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GMS Current Topics in Computer and Robot Assisted Surgery

Deutsche Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC)

ISSN 1863-3153

Solving the positioning problem in TMS

Research Article

  • corresponding author Lars Matthäus - Institute for Robotics and Cognitive Systems, University of Lübeck, Germany
  • author Alf Giese - Clinic for Neurosurgery, University of Göttingen, Germany
  • author Peter Trillenberg - Clinic for Neurology, University of Lübeck, Germany
  • author Daniel Wertheimer - Clinic for Neurosurgery, University Hospital Hamburg-Eppendorf, Germany
  • author Achim Schweikard - Institute for Robotics and Cognitive Systems, University of Lübeck, Germany

GMS CURAC 2006;1:Doc06

Die elektronische Version dieses Artikels ist vollständig und ist verfügbar unter:

Veröffentlicht: 30. August 2006

© 2006 Matthäus et al.
Dieser Artikel ist ein Open Access-Artikel und steht unter den Creative Commons Lizenzbedingungen ( Er darf vervielfältigt, verbreitet und öffentlich zugänglich gemacht werden, vorausgesetzt dass Autor und Quelle genannt werden.


Transcranial Magnetic Stimulation (TMS) is a powerful method to examine the brain and tread disorders of the head painlessly and non-invasively. With TMS it is possible to stimulate regions of the motoric cortex which results in the activation of the corresponding muscles. Furthermore, TMS is becoming an alternative treatment for depressions. In all cases correct placement of the TMS coil at the patients head is crucial to the success of the application. We developed a way to guide the TMS coil by a KUKA robot with six degrees of freedom and navigate it using an online registration of the subject's head to its 3D magnetic resonance imaging (MRI) data. Furthermore, we used the advantages of a robotized system to acquire detailed magnetic field data for the TMS coil in use. Combining them with navigated measures of motor evoked potential using techniques from multimodal image registration gave rise to an alternative way of brain mapping.

Keywords: robotized navigated transcranial magnetic stimulation, brain mapping, neuronavigation, correlation ratio


Transcranial Magnetic Stimulation is a powerful method to examine the brain and treat disorders of the central nervous system non-invasively. TMS works by generating a strong magnetic field in a very short time and thus inducing a current in adjacent nerves. The generated activation depends on the change of the electric field along the nerve [1]. Modern TMS coils produce very dense and defined fields, which means that small shifts or turns of the coil lead to substantial changes of the electric field delivered to a nerve and thus to strong variation in the activation of the target nerves. This explains the urgent need for technologies supporting precise navigation and positioning of TMS coils. Until now work on navigated TMS application relies on tracking the patient's head and the coil, either with optical tracking systems [2], [3], [4], [5], [6] or by joint sensors in mechanical arms carrying the coil [7]. By registering 3D image data (MRI, fMRI) with the patient's head and by tracking the coil, the site of stimulation can be displayed with respect to the image data [3]. Thus, the site of stimulation can be determined easily. But this method has also a major disadvantage: Exact stimulation at a pre-defined point is hard to achieve, even more if the site is to be stimulated several times or continuously as in the treatment of depressions. Either head movements must be followed by manually adjusting the coil continuously or the head must be fixed. This results in a loss of accuracy or problems with respect to safety, patient comfort, and durability of the fixation. Our approach of tracking the head and compensate for its movements by positioning the coil with a robot overcomes these disadvantages. A robot can position and orient the coil much more accurately than a human operator. Furthermore, a navigated robotized system allows for real-time motion compensation [8]. Thus, a fixation of the head becomes obsolete. The first part of the article describes the setup of our robotized TMS system and explains the steps necessary for a successful application.

The second part of the paper describes a novel approach to brain mapping using TMS. Navigated TMS systems for motor cortex mapping have already been reported from [5], [6] and [7] but none uses the field information obtained from the coil. In our approach we map the characteristic field of a TMS coil and register this field to the field of MEP measurements obtained from stimulation. The representation site for a muscle is found as the point maximizing a special registration measure.

Hardware setup

For stimulations we use the MagPro (Medtronic, Denmark) system with the circular coils MC125 and MFC75. The robot used for positioning the coil is a KUKA KR3 robot. It possesses six degrees of freedom, so that arbitrary positions and coil orientations can be archived within the workspace of the robot. For tracking the head and for calibrating the coils we use the POLARIS optical tracking system (NDI, Ontario, Canada). For tracking the patient's head a headband with passive POLARIS markers is worn. When mounting the TMS coil to the robot, a transformation from the robot coordinate system to the coil coordinate system must be determined. For that purpose we developed a calibration tool with POLARIS passive spherical markers (Figure 1 [Fig. 1], Figure 2 [Fig. 2]). The calibration tool position and the robot position are measured using the POLARIS system and the robot sensors respectively. Thus the transformation from the robot coordinate system to the coil coordinate system can be calculated. Using the inverse transformation we get the necessary robot position for a given coil position.


The system for robotic navigated TMS application is based on the following steps: (1) Creating a virtual reality model of the head, (2) Registering the virtual world with the real world, (3) Planning the stimulation in VR, (4) Moving the robot correspondingly, and (5) evaluating the response to stimulation. The following sections describe each step in detail.

Creating a virtual head model

In this first step a virtual reality model of the head is created. First, a 3D MRI dataset of the patient's head is obtained using a standard 1.5 T MR scanner. Second, the open source software VTK [9] is used to segment the cranium surface from the 3D MRI data and visualize the data (Figure 3 [Fig. 3]). This step must be performed only once for each patient and is usually performed before the treatment.

Registration VR vs. Real Head

In a second step the virtual head model is registered to the real head. This is achieved by a combined landmark and surface matching method. We use the POLARIS optical tracking system to acquire three landmark points on the head, e.g. the left and right lateral orbital rim and the tip of the nose, and several hundred surface points. The surface points are taken continuously when moving a pointer over the head's surface, so that the whole process takes less than three minutes. The user marks the landmarks on the virtual cranium surface. Then a coarse registration via point-to-point correspondence is performed. The exact registration is obtained by using the results of the landmark step as start value for an iterative closest point scheme (Figure 4 [Fig. 4]).

The registration step already allows for a moving head, i.e. there is no need for a fixation of the head during the acquisition of the landmark and surface points. Each acquired point is related to the coordinate system defined by the markers from the headband worn by the patient. Thus a movement of the head results in a movement of the head coordinate system as well as the pointer coordinate system. The relative position of the pointer to the headband stays fix (Figure 5 [Fig. 5]).

Planning and delivering the stimulation

The registration together with the head tracking establishes a real-time link between the virtual reality and the robot work space. The robot is now used to position the TMS coil according to the planning in VR. Here, the user picks a target point on the virtual cranium, chooses the desired distance of the coil from the head and the desired coil orientation. The virtual coordinates are then transformed into world coordinates by relating them to the headband defined coordinate system, which in course is related to the robot coordinate system using the tracking system (Figure 6 [Fig. 6], Figure 7 [Fig. 7]).

The robot now moves the coil to the target position. It must be ensured that the trajectory of the robot and the coil are valid, i.e. the transition from one stimulation point to the next must not interfere with the patient's head. Therefore, a module for trajectory planning is included in our system. In short, the coil is moved away from the head, then along an arc around the head over the target region and then towards the head again.

When the robot has reached the desired position at the head, a motion compensation module can be activated. The position of the head is then continuously monitored and changes are translated into robot movements so that the coil is held at exactly the same point relative to the head. This proved especially useful when delivering several stimulations to the same point, e.g. for control reasons or in the treatment with rTMS.

Data handling

All defined target positions are stored relative to the coordinate system defined by the MRI data. If a TMS session is to be repeated or extended at a later time, the old coil positions relative to the head can be recalled and re-approached by the robot. This is especially useful during a repeated therapy over several days as in the treatment of depressions. Note that by storing the stimulation points relative to the virtual head there is no need for attaching the headband always in the same position.

Furthermore, the physician can assign response values to the stimulation positions. Such values can be measured muscle responses like motor evoked potentials (MEPs) or subjective evaluations from the patients like relief from pain or strength of visual impressions induced by TMS. This way a simple visual inspection of the stimulation results is possible. Nevertheless it must be noted that this visualization does not take the different coil characteristics into account. Especially when using a circular coil, the site of stimulation is not under the center of the coil, but at a circular region of about two thirds of the coil radius as our mapping experiments show.

Brain mapping

The presented robotized navigated TMS system allows stimulating and testing a large number of target points around the vertex with high precision. It is an open question how to translate the results into exact maps of the cortical function at the brain surface. Several procedures have been described: projecting the stimulation point with the strongest response to the brain surface [7], calculating the center of gravity for all measurements [4], or simulating the propagation of the induced electric field from firing the TMS coil [10]. No algorithm so far uses real field information for the specific TMS coil. We suggest a novel method which incorporates field measurements from the coil obtained in a separate experiment.

Measuring the characteristic field of a TMS coil

In the following, the characteristic field of a coil denotes the maximum electric field produced by firing the coil. Since modern coils possess a non-trivial arrangement of their windings, Maxwell's equations cannot be solved explicitly to obtain the electric field. Rather than approximating it as done by [11], [12] we measure it directly. Therefore the circular TMS coil is mounted to the robot as described above. A straight copper wire of one centimeter length is used as a simple sensor for the local electric field. From the theory of Maxwell it is known that the induced electric field of a wire loop in a plane parallel to the loop is tangent to concentric circles around the loop center [13]. Hence the sensor is placed in a plane parallel to the coil and in direction tangent to the coil. By connecting the probe to an oscilloscope and measuring the maximum induced voltage when firing the coil, we obtain a voltage directly proportional to the electric field. The sensor is connected to the oscilloscope by shielded cables which run orthogonal to the coil plane to minimize voltage coming from the cables rather than the probe. The robot moves the coil over the sensor along a rectangular grid, varying the distance r from the sensor to the coil center and the height h of coil above the sensor. Firing the coil at the vertices of the grid, a total of 50 x 30 measurements are obtained. The full 3D characteristic field is calculated by rotating the measurements around the z-axis of the coil, using the symmetry of the coil (Figure 8 [Fig. 8], Figure 9 [Fig. 9]).

Calculating the site of simulation

From the stimulation of the patient we obtain the field of motor evoked potentials (MEPs). The coil is set to different target points around the head, fired, and the measured MEP at a target muscle is assigned as scalar field value to the coil position. As explained in [1], the strength of response of an axon to stimulation depends on the change of the electric field along the nerve. Assuming that the orientations of the axons in the brain representing the target muscle are distributed equally, the evoked muscle potential from a magnetic stimulation at the head depends only on the strength of the electric field at the representation site for the muscle. Since the processes translating the stimulation of the axons in the brain into muscle responses are quite complex, we do not try to give a model for the dependency of the MEP measurements from the electric field strength. Despite, we only assume that there is a functional correspondence between the electric field at the representation site and the muscles response.

The task now is to calculate the representation site n r from the knowledge of the stimulation sites p i , the obtained MEPs mi, and the shape of the characteristic field f of the coil. (We denote scalar values with normal letters and vectors with bold font.) Define fi(n) as the value of the characteristic field at point n when centered at p i . Note that by the use of cylindrical coordinates to encode f, the value of fi(n) can be calculated fast, since it depends only on the distance h from the coil plane and the radius r, i.e. the distance from the coil normal.

We conjecture from the discussion above that the functional dependence between fi(n) and mi is highest for n = n r , i.e. the correct representation site. The amount of functional dependence between two scalar sets is measured by the Correlation Ratio, see [14]. Hence n r is found by maximizing CR({fi(n)}, {mi}) over n. In practical implementation any nonlinear optimizer can be used to find n; in our program this was done by Powell's method as described in [15].

Discussion and future work

We presented a robotized navigated TMS application system, which allows for planning in virtual reality, motion compensation, and repeated stimulation at defined points. First experiments show that this system provides a save, reliable, and exact way for delivering transcranial magnetic stimulation.

First coarse measurements of the accuracy of positioning the coil estimate the maximum error to less than 3mm. The error is mainly due to small shifts of the headband and problems in acquisition of the head outline, i.e. difficulties of having the pointer always on the scalp. This leads to small errors in registration and hence to inaccurate target positions for the robot. We plan to accompany the marker based tracking with a marker free video-optical tracing of the face to reduce the error further. The latency of the robot motion compensation module is about 0.5s. This value will be reduced in future by optimizing the robots real time capabilities and fine tuning of the POLARIS-KUKA-connection.

The use of the robot prepares the ground for a novel way of mapping the motoric cortex by directly measuring the characteristic field of the TMS coil and registering this field to the field of motor evoked potentials. The evaluation of the correlation of this mapping with other functional mapping methods like functional Magnetic Resonance Imaging (fMRI), Positron Emission Tomography (PET) or direct electrical stimulation will be performed in the near future.


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