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Claims  |
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I claim:
1. A system for determining the positions and orientations of at least two
physically unconnected, separately moveable objects absolutely and with
respect to each other in the same three dimensional space, and
electronically displaying the relationship between said objects,
comprising:
at least one electronically displayable image of an interior portion of at
least a first of said objects;
an electronically stored file comprising said at least one image having the
capability of being sorted and electronically displayed on an electronic
screen;
computer means for storing and sorting said image, and for causing at least
one said sorted image to be electronically displayed;
electronic display means for displaying said sorted image;
a three dimensional volume described by a fixed coordinate system;
a first object, which is said internally imaged object, having at least
three light emitting first sensible points associated therewith, which is
located within said three dimensional space and is moveable therein, and
whose position and orientation within said three dimensional space is
defined in said fixed coordinate system;
means to move said first object in said three dimensional space;
a second object, physically unconnected to said first object, having at
least two light emitting second sensible points associated therewith,
which is located within said coordinate system and is moveable in said
three dimensional space in relation to said first moveable object, whose
position and orientation within said three dimensional space is defined in
said fixed coordinate system;
means to move said second object in said three dimensional space;
at least three spaced apart light detecting means, situated in known
positions in said fixed coordinate system, for independently, respectively
detecting light radiation from at least three of said first light emitting
sensible points and for detecting at least two of said second light
emitting sensible points, which number of detected light emitting sensible
points are sufficient to determine the position and orientation of said
first and second objects, respectively;
means, responsive to said light sensing detecting means, for converting the
detection of said at least three first sensible points and said at least
two second sensible points to locations of said first points and said
second points, respectively, in said fixed coordinate system in said three
dimensional space;
wherein said detection of said first light emitting sensible points and the
determination of the locations of said first sensible points are
determined independently of the detection of said second light emitting
sensible points and the determination of the locations of said second
sensible points;
means for converting the locations of said first sensible points into a
determined position and orientation of said first moveable object in said
three dimensional space;
means for converting the locations of said second sensible points into a
determined position and orientation of said second moveable object in said
three dimensional space;
means for cross correlating said determined position and orientation of
said first moveable object with the independently determined position and
orientation of said second moveable object to establish the spacial
relationship of said first moveable object and said second moveable
object, respectively, in said three dimensional space;
means for automatically repeating said independent detecting, converting
and cross correlating functions sufficiently frequently to track and
correlate the movement of said first and said second objects absolutely
and relative to each other in real time;
means to select at least one of said internal images which includes at
least one preselected sensible point of said first object;
means for displaying said at least one previously taken, selected image of
an interior of said first object on said electronic screen;
means to display a representation of said second object on said electronic
screen superimposed on said displayed interior image of said first object
such that at least a preselected point of said representation of said
second object appears accurately positioned in relation to said selected
interior image;
means to automatically change the selected interior image as a function of
the movement of said first and second objects relative to each other; and
means to maintain said representation of said second object on said
electronic screen superimposed on the correct changing interior image such
that at least said preselected point of said representation of said second
object continues to be accurately positioned in relation to said changing
selected interior image taking into account the movement of said first and
second objects relative to each other.
2. The system of claim 1 comprising a first and a second light sensing
detecting means wherein at least one of said detecting means include:
linear receptor means adapted to create a signal indicative of the
direction from which an incident light ray impinges on said receptor
means; and
optical means for focussing light rays from the light emitters onto said
linear receptor means.
3. The system of claim 2 further including:
means for receiving said direction indicative signal from the linear
receptor means; and
means, responsive to said direction indicative signals from said receiving
means, for ascertaining the coordinates of at least one point at a time of
said second moveable object in said three-dimensional space.
4. The system of claim 3 further including means responsive to said
direction indicative signal for finding the location of at least one point
at a time of said second moveable object relative to said first moveable
object in said three dimensional space.
5. The system of claim 1 including:
means fixedly attached to the first moveable object for supporting said at
least three first sensible means and
means coupled to the detecting means for establishing the location of said
sensible points, and therefore to establish the position and orientation
of the first three-dimensional object relative to the second moveable
object in said three-dimensional space.
6. The system as claimed in claim 1 wherein said preselected point of said
second moveable object is out of line of sight of said detecting means,
and wherein system further comprises means for determining the location of
said point on said out of sight portion of said second moveable object in
relation to said first moveable object from the determined location of
said at least two non-linear sensible points which are within lines of
sight of said detecting means.
7. The system as claimed in claim 6 wherein said first moveable object is a
part of body of an animal and said second moveable object is a surgical
tool.
8. The system as claimed in claim 1 wherein the same detecting means
detects the locations of all of said detected first and second sensible
points.
9. The system as claimed in claim 8 further including means to distinguish
between detectable emissions from each of said sensible points.
10. The system as claimed in claim 8 further including means to determine
the location of each of said first sensible points at a different
frequency than the determination of the location of each of said second
sensible points.
11. The system as claimed in claim 8 further including means to determine
the location of each of said first sensible points at substantially the
same frequency as the determination of the location of each of said second
sensible points.
12. The system as claimed in claim 1 further including:
means to determine the angles, respectively, between lines extending
between said at least three first sensible points, respectively, and said
detecting means, and between said at least two second sensible points and
said detecting means, respectively; and means for converting said angles
to a specific location in said fixed coordinate system of each of said
detected sensible means.
13. A system as claimed in claim 1 wherein said first sensible points are
disposed on frame means attached to said first object and said second
sensible points are disposed in a manner which is not attached to said
frame means.
14. A method of determining, and electronically visualizing, the relative
spatial relationship of at least first and second objects, which are in
physical contact with each other, but are not physically connected to each
other, in a fixed coordinate system in the same three dimensional space,
wherein each object is moveable in relation to the other, both objects are
moveable into and out of physical contact with the other, and both objects
are moveable in relation to said three dimensional coordinate system,
which method comprises:
emitting light from at least three first sensible points on said first
object and emitting light from at least two second sensible points on said
second object;
detecting emitted light from at least three of said first sensible points
and at least two of said second sensible points at a multiplicity of
spaced apart light sensing means, capable of independently determining the
locations of at least three of said first sensible points and at least two
of said second sensible points which number and location of sensed
sensible points are sufficient to independently determine the position and
orientation of each of said physically unconnected first and second
objects, respectively, in said fixed coordinate system;
sensing a set of first straight light lines between each of said at least
three of said first sensible points and at least two of said sensing
means, and independently sensing a set of second straight light lines
between each of said at least two of said second sensible points and at
least two of said sensing means, respectively;
from angles between said straight light lines and reference lines in known
relationship to said sensing means, respectively, determining the
locations of said sufficient number of said first sensible points and of
said sufficient number of said second sensible points, respectively, in
said fixed coordinate system, to determine the position and orientation of
said first and second objects;
converting locations of said first sensible points into a position and
orientation of said first object in relation to said three dimensional
coordinate system, and independently converting locations of said second
sensible points into a position and orientation of said second object in
relation to said three dimensional coordinate system;
correlating the independently determined positions and orientations of said
first and second objects in relation to said fixed coordinate system,
respectively, and thereby determining the position and orientation of each
of said first and second objects relative to the other;
storing said independently determined positions and orientations of said
first and second objects in a first searchable electronic file;
prior to said independent determination of the positions and orientations
of said first and second objects in real time and the storage of said
information in said electronic file, imaging at least one interior portion
of said first object and storing at least one of said first object
interior portion images in a second searchable electronic file;
correlating said searchable electronic files to determine at least one
electronic image which corresponds to the real time position and
orientation of at least one point on said second object;
selecting at least one of said sorted interior portion images;
electronically displaying at least one of said selected images and a
representation of said second object superimposed thereon accurately
showing at least one point on said second object in accurate real time
position and orientation with respect to said selected interior portion
image;
moving at least one of said objects in said three dimensional space
relative to the other in real time;
repeating said independent sensing, determining, converting, selecting and
correlating steps sufficiently frequently, relative to said movement, to
automatically track said movement of both of said objects relative to each
other and relative to said three dimensional coordinate system in the same
real time;
as a function of the real time movement of said first and second objects
relative to each other, selecting other of said stored internal images to
maintain superposition of the current real time position and orientation
of said at least one point on said second object on the correct location
of the correct internal portion image of said first object; and
electronically displaying the movement of said first and second objects
relative to each other in the form of an accurate real time position and
orientation of said point on said second object relative to an accurately
selected, previously taken, image of an internal portion of said first
object.
15. The method as claimed in claim 14 wherein said sensible points comprise
energy emitting means, and wherein said method further includes sensing
said straight lines between each of said energy emission points and each
of a single set of at least three spaced apart energy detection means; and
distinguishing between energy emitted from each of said energy emission
means; whereby distinguishing between each of said lines.
16. The method as claimed in claim 15 wherein said energy is light
radiation.
17. The method as claimed in claim 14 wherein said energy emissions are
light beams of different wave lengths.
18. A method as claimed in claim 14 further including disposing said first
sensible points on a frame means attached to said first object, and
disposing said second sensible points on said second object in a manner
which is not physically attached to said frame means. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to locating the position of an object relative to a
three-dimensional object in a three-dimensional space.
2. Brief Description of the Prior Art
Computed tomography (CT), magnetic resonance imaging (MRI), and other
methods provide important detailed internal diagnostic images of human
medical patients. However, during surgery there often is no obvious,
clear-cut relationship between points of interest in the diagnostic images
and the corresponding points on the actual patient. While anomalous tissue
may be obviously distinct from normal healthy tissue in the images, the
difference may not be as visible in the patient on the operating table.
Furthermore, in intracranial surgery, the region of interest may not
always be accessible to direct view. Thus, there exists a need for
apparatus to help a surgeon relate locations in the diagnostic images to
the corresponding locations in the actual anatomy and vice versa.
The related prior art can be divided into art which is similar to the
present invention as a whole and art which is related to individual
components of this invention.
Prior art similar to the present invention as a whole includes methods of
correlating three-dimensional internal medical images of a patient with
the corresponding actual physical locations on the patient in the
operating room during surgery. U.S. Pat. No. 4,791,934 does describe a
semi-automated system which does that, but it requires additional
radiographic imaging in the operating room at the time of surgery as the
means to correlate the coordinate systems of the diagnostic image and the
live patient. Furthermore, the system uses a computer-driven robot arm to
position a surgical tool. In particular, it does not display the location
of an input probe positioned interactively by the surgeon.
There have been other attempts to solve the three-dimensional location
problem specifically for stereotactic surgery. One class of solutions has
been a variety of mechanical frames, holders, or protractors for surgery
(usually intracranial surgery). For examples see U.S. Pat. Nos. 4,931,056;
4,875,478; 4,841,967; 4,809,694; 4,805,615; 4,723,544; 4,706,665;
4,651,732; and 4,638,798. Generally, these patents are intended to
reproduce angles derived from the analysis of internal images, and most
require rigidly screwing a stereotactic frame to the skull. In any case,
these methods are all inconvenient, time-consuming, and prone to human
error.
A more interactive method uses undesirable fluoroscopy in the operating
room to help guide surgical tools (U.S. Pat. No. 4,750,487).
More relevant prior art discloses a system built specifically for
stereotactic surgery and is discussed in the following reference:
David W. Roberts, M.D., et al; "A Frameless Stereotaxic Integration of
Computerized Tomographic Imaging and the Operating Microsope", J.
Neurosurgery 65, October 1986.
It reports how a sonic three-dimensional digitizer was used to track the
position and orientation of the field of view of a surgical microscope.
Superimposed on the view in the microscope was the corresponding internal
planar slice of a previously obtained computed tomographic (CT) image. The
major disadvantages reported about this system were the inaccuracy and
instability of the sonic mensuration apparatus.
Although the present invention does not comprise the imaging apparatus used
to generate the internal three-dimensional image or model of the human
patient or other object, the invention does input the data from such an
apparatus. Such an imaging device might be a computed tomography (CT) or
magnetic resonance (MRI) imager. The invention inputs the data in an
electronic digital format from such an imager over a conventional
communication network or through magnetic tape or disk media.
The following description concentrates on the prior art related
specifically to the localizing device, which measures the position of the
manual probe and which is a major component of this invention. Previous
methods and devices have been utilized to sense the position of a probe or
object in three-dimensional space, and employ one of various mensuration
methods.
Numerous three-dimensional mensuration methods project a thin beam or a
plane of light onto an object and optically sense where the light
intersects the object. Examples of simple distance rangefinding devices
using this general approach are described in U.S. Pat. Nos. 4,660,970;
4,701,049; 4,705,395; 4,709,156; 4,733,969; 4,743,770; 4,753,528;
4,761,072; 4,764,016; 4,782,239; and 4,825,091. Examples of inventions
using a plane of light to sense an object's shape include U.S. Pat. Nos.
4,821,200, 4,701,047, 4,705,401, 4,737,032, 4,745,290, 4,794,262,
4,821,200, 4,743,771, and 4,822,163. In the latter, the accuracy of the
surface sample points is usually limited by the typically low resolution
of the two-dimensional sensors usually employed (currently about 1 part in
512 for a solid state video camera). Furthermore, these devices do not
support the capability to detect the location and orientation of a
manually held probe for identifying specific points. Additionally, because
of line-of-sight limitations, these devices are generally useless for
locating a point within recesses, which is necessary for intracranial
surgery.
The internal imaging devices themselves (such as computed tomography,
magnetic resonance, or ultrasonic imaging) are unsuited for tracking the
spatial location of the manually held probe even though they are
unencumbered by line-of-sight restrictions.
A few other methods and apparatus relate to the present invention. They
track the position of one or more specific moveable points in
three-dimensional space. The moveable points are generally represented by
small radiating emitters which move relative to fixed position sensors.
Some methods interchange the roles of the emitters and sensors. The
typical forms of radiation are light (U.S. Pat. No. 4,836,778), sound
(U.S. Pat. No. 3,821,469), and magnetic fields (U.S. Pat. No. 3,983,474).
Other methods include clumsy mechanical arms or cables (U.S. Pat. No.
4,779,212). Some electro-optical approaches use a pair of video cameras
plus a computer to calculate the position of homologous points in a pair
of stereographic video images (for example, U.S. Pat. Nos. 4,836,778 and
4,829,373). The points of interest may be passive reflectors or flashing
light emitters. The latter simplify finding, distinguishing, and
calculating the points.
Probes with a pointing tip and sonic localizing emitters on them have been
publicly marketed for several years. The present invention also utilizes a
stylus, but it employs tiny light emitters, not sound emitters, and the
method of sensing their positions is different.
Additional prior art related to this patent is found in these references:
Fuchs, H.; Duran, J.; Johnson, B.; "Acquisition and 10 Modeling of Human
Body Form Data", Proc. SPIE, vol. 166, 1978, pp. 94-102.
Mesqui, F.; Kaeser, F.; Fischer, P.; "Real-time, Non-invasive Recording and
3-D Display of the Functional Movements of an Arbitrary Mandible Point",
SPIE Biostereometrics, Vol. 602, 1985, pp. 77-84.
Yamashita, Y.; Suzuki, N.; Oshima, M. "Three-Dimensional Stereometric
Measurement System Using Optical Scanners, Cylindrical Lenses, and Line
Sensors", Proc. SPIE, vol. 361, 1983, pp. 67-73.
The paper by Fuchs, et al., (1978) best describes the method used by the
present invention to track the surgical probe in three-dimensional space.
It is based on using three or more one-dimensional sensors, each
comprising a cylindrical lens and a linear array of photodetectors such as
a charge-coupled semiconductor device (CCD) or a differential-voltage
position sensitive detector (PSD). The sensors determine intersecting
planes which all contain a single radiating light emitter. Calculation of
the point of intersection of the planes gives the location of the emitter.
The calculation is based on the locations, orientations, and other details
concerning the one-dimensional sensors and is a straightforward
application of analytic geometry. This electro-optical method, however,
has not been previously used for the purpose of the present invention.
Thus, there still remains a need for a complete apparatus which provides
fast, accurate, safe, convenient mensuration of the three-dimensional
position of a manual probe and which visually relates that position to the
corresponding position on the image of a previously-generated
three-dimensional model of an object.
SUMMARY OF THE INVENTION
A first objective of the present invention is to provide accurate,
three-dimensional mensuration of the location and orientation of an
instrument on or inside an object, which could be (but is not limited to)
a surgical patient in an operating room.
A second objective of this invention is to provide an electro-optical
mensuration system which is inexpensive, easy to use, reliable, and
portable and which employs a manually positioned probe or other pointing
instrument.
A third objective of this invention is to provide a simple, non-invasive
means of establishing a correspondence between a predetermined coordinate
system of the object and a coordinate system of a three-dimensional,
geometrical computer model of that object where the computer model has
been provided as input data to this invention.
A fourth objective of this invention is to relate a measured location on or
inside the object to the corresponding location in the computer model of
that object according to the established correspondence between the
coordinate systems of the object and the model.
A fifth objective of this invention is to display a cut-away view or a
cross-sectional slice of that model on the graphics screen of the
invention, where the slice may be a planar cross-section of the
geometrical model, where the slice approximately intersects the location
in the model corresponding to the measured location. A marker may then be
superimposed on the displaced slice to indicate the location on the slice
corresponding to the measured location.
A sixth objective of this invention, is specifically to help a surgeon
locate diseased tissue while avoiding healthy critical structures,
especially in cranial neurosurgery.
Additional objects, advantages, and novel features of the invention shall
be set forth in part in the following description and in part will become
apparent to those skilled in the art upon examination of the following or
may be learned by the practice of the invention. The objects and the
advantages of the invention may be realized and attained by means of the
instrumentalities and in combinations particularly pointed out in the
appended claims.
To achieve the foregoing and other objects and in accordance with the
invention, as embodied and broadly described herein, the optical
mensuration and correlation apparatus comprises a hand held probe having
an invasive tip for touching or for inserting into an object. Two or more
light emitters mounted in spaced relation to each other on the external
portion of the probe remaining outside the object are sequentially strobed
to emit light. Three or more light sensors or detectors, the positions of
which are known with respect to a predetermined coordinate system, detect
the positions of the two or more light emitters positioned on the probe as
they are strobed. A computer coupled to the probe and to the light sensors
receives data from the sensors and calculates the position and orientation
of the probe with respect to the predetermined coordinate system. The
computer then determines the position and orientation of the invasive
portion of the probe inside the object by correlating the position of the
invasive portion of the probe relative to the predetermined coordinate
system with a model of the object defined relative to the predetermined
coordinate system. A display device coupled to the computer indicates the
location of the invasive portion of the probe in the object by displaying
a representation of the location of the invasive portion of the probe with
respect to the model of the object.
The method of this invention includes the steps of detecting the position
of the probe relative to the predetermined coordinate system, computing
the position and orientation of the invasive portion of the probe relative
to the predetermined coordinate system, determining the position and
orientation of the invasive portion of the probe inside the object by
correlating the position of the invasive portion of the probe relative to
the predetermined coordinate system with the model of the object, and
indicating the location of the invasive portion of the probe in the object
by displaying a representation of the location of the invasive portion of
the probe with respect to the model of the object.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawing figures, illustrate a preferred embodiment of the
present invention and, together with the description, serve to explain the
principles of the invention.
FIGS. 1A and 1B are a block diagram of the optical mensuration and
correlation apparatus of the present invention showing the major
components.
FIG. 1B is a block diagram similar to FIG. 1A, but also showing an
additional set of emitters in fixed relation to the object for automatic
correlation of reference points to the system.
FIG. 2 is a perspective drawing illustrating the invention in use by a
surgeon performing intracranial surgery on a patient, and showing a cursor
on the display screen that marks the corresponding position of the
invasive tip of the probe within the image of previously obtained model
data.
FIG. 3 is a sample of the display showing a position of tip of the probe
with respect to previously obtained model data and showing the reference
points on the patient's skull display as triangles.
FIG. 4 is a schematic perspective representation of one of the
one-dimensional photodetectors of the present invention.
FIG. 5 is a graph of the image intensity (manifested as a voltage or
current) versus locations on the photodetector surface for a typical light
detector used by the optical mensuration and correlation apparatus of the
present invention.
FIGS. 6 and 7 are diagrams of the major steps performed by the computer to
calculate the position of the invasive portion of the probe with respect
to the model of the object and to display the image slice.
FIG. 8 is an illustration of the manner in which the three one-dimensional
measurements determine three intersecting planes intersecting at a
uniquely determined point.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The optical mensuration and correlation apparatus 10 of the present
invention is shown schematically in FIG. 1A and comprises a hand-held
invasive probe 12 housing at least two light emitters 14, 16, mounted
co-linear with one another and with the tip 18 of the probe 12. At least
three remotely located, one-dimensional light sensors 20, 22, and 24 are
mounted in fixed, spaced relationship to each other and are located at
known positions and orientations with respect to a predetermined reference
coordinate system frame 80. Three light sensors 20, 22, and 24 sense the
light projected by the individual light emitters 14, 16 and generate
electrical output signals from which are derived the location of the probe
12 and, consequently, the probe tip 18, with respect to the fixed
coordinate system 80. In addition, the three sensors 20, 22, 24 could
sense and derive the locations of other, optional reference emitters 70,
72, and 74 (FIG. 1B) in the same manner as for the probe emitters 14 and
16. The role of these reference emitters is to automate the calculation of
the transformation matrix between the coordinate system of the model's
image 13 (FIG. 2) of the object and the coordinate system of the sensors
and the object itself 11.
A control unit 30 connected to the moveable probe 12 via a data line 26 and
coupled to the remotely located sensors 20, 22, and 24 via data lines 28,
32, and 34, respectively, synchronizes the time multiplexing of the two
light emitters 14, 16, controls the operation of the sensors 20, 22, and
24, and receives data from these sensors as will be completely described
below. A coordinate computer 36, coupled to the control unit 30 by a data
line 38, calculates the three-dimensional spatial positions of the probe
12 and the probe tip 18 (not shown in FIG. 2), and correlates those
positions with data from a model 40 of the object 11 which has been
previously stored electronically in an electronically accessible database
40 and from correlation information 42. The model data 40 with the spacial
position of the probe tip 18 are shown at 13 on a display screen 44 (FIG.
2) as will be fully described below. The probe 12 can be used without the
cable 26 coupling it to the control unit 30 by employing distinctive
modulation of the light emitters 14 and 16. For example, the pulse
durations or frequencies of each can be different. The controller 30, by
detecting the pulse duration or frequency, can determine to which light
emitter the sensors 20, 22, and 24 are reacting.
The optical mensuration and correlation apparatus 10 of the present
invention is primarily designed to aid surgeons performing delicate
intracranial surgery, and the remaining description is directed to such a
surgical embodiment although many other surgical applications besides
cranial surgery are possible. Moreover, the optical mensuration and
correlation apparatus 10 of this invention may be used for other purposes
in many various non-medical fields. In the described embodiment, the
physical object 11 of interest is the head or cranium of a patient, and
the model of the cranium is constructed using a series of parallel
internal image slices (of known mutual spatial relationship) such as those
obtained by means of computed tomography (CT) or nuclear magnetic
resonance (NMR). These image slices are then digitized, forming a
three-dimensional computer model of the patient's cranium which is then
stored in the electronically accessible database 40.
As shown in FIGS. 1A, 1B, 2, and 3 a surgeon places the tip 18 of the probe
12 at any point on or inside the cranium 11 of the patient. The position
sensors 20, 22, and 24 detect the locations of the emitters 14, 16
attached to the portion of the probe 12 that remains outside the patient's
body. That is, the light produced by the emitters 14, 16 must be visible
to the sensors 20, 22, and 24. These point emitters 14, 16 radiate light
through a wide angle so that they are visible at the sensors over a wide
range of probe orientations.
The sensors 20, 22, and 24, the control unit 30, and the computer 36
determine the three-dimensional location of each emitter 14, 16, and
compute its coordinates in the predetermined coordinate system 80. The
computer 36 can then calculate the location of the tip 18 of the probe 12
with respect to the predetermined coordinate system 80, according to the
locations of the emitters with respect to the predetermined coordinate
system 80 and the dimensions of the probe, which dimensions have been
placed into the memory (not shown) of the computer 36 beforehand as will
be described filly below. Once the computer 36 has calculated the location
of the probe tip 18 with respect to the predetermined coordinate system
80, the computer 36 then uses the relationship between the model of the
cranium stored in the database 40 and the coordinate system 80 to
calculate the location of the probe tip 18 in relation to the model 11.
Finally, the computer 36 displays the model-relative location of the tip
18 on a display screen 44. In a simple form of the preferred embodiment,
the computer 36 accomplishes this display by accessing a CT or NMR image
slice 13 stored in the database 40 that is closest to the location of the
probe tip 18, and then superimposes a suitable icon 76 representing the
tip 18 on the image 13 as shown in FIGS. 2 and 3. Thus, the surgeon knows
the preci | | |
