Patent Description:
Surgical navigation systems are typically configured to track a surgical instrument operated by the surgeon relative to a patient or other object. Based on the tracked surgical instrument, the surgical navigation system provides visual or acoustic instructions to guide the surgeon when operating the surgical instrument.

A common procedure for surgical navigation is to track both the surgical instrument and the patient. The surgical navigation system can thus display image data of the patient (e.g., a computer tomography scan) relative to a visual representation of the surgical instrument or a part thereof. In such a visual representation, a tip of the surgical instrument is commonly represented in form of a point or icon.

Tissue manipulation such as cutting, milling or drilling is largely affected by a size of the instrument tip. The following two examples illustrate that visually representing the instrument tip in the form of a point can impair the accuracy of the guidance provided to the surgeon.

<FIG> shows a spherically shaped instrument tip <NUM> (e.g., a burr) having a distal end point <NUM>. An instrument axis <NUM> extending through the end point <NUM> is arranged perpendicularly to a surface of tissue <NUM> (e.g., bone). <FIG> shows an opening that has been cut by the instrument tip <NUM> into the tissue <NUM> in a direction parallel to the instrument axis <NUM>. Since the instrument axis <NUM> extends parallel to the opening cut into the tissue <NUM>, the end point <NUM> is positioned at a bottom of the opening.

When visually representing a calculated location of the end point <NUM> relative to the tissue <NUM> on a display, the location of the visualized end point <NUM> properly coincides with the bottom of the opening. As such, the surgeon is correctly informed about, for example, an extension and a depth of the opening.

<FIG> shows the same instrument tip <NUM> as shown in <FIG>, but with the instrument axis <NUM> oriented at a non-perpendicular angle relative to the surface of the tissue <NUM>. Therefore, when cutting an opening into the tissue <NUM> perpendicular to the surface of the tissue <NUM>, the instrument axis <NUM> does not extend parallel to the opening. <FIG> shows that cutting an opening into the tissue <NUM> in the scenario of <FIG> results in the path of the end point <NUM> to be arranged offset to the cutting path of the opening. When a surgical navigation system uses the end point <NUM> as reference for the cutting path, the calculated cutting path will by offset relative to the actual cutting path. As such, the extension of the cutting path cannot be properly visualized. Moreover, the calculated location of the end point <NUM> is no longer indicative of a depth of the opening.

<FIG> illustrates an exemplary visual guidance that may be provided to the surgeon on a display. The visual guidance includes displaying a visual representation of a spherically shaped instrument tip in the form of an end point <NUM> relative to image data of tissue <NUM>. The image data comprises a non-target area <NUM> that must not be affected by the surgical instrument. The visual guidance shown in <FIG> visualizes the end point <NUM> outside the non-target area <NUM>, seemingly indicating that the instrument is not cutting into the non-target area <NUM>. <FIG> shows the actual tissue <NUM> with the actual instrument tip <NUM>. Since the end point <NUM> shown in <FIG> does not account for the radius of the instrument tip <NUM>, the visual guidance of <FIG> does not indicate that the instrument tip <NUM> is in fact cutting into the non-target area <NUM>.

As described in the two scenarios above, a visual representation in form of a point does not take the form, size and orientation of the instrument tip into account. Such an incomplete visualization can negatively affect the accuracy of the guiding instructions provided by the surgical navigation system.

The surgical instrument described with reference to <FIG> and <FIG> has an instrument tip with a spherically shaped surface portion that defines a radius, which may be unknown or require verification. The radius of the instrument tip can differ due to the availability of a set of instrument tips from which one may be selected by the surgeon depending on the prevailing surgical situation.

In order to provide the surgeon with accurate guiding information in the scenarios discussed above, and in other scenarios, the surgical navigation system requires precise knowledge of the radius of the spherically shaped surface portion. In some cases, the instruments are provided with labels that indicate the radius of their tips. However, relying on the surgeon to properly input the selected instrument or the associated tip radius via a keyboard or graphical user interface has turned out to be error-prone and tedious during on-going surgery. Moreover, the use of labels does not take into account a radius change caused by wear or other effects. As a consequence, relying on the surgeon to properly identify the radius of a selected instrument tip is error prone, time-inefficient and potentially unsafe for the patient.

Document <CIT> discloses surgical instrument calibration methods, systems, and devices that allow a virtual representation of a surgical instrument to be modified to adjust for any variations in a distal tip of a surgical instrument. An instrument calibration system is disclosed that can have a surgical instrument, a calibration instrument, and a monitoring system. The surgical instrument can have a distal tip and an orientation element thereon, and the calibration instrument can have a pivot point thereon and a calibration reference element attached thereto. The monitoring system can be configured to record movement of the surgical instrument with respect to the calibration instrument when the tip of the surgical instrument is inserted into the pivot point of the calibration instrument, and to calculate a deviation of the tip of the surgical instrument from a predefined ideal tip based on the recorded movement.

Document <CIT>discloses a registration and identification tool for an instrument. The instrument comprises a body, a marker member which is optically detectable and provided on the body, and a recess in the body which extends from an outer surface of the body into the inside of the body, thereby defining an extension direction of the recess. The recess has a shape such that a lateral extension of the recess decreases in the direction from the outer surface of the body towards the inside of the body. A method for registration and identification of an instrument comprises placing a surgical tool of the surgical instrument into the recess of the tool, pivoting the surgical instrument relative to the marker member while the surgical tool is placed inside the recess, performing a detecting process of the relative movement of the surgical instrument, and identifying geometrical characteristics of the surgical tool and/or registering the relative position of the surgical tool to the remainder of the surgical instrument using the results of the detection process.

There is a need for a technique that solves one or more of the aforementioned or other problems.

According to one aspect, a computer-implemented method for determining a radius of a spherically shaped surface portion of a tip of an instrument is provided. A calibration device is provided that comprises a flat calibration surface and a calibration structure, wherein the calibration structure defines an opening angle and a real or imaginary first reference point relative to which the opening angle is defined. The calibration device comprises a first tracker trackable by a tracking system and arranged in a first predetermined relationship relative to the first reference point and in a second predetermined relationship relative to the calibration surface. The instrument comprises a second tracker trackable by the tracking system. The method comprises multiple steps performed by a computer system. The method comprises determining a first pose of the first tracker and a second pose of the second tracker while the spherically shaped surface portion is in abutment with the calibration structure. The method further comprises determining a reference position of the first reference point relative to the second tracker when the first tracker is in the first pose and the second tracker is in the second pose based on the first pose, the second pose, and the first predetermined relationship. The method comprises determining a third pose of the first tracker and a fourth pose of the second tracker while the spherically shaped surface portion is in abutment with the calibration surface. The method further comprises determining the radius of the spherically shaped surface portion based on the third pose, the second predetermined relationship, the reference position, the fourth pose, and the opening angle.

Determining the radius of the spherically shaped surface portion may comprise determining a second reference point based on the fourth pose and the reference position, determining a reference distance defining a distance between the second reference point and the calibration surface based on the second reference point, the third pose, and the second predetermined relationship, and determining the radius based on the reference distance and a trigonometric function of the opening angle.

The second pose may define a first calibration orientation of the second tracker and the fourth pose may define a second calibration orientation of the second tracker. A reorientation angle may define an angular difference between the first calibration orientation and the second calibration orientation, and a surface angle may define an angular difference between a normal vector of the calibration surface and a bisector of the opening angle. In such a scenario, the method may further comprise determining a pivot angle that defines an angle based on the reorientation angle and the surface angle. The pivot angle may be determined as a polar angular component in regard to the surface normal of a sum of the reorientation angle and the surface angle.

Determining the radius of the spherically shaped surface portion may further be based on the pivot angle.

The method may comprise determining a position of a centre point of the spherically shaped surface portion relative to the second tracker based on the third pose, the second predetermined relationship, the reference position, the fourth pose, the opening angle, and the radius. The method may comprise determining a second reference point based on the fourth pose and the reference position. The method may comprise determining a reference axis through the second reference point and perpendicular to the calibration surface. The method may further comprise determining a position of a centre point of the spherically shaped surface portion relative to the second tracker along the reference axis at a distance of the radius from the reference surface in a direction away from the calibration device.

The method may further comprise rotating the reference axis around the second reference point by the pivot angle before determining the position of the centre point along the reference axis.

According to a second aspect, a computer-implemented method for determining a radius of a spherically shaped surface portion of a tip of an instrument is provided. The spherically shaped surface portion has a centre point. A calibration device is provided that comprises a calibration structure defining an opening angle and that is configured to cooperate with the spherically shaped surface portion so as to guide a tilting movement of the instrument tip around the centre point. The calibration device comprises a first tracker trackable by a tracking system and arranged in a predetermined relationship relative to the calibration structure. The instrument comprises a second tracker trackable by the tracking system. The method is performed by a computer system and comprises determining a first pose of the first tracker. The method further comprises determining positional data of the second tracker for different tilting positions of the instrument while the spherically shaped surface portion is in abutment with the calibration structure. The method further comprises determining a position of the centre point relative to the second tracker based on the positional data. The method also comprises determining the radius of the spherically shaped surface portion based on the position of the centre point, the first pose, the predetermined relationship, and the opening angle.

The method of the second aspect may comprise determining the radius based on a centre distance between the position of the centre point, a real or imaginary point relative to which the opening angle is defined and a trigonometric function of the opening angle. As an example, determining the radius may be based on the sinus of half the opening angle. Evidently, the sinus can be replaced by other trigonometric functions as generally known in the art.

The following observations pertain to both the method of the first aspect and the method of the second aspect.

The method may comprise tracking a third tracker of an object (and trackable by the tracking system) to track an object pose of image data of the object in a virtual space. The method may comprise tracking the second tracker to track a position of the centre point in the virtual space based on the position of the centre point relative to the second tracker. Further still, the method may comprise generating first display instructions for displaying in the virtual space, based on the object pose of the image data of the object in the virtual space, the position of the centre point in the virtual space and the radius, a visual representation indicative of the radius relative to the image data of the object.

As understood herein, the display instructions are configured to control a display such that certain information is visually output to a user. As such, the display instructions will typically take the form of analog or digital signals.

The visual representation indicative of the radius may have been generated (e.g., scaled) such that the display properly reflects the actual location of the spherically shaped surface portion relative to the actual location of the object (e.g., relative to a surface portion of the object). As such, the image data of the object and the radius indication may be converted to a common scale for visualization.

The calibration structure may be configured to centre the centre point onto a central axis of the calibration structure. The object may be a surgical object, such as a second instrument or a patient. The image data of the object may be captured using a conventional camera (e.g., a stereo camera), computer tomography, magnetic resonance imaging or any other medical imaging procedure.

The tracking system may be configured to apply one or more of an optical tracking technique, an electromagnetic tracking technique and an ultrasound tracking technique. The optical tracking technique may rely on one or both of infrared and visible light. The initial calibration steps may be performed using an optical tracking technique and the later tracking steps may be performed using an electromagnetic tracking technique, or vice versa.

The method may comprise determining the radius by multiplying the sinus of half of the opening angle with a distance between the position of the centre point and a real or imaginary point relative to which the opening angle is defined.

The calibration device may comprise a plurality of calibration structures, wherein the first tracker is arranged in a predetermined manner relative to each of the plurality of calibration structures. The method may further comprise determining the position and, optionally, the opening angle of the calibration structure in which the instrument tip is arranged by identifying the calibration structure based on the position of the centre point. The central axis of at least two calibration structures may be arranged parallel to each other. The central axis of at least two calibration structures may alternatively be arranged non-parallel to each other, such as at an angle of <NUM>°.

The positional data may comprise at least two different tilt poses of the second tracker for the different tilting positions. Alternatively, or additionally, the positional data may comprise at least four different positions of the second tracker for the different tilting positions.

The method may comprise receiving an expected radius value and validating whether the determined radius corresponds to the expected radius value. The validation may be performed based on a threshold difference between the expected radius value and the determined radius. The method may comprise receiving the expected radius value as user input (e.g., entered via a keyboard or graphical user interface). The method may further comprise generating display instructions for displaying a result of the validation.

The method may further comprise outputting, on a display, instructions to tilt the instrument for calibration purposes. The instructions may indicate when to start and/or to stop tilting the instrument.

The method may comprise generating region display instructions for displaying a non-target region in the image data for which contact with the instrument is to be avoided. The method may comprise outputting a warning when the instrument tip comes in contact with the non-target region and/or a threshold region around the non-target region. The warning may be at least one of an acoustic, optical, and haptic warning.

The method may comprise generating progress display instructions for displaying a progress of object manipulation based on a path of the instrument tip. The progress of object manipulation may be based on a surface generated from a circle or sphere with the determined radius and a tracked movement of the centre point as a generatrix.

The method may comprise displaying, on a display, a visual representation (e.g., an icon) of at least a portion of the instrument relative to the image data of the object. The display may be part of the tracking system, a surgical navigation system or be a separate display that is communicatively coupled with the tracking system or the surgical navigation system.

The calibration structure may have a shape of a cone or a pyramid, or a portion thereof, defining the opening angle. The calibration structure may comprise plates or other rigid structures that form a (e.g., partial) cone or partial pyramid. The calibration structure may have a shape of a truncated cone or pyramid.

The method may further comprise determining from a pre-determined list of radii a subset of (one or more) radii that meet a similarity criterion with respect to the determined radius. The similarity criterion may comprise having a radius that differs by not more than a difference threshold from the determined radius. Additionally, or alternatively, the similarity criterion may comprise a number of radii that are closest to the determined radius. The method may further comprise generating an output for a user selection or confirmation, wherein the output comprises at least one of information about the subset of radii and information about instrument tips associated with the subset of radii. The user may thus select, or confirm, a particular instrument tip attached to or inserted into the (e.g., powered) instrument.

The visual representation may comprise an icon representative of the centre point and at least a part of a circle or a sphere with the determined radius of the spherically shaped surface portion around the icon. The icon may further be representative of the centre point with the determined radius of the spherically shaped surface portion around the centre point. The icon may be representative of an actual instrument tip (e.g., as selected or confirmed by a user).

A pose of an instrument axis may be determined on the basis of tracking the second tracker while the instrument is rotated about the instrument axis. Alternatively, the pose of the instrument axis may be determined on the basis tracking the second tracker and evaluating a known predetermined spatial relationship between the second tracker and the instrument axis. The visual representation may be indicative of the pose of the instrument axis in the virtual space. The instrument axis may be represented in the virtual space as a line that extends towards the centre point of the spherically shaped surface portion.

According to a third aspect, a computer program product is provided, comprising instructions that, when executed on at least one processor, cause the at least one processor to carry out any of the methods described herein. The computer program product may be stored on a non-volatile memory, such as a hard disc drive, a flash memory, a read-only memory, or an optical disc.

According to a fourth aspect, a device for determining a radius of a spherically shaped surface portion of a tip of an instrument is provided. A calibration device is provided that comprises a flat calibration surface and a calibration structure, wherein the calibration structure defines an opening angle and a real or imaginary first reference point relative to which the opening angle is defined. The calibration device comprises a first tracker trackable by a tracking system and arranged in a first predetermined relationship relative to the first reference point and in a second predetermined relationship relative to the calibration surface, and wherein the instrument comprises a second tracker trackable by the tracking system. The device is configured to determine a first pose of the first tracker and a second pose of the second tracker while the spherically shaped surface portion is in abutment with the calibration structure. The device is further configured to determine a reference position of the first reference point relative to the second tracker when the first tracker is in the first pose and the second tracker is in the second pose based on the first pose, the second pose, and the first predetermined relationship. The device is configured to determine a third pose of the first tracker and a fourth pose of the second tracker while the spherically shaped surface portion is in abutment with the calibration surface. The device is further configured to determine the radius of the spherically shaped surface portion based on the third pose, the second predetermined relationship, the reference position, the fourth pose, and the opening angle.

According to a fifth aspect, a device for determining a radius of a spherically shaped surface portion of a tip of an instrument is provided. The spherically shaped surface portion has a centre point. A calibration device is provided that comprises a calibration structure defining an opening angle and that is configured to cooperate with the spherically shaped surface portion so as to guide a tilting movement of the instrument tip around the centre point. The calibration device comprises a first tracker trackable by a tracking system and arranged in a predetermined relationship relative to the calibration structure and wherein the instrument comprises a second tracker trackable by the tracking system. The device is configured to determine a first pose of the first tracker. The device is further configured to determine positional data of the second tracker for different tilting positions of the instrument while the spherically shaped surface portion is in abutment with the calibration structure. The device is configured to determine a position of the centre point relative to the second tracker based on the positional data. The device is configured to determine the radius of the spherically shaped surface portion based on the position of the centre point, the first pose, the predetermined relationship, and the opening angle.

The calibration structure may define a real or imaginary first reference point relative to which the opening angle is defined and the predetermined relationship may define a position of the first reference point relative to the first tracker.

The device of the fourth or fifth aspect may be configured to perform any of the method steps described herein. The device may be a computer system or a part of a computer system.

According to one example, a calibration system is provided. The calibration system comprises the device for determining a radius as described herein. The calibration system may further comprise the calibration device with the first tracker coupled thereto and the instrument with the second tracker coupled thereto.

According to another example a surgical navigation system is provided. The surgical navigation system comprises the calibration system as described herein. The surgical navigation system further comprises the tracking system, wherein the tracking system comprises or is communicatively coupled to the device for enabling a radius determination.

According to another example, a method for enabling a visualization of an indication of a radius of a spherically shaped surface portion of a tip of an instrument relative to image data of an object in a virtual space is provided. The spherically shaped surface portion has a centre point. A calibration device is provided that comprises a calibration structure defining an opening angle and that is configured to cooperate with the spherically shaped surface portion so as to guide a tilting movement of the instrument tip around the centre point. The calibration device comprises a first tracker trackable by a tracking system and arranged in a predetermined relationship relative to the calibration structure. The instrument comprises a second tracker and the object comprises a third tracker trackable by the tracking system. The method is performed by a computer system and comprises determining a first pose of the first tracker. The method further comprises determining positional data of the second tracker for different tilting positions of the instrument while the spherically shaped surface portion is in abutment with the calibration structure. The method also comprises determining the radius of the spherically shaped surface portion and a position of the centre point relative to the second tracker based on the first pose, the positional data, the predetermined relationship, and the opening angle. The method comprises tracking the third tracker to track a second pose of the image data of the object in the virtual space. The method comprises tracking the second tracker to track a position of the centre point in the virtual space based on the position of the centre point relative to the second tracker. Further still, the method comprises generating first display instructions for displaying in the virtual space, based on the second pose of the image data of the object in the virtual space, the position of the centre point in the virtual space and the radius, a visual representation indicative of the radius relative to the image data of the object.

Further details, advantages and aspects of the present disclosure will become apparent from the following embodiments when taken in conjunction with the drawings, wherein:.

In the following description of exemplary embodiments, the same reference numerals are used to denote the same or similar components.

The embodiments described hereinafter are directed to determining a radius of a spherical surface of an instrument tip. The instrument may be used in various technical fields such as in robotics, material science, or medical procedures. The following embodiments exemplarily relate to surgical navigation of a surgical instrument.

<FIG> shows an embodiment of a surgical navigation system <NUM> comprising a device <NUM> configured for determining the radius of a spherical surface of an instrument tip. The device <NUM> shown in <FIG> may be comprised by a dedicated computer system <NUM>. Alternatively, or in addition, the device <NUM> may by comprised by cloud computing resources.

The surgical navigation system <NUM> further comprises a tracking system <NUM>. The tracking system <NUM> shown in <FIG> comprises a camera (e.g., a stereo camera) for optical tracking. Additionally, or alternatively, the tracking system <NUM> comprises an electromagnetic field generator for electromagnetic tracking. The tracking system <NUM> is configured to gather tracking data within a surgical environment <NUM>. The tracking data may take the form of images of the camera or electrical currents induced in an electromagnetic tracker (e.g., in one or more coils).

<FIG> also illustrates a user <NUM> (e.g., a surgeon or medical staff) moving a surgical instrument <NUM> relative to a calibration device <NUM> in the surgical environment <NUM>. The associated calibration procedure targets at determining a tip radius of the surgical instrument <NUM>. The device <NUM>, the calibration device <NUM> and the surgical instrument <NUM> are part of a calibration system <NUM> comprised by the surgical navigation system <NUM>.

As shown in <FIG>, the calibration device <NUM> comprises a first tracker <NUM> and the surgical instrument <NUM> comprises a second tracker <NUM>. The first and second trackers <NUM>, <NUM> are both trackable by the tracking system <NUM>. The first and second trackers <NUM>, <NUM> exemplarily shown in <FIG> are passive trackers with reflective markers (e.g., reflective spheres). Alternatively, the first and second trackers <NUM>, <NUM> may be active trackers with light emitting elements. Further alternatively, the first and second trackers <NUM>, <NUM> may comprise coils for electromagnetic tracking. As a still further alternative, the surgical instrument <NUM> and the calibration device <NUM> as such may also constitute respective trackers <NUM>, <NUM>. For example, using a stereo camera of the tracking system <NUM>, the tracking system <NUM> may simply track the known shapes of the one or both of the surgical instrument <NUM> and calibration device <NUM> for determining their positions or poses within the surgical environment <NUM>.

<FIG> shows an enlarged view of an exemplary instrument tip <NUM> of the surgical instrument <NUM>. The instrument tip <NUM> has a radius <NUM> that is defined by a spherically shaped surface portion <NUM> around a centre point <NUM>. The surface portion <NUM> may have openings or rake structures (e.g., in the form of cutting flutes) and may therefore not form one continuous surface. In some variants, the instrument tip <NUM> may be a burr.

The surface portion <NUM> of the instrument tip <NUM> shown in <FIG> forms almost a complete sphere with the exception of an attachment region <NUM> where the tool tip <NUM> is connected to a shaft of the surgical instrument <NUM>. The shaft with the tool tip <NUM> may be removable from the surgical instrument <NUM>, so that the user <NUM> may selectively use the surgical instrument <NUM> with different tool tips <NUM> having different radii.

Alternatively to the example illustrated in <FIG>, the spherically shaped surface portion <NUM> may form a smaller portion of a sphere. <FIG> shows an instrument tip <NUM> with a surface portion <NUM> that forms a half sphere. The surface portion <NUM> may form any other portion of a sphere such as a third, or a quarter of a sphere. <FIG> shows an instrument tip <NUM> in the form of a drill bit with an essentially spherically shaped surface portion <NUM> and an essentially cylindrical surface portion <NUM>. The instrument tip <NUM> comprises one or more grooves <NUM> that interrupt a continuous surface of the spherically shaped surface portion <NUM>.

In the examples illustrated in <FIG>, the spherically shaped surface portion <NUM> defines a virtual sphere with the radius <NUM> and the centre point <NUM>. Points on the surface portion <NUM> are arranged with a distance of the radius <NUM> away from the common centre point <NUM>. Prior to actual surgery, the radius <NUM> of the spherically shaped surface portion <NUM> will need to be determined by the user <NUM> using the calibration device <NUM>.

<FIG> shows an example of the calibration device <NUM> with the first tracker <NUM> and a calibration structure <NUM> defining an opening angle <NUM>. The first tracker <NUM> needs to be trackable by the tracking system <NUM> of the surgical navigation system <NUM>. Therefore, in the above example of a camera-based optical navigation system <NUM>, the first tracker <NUM> is an optical tracker as shown in <FIG> with three (or more) reflective spheres. In case the surgical navigation system <NUM> employs electromagnetic tracking, the first tracker <NUM> may comprise one, two or more coils as shown in <FIG>.

The calibration structure <NUM> shown in <FIG> is formed as a cone-shaped surface opening in a plate-shaped body <NUM>. The resulting cone <NUM> defines a central axis <NUM> through an apex <NUM> of the cone <NUM>. The cone <NUM> has an opening angle <NUM> that is defined as twice the angle between the central axis <NUM> and any surface line of the cone <NUM> lying in the same plane as the central axis <NUM>. The opening angle <NUM> may also be defined as the largest angle between two surface lines of the cone <NUM> lying in the same plane as the central axis <NUM>. The opening angle <NUM> may be between <NUM>° and <NUM>°, such as between <NUM>° and <NUM>°. The opening angle may for example, be selected to be <NUM>°, <NUM>° or <NUM>°.

<FIG> shows the instrument tip <NUM> arranged inside the cone-shaped calibration structure <NUM> of <FIG>. As shown in <FIG>, the cone <NUM> is a circular cone, which means a plane perpendicular to the central axis <NUM> intersects the cone not in an oval but a circle. Consequently, the spherically shaped surface portion <NUM> abuts against the cone <NUM> in a circular contact region. <FIG> shows a top view of the cone <NUM> shown in <FIG> and the circular contact region <NUM>. In the top view, a centre of the circular contact region <NUM> aligns with the apex <NUM> and therefore with the central axis <NUM>. Due to the rotational symmetry of the contact region <NUM> and the spherically shaped surface portion <NUM>, the centre point <NUM> of the spherically shaped surface portion <NUM> is centred by the cone <NUM> onto the central axis <NUM>. The centre point <NUM> is arranged on the central axis <NUM> independently of the radius <NUM> of the surface portion <NUM> (as long as the surface portion <NUM> fits into the cone <NUM>). However, the radius <NUM> correlates with a distance of the centre point <NUM> relative to the apex <NUM> of the cone <NUM>. A smaller radius <NUM> of the surface portion <NUM> results in a shorter distance between the centre point <NUM> and the apex <NUM> compared to a larger radius <NUM> of the surface portion <NUM> that results in a larger distance between the centre point <NUM> and the apex <NUM>.

The centring function of the calibration structure <NUM> does not necessarily require a cone shaped opening. Alternatively, the calibration structure <NUM> can have an opening with the shape of a regular pyramid, which means that a plane perpendicular to a central axis of the pyramid intersects the pyramid in a regular polygon (with equal side lengths and inner angles). As an example, the pyramid can have three, four, five, or more sides. <FIG> shows a pyramidal calibration structure <NUM> with an inverted regular pyramid with three sides. <FIG> shows a top view of the pyramid of the calibration structure <NUM> and three contact regions <NUM>.

<FIG> shows another example of a pyramidal calibration structure <NUM> with an inverted regular pyramid with six sides. <FIG> shows a top view of the pyramid of the calibration structure <NUM> and six contact regions <NUM>. The contact regions of the pyramid are positioned along a circle with a centre point that is arranged on a central axis <NUM> of the pyramid. For a pyramid, the opening angle is defined as twice the angle between a pyramid side and the central axis <NUM>. In case of a pyramid with an even amount of sides, the opening angle is also the angle between two opposite pyramid sides.

A calibration structure <NUM> in the shape of a cone or a pyramid with at least three sides, such as described above, results in a circular contact region or at least three contact regions that confine the centre point <NUM> of the spherically shaped surface portion <NUM> onto a single point.

The various calibration structures <NUM> described herein are capable of receiving the instrument tip <NUM> and are configured to cooperate with the spherically shaped surface portion <NUM> so as to guide a tilting movement of the instrument tip <NUM> around the centre point <NUM> of the spherically shaped surface portion <NUM>. In the process of guiding the tilting movement, the spherically shaped surface portion <NUM> slides along the calibration structure <NUM>. Therefore, the calibration structure <NUM> preferably comprises a hard material with a Young's modulus larger than <NUM> GPa such as ceramics or metal (e.g., stainless steel).

As can be seen if <FIG> and <FIG>, the tracker of the calibration device <NUM> is arranged in a predetermined relationship relative to the calibration structure <NUM>. The predetermined relationship may be defined by a pose (i.e., orientation and position) or position of the apex <NUM> relative to the first tracker <NUM> of the calibration structure. The predetermined relationship may, for example, be defined as a matrix transformation or vector in a coordinate system <NUM> (see <FIG>) of the tracking system <NUM> that maps a pose or position of the apex <NUM> onto the first tracker <NUM> (or vice versa). Alternatively, or additionally, the surgical navigation system <NUM> may have access to geometrical properties (e.g., a digital model) of the calibration device <NUM>.

As will be described below, the calibration device <NUM> and similar calibration devices can be used for determining the radius <NUM> of the spherically shaped surface portion <NUM>. Based on the radius <NUM> thus determined, in optional subsequent steps, display instructions can then be generated during a later surgical procedure to cause a display to output a visual representation indicative of the determined radius <NUM> relative to image data of a patient.

<FIG> shows a flow diagram <NUM> of a first embodiment of a computer-implemented method for determining a radius <NUM> of the spherically shaped surface portion <NUM> of the tip <NUM> of the surgical instrument <NUM> using the calibration device <NUM>.

The method comprises determining, in step <NUM>, a pose of the first tracker <NUM> as associated with the calibration device <NUM>. The pose of the first tracker <NUM> comprises a position and orientation of the first tracker <NUM> and may be determined in the coordinate system <NUM> of the tracking system <NUM>. Any technique known in the prior art may be used for determining the pose of the tracker <NUM>. For optical tracking, a common approach is to capture one or more images of the reflective markers of the tracker <NUM> and determine the pose based on a known geometric arrangement of the markers relative to each other (<FIG>). For electromagnetic tracking, a common approach is for a field generator of the surgical navigation system <NUM> to generate an electric field that induces currents in coils constituting the tracker <NUM> (<FIG>). Based on a measurement of the induced currents, the pose of the first tracker <NUM> may be determined.

The method further comprises determining, in step <NUM>, positional data of the second tracker <NUM> associated with the surgical instrument <NUM>, referred to as instrument tracker <NUM> hereinafter (see <FIG>), for different tilting positions of the surgical instrument <NUM> while the spherically shaped surface portion <NUM> remains in abutment with the calibration structure <NUM>. The positional data may comprise at least two different tilting poses of the instrument tracker <NUM> for the different tilting positions and/or at least four different positions of the instrument tracker <NUM> for the different tilting positions.

<FIG> shows examples of three different tilting positions of the surgical instrument <NUM> while the spherically shaped surface portion <NUM> remains in abutment with the calibration structure <NUM>. The different tilting positions of the surgical instrument <NUM> cause the instrument tracker <NUM> to move along a sphere around the centre point <NUM>. The position and orientation of the first tracker <NUM> coupled to the calibration device <NUM> is, on the other hand, not affected by the different tilting positions of the surgical instrument <NUM>.

The method optionally comprises generating user instructions for displaying on a display of the surgical navigation system <NUM> (or of another computing device communicatively connected with the surgical navigation system <NUM>) instructions to tilt the surgical instrument <NUM> for calibration purposes. Such user instructions will initially request the user <NUM> to start moving the surgical instrument <NUM> for acquisition of pose or position data and will inform him or her once sufficient data for radius calculation have been acquired.

The method further comprises determining, in step <NUM>, a position of the centre point <NUM> relative to the second tracker <NUM> based on the positional data.

According to geometrical principles, the radius <NUM> can be determined based on the position of the centre point <NUM> of the instrument tip <NUM>. The positional data acquired for the instrument tracker <NUM> can be used in this regard to determine a position of the centre point <NUM> of the spherically shaped surface portion <NUM>. Depending on whether the positional data comprises poses of the instrument tracker <NUM> or only positions of the instrument tracker <NUM>, two different approaches can be performed in order to determine the position of the centre point <NUM>.

In the first approach for determining the position of the centre point <NUM>, the positional data comprises at least two different poses of the instrument tracker <NUM> for the different tilting positions. <FIG> shows a side view of the spherically shaped surface portion <NUM> in abutment with the calibration structure <NUM>. While the instrument tip <NUM> remains in abutment with calibration structure <NUM>, the calibration structure <NUM> guides tilting of the instrument tip <NUM> (and, thus, of the surgical instrument <NUM> and the instrument tracker <NUM>) around the centre point <NUM>. Therefore, two different poses of the instrument tracker <NUM> for two different tilting positions differ (at least partly) in a rotation around the centre point <NUM>. The position of the centre point <NUM> may be determined based on a transformation comprising a rotational transformation that maps one of the two poses onto the other pose. The position of centre point <NUM> is a position of unity (i.e., the only position unaltered by the transformation) of the rotation transformation.

Another way to determine the position of the centre point <NUM> based on the two poses is to determine for each marker of the instrument tracker <NUM> a linear vector that translates the marker between the two poses. For each translation vector a halfway point is further determined that is arranged in the centre between the positions of the marker for each of the poses. Due to the poses being arranged on a sphere, a connection vector from the halfway point to the (yet unknown) centre point <NUM> is arranged orthogonally to the direction of the translation vector. Therefore, a scalar product between the connection vector and the translation vector is zero. This allows defining, for each reflective marker of the instrument tracker <NUM>, an equation that includes the position of the centre point <NUM> (in form of the connection vector). These equations can be solved for the position of the centre point <NUM>.

It should be noted that the calculations described above require at least two poses of the instrument tracker <NUM>. To increase the overall precisions, more than two poses may be captured, and determining the position of the centre point <NUM> may be performed with the more than two poses. A final position of the centre point <NUM> may be calculated from an average of multiple positions of the centre point <NUM> determined for the more than two poses of the instrument tracker <NUM>. Determining the centre point <NUM> on the basis of more than two poses generally decreases a statistical error of the calculation.

In the second approach, the positional data comprises at least four different positions of the instrument tracker <NUM> for the different tilting positions. When the surgical instrument <NUM> is tilted around the centre point <NUM>, the position of a centre of the instrument tracker <NUM> is moved on a sphere around the centre point <NUM>. A sphere can be defined by, and reconstructed from, four points of the sphere (not arranged in a common plane). Therefore, the four positions of the instrument tracker <NUM> contain enough information for determining the sphere and, consequently, the position of its centre point <NUM>. One way to determine the centre point <NUM> is to set up equations that define a distance (e.g., via Pythagorean equations) between the four tracker positions relative to the unknown point centre <NUM> and equate the distance to an unknown radius. The four equations include four unknown variables (i.e., three coordinates of the position of the centre point <NUM> and the radius) and therefore form a determined system that is mathematically solvable. It should be noted that the radius of the sphere in these equations is not the radius of the spherically shaped surface portion <NUM>, but the distance between the centre point <NUM> and the centre of the instrument tracker <NUM>. In order to reduce the statistical error of the calculation, the position of the centre point <NUM> may of course be determined based on more than four positions of the instrument tracker <NUM>.

It should be noted that both approaches are not exclusive to each other. For example, in the case that the positional data comprise more than three poses of the instrument tracker <NUM>, both approaches can be applied simultaneously. The position of centre point <NUM> may be determined from the positions obtained by both approaches (e.g., applying an averaging algorithm).

The method further comprises determining, in step <NUM>, the radius <NUM> of the spherically shaped surface portion <NUM> based on the position of the centre point <NUM>, the first pose of the first tracker <NUM>, the predetermined relationship between the first tracker <NUM> and the calibration structure <NUM>, and the opening angle <NUM> of the calibration structure <NUM>.

Based on the first pose of the first tracker <NUM> of the calibration device <NUM> and the predetermined relationship between the first tracker <NUM> and the calibration structure <NUM>, a position of the apex <NUM> of the calibration structure <NUM> may be determined. <FIG> shows geometrical relationships between the tracking system <NUM>, the surgical instrument <NUM>, and the calibration structure <NUM>. The geometrical relationships are in the following described as transformations that map one point in space onto another point in space. The transformations may, for example, be defined as mathematical transformations such as a matrix (for translating a pose or position) or a vector (for translating a position). It should be noted that any transformation as described herein may alternatively be defined as its inverse transformation.

The tracking system <NUM> is configured to determine a pose of the instrument tracker <NUM> in form of a first transformation <NUM> and a pose of the first tracker <NUM> of the calibration device <NUM> in form of a second transformation <NUM>. The first and second transformations <NUM>, <NUM> may be defined as transformations from centres of each of the two trackers <NUM>, <NUM> to an origin <NUM> of the coordinate system <NUM> of the tracking system <NUM>. The origin <NUM> may, for example, be positioned in an optical centre of the camera of the tracking system <NUM>. In the case of a stereo camera with two camera units, the origin <NUM> may be positioned in the optical centre of one of the two camera units or positioned between the optical centres of the two camera units.

The relationship between the first tracker <NUM> of the calibration device <NUM> and the calibration structure <NUM> shown in <FIG> may be a geometric relationship as defined by a third transformation <NUM> that maps a position of the apex <NUM> onto the centre of that tracker <NUM>. A fourth transformation <NUM> can be defined based on the determined position of the centre point <NUM> and a pose determined for the instrument tracker <NUM>.

Further, a fifth transformation <NUM> can be defined that maps the position of the centre point <NUM> onto the apex <NUM>. As can be seen in <FIG>, the first, second, third, fourth, and fifth transformations <NUM>, <NUM>, <NUM>, <NUM>, <NUM> jointly describe a closed circle of transformations. Consequently, the fifth transformation <NUM> can be determined by a sum of the first, second, third, and fourth transformations <NUM>, <NUM>, <NUM>, <NUM>. Based on the determined fifth transformation <NUM>, a centre distance <NUM> between the position of the apex <NUM> and the position of the centre point <NUM> can be calculated. The centre distance <NUM> thus calculated can be used to determine the radius <NUM>, as described below.

<FIG> shows an enlarged view of the spherically shaped surface portion <NUM> in abutment with the calibration structure <NUM> and geometric parameters relevant for determining the radius <NUM>. As can be seen in <FIG>, the radius <NUM> of the spherically shaped surface portion <NUM> can be calculated by multiplying the centre distance <NUM> with a sinus of half of the opening angle <NUM>. It should be noted that in <FIG>, the centre distance <NUM> can be defined as the distance between the centre point <NUM> and the apex <NUM>, because the calibration structure <NUM> has an apex <NUM>. In case the calibration structure <NUM> has a shape without an apex <NUM> such as a frustum (i.e., a truncated pyramid or cone), the centre distance <NUM> may generally be defined as a distance between the position of the centre point <NUM> and an imaginary point ("imaginary apex") relative to which the opening angle <NUM> is defined.

The first method embodiment illustrated in <FIG> in some implementations includes pivoting the surgical instrument <NUM> in the calibration structure <NUM> to arrive at different tilting positions, although the surgical instrument <NUM> could also be removed from the calibration structure <NUM> after a first tilting position has been recorded and placed therein a second time to record of a second tiling position, and so on. If pivoting is used to arrive the different tiling positions, there is a risk that a sharp instrument tip <NUM> will damage (e.g., cut into) the calibration structure <NUM>. For this reason, in certain implementations a radius determination approach may be desired that does not necessarily rely on a pivoting instrument movement, as will now be described with reference to another calibration device example.

<FIG> shows a second example of a calibration device <NUM> with a first tracker <NUM> and a calibration structure <NUM> defining an opening angle <NUM> (as generally described above with reference to the first calibration device example). The calibration structure <NUM> shown in <FIG> is formed as a cone-shaped surface opening in a plate-shaped body <NUM>. The calibration structure <NUM> defines a real or imaginary first reference point <NUM> relative to which the opening angle <NUM> is defined. In the example depicted in <FIG>, the calibration structure <NUM> is a cone and the first reference point <NUM> is located at the apex of the cone. In the case of a truncated cone, the first reference point <NUM> is located at a position where a non-truncated version of the truncated cone would have an apex. The calibration structure <NUM> has a central axis <NUM> that forms a bisector of the opening angle <NUM>. The first tracker <NUM> is trackable by the tracking system <NUM> of the surgical navigation system <NUM>.

The first tracker <NUM> is arranged in a first predetermined relationship relative to the first reference point <NUM>. The first predetermined relationship may be defined by a position of the first reference point <NUM> relative to first tracker <NUM> of the calibration structure <NUM> (e.g., as described above with reference to <FIG>).

The calibration device <NUM> further comprises a flat calibration surface <NUM>. The calibration surface <NUM> is configured for abutment with the spherically shaped surface portion <NUM> of the instrument tip <NUM>. The calibration surface <NUM> defines a surface normal <NUM> that is arranged perpendicular to the calibration surface <NUM>. For the calibration device <NUM> depicted in <FIG>, the central axis <NUM> and surface normal <NUM> are arranged parallel to each other. Alternatively, the central axis <NUM> and the surface normal <NUM> may be arranged at any other angle relative to each other, such as <NUM>°, <NUM>°, <NUM>°, <NUM>°, <NUM>° (see the <NUM>° example as depicted in <FIG>).

The calibration surface <NUM> is arranged in a second predetermined relationship relative to the first tracker <NUM> of the calibration device <NUM>. The second predetermined relationship may comprise a transformation of the first tracker <NUM> onto a point of the calibration surface <NUM>. For example, the second predetermined relationship may comprise (or define) a transformation of the pose of the first tracker <NUM> onto a centre point (or corner point) of the reference surface <NUM>, wherein at the centre point is defined a vector perpendicular to the reference surface <NUM> or a coordinate system defining two (non-parallel) axes that are arranged parallel to the reference surface <NUM>. An intermittent geometrical relationship between the calibration surface <NUM> and the first reference point <NUM> may be provided. The second predetermined relationship may then be determined based on the first predetermined relationship and the intermittent geometrical relationship.

The first example of the calibration device <NUM> depicted in <FIG> and the second example of the calibration device <NUM> depicted in <FIG> essentially differ by the calibration surface <NUM>. It should be noted that the first method embodiment is compatible with a calibration device <NUM> that comprises a calibration surface <NUM>, as the calibration surface <NUM> does not prohibit any of the steps <NUM> to <NUM> of the method according to the first embodiment. Similarly, the calibration device <NUM> shown in <FIG> also comprises flat surfaces, such as a surface around the calibration structure <NUM>, which can be used as calibration surface for the purpose of the second method embodiment. Therefore, the different examples of calibration devices <NUM> described herein are not necessarily exclusive to one of the method embodiments described therewith, but may be compatible with both method embodiments.

The calibration surface <NUM> may be a specific marking on the calibration device <NUM>. The marking may be printed (e.g., as a circle, point, cross or, as illustrated in <FIG>, as a rectangle). The calibration surface <NUM> may be recessed into the plate-shaped body <NUM> of the calibration device (such as depicted in <FIG>) or may be at least partially surrounded by a wall in order to prevent an abutting tip <NUM> from slipping away from the calibration surface <NUM>.

<FIG> shows a flow diagram <NUM> of a second embodiment of a computer-implemented method for determining a radius <NUM> of the spherically shaped surface portion <NUM> of the tip <NUM> of the surgical instrument <NUM> using the second example of the calibration device <NUM> as illustrated in <FIG>.

The method illustrated in <FIG> comprises determining, in step <NUM>, a first pose of the first tracker <NUM> and a second pose of the second tracker <NUM> (subsequently called instrument tracker <NUM>), while the spherically shaped surface portion <NUM> is in abutment with the calibration structure <NUM>. Both poses may be determined substantially at the same point in time.

<FIG> shows the spherically shaped surface portion <NUM> in abutment with the calibration structure <NUM>. <FIG> shows the geometrical relationship between the tracking system <NUM>, the first tracker <NUM>, the instrument tracker <NUM>, and the first reference point <NUM>. The tracking system <NUM> may be configured to determine the first pose of the first tracker <NUM> in form of a first transformation <NUM> and the second pose of the instrument tracker <NUM> in form of a second transformation <NUM>. The first and second transformations <NUM>, <NUM> may be defined as transformations from centres of each of the two trackers <NUM>, <NUM> to an origin <NUM> of the coordinate system <NUM> of the tracking system <NUM>. The origin <NUM> may, for example, be positioned in an optical centre of the camera of the tracking system <NUM>. In the case of a stereo camera, the origin <NUM> may be positioned in the optical centre of one of the two camera units s or positioned between the optical centres of the two camera units.

The method further comprises determining, in step <NUM>, a reference position <NUM> of the first reference point <NUM> relative to the instrument tracker <NUM> when the first tracker <NUM> is in the first pose and the second tracker <NUM> is in the second pose based on the first pose, the second pose, and the first predetermined relationship <NUM>.

The position of the first reference point <NUM> can be located based on the first pose of the first tracker <NUM> and the first predetermined relationship. For example, the position of the first reference point <NUM> may be determined based on a combination of matrix transformations or vector sums of the first transformation <NUM> and the first predetermined relationship <NUM>.

For example, in the case of translations in form of vectors and using the example depicted in <FIG>, the reference position <NUM> can be determined from a sum of vectors of the first transformation <NUM>, the second transformation <NUM>, and the first predetermined relationship <NUM>. Considering the vector directions shown in <FIG>, the reference position <NUM> can be determined by subtracting a vector of the second transformation <NUM> from a sum of vectors of the first transformation <NUM> and the first predetermined relationship <NUM>. Since a vector direction can generally be defined in either way, the algebraic signs in the sum changes with different definitions of vector directions.

The method further comprises determining, in step <NUM>, a third pose of the first tracker <NUM> and a fourth pose of the instrument tracker <NUM> while the spherically shaped surface portion <NUM> is in abutment with the calibration surface <NUM>. Both poses may be determined substantially at the same point in time.

<FIG> shows the spherically shaped surface portion <NUM> in abutment with the calibration surface <NUM>. <FIG> shows the geometrical relationship between the tracking system <NUM>, the first tracker <NUM>, the instrument tracker <NUM>, the first reference point <NUM>, a second reference point <NUM>, the second predetermined relationship <NUM> and the reference surface <NUM>. The tracking system <NUM> may be configured to determine the third pose of the first tracker <NUM> in form of a third transformation <NUM> and the fourth pose of the instrument tracker <NUM> in form of a fourth transformation <NUM>.

It should be noted that the first pose and the third pose may be at least essentially identical. This may be the case, for example, when the calibration device <NUM> is fixedly arranged relative to the tracking system <NUM> (e.g., on a table) and the surgical instrument <NUM> is moved by the user relative to the calibration device <NUM>. Similarly, the second and fourth pose of the instrument tracker <NUM> may be at least essentially identical. This may be the case, for example, when the surgical instrument <NUM> (for example in form of a robotic arm) is fixedly arranged relative to the tracking system <NUM> and the calibration device <NUM> is moved by the user relative to the calibration device <NUM>. Furthermore, the first pose may not be identical to the third pose and the second pose may not be identical to the fourth pose. This may be the case, for example, when the surgical instrument <NUM> and the calibration device <NUM> are both manually moved relative to each other.

The method also comprises determining, in step <NUM>, the radius <NUM> of the spherically shaped surface portion <NUM> based on the third pose, the second predetermined relationship <NUM>, the reference position <NUM>, the fourth pose, and the opening angle <NUM>.

The third pose, the second predetermined relationship <NUM>, the reference position <NUM>, the fourth pose, and the opening angle <NUM> form five parameters that are sufficient for determining the radius <NUM>. In the following, determining the radius <NUM> will be described in an intuitively accessible way. However, it should be understood, that the five parameters, or parameters derived therefrom, may be combined or processed in any other way that allows determining the radius <NUM>.

The reference position <NUM> may be combined with the third pose in order to determine the second reference point <NUM>. The second reference point <NUM> may be determined, for example, by a vector sum or matrix product of the fourth transformation <NUM> and the reference position <NUM>. Alternatively, the first reference point <NUM> may be registered with the instrument tracker <NUM>, while the instrument tracker <NUM> is in the second pose such that the registered first reference point <NUM> aligns with the second reference point <NUM> when the instrument tracker <NUM> is in the fourth pose.

The reference surface <NUM> can be constructed based on the third pose of the first tracker <NUM> and the second predetermined relationship <NUM>. The reference surface <NUM> may be similarly reconstructed using a vector sum or matrix product of the third transformation <NUM> and the second predetermined relationship <NUM>.

The radius <NUM> can be determined using a reference distance between the reference surface <NUM> and the second reference point <NUM>. In order to better understand the correlation between the reference distance and the radius <NUM>, the geometrical relationships of components involved in determining the radius <NUM> are discussed first.

<FIG> shows geometric relationships between the radius <NUM>, the first reference point <NUM>, the spherically shaped surface portion <NUM>, and the opening angle <NUM>. The spherically shaped surface portion <NUM> abuts at an abutment point <NUM> against a surface of the calibration structure <NUM>. The centre point <NUM>, the abutment point <NUM>, and the first reference point <NUM> form a triangle with a <NUM>° angle at the abutment point <NUM> and half the opening angle <NUM> at the first reference point <NUM>. The distance between the centre point <NUM> and the first reference point <NUM> is a sum of the radius <NUM> and a reference distance <NUM> between the first reference point <NUM> and (a closest point of) the spherically shaped surface portion <NUM>. This geometrical relationship in the triangle can be described with the following equation: <MAT> with r as the radius <NUM>, d as the reference distance <NUM>, and θ as the opening angle <NUM>. Solving equation (<NUM>) for r results in the following equation: <MAT>.

Since the opening angle <NUM> is one of the five known parameters, the radius <NUM> can be determined if the reference distance <NUM> is known. The reference distance <NUM> is defined by a distance between the first reference point <NUM> and the spherically shaped surface portion <NUM>. Since the first reference point <NUM> and the second reference point <NUM> are both located at the reference distance <NUM> relative to the instrument tracker <NUM>, the distance between the second reference point <NUM> and the spherically shaped surface portion <NUM> (when in abutment with the calibration surface <NUM>) is the same as the reference distance <NUM>. The equal distance is indicated by dashed lines in <FIG>.

As described above, the calibration surface <NUM> can be determined based on the third pose and the second predetermined relationship <NUM> and the second reference point <NUM> can be determined based on the fourth pose and the reference distance <NUM>. Therefore, the reference distance <NUM> can be determined by a distance between the calibration surface <NUM> and the second reference point <NUM> as shown in <FIG>. The distance can be determined based on common mathematical equations for determining a distance between a plane and a point. One example is to define an arbitrary vector between the second reference point <NUM> and a point on the calibration surface <NUM>, projecting the arbitrary vector onto a surface normal of the calibration surface <NUM> and determining the length of the projected vector. The radius <NUM> can then be determined using equation (<NUM>).

As pointed out earlier, the approach for determining the radius <NUM> presented above is described in an intuitively accessible way. Since the radius <NUM> can be determined mathematically based on the above five parameters, the radius <NUM> can be determined by only using equations without requiring an actual geometrical construction in a coordinate system.

The second method embodiment for determining the radius <NUM> requires not pivoting of the instrument tip <NUM> inside the calibration structure <NUM> and therefore reduces the risk of damages, such as abrasion of the instrument tip <NUM> and of the calibration structure <NUM>.

The method of the second embodiment may optionally comprise determining the position of the centre point <NUM>. To this end, the method may include determining the second reference point <NUM> based on the fourth pose and the reference position <NUM>, as described above.

<FIG> shows a geometrical relationship between the second reference point <NUM>, the calibration surface <NUM>, the radius <NUM>, and the centre point <NUM>. The method may further comprise determining a reference axis <NUM> through the second reference point <NUM> and perpendicular to the calibration surface <NUM>. The reference axis <NUM> may be defined by any mathematical term that defines a position and orientation of a line, such as a vector sum of a position vector (e.g., the second reference point <NUM>) and an orientation vector (e.g., a vector perpendicular to the calibration surface <NUM>). The method may further comprise determining a position of the centre point <NUM> of the spherically shaped surface portion <NUM> relative to the second tracker <NUM> along the reference axis <NUM> at a distance of the radius <NUM> from the reference surface <NUM> in a direction away from the calibration device <NUM>. When the instrument tracker is in the fourth pose, the spherical surface portion <NUM> abuts against the calibration surface <NUM>. Therefore, the centre point <NUM> is located at a distance of the radius <NUM> away from the calibration surface <NUM>. The centre point <NUM> can be determined, for example, at an intersection of the reference axis <NUM> with a plane that is parallel to the calibration surface <NUM> and spaced at a distance of the radius <NUM> away from the calibration surface <NUM>. A different way to determine the centre position by adding a vector with the orientation of the reference axis <NUM> and the combined distance of the radius <NUM> and the reference distance <NUM> to a position vector that locates the second reference point <NUM>.

The radius determination approach described above is most accurate for determining the radius <NUM>, and optionally, the position of the centre point <NUM>, when the surgical instrument <NUM> is oriented identically relative the central axis <NUM> (when abutted against the calibration structure <NUM>) and the surface normal <NUM> (when abutted against the calibration surface <NUM>). Different orientations of the surgical instrument <NUM> in the two abutment positions may result in a less accurate result for the radius <NUM>. Such identical or different orientations are now explained with reference to <FIG>.

<FIG> shows an example of the calibration device <NUM>, wherein the central axis <NUM> of the calibration structure <NUM> is arranged parallel to the surface normal <NUM> of the calibration surface <NUM>. A surface angle may define an angular difference between a normal vector of the calibration surface <NUM> (i.e., the surface normal <NUM>) and a bisector of the opening angle (i.e., the central axis <NUM>). The surface angle of the example shown in <FIG> is zero.

<FIG> shows an example of the calibration device <NUM>, wherein the central axis <NUM> of the calibration structure <NUM> is not arranged parallel to the surface normal <NUM> of the calibration surface. The surface angle of the example shown in <FIG> is <NUM>° and therefore not zero.

<FIG> shows the example of the calibration device <NUM> depicted in <FIG>, wherein the orientation of the instrument tip <NUM>, and therefore also for the instrument tracker <NUM>, is identical for the second pose and the fourth pose of the instrument tracker <NUM>. The second pose may define a first calibration orientation of the second tracker <NUM> and the fourth pose may define a second calibration orientation of the second tracker <NUM>, wherein a reorientation angle defines an angular difference between the first calibration orientation and the second calibration orientation. In the example shown in <FIG>, the first calibration orientation and the second calibration orientation are identical. Therefore, the reorientation angle is zero.

<FIG> shows the example of the calibration device <NUM> depicted in <FIG>, wherein an orientation of the instrument tip <NUM> and consequently the instrument tracker <NUM> does not change relative to the central axis <NUM> and the surface normal <NUM>. However, as the central axis <NUM> and the surface normal <NUM> are not arranged parallel, the first calibration orientation and the second calibration orientation are not identical and the reorientation angle is not zero.

Therefore, the approach suggested herein may further comprise determining a pivot angle based on the reorientation angle and the surface angle. For example, the pivot angle may be defined as a polar angle component in regard to the surface normal <NUM> of a sum of the reorientation angle and the surface angle. Alternatively, the pivot angle may be defined as a polar angle relative to the surface normal <NUM> that is required in order to rotate the second calibration orientation relative to the surface normal <NUM> such that the orientation of the second calibration orientation relative to the surface normal <NUM> is identical to the orientation of the first calibration orientation relative to the central axis <NUM>. In the example shown in <FIG>, the reorientation angle and the surface angle are both zero. Therefore, the sum of the reorientation angle and the surface angle is also zero. Consequently, the pivot angle is also zero.

Another way to determine the pivot angle is to determine a first rotation transformation that rotates the surface normal <NUM> onto the central axis <NUM>, and to determine a second rotation transformation that rotates the first calibration orientation onto the second orientation calibration. A combined rotation transformation obtained from a product of the first and second rotation transformation is applied to the surface normal <NUM>, wherein the pivot angle can be determined from the resulting rotation of the surface normal <NUM>.

In <FIG>, the first calibration orientation and the second calibration orientation are not identical with a reorientation angle of <NUM>° and that is directed clockwise. Similarly, the surface angle is <NUM>° and directed counter-clockwise. Therefore, the reorientation angle and the surface angle cancel each other out, such that the sum of the two angles is zero. As a result, the pivot angle in the example shown in <FIG> is also zero.

<FIG> shows the example of the calibration device <NUM> depicted in <FIG>, wherein an orientation of the instrument tip <NUM> and consequently the instrument tracker <NUM> changes relative to the central axis <NUM> and the surface normal <NUM>.

Therefore, the reorientation angle is not zero. Since the central axis <NUM> and the surface normal <NUM> are parallel, the surface angle is zero. The sum of the surface angle and the reorientation angle is the reorientation angle. In the example shown in <FIG>, the reorientation angle only has a polar angle component and no azimuth angle component in regards to the surface normal <NUM>. Therefore, the reorientation angle is also the pivot angle.

<FIG> shows the example of the calibration device <NUM> depicted in <FIG>, wherein the reorientation angle and surface angle are both not zero and do not cancel each other out. In the example depicted in <FIG>, the sum of the reorientation angle and the surface angle only has a polar angle component and no azimuth angle component in regard to the surface normal <NUM>. Therefore, the pivot angle is the sum of the reorientation angle and the surface angle.

In summary, <FIG> show examples in which the pivot angle is zero and <FIG> show examples in which the pivot angle is not zero. Therefore, the approach described above for determining the radius <NUM> and the position of the centre point <NUM> yield accurate results for the examples shown in <FIG>, but would yield results with errors that increase with the pivot angle for the examples shown in <FIG>.

The error can be minimized by instructing the user to orient the surgical instrument <NUM> in a way that minimizes the pivot angle. Corresponding instructions may be output to a user by the computer system <NUM> (see <FIG>), e.g., as part of a radius calibration procedure. Alternatively, or additionally, a guiding device can be provided that guides movement of the surgical instrument <NUM> such that the pivot angle is minimized (e.g., by a funnel or a structure with an opening).

Furthermore, the second method embodiment may comprise determining the pivot angle and generating output information related to the pivot angle. The output information may include at least one the determined pivot angle and information (e.g., textual information) about the pivot angle exceeding a pivot angle threshold. The pivot angle threshold may be higher than <NUM>°, <NUM>°, <NUM>°, <NUM>°, <NUM>° and <NUM>°. The pivot angle threshold may be <NUM>° or lower, for example <NUM>° or lower. The output information may comprise re-calibration instructions (e.g., a request to repeat the measurement with a smaller pivot angle).

The method may comprise determining the radius <NUM> also on the basis of an axis pose of an instrument axis relative to the instrument tracker <NUM> that extends through the centre point <NUM>. The axis pose may be predetermined or determined in a separate step of the method. For example, the axis pose may be determined based on tracking data obtained from the instrument tracker <NUM> while the surgical instrument <NUM> is rotated about the instrument axis.

Another approach is for the step of determining the radius <NUM> to further be based on the pivot angle. For example, equation (<NUM>) described above may be modified to further include the pivot angle. <FIG> shows the geometrical relationship between the radius <NUM>, the reference distance <NUM> and the pivot angle <NUM>, which may form the basis for a modified equation.

In case the pivot angle <NUM> were zero, a hypothetical second reference point <NUM> would be located along a line through the centre point <NUM> and perpendicular to the calibration surface <NUM> and at a target distance <NUM> equal to the distance between the first reference point <NUM> and the spherically shaped surface portion <NUM> when in abutment with the calibration structure <NUM>. However, in the case the pivot angle <NUM> is not zero, the second reference point <NUM> is rotated around the centre point <NUM> by the pivot angle. As a result, the reference distance <NUM> is shortened. If the shorter reference distance <NUM> were to be used in equation (<NUM>), a radius <NUM> shorter than the actual radius <NUM> would be obtained.

Since the position of the centre point <NUM> and the second reference point <NUM> relative to the instrument tracker <NUM> is independent from the pivot angle, the distance between the centre point <NUM> and the second reference point <NUM> is unchanged. From the geometrical relationship depicted in <FIG> can be obtained the following equation: <MAT> with r as the radius <NUM>, d is the determined reference distance <NUM>, h is a hypothetical reference distance <NUM> between the calibration surface <NUM> and the hypothetical second reference point <NUM>, and a is the pivot angle <NUM>.

Equation <NUM> also describes the geometrical relationship when using the hypothetical reference distance <NUM> for d. For the sake of better legibility, equation (<NUM>) can be simplified to <MAT>.

Inserting equation (<NUM>) into equation (<NUM>) results in <MAT>.

Solving equation (<NUM>) for h results in <MAT>.

Combining equation (<NUM>) with equation (<NUM>) results in the following equation for determining the radius <NUM>: <MAT>.

Equation (<NUM>) allows determining the radius <NUM> based on the reference distance <NUM>, the opening angle <NUM> and the pivot angle <NUM>. These three parameters are known or can be determined as described above.

For larger pivot angles <NUM> (in particular when the pivot angle is equal to <NUM>° minus half the opening angle <NUM>), the second reference point <NUM> is located on or close to the reference surface <NUM>. In such a case, the reference distance <NUM> may shorten to such a small length that a finite resolution of the tracking system <NUM> may not be able to accurately determine the reference distance <NUM>. Therefore, the method may comprise generating output information about the pivot angle exceeding a pivot angle threshold. The pivot angle threshold may be below <NUM>°, <NUM>°, <NUM>°, or <NUM>°. The output information may comprise instructions to repeat the measurement with a smaller pivot angle.

Since equation (<NUM>) allows determining the radius <NUM> exactly, the position of the centre point <NUM> can also be determined exactly as will be described below.

As shown in <FIG>, in the case of a pivot angle that is zero, the centre point <NUM> is located on a reference axis <NUM> that is arranged perpendicular to the calibration surface <NUM>. In the case that the pivot angle is not zero, the positions of the centre point <NUM> and the second reference point <NUM> relative to the instrument tracker <NUM> is still unchanged. Therefore, the reference axis <NUM> can still be defined through the centre point <NUM> and the second reference point <NUM>. However, the reference axis <NUM> is then not arranged perpendicular to the calibration surface <NUM>, but rotated by the pivot angle. Such a construction can be used to determine the position of the centre point <NUM> as described below.

<FIG> shows the geometrical relationship of the second reference point <NUM>, the centre point <NUM>, the reference axis <NUM>, and the pivot angle <NUM>. The second method embodiment may comprise defining a reference axis <NUM> that extends through the second reference point <NUM> and is initially arranged perpendicular to the calibration surface <NUM>. The method may also comprise rotating the reference axis <NUM> around the second reference point <NUM> by the pivot angle <NUM>. The method may further comprise determining the position of the centre point <NUM> along the reference axis <NUM> at a distance of the radius <NUM> from the reference surface <NUM> in a direction away from the calibration device <NUM>. As can be seen in <FIG>, the distance of the radius <NUM> is not measured along the reference axis <NUM>, but perpendicular to the calibration surface <NUM>. The method may further comprise reconstructing the radius <NUM> around the centre point <NUM>, as shown in <FIG>.

It should be noted that the way to determine the position of the centre point <NUM> described above is an intuitively accessible way and the position may be alternatively determined in a different way such as an equation-based approach that requires no actual construction of axes and points.

Generally, the method of the second embodiment may comprise determining the position of the centre point <NUM> based on the third pose, the second predetermined relationship <NUM>, the reference position <NUM>, the fourth pose, the opening angle <NUM>, and the radius <NUM> and optionally in the case that the central axis <NUM> and surface normal <NUM> are not parallel, the orientation of the central axis <NUM> and the surface normal <NUM>. For example, the method may comprise determining the position of the centre point <NUM> based on the second reference point <NUM> (which can be determined based on the fourth pose and the reference position <NUM>), the calibration surface <NUM> (which can be determined based on the third pose and the second predetermined relationship), the pivot angle (which can be determined based on the second pose and the fourth pose, and, optionally in the case that the central axis <NUM> and surface normal <NUM> are not parallel, the orientation of the central axis <NUM> and the surface normal <NUM>), and the radius <NUM>.

All method embodiments described above allow determining the radius <NUM> of the spherically shaped surface portion <NUM> and, optionally, determining the position of the centre point <NUM>. The method embodiments may optionally include further steps that use the radius <NUM> (and optionally the position of the centre point <NUM>) as will be described below.

For example, the methods embodiments may further include generating display instructions for displaying a visual representation of the radius <NUM> in a virtual space (e.g., on a display). As such, the methods may further comprise tracking, during a surgical procedure, a further tracker to register or track an image pose of image data of an object (e.g., a part of a patient anatomy) in the virtual space (e.g., defined by coordinates of the coordinate system <NUM> of the tracking system <NUM> or of a coordinate system of image data). <FIG> shows an enlarged view of a surgical scenario with the instrument tracker <NUM> and a patient tracker <NUM> being tracked by the tracking system <NUM>. The patient tracker <NUM> shown in <FIG> is coupled to an object <NUM> (in form of a vertebra) to be treated by the surgical instrument <NUM>. As explained above, also the vertebra <NUM> itself may constitute the patient tracker <NUM>.

The methods may also comprise tracking the instrument tracker <NUM> to track a position of the centre point <NUM> of the instrument tip <NUM> (that has been determined as explained above) in the virtual space based on the position of the centre point <NUM> relative to the instrument tracker <NUM>. For example, the position of the centre point <NUM> relative to the instrument tracker <NUM> may be described by the fourth transformation <NUM> (see <FIG>), the reference position <NUM> (see <FIG>) or otherwise. The position of the centre point <NUM> may then be tracked by tracking the instrument tracker <NUM> and applying the fourth transformation <NUM> or the reference position <NUM> onto the pose of a centre of the instrument tracker <NUM> thus determined.

As can be seen in <FIG>, the instrument tip <NUM> is in this example used to manipulate the vertebra <NUM> by burring or drilling a hole into the vertebra <NUM>. However, from the outside, the user <NUM> has only a limited view of the manipulation occurring inside the vertebra <NUM>. The methods thus may further comprise generating display instructions for displaying in the virtual space a visual representation indicative of the radius <NUM> relative to the image data of the vertebra <NUM>. The display instructions are generated based on the pose of the image data of the vertebra <NUM> in the virtual space, the position of the centre point <NUM> in the virtual space, and the radius <NUM> (possibly after a preceding image data registration as known in the art).

<FIG> shows a first example of a virtual space <NUM> with a visual representation <NUM> indicative of the radius <NUM> arranged relative to image data <NUM> of the vertebra <NUM> of <FIG>. The image data <NUM> may, for example, comprise a point cloud or polygon mesh captured using computer tomography, magnetic resonance imaging, or any other medical imaging procedure. The image data <NUM> can be arranged in the virtual space <NUM> based on the image pose of the image data, which was determined based on tracking the tracker <NUM> and a preceding registration. The visual representation <NUM> can be arranged and updated in the virtual space <NUM> based on the tracked instrument tracker <NUM>. Consequently, the image data <NUM> and the visual representation can be arranged relative to each other in the virtual space <NUM>. The virtual space <NUM> may be defined, for example, by a coordinate system of the tracking system <NUM> or a coordinate system of the image data <NUM>.

The exemplary visual representation <NUM> shown in <FIG> comprises a virtual centre point <NUM> at the position of the centre point <NUM> and a circle <NUM> around the centre point <NUM> with the radius <NUM> as determined during the calibration procedure. In some variants, the radius visualization may comprise an icon selected based on the determined radius <NUM> (e.g., an icon of the instrument tip <NUM>). Of course, in other examples, only the circle <NUM> or only a portion thereof may be visualized. Needless to say that the image data <NUM> and any radius indication may need to be converted to a common scale for visualization.

Through the vertebra extends a spinal cord <NUM> that is not to be touched by the instrument tip <NUM>. Since the visual representation <NUM> includes an indication of the radius <NUM>, the user <NUM> can see when the instrument tip <NUM> comes too close to the spinal cord <NUM> and is guided to adapt instrument movement accordingly. As the radius <NUM> has exactly been determined earlier, the corresponding visual guidance is very precise.

Optionally, the method embodiments may include generating display instructions for displaying a non-target region <NUM> in the image data <NUM> for which contact with the instrument <NUM> is to be avoided. In the example shown in <FIG>, the non-target region <NUM> is identical with the region of the spinal cord <NUM>. Alternatively, the non-target region may be larger than the spinal cord <NUM> or comprise a threshold region around the region of the spinal cord <NUM>. The method embodiments may comprise tracking the position of the radius <NUM> of the instrument tip <NUM> and outputting a warning when the tracked instrument tip <NUM> comes in contact with the non-target region <NUM> and/or the threshold region. The warning may be at least one of an acoustic, optical, and haptic warning.

<FIG> shows a second example of a virtual space <NUM> with a visual representation <NUM> indicative of the radius <NUM> arranged relative to image data <NUM> of the vertebra (see <FIG>). The visual representation <NUM> comprises the position of the centre point <NUM> and a radius indication <NUM> in form of a point arranged at a distance of the radius <NUM> from the centre point <NUM>. The radius indication <NUM> covers less area of the image data <NUM> of the vertebra, giving the user <NUM> a better view of the image data <NUM>. The radius indication <NUM> may be stationary (e.g., relative to an instrument axis <NUM> or the virtual space <NUM>). Alternatively, the method may comprise determining a movement direction of the instrument tip <NUM> and generating display instructions for which the radius indication <NUM> moves towards the determined movement direction of the instrument tip <NUM>. The radius indication <NUM> may be larger than a point.

As shown <FIG>, the visual representation <NUM> may further be indicative of the instrument axis <NUM>. A pose of the instrument axis <NUM> may be determined on the basis of tracking the instrument tracker <NUM> while the surgical instrument <NUM> is rotated about the instrument axis <NUM>. Alternatively, or additionally, the instrument axis <NUM> may be determined based on tracking the instrument tracker <NUM> and having access to a known predetermined spatial relationship between the instrument tracker <NUM> and the instrument axis <NUM>. The predetermined spatial relationship may be provided in form of a transformation that maps the pose of the instrument tracker <NUM> onto the pose of the instrument axis <NUM>. The pose of the instrument axis <NUM> can therefore be determined by tracking the instrument tracker <NUM> in order to obtain the pose of the instrument tracker <NUM> and applying the transformation onto the pose of the instrument tracker <NUM>.

<FIG> shows a third example of a virtual space <NUM> with a visual representation <NUM> of the instrument <NUM> arranged relative to image data <NUM> of an object in form of a bone surface. The visual representation <NUM> comprises the position of the centre point <NUM> (optional) and a sphere <NUM> around the centre point <NUM> with the determined radius <NUM>. Displaying the radius <NUM> in form of a three dimensional sphere <NUM> may be used when the image data <NUM> or a tissue manipulation progress is also displayed in a three dimensional space. Fig. 13C shows a tissue manipulation progress <NUM> determined for a path of the visual representation <NUM>. The tissue manipulation progress <NUM> may be determined based on the determined radius <NUM>, a tracking of the instrument tracker <NUM>, and the image data <NUM>.

The method embodiments may further comprise outputting, on a display, the determined radius <NUM> of the spherically shaped surface portion <NUM> of the instrument tip <NUM> as a numerical value. The user <NUM> may be requested to confirm the numerical value prior to the surgical procedure.

The method embodiments may further comprise displaying, on a display (e.g., of the tracking system <NUM> or surgical navigation system <NUM>), a visual representation of the instrument <NUM> arranged relative to the image data of the object. The visual representation of the instrument <NUM> may take the form of an icon.

The method embodiments may further comprise determining from a pre-determined list of radii a subset of radii that meet a similarity criterion with respect to the determined radius <NUM>. The pre-determined list of radii may comprise the radii of various instruments tips <NUM> the user may selectively attach to the instrument <NUM> or of various instruments <NUM> with different instrument tips <NUM>. The instrument tips <NUM> may differ in the tip radii and in the tip configurations (see <FIG>). The same radius may be associated with different tip configurations, and the same tip configuration may be associated with different radii. The list may have a length of <NUM>, <NUM> or more list entries.

The similarity criterion may comprise being a radius from the subset that differs by not more than a difference threshold from the determined radius <NUM>. For example, the similarity criterion may comprise being a radius that differs by not more than <NUM> from the determined radius <NUM>. Given a scenario where the determined radius <NUM> were to be determined as <NUM>, the subset would include radii from an interval of <NUM> and <NUM>. The difference threshold may define any other distance such as <NUM>, <NUM>, <NUM>, or <NUM>.

Additionally, or alternatively, the similarity criterion may comprise a number of radii that are closest to the determined radius <NUM>. The number of radii closest to the determined radius <NUM> may be any number larger than one, such as two, three, four, five, or more. For example, if the number of radii closest to the determined radius <NUM> is five, a subset of radii may be determined that comprises the five radii that are the closest to the determined radius <NUM>.

The similarity criterion may combine multiple criteria. For example, in a first step an intermediate set of radii that differ by not more than a difference threshold is determined. In a subsequent step, of the intermediate set of radii a subset of a number of radii that are closest to the determined radius <NUM> is determined.

The similarity criterion may vary with the pivot angle. For example, the difference threshold and/or number or radii that are closest to the determined radius <NUM> may increase with the pivot angle <NUM>.

<FIG> shows a subset of radii <NUM> that meet a similarity criterion with a difference threshold. <FIG> may show a visual representation of data of the device <NUM> that comprises the subset of radii <NUM> or may alternatively show an output on a display for a user about the determined subset of radii <NUM>. In the example shown in <FIG>, a radius <NUM> of <NUM> has been determined, which may optionally be display to the user in form of a numerical radius output <NUM>.

The subset of radii <NUM> may be displayed isolated from the rest of the predetermined list of radii as shown in <FIG>. Alternatively, at least a part of the pre-determined list may be displayed, wherein the subset of radii <NUM> is highlighted. <FIG> shows a display output <NUM> displaying a subset of radii <NUM> highlighted within the pre-determined list of radii.

The method may further comprise generating an output for a user selection or confirmation, wherein the output comprises at least one of information about the subset of radii <NUM> and information about instrument tips <NUM> associated with the subset of radii <NUM>. The information about instrument tips <NUM> may comprise at least one of tip name, tip material, tip manufacturer, instrument tip use, previous use of an instrument tip, and compatibility with a current or planned surgical procedure. <FIG> shows a display output <NUM> displaying a subset of radii <NUM> with information about the subset of radii <NUM> and information about instrument tips <NUM> associated with the subset of radii <NUM>. In the example shown in <FIG>, the information about instrument tips <NUM> comprises a name of the instrument (e.g., manufacturer name or a label of the instrument tip <NUM>) and material (e.g., martensitic, austenitic or ferritic steel), but may alternatively, or additionally, comprise any other information as described above. The display output <NUM> further comprises an input region <NUM> that allows the user to select or confirm an instrument tip <NUM> from the subset of radii <NUM>. The input region <NUM> may overlap or coincide with any information shown of the corresponding instrument tip <NUM> (e.g., the user may select an instrument tip <NUM> by clicking on the name or the radius of the instrument tip <NUM>).

The list of radii may comprise multiple instrument tips <NUM> with a same radius that differ in a different quality such as material or manufacturer. Determining the radius <NUM> of the instrument tip <NUM> may not allow distinguishing between instrument tips <NUM> with the same radius. The subset of radii may inform the user that not a single instrument tip <NUM> is assigned to the determined radius <NUM>. In such a case, user selection or confirmation of the instrument tip allows determining the correct instrument tip <NUM>.

<FIG> shows a display output displaying a subset of radii <NUM> with information about the subset of radii <NUM>, wherein some instrument tips <NUM> have the same radius <NUM> (e.g., two instrument tips <NUM> with a radius of <NUM>), but differ in the tip shape (see <FIG>). The display output <NUM> further comprises an input region <NUM> that allows the user to select or confirm an instrument tip <NUM> from the subset of radii <NUM>.

In the case that determining the radius <NUM> contains errors, the determined radius <NUM> may not properly reflect the actual radius. The list of radii indicates likely candidates of the actual radius. User selection or confirmation may therefore provide the required information for correctly identifying the actual radius (as used, later on, for example in a navigation procedure as illustrated in <FIG>).

The method embodiments may comprise determining the instrument tip <NUM> based on at least one of the determined radius <NUM>, a confirmation of the user, and a selection of the user. The visual representation <NUM> indicative of the radius <NUM> may comprise a two-dimensional or three-dimensional instrument model icon of the determined instrument tip <NUM>. <FIG> shows a fourth example of a virtual space <NUM> with an instrument model icon as a visual representation <NUM> indicative of the radius <NUM> arranged relative to image data <NUM> of the vertebra <NUM>. The visual representation <NUM> is a two-dimensional instrument model icon of the determined instrument <NUM>. An end portion of the instrument model comprises a radius indication <NUM>.

<FIG> shows a fifth example of a virtual space <NUM> with an instrument model icon as a visual representation <NUM>. The fifth example essentially differs from the fourth example in that the visual representation <NUM> further indicates a position of the centre point <NUM>. The centre point <NUM> may alternatively or additionally be indicated by a reticle such as a crosshair, for example as shown in <FIG>.

<FIG> shows a sixth example of a virtual space <NUM>, wherein the visual representation comprises a three-dimensional model of the surgical instrument <NUM> (e.g., in the form of an icon). The three-dimensional model can be rotated and therefore is able to fully reflect an orientation of the surgical instrument <NUM>. A three-dimensional model is in particular suitable for navigating a surgical instrument <NUM> relative to three dimensional image data <NUM>.

The calibration devices <NUM> described herein may comprise a plurality of calibration structures <NUM>. Such a calibration device <NUM> allows simultaneous calibration for a plurality of surgical instruments <NUM>. Additionally, at least two of the calibration structures <NUM> may have a different opening angle <NUM>. <FIG> shows a calibration device <NUM> with a first calibration structure 38A and a second calibration structure 38B. The first calibration structure 38A has a first opening angle 40A and the second calibration structure 38B has a second opening angle 40B, wherein the first opening angle 40A is larger than the second opening angle 40B. For the calibration structures 38A, 38B, the central axes are arranged in parallel. Alternatively, the central axes of the calibration structures 38A, 38B may be arranged in a non-parallel way (e.g., <NUM>°, <NUM>° or <NUM>°).

The first opening angle 40A results in a larger diameter of the opening of the first calibration structure 38A and consequently allows insertion of an instrument tip <NUM> with a larger radius <NUM> compared to the second calibration structure 38B. On the other hand, the comparably smaller second opening angle 40b of the second calibration structure 38B translates a difference of the radius <NUM> of the instrument tip <NUM> to a larger difference of the centre distance <NUM> between the position of the apex <NUM> and the position of the centre point <NUM> and the spherically shaped surface portion <NUM>. Since the larger difference of the centre distance <NUM> can be better resolved with a limited spatial accuracy of the surgical navigation system <NUM>, the second calibration structure 38B provides a more accurate radius determination. The calibration device <NUM> can therefore be used in combination with instrument tips <NUM> that have a much larger or smaller radius. As a result, a calibration device <NUM> with different opening angles 40A, 40B increases a range of usable tip radii <NUM> and consequently increases the flexibility of instrument selection for the user <NUM>.

However, since the opening angle 40A, 40B is required for determining the radius <NUM>, as an intermediate step, the method may include a step for determining the position and, optionally in case the opening angles 40A, 40B differ, the opening angle 40A, 40B of the calibration structure 38A, 38B in which the instrument tip is arranged by identifying the calibration structure 38A, 38B based on the position of the centre point <NUM>.

The calibration structure 38A, 38B may be identified based the position of the centre point <NUM> and on the predetermined first relationship alone, e.g., based on a vicinity of the centre point <NUM> relative to the apex <NUM>. Additional information may be provided, such as coordinates of a volume inside the calibration structure 38A, 38B. The calibration structure 38A, 38B may then be identified based on whether or not the position of the centre point <NUM> is inside the volume of either one of the calibration structures 38A, 38B.

In case a calibration structure 38A, 38B cannot be identified (e.g., the distance to the apex <NUM> exceeds a predetermined threshold, or the position of the centre point <NUM> is outside a volume of both calibration structures 38A, 38B), the method may comprise outputting an error message to the user <NUM>.

Determining the radius <NUM> of the spherically shaped surface portion <NUM> gives access to valuable information for the user <NUM>. The user <NUM> can obtain or verify the radius <NUM> right before moving the surgical instrument <NUM> in a surgical procedure, eliminating the risk of a mix up of an instrument tip <NUM> with a different radius and eliminating the need of managing labels or interaction with a user interface. The user <NUM> can consequently work more time efficiently and with a lower probability of causing harm to the patient. The surgical navigation system <NUM> gains the ability to improve accuracy of tracking the instrument tip <NUM>, guiding the user <NUM>, and planning tissue manipulation carried out with the instrument tip <NUM>. The surgical procedure can therefore be carried out more efficiently and safely.

The tracking system <NUM> need not be attached to a surgical object such as the surgical instrument <NUM>, the calibration device <NUM>, or the patient. Instead, the tracking system <NUM> may be provided spatially separate from the surgical objects, overlooking the entire surgical environment <NUM>. Such a position enables the tracking system <NUM> to track a plurality of surgical objects inside the surgical environment <NUM> and not only the surgical object to which the tracking system <NUM> is attached. When tracking a plurality of surgical objects, the surgical navigation system <NUM> is able to apply the determined radius <NUM> to interactions between the surgical instrument <NUM> and other tracked surgical objects. The surgical navigation system <NUM> tracks the surgical instrument <NUM> and the patient. Once the radius <NUM> has been determined, the device <NUM> can guide the user more accurately. The accuracy of the surgical procedure is therefore improved.

It is to be noted that the various visualization approaches taught herein (see, e.g., <FIG> and <FIG>) are based on a radius determination (also called radius calibration herein) of a spherically shaped portion of an instrument tip. In the present disclosure, various radius determination techniques have been presented. It is to be understood that the visualization approaches taught herein could also be implemented using any other radius determination technique, including radius determination by user input or user selection, radius measurement using other calibration structures, and so on. As such, embodiments of the visualization approaches taught herein could in general be based on a pre-determined radius of a spherically shaped portion of an instrument tip, no matter how the radius is input, measured, calibrated or determined otherwise.

Claim 1:
A computer-implemented method (<NUM>) for determining a radius (<NUM>) of a spherically shaped surface portion (<NUM>) of a tip (<NUM>) of an instrument (<NUM>), wherein a calibration device (<NUM>) is provided that comprises a flat calibration surface (<NUM>) and a calibration structure (<NUM>), wherein the calibration structure defines an opening angle (<NUM>) and a real or imaginary first reference point (<NUM>) relative to which the opening angle (<NUM>) is defined, wherein the calibration device (<NUM>) comprises a first tracker (<NUM>) trackable by a tracking system (<NUM>) and arranged in a first predetermined relationship (<NUM>) relative to the first reference point (<NUM>) and in a second predetermined relationship relative to the calibration surface (<NUM>), and wherein the instrument (<NUM>) comprises a second tracker (<NUM>) trackable by the tracking system (<NUM>), the method (<NUM>) comprising the following steps performed by a computer system (<NUM>):
determining (<NUM>) a first pose of the first tracker (<NUM>) and a second pose of the second tracker (<NUM>) while the spherically shaped surface portion (<NUM>) is in abutment with the calibration structure (<NUM>);
determining (<NUM>) a reference position (<NUM>) of the first reference point (<NUM>) relative to the second tracker (<NUM>) when the first tracker (<NUM>) is in the first pose and the second tracker (<NUM>) is in the second pose based on the first pose, the second pose, and the first predetermined relationship (<NUM>);
determining (<NUM>) a third pose of the first tracker (<NUM>) and a fourth pose of the second tracker (<NUM>) while the spherically shaped surface portion (<NUM>) is in abutment with the calibration surface (<NUM>); and
determining (<NUM>) the radius (<NUM>) of the spherically shaped surface portion (<NUM>) based on the third pose, the second predetermined relationship, the reference position (<NUM>), the fourth pose, and the opening angle (<NUM>).