critical in many cases in diagnostic radiology and radiotherapy. The particular, fluoroscopy based application that has been presented can be applied to these cases where localisation of high contrast structures is sought. A feasibility study for DTS based radiotherapy treatment planning for AVMs (Arteriovenous Malformations) has shown that the availability of both planar and projection information can be optimally exploited to enhance localisation accuracy [25]. A DTS system used in combination with advanced technology can provide an alternative approach to fusing multimodality data in order to acquire 3-D images with vascular content, to be used for treatment planning for stereotactic radiotherapy of AVMs. Similarly, the system has applications in brachytherapy, particularly in cases where differentiation between overlapping structures is difficult. In radiology, applications envisaged are in particular areas of diagnostic imaging, such as vascular orthopedic or contrast enhanced imaging, where the anatomical structures of interest are characterized by high contrast against their surrounding tissues. 5. Conclusions The investigation presented here, has revealed the potential to improve localisation accuracy, by correlation of tomographic and projection data in an iterative process, involving the identification of any given point and the verification of this hypothesis, through direct feedback. As such system has promising applications in several areas of radiology where precise identification in space is required. Appendix Tomographic Plane Determination The MPA algorithm for DTS involves a transformation in the form of translations in the projection images and subsequently the superimposition of the transformed matrices. This results in coincidence of structures lying in the fulcrum plane, with concurrent defocusing of out of plane information. Alternatively, the extent of the translations necessary to bring the loci of the projection of a point, in the two radiographs, to coincidence can be used to compute the height of the fulcrum plane. In coronal plane reconstruction, the columns are relo-

8 108 G. Messaris et al./ Medical Engineering & Physics 21 (1999) cated during reconstruction. For each viewing angle the acquired image matrix is geometrically projected onto the so-called Image formation plane, which will host the final image. This is a plane, parallel to the reconstruction plane where the integration of the transmission signal over the entire acquisition arc, would actually yield the tomographic image. The principle of image formation is illustrated for the geometry of the isocentric rotation in Fig. 7. Here S and S are two positions of the X-ray source corresponding to two different gantry positions. Constants x and d are the source to isocenter and source to image intensifier distances, respectively. If P is the point of interest situated in the anatomical plane at height z R, then P P is its projection on the Image Intensifier (II) plane. If x p I h P h is the position of a column in the original acquired projection, this is translated to position h p I h P h, through geometric projection onto the horizontal plane passing through the intersection of the beam s central axis and the image intensifier plane, according to the relation: h p x P d dcos x P sin The whole projected matrix is then shifted by a vector h Q h I h where: h z Rdsin bcos z R The resulting matrix is subsequently normalised to the magnification of the isocenter plane by a magnification factor: m 1 Fig. 7. z R bcos Schematic representation of the image formation procedure. The operations performed by the algorithm can be summarised in the expression: x i (h p h)m where x i Q i P i is the column position in the tomosynthesised plane. Assuming the inverse process, if two projection images corresponding to the angles 1 and 2 are considered, and the columns x p1 and x p2 are perceived by the user as containing the projection of point P then we can apply the inverse process to calculate the height z R where P is located. These two columns must be appropriate translated by the reconstruction process in order to coincide at position x i on the image formation plane. Therefore: (h p1 h 1 )m 1 (h p2 h 2 )m 2 and the height z R of the tomographic plane which contains the structure of interest is given by the expression: z R (h 2 h 1 )bcos 1 cos 2 cos 1 (h 2 dsin 2 ) cos 2 (h 1 dsin 1 ). References [1] Noorbehesht B, Fabrikant JI, Enzmann DR. Size determination of supratentorial arteriovenous malformations by MR, CT and Angio Neuroradiology 1987;29: [2] Henkelman RM. New Imaging Technologies: Prospects for target definition. Int J Radiat Oncol Biol Phys 1992;22: [3] Serago CF, Lewin AA, Houdek PV, Gonzalez-Arias S, Hartmann GH, Abitbol AA, Schwade SG. Stereotactic target point verification of an x ray and CT localizer. Int J Radiat Oncol Biol Phys 1991;20: [4] Bergström M, Greitz T, Ribbe T. A method of stereotaxic localisation adopted for conventional and digital radiography. Neuroradiology 1986;28: [5] Brinkmann DH, Kline RW. Automated seed localization from CT datasets of the prostate. Med Phys 1998;25(9): [6] Weaver KA, Pickett B, Roberts LW, Stuart A. Source localisation for template implants with particular reference to stepping-source afterloaders. Med Phys 1995;22:83 8. [7] Sherlock RA, Aitken WM. A method of precision position determination using x-ray stereography. Phys Med Biol 1980;25(2): [8] Christopherson DA, Jones D. A general approach to the location of radiopaque objects, with applications in radiotherapy. Phys Med Biol 1984;29(12): [9] Amols HI, Rosen II. A three-film technique for reconstruction of radioactive seed implants. Med Phys 1981;8(2): [10] Jackson DD. An automatic method for localizing radioactive seeds in implant dosimetry. Med Phys 1983;10(3): [11] Rosenthal MS, Nath R. An automatic seed identification technique for interstitial implants using three isocentric radiographs. Med Phys 1983;10(4): [12] Siddon RL, Chin LM. Two-film brachytherapy reconstruction algorithm. Med Phys 1985;12:77 83.

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