IEEE Robotics & Automation Magazine - September 2023 - 85

selected target in the echographic imaging RF; k is the
pixel-to-meter conversion factor; and f hifu
focus in the HIFU transducer RF. Figure 5 presents these
RFs and points for further clarification.
3) Motion compensation: Organs in the abdominal area (such
as the liver, kidneys, and pancreas) are subjected to motion
due mainly to physiological breathing. This motion is typically
periodic in time (with breathing frequency usually
between 0.2 and 0.3 Hz) and linear in space (up to 2 cm)
[20]. As a drawback, this can either cause lesions on undesired
targets or reduce treatment efficiency. The HIFUSK
platform exploits robotic control and machine learning to
track and compensate for target motions. The physician
can select a region of interest (ROI) in the echographic
images of the area surrounding the target defined in step 2.
This ROI is tracked in the subsequent images, and its
motion is learned for controlling the robot and keeping the
HIFU focus where the target is estimated to be. The
motion compensation embedded in the HIFUSK platform
stems from a previous work of the authors [21].
Specifically, the HIFUSK motion compensation functionality
encompasses three subblocks (Figure 6): the imagebased
tracking, the trajectory learning, and the robotic
control, described as follows:
* The image-based tracking detects the ROI, which was
selected by the physician together with the target, across
the new images from the US probe. This tracking is
based on the Tracking-Learning-Detection (TLD) algorithm
[22], which is suited for frame-to-frame, long-term
tracking of unknown objects. Additionally, TLD is capable
of adapting to changes in the appearance of the target
region, and it features robustness to false positives.
Thus, it fits our purpose of tracking a target area on
B-mode US images during HIFU treatments. The trajectory
of the ROI barycenter [,nROI
im ^h where n is the
time sample] is mapped on the target selected by the
is the HIFU
physician so that the target coordinates []
im TROIimtn
r^h in each
frame are identified. This is accomplished by assuming
a rigid transformation ()t
between the target and
ROI barycenter in the imaging frame at the physician's
selection. Finally, the target trajectory is reported in the
robot base RF [].tnrb r^h
* The trajectory learning takes as an input the target trajectory
[],tnrb r^h and it estimates its periodic motion
[].tn rbu^h This prediction is required to consider the delay
in the robot control (in our platform, it is estimated as
100 ms). The trajectory learning is achieved by using
windowed sinusoidal regression: after each time window
(3s), sinusoidal regression is performed on the three
components (x, y, and z) of
rbtn ,
r^h considering all the
points from the latest three-time windows (i.e.,
[, ]).
nt -
! now 9s tnow
* The robotic control enables compensating for the estimated
motion of the target. This is performed by rotating
the HIFU transducer around a virtual pivot point ( ),p
while the focal depth (
hifuf) is continuously adjusted
thanks to the axial electronic steering capabilities of the
HIFU transducer. By keeping the same contact point
between the transducer and the patient's skin (i.e., the
virtual pivot point), variations in the acoustic window
are minimized. Specifically, the HIFU transducer is
rotated at an angle a around the axis v passing through
the pivot point p and normal to the imaging plane. Such
an angle is computed as
a = cos
-1 e rb
rb
where tn 1
()()
()()
uu
uu
tn ptnp
tn ptnp
^
^
h
h
-- -
-- -
rb
rb
$
$
rb
rb
^
^
1
1
h
h
rb
rb
positions in the robot base RF at time n 1respectively,
and prb
RF. This point p rb is defined as
o
(2)
rbu^h and tn rb u^h are the estimated target
-
and n ,
is the pivot point in the robot base
Legend
HIFU Focus
Relevant Points
f = HIFU Focus
t = Treatment Target
p = Pivot Point
Reference Frames
RFrb = Robot Base
RFee = Robot End Effector
RFhifu = HIFU Transducer
RFim = Echographic Imaging
RFee
RFhifu
RFim
z
z
z
p
f
Overall Objective
of Robotic Control
x
x
x
RFrb
t
To Guarantee Matching Between
HIFU Focus and Treatment Target
rbf = rbTee ∗ eeThifu ∗ hifuf
rbTee Variable and From
Forward Kinematics
eeThifu Constant and From CAD Model
eeTim Constant and From CAD Model
k = Pixel-to-Meter
Conversion Factor = 4∗10-4
rbt = rbTee ∗ eeTim ∗ k ∗ imt
FIGURE 5. The HIFUSK platform in terms of relevant RFs, salient points throughout the treatment, and system parameters.
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
85
hifufz = -f0 + ∆s With f0 = 0.12 m
∆s ∈[-0.02; +0.02] m (Electronic Steering)
RF Registrations
IEEE Robotics & Automation Magazine - September 2023

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