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1. WO2020192872 - METHOD OF ESTIMATING A POSITION OF A MEDICAL INSTRUMENT TIP

Note: Text based on automatic Optical Character Recognition processes. Please use the PDF version for legal matters

[ EN ]

METHOD OF ESTIMATING A POSITION OF A MEDICAL INSTRUMENT TIP

FIELD OF THE INVENTION

The present invention relates to a computer-implemented medical method of estimating a position of a medical instrument tip, a use of the estimated position of the instrument tip, an instrument calibration system, a surgical navigation system for computer assisted surgery as well as a computer program.

TECHNICAL BACKGROUND

Calibration of surgical instruments is commonly carried out by holding an instrument onto a calibration device. This features a calibration workflow to calibrate and verify surgical instruments. The instrument is held into a fitting hole or into indentations or protrusions so the instrument tip can be held in a fixed position regarding its own tracker and the tracked calibration device. The navigation system then calculates the instrument tip from knowing the calibration device’s reference point by selecting or automatically detecting it from special instrument movements.

There are many instruments and tips that do not fit in any of the provided shapes/indentations on common calibration devices, so unwanted systematic error is introduced. Assembling a calibration device featuring all possible tips shapes has been declined due to many reasons, in particular usability and expenses.

The present invention can be used for calibration procedures e.g. in connection with a system for image-guided surgery such as in Spine & Trauma navigation.

Aspects of the present invention, examples and exemplary steps and their embodiments are disclosed in the following. Different exemplary features of the

invention can be combined in accordance with the invention wherever technically expedient and feasible.

EXEMPLARY SHORT DESCRIPTION OF THE INVENTION

In the light of the prior art descripted hereinbefore, it may be seen as the object of the present invention to provide an improved method for estimating a position of an arbitrarily medical instrument tip in an indentation, in particular for calibration of the instrument tip.

In the following, a short description of the specific features of the present invention is given which shall not be understood to limit the invention only to the features or a combination of the features described in this section.

A computer implemented medical method of estimating a position of a medical instrument tip is presented.

In particular, this method calculates a new or updated reference point for a surgical navigation system, which deviates from the reference point of the calibration device. This new reference point is the estimated position of the instrument tip as calculated by the presented method. One technical effect of the invention is that the position of any arbitrary medical instrument tip, in particular in an indentation of a calibration device, can be estimated. This is an improvement of accuracy in view of the generic approach of using the same reference point of the indentation of the calibration device for any arbitrary medical instrument tip.

For this purpose a virtual model of a shape of a medical instrument, in particular the instrument tip, is matched onto a virtual model of a shape of a calibration device, in particular an indentation of the calibration device.

GENERAL DESCRIPTION OF THE INVENTION

In this section, a description of the general features of the present invention is given for example by referring to possible embodiments of the invention.

This is achieved by the subject-matter of the independent claims, wherein further embodiments are incorporated in the dependent claims and the following description.

The described embodiments similarly pertain to the computer-implemented medical method of estimating a position of a medical instrument tip, the use of the estimated position of the instrument tip, the instrument calibration system, the surgical navigation system for computer assisted surgery and the computer program. Synergetic effects may arise from different combinations of the embodiments although they might not be described in detail hereinafter. Furthermore, it shall be noted that all embodiments of the present invention concerning a method, might be carried out with the order of the steps as explicitly described herein. Nevertheless, this has not to be the only and essential order of the steps of the method. The herein presented methods can be carried out with another order of the disclosed steps without departing from the respective method embodiment, unless explicitly mentioned to the contrary hereinafter.

Technical terms are used by their common sense. If a specific meaning is conveyed to certain terms, definitions of terms will be given in the following in the context of which the terms are used.

According to the present disclosure, a computer implemented medical method of estimating a position of a medical instrument tip is provided. The method comprises the step of providing a virtual model of a shape of a medical instrument comprising the instrument tip. Furthermore, providing a virtual model of a shape of a calibration device comprising an indentation onto which the instrument tip is introduced for calibration. The method further comprises the step of matching the model of the shape of the instrument tip onto the model of the shape of the calibration device thereby estimating a position of the instrument tip.

In other words, the method presented herein is directed to the calculation of a new or updated reference point for a surgical navigation system, which deviates from the reference point of the calibration device. This new reference point is the estimated position of the instrument tip, as calculated by the method of the present invention. The new reference point is defined by the estimated position of the instrument tip.

Thus, a position of an instrument tip can be estimated for any arbitrary instrument tip.

The term“matching onto”, as used herein, comprises finding collision points between the shape of the medical instrument and the shape of the calibration device relating to a possible position of the instrument tip.

In a preferred embodiment, the model of the shape of the medical instrument and/or the model of the shape of the calibration device are 3D models.

The calibration device can be formed as a separate device. However, preferably, the calibration device is integrated in an already existing device, like for example an instrument itself. Generally, any trackable device comprising a suitable indentation can be used for calibration.

In a preferred embodiment, a patient reference array attached to the patient comprises the indentation onto which the instrument tip is introduced for calibration.

The indentation preferably is cone shaped. However, other shapes are possible as well. In view of the variety of different shapes of available instrument tips, an indentation with a constant gradient is preferred.

The term“model of the instrument“ and/or“model of the calibration device” preferably relate to the instrument and/or calibration device, respectively. It is therefore clear that in the computer implemented medical method models of the instrument and/or the calibration are used relating to the instrument and/or the calibration device, respectively.

In the following definitions for the terms used in in the context of the first aspect of the present invention are provided.

Computer implemented method

The method in accordance with the invention is for example a computer implemented method. For example, all the steps or merely some of the steps (i.e. less than the total number of steps) of the method in accordance with the invention can be executed by a computer (for example, at least one computer). An embodiment of the computer implemented method is a use of the computer for performing a data processing method. An embodiment of the computer implemented method is a method concerning the operation of the computer such that the computer is operated to perform one, more or all steps of the method.

The computer for example comprises at least one processor and for example at least one memory in order to (technically) process the data, for example electronically and/or optically. The processor being for example made of a substance or composition which is a semiconductor, for example at least partly n- and/or p-doped semiconductor, for example at least one of I I-, III-, IV-, V-, Vl-semiconductor material, for example (doped) silicon and/or gallium arsenide. The calculating or determining steps described are for example performed by a computer. Determining steps or calculating steps are for example steps of determining data within the framework of the technical method, for example within the framework of a program. A computer is for example any kind of data processing device, for example electronic data processing device. A computer can be a device which is generally thought of as such, for example desktop PCs, notebooks, netbooks, etc., but can also be any programmable apparatus, such as for example a mobile phone or an embedded processor. A computer can for example comprise a system (network) of "sub-computers", wherein each sub-computer represents a computer in its own right. The term "computer" includes a cloud computer, for example a cloud server. The term "cloud computer" includes a cloud computer system which for example comprises a system of at least one cloud computer and for example a plurality of operatively interconnected cloud computers such as a server farm. Such a cloud computer is preferably connected to a wide area network such as the world wide web (WWW) and located in a so-called cloud of computers which are all connected to the world wide web. Such an infrastructure is used for "cloud computing", which describes computation, software, data access and storage services which do not require the end user to know the physical location and/or configuration of the computer delivering a specific service. For example, the term "cloud" is used in this respect as a metaphor for the Internet (world wide web). For example, the cloud provides computing infrastructure as a service (laaS). The cloud computer can function as a virtual host for an operating system and/or data processing application which is used to execute the method of the invention. The cloud computer is for example an elastic compute cloud (EC2) as provided by Amazon Web Services™. A computer for example comprises interfaces in order to receive or output data and/or perform an analogue-to-digital conversion. The data are for example data which represent physical properties and/or which are generated from technical signals. The technical signals are for example generated by means of (technical) detection devices (such as for example devices for detecting marker devices) and/or (technical) analytical devices (such as for example devices for performing (medical) imaging methods), wherein the technical signals are for example electrical or optical signals. The technical signals for example represent the data received or outputted by the computer. The computer is preferably operatively coupled to a display device which allows information outputted by the computer to be displayed, for example to a user. One example of a display device is a virtual reality device or an augmented reality device (also referred to as virtual reality glasses or augmented reality glasses) which can be used as "goggles" for navigating. A specific example of such augmented reality glasses is Google Glass (a trademark of Google, Inc.). An augmented reality device or a virtual reality device can be used both to input information into the computer by user interaction and to display information outputted by the computer. Another example of a display device would be a standard computer monitor comprising for example a liquid crystal display operatively coupled to the computer for receiving display control data from the computer for generating signals used to display image information content on the display device. A specific embodiment of such a computer monitor is a digital lightbox. An example of such a digital lightbox is Buzz®, a product of Brainlab AG. The monitor may also be the monitor of a portable, for example handheld, device such as a smart phone or personal digital assistant or digital media player.

The invention also relates to a program which, when running on a computer, causes the computer to perform one or more or all of the method steps described herein and/or to a program storage medium on which the program is stored (in particular in a non-transitory form) and/or to a computer comprising said program storage medium and/or

to a (physical, for example electrical, for example technically generated) signal wave, for example a digital signal wave, carrying information which represents the program, for example the aforementioned program, which for example comprises code means which are adapted to perform any or all of the method steps described herein.

Within the framework of the invention, computer program elements can be embodied by hardware and/or software (this includes firmware, resident software, micro-code, etc.). Within the framework of the invention, computer program elements can take the form of a computer program product which can be embodied by a computer-usable, for example computer-readable data storage medium comprising computer-usable, for example computer-readable program instructions, "code" or a "computer program" embodied in said data storage medium for use on or in connection with the instructionexecuting system. Such a system can be a computer; a computer can be a data processing device comprising means for executing the computer program elements and/or the program in accordance with the invention, for example a data processing device comprising a digital processor (central processing unit or CPU) which executes the computer program elements, and optionally a volatile memory (for example a random access memory or RAM) for storing data used for and/or produced by executing the computer program elements. Within the framework of the present invention, a computer-usable, for example computer-readable data storage medium can be any data storage medium which can include, store, communicate, propagate or transport the program for use on or in connection with the instruction-executing system, apparatus or device. The computer-usable, for example computer-readable data storage medium can for example be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, apparatus or device or a medium of propagation such as for example the Internet. The computer-usable or computer-readable data storage medium could even for example be paper or another suitable medium onto which the program is printed, since the program could be electronically captured, for example by optically scanning the paper or other suitable medium, and then compiled, interpreted or otherwise processed in a suitable manner. The data storage medium is preferably a non-volatile data storage medium. The computer program product and any software and/or hardware described here form the various means for performing the functions of the invention in the example embodiments. The computer and/or data processing device can for example include a

guidance information device which includes means for outputting guidance information. The guidance information can be outputted, for example to a user, visually by a visual indicating means (for example, a monitor and/or a lamp) and/or acoustically by an acoustic indicating means (for example, a loudspeaker and/or a digital speech output device) and/or tactilely by a tactile indicating means (for example, a vibrating element or a vibration element incorporated into an instrument). For the purpose of this document, a computer is a technical computer which for example comprises technical, for example tangible components, for example mechanical and/or electronic components. Any device mentioned as such in this document is a technical and for example tangible device.

Marker

It is the function of a marker to be detected by a marker detection device (for example, a camera or an ultrasound receiver or analytical devices such as CT or MRI devices) in such a way that its spatial position (i.e. its spatial location and/or alignment) can be ascertained. The detection device is for example part of a navigation system. The markers can be active markers. An active marker can for example emit electromagnetic radiation and/or waves which can be in the infrared, visible and/or ultraviolet spectral range. A marker can also however be passive, i.e. can for example reflect electromagnetic radiation in the infrared, visible and/or ultraviolet spectral range or can block x-ray radiation. To this end, the marker can be provided with a surface which has corresponding reflective properties or can be made of metal in order to block the x-ray radiation. It is also possible for a marker to reflect and/or emit electromagnetic radiation and/or waves in the radio frequency range or at ultrasound wavelengths. A marker preferably has a spherical and/or spheroid shape and can therefore be referred to as a marker sphere; markers can however also exhibit a cornered, for example cubic, shape.

Marker device

A marker device can for example be a reference star or a pointer or a single marker or a plurality of (individual) markers which are then preferably in a predetermined spatial relationship. A marker device comprises one, two, three or more markers, wherein two

or more such markers are in a predetermined spatial relationship. This predetermined spatial relationship is for example known to a navigation system and is for example stored in a computer of the navigation system.

In another embodiment, a marker device comprises an optical pattern, for example on a two-dimensional surface. The optical pattern might comprise a plurality of geometric shapes like circles, rectangles and/or triangles. The optical pattern can be identified in an image captured by a camera, and the position of the marker device relative to the camera can be determined from the size of the pattern in the image, the orientation of the pattern in the image and the distortion of the pattern in the image. This allows determining the relative position in up to three rotational dimensions and up to three translational dimensions from a single two-dimensional image.

The position of a marker device can be ascertained, for example by a medical navigation system. If the marker device is attached to an object, such as a bone or a medical instrument, the position of the object can be determined from the position of the marker device and the relative position between the marker device and the object. Determining this relative position is also referred to as registering the marker device and the object. The marker device or the object can be tracked, which means that the position of the marker device or the object is ascertained twice or more over time.

Marker holder

A marker holder is understood to mean an attaching device for an individual marker which serves to attach the marker to an instrument, a part of the body and/or a holding element of a reference star, wherein it can be attached such that it is stationary and advantageously such that it can be detached. A marker holder can for example be rod shaped and/or cylindrical. A fastening device (such as for instance a latching mechanism) for the marker device can be provided at the end of the marker holder facing the marker and assists in placing the marker device on the marker holder in a force fit and/or positive fit.

Pointer

A pointer is a rod which comprises one or more - advantageously, three - markers fastened to it and which can be used to measure off individual co-ordinates, for example spatial co-ordinates (i.e. three-dimensional co-ordinates), on a part of the body, wherein a user guides the pointer (for example, a part of the pointer which has a defined and advantageously fixed position with respect to the at least one marker attached to the pointer) to the position corresponding to the co-ordinates, such that the position of the pointer can be determined by using a surgical navigation system to detect the marker on the pointer. The relative location between the markers of the pointer and the part of the pointer used to measure off co-ordinates (for example, the tip of the pointer) is for example known. The surgical navigation system then enables the location (of the three-dimensional co-ordinates) to be assigned to a predetermined body structure, wherein the assignment can be made automatically or by user intervention.

Reference star

A "reference star" refers to a device with a number of markers, advantageously three markers, attached to it, wherein the markers are (for example detachably) attached to the reference star such that they are stationary, thus providing a known (and advantageously fixed) position of the markers relative to each other. The position of the markers relative to each other can be individually different for each reference star used within the framework of a surgical navigation method, in order to enable a surgical navigation system to identify the corresponding reference star on the basis of the position of its markers relative to each other. It is therefore also then possible for the objects (for example, instruments and/or parts of a body) to which the reference star is attached to be identified and/or differentiated accordingly. In a surgical navigation method, the reference star serves to attach a plurality of markers to an object (for example, a bone or a medical instrument) in order to be able to detect the position of the object (i.e. its spatial location and/or alignment). Such a reference star for example features a way of being attached to the object (for example, a clamp and/or a thread) and/or a holding element which ensures a distance between the markers and the object (for example in order to assist the visibility of the markers to a marker detection device) and/or marker holders which are mechanically connected to the holding element and which the markers can be attached to.

Navigation system

The present invention is also directed to a navigation system for computer-assisted surgery. This navigation system preferably comprises the aforementioned computer for processing the data provided in accordance with the computer implemented method as described in any one of the embodiments described herein. The navigation system preferably comprises a detection device for detecting the position of detection points which represent the main points and auxiliary points, in order to generate detection signals and to supply the generated detection signals to the computer, such that the computer can determine the absolute main point data and absolute auxiliary point data on the basis of the detection signals received. A detection point is for example a point on the surface of the anatomical structure which is detected, for example by a pointer. In this way, the absolute point data can be provided to the computer. The navigation system also preferably comprises a user interface for receiving the calculation results from the computer (for example, the position of the main plane, the position of the auxiliary plane and/or the position of the standard plane). The user interface provides the received data to the user as information. Examples of a user interface include a display device such as a monitor, or a loudspeaker. The user interface can use any kind of indication signal (for example a visual signal, an audio signal and/or a vibration signal). One example of a display device is an augmented reality device (also referred to as augmented reality glasses) which can be used as so-called "goggles" for navigating. A specific example of such augmented reality glasses is Google Glass (a trademark of Google, Inc.). An augmented reality device can be used both to input information into the computer of the navigation system by user interaction and to display information outputted by the computer.

The invention also relates to a navigation system for computer-assisted surgery, comprising:

a computer for processing the absolute point data and the relative point data;

a detection device for detecting the position of the main and auxiliary points in order to generate the absolute point data and to supply the absolute point data to the computer; a data interface for receiving the relative point data and for supplying the relative point data to the computer; and

a user interface for receiving data from the computer in order to provide information to the user, wherein the received data are generated by the computer on the basis of the results of the processing performed by the computer.

Surgical navigation system

A navigation system, such as a surgical navigation system, is understood to mean a system which can comprise: at least one marker device; a transmitter which emits electromagnetic waves and/or radiation and/or ultrasound waves; a receiver which receives electromagnetic waves and/or radiation and/or ultrasound waves; and an electronic data processing device which is connected to the receiver and/or the transmitter, wherein the data processing device (for example, a computer) for example comprises a processor (CPU) and a working memory and advantageously an indicating device for issuing an indication signal (for example, a visual indicating device such as a monitor and/or an audio indicating device such as a loudspeaker and/or a tactile indicating device such as a vibrator) and a permanent data memory, wherein the data processing device processes navigation data forwarded to it by the receiver and can advantageously output guidance information to a user via the indicating device. The navigation data can be stored in the permanent data memory and for example compared with data stored in said memory beforehand.

Referencing

Determining the position is referred to as referencing if it implies informing a navigation system of said position in a reference system of the navigation system.

For example, the invention does not involve or in particular comprise or encompass an invasive step which would represent a substantial physical interference with the body requiring professional medical expertise to be carried out and entailing a substantial health risk even when carried out with the required professional care and expertise.

For example, the invention does not comprise a step of positioning a medical implant in order to fasten it to an anatomical structure or a step of fastening the medical implant to the anatomical structure or a step of preparing the anatomical structure for having the medical implant fastened to it. More particularly, the invention does not involve or in particular comprise or encompass any surgical or therapeutic activity.

In the following preferred embodiments will be described in more detail.

According to another exemplary embodiment of the present invention, the method comprises the step of using the estimated position of the instrument tip as an updated reference point in a surgical navigation system.

Thus, the estimated position of the instrument tip is more accurate than the generic reference point of a calibration device for a surgical navigation system, in particular of an indentation of the calibration device. Therefore, the accuracy of a calibration of the instrument tip with the calibration device is improved.

According to another exemplary embodiment of the present invention, the method comprises the step of tracking the instrument by a tracking device and a, preferably passive, tracker arranged on the instrument.

The step of tracking is preferably carried out during the matching process, which results in the estimated position of the instrument tip.

Thus, dependent on the estimated position of the instrument tip, the tracking of the instrument can be improved.

According to another exemplary embodiment of the present invention, the method comprises the step of determining an actual spatial orientation of the instrument, preferably along an axis of the instrument and of using said determined actual spatial orientation during matching the model of the instrument tip onto the model of the calibration device.

The actual spatial orientation of the instrument preferably relates to an angle, in which the instrument is arranged in the indentation.

The term“actual spatial orientation” relates to the current spatial orientation.

The spatial orientation preferably comprises the position of the instrument. Further preferably, it is always kept track of the instrument tip and an instrument handle as well as three axes of the instrument. For example, the Instrument features a pre-calibrated axis, but the instrument tip still has to be calibrated. In this case, the axis of the instrument has to be intersected with a plane on the calibration device so a good estimation of the length of the instrument can be achieved. The length of the instrument is used to check the distance of the instrument to the indentation of the calibration device.

According to another exemplary embodiment of the present invention, the actual spatial orientation is determined based on a result of tracking the instrument.

Thus, the determination of the actual spatial orientation of the instrument is further improved.

According to another exemplary embodiment of the present invention, the method comprises the step of determining the actual spatial orientation based on an estimation of the axis of the instrument and/or based on learning from a rotation movement of the instrument tip in the indentation, which is recorded by a tracking device.

In a preferred embodiment, the actual spatial orientation is determined based on a calibration of the axis of the instrument. Thus, the position of the instrument tip and the instrument handle can be determined. Knowing the position and/or the extent of the axis of the instrument allows for an improved determination of the actual spatial orientation of the instrument. The position of the axis of the instrument might also be known from a stored pre- calibration of the axis of the instrument. Additionally, the position of the axis of the instrument can be derived from knowing a tracker location and orientation of the instrument.

Thus, the determination of the actual spatial orientation of the instrument is further improved.

According to another exemplary embodiment of the present invention, the method comprises the step of measuring, calibrating, validating and/or verifying the medical instrument using the estimated position of the instrument tip as an updated reference point.

Measuring the instrument preferably comprises determining data of the shape of the individual medical instrument currently used by the doctor.

Calibrating the instrument preferably comprises updating data stored in the navigation system about the shape of the individual medical instrument and/or about the reference point of the calibration device, which is the estimated position of the instrument tip as well as determining the axis of the instrument. Thus, the tip, the axis near the tip and the axis between the tip and the instrument handle is calibrated. Furthermore, the model of the shape of the instrument tip is also calibrated. Calibrating further comprises finding the axis of the instrument. At many shapes of the instrument, in particular curved instruments there is no generic relation between shape of the instrument and axis of the instrument. Thus, preferably the instrument tip, the axis near the instrument tip, in particular for the elongation of the instrument, and the axis between the instrument tip and the instrument handle is stored and calibrated. Additionally, the shape of the 3D model is also calibrated, wherein the user for example puts the instrument onto a pre-defined plane on the calibration device, so the instrument is assumed to be a flat tip, chisel tip, tap or screw depending on the location on the calibration device.

Validating the instrument preferably comprises determining if the estimated position of the instrument tip corresponds to the position of the instrument tip according to the tracking device.

Verifying the instrument preferably comprises determining the discrepancy between the estimated positon of the instrument tip and the position of the instrument tip according to the tracking device. This may comprise a comparison with a pre-defined

threshold value to reflect deviations acceptable for a doctor or a surgical navigation system.

According to another exemplary embodiment of the present invention, the method comprises the step of generating a plurality of frames of different positions of the instrument tip in the indentation by using a surgical navigation device. Furthermore, matching the model of the shape of the instrument tip onto the model of the shape of the calibration device for each frame and estimating a position of the instrument tip for each frame. The method further comprises the step of calculating an average position of the instrument tip based on the estimated positions of the instrument tip of every frame.

Thus, the estimation of the position of the instrument tip is repeated for a plurality of frames during the calibration process.

Preferably, estimated positions of the instrument tip outside of a predetermined standard deviation may not be considered.

The plurality of frames is around or larger than 100 frames.

Preferably, the instrument tip is rotated within the indentation of the calibration device. Further preferably, the instrument tip is rotated within the indentation of the calibration device until a stop criterion is met. The stop criterion preferably is met after the rotation of the instrument tip of a predetermined angle, when a predetermined amount of frames within a predetermined standard deviation is determined and/or when a predetermined amount of consecutive frames outside of the predetermined standard deviation are determined.

The reference point of the model of the calibration device correlates to a predetermined ideal position of the instrument tip in the indentation. In a cone shaped or pyramid shaped indentation of the calibration device the predetermined ideal position of the instrument tip preferably is the tip of the cone shape.

Preferably, the instrument tip is rotated within the indentation of the calibration device, thereby generating a plurality of frames of different positions of the instrument tip in the indentation by using a surgical navigation device. Preferably, different angles leading to different positions of the instrument tip are necessary while generating the frames.

According to another exemplary embodiment of the present invention, the method comprises the step of using the calculated average position of the instrument tip as an updated reference point in a surgical navigation system.

Thus, the accuracy of the surgical navigation system can be improved.

According to another exemplary embodiment of the present invention, the matching of the models comprises the step of calculating, based on the model of the instrument tip and the model of the calibration device, at least one collision point between the model of the instrument tip and the model of the calibration device.

In order to estimate the real position of the instrument tip in the indentation of the calibration device, collision points have to be found. The collision points, relate to the points, where the calibration device and the instrument tip touch, when the instrument tip is arranged within the indentation of the calibration device.

According to another exemplary embodiment of the present invention, the method comprises the step of placing the model of the instrument tip onto a reference point of the model of the calibration device. Furthermore, executing an elevation step, thereby elevating the model of the instrument tip onto the model of the indentation along a base axis perpendicular to a surface of the model of the calibration device, thereby determining a first collision point. The method further comprises the step of executing at least one first descending step, thereby shifting the model of the instrument tip onto the model of the indentation along a known gradient of the indentation from the first collision point towards the reference point of the calibration device, thereby determining a second collision point and a shifted first collision point.

Shifting the model of the instrument tip comprises storing and collecting all shift transformations and interpreting the original surface points in transformed coordinates.

Preferably, a shifting vector is determined for every step, like elevation and/or descending, and the whole model of the instrument tip is shifted.

Preferably, the first collision point is shifted along the gradient of the indentation from towards the reference point of the calibration device onto a shifted first collision point. This shift is dependent on the first descending step.

Executing those steps, the model of the instrument tip and the model of the indentation are arranged in a fashion that relates to the reality of the instrument tip being disposed within the indentation. Since two collision points are found, a first estimation of the position of the instrument tip with in the indentation can be executed.

Preferably, the method comprises the step of executing at least one second descending step, thereby shifting the model of the instrument tip onto the model of the indentation along a gradient of the indentation from a centre point between the first collision point and the second collision point towards the reference point of the calibration device, thereby determining a third collision point.

According to another exemplary embodiment of the present invention, the method comprises the step of determining a third collision point by virtually shifting the model of the instrument tip onto the model of the indentation along a horizontal shifting vector, which is a projection of a gradient of the indentation from a centre point between the shifted first collision point and the second collision point towards the reference point of the calibration device in a horizontal plane through the centre point. Furthermore, repositioning the model of the instrument tip to an average position between the shifted first collision point, the second collision point and the third collision point in the horizontal plane. The method further comprises the step of descending the model of the instrument tip onto the model of the indentation along the base axis, thereby determining a final collision point.

Virtually shifting the model of the instrument tip differs from shifting the model of the instrument tip by not actually shifting the model of the instrument tip, but determining a location of a certain point of the model of the instrument tip, if the model of the instrument tip actually would have been shifted. In this case, only the third collision point of the model of the instrument tip with the model of the indentation is important for further calculations. Therefore, the model of the instrument tip is not actually shifted but only virtually shifted.

Thus, an improved estimation for the instrument tip is found.

In a preferred embodiment, the horizontal plane is defined by the surface of the calibration device outside of the indentation.

Some instrument tips might collide with the indentation when moving along the gradient of the indentation, although the global optimum for a collision point is not found, in particular when the starting point is not good.

However, by shifting the instrument tip in a horizontal plane, repositioning the instrument tip and descending the instrument tip along the base axis, an improved estimate of the position of the instrument tip can be found.

Preferably, the first descending step for determining the second collision point, the steps of repositioning and descending for determining the third collision point and the step of descending along the base axis for determining the final collision point can be repeated to iteratively find the optimal position of the instrument tip.

According to another exemplary embodiment of the present invention, the model of the instrument tip comprises a mesh of surface points, wherein the elevation of the instrument tip onto the indentation is determined by an elevation vector, being the longest vector between the respective surface points of the instrument tip and the indentation along the base axis.

Thus an efficient way of determining the elevation amount of the elevation step is provided.

According to another exemplary embodiment of the present invention, the gradient of the indentation of the calibration device determines a common shifting direction vector towards the reference point of the calibration device. A shifting amount is determined by a shifting vector, being the shortest vector between the respective surface points of the instrument tip and the indentation along the common shifting direction vector.

Thus an efficient way of determining the shifting amount of the descending steps is provided.

According to another exemplary embodiment of the present invention, the method comprises the step of determining a force vector correlating to an estimated force applied onto the instrument by a user based on the shape of the indentation. Furthermore, the method comprises the step of executing a force shifting step, shifting the instrument tip onto the indentation along the determined force vector.

In a preferred embodiment, a back shifting step, is executed after the force shifting step, shifting the model of the instrument tip onto the model of the indentation along the gradient of the indentation towards the reference point of the indentation. The back shifting step further preferably relates to another first descending step.

In a preferred embodiment, the force shifting step is executed after determining the second collision point and/or after determining the third collision point.

Thus, the force used by the user of the instrument in order to hold the instrument tip within the indentation of the calibration device can be considered. Therefore, the determination of the estimated position of the instrument tip can be improved.

In a preferred embodiment of the present invention the shape of the indentation is a cone or a pyramid.

Thus, a shape of the indentation, which is optimized for the method estimating a position of a medical instrument tip. Preferably, the shape of the indentation of the calibration device comprises a continuous gradient, allowing for intersecting the model of the instrument tip with the model of the indentation with a mathematically efficient algorithm and/or allowing for a fast descent search towards the reference point of the calibration device.

According to another exemplary embodiment of the present invention, the surface of the model of the instrument comprises a mesh of surface points, wherein the method comprises the step of optimizing the surface of the model of the instrument by reducing the surface of the instrument to a relevant surface, by mesh optimization and/or by transforming the surface of the model of the instrument into a local coordinate system of the indentation.

The relevant surface of the model of the instrument preferably is determined by the length of the graduation of the indentation. Thus improving an intersection calculation performance.

According to the present disclosure, a use of the estimated position of the instrument tip estimated by a method, as disclosed herein, in a surgical navigation system is provided.

According to the present disclosure, an instrument calibration system comprising a medical instrument with a tracker and a tracking device, configured for tracking the tracker arranged on the medical instrument, the instrument calibration system being configured for executing the method, as described herein, is provided.

According to the present disclosure, a surgical navigation system for computer assisted surgery, the system comprising an instrument calibration system, as described herein, is provided.

According to the present disclosure, a computer program is provided, which, when running on a computer or when loaded onto a computer, causes the computer to perform the method steps of the method, as described herein. Furthermore, a program storage medium is provided, on which the program is stored. Furthermore, a computer is provided, comprising at least one processor and a memory and/or the program storage medium, wherein the program is running on the computer or loaded into the memory of the computer. A signal wave or a digital signal wave, carrying information which represents the program is provided. A data stream which is representative of the program is provided.

For example the aforementioned program, which for example comprises code means which are adapted to perform any or all of the steps of the method according to the first aspect. A computer program stored on a disc is a data file, and when the file is read out and transmitted it becomes a data stream for example in the form of a (physical, for example electrical, for example technically generated) signal. The signal can be implemented as the signal wave which is described herein. For example, the signal, for example the signal wave is constituted to be transmitted via a computer network, for example LAN, WLAN, WAN, for example the internet. The invention according to the second aspect therefore may alternatively or additionally relate to a data stream representative of the aforementioned program.

In a third aspect, the invention is directed to a non-transitory computer-readable program storage medium on which the program according to the fourth aspect is stored.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention is described with reference to the appended figures which give background explanations and represent specific embodiments of the invention. The scope of the invention is however not limited to the specific features disclosed in the context of the figures, wherein

Fig. 1 schematically shows a flow diagram of the method of the present invention;

Fig. 2a schematically shows a medical instrument tip in accordance to a first embodiment;

Fig. 2b schematically shows a medical instrument tip in accordance to a second embodiment;

Fig. 2c schematically shows a medical instrument tip in accordance to a third embodiment;

Fig. 2d schematically shows a medical instrument tip in accordance to a fourth embodiment;

Fig. 2e schematically shows a medical instrument tip in accordance to a fifth embodiment;

Fig. 2f schematically shows a medical instrument tip in accordance to a sixth embodiment;

Fig. 3a schematically shows an instrument tip and an indentation of a calibration device before an elevation step;

Fig. 3b schematically shows an instrument tip and an indentation of a calibration device after an elevation step;

Fig. 4a schematically shows an instrument tip and an indentation of a calibration device before a first descending step;

Fig. 4b schematically shows an instrument tip and an indentation of a calibration device after a first descending step;

Fig. 5a schematically shows a top view of an instrument tip and an indentation of a calibration device before a descending step; Fig. 5b schematically shows a perspective view of an instrument tip and an indentation of a calibration device before a descending step; Fig. 6a schematically shows a top view of an instrument tip and an indentation of a calibration device after a descending step;

Fig. 6b schematically shows a perspective view of an instrument tip and an indentation of a calibration device after a descending step; Fig. 7a schematically shows a top view of shifting an instrument tip onto an indentation of a calibration device along a horizontal shifting vector;

Fig. 7b schematically shows a perspective view of shifting an instrument tip onto an indentation of a calibration device along a horizontal shifting vector;

Fig. 8a schematically shows a top view of an instrument tip and an indentation after the horizontal shifting and before repositioning the instrument tip to an average position between the shifted first collision point, the second collision point and the third collision point in the horizontal plane;

Fig. 8b schematically shows a perspective view of an instrument tip and an indentation after the horizontal shifting and before repositioning the instrument tip to an average position between the shifted first collision point, the second collision point and the third collision point in the horizontal plane;

Fig. 9a schematically shows a top view of descending an instrument tip onto an indentation of a calibration device along a base axis;

Fig. 9b schematically shows a perspective view of descending an instrument tip onto an indentation of a calibration device along a base axis;

Fig. 10a schematically shows a top view of a final estimated position of an instrument tip in an indentation of a calibration device;

Fig. 10b schematically shows a perspective view of a final estimated position of an instrument tip in an indentation of a calibration device;

Fig. 1 1 a schematically shows a force shifting step of an instrument tip onto an indentation of a calibration device;

Fig. 1 1 b schematically shows a back shifting step of an instrument tip onto an indentation of a calibration device after a force shifting step; and

Fig. 12 schematically shows a surgical navigation system.

DESCRIPTION OF EMBODIMENTS

Figure 1 illustrates the basic steps of the computer implemented medical method of estimating a position of a medical instrument tip 1 1 . Step S10 encompasses providing a virtual model of a shape of a medical instrument 10 comprising the instrument tip 1 1 . Step S20 encompasses providing a virtual model of a shape of a calibration device 20 comprising an indentation 21 onto which the instrument tip 1 1 is introduced for calibration. Step S30 encompasses matching the model of the shape of the instrument tip 1 1 onto the model of the shape of the calibration device 20 thereby estimating a position of the instrument tip 1 1 .

Figures 2a to 2f show different shapes of medical instrument tips 1 1 of a medical instrument 10. In order to use such an instrument 10 in a surgical navigation device, a tracking device needs to be able to track movements of the instrument 10. Therefore, in a first step, the instrument 10 needs to be calibrated in view of a tracking device 30. For this purpose, a calibration device 20 comprising at least one tracker is used for calibrating the instrument 10, which also comprises at least one tracker. During

calibration of the instrument tip 1 1 , the instrument 10 is held into the indentation 21 so the instrument tip 1 1 can be held in a fixed position regarding its own tracker and the tracked calibration device 20. In this exemplary embodiment, the indentation 21 has a cone shaped form extending from a surface of the calibration device 20 into the calibration device 20. When the instrument tip 1 1 is held into the indentation 21 , the tracking device assumes that the instrument tip 1 1 is held in a fixed position at a reference point P. The reference point P in this case is the deepest point of the cone shaped indentation.

As described above, there are many instruments 10 and instrument tips 1 1 that do not fit in any provided indentation 21 on the calibration device 20. Therefore, the reference point P relating to the tip of the indentation 21 does not accurately reflect the real position of the instrument tip 1 1 .

Figure 2a schematically shows an instrument tip 1 1 a in accordance to a first embodiment. The instrument tip 1 1 a is cylinder shaped. As can be seen, the instrument tip 1 1 a does not perfectly fit into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 a very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 a. When holding the instrument perpendicular to the surface of the calibration device 20 into the indentation 21 , the real position of the instrument tip 1 1 a would lie in the deepest point of the cylinder in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation 21 depending on the shape of the instrument tip 1 1 a. The distance between the reference point P and the real position relates to a systemic error, the tracking device of the surgical navigation system faces, when assuming the position of the instrument tip 1 1 dependent on the reference point P.

Fig. 2b schematically shows an instrument tip 1 1 b in accordance to a second embodiment. The instrument tip 1 1 b has the form of a threaded cylinder. This instrument tip 1 1 b does also not fit perfectly into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 b very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 b. When holding the instrument perpendicular to the surface of the calibration device 20 into the indentation 21 , the real position would lie in the deepest point of the cylinder in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation 21 depending on the shape of the instrument tip 1 1 b.

Fig. 2c schematically shows an instrument tip 1 1 c in accordance to a third embodiment. The instrument tip 1 1 c has the form of a cylinder with a spherical ground shape. This instrument tip 1 1 c does also not fit perfectly into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 c very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 c. When holding the instrument perpendicular to the surface of the calibration device

20 into the indentation 21 , the real position would lie in the deepest point of the spherical ground shape in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation

21 depending on the shape of the instrument tip 1 1 c.

Fig. 2d schematically shows an instrument tip 1 1 d in accordance to a fourth embodiment. The instrument tip 1 1 d has the form of a cylinder with a toothed ground shape. This instrument tip 1 1 d does also not fit perfectly into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 d very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 d . When holding the instrument perpendicular to the surface of the calibration device 20 into the indentation 21 , the real position would lie in the deepest point of the toothed ground shape in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation 21 depending on the shape of the instrument tip 1 1 d .

Fig. 2e schematically shows an instrument tip 1 1 e in accordance to a fifth embodiment. The instrument tip 1 1 e has the form of a sphere. This instrument tip 1 1 e does also not fit perfectly into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 e very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 e. When holding the instrument perpendicular to the surface of the calibration device 20 into the indentation 21 , the real position would lie in deepest point of the sphere in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation 21 depending on the shape of the instrument tip 1 1 e.

Fig. 2f schematically shows an instrument tip 1 1 f in accordance to a sixth embodiment. The instrument tip 1 1 f has the form of a sickle. This instrument tip 1 1 f does also not fit perfectly into the indentation 21 . Therefore, as illustrated, the reference point P relating to the tip of the indentation 21 does not match a real position of the instrument tip 1 1 f very well. Therefore, an updated reference point Pi should be determined, better reflecting the real position of the instrument tip 1 1 f. When holding the instrument perpendicular to the surface of the calibration device 20 into the indentation 21 , the real position would lie in deepest point of the sickle in the indentation 21 . The real position differs from the reference point P. Holding the instrument in another angle to the surface of the calibration device 20 might change the position of the real position in the indentation 21 depending on the shape of the instrument tip 1 1f.

Fig. 3a shows a virtual model of a shape of an instrument comprising an instrument tip 1 1 . Additionally, Fig. 3a shows a virtual model of a shape of a calibration device 20 comprising an indentation 21 . For matching the instrument tip 1 1 onto the calibration device 20, in a first step, the instrument tip 1 1 is placed onto a reference point P of calibration device 20. In this exemplary embodiment, the instrument tip 1 1 comprises a roughly cylindrically shaped end. The position of the instrument tip 1 1 is hereby defined as the centre of the cylindrical ground surface of the end of the instrument tip 1 1 . Thus, the centre of the cylindrical ground surface of the end of the instrument tip 1 1 is placed onto the reference point P. In this exemplary embodiment, the indentation

is formed cone shaped. Therefore, the reference point P is the deepest point of the cone into the calibration device 20.

After placing the instrument tip 1 1 onto the reference point P, an elevation step is executed. The instrument tip 1 1 is elevated on the indentation 21 along a base axis Z. The base axis Z is defined perpendicular to the surface C of the calibration device 20 outside of the indentation 21 . The elevation amount, which the instrument tip 1 1 is elevated until it hits the indentation 21 is the maximum distance of all surface points of the surface C of the calibration device 20 on a common elevation direction vector along the base axis Z. In other words, from a plurality elevation direction vectors V1 * (dotted vectors) of different surface points of the instrument tip 1 1 towards the indentation 21 along the common elevation direction vector, the longest vector is determined to be an elevation vector V1 , which defines the elevation amount, which the instrument tip 1 1 is elevated onto the indentation 21 . Thus, the common elevation direction vector and the elevation direction vectors V1 * only describes the direction of the vector, but does not include a length. In contrast, the elevation vector V1 describes a direction and a length of the vector.

Fig. 3b shows the point, where the instrument tip 1 1 collides with the indentation 21 by the elevation step. This point is called first collision point C1 .

Fig. 4a shows the next matching step. The instrument tip 1 1 is shifted deeper into the indentation 21. This step is called first descending step. The instrument tip 1 1 is shifted onto the indentation 21 along a known gradient of the indentation 21 from the first collision point C1 towards the reference point P of the calibration device 20. The vectors shown in Fig. 4a represent the gradient of the indentation 21 from different points of the instrument tip 1 1 . The shifting amount, which the instrument tip 1 1 is shifted until it hits the indentation 21 is the minimum distance of all surface points of the surface of the instrument tip 1 1 on a common first shifting direction vector along the gradient of the indentation 21. Thus, from all first shifting direction vectors V2* (dotted vectors) of different surface points of the instrument tip 1 1 towards the indentation 21 along the common first shifting vector, the shortest vector is determined to be a first shifting vector V2, which defines the shifting amount, which the instrument tip 1 1 is shifted onto the indentation 21 . In this case, the indentation 21 has the shape of a cone. The distances can be calculated by defining a line through each surface point with direction of the common first shifting direction vector and by intersecting these lines with the indentation 21 . Thus, dependent on the shape of the indentation 21 , the mathematical formula for intersecting the line with the cone shape can be simplified in the local coordinate system. In this exemplary embodiment, wherein the shape of the indentation 21 has a fixed gradient from the first collision point C1 to the reference point P, a second collision point C2 can be found in one descending step.

Fig. 4b shows the point, where the instrument tip 1 1 collides with the indentation 21 by the first descending step. This point is called second collision point C2. Based only on the first collision point C1 and the second collision point C2, a first estimation of the estimated position of the instrument tip 1 1 can be done. This shows, how far away the estimated position of the instrument tip 1 1 is from the real position.

In Fig. 5 to 9 a more detailed view of the matching steps is illustrated. In contrast to the illustrations of Fig. 3 to Fig. 4, which show an example, wherein the first descending step already gives a good estimate for the instrument 10 being held into the indentation 21 , Fig. 5 to Fig. 9 illustrate a more problematic example of a triangular instrument tip 1 1 , wherein more steps are necessary to fit the instrument tip 1 1 into the indentation 21 .

Fig. 5a is a top view of the indentation 21 and the instrument tip 1 1 . Fig. 5b is a perspective view of the same situation as illustrated in Fig. 5a. As can be seen from Fig. 5a and Fig. 5b, the instrument tip 1 1 of this exemplary embodiment has the shape of an extruded triangle with a triangular ground shape. Additionally, the indentation 21 has the shape of a cone. A tip of the cone shape marks the reference point P. Fig. 5a and Fig 5b also already show the first collision point C1 . Therefore, the elevating step has already been executed. Thus, the first descending step is shown. The instrument tip 1 1 is shifted onto the indentation 21 along the gradient of the indentation 21 from the first collision point C1 towards the reference point P of the indentation 21 . The gradient of the indentation 21 defines the plurality first shifting direction vectors (not shown). The point, where the instrument tip 1 1 collides with the indentation 21 along the first shifting direction vector (not shown) defines a second collision point C2. From all first shifting direction vectors (not shown) of different surface points of the instrument tip 1 1 towards the indentation 21 along the first shifting direction vector (not shown), the shortest vector is determined to be the first shifting vector V2, which defines the elevation amount, which the instrument tip 1 1 is shifted onto the indentation 21 .

Fig. 6a and Fig. 6b show the instrument tip 1 1 and the indentation 21 of Fig. 5a and Fig. 5b after the first descending step is finished. Since the instrument tip 1 1 has been shifted along the gradient of the indentation 21 , the first collision point C1 has moved along the first shifting vector V2 onto a shifted first collision point C1’.

The illustrations of Fig. 7a to 9b describe, how a third collision point C3 is determined.

Fig. 7a and Fig. 7b show the instrument tip 1 1 and the indentation 21 of Fig. 6a and Fig. 6b. Additionally, a horizontal shifting vector V3 is illustrated, indicating a shifting of the instrument tip 1 1 onto the indentation 21 along the horizontal shifting vector V3. A horizontal shifting direction vector (not shown) is determined by searching the centre point M12 between the shifted first collision point CT and the second collision point C2. The horizontal shifting direction vector is then defined as the vector from the centre point M 12 towards the reference point P, however projected into a horizontal plane through the centre point M12. The horizontal plane preferably extends parallel to the surface C of the calibration device 20 outside of the indentation 21 . The third collision point C3 is found, when the instrument tip 1 1 is shifted onto the indentation 21 . In other words, from all horizontal shifting direction vectors of different surface points of the instrument tip 1 1 towards the indentation 21 along the common horizontal shifting direction vector, the shortest vector is determined to be a horizontal shifting vector V3, which defines the shifting amount, which the instrument tip 1 1 is shifted onto the indentation 21 .

Fig. 8a and Fig. 8b show the instrument tip 1 1 and the indentation 21 of Fig. 7a and Fig. 7b after the instrument tip 1 1 was virtually shifted along the horizontal shifting vector V3 onto the indentation 21 .

As illustrated in Fig. 9a and Fig. 9b, when the first collision point C1 , in particular the shifted first collision point CT, the second collision point C2 and the third collision point C3 are defined, a repositioning step is executed, repositioning the instrument tip 1 1 to an average position between the shifted first collision point C1’, the second collision point C2 and the third collision point. The average position between the shifted first collision point CT, the second collision point C2 and the third collision point is found in relation to the horizontal plane without a change of position of any of the collision points CT, C2 and C3 along the base axis Z. In this exemplary embodiment, the shifted first collision point CT, the second collision point C2 and the third collision point lie in the same horizontal plane since the instrument tip 1 1 is held within the indentation 21 perpendicular to the surface C of the calibration device 20 outside of the indentation 21 .

In a final descending step, the instrument tip 1 1 is descended onto the indentation 21 along a descending vector V4 along the base axis Z. Since the gradient of the indentation 21 is fixed, the descending vector V4, being the shortest of a plurality of descending direction vectors (not shown), from the shifted first collision point CT, the second collision point C2 and the third collision point C3 along the base axis Z onto the indentation 21 is equally long from all three of those points. Thus, a final first collision point C1”, a final second collision point C2’ and a final third collision point C3’ can be determined on the indentation 21 , as can be seen in Fig. 10a and Fig. 10b. In this case, the distances from the first collision point C1”, the second collision point C2’ and the third collision point C3’ to the indentation 21 , respectively, are identical. Thus, three final collision points can be found. In general, the collision point with the shortest distance to the indentation 21 along the base axis Z determines the final collision point.

Fig. 10a and Fig. 10b show the instrument tip 1 1 and the indentation 21 after the matching of the instrument tip onto the indentation of the calibration device 20 is finished.

Thus, the position of the instrument tip 1 1 can be estimated within the indentation 21 . Dependent on the estimated position of the instrument tip 1 1 an updated reference point Pi can be determined for usage in a surgical navigation system. The matching algorithm determines the estimated position of the instrument tip 1 1 in the aforementioned way, however this estimated position is only a snapshot. One calculation based on the matching algorithm therefore relates to one single frame taken by a tracking device. In order to improve the accuracy of the estimated position, the

matching algorithm is executed depending on multiple frames. Preferably, the spatial orientation of the instrument tip 1 1 in the indentation 21 is different for each different frame. Further preferably, the instrument tip 1 1 is rotated within the indentation 21 while the different frames of the instrument tip 1 1 are taken. From the different estimated positions of the instrument tip 1 1 based on the different frames, an average position of the instrument tip 1 1 can be determined. Thus, the accuracy of the estimated position can be further improved.

Fig. 1 1 a illustrates an extension of the presented matching algorithm. In real life, the user of the instrument might not use the instrument within the indentation 21 of the calibration device 20 in the most ideal way. If the user holds the instrument in a very acute angle to the surface C of the calibration device 20, the instrument tip 1 1 might not behave the usual way within the indentation 21 . The user generally presses the instrument with some force from the instrument handle to the instrument tip 1 1 . The force will likely cause the instrument tip 1 1 to be only blocked by an opposing surface of the indentation 21 . Therefore, the instrument tip is modelled to ascend in a force shifting step within the indentation 21 by a given threshold along a force vector Vf. Thus, from all force shifting direction vectors (not shown) of different surface points of the instrument tip 1 1 towards the indentation 21 along a common force shifting direction vectors (not shown), the shortest vector is determined to be the force vector Vf, which defines the ascending amount, which the instrument tip 1 1 is ascended onto the indentation 21 .

Afterwards, a back shifting step is executed, which is illustrated in Fig. 1 1 b. The back shifting step basically works like the first descending step. The instrument tip 1 1 is shifted onto the indentation 21 along the gradient of the indentation 21 towards the reference point P of the indentation 21 . The gradient of the indentation 21 defines a common first shifting direction vector (not shown). The point, where the instrument tip 1 1 collides with the indentation 21 along a first shifting direction vector (not shown) defines the collision point of the instrument tip 1 1 with the indentation 21 . From all first shifting direction vectors (not shown) of different surface points of the instrument tip 1 1 towards the indentation 21 along the common first shifting direction vector (not shown), the shortest vector is determined to be a first shifting vector V2, which defines the shifting amount, which the instrument tip 1 1 is shifted onto the indentation 21 .

Fig. 12 schematically shows an instrument calibration system 100 comprising a medical instrument 10 with a tracker and a tracking device 30, configured for tracking the tracker arranged on the medical instrument 10. The instrument calibration system 100 is configured for executing the described method of estimating a position of a medical instrument tip 10.

For a precise tracking, the instrument 10 has to be calibrated by the calibration device 20, so the tracking device 30 is provided with a calibrated position of the instrument 10. Based on the calibrated position of the instrument 10, relative movements of the instrument 10 can be tracked by the tracking device 30. A surgical navigation system using the calibrated instrument 10 therefore is always aware of the exact position of the instrument 10 relative to the tracking device 30.