IEEE Robotics & Automation Magazine - September 2018 - 74

Theory: Magnetic Actuation
The steering of magnetically actuated catheters is achieved by
exerting wrenches caused by the Lorentz force on the flexible
body of the instrument. The resulting internal bending
moment propagates along the catheter toward its base, correlating with the Euler-Bernoulli beam theory. By controlling
the magnetic wrenches, the user can drive the deflection of
the catheter to achieve the desired configuration of the device,
most often expressed in terms of the catheter tip pose. The
Lorentz force itself occurs between the magnetic component
of the catheter [described by its dipole moment (m ! R 3)],
located at a position (p ! R 3), and experiencing the external magnetic field ^B (p) ! R 3h. The resulting wrench
(W ! R 6) comprises force (F ! R 3) and torque (T ! R 3),
and is defined as
d ^m $ B ^phh
G.
W =8FB==
T
m # B ^ph

(1)

Each method of exploiting magnetic interaction (1) for
catheter steering is highly device specific, with numerous,
diverging approaches presented. This creates a significant
challenge to provide a useful classification for magnetically
actuated catheters, as the principles behind such devices can
vary significantly. Nevertheless, in each case, the magnetic
interaction occurs between two principal agents: the dipole
m attached to the device and the field B (p), which is a property of the external environment.
Based on that notion, the magnetically actuated catheters
are divided into two groups. The first group consists of magnetic catheters, which are actuated by modifying the catheter
dipole m in a static magnetic field. Such catheters are called
active magnetic instruments, as they require electrical or
mechanical power to be transmitted to the catheter tip. In
contrast, the second group of magnetic catheters comprises
instruments that host permanent dipole and are actuated by
varying the external field B (p). These catheters do not host
any active elements and are steered merely by exploiting their
MR Bore

Catheter

B(p)
T
Winding I
Direction

x
p
z

Solenoid

Figure 3. The deflection of a catheter with a solenoid tip inside
an MR scanner. Once a current I is applied, the magnetic field
B (p) induces a torque T on the solenoid tip p to cause a
parallel alignment of the dipole moment direction m with the
direction of the magnetic field of the scanner. The inset shows
the wire solenoid wound around the catheter tip.

IEEE ROBOTICS & AUTOMATION MAGAZINE

september 2018

response to a changing external environment. Therefore,
they are called passive magnetic instruments.
Active Magnetic Actuation
Active magnetic systems are primarily based on the interaction between variable magnetic dipoles generated by
microcoils and the magnetic field provided by MR scanners.
Earlier work [19] demonstrates that the strong magnetic field
in an MR scanner offers a unique environment for steering
flexible devices (Figure 3). A solenoid embedded on a
catheter induces a magnetic moment (m ! R 3), given by
the following:
m = nIA,

(2)

where n ! Z + is the number of turns in the solenoid, I ! R
is the input current, and A ! R 3 is the vector cross-sectional
area of the solenoid. The magnetic field provided by an MR
scanner is static and produced by powerful, superconducting
electromagnets. Therefore, the catheter with microcoils is
actuated by controlling I ! R, and thus changes the dipole
moment m of a microcoil. As a result, a variable magnetic
torque T can be prescribed. Moreover, since the magnetic
field inside the MR bore is homogeneous, the field gradients
are zero in the entire workspace, and results in the magnetic
force F being zero. The total magnetic wrench is therefore a
pure torque, allowing for two degrees of freedom (2 DoF)
actuation sufficient for the deflection of the catheter tip.
Nevertheless, the orientation of the field B (p) is constant
and parallel to the symmetry axis of the MR bore, but no
torque can be generated in that direction. The effect of the
resulting actuation singularity can be overcome by including
multiple components in the catheter, each with a different
dipole direction [20].
The theory behind steering catheters with the magnetic
field of an MR scanner has traditionally been investigated on
currents running through a wire solenoid or Helmholtz-type
coils [19]. The exception is the use of ferromagnetic spheres
in the catheter tip [Figure 2(a)] demonstrated by Gosselin
et al. [21]. Using spheres in an MR setting has shown some
promise [22]; however, since they create large artifacts during
the in vivo image capturing of the catheter, it is difficult to
navigate into smaller branches.
Another example of a catheter with microcoils on the tip
[Figure 2(b)] demonstrates a three-axis coil by Roberts et al.,
which was wound up on a 1.5 Fr cylindrical catheter and
guided inside a 2 T MR scanner [19]. Losey et al. [17] designed the magnetically assisted remote-controlled endovascular catheter (MARC), which was specifically guided inside
an MR unit bore. Settecase et al. [20] continued the theory of
Roberts et al., and demonstrated the steering of the MARC
inside a 1.5 T magnetic field. Their findings expressed an
accurate deflection prediction, but it was also confirmed that
the catheters could only tolerate a maximum current of 1 A
for more than 1 min before the wire insulation melted. This
drawback was further investigated by Hetts et al. [23] who

IEEE Robotics & Automation Magazine - September 2018

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