Introduction - Microsurgery: Advances, Simulations, and Applications - page 19

When the force sensor presented in Fig. 1.9 is combined with
the slave system shown in Fig. 1.16 and the master device shown
in 1.15, the tele-operation system for catheter manipulation can
be described by the diagram shown in Fig. 1.19 and the following
equations [52]:

mx cx g f (1.1)

MM MM M M

mx cx g f (1.2)

SS SS S S

where the sub-indexes M and S stand for parameters belonging to
the master and slave respectively, m M and m S the mass of each device,
c M and c S their viscosity coeficient, x M and x S their displacement, g M
and g S the applied forces from the actuators, f M the force applied
from an operator to the master, and f S the force applied by the slave
to the environment. This system is described by

gKx x Kx x ( ) ( ) (1.3)

S P MS V MS

where K P and K V are the constant coeficients for position and
velocity feedback. On the other hand, the master device should have
variable impedance that relates with the interaction of the catheter
with vasculature. For that g M is deined as follows:

g ( F F ) ( K f K f Mx C x ) (1.4)

M sensor V FS s FStip stip V M V M

where F sensor is the sum of the force measurements given by the
sensors f s and f stip multiplied by their respective coeficients K FS
and K FStip . F V is a virtual resistant force while mass M V and viscosity
coeficient C V are variable depending on the diameter of the blood
vessel where the tip is located, catheter position (expressed using
the axial motion and twisting motion), and blood pressure [52].
For applying telesurgery to endovascular intervention, several
additional challenges have to be solved as the end effector is a
catheter or guide wire, which are lexible bodies. These intravascular
tools are in contact with human blood along the surgery; therefore
the grasping mechanism should be compatible with sterilization
process and also grasp them irmly without damaging them or
without slips. If the catheter slips from the grasping mechanism, the
shape of the catheter within the blood vessel may change and the
encoders or accelerometers used for motion encoding may provide
inaccurate measurements for the amount of catheter inserted and