Abstract:
Apparatus for determining a proper insertion depth of a biopsy needle so that a sampling end of the needle just reaches to a designated target area within the body comprises at least one straight calibrated pointing device aligned to point through the selected point in a straight line passing through the designated target region. The pointing device exhibits first and second markers along its length such that respective images are formed on a first image plane by utilizing radiation from a radiation source, along with images corresponding to the selected point and the target area. The images are formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region. The apparatus includes an arrangement for measuring distances on the image plane between images (A), (B), (C), and (D) and a calculator for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined.

Description:
The present invention relates to a system, apparatus, and method for accurate positioning of a surgical tool, such as a biopsy needle, with respect to a deep seated target inside a patient and, more specifically, a positioning device that takes as its input a needle entry point and a target point selected on the screen of a fluoroscope for automatically positioning a needle guide and indicating the depth to the target point. 
     BACKGROUND OF THE INVENTION 
     The subject matter of the following copending patent applications being filed on even date herewith is closely related to the subject matter of the present application and is incorporated herein by reference to the extent it is not incompatible with the present disclosure: APPARATUS AND METHOD FOR POSITIONING A BIOPSY NEEDLE (Ser. No. 08/722,725), APPARATUS AND METHOD FOR AUTOMATICALLY POSITIONING A BIOPSY NEEDLE (Ser. No. 08/722,707), and TRIGONOMETRIC DEPTH GAUGE FOR BIOPSY NEEDLE (Ser. No. 08/722,724, now abandoned). All are filed in the names of Navab and Geiger, the present inventors, and all are assigned to Siemens Corporate Research, Inc., as is the present application. 
     Needle biopsy is one of the most frequent surgical interventions. Typically, a fine needle is used to remove tissue portions from a lesion inside the body. If the lesion is very small and is deep-seated within the body or is not palpable, the surgeon needs guidance in order to make sure that the tip of the needle reaches the desired location. 
     Currently used image based guidance methods include the following. Ultrasound (US), X-ray fluoroscopy, computerized tomography (CT) fluoroscopy and computerized tomography/magnetic resonance imaging (CT/MRI) in combination with real time registration tools. The first three methods provide real time intra-operative images of the patient and enable the surgeon to see the needle as it approaches the target. 
     Ultrasound is relatively inexpensive and is a readily available image modality. However, its usage for guidance is limited to lesions that are close to the skin and that show a well defined signal. 
     The X-ray fluoroscope is a widely available, low cost two-dimensional (2D) imaging equipment. Since it shows a two-dimensional projection, two (generally orthogonal) views are necessary in order to determine the biopsy needle position. This can be done by turning the arm of a simple fluoroscope, such as a C-arm fluoroscope, an example of which is shown in FIG. 1, or by using a fluoroscope such as that illustrated in FIG. 2 that provides two simultaneous orthogonal views. Since the needle has to be manipulated in the image field, one cannot avoid a X-ray exposure of the physician when using such techniques. As is well-known, unnecessary exposure of health workers to X-ray radiation is believed to be hazardous to health and it is desirable that it should be avoided to the extent possible. 
     CT-Fluoroscopy permits real-time display of CT images. The physician controls X-ray exposure during continuous tube rotation. The exact position of the needle can be traced by moving the table. In the case for CT-Fluoroscopy also, the surgeon is exposed to X-rays. 
     CT/MRI in combination with real time registration tools is based on pre-operative 3-D data acquisition (CT or MRI). The lesion is outlined in the resulting dataset. During the actual biopsy, the position and orientation of the patient and the needle have to be known precisely and aligned with the pre-operative data. 
     Therefore two registrations have to be used for guiding the needle: the pre-operative data showing the lesion has to be registered with the patient. This can be done by attaching invariant markers to the patient (stereo-tactic frames) before data acquisition or by matching invariant patient features, such as the skull or bones. 
     The needle has to be registered with the patient. One possibility is to attach optical markers to the needle which can be tracked by a system of cameras or by X-ray fluoroscopy, or to use mechanical devices like passive robot arms that register the position of the needle at any moment. This technique requires highly specialized and costly 3-D imaging facilities that are typically only available at a few research sites. Despite the image guidance, a successful biopsy procedure still depends on the manual skills and judgement of the surgeon who is manipulating the needle. 
     SUMMARY OF THE INVENTION 
     There is a need herein recognized for an alignment device that is adjustable to the right direction and that indicates the distance to a deep-seated target. Among the benefits that result from such a device are acceleration of the procedure, increase of the safety of the procedure, and reduction of radiation exposure for both the patient and for the surgeon. 
     In accordance with the objects of the present invention, an X-ray image guided system provides assistance in the execution of needle biopsy. It can also be used for minimal access surgical procedures, known as &#34;keyhole surgery&#34;. One of the objects of the present system, which is simple and readily implemented, is to help surgeons overcome difficulties associated with positioning the biopsy needle or performing minimally invasive surgery in three dimensions while utilizing two-dimensional images for guidance in the procedure. 
     Another object of the present invention is to practically eliminate or reduce to a minimum the need for a surgeon&#39;s reliance on a radiologist to open an access track pre-operatively in the radiology suite. 
     Furthermore, another object of the invention is to practically eliminate the need for accurate geometrical calibration. The present invention is believed to provide a first opportunity in which quantitative imaging guidance is made possible without a dedicated geometrical calibration procedure. 
     The invention permits the accurate positioning of a surgical tool, such as biopsy needle, with respect to a deep seated target inside a patient. It is the practical application of an algorithm in accordance with the invention which makes the accurate positioning possible. 
     In accordance with the invention, the depth of a deep-seated target within a patient&#39;s body is readily computed from one single radiographic image. Based on geometrical reasoning involving a mechanical device, simple in conception, in accordance with the invention, biopsy needles may be considered in the context of the invention as an adjunct to traditional medical imaging systems such as C-arm equipment and fluoroscopes. 
     Generally, a preferred position for a biopsy needle from the surgical point of view is a position above the patient from which it goes through the organ of interest. In addition, the surgeon needs to know the depth of the target in order to correctly insert the needle. 
     In accordance with another aspect of the invention, apparatus for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body, comprises: at least one straight calibrated pointing device aligned to point through the selected point in a straight line passing through the designated target region, the pointing device exhibiting first and second markers along its length such that respective images are formed on each of first and second image planes by utilizing radiation from respective first and second radiation source positions, along with images corresponding to the selected point and the target area, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region; apparatus for measuring distances on at least one of the first and second image planes between images (A), (B), (C), and (D); and apparatus for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
     In accordance with another aspect of the invention, apparatus for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body, comprises: at least one straight calibrated pointing device aligned to point through the selected point in a straight line passing through the designated target region, the pointing device exhibiting first and second markers along its length such that respective images are formed on a first image plane by utilizing radiation from a radiation source, along with images corresponding to the selected point and the target area, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region; apparatus for measuring distances on the image plane between images (A), (B), (C), and (D); and apparatus for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
     In accordance with another aspect of the invention, the cross ratio is given by the equation ##EQU1## whereby the cross ratio is invariant for a given configuration for (a) the physical arrangement of the first marker, the second marker, the selected point, and the target region; (b) the images thereof on the first image plane; and the images thereof on the second image plane, so that upon equating a cross ratio for the physical arrangement and for one of the images, the only unknown, distance CD in the physical arrangement, is obtained. 
     In accordance with another aspect of the invention, a method for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body, the method comprises the steps of: aligning at least one straight calibrated pointing device so as to point through the selected point in a straight line passing through the designated target region, the pointing device exhibiting first and second markers along its length; forming respective images on an image plane by utilizing radiation from a radiation source, along with images corresponding to the selected point and the target area, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region; measuring distances on the image plane between images (A), (B), (C), and (D); and calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
     In accordance with another aspect of the invention, the step of calculating the cross ratio of the distances comprises applying the equation ##EQU2## whereby the cross ratio is invariant for a given configuration for (a) the physical arrangement of the first marker, the second marker, the selected point, and the target region; (b) the images thereof on the first image plane; and the images thereof on the second image plane, so that upon equating a cross ratio for the physical arrangement and for one of the images, the only unknown, distance CD in the physical arrangement, is obtained. 
     In accordance with another aspect of the invention, apparatus for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body, comprises: at least one straight calibrated pointing device exhibiting first and second markers along the length thereof; positioning apparatus for automatically positioning or aligning the at least one straight calibrated pointing device as a guide for a biopsy needle for proper insertion into the body of a patient from a selected point on a surface of the body, so as to enter in a straight line passing through a designated target region within the body, in conjunction with an imaging system utilizing radiation from a first source position for deriving a first radiographic image on a first image plane of a portion of the body including a first image of the selected point and a first image of the target region, the first source position, the first image of the selected point, and the first image of the target region defining a first viewing plane π, the imaging system utilizing radiation from a second source position for deriving a second radiographic image on a second image plane of the portion of the body, including a second image of the selected point and a second image of the target region, the second source position, the second image of the selected point, and the second image of the target region defining a second viewing plane π&#39;, the positioning apparatus comprising: automatic first control and measurement apparatus for determining an angle Θ 1  for a selected first auxiliary plane and an angle Θ 2  for a selected second auxiliary plane with respect to a selected set of coordinates and for storing the angles, the second plane angle being different from the first plane angle such that the first and second auxiliary planes form an intersection line ; automatic alignment and control apparatus for constraining the calibrated pointing device for moving rotatably about the selected point and within the first auxiliary plane to a first angle of inclination φ 1  relative to the set of coordinates and for controlling the calibrated pointing device such that a projection or extension of an image of the calibrated pointing device on the first image plane passes through the first image of the target region and for storing the angle φ 1 , the alignment and control apparatus further controlling the calibrated pointing device for moving rotatably about the selected point and within the second auxiliary plane to a second angle of inclination φ 2  relative to the set of coordinates such that a projection or extension of an image of the calibrated pointing device on the second image plane passes through the second image of the target region and for storing the angle φ 2 , whereby the first viewing plane π is uniquely defined by the angles Θ 1 , Θ 2 , φ 1 , and φ 2  relative to the set of coordinates; automatic apparatus for calculating orientation angles α and Θ 3  of the viewing plane π from stored values of the angles Θ 1 , Θ 2 , φ 1 , and φ 2 , and storing the angles α and Θ 3  ; and automatic control apparatus for moving the calibrated pointing device rotatably about the selected point and within the first viewing plane π, as defined by the angles α and Θ 3 , to a third angle of inclination φ 3  relative to the set of coordinates such that a projection or extension of an image of the calibrated pointing device on the second image plane passes through the further image of the target region, whereby the pointer points directly through the selected point toward the target region, such that that respective images of the first and second markers are formed on the first and second image planes, along with images corresponding to the selected point and the target area, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region; apparatus for measuring distances on the image plane between images (A), (B), (C), and (D); and apparatus for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
     In accordance with another aspect of the invention, the apparatus for calculating the cross ratio of the distances applies the equation ##EQU3## whereby the cross ratio is invariant for a given configuration for (a) the physical arrangement of the first marker, the second marker, the selected point, and the target region; (b) the images thereof on the first image plane; and the images thereof on the second image plane, so that upon equating a cross ratio for the physical arrangement and for one of the images, the only unknown, distance CD in the physical arrangement, is obtained. 
     In accordance with another aspect of the invention, in an apparatus for automatically positioning or aligning a biopsy needle for proper insertion into the body of a patient at a selected point on a surface of the body, so as to enter in a straight line passing through a designated target region within the body, in conjunction with an imaging system utilizing radiation from a first source position for deriving a first radiographic image on a first image plane of a portion of the body including a first image of the selected point and a first image of the target region, the first source position, the first image of the selected point, and the first image of the target region defining a first viewing plane π, the imaging system utilizing radiation from a second source position for deriving a second radiographic image on a second image plane of the portion of the body, including a second image of the selected point and a second image of the target region, the second source position, the second image of the selected point, and the second image of the target region defining a second viewing plane π&#39;, depth apparatus for determining a proper insertion depth of the biopsy needle into the body of the so that a sampling end of the needle just reaches to the target area, the depth apparatus comprises: at least one straight calibrated pointing device aligned to point through the selected point in a straight line passing through a designated target region, the pointing device exhibiting first and second markers along its length such that respective images are formed on each of the first and second image planes, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region; apparatus for measuring distances on at least one of the first and second image planes between images (A), (B), (C), and (D); and apparatus for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
     In accordance with another aspect of the invention, the apparatus for calculating the cross ratio of the distances applies another equation, functionally equivalent to the equation ##EQU4## whereby the cross ratio is invariant for a given configuration for (a) the physical arrangement of the first marker, the second marker, the selected point, and the target region; (b) the images thereof on the first image plane; and the images thereof on the second image plane, so that upon equating a cross ratio for the physical arrangement and for one of the images, the only unknown, distance CD in the physical arrangement, is obtained. 
     In accordance with another aspect of the invention, apparatus for determining a proper insertion depth of a biopsy needle to be inserted at a selected point on the body of a patient so that a sampling end of the needle just reaches to a designated target area within the body comprises at least one straight calibrated pointing device aligned to point through the selected point in a straight line passing through the designated target region, the pointing device exhibiting first and second markers along its length such that respective images are formed on a first image plane by utilizing radiation from a radiation source, along with images corresponding to the selected point and the target area, the images being formed along a straight line in this order: (A) the first marker, (B) the second marker, (C) the selected point, and (D) the target region. The apparatus includes an arrangement for measuring distances on the image plane between images (A), (B), (C), and (D); and a calculator for calculating the cross ratio of the distances, whereby the proper insertion depth of the biopsy needle is determined. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     The invention will be further understood from the detailed description of the prefered embodiments, in conjunction with the drawing in which: 
     FIG. 1 shows a known type of C-arm fluoroscope, such as may be utilized in conjunction with the present invention; 
     FIG. 2 shows a known type of fluoroscope with two simultaneous orthogonal views, such as may be utilized in conjunction with the present invention; 
     FIG. 3 shows a diagrammatic configuration of imaging radiation sources, image screens and a target area, helpful in understanding the invention; 
     FIGS. 4, 5, and 6 show various steps of a method utilizable in conjunction with the invention; 
     FIGS. 7 and 8 show diagramatic representations of principles and apparatus in accordance with the invention; 
     FIGS. 9, 10, and 11 show various steps of a method utilizable in conjunction with the invention; 
     FIGS. 12, 13, and 14 show diagramatically apparatus and principles in accordance with the invention; 
     FIG. 15 shows a system diagram in accordance with the invention; 
     FIG. 16 a diagramatic representation of apparatus helpful to an understanding of the objects of the invention; 
     FIGS. 17, 18, and 19 show flow charts helpful to gaining an understanding of the invention; 
     FIG. 20 shows components of an automatic system and their interrelationship of a method utilizable in conjunction with the invention; 
     Apparatus and diagram drawings are not necessarily to scale. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Steps I, II, and III establish certain useful information for the application of the invention and are accordingly described herein. They form the subject matter of the above-mentioned copending patent applications entitled APPARATUS AND METHOD FOR POSITIONING A BIOPSY NEEDLE and APPARATUS AND METHOD FOR AUTOMATICALLY POSITIONING A BIOPSY NEEDLE. 
     FIG. 3 shows the geometry desirable for the surgeon. Preferably, the biopsy needle should be positioned such that its straight line continuation, or virtual extension, passes through a deep-seated target T inside the patient. During the manual procedure, the surgeon keeps the bottom end F of the needle on or near the patient&#39;s body and changes its direction until the virtual extension of the needle passes through the radiographic image t of the target T. The correct needle direction has to be verified on two radiographs that are taken from different angles. 
     In accordance with the present invention an apparatus has a geometrical configuration embodying a reasoned interpretation of what the surgeon seeks to do intuitively during a manual adjustment procedure. Clearly, the surgeon does not compute the exact or relative position and orientation of the C-arm and the image plane during a more or less refined &#34;hit or miss&#34; procedure. Rather, the surgeon proceeds by simple reasoning directly from radiographic images to the moving needle. 
     Referring again to FIG. 3, the imaging system is modelled approximately as a &#34;pinhole camera&#34; model. The optical center, S, represents the location of the X-ray source and the position and orientation of an image intensifier defines the image plane, I. The deep-seated target inside patient&#39;s body is indicated by T, with t being its radiographic image. 
     F is a fixed point from where the surgeon wishes to insert the biopsy needle. f is its radiographic image. The viewing plane π is defined by the optical center, S, the target on the image, t, and the fixed point, F, and its radiographic image, f. 
     All the entities and reference letters relating to a second position of the X-ray and therefore to a second radiographic image are noted by prime, such as S&#39;, π&#39;, and so on. 
     Initially, it is recognized that the three-dimensional position of viewing plane π, while obtainable in accordance with the present disclosure, as will be shown, is not known in a facile manner to the user. 
     Generally, images of all lines lying on the plane π which do not pass through the optical center S, are collinear to the line ft on the radiographic image I. Since the depth of the target T, or ||FT||, is unknown, the maximum information that can be obtained on the position and orientation of the biopsy needle from a sequence of images taken from a single viewpoint is the three dimensional position of the plane π. Accordingly, a first part of the algorithm can be established in Step I, as follows. 
     Any plane π 1  passing through the fixed point F, other than the plane π itself, intersects the plane π in one line. This line clearly contains the point F and therefore its image must pass through the image f of the fixed point F on the image on image plane I. The first two steps of the algorithm can now be defined, resulting in a method of accurately obtaining the three dimensional coordinates of the viewing plane π. A metallic, or other radiation-opaque, bar is rotated around the fixed point F in an arbitrary plane π 1  passing through the fixed point F. See FIG. 4, which illustrates the step of finding a three-dimensional line lying on the viewing plane π. The shortest distance of the projection line of the three-dimensional line from the target t on the image is called h 1 . 
     This h 1  distance decreases as the angle between them closes, and projection line approaches line L 1 , representing the intersection of the planes π and π 1 , and vanishes at the intersection of these two planes. This provides a simple way to control the metallic bar under automatic images guidance and move it until it lies on the plane π. 
     In a further step, Step II, a metallic (X-ray opaque) bar is rotated around the fixed point F in a second plane π 2  passing through the fixed point F, and different from π 1  used in the Step I, see FIG. 5, which illustrates the procedure for finding a second three-dimensional line on the viewing plane π. Preferably, the plane passing through F and orthogonal to π 1  is selected as π 2 . The distance of its projection line from the target t on the image, is called h 2 . This distance decreases as the projection line of π 2  approaches line L 2 , representing the intersection of the planes π and π 2  and this distance, h 2  vanishes at the intersection line of these two planes. 
     This provides a way to control a second metallic bar under automatic images guidance and move it until it also lies on the plane π. Now two distinct lines, L 1  and L 2 , having a non-zero angle of intersection therebetween, are identified on the plane π. These lines uniquely define the plane π in three dimensional space. This is the maximum information that can be had from a single viewpoint with no calibration data. 
     A next step in accordance with Step III, is the use of a second viewpoint. The radiographic image from a second viewpoint can be obtain either by moving the C-arm of the machine arbitrarily; the larger is the angle of rotation the more accurate is the resulting position and orientation of the needle. 
     The plane defined by the optical center, the X-ray source S&#39; of the new configuration of the imaging system, the target T and the fixed point F is designated as π&#39;, analogous to plane π in the previous determination. See FIG. 6 which shows the procedure for finding the right orientation for the biopsy needle. 
     A metallic bar is rotated around the fixed point F in the plane π obtained in step II. The distance of its projection line, 1&#39;, from the target t&#39; on the image taken from the new viewpoint, is called h&#39;. This distance decreases as one gets closer to the line L&#39;, representing the intersection of the planes π and π&#39; and this distance vanishes at the intersection of these two planes. 
     This provides a way to control the metallic bar manually or automatically using image guidance and move it until the line FT is found. FT is the line of intersection of the two flat planes π and π and it therefore represents a vector direction in space passing through the proposed fixed insertion point F and, when produced, through the target T. Now, the surgeon can be guided to the correct positioning of the biopsy needle. The Step IV, in accordance with the invention, is to let the surgeon know how deep the target T is inside the patient. 
     The cross ratio is a fundamental invariant of perspective projection. See, for example, O. D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint; MIT Press, Cambridge, Mass.; 1993. This invariant can be used here to accurately compute FT, the depth of the target inside patient&#39;s body. 
     Referring to FIG. 7, consider the four points A, B, C, and D, on a line in space. The cross ratio of these four points can be defined as ##EQU5## The perspective projection of these four points on any plane and with respect to any projection center, for example {a,b,c,d} and {e,f,g,h} in FIG. 7 results in the same cross ratio between the projected points: ##EQU6## 
     For the case of two markers, M 1  and M 2 , on the metallic bar used in step III, such that ||M 1  F|| and ||M 2  F|| are accurately known, and m 1  &#39; and m 2  &#39;, their radiographic images, are easily and accurately detectable, see FIG. 8. The assumptions made are reasonable and readily realized in practice. The cross ratio computed for the image points [m&#39;1, m&#39;2, f&#39;, t&#39;] is the same as the cross ratio of the four points [M 1 , M 2 , F, T] in the three dimensional space. The positions of all these points other than T are known. FT is then computed from the following equation: ##EQU7## 
     The positioning in accordance with the invention is designed based on the algorithm disclosed above. FIGS. 12, 13, 14, and 16 show a design configuration in accordance with the invention. A part of the apparatus is a semi-circle that can rotate at least from 0 to 180 degrees around the center of a circular base. This rotation angle is designated by a in FIG. 12. This semi-circle has a second degree of freedom: it can also turn around its own baseline from 0 to 180 degrees. This rotation angle is designated by Θ in FIG. 12. A metallic bar can rotate on the plane defined by this semi-circle from 0 to 180 degrees. This rotation angle is noted by φ in FIG. 12. In accordance with the invention, this provides all that is required. All rotations can be done either by hand, by command, or automatically. The parallel or serial connection between a computer, such as a personal computer (PC), and a positioning device can guide the system based on the minimization of h 1 , h 2  and h&#39; on the radiographic images. 
     FIGS. 9, 10, and 11 provide bridging information to facilitate an understanding of the relationship between the foregoing algorithm and the design herein described. These figures include some of the constructions shown in previous figures and are helpful to bridging the steps between the geometric principles forming a basis for the present invention and the practical apparatus and method herein disclosed. 
     FIG. 9 shows the procedure utilized in finding one three dimensional line lying on the viewing plane π. This comprises positioning the semi-circle at an arbitrary position to define a plane π 1  and then moving the metallic bar mounted on the semi-circle to a position where its image passes through f and t on the image. This process can be done automatically. The metallic bar is moved to minimize the distance h 1  on the image. This process is not time-consuming and is readily carried out in real time. 
     FIG. 10 shows Step II, the process of finding a second three dimensional line lying on the viewing plane π. This is similar to the previous step, but the semi circle has turned by an angle in the order 90 degrees around its based line defining a new plane π 2 . 
     FIG. 11 shows Steps III &amp; IV: Finding the right orientation of the biopsy needle and the depth of the target T inside the patient&#39;s body. This comprises positioning the semi-circle in the plane, π&#39; defined by the metallic bar in steps I and II, and then rotating the metallic bar until its radiographic view from the new viewpoint passes through f&#39; and t&#39;. The center of the circular base, F, and the target inside patient&#39;s body, T, lie on the both planes π and π&#39;. Their intersection is therefore FT the correct direction of the biopsy needle. The depth of the target, |FT|, can then be computed using the invariance of cross ratios by perspective projection; see the previous section on the geometrical description. The whole process, steps I through IV, can be done in real time and the surgeon can easily move the device and find the new orientation of the biopsy needle and depth of the target at any other contact point on the patient&#39;s body. This design lends itself readily to economical implementation. 
     The interactive system has the advantage of being an independent unit which can be used together with any kind of X-ray fluoroscopes or C-arm imaging system and it needs no physical connections with the imaging system. The unit is entirely and readily portable. Furthermore, the operating surgeon has no radiation exposure at all during the search for the correct position. 
     FIG. 15 shows a protocol for the interactive system as herein described. In this case the apparatus is fixed on the patient on top of the desired entry point defined by the surgeon. The surgeon works with the control device while looking at the radiographs and can be in the same room or in another room where the radiographic images can be observed without the surgeon&#39;s being exposed to the radiation. 
     These are the consecutive steps of the process. 
     A first plane is taken by fixing α=0 and Θ=Θ 1 . See FIG. 13. Note that Θ 1  is quite arbitrary. A user can choose this plane so as to maintain a clear view of the metallic bar. This can be done using the control buttons, π 1 , +α, -α, +Θ and -Θ, as shown in FIG. 15. 
     The user then selects the proper angle φ by moving the metallic bar until its radiographic image passes through the target point. This can be done by using buttons +φ and -φ as in FIG. 15. The orientation of the metallic bar is then defined as: 
     
         L.sub.1 =[sin(φ.sub.1)sin(θ.sub.1), sin(φ.sub.1)cos(θ.sub.1), cos(φ.sub.1)]] 
    
     See FIG. 13. Note that Θ 2  is also arbitrary. A user can choose this plane in order to have a clear view of the metallic bar. This can be done using the control buttons, π 2 , +Θ, and -Θ, as in FIG. 15. 
     A user finds the right angle φ by moving the metallic bar until its radiographic image passes through the target point. This can be done by using buttons +φ and -φ, as in FIG. 15. The orientation of the metallic bar is then defined as: 
     
         L.sub.2 =[sin(φ.sub.2)sin(θ.sub.2), sin(φ.sub.2)cos(θ.sub.2), cos(φ.sub.2)] 
    
     The final viewing plane (see FIG. 14) is then defined by ##EQU8## where 79  is the vector product defined in R 3  , 3-dimensional space. The system will automatically move to the right position and the user has no need to adjust Θ and α in this case. 
     The user then uses the image on the second image intensifier or moves the C-arm to a new position. 
     The user finds the proper angle φ by moving the metallic bar until its radiographic images passes through the target point. This can be done by using buttons +φ and -φ as shown in FIG. 15. This is the correct orientation of the needle to be used for the biopsy. 
     In order to compute the depth of the target in this case, two other auxiliary needles are placed on the base line of the semi-circle; see FIG. 16. In order not to disturb the image of the main needle, these needles can be made in acrylic (transparent to X-ray) with only a few metallic markers to be aligned with the deep seated target. The determination of depth is arrived at by a process of triangulation in which a base-line forms the base of a triangle with the directions of the other two sides of the triangle being determined by respective angles subtended by the base and the respective side. Accordingly, the accuracty is grater where the angle between a needle and the metallic bar is treater. Hence, two alternative needles are provided so that that needle is utilized which is on the side of the obtuse angle made by the metallic bar with the plane of the diameter of the semicircle. 
     Each of these needles can rotate in the plane defined by this semi-circle around a fixed point other than the entry point. In accordance with the present embodiment, the two end points of the base line are used as the two centers of rotation. In the final position, the plane defined by the semi-circle also includes the deep seated target. 
     Once the correct orientation of the needle is found, the system activates that one of the auxiliary needles which has the greater angle with the main needle. The user moves this needle to align it with the target on the image. The system computes the depth of the target by computing the distance between the entry point and the intersection of the main needle and the active auxiliary needle. FIG. 16 shows this construction in detail. 
     The depth to the target, AC, is given by the trigonometric formula ##EQU9## 
     FIG. 17 shows a flowchart of the interactive process in accordance with the principles of the invention. 
     A semi-automatic system in accordance with the invention reduces the human interaction to the initial fixation of the unit on the patient, a definition, such as a manual definition, of the tumor on a computer display, and the final insertion of the needle, that will remain fully under the control of the surgeon. 
     The search for the optimal needle position and the calculation of the target depth is done automatically. The benefits of such a system are substantially increased speed of operation and thus less patient discomfort, reduced risk of patient motion, reduced radiation for the patient, and complete elimination of radiation for the surgeon during the search for the position. 
     The automatic system utilizes as a starting point the same basic arrangement as the manual version with additional features. Three effectors are included, such as drive motors, to change the needle position. One each is utilized for Θ, one for φ, and one for the rotation α, respectively. X-ray opaque markers are provided on the biopsy needle guidance so as to be visible on the fluoroscopic images and to be readily detectable by an image processing unit. 
     A computer is linked to the fluoroscope so as to be able to capture and store the X-ray images and to perform the necessary image processing to detect the needle markers. A computer stores and calculates needle positions and commands the effectors so as to move the needle positioner. Furthermore, a user interface to the computer allows the surgeon to draw the outline of the target on the fluoroscopy image with a computer &#34;mouse&#34; coordinate translator or by using a graphics tablet. 
     Essentially, the procedure is as follows. The unit is installed on the patient. One single image from the fluoroscope is stored and displayed on the computer screen. The surgeon outlines manually the tumor on this image using the mouse. During this stage of the interaction, the fluoroscope is turn off, thereby reducing radiation exposure. The computer selects a first plane Θ and performs a task that is known as visual servoing. See FIG. 18. It changes the needle position, thereby varying φ and detects the needle markers on the fluoroscopic image. From the markers, it can determine the projection of the needle, that is the axial center-line of the needle produced or continued beyond the needle. 
     The closest distance of this &#34;virtual needle&#34; to the target in the image can be calculated. The position of the needle is changed until this distance is reduced to a minimal amount and the projection of the needle passes through the target. The parameters Θ and φ of the needle position are stored. This step is repeated for a different choice of Θ in order to find a second needle position. Then the C-arm position has to be changed, and the target must be outlined once again on a first image. From the two previous needle positions, the computer calculates the necessary rotations α and Θ to bring the needle in the final plane. 
     Then the visual servoing step is repeated. The final position φ is the one that passes through the target. The needle guidance system has to be blocked in that position, either using the effectors or by actuating an additional blocking or position locking device. The fluoroscopy unit is switched on for two initial images that are used for outlining the target, and during the visual servoing steps. This procedure is usually very brief. The system then uses the needle markers in order to automatically compute the depth of the target from the entry point. Depending on the speed of the effectors, the described system is able to find the optimal needle position and the depth of the target in a few seconds. FIG. 19 shows a flowchart of this automatic process. FIG. 20 shows the connection and relationship between the different components of the automatic system. 
     It generally noted that apparatus parts should be X-ray transparent unless they are required to be visible in the image, such as, for example, needles and markers. 
     While the invention has been described in terms of exemplary embodiments, it will be apparent to one of skill in the art to which it pertains that various changes and modifications can be made without departing from the spirit of the invention. For example, circular scales are defined in the traditional manner of a circular protractor for portions of apparatus defining a plane and providing angle measure. Clearly, such parts need not be circular to provide such functions. Furthermore, it is noted that the cross-product, while conveniently defined and used in a particular manner herein, such as A,B and C,D, can utilize other dimensions in the constellation so as to obtain the depth. These are equivalent cross-product functions and can be substitute where appropriate. Such changes and modifications and the like are intended to be within the scope of the invention which is defined by the claims following.