Ma&weric Resonance Printed in the USA.
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Imaging, Vol. IO, pp. 609-621, All rights reserved.
1992 Copyright
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0730-725X/92 $5.00 + .@I 1992 Pergamon PressLtd.
Original Contribution CORRECTION OF SPATIAL DISTORTION ANGIOGRAPHY FOR RADIOSURGICAL OF CEREBRAL ARTERIOVENOUS
IN MAGNETIC RESONANCE TREATMENT PLANNING MALFORMATIONS
LOTHAR R. SCHAII,*I_ HANS-H. EHRICKE,~ BERNDT WOWRA,~ G~NTER LAYER,* RITA ENGENHART, 11HANS-U. KAUCZOR,* HANS-J. Z-EL,* GUNNAR BRIX,* AND WALTER J. LORENZ* *Institute of Radiology and Pathophysiology, German Cancer Research Center, Heidelberg; Jthe Siemens Medical Division, Erlangen; §Department of Neurosurgery, Heidelberg University; 1Department of Radiotherapy, Heidelberg University, Germany A treatment planning system based on magnetic resonance (MR) angiograpbic imaging data for the radiosurgery of inoperable cerebral arteriovenous malformations is reported. MR angiographywas performedusing a threedimensional (3D) velocity-compensated fast imaging with steady-state precession (FISP) sequence. Depending on the individual MR system, inhomogeneitiesand nonlinearitiesinduced by eddy currents during the pulse sequence can distort the images and produce spurious displacements of the stereotactic coordinates in both the x-y plane and the z axis. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system-a ‘2D-phantom” displaying “pincushion” distortion in the image, and a “3D-phantom” displayingdisplacement,warp, and tilt of the imageplane itself. The pincushion distortion can be %orrected” (reducing displacements from 2-3 mm to 1 mm) by calculations based on modeling the distortion as a fourth order 2D polynomial. Displacement, warp, and tilt of the image plane may be corrected by adjustment of the gradient shimming currents. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Precise definition of the target volume could be performedby the therapist either directly in the MR images or in calculated projection MR angiograms obtained by a maximum intensity projection algorithm. MR angiography provides a sensitive, noninvasive 3D method for defining target volume and critical structures, and for calculating precise dose distributions for radiosurgery of cerebral arteriovenous malformations. Keywords:
Treatment planning; Brain neoplasms;
Stereotaxy; Radiosurgery; Magnetic resonance angiography.
INTRODUCTION
was initially performed for the treatment of tumors and AVM with heavy charged particle beams from cyclotrons4.5 and later by the Gamma unit published as a case report.6 The precise localization of the target point and a steep dose gradient outside the target volume allow application of high doses to the AVM without damage to the surrounding normal brain tissue. According to this features radiosurgery is an effective therapy for AVM leading to the development of linear accelerator based radiosurgical techniques at different radiation oncology centers.‘-’ In general, the sole use of MR data as a base for treatment planning is often not feasible because (a) pixel intensities are unrelated to electron densities and
Cerebral arteriovenous malformations (AVM) are vascular malformations conceived as congenital anomalies. Surgical excision is the treatment of choice; an alternative is embolization. Radiation therapy is indicated (a) for AVM in vital or sensitive regions of the brain where they cannot be excised without the risk of a disabling neurological deficit, and (b) for residual AVM after partial embolization or incomplete surgical removal. Since the pioneering work of Leksell in
1951,’ radiosurgery has become the most effective radiotherapy for AVM. 2~3Radiosurgery describes stereotactically guided single high-dose irradiation and
gie, Deutsches Krebsforschungszentrum, D-6900 Heidelberg, Germany.
RECEIVED 10/l/91; ACCEPTED l/22/92. Address correspondence and reprint requests to PD Dr. L.R. Schad, Institut fiir Radiologie und Pathophysiolo-
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are strongly dependent on the specific imaging sequences employed; (b) inhomogeneous radiofrequency (RF) fields yield intensity variations in the MR images; (c) complex bone/air inhomogeneities, important in calculating beam penetration, are not imaged; and (d) various geometrical distortions in all three dimensions are produced by the inhomogeneity of the main magnetic field and noniinearities of the gradients. lo On the other hand, film dosimetric phantom measurements have shown that tissue inhomogeneities do not significantly influence the shape of the relative dose distribution in radiosurgery of deeply positioned lesions of the brain.8s1’ Under this circumstance, the dose calculation of radiosurgery can be based only on
Instrumentation MR angiography (MRA) was performed on a 64 MHz Magnetom (Siemens, Erlangen, Germany) superconducting whole body imager using a 3D velocitycompensated fast imaging with steady-state precession
(4
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the 3D geometric conformation of the patient’s head. Therefore multiplanar MR imaging data are a possible input basis for dose calculation if they are free of geometric distortion. In this case a simple algorithm for treatment planning of AVM radiosurgery can be used and based on multiplanar MR angiographic data. METHODS AND MATERIALS
Fig. 1. (A) Patient positioning in the stereotactic guidance system. A rigid frame made of wood was fixed to the patient either using a special mask or by means of carbon-fiber pins. Plexiglas squares embedded with steel wires for conventional angiography, or plastic tubes filled with a 5 mmol/liter Gd-DTPA solution (Schering, Berlin, Germany) for MR angiography were attached to the stereotactic head frame and served as landmarks in the images, from which the stereotactic coordinate system could be derived. The radiofrequency transmitting and receiving unit consisted of a homemade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system. (B) Patient positioning during irradiation. A special device was fixed to the frame that enabled adjustments of the target point coordinates to the isocenter of the therapy machine. This device was removed prior to the irradiation. Precise positioning was controlled by a laser system and allowed fitting of the target point onto the isocenter of the therapy machine with a positional error of +O.S mm. (Figure continued on facing page.)
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(FISP) sequence. The sequence parameters included a flip angle of 15”, a repetition time (TR) of 40 msec, an echo time (TE) of 7 msec, one acquisition, and a 256 x 256 image matrix with a 64-partition slab. The total volume of interest was acquired in successive and 10 slices overlapping slabs in the axial direction. The minimal field-of-view was restricted to 260 mm in order to image the reference points of the stereotactic localization system; slab thickness was 64 mm for the 64 partitions, resulting in an effective voxel size of 1 mm3. The RF transmitting and receiving unit consists of a selfmade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system (Fig. 1A). The MR computer (MICRO-VAX, DEC, Maynard, MA, U.S.A.) was connected directly (DEC-NET, DEC, link) to a central computer (VAX-WORKSTATION/3600, DEC) where the software developed by our group for treatment planning of AVM radiosurgery was running. l2 After data acquisition, images were transferred to the central computer and postprocessed with a maximum-intensity projection (MIP) method. l3 For treatment planning of AVM radiosurgery, typically 36 angiographic projection images were reconstructed with angles of rotation about the headfeet axis ranging from 0” to 360”.
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Localization Technique The localization system is based on the Riechert and Mundinger stereotactic head frame, which was modified for use with CT, MR, and PET scanners or conventional angiography. *0,r4A rigid frame made of wood was fixed to the patient either using a special mask (Fig. 1A) or by means of carbon-fibre pins. Plexi-glass squares embedded with steel wires for conventional angiography, or plastic tubes filled with a 5 mmol/liter Gd-DTPA solution (Schering, Berlin, Germany) for MR were attached to the stereotactic head frame and served as landmarks in the images, from which the stereotactic coordinate system could be derived (Fig. lC,D). By employing this system and special computer programs, the information about size, shape, and localization of the target volume can precisely be transferred either between the imaging modalities (MRA, conventional angiography) or to the stereotactic coordinate system defined by the head frame. This frame remains fixed to the patient’s head during the irradiation. It is attached to the treatment table, providing a rigid and immobile connection between the patient’s head and the treatment table. After the target point coordinates are determined with reference to the head frame, a special device is fixed to the frame that enables these coordinates to be adjusted to the isocenter of the therapy machine (Fig. 1B).
transaxial image
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Fig. 1 continued. (C) Evaluation of the stereotactic z coordinate. The z coordinate was directly determined by the distance between two reference points, because the angle between the reference tubes is cr = 2 arctan(0.5) and they cross at the stereotactic zero plane. (D) Schematic drawing of an axial image shows the tube reference points of the stereotactic guidance system and definition of the stereotactic coordinate system.
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This device is removed prior to the irradiation. Precise positioning is controlled by a laser system and allows fitting of the target point onto the isocenter of the therapy machine with an positional error of kO.5 mm. Correction of Spatial Distortion in MR The use of MR for stereotactic locations requires accurate spatial information from MR images. Depending on the individual imaging system, eddy currents of the pulsed gradients, excited in the cryo shield during the imaging sequence, can introduce geometrical distortions in all three dimensions. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system-a “2D-phantom” displaying “pincushion” distortion in the image (x-y plane), and the “3D-phantom” displaying displacement, warp, and tilt of the image plane itself. 2D-phantom measurement. The first, the “2D”phantom, is used to measure the geometrical distortions within the imaging plane (Fig. 2A). It consists of a water-filled cylinder 17 cm in radius and 10 cm in depth, containing a rectangular grid of plastic rods spaced 2 cm apart and oriented in the z direction (i.e., perpendicular to the imaging plane). Since the exact positions (x, y) of these rods are known a priori, their positions (u, v) in the 2D-phantom reflect the geometric distortion in the imaging plane and may be used to calculate the coordinate transformation that mathematically describes the distortion process. The x-y plane distortion of axial MRA images of the 2D-phantom can be “corrected” (reducing displacements to the size of a pixel) by calculations based on modeling the distortion as a fourth order 2D polynomial: uk =
cN~ ‘x~ u;j
‘ye
be calculated and the distortion corrected. Thereby, the selection of N = 4 is a compromise between computational burden and reduction in distortion. A more quantitative, direct measurement of distortion is provided by the distortion vector, which measures the discrepancy between the true (x,y)k position of a pin in the 2D-phantom and its apparent position in the image (u,v)k: dk = I(& - (u,u)~[ (i.e., the vectoral distance between the true and apparent positions). Reduction in distortion is demonstrated in Fig. 2C - a comparison of the distribution of dk in the uncorrected and corrected images. The distribution of dk in the corrected 2D-phantom image shows that the positional errors are reduced from about 2-3 mm (Fig. 2C, solid line) to about 1 mm across the entirety of the 2D-phantom (Fig. 2C, dotted line). No further attempts were made to reduce this residual error, because this approximates the dimensions of the image pixels (256 x 256 matrix). 3D-phantom measurement. After correcting for distortion in the imaging plane, the 3D position of the imaging plane was assessed with the “3D” phantom (Fig. 3A). This is necessary because inhomogeneities of the gradient fields that define the imaging plane can
,
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where (x, y) are the true pin positions of the 2D-phantom (Fig. 2B; “+‘‘-symbols); (u, v) are the distorted positions measured on the image (Fig. 2B; “x’‘-symbols), N (= 4) is the order of the polynomial, and M (= 249) is the total number of pin positions of the 2Dphantom. Note that the origin of the U, v coordinate system corresponds to the origin of the x, y coordinate system and lies in the center of the image, the area free of distortion. Equations 1 and 2 applied to all M pin positions of the 2D-phantom form a system of simultaneous linear equations, from which the coefficients Uj and yj can
Fig. 2. (A) The 2D phantom
for measuring the geometrical distortions within the imaging plane. It consists of a waterfilled cylinder 17 cm in radius and 10 cm in depth, containing a rectangular grid of plastic rods spaced 2 cm apart and oriented in the z direction (i.e., perpendicular to the imaging plane). (Figure continued on facing page.)
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Fig. 2 continued. (B) Typical example of a 2D-phantom measurement using a velocity-compensated FISP sequence. The a priori known regular grid of the plastic rods (“+“-symbols: calculated points) was deformed to a pincushion-like pattern (“x”symbols: measured points) from which the 2D-distortion polynominal could be derived. Note that the origin of the roordinate system of both the calculated and measured points lies in the center of the image, the area free of distortion. (C) Distributions of lengths of distortion vector (magnitude of positional errors) of the ZD-phantom pins in the uncorrected (solid line) and in corrected image (dotted line) calculated with N = 4 (expansion order of the 2D polynomial). Magnitude of positional errors in uncorrected image was about 2-3 mm at outer range of phantom (i.e., at the position of the reference points of the stereotactic guidance system). These errors were reduced to about 1 mm in corrected image, which corresponded to the pixel resolution of the image.
(D)
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Fig. 3. (A) The 3D phantom mounted in the stereotactic guidance system for measuring 3D position of MR imaging plane. This was comprised of a regular grid of water-filled rectangular boreholes, with oblique water-filled boreholes in between. This produced a pattern of reference points surrounded by measurement points in axial image from which the 3D position of the imaging plane can be reconstructed. (B) Schematic illustration of 3D-phantom measurement. The distance d between reference point (rectangular water-filled borehole) and measurement point (oblique water-filled borehole) is a direct measure of the z coordinate of the imaging plane at the reference point, since the angle between oblique water-filled borehole is 01 = 2 arctan(0.5). Systematic discrepancy in the distance measurements of d, > d2 > d3 > d4 > d5 > de would be detected if the imaging plane were tilted. (C) Axial image of the 3D phantom. The 3D position of the imaging plane can be reconstructed from the measured points. (D) Typical example of the 3D position of the imaging plane with properly adjusted shims. Deviations in z direction were reduced to about 1 mm, which approximated again the dimensions of the image pixels (l-mm slice thickness). Mathematical correction of these discrepancies in the z direction was not pursued, since properly adjusted shims avoid deformation or tilting of the imaging plane.
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produce deformation or tilting of the plane in space not apparent in the 2D-phantom measurements. For the measurements, the 3D-phantom was fixed in the stereotactic guidance system and axial orientated MRA images were obtained and initially corrected using the 2D polynomial. These corrected images display a regular pattern of points emanating from the water-filled boreholes (Fig. 3C). Each reference point produced by a rectangular borehole is encircled by several measurement points coming from neighboring oblique boreholes. The distance between the reference and measurement points is a direct measure of the z coordinate of the imaging plane at the reference point (Fig. 3B). In this manner, the z coordinates of the imaging plane were measured at every reference point
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and the imaging plane was reconstructed and its position, shape, and orientation assessed. Figure 3D is a typical example of the initial reconstruction of the imaging plane, showing a nearly horizontal imaging plane with some discrepancies in z components to the order of 1 mm which approximates again the dimensions of the image pixels (l-mm slice thickness). Mathematical correction of these discrepancies in the z direction was not pursued, because properly adjusted shims avoid deformation or tilting of the imaging plane. Test of accuracy. The precision of MR stereotaxy and the importance of geometric corrections may be tested by assessing the stereotactic coordinates of a
4. Definition of the target volume for treatment planning of AVM radiosurgery. The 3D angiograms (TR/TE = 40/7, 15” flip angle, FISP, maximum-intensity projection) were obtained in a large volume (156 mm thick, 156 slices) using a homemade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system. The target volume can only be defined by the therapist interactively with a digitizer. The therapist can define the target volume either on the original images (upper right) or on MR angiography images at axial (upper left), sagittal (lower right) or frontal (lower left) projections. Thereby the computer calculates automatically the stereotactic z coordinate (= slice position) and the stereotactic coordinate system with the help of reference points seen as landmarks in the original images. Fig.
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point source with and without correction, and comparing these with those measured manualIy. For this purpose a cross plastic tube (1 mm inner diameter) filled with Gd-DTPA solution was placed in the stereotactic guidance system. The cross was aligned in the z direction and the stereotactic coordinates of its crosspoint were measured (3D-FISP sequence) from axial MRA images. The stereotactic z coordinate (i.e., the distance of the image plane from the stereotactic zero plane) was determined by the distance between two reference points (Fig. 1D) produced by the obliquely oriented plastic tubes of the guidance system (Fig. 1C). The stereotactic x and y coordinates were measured with respect to the stereotactic zero point (midpoint of the guidance system). The manual measured exact stereotactic coordinates of the crosspoint were P,,,(x, y,z) = (48.5,-27.5,78.5) mm compared with the image-based evaluated coordinates Pi,, (x, y,z) = (47.6,-27.7,78.0) mm, whereas discrepancies of about 2 mm appeared mainly in the z coordinate without correction of geometric distortion. The magnitude of the error in z coordinate increases with the z coordinate. This is related in part to the pincushion-like distortion pattern of the axial images, since z coordinates are calculated from and therefore ultimately dependent on the fidelity of the x,y components. In both the uncorrected and corrected images the calculated z component corresponds to the distance between the x,y components of two reference points. Ideally, and in the corrected images, this distance increases linearly with the true z component. However, in the case of the uncorrected images the distance, due to the pincushion effect which is not
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negligible at the position of the reference points, increases nonlinearly-the z component measured lying on an “arc” rather than on a proper “straight line.” Hence, disparity of these two measurements increases with increasing z coordinate. In addition, an anatomical check of the correction method (i.e., correction of anatomic images via phantom measurements) was done by assessing the stereotactic position of the middle cerebral artery, and comparing these measurements with those obtained using the same stereotactic system with CT. This proves that after correction the locations in CT and MR correspond to the same anatomical focus, and a detailed description of the anatomical verification is given elsewhere.” After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Such a correction provides for the more accurate transfer of anatomical/ pathological informations and target point coordinates to the isocenter of the therapy machine so essential for the stereotactic radiation technique. RESULTS
Definition of Head Contour and Target Volumes In the first step of treatment planning of AVM radiosurgery, regions of interest may be drawn either interactively with a digitizer or traced automatically by a contour finding algorithm. For automatic contouring the user selects a threshold value and a starting point inside the volume of interest. The computer then traces the contour until a closed loop has been found. The
distance-test
501 80
90
100
110
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130
140
150
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Fig. 5. Computer evaluated stereotactic z coordinates in a series of 70 axial MR images. The stereotactic z coordinate is directly determined by the distance between two reference points, because the angle between the reference tubes is OL= 2 arctan (0.5) and they cross at the stereotactic zero plane. The result of a linear fit which describes excellently the correlation of slice numbers (x-axis) and stereotactic z coordinates (y-axis) is stored in a look-up table for the following treatment planning process.
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Fig. 6. Conventional brain angiograms of the same : patient in frontal (A) and sagittal (B) projections. Because the patient’s head was fixed in the same stereotactic loca Gzation system, the information about target volumes ant d target points could be precisely transferred from MR angi iograms to conventional angiograms for comparison.
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target volume, as a general rule, can only be defined by the therapist and is based on the information provided by the MR images (Fig. 4). The therapist can define the target volume on a set of original or projection images and have these regions accurately transferred between them. The stereotactic z coordinates were directly determined by a “distance-test,” where the distance between the reference points of the stereotactic system in the original axial slices has been measured, fitted, and stored in a look-up table, which contains the correlation of slice numbers and stereotactic z coordinates (Fig. 5). Additionally, each contour is processed after input, for example, the number of contour points is reduced to a minimum by omission of redundant points. Isodose curves are extracted from dose matrices of parallel transverse planes. The contour finding algorithm traces isodose lines of a specified dose level and stores the isodoses in the same data base as the volumes of interest. For each patient the MR angiograms were compared with the available conventional brain angiograms (Fig. 6). The AVM were assessed for the size of the nidus, the origin of the feeding arteries, and the pattern of venous drainage. Since the patient’s head
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was fixed in the same stereotactic localization system for conventional angiography, the information about target volumes and target points could be precisely transferred from MR angiograms to conventional angiograms for comparison. Irradiation Technique Irradiation was performed using the 15MV X-ray beam of a linear accelerator. The irradiation technique is shown in Fig. 7 and is described in detail elsewhere.8 Figure 8 shows the dose distributions of three target points calculated in an angiographic MR data set of a patient with an AVM, treated by stereotactic convergent photon beam irradiation. The dose calculation was performed on the basis of MR data only. The 80%, 50%, and 30% isodose lines are indicated and emphasize the steep dose gradient. DISCUSSION Linac-based radiosurgery of AVM represents a valid option for AVM in vital or sensitive regions of the brain where they cannot be excised without the risk of disabling neurological deficits and for AVM after
7. Schematic illustration of the irradiation technique. Radiosurgery has been realized by a total of nine moving field irradiations, while rotating the treatment table by steps of 20” before starting the next moving field irradiation. Each of these irradiations consist of a semicircular gantry movement ranging from 20 to 160” or from 200 to 340”, depending on the treatment table position.
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(B) Fig. 8. Dose distributions of three target points calculated in an angiographic MR data set of a patient with an AVM, treated by st:ereotactic convergent photon beam irradiation. The dose calculation was performed on the basis of MR data only. The 80% (solid line), 50% (dotted line), and 30% (dashed line) isodose lines are indicated and emphasize the steep dose gradient illusl trated in frontal (A) and sagittal (B) section.
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partial embolization or incomplete surgical removal.2,3~8~9An indispensable prerequisite for stereotactically directed, local, high dose irradiation is the accurate delineation of the target volume for treatment planning. In an attempt to achieve this we have incorporated MR angiography into our treatment planning protocol. This in turn allows the therapist to interactively define volumes of interest (target volume, organs at risk, etc.) on a set of original MR images or directly on calculated MR angiograms. A major problem in MR imaging is the production of a uniform main magnetic field and linear orthogonal field gradients. Inhomogeneities and nonlinearities introduce geometric distortion in MR images. One major source of these distortions are eddy currents produced during the imaging sequence. Depending on the individual MR system, these effects may produce errors of up to 2-3 mm in the calculation of stereotactic coordinates from uncorrected MR images. For stereotactic radiotherapy in cases, where accurate positioning are critical, such distortions are not negligible. With the help of phantom measurements, numeric calculation, and shim adjustment, these may be readily reduced. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). In general, the exclusive use of MR imaging data for treatment planning is not possible because image information does not correlate with electron densities, and thus does not take into account important parameters for dose calculation such as bone structures. Additionally, inhomogeneities of the RF field would vary the pixel intensities of MR images. Therefore the variability of the MR imaging data does not allow pixeloriented, MR-based radiotherapy planning generally. In radiosurgery, however, tissue inhomogeneities do not significantly influence the shape of the relative dose distribution. Under this circumstance, the dose calculation can be based only on the 3D geometric conformation of the patient’s head, and a simple algorithm for treatment planning of AVM radiosurgery can be used and based on multiplanar MR angiographic data if they are free of geometric distortion. MR angiography provides accurate 3D information about the anatomy and topography of AVM, but it does not yet provide the detailed vascular information obtained with conventional angiography. On the other hand, the nidus of the lesions can be easily and precisely assessed on original images or on 3D angiographic projections, which correlates well with conventional angiography in most of the cases. l5 This is consistent with observations made by other authors.‘6*17 Partial darkening of the AVM could be observed in MR angiography after 6 mo in a few patients
and in more than 50% of the patients 1 yr after radiosurgery. l5 Since 1984, 110 patients with AVM underwent stereotactic radiosurgery with the linac-based radiosurgical method developed at our institution in Heidelberg.8 Because of the inherent risk and discomfort of repeated conventional angiographic examinations, MR angiography became a useful method in our treatment protocol (since 1990) for planning of radiosurgery and follow-up for studying the dynamic process of obliteration after radiation. REFERENCES 1. Leksell, L. The the brain. Acta R.; 2. Engenhart, Hover, K.H.; Stereotaktische
stereotaxic
method
and radiosurgery of 1951. Kimmig, B.; Wowra, B.; Sturm, V.; Schneider, S.; Wannenmacher, M. Einzeitbestrahlung cerebraler Angiome.
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Radiologe 29:219-223; 1989. E.B.; Pla, M.; 3. Souhami, L.; Oliver, A.; Podgorsak, Pike, G.B. Radiosurgery of cerebral arteriovenous malformations with the dynamic stereotactic irradiation.
Int. J. Radiat. Oncol. Biol. Phys. 19:775-782; 1990. 4. Kjellberg, R.N.; Davis, K.R.; Lyons, S.L.; Butler, W.; Adams, R.D. Bragg peak proton beam therapy for arteriovenous malformation of the brain. Clin. Neurosurg. 31:248-290; 1983. B.; Leksell, L.; Rexed, B.; Sourander, P.; 5. Larsson, Mair, W.; Anderson, B. The high energy proton beam as a neurosurgical tool. Nature 182: 1222-1223; 1958. 6. Steiner, L.; Leksell, L.; Greitz, T.; Forster, D.M.C.; Backlund, E.O. Stereotaxic radiosurgery for cerebral arteriovenous malformations. Report of a case. Acta Chir.
Stand. 138:459-464; 1972. 7. Colombo, F.; Benedetti, A.; Pozza, F., Avanzo, R.C.; Marchetti, C.; Chierego, G.; Zanardo, A. External stereotactic irradiation by linear accelerator. Neurosurgery 16:154-160; 1985. 8. Hartmann, G.H.; Schlegel, W.; Sturm, V.; Kober, B.; Pastyr, 0.; Lorenz, W.J. Cerebral radiation surgery using moving field irradiation at a linear accelerator facility. J. Radiat. Oncol. Biol. Phys. 11:1185-1192; 1985. 9. Podgorsak, E.B.; Oliver, A.; Pla, M. ; Lefebvre, P.Y.; Hazel, J. Dynamic stereotactic radiosurgery. Znt. J. Radiat. Oncol. Biol. Phys. 14:115-125; 1988. 10. Schad, L.; Lott, S.; Schmitt, F.; Sturm, V.; Lorenz, W.J. Correction of spatial distortion in MR imaging: A prerequisite for accurate stereotaxy. .I. Comput. Assist.
Tomogr. 11(3):499-505; 1987. 11. Schad, L.R.; Boesecke, R.; Schlegel, W.; Hartmann, G.; Sturm, V.; Strauss, L.; Lorenz, W.J. Three dimensional image correlation of CT, MR, and PET studies in radiotherapy treatment planning of brain tumours. J. Comput. Assist. Tomogr. 11(6):948-954; 1987. 12. Ehricke, H.H., Schad, L.R., Gademann, G., Wowra, B., Engenhart, R., Lorenz, W. J. Use of M.R. angiography for stereotactic planning. J. Comput. Assist.
Tomogr. 16~35-40, 1992.
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13. Laub, G.A.; Kaiser, W.A. MR angiography with gradient motion refocusing. J. Comput. Assist. Tomogr. 12: 377-382; 1988. 14. Pastyr, 0.; Hartmann, G.H.; Schlegel, W.; Schabbert, S.; Treuer, H.; Lorenz, W-J.; Sturm, V. Stereotactically guided convergent beam irradiation with a linear accelerator: Localization technique. Acta Neurochir. (Wien) 99:61-64; 1989. 15. Layer, G.; Semmler, W.; Schad, L.R.; Wowra, W.; van Kaick, G. MR-Tomographie und MR-Angiographie cerebraler arteriovenoser Malformationen. Fortschr Riintgenstr 154(4):438-444; 1991.
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16. Edelmann, R.R.; Wentz, K.U.; Mattle, H.P.; O’Reilly, G.V.; Candia, G.; Liu, C.; Zhao, B.; Kjellberg, R.N.; Davis, K.R. Intracerebral arteriovenous malformations: Evaluation with selective MR angiography and venography. Radiology 173:831-837; 1989. 17. Marchal, G.; Bosmans, H.; Van fraeyenhoven, L.; Wilms, G.; Van Hecke, P.; Plets, C.; Baert, A.L. Intracranial vascular lesions: Optimization and clinical evaluation of three-dimensional time-of-flight MR angiography. Radiology 175:443-448; 1990.
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Imaging, Vol. IO, pp. 609-621, All rights reserved.
1992 Copyright
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0730-725X/92 $5.00 + .@I 1992 Pergamon PressLtd.
Original Contribution CORRECTION OF SPATIAL DISTORTION ANGIOGRAPHY FOR RADIOSURGICAL OF CEREBRAL ARTERIOVENOUS
IN MAGNETIC RESONANCE TREATMENT PLANNING MALFORMATIONS
LOTHAR R. SCHAII,*I_ HANS-H. EHRICKE,~ BERNDT WOWRA,~ G~NTER LAYER,* RITA ENGENHART, 11HANS-U. KAUCZOR,* HANS-J. Z-EL,* GUNNAR BRIX,* AND WALTER J. LORENZ* *Institute of Radiology and Pathophysiology, German Cancer Research Center, Heidelberg; Jthe Siemens Medical Division, Erlangen; §Department of Neurosurgery, Heidelberg University; 1Department of Radiotherapy, Heidelberg University, Germany A treatment planning system based on magnetic resonance (MR) angiograpbic imaging data for the radiosurgery of inoperable cerebral arteriovenous malformations is reported. MR angiographywas performedusing a threedimensional (3D) velocity-compensated fast imaging with steady-state precession (FISP) sequence. Depending on the individual MR system, inhomogeneitiesand nonlinearitiesinduced by eddy currents during the pulse sequence can distort the images and produce spurious displacements of the stereotactic coordinates in both the x-y plane and the z axis. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system-a ‘2D-phantom” displaying “pincushion” distortion in the image, and a “3D-phantom” displayingdisplacement,warp, and tilt of the imageplane itself. The pincushion distortion can be %orrected” (reducing displacements from 2-3 mm to 1 mm) by calculations based on modeling the distortion as a fourth order 2D polynomial. Displacement, warp, and tilt of the image plane may be corrected by adjustment of the gradient shimming currents. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Precise definition of the target volume could be performedby the therapist either directly in the MR images or in calculated projection MR angiograms obtained by a maximum intensity projection algorithm. MR angiography provides a sensitive, noninvasive 3D method for defining target volume and critical structures, and for calculating precise dose distributions for radiosurgery of cerebral arteriovenous malformations. Keywords:
Treatment planning; Brain neoplasms;
Stereotaxy; Radiosurgery; Magnetic resonance angiography.
INTRODUCTION
was initially performed for the treatment of tumors and AVM with heavy charged particle beams from cyclotrons4.5 and later by the Gamma unit published as a case report.6 The precise localization of the target point and a steep dose gradient outside the target volume allow application of high doses to the AVM without damage to the surrounding normal brain tissue. According to this features radiosurgery is an effective therapy for AVM leading to the development of linear accelerator based radiosurgical techniques at different radiation oncology centers.‘-’ In general, the sole use of MR data as a base for treatment planning is often not feasible because (a) pixel intensities are unrelated to electron densities and
Cerebral arteriovenous malformations (AVM) are vascular malformations conceived as congenital anomalies. Surgical excision is the treatment of choice; an alternative is embolization. Radiation therapy is indicated (a) for AVM in vital or sensitive regions of the brain where they cannot be excised without the risk of a disabling neurological deficit, and (b) for residual AVM after partial embolization or incomplete surgical removal. Since the pioneering work of Leksell in
1951,’ radiosurgery has become the most effective radiotherapy for AVM. 2~3Radiosurgery describes stereotactically guided single high-dose irradiation and
gie, Deutsches Krebsforschungszentrum, D-6900 Heidelberg, Germany.
RECEIVED 10/l/91; ACCEPTED l/22/92. Address correspondence and reprint requests to PD Dr. L.R. Schad, Institut fiir Radiologie und Pathophysiolo-
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are strongly dependent on the specific imaging sequences employed; (b) inhomogeneous radiofrequency (RF) fields yield intensity variations in the MR images; (c) complex bone/air inhomogeneities, important in calculating beam penetration, are not imaged; and (d) various geometrical distortions in all three dimensions are produced by the inhomogeneity of the main magnetic field and noniinearities of the gradients. lo On the other hand, film dosimetric phantom measurements have shown that tissue inhomogeneities do not significantly influence the shape of the relative dose distribution in radiosurgery of deeply positioned lesions of the brain.8s1’ Under this circumstance, the dose calculation of radiosurgery can be based only on
Instrumentation MR angiography (MRA) was performed on a 64 MHz Magnetom (Siemens, Erlangen, Germany) superconducting whole body imager using a 3D velocitycompensated fast imaging with steady-state precession
(4
0%
the 3D geometric conformation of the patient’s head. Therefore multiplanar MR imaging data are a possible input basis for dose calculation if they are free of geometric distortion. In this case a simple algorithm for treatment planning of AVM radiosurgery can be used and based on multiplanar MR angiographic data. METHODS AND MATERIALS
Fig. 1. (A) Patient positioning in the stereotactic guidance system. A rigid frame made of wood was fixed to the patient either using a special mask or by means of carbon-fiber pins. Plexiglas squares embedded with steel wires for conventional angiography, or plastic tubes filled with a 5 mmol/liter Gd-DTPA solution (Schering, Berlin, Germany) for MR angiography were attached to the stereotactic head frame and served as landmarks in the images, from which the stereotactic coordinate system could be derived. The radiofrequency transmitting and receiving unit consisted of a homemade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system. (B) Patient positioning during irradiation. A special device was fixed to the frame that enabled adjustments of the target point coordinates to the isocenter of the therapy machine. This device was removed prior to the irradiation. Precise positioning was controlled by a laser system and allowed fitting of the target point onto the isocenter of the therapy machine with a positional error of +O.S mm. (Figure continued on facing page.)
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(FISP) sequence. The sequence parameters included a flip angle of 15”, a repetition time (TR) of 40 msec, an echo time (TE) of 7 msec, one acquisition, and a 256 x 256 image matrix with a 64-partition slab. The total volume of interest was acquired in successive and 10 slices overlapping slabs in the axial direction. The minimal field-of-view was restricted to 260 mm in order to image the reference points of the stereotactic localization system; slab thickness was 64 mm for the 64 partitions, resulting in an effective voxel size of 1 mm3. The RF transmitting and receiving unit consists of a selfmade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system (Fig. 1A). The MR computer (MICRO-VAX, DEC, Maynard, MA, U.S.A.) was connected directly (DEC-NET, DEC, link) to a central computer (VAX-WORKSTATION/3600, DEC) where the software developed by our group for treatment planning of AVM radiosurgery was running. l2 After data acquisition, images were transferred to the central computer and postprocessed with a maximum-intensity projection (MIP) method. l3 For treatment planning of AVM radiosurgery, typically 36 angiographic projection images were reconstructed with angles of rotation about the headfeet axis ranging from 0” to 360”.
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Localization Technique The localization system is based on the Riechert and Mundinger stereotactic head frame, which was modified for use with CT, MR, and PET scanners or conventional angiography. *0,r4A rigid frame made of wood was fixed to the patient either using a special mask (Fig. 1A) or by means of carbon-fibre pins. Plexi-glass squares embedded with steel wires for conventional angiography, or plastic tubes filled with a 5 mmol/liter Gd-DTPA solution (Schering, Berlin, Germany) for MR were attached to the stereotactic head frame and served as landmarks in the images, from which the stereotactic coordinate system could be derived (Fig. lC,D). By employing this system and special computer programs, the information about size, shape, and localization of the target volume can precisely be transferred either between the imaging modalities (MRA, conventional angiography) or to the stereotactic coordinate system defined by the head frame. This frame remains fixed to the patient’s head during the irradiation. It is attached to the treatment table, providing a rigid and immobile connection between the patient’s head and the treatment table. After the target point coordinates are determined with reference to the head frame, a special device is fixed to the frame that enables these coordinates to be adjusted to the isocenter of the therapy machine (Fig. 1B).
transaxial image
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Fig. 1 continued. (C) Evaluation of the stereotactic z coordinate. The z coordinate was directly determined by the distance between two reference points, because the angle between the reference tubes is cr = 2 arctan(0.5) and they cross at the stereotactic zero plane. (D) Schematic drawing of an axial image shows the tube reference points of the stereotactic guidance system and definition of the stereotactic coordinate system.
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This device is removed prior to the irradiation. Precise positioning is controlled by a laser system and allows fitting of the target point onto the isocenter of the therapy machine with an positional error of kO.5 mm. Correction of Spatial Distortion in MR The use of MR for stereotactic locations requires accurate spatial information from MR images. Depending on the individual imaging system, eddy currents of the pulsed gradients, excited in the cryo shield during the imaging sequence, can introduce geometrical distortions in all three dimensions. If necessary, these errors in position can be assessed by means of two phantoms placed within the stereotactic guidance system-a “2D-phantom” displaying “pincushion” distortion in the image (x-y plane), and the “3D-phantom” displaying displacement, warp, and tilt of the image plane itself. 2D-phantom measurement. The first, the “2D”phantom, is used to measure the geometrical distortions within the imaging plane (Fig. 2A). It consists of a water-filled cylinder 17 cm in radius and 10 cm in depth, containing a rectangular grid of plastic rods spaced 2 cm apart and oriented in the z direction (i.e., perpendicular to the imaging plane). Since the exact positions (x, y) of these rods are known a priori, their positions (u, v) in the 2D-phantom reflect the geometric distortion in the imaging plane and may be used to calculate the coordinate transformation that mathematically describes the distortion process. The x-y plane distortion of axial MRA images of the 2D-phantom can be “corrected” (reducing displacements to the size of a pixel) by calculations based on modeling the distortion as a fourth order 2D polynomial: uk =
cN~ ‘x~ u;j
‘ye
be calculated and the distortion corrected. Thereby, the selection of N = 4 is a compromise between computational burden and reduction in distortion. A more quantitative, direct measurement of distortion is provided by the distortion vector, which measures the discrepancy between the true (x,y)k position of a pin in the 2D-phantom and its apparent position in the image (u,v)k: dk = I(& - (u,u)~[ (i.e., the vectoral distance between the true and apparent positions). Reduction in distortion is demonstrated in Fig. 2C - a comparison of the distribution of dk in the uncorrected and corrected images. The distribution of dk in the corrected 2D-phantom image shows that the positional errors are reduced from about 2-3 mm (Fig. 2C, solid line) to about 1 mm across the entirety of the 2D-phantom (Fig. 2C, dotted line). No further attempts were made to reduce this residual error, because this approximates the dimensions of the image pixels (256 x 256 matrix). 3D-phantom measurement. After correcting for distortion in the imaging plane, the 3D position of the imaging plane was assessed with the “3D” phantom (Fig. 3A). This is necessary because inhomogeneities of the gradient fields that define the imaging plane can
,
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Fig. 2. (A) The 2D phantom
for measuring the geometrical distortions within the imaging plane. It consists of a waterfilled cylinder 17 cm in radius and 10 cm in depth, containing a rectangular grid of plastic rods spaced 2 cm apart and oriented in the z direction (i.e., perpendicular to the imaging plane). (Figure continued on facing page.)
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Fig. 2 continued. (B) Typical example of a 2D-phantom measurement using a velocity-compensated FISP sequence. The a priori known regular grid of the plastic rods (“+“-symbols: calculated points) was deformed to a pincushion-like pattern (“x”symbols: measured points) from which the 2D-distortion polynominal could be derived. Note that the origin of the roordinate system of both the calculated and measured points lies in the center of the image, the area free of distortion. (C) Distributions of lengths of distortion vector (magnitude of positional errors) of the ZD-phantom pins in the uncorrected (solid line) and in corrected image (dotted line) calculated with N = 4 (expansion order of the 2D polynomial). Magnitude of positional errors in uncorrected image was about 2-3 mm at outer range of phantom (i.e., at the position of the reference points of the stereotactic guidance system). These errors were reduced to about 1 mm in corrected image, which corresponded to the pixel resolution of the image.
(D)
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Fig. 3. (A) The 3D phantom mounted in the stereotactic guidance system for measuring 3D position of MR imaging plane. This was comprised of a regular grid of water-filled rectangular boreholes, with oblique water-filled boreholes in between. This produced a pattern of reference points surrounded by measurement points in axial image from which the 3D position of the imaging plane can be reconstructed. (B) Schematic illustration of 3D-phantom measurement. The distance d between reference point (rectangular water-filled borehole) and measurement point (oblique water-filled borehole) is a direct measure of the z coordinate of the imaging plane at the reference point, since the angle between oblique water-filled borehole is 01 = 2 arctan(0.5). Systematic discrepancy in the distance measurements of d, > d2 > d3 > d4 > d5 > de would be detected if the imaging plane were tilted. (C) Axial image of the 3D phantom. The 3D position of the imaging plane can be reconstructed from the measured points. (D) Typical example of the 3D position of the imaging plane with properly adjusted shims. Deviations in z direction were reduced to about 1 mm, which approximated again the dimensions of the image pixels (l-mm slice thickness). Mathematical correction of these discrepancies in the z direction was not pursued, since properly adjusted shims avoid deformation or tilting of the imaging plane.
axial imaging plane
MRA: 3Dphantom distortion
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produce deformation or tilting of the plane in space not apparent in the 2D-phantom measurements. For the measurements, the 3D-phantom was fixed in the stereotactic guidance system and axial orientated MRA images were obtained and initially corrected using the 2D polynomial. These corrected images display a regular pattern of points emanating from the water-filled boreholes (Fig. 3C). Each reference point produced by a rectangular borehole is encircled by several measurement points coming from neighboring oblique boreholes. The distance between the reference and measurement points is a direct measure of the z coordinate of the imaging plane at the reference point (Fig. 3B). In this manner, the z coordinates of the imaging plane were measured at every reference point
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and the imaging plane was reconstructed and its position, shape, and orientation assessed. Figure 3D is a typical example of the initial reconstruction of the imaging plane, showing a nearly horizontal imaging plane with some discrepancies in z components to the order of 1 mm which approximates again the dimensions of the image pixels (l-mm slice thickness). Mathematical correction of these discrepancies in the z direction was not pursued, because properly adjusted shims avoid deformation or tilting of the imaging plane. Test of accuracy. The precision of MR stereotaxy and the importance of geometric corrections may be tested by assessing the stereotactic coordinates of a
4. Definition of the target volume for treatment planning of AVM radiosurgery. The 3D angiograms (TR/TE = 40/7, 15” flip angle, FISP, maximum-intensity projection) were obtained in a large volume (156 mm thick, 156 slices) using a homemade, linear polarized head coil (made by HJZ) with an inner diameter of 31 cm, which fits very closely to the stereotactic localization system. The target volume can only be defined by the therapist interactively with a digitizer. The therapist can define the target volume either on the original images (upper right) or on MR angiography images at axial (upper left), sagittal (lower right) or frontal (lower left) projections. Thereby the computer calculates automatically the stereotactic z coordinate (= slice position) and the stereotactic coordinate system with the help of reference points seen as landmarks in the original images. Fig.
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point source with and without correction, and comparing these with those measured manualIy. For this purpose a cross plastic tube (1 mm inner diameter) filled with Gd-DTPA solution was placed in the stereotactic guidance system. The cross was aligned in the z direction and the stereotactic coordinates of its crosspoint were measured (3D-FISP sequence) from axial MRA images. The stereotactic z coordinate (i.e., the distance of the image plane from the stereotactic zero plane) was determined by the distance between two reference points (Fig. 1D) produced by the obliquely oriented plastic tubes of the guidance system (Fig. 1C). The stereotactic x and y coordinates were measured with respect to the stereotactic zero point (midpoint of the guidance system). The manual measured exact stereotactic coordinates of the crosspoint were P,,,(x, y,z) = (48.5,-27.5,78.5) mm compared with the image-based evaluated coordinates Pi,, (x, y,z) = (47.6,-27.7,78.0) mm, whereas discrepancies of about 2 mm appeared mainly in the z coordinate without correction of geometric distortion. The magnitude of the error in z coordinate increases with the z coordinate. This is related in part to the pincushion-like distortion pattern of the axial images, since z coordinates are calculated from and therefore ultimately dependent on the fidelity of the x,y components. In both the uncorrected and corrected images the calculated z component corresponds to the distance between the x,y components of two reference points. Ideally, and in the corrected images, this distance increases linearly with the true z component. However, in the case of the uncorrected images the distance, due to the pincushion effect which is not
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negligible at the position of the reference points, increases nonlinearly-the z component measured lying on an “arc” rather than on a proper “straight line.” Hence, disparity of these two measurements increases with increasing z coordinate. In addition, an anatomical check of the correction method (i.e., correction of anatomic images via phantom measurements) was done by assessing the stereotactic position of the middle cerebral artery, and comparing these measurements with those obtained using the same stereotactic system with CT. This proves that after correction the locations in CT and MR correspond to the same anatomical focus, and a detailed description of the anatomical verification is given elsewhere.” After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). Such a correction provides for the more accurate transfer of anatomical/ pathological informations and target point coordinates to the isocenter of the therapy machine so essential for the stereotactic radiation technique. RESULTS
Definition of Head Contour and Target Volumes In the first step of treatment planning of AVM radiosurgery, regions of interest may be drawn either interactively with a digitizer or traced automatically by a contour finding algorithm. For automatic contouring the user selects a threshold value and a starting point inside the volume of interest. The computer then traces the contour until a closed loop has been found. The
distance-test
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90
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130
140
150
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Fig. 5. Computer evaluated stereotactic z coordinates in a series of 70 axial MR images. The stereotactic z coordinate is directly determined by the distance between two reference points, because the angle between the reference tubes is OL= 2 arctan (0.5) and they cross at the stereotactic zero plane. The result of a linear fit which describes excellently the correlation of slice numbers (x-axis) and stereotactic z coordinates (y-axis) is stored in a look-up table for the following treatment planning process.
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Fig. 6. Conventional brain angiograms of the same : patient in frontal (A) and sagittal (B) projections. Because the patient’s head was fixed in the same stereotactic loca Gzation system, the information about target volumes ant d target points could be precisely transferred from MR angi iograms to conventional angiograms for comparison.
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target volume, as a general rule, can only be defined by the therapist and is based on the information provided by the MR images (Fig. 4). The therapist can define the target volume on a set of original or projection images and have these regions accurately transferred between them. The stereotactic z coordinates were directly determined by a “distance-test,” where the distance between the reference points of the stereotactic system in the original axial slices has been measured, fitted, and stored in a look-up table, which contains the correlation of slice numbers and stereotactic z coordinates (Fig. 5). Additionally, each contour is processed after input, for example, the number of contour points is reduced to a minimum by omission of redundant points. Isodose curves are extracted from dose matrices of parallel transverse planes. The contour finding algorithm traces isodose lines of a specified dose level and stores the isodoses in the same data base as the volumes of interest. For each patient the MR angiograms were compared with the available conventional brain angiograms (Fig. 6). The AVM were assessed for the size of the nidus, the origin of the feeding arteries, and the pattern of venous drainage. Since the patient’s head
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was fixed in the same stereotactic localization system for conventional angiography, the information about target volumes and target points could be precisely transferred from MR angiograms to conventional angiograms for comparison. Irradiation Technique Irradiation was performed using the 15MV X-ray beam of a linear accelerator. The irradiation technique is shown in Fig. 7 and is described in detail elsewhere.8 Figure 8 shows the dose distributions of three target points calculated in an angiographic MR data set of a patient with an AVM, treated by stereotactic convergent photon beam irradiation. The dose calculation was performed on the basis of MR data only. The 80%, 50%, and 30% isodose lines are indicated and emphasize the steep dose gradient. DISCUSSION Linac-based radiosurgery of AVM represents a valid option for AVM in vital or sensitive regions of the brain where they cannot be excised without the risk of disabling neurological deficits and for AVM after
7. Schematic illustration of the irradiation technique. Radiosurgery has been realized by a total of nine moving field irradiations, while rotating the treatment table by steps of 20” before starting the next moving field irradiation. Each of these irradiations consist of a semicircular gantry movement ranging from 20 to 160” or from 200 to 340”, depending on the treatment table position.
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(B) Fig. 8. Dose distributions of three target points calculated in an angiographic MR data set of a patient with an AVM, treated by st:ereotactic convergent photon beam irradiation. The dose calculation was performed on the basis of MR data only. The 80% (solid line), 50% (dotted line), and 30% (dashed line) isodose lines are indicated and emphasize the steep dose gradient illusl trated in frontal (A) and sagittal (B) section.
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partial embolization or incomplete surgical removal.2,3~8~9An indispensable prerequisite for stereotactically directed, local, high dose irradiation is the accurate delineation of the target volume for treatment planning. In an attempt to achieve this we have incorporated MR angiography into our treatment planning protocol. This in turn allows the therapist to interactively define volumes of interest (target volume, organs at risk, etc.) on a set of original MR images or directly on calculated MR angiograms. A major problem in MR imaging is the production of a uniform main magnetic field and linear orthogonal field gradients. Inhomogeneities and nonlinearities introduce geometric distortion in MR images. One major source of these distortions are eddy currents produced during the imaging sequence. Depending on the individual MR system, these effects may produce errors of up to 2-3 mm in the calculation of stereotactic coordinates from uncorrected MR images. For stereotactic radiotherapy in cases, where accurate positioning are critical, such distortions are not negligible. With the help of phantom measurements, numeric calculation, and shim adjustment, these may be readily reduced. After correction, the accuracy of the geometric information is limited only by the pixel resolution of the image (= 1 mm). In general, the exclusive use of MR imaging data for treatment planning is not possible because image information does not correlate with electron densities, and thus does not take into account important parameters for dose calculation such as bone structures. Additionally, inhomogeneities of the RF field would vary the pixel intensities of MR images. Therefore the variability of the MR imaging data does not allow pixeloriented, MR-based radiotherapy planning generally. In radiosurgery, however, tissue inhomogeneities do not significantly influence the shape of the relative dose distribution. Under this circumstance, the dose calculation can be based only on the 3D geometric conformation of the patient’s head, and a simple algorithm for treatment planning of AVM radiosurgery can be used and based on multiplanar MR angiographic data if they are free of geometric distortion. MR angiography provides accurate 3D information about the anatomy and topography of AVM, but it does not yet provide the detailed vascular information obtained with conventional angiography. On the other hand, the nidus of the lesions can be easily and precisely assessed on original images or on 3D angiographic projections, which correlates well with conventional angiography in most of the cases. l5 This is consistent with observations made by other authors.‘6*17 Partial darkening of the AVM could be observed in MR angiography after 6 mo in a few patients
and in more than 50% of the patients 1 yr after radiosurgery. l5 Since 1984, 110 patients with AVM underwent stereotactic radiosurgery with the linac-based radiosurgical method developed at our institution in Heidelberg.8 Because of the inherent risk and discomfort of repeated conventional angiographic examinations, MR angiography became a useful method in our treatment protocol (since 1990) for planning of radiosurgery and follow-up for studying the dynamic process of obliteration after radiation. REFERENCES 1. Leksell, L. The the brain. Acta R.; 2. Engenhart, Hover, K.H.; Stereotaktische
stereotaxic
method
and radiosurgery of 1951. Kimmig, B.; Wowra, B.; Sturm, V.; Schneider, S.; Wannenmacher, M. Einzeitbestrahlung cerebraler Angiome.
Chir. Scan. 102:316-319;
Radiologe 29:219-223; 1989. E.B.; Pla, M.; 3. Souhami, L.; Oliver, A.; Podgorsak, Pike, G.B. Radiosurgery of cerebral arteriovenous malformations with the dynamic stereotactic irradiation.
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