RU2574374C2 - Determination of object's particular orientation - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: medical system of image formation contains means for obtaining two-dimensional image of object, where object is provided with three markers, data-processing unit, made with possibility of detecting markers, identification of spatial location and angle of rotation of object relative to system geometry, calculation of configuration of markers and creation of projection of calculated marker configuration, and display, presenting object indicator and created projection as target indicator. Computer-readable carrier contains elements of program, providing operation of image formation system.

EFFECT: application of invention makes it possible to accurately determine location and orientation of object in space.

10 cl, 13 dwg

Description

FIELD OF THE INVENTION

The present invention relates to determining a specific orientation of an object. In particular, the present invention relates to a medical imaging system and a method of operating a medical imaging system, as well as to an element of a computer program for controlling a medical imaging system and to a computer readable storage medium on which such an element of a computer program is stored.

BACKGROUND OF THE INVENTION

To determine the position of an object located in a region of interest, medical imaging systems provide the user with two-dimensional image data. A method is known from WO 2006/114721 A2 in which the tool is provided with markers visible on images obtained by the image forming system. Information about the location of the markers in the images can be derived information about the location of the tool. But two markers do not provide any rotation information.

Disclosure of invention

As an additional drawback, markers do not necessarily give the user direct information about the actual location of the object. In particular with regard to asymmetric objects, there is such a need to provide the user with information about the corresponding actual rotation.

The present invention is to provide the user with improved information about the location of the object.

The objective of the present invention is solved by a combination of features of the independent claims, moreover, additional embodiments are included in the dependent claims.

It should be noted that the following described aspects of the invention are also applied to the medical imaging system, method, program element and computer-readable storage medium.

In accordance with an aspect of the invention, the medical imaging system comprises imaging means, a data processing unit, and a display. The obtaining means is configured to receive two-dimensional image data of the object, the object being provided with at least three markers visible in the two-dimensional image. The data processing unit is configured to detect markers in a two-dimensional image and to identify the spatial location and angle of rotation of the object relative to the geometry of the system, based on markers. The display is configured to display an indicator of an object indicating the spatial location and angle of rotation of the object.

In accordance with another aspect of the invention, there is provided a method of operating a medical imaging system comprising the steps of: a) obtaining two-dimensional image data of an object using an image forming system, wherein the object is provided with at least three markers visible in the two-dimensional image; b) detect markers in a two-dimensional image; c) identify the spatial location and angle of rotation of the object relative to the geometry of the system, based on markers; and d) display an object indicator indicating the spatial location and angle of rotation of the object.

Within the context of the present invention, the term “rotation” refers to rotation about the axis of an object. The term “location” or position refers to a location in space, that is, a three-dimensional location or position.

The indicator of the object provides direct information, that is, information that does not need any decoding steps or spatial imagination of the user, so that the user is provided with direct information, and he is only minimally distracted from other procedural steps. Thus, the user's concentration of attention is not further dispersed, so that the user can focus on his direct tasks, which, for example, with regard to surgeons in a hospital, may be preferable.

In accordance with another aspect of the invention, a three-dimensional image is recorded with two-dimensional image data, and an object indicator is displayed together with image data of registered three-dimensional and two-dimensional images.

This provides the advantage that the user is provided with information about the spatial location of the object relative to the volume or region of interest of the object. In other words, spatial information containing both position information and rotation information is provided in an improved spatial context through three-dimensional image information.

In accordance with another aspect of the invention, before step a), the required spatial location and rotation angle of the object are preliminarily determined, and the marker configuration for the desired position is calculated. Additionally, a projection of the calculated marker configuration is created in accordance with the geometry of the system during the acquisition of a two-dimensional image in step a). In addition, the created projection is displayed as a target indicator.

This provides the advantage that the created projection provides visual information about the location of the target for the object. Thus, the user is provided with information about the relationship between the actual position of the object and the target position, or about the index or installation position. For example, in the case when the user tries to move the object to a specific destination or the desired position and with the desired angle of rotation, by providing visual information about the actual position and the desired position, the user can derive a spatial "delta" or difference from the displayed images, so that the user can easily evaluate the necessary additional steps of moving to place the object in the desired position.

As an essence of the invention, the determination of the spatial location and angle of rotation of the object and the provision of this information in an intuitive way to the user can be considered, so that the user is not distracted from other tasks, and thus facilitate the user understanding of the actual spatial situation in relation to the object of interest.

These and other aspects of the present invention will become apparent and will be explained in detail with reference to the embodiments described below.

Brief Description of the Drawings

Examples of embodiments of the invention will be described below with reference to the following drawings:

FIG. 1 illustrates a medical imaging system according to an example of an embodiment of the invention.

FIG. 2 schematically illustrates the main steps of a method of operating a medical imaging system according to an example embodiment of the invention.

FIG. 3 represents the steps of a method according to another example of an embodiment of the invention.

FIG. 4 represents the steps of a method according to another example of an embodiment of the invention.

FIG. 5 represents a further example of an embodiment of the method of the invention.

FIG. 6 represents a further example of an embodiment of the method of the invention.

FIG. 7 represents a further example of an embodiment of the method of the invention.

FIG. 8 represents a further example of an embodiment of the method of the invention.

FIG. 9 represents a further example of an embodiment of the method of the invention.

FIG. 10 represents a further example of an embodiment of the method of the invention.

FIG. 11 shows examples of embodiments of asymmetric objects.

FIG. 12 shows two-dimensional images corresponding to an example of an embodiment of the invention.

FIG. 13 shows two-dimensional images corresponding to another example of an embodiment of the invention.

The implementation of the invention

In FIG. 1, a medical imaging system 100 is provided, said system comprising imaging means 110, data processing unit 112 and a display 114. The acquiring means 110 comprises an x-ray source 116 and a detector device 118. Additionally, a table 120 may be provided on which an object of interest, such as a patient 122, may be located. To obtain an image using the receiving means 110, a patient 122 located on the table 120 may be located between the x-ray source 116 and the detector device 118, so that the x-rays 124 emitted by the x-ray source in the direction of the detector device 118 pass through the patient area of interest 122.

Additionally, an object 126 is shown provided with at least three markers visible in a two-dimensional image obtained by the obtaining means 110. It should be noted that in FIG. 1 markers not shown. The obtaining means 110 is arranged to receive two-dimensional image data of an object, for example, an object 126 with three markers. In the shown example of an embodiment, the markers are impervious to radiation and are thus visible in the x-ray image.

The obtaining means 110 is connected to the data processing unit, for example, via an information connection 128. Thus, image data provided by the detector device 118 is provided to the processing unit 112.

The data processing unit 112 is configured to detect markers in a two-dimensional image and to identify the spatial location and rotation angle of an object, for example, object 126 with markers, relative to the geometry of the system, based on markers.

In other words, the two-dimensional image data is analyzed in the processing unit 112 and the markers visible in the two-dimensional image are detected and used for additional calculations of the spatial location and the angle of rotation of the object.

The data processing unit 112 is connected to the display 114 via an information connection 113.

Of course, data connections 128 and 130, shown as wired connections, can also be provided as wireless connections.

The display 114 is configured to display an indicator of an object indicating the spatial location and angle of rotation of the object. An object indicator is calculated based on the identified spatial location and rotation angle.

As can be seen in FIG. 1, a medical imaging system 100 is shown as a computed tomography (CT) system with gantry 132 with an X-ray source 116 and detector device 118 that can rotate around patient 122, thereby creating three-dimensional image data.

It should be noted that the medical imaging system can also be provided in another form, for example, in the form of a so-called "C-arc" type X-ray system, on which the detector device 118 and the X-ray source 116 are mounted at opposite ends of the C-arc, The c-arc can move, for example, rotate around the patient 122.

However, of course, it is also possible to provide a medical imaging system with a statically stationary imaging means, that is, imaging means, where the detector device 118 and the x-ray source 116 are fixed without movement.

According to a further exemplary embodiment, the data processing unit 112 is also adapted to register a three-dimensional image, for example obtained by the image acquiring means 110, with two-dimensional image data. Additionally, the display 114 is configured to display an indicator of an object along with image data of registered two-dimensional and three-dimensional images.

According to a further example of an embodiment of the invention, although not shown, the image acquiring means obtains two-dimensional image data by ultrasound. In this case, the object is provided with at least three markers visible in the ultrasound image data, that is, the markers are arranged so that the ultrasound is reflected in a predetermined manner.

According to a further example of an embodiment, which is also not shown, the above-described image acquisition principles, that is, x-rays, ultrasound or magnetic resonance imaging (MR), can be combined, for example, in an x-ray imaging system where two-dimensional image data is obtained by X-ray and markers are also visible in images obtained using ultrasound or MR. Of course, any other combination is also possible.

Next, with reference to FIG. 2, the main steps of the method of action of the medical imaging system, for example, the medical imaging system 100 corresponding to FIG. one.

At step 12, obtaining two-dimensional image data of the object is obtained using the imaging system. The object is provided with at least three markers visible in the two-dimensional image (reference position 14 of the image data). Additionally, in step 16 of the detection, markers are detected in a two-dimensional image. Then, at the identification step 18, the spatial location and rotation angle 20 of the object is identified with respect to the geometry of the system based on markers.

Next, in the display step 22, an object indicator 24 is displayed indicating the spatial location and rotation angle of the object, the object indicator 24 being calculated based on the identified spatial location and rotation angle 20.

According to a further example embodiment, although not shown, the object indicator 24 is a symbol indicating a central axis along the length of the model. Additionally, external edge points and / or an outline of an object may be shown.

According to another example embodiment, the object indicator is a visualization of an object model. For example, an indicator of an object may also be a wireframe model of an object.

In the case where the medical imaging system 100 corresponding to FIG. 1, two-dimensional image data is obtained using x-rays, and the markers are impervious to radiation.

According to a further example of an embodiment of the method, two-dimensional image data is obtained by ultrasound or MR, and markers are visible in the ultrasound image data or the MR image data, and an object indicator is displayed, for example, in addition to an x-ray image.

According to the exemplary embodiment shown in FIG. 3, a three-dimensional image is registered with the two-dimensional image data 14 in the registration step 32. A three-dimensional image or image data 30 may, for example, be obtained before the acquisition step 12 as a preliminary acquisition step 34.

According to another example embodiment, a three-dimensional image 30 is provided, for example, by a data bank stored in memory.

As can be seen in FIG. 3, an object indicator 24 is displayed together with image data of registered three-dimensional and two-dimensional images 36 provided at the registration step 32, and their joint display is indicated by an arrow 38 pointing to a rectangle of the display step 22.

According to a further exemplary embodiment, the three-dimensional data 30 is an anatomical model extracted from the obtained three-dimensional image data, but which is not shown further in FIG. 3.

As mentioned above, the indicator 24 of the object may contain an indication of the contour of the object.

According to a further exemplary embodiment, the object is an expanding object and the object indicator comprises, an indication of the contour of the object in the final expanded state in addition to the location and angle of rotation of the object.

For example, if the object is a stent, the user is thus provided with information about where and in what condition the stent will be located when the stent is opened. This may be useful for stent placement procedures, since the stent deployment or expansion step is irreversible.

For example, a stent is fed through a catheter, and it has only two degrees of freedom, rotation and translational movement along the axis of the catheter. According to a further exemplary embodiment, the object is elongated, and the rotation of the object is detected based on the corresponding number of markers, and a rotation indicator is displayed, for example, in combination with an object indicator (not shown further).

According to a further exemplary embodiment shown in FIG. 4, before the acquisition step 12, the desired spatial arrangement and the angle of rotation of the object 40 is previously determined at the preliminary determination step 42. Accordingly, the configuration 44 of the markers is determined by computing from information about the position and rotation of the object at step 46 of the calculation for the desired position 40.

Additionally, at creation step 48, a projection 50 of the calculated marker configuration 44 is created in accordance with the geometry of the system during the two-dimensional image acquisition step 12. The created projection 50 is then displayed in a display step 52 as a target indicator 54.

As an example, the projection 50 may be a two-dimensional projection.

According to a further exemplary embodiment, schematically represented in FIG. 5, the created projection 50 is superimposed on the two-dimensional image in the combining step 56, thereby providing an improved two-dimensional image 58.

According to a further exemplary embodiment, the three-dimensional image 60 is registered with the two-dimensional image data 14 in the registration step 62, and the created projection 50 associated with the desired position is displayed together with the image data of the registered three-dimensional and two-dimensional images 64 in the combined display step 66, providing: thus, further improved image information 68.

According to a further exemplary embodiment shown in FIG. 7, the identified actual spatial location and rotation angle 20 of the object is compared with a predetermined spatial location and rotation angle 40 of the object in the comparison step 70, providing vector registration information 72. Additionally, based on the vector registration information 72, at the creation step 76, a direction indicator 74 is provided, which is displayed in such a way that the maneuvering of the object is facilitated.

For example, to maneuver or move an object to the desired or target position, the actual position and angle of rotation are reduced to a given position and angle of rotation.

According to a further exemplary embodiment (not shown), the direction indicator 74 comprises a direction signal in which the spatial orientation of the user is taken into account such that the direction signal indicates the actual direction of movement by the user required to move the object toward the target position and the orientation.

In other words, the user is provided with information in which direction he should move, for example, the manipulator in order to achieve the correct location of the object. For example, an object can be located inside a complex structured volume, and the manipulator can contact the object only from a certain destination or from a certain direction, the movement necessary for the user can display the information shown on the display, or be opposite to the information shown on the display. In this case, the direction signal provided to the user can give him or her direct commands on how to move, without the need to analyze the correct spatial relationships of the current situation.

According to a further example of an embodiment of the invention, an automatic arrangement of the object is provided. Therefore, the location data is provided so that the manipulation device can move the object to the desired or target position with the desired or target rotation.

According to a further exemplary embodiment shown in FIG. 8, during the preliminary determination step 42, where the desired spatial location and the angle of rotation of the object are preliminarily determined, the optimal projection direction 80 for the obtained two-dimensional image data is determined at the determination step 82 based on the predetermined spatial location and the angle of rotation of the object. The optimal projection direction 80 is then applied during the 12th step of obtaining a two-dimensional image indicated by arrow 84 going to the corresponding rectangle of the receiving step 12.

According to a further exemplary embodiment shown in FIG. 9, in a preliminary determination step 87, for at least one additional location and rotation angle 85, the additional configuration 86 is predefined. Additionally, the additional configuration 86 is displayed as additional information 89 in the display step 90.

For example, the additional configuration 86 relates to undesired orientation and position, and the additional configuration 86 is displayed differently than the calculated configuration in the display step 52.

According to a further example of an improved embodiment of the invention, the actual orientation and position, that is, the spatial arrangement and the angle of rotation 20, are compared with the additional configuration 86 in the comparison step 91 and, in the case of a predetermined degree of correlation, an alarm 92 is provided.

As already mentioned above, the object can be, for example, a stent, which can be delivered through a catheter. For example, a stent has only two degrees of freedom, rotation and longitudinal movement along the axis of the catheter.

Stents are becoming increasingly important; for example, at present, an increasing number of vascular diseases can be treated minimally invasively using x-rays. To achieve this, more and more sophisticated stents are being developed for various applications: stents with an artificial heart valve inside, stents with openings for the lateral branches (fenestrated stents), branched stents for bifurcations, stents with a silk coating on the aneurysm neck. An example of a lateral branch coronary stent is shown in FIG. eleven.

Unlike traditional stents, these stents are virtually no longer symmetrical, and stents must be implanted with a certain angle of rotation. However, due to the projection nature of imaging systems, such as x-ray imaging systems, it is difficult to implant a stent in a given orientation.

Therefore, the above-described example of an embodiment helps to implant a stent in a specific orientation.

The difficulty in determining the orientation of the stent using x-rays, in particular, occurs when the stent has not yet been fully opened. For example, for an aortic valve stent, valve flaps are not visible at all in the x-ray image, and the stent itself is actually still symmetrical. An example of an aortic valve stent is also shown in FIG. eleven.

According to a further aspect of the invention, the steps of the method described above will be explained with reference to an aortic valve stent as an example. However, embodiments for other applications will be similar to it.

According to the embodiment shown in FIG. 12, the required position and orientation were determined at the planning stage. As an example, this can be done either manually or using three-dimensional segmentation to automatically calculate the optimal position and orientation of the stent. From this, as mentioned above, the desired three-dimensional position of the markers can be calculated.

During the operation, information about the geometry of the X-ray system, the location of the patient, and the desired location of the stent and its markers are used to calculate the target projection points. They are superimposed on the x-ray image, as shown in FIG. 12A, where the target projection points are indicated by small circles 212, 214 and 216. Thus, the target position of the markers is provided to the user. In FIG. 12, a stent 218 is shown with three visible markers denoted by reference numerals 220, 222, and 224. As can be seen in FIG. 12A, only one of the markers, namely marker 220, coincides with one of the target projection points, namely, circle 214. Thus, the user is provided with information about the relationship between the actual position and the target position of stent 218. Then, the user can move the stent according to the information obtained from FIG. 12A. The result of correct adjustment of the rotation angle is shown in FIG. 12B. It should be noted that the markers 220, 222 and 224 coincide with the corresponding target positions 212, 214 and 216. Thus, the user is provided with information that the stent 118 is now in the correct position, as well as in the correct orientation, that is, it has the right angle of rotation , and, as a next step, the user can open the stent, since it is in the final, that is, the desired position. The result of stent deployment is shown in FIG. 12C.

According to an example embodiment of the method described above, it is also possible to display the current orientation of the implant, such as a stent, relative to the target orientation.

As can be seen in FIG. 13, a cross-sectional view of the aortic valve and bulb is shown together with an inserted stent indicated by visualizing a stent model in an open version, which is shown as a circle 312 including three radial lines 314, representing the location of the heart valve.

During surgery, markers are tracked as described above. Then, the geometric information of the x-ray system, the three-dimensional position of the markers relative to each other, and information about the projection points of the markers in the x-ray image are used to determine the three-dimensional position of the markers.

Based on this, the current orientation of the stent can be reconstructed, and the result can be displayed in a three-dimensional image, as shown by way of example in FIG. 13. In addition to the actual position of the stent 312, the user is provided with information on how the stent will be placed in the open state using the model shown. For proper rotation, the desired or target position is indicated by a target indicating symbol 316 for indicating a target, for example, a dashed line representing the structure of the heart valve. As can be seen in FIG. 13A, the actual position and the desired position do not yet coincide, whereas in FIG. 13B, after adjusting the rotation angle, the projection indicated by the target indicator 316 is covered by a model representing the stent in the final state 312. Consequently, the user is provided with information that the stent is now in the correct position and can thus be opened. Of course, for the correct arrangement in the length direction, which is not visible in the cross section according to FIG. 13, the user may also be provided with relevant information, for example, in cross section along a length that is not further shown here.

In accordance with an example embodiment of the invention, the markers should be located at different heights and different angles of the object. If they are placed at different heights, they cannot overlap in terms of the object drawn in perspective, and they are easier to distinguish. Placing at different angles provides the advantage that only two orientations can match markers in a two-dimensional image. The uniqueness of the match can be achieved when it is known which marker is closest, or when, for example, a false marker is added, or when these three markers can be distinguished from each other.

In another example of an embodiment of the present invention, there is provided a computer program or a computer program element, which is characterized in that it is capable of performing steps of a method on one of the preceding embodiments on an appropriate system.

An element of a computer program, therefore, may be stored on a computer unit, which may also be part of an embodiment of the present invention. This computer unit may be configured to perform or encourage the execution of the steps of the method described above. In addition, it can be configured to control the components of the device described above. The computer unit may be configured to automatically control and / or carry out user commands. A computer program may be loaded into the processor RAM. The processor may thus be equipped to carry out the method of the invention. This example embodiment of the invention encompasses both a computer program that uses the invention from the very beginning, and a computer program that, by updating, converts an existing program into a program that uses the invention. Further, the computer program element may be able to provide all the necessary steps for performing the procedure of an example embodiment of the method, as described above. According to a further example embodiment of the present invention, a computer-readable storage medium such as a CD-ROM is provided, and a computer-readable storage medium has a computer program element recorded thereon, the computer program element being described in the previous section.

The computer program may be stored and / or distributed on an appropriate storage medium, such as optical media or semiconductor media provided with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless systems communication.

However, a computer program can also be presented over a network, such as the World Wide Web, and can be downloaded to the processor’s RAM from such a network. According to a further exemplary embodiment of the present invention, an environment is provided to make a computer program element available for download, the computer program element being configured to execute a method corresponding to one of the previously described embodiments of the invention.

It should be noted that embodiments of the invention are described with reference to various objects of the invention. In particular, some embodiments are described with reference to the claims of the method type, while other embodiments are described with reference to the claims of the device type. However, one skilled in the art will understand from the foregoing and the following description that, unless otherwise indicated, in addition to any combination of features belonging to one type of object of the invention, any combination between features related to different objects of the invention is also considered disclosed in this application . However, all symptoms can be combined, providing synergistic effects that are greater than a simple summation of the symptoms.

In the claims, the word “comprising” does not exclude other elements or steps, and the singular form does not exclude the presence of a plurality. A single processor or other unit may fulfill the functions of several items described in the claims. The simple fact that certain features are given in mutually different dependent claims does not indicate that the combination of these features cannot be used to achieve an advantage. Any reference signs in the claims should not be construed as limiting the scope of the invention.

Claims (10)

1. A medical imaging system (100), comprising:
means (110) for obtaining images;
a data processing unit (112); and
display (114),
moreover, the obtaining means (110) is configured to obtain two-dimensional (2D) image data of the object, the object being provided with at least three markers visible in the two-dimensional image;
moreover, the data processing unit (112) is configured to detect markers in a two-dimensional image and to identify the spatial location and angle of rotation of the object relative to the geometry of the system, based on markers; and
moreover, the display (114) is configured to display an indicator of the object indicating the spatial location and angle of rotation of the object;
moreover, the data processing unit (112) is configured, before the receiving means (110) receives two-dimensional image data of the object, to calculate (46) the configuration (44) of the markers for the desired desired spatial location and angle (40) of rotation of the object;
moreover, the data processing unit (112) is arranged to create a projection (50) of the calculated marker configuration in accordance with the geometry of the system during two-dimensional image acquisition; and
moreover, the display (114) is configured to display the created projection as a target indicator (54). 2. The system of claim 1, wherein the obtaining means (110) is configured to obtain two-dimensional image data using x-rays, and in which the markers are impervious to radiation. 3. The system according to claim 1 or 2, in which the data processing unit (112) is configured to register (32) a three-dimensional (3D) image (30) with two-dimensional image data, and in which the display (114) is configured to display an indicator object along with image data of registered three-dimensional and two-dimensional images (36). 4. The system of claim 3, wherein the three-dimensional image data is an anatomical model extracted from the obtained three-dimensional image data. 5. The system of claim 1, wherein the object is an elongated object, and in which the data processing unit (112) is configured to detect rotation of the object, and wherein the display (114) is configured to display a rotation indicator. 6. The system of claim 1, wherein the data processing unit (112) is configured to superimpose (56) the created projection (50) onto the two-dimensional image (14). 7. The system according to claim 1 or 6, in which the data processing unit (112) is configured to compare (72) the identified actual spatial location and rotation angle (20) of the object with the desired spatial location and rotation angle (40) of the object, and data processing unit (112)
configured to provide (76) an indicator (74) of the direction of movement, so that maneuvering of the object is facilitated. 8. The system of claim 1, wherein the data processing unit (112) is configured to determine (82) the optimal projection direction (80) to obtain two-dimensional image data based on a given desired spatial location and rotation angle (40) of the object; moreover, the obtaining means (110) is configured to obtain the optimal projection direction (80) used (48) during the acquisition of two-dimensional image data of the object by the receiving means (110). 9. The system of claim 1, wherein the data processing unit (112) is configured to specify (88) an additional configuration (86) for at least one additional location and rotation angle (84); and in which the display (114) is configured to display (90) an additional configuration. 10. A computer-readable storage medium that stores a program element for controlling a system according to claim 1, which, when executed by a computing processing unit, is configured to perform steps in which:
a) obtain (12) a two-dimensional image (14) of the object (126; 218) using the image acquisition system (100), the object being provided with at least three markers (220, 222, 224) visible in the two-dimensional image;
b) detect (16) markers in a two-dimensional image;
c) identify (18) the spatial location and angle (20) of rotation of the object relative to the geometry of the system, based on markers;
d) display (22) an indicator (24) of the object indicating the spatial location and angle of rotation of the object;
moreover, prior to step a), the required spatial location and rotation angle (40) of the object are set, and the configuration (44) of markers for the desired position is calculated (46);
moreover, a two-dimensional projection (50) of the calculated marker configuration is created (48) in accordance with the geometry of the system during the acquisition of a two-dimensional image in step a); and
moreover, the created projection is displayed (52) as a target indicator (54).

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