Biomedical Engineering Reference
2.1 Principle of End-to-End Accuracy
In general, TMS is applied for cortical brain stimulation. The target region is
therefore located approximately 10-40 mm beneath the TMS coil [ 6 , 22 ]. For an
optimal stimulation the investigator aligns the coil tangentially to the cranium.
For TMS, the coil produces a rapidly changing magnetic field. The magnetic
field passes through the skull and induces an electric field inside the cortex which
leads to cortical stimulation [ 19 , 20 ]. A closer look at the magnetic field of a
typical figure-of-eight coil reveals that the magnetic field is virtually parallel to the
coil's principal axis (z-axis) in the target range. Figure 1.1 depicts the properties of
the magnetic field B produced by a TMS coil. 1 In the target region it can therefore
be assumed that the induced electric field E is perpendicular to the coil's principal
axis. Hence, the z-directed induced electric field E z is assumed to be zero [ 21 ].
Note that for circular coils the target region is circular beneath the full coil instead
of below the coil's center as it is for figure-of-eight coils. Nonetheless, the same
principle is also valid for circular coils.
A slight tilt of the coil, however, will also lead the magnetic field to be slightly
non-perpendicular to the cortex. Nevertheless, the primary component of stimu-
lation will be parallel to the cortex surface. Therefore, the z-component of the
electric field is neglected.
We use a field sensor embedded in a human head phantom that exactly cor-
responds to the stimulation process in the cortex. This sensor measures the induced
electric field E in the cortex in the x/y-plane. Figure 2.1 illustrates measuring the
induced electric field inside the cortex with the field sensor.
Besides the magnitude of the induced electric field, the orientation plays an
important role for figure-of-eight coils [ 2 , 12 , 23 ]. It has been shown that the
optimal current direction induced in the brain is almost perpendicular to the central
sulcus [ 3 , 10 ]. With our setup, we can also measure the orientation of the induced
electric field with respect to the x/y-plane.
To study the impact of motion on the stimulation accuracy, we record actual
head motion during realistic TMS treatment scenarios. An optical tracking system
records position and orientation of a marker integrated in a headband which a
subject wears. The subject sits in front of a robotized TMS system and the marker
is tracked. The tracking system is calibrated to the robot and therefore we can
directly record marker and head motion in robot coordinates (cf. Sect. 4.1 ).
Figure 2.2 illustrates this setup schematically. In this way, we record for each
timestamp t a homogeneous 4 4 transformation matrix M. This matrix consists
Throughout this work the following notation applies: Vectors are denoted with an arrow, such
as A. Uppercase letters, e.g. M, refer to matrices. Coordinate systems are expressed in bold
uppercase letters, such as C. Transformation matrices from a coordinate system C to another
coordinate system D are described by C T D . Scalars and constant values are denoted with italic
lowercase letters, e.g. m. An entire symbols can be found in the frontmatter of this topic.