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TBME-00524-2006-R3-preprint 1
Abstract—This study shows that even a simple Proportional-
Integral-Derivative (PID) controller can be used in a clinical MRI
system for real-time navigation of a ferromagnetic bead along a
pre-defined trajectory. Although the PID controller has been
validated in vivo in the artery of a living animal using a
conventional clinical MRI platform, here the rectilinear
navigation of a ferromagnetic bead is assessed experimentally
along a two-dimensional (2D) path as well as the control of the
bead in a pulsatile flow. The experimental results suggest the
likelihood of controlling untethered microdevices or robots
equipped with a ferromagnetic core inside complex pathways in
the human body.
Index Terms—Real-time control, magnetic resonance,
minimally invasive interventions, blood vessels, ferromagnetic
I. INTRODUCTION
Minimally invasive interventions (MII) are a modality
increasingly considered by physicians as a way to reduce
potential risks and injuries incurred to patients while allowing
shorter recovery periods. One of these modalities, catheterism,
offers an efficient way to reach remote areas. Nevertheless,
being restricted by its radius of curvature and frictions on the
endothelial membrane, catheters have limitations in sinuous
and narrow vessels.
Although the use of catheters or probes remain
advantageous in many cases, new techniques aimed to alleviate
Copyright (c) 2006 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending an email to [email protected].
Manuscript received July 26, 2006; revised April 24, 2007. This work was
supported in part by a strategic grant from the Natural Sciences and
Engineering Research Council of Canada (NSERC) and in part by the Canada
Research Chair (CRC) in Conception, Fabrication and Validation of
Micro/Nanosystems and grants from the Canadian Funds for Innovation
(CFI). Asterisk indicates corresponding author.
S. Tamaz was with École Polytechnique de Montréal (EPM), Montréal,
QC, H3C 3A7, Canada.
R. Gourdeau and J.-B. Mathieu are with École Polytechnique de Montréal
(EPM), Montréal, QC, H3C 3A7, Canada.
A. Chanu is with iMetrik, Montréal, QC, H3C 3X6, Canada.
*S. Martel is with École Polytechnique de Montréal (EPM), Montréal, QC
H3C 3A7, Canada (e-mail: [email protected],
www.nano.polymtl.ca).
these limitations are beginning to appear in the medical field.
In [1] for instance, a camera capsule pill is carried naturally
through the gastrointestinal pathway and acts as an untethered
endoscope. Nonetheless, MII involving cardiovascular
navigation of untethered devices for applications such as
highly localized drug delivery for deep-seated tumor cells,
thermal treatment at specific sites, diagnosis or surgeries, and
conveyance of magnetic resonance imaging (MRI) contrast
mediums to name but a few possibilities, may provide highly
valuable tools in the future to the medical practitioners.
Hence, in order to reach remote areas within the complex
cardiovascular pathway, magnetic propulsion [2-9] offers an
advantage at such a scale over other proposed actuation
methods [10, 11] for operation in the human body. Other
demonstrations of controlling the displacement of a
ferromagnetic device in vitro using magnetic gradients [2, 9]
for future potential uses in humans have been performed
without initially considering during the tests, an imaging
modality capable of localizing such a device inside the human
body. Here, the displacement control of a ferromagnetic core
is performed using the imaging gradient coils of a clinical MRI
system in order to validate the approach under the constraints
imposed by such a platform capable of providing feedback
position of the device inside the human body. Considering
existing constraints, such as delays imposed by MR-imaging
sequences, or communication between hardware and software
modules in the MRI platform, to name but only two examples,
the results would reflect a more realistic view of controlled
navigation of a ferromagnetic device inside the human
cardiovascular network. In sight of such an application, an
MRI system by comparison to other apparatus found in clinics
is an ideal platform, providing not only enhanced soft tissue
imaging contrasts, but also magnetic gradient propulsion,
imaging, interfaces, and the control capabilities required for
endovascular navigation.
Reference [12] mentions the difficulty of propelling
microdevices in a cardiovascular system due to the relative
wide range of vessels’ diameters. Thus, the control algorithm
presented here is dedicated for macro scale navigation, which
focuses in conveying the device in vessels such as arteries and
arterioles whereas microscale navigation is introduced in [13].
The damage that the bead will induce on the vessel’s walls,
either by collision or friction, is considered to be negligible.
Real-time MRI-based Control of a
Ferromagnetic Core for Endovascular
Navigation
Samer Tamaz, Richard Gourdeau, Member, IEEE, Arnaud Chanu, Jean-Baptiste Mathieu, Student
Member, IEEE-EMBS, and Sylvain Martel*, Senior Member, IEEE
TBME-00524-2006-R3-preprint 2
Nevertheless, to insure a smooth conveyance of the bead to
destination, collisions and the risk that the bead gets trapped in
the endothelium need to be minimized and as such, an
appropriate explorative 2D control strategy is adopted based
on the PID controller. This control algorithm can be easily
adapted to 3D and tested once the MRI is equipped with
additional coils capable of generating magnetic gradients
susceptible to levitate the bead.
Controlling a device in the human cardiovascular system
proves to be quite challenging due to the non-negligible
pulsatile blood flow, whose variations in waveform amplitude
and frequency from one vessel to another, add complexity in
the conveyance of the device to the targeted area through a
pre-assigned path. In such a complex environment, proper
delay in the software architecture is essential to sustain stable
control of the device and guarantee real-time navigation.
Operating in an MRI system prevents propulsion and
tracking to be applied simultaneously therefore adding another
major constraint to such a control application. Hence, by
alternating between these two processes, we demonstrate that it
is still possible to convey the device from one location to
another along a pre-determined path using MRI-based
navigation capabilities. This path is acquired at a preliminary
stage of the intervention and fragmented into rectilinear
segments [14] which are then delimited by waypoints. Along
each segment, a PID-based feedback controller calculates the
propulsion command to be applied to the device based on its
acquired position [15, 16]. The operation modes of the
tracking, propulsion and control subsystems are scheduled by
the MRI software architecture [17,18].
This paper presents the first 2D in vitro control experiments
using a clinical MRI system.
II. METHOD
A. Software Architecture
The presented architecture allows the guidance of a
ferromagnetic microdevice through the use of a standard real-
time clinical MRI system [19] in a specially designed
phantom. In this study, a Siemens Avanto 1.5 T clinical MRI
system is used. The architecture and sequence presented here
are analyzed in terms of their impact on the controller needs
and the minimum reachable real-time feedback time.
1. Real-time MRI Environment
The propulsion and navigation of the device is made
possible through a seamless interaction with the MRI imaging
gradient coils that are able to induce a force on the
ferromagnetic core as explained in more details in Sect. II.A.3.
Such propulsion capabilities are thus intimately linked with the
MRI specifications, allowing the displacement of the device.
However, another major key aspect in the feasibility of the
software architecture is the real-time aspect of the Siemens
Avanto MRI system. Since most clinical and interventional
MRI systems are now engineered with real-time capabilities,
an application such as the MR-Sub project [20] is feasible on
most upcoming hardware systems.
The environment considered here includes two main
modules that are used during every Siemens MRI acquisition.
The first module known as Integrated Development
Environment for Applications (IDEA) is the sequence module
used to design and run the developed sequences for propulsion
and tracking. The other module is the Image Calculation
Environment (ICE) and is mainly responsible for the image
reconstruction using the k-space data acquired during the
sequence. A common sequence would then excite the protons
using an RF wave and encode the frequencies and phases of
the proton volume in the k-space matrix. Each line of the k-
space would be sent to the ICE module for image construction
by inverse Fourier Transforms. Using the provided real-time
MRI capabilities, one can react on the running sequence from
the ICE module. That is, gradient amplitudes and directions,
RF wave and ADC parameters can be changed on the fly
through the use of the real-time special framework. Such real-
time changes can trigger special events in the sequence and
generate new data for the ICE module, hence creating a real-
time feedback loop between the two modules. By integrating a
real-time controller in the ICE real-time framework, it is
possible to constantly monitor the acquired data for device
tracking and apply the required gradient strength and direction
for propelling the device towards a given target.
2. System Overview
An overview of the system software architecture is depicted
in Fig. 1. It illustrates all the required components and
interactions between the modules to allow the 3D navigation
of a microdevice in complex vascular networks. As shown in
Fig. 1, three sub-modules (Positioning, RoadMap and
Gradients calculation) and one Main Agent embedded in the
ICE module were implemented to allow propulsion and
steering control of the microdevice. For endovascular
navigation, high definition angiography images for target
selection by a potential user may be required. The RoadMap
module takes care of this operation by gathering the
appropriate image of the region of interest until the user has
made the target selection. The target position is then
transmitted to the main agent for final destination coordinates.
But at present, this RoadMap module is only used to embed a
pre-selected path into the architecture at runtime. This path is
in the form of a text file containing the x, y and z positions of
the desired waypoints to be followed by the device. The
Position module is responsible for the device’s position
calculation, based on the acquired projections — rather than
standard MR 2D images that would be affected by artifacts —
through an MR-sequence based on magnetic signature
selective excitation [21-23]. These projections are correlated
with an initial position mask, constructed during the first
acquisition of the sequence. The maximum amplitude from the
correlation is used as the actual shift in position on a given
axis in the MRI referential.
These positions are then used by the Gradients calculation
TBME-00524-2006-R3-preprint 3
module to compute the correct gradient amplitudes for the next
waypoint in the planned path to the final target. These data are
sent to the Main Agent that acts as a manager for
communication between both sides of the framework, namely
IDEA and ICE.
The Main Agent sends the new gradient vector to the
running sequence through the real-time framework. The main
concern in this system is the time delay for a given feedback
loop. As described in more details in Sect. II.A.3, this delay is
responsible for the controller’s sample time and is directly
proportional to the complexity of the controller itself.
3. Suggested Architecture and Sequence Design
In order to evaluate the most appropriate control
environment, we developed a 3D navigation capable sequence
for 1D and 2D experiments for which the presented controller
(see Sect. II.B) is implemented. We present in Fig. 1 the
selected sequence and illustrate the three aspects relevant for
the controller’s performance; i.e. the time delay between a
position request on a given axis and the actual propulsion of
the device on the same axis denoted tdelay, the sampling time h
that represents the time between two successive position
requests, and the feedback time which stands for the minimum
allowed delay between a call to the ICE real-time controller
function and the return to the paused running sequence
denoted tfeedback. Fig. 2 illustrates the timing and event
occurrences of the sequence design for 3D control.
The Tracking module considers the first acquired position
as the origin of the Cartesian reference mark. From data in our
previous experiments [21,22] the minimal time to acquire the
xyz-coordinates of a current position is tgpos = 16 ms. The
minimal paused running sequence obtained experimentally is
tfeedback = 30 ms, which is closely related to the complexity of
the controller as noted in Sect. II.A.2.
Fig. 1 Overview of the software system architecture adapted from [17].
Fig. 2. Overview of the real-time sequence for the 3D control environments with time multiplexed positioning and propulsion phases.
TBME-00524-2006-R3-preprint 4
Therefore, the time left to apply the propulsion gradients is
tgprop = tfeedback - tgpos = 14 ms. Experiments are thus carried out
with h = tfeedback + tadc = 33.8 ms, and tdelay = h + tgpos + tadc =
53.7 ms as depicted in Fig. 1. A minimal tfeedback is chosen to
minimize tdelay. Therefore a duty cycle tgprop/h = 41.37 % is
obtained.
Fig. 3. MRI Cartesian coordinates referential.
B. Control
To ensure the rectilinear motion of the core along the
segments traveled by the ferromagnetic bead in 2D in the
presence of a flow, the commands applied along the x and z
axes are determined based on Tangent-Normal-Binomial
(TNB) frame and then converted to the Cartesian coordinate
system. The resulting command is directly proportional to the
magnetic force generated by the MR-imaging coils defined as
HMVF mm
(1)
where is the permeability of free space,
mV is the
magnetic volume of the ferromagnetic bead, M
its
magnetization, H
is the magnetic field and the gradient
operator.
Fig. 3 illustrates the orientation of the Cartesian system with
respect to the MRI bore. A discrete regulator makes use of a
PID controller acting along the tangent direction of the
trajectory segment and a PD controller acting along the normal
direction (represented as N
in Fig. 4). When the bead
navigates along a vessel subjected to a flow, the normal steady
state error is negligible compared to the tangential error.
Therefore, the integral term of former controller is discarded.
e
e
Ne
x
Te
x
e
x
),( zx
N
x
T
x
),( ww zx
x
re
x
z
wr
Fig. 4. Cartesian and polar systems in the horizontal plane of the MRI
system.
The Laplace transfer function of the tangent controller is
expressed as
s
KsKK
sE
sUsK TI
TDTP
T
TT
)(
)()( . (2)
Using the backward rule transformationzh
zs
1, the
discrete transfer function of the tangent controller becomes
1
1
)(
)()(
z
zhK
zh
zKK
zE
zUzK TITDTP
T
TT
. (3)
In (3), UT is the magnitude of the command along the
tangent direction of the current segment wr
, with KTP, KTD,
and KTI representing the tangent proportional, derivative, and
integral gains respectively, ET represents the tangent quadratic
distance separating the targeted position of the bead from its
current position, defined as
)()sin()()( eerT signzEzE (4)
where αe represents the angle formed by the quadratic error
vector re
and the normal quadratic error vector Ne
. The third
term on the r.h.s. of (4) acknowledges the sign of the error so
that tangent error vector Te
is always pointing towards the
waypoint.
The time based error is the quadratic error defined as
22)()()( tzztxxte wwr
(5)
where wx and wz are the waypoint’s coordinates, and )(tx
and )(tz are the current position’s coordinate with respect to
time. The angle from (4) is defined as
ww
ww
xx
zz1tan
(6)
where wx and wz are the previous waypoint’s coordinates.
The commands along the x and z axes are derived
respectively by the following equations
)()sin()()(
)()cos()()(
zUzUzU
zUzUzU
zNTz
xNTx
(7)
where UNx and UNz represent respectively the magnitudes of
the command along the x and z coordinates which are applied
along the normal direction of the segment wr
, as described
by the following equations
).sin()()sin()()(
)cos()()cos()()(
vNNDeNNPzN
vNNDeNNPxN
zVKzEKzU
zVKzEKzU
(8)
The angles from (8) e and
v are respectively formed by
TBME-00524-2006-R3-preprint 5
the positive x-axis and the normal error EN and the normal
velocityNV . The angle e from (4) is defined as
.)(
)(tan 1
txx
tzz
w
w
e
(9)
A linear normalization is used to ensure that the commands
applied do not exceed the gradient limits of the x and z axes. A
saturator is applied to the integral component of the PID in
order to avoid the integral windup effect. A formal stability
analysis based on Lyapunov was undertaken but its full report
is beyond the limits of the manuscript.
C. Model
A simplified model for simulating the 3D MRI-based
navigation of a ferromagnetic spherical bead in a fluidic in
vitro environment is considered. Besides the magnetic force
exposed in Sect. II.B, the model regroups four other major
forces acting on the bead as illustrated in Fig. 5. The fluid drag
is expressed as
u
uCAuD Dtf
2
2
1 (10)
where ρf is the fluid density, u
is the relative velocity
between the bead and the fluid, u
it’s norm, At is the cross-
sectional area of the bead, and DC is the drag coefficient for a
sphere defined as
;4.0Re1
6
Re
24DC .102Re0 5
(11)
In (11), Re is the Reynolds number and it is defined as
bf du
Re (12)
where μ is the fluid viscosity, and db is the diameter of the
bead. The infinite sign in (11) indicates that the formula do not
take into account the wall effect. The weight of the bead is
defined as
gV W
(13)
with ρ underlying the mass density of the bead. The
buoyancy force is expressed as
gV b
f (14)
where V is the physical volume of the bead and g
is the
gravitational acceleration.
As explained in [20] a ferromagnetic sphere propelled on a
surface inside the MRI bore will roll along the x-axis and will
slide along the z-axis since the z-axis has the same orientation
as the DC flux density Bo (here at 1.5 T). Therefore, both types
of frictions force have been taken into account. The sliding
friction force is defined as
bWf xs
(15)
with x
is the sliding friction coefficient, which can either
be statics
or kinetic k . The rolling friction force [24] is
defined as
bWR
aff
g
r
(16)
where R is the radius of the bead, gf is the rolling friction
coefficient. In (16), a is the radius of the contact circle
between both objects (bead, static surface) defined as
.4
)(3 31
*E
rbWa (17)
In (17), the Young's modulus *E and the equivalent radius
r are defined respectively as
21
2
2
2
1
2
1
*
111
,111
RRr
E
v
E
v
E (18)
where 1v and
2v represent the Poisson's ratio of the static
and the moving object respectively, 1E and
2E their Young's
modulus and 1R and
2R their radii.
z Dz
W
FMz
FMx
x
y
b
fz
Dx
fx
Bo
Trajectory
Fig. 5. Kinematics and dynamic motion description of the bead in the
horizontal 2D plane.
III. EXPERIMENTS
Two types of experiments were carried out in order to
evaluate the performance of the controller in a 2D
environment. At first, a quiescent flow environment in a two
dimensional environment followed by a pulsatile flow along
one dimension only. All experiments used a chrome steel bead
of 1.5 mm diameter [25] and mass density ρ = 8410 kg/m3. A
value of 1.35x106 A/m (1.69 T) for the saturation
magnetization of the bead was measured with a VSM (Walker
Scientific MG-50) under an applied field Bo = 1.5 T. The
TBME-00524-2006-R3-preprint 6
maximum peak magnetic gradient amplitudes along the x and z
axes were set to ±40 mT/m.
The immersion of both setups in water is required in order
to acquire the position of the sphere with an MR-tracking
technique using RF excitation of the surrounding protons
excited by the bead’s magnetic field [21,22].
The 2D controller described in Sect. II.B is used to perform
the closed loop control experiments. According to [26], the
static friction coefficient between steel and
polymethylmethacrylate (PMMA) is 0.5. Taking into account
these parameters, the simulations were carried out with
MATLAB/SIMULINK whose block diagram is shown in Fig.
6. Based on the simulation, the control gains were adjusted
heuristically in order to minimize the steady state error, the
oscillations and the percentage overshoot.
Fig. 6. Block diagram of the discrete closed loop control system.
Fig. 7. 2D experimental setup in quiescent flow.
A. 2D Quiescent Flow Control Experiment
1. 2D Quiescent Flow Setup
The ferromagnetic sphere is placed on a thin rigid PMMA
plate that is mounted on three threaded nylon rods equipped
with nylon nuts which are tightened to a thick PMMA plate
forming the base of the setup. By adjusting nuts height on the
threaded rods, the horizontality of the thin plate is attained
based on an air level. A PMMA lid is placed on the thin plate
to trap the bead that allows a 3 mm vertical gap. The lid is
fastened using rubber bands as shown in Fig. 7.
Due to the significant friction forces existing between the
bead and the PMMA plate, open loop experiments were
conducted in order to evaluate the kinetic friction coefficients
along both the x and z axes individually (Fig. 8 and Fig. 9) and
simultaneously (Fig. 10). The same upward gradients along y
are applied in order to reduce the effects of friction.
The rolling friction forces between steel and PMMA is
evaluated at 73.9 nN, based on equations (16), (17) and (18)
where 29.01v , 33.02v , PaE 11
1 1005.2 ,
PaE 11
2 101.3 , 5.11R mm and 2R were considered
[27].
Fig. 8. Plot of the position in x versus time of an open loop control
experiment carried out along the x-axis withxB = 15 mT/m and
yB = 30
mT/m, with two corresponding simulation plots considering s
= 0.5, and
xk= 0.1 and
xk= 0 respectively and one simulation plot considering a
73.9 nN rolling friction force.
2. 2D Quiescent Flow Results
Results of the open loop experiment along x that are shown
in Fig. 8 reveal that when correlating the simulation to the
experimental curve, the kinetic coefficient is approximated to
0.1, producing a kinetic sliding friction force of 12.8 μN.
Along z, open loop results presented in Fig. 9 disclosed a
kinetic coefficient zk= 0.4 which is close to values from the
literature [28]. Fig. 10 illustrates results carried out along the
horizontal plane. The gradients in z were set higher than the
gradients in x to ensure a diagonal motion of the bead. Once
again, upon fitting the simulated curve to the experimental
one, the closest kinetic coefficients obtained are xk= 0.1 and
zk = 0.3.
Closed loop experiments were carried out by providing
waypoints coordinates to the ICE as well as the control gains.
These were conducted along the x and z axes following the
waypoint track. Fig. 13.(A) and Fig. 13.(B) show the same
experimental data correlated with simulation data differing in
the choice of friction coefficient values. Fig. 14 illustrates the
data of an experiment where there are no intermediate
waypoints along the first segment.
In the simulation, the water density ρf and viscosity μ are
respectively set to 1 g/cm3 and 0.001002 Pa.s. Based on the
TBME-00524-2006-R3-preprint 7
tuning technique, the controller gains were adjusted to KTP = 2,
KTD = 0.02, KTI = 0.05, KTNP = 5 and KTND = 0.1. The anti-
windup limits were set to half the maximum gradient’s peak
magnitude.
Fig. 9. Plot of the position in z versus time of an open loop control experiment
carried out along the z-axis withzB = -26 mT/m and
yB = 30 mT/m, with
two corresponding simulation plots considering as
= 0.5, and axk= 0.4
and azk= 0.46 respectively.
Fig. 10. Plot of the position in z versus the position in x of an open loop
control experiment carried out along the horizontal plane withxB = -15
mT/m, yB = 30 mT/m and
zB = -26 mT/m, with three corresponding
simulation plots considering s
= 0.5, xk
= 0.1 and zk
= 0.3, zk
= 0.4,
zk= 0.46 respectively, t = 2.64.
The choice of coefficients obtained in the 2D open loop
experiments is confirmed from the results displayed in Fig. 10.
In Fig. 13.(A), the simulated curve is delayed with respect to
the experimental curve, whereas in Fig. 13.(B), the simulated
and experimental plots reach the same level along the
waypoint track.
Fig. 11. 1D pulsatile flow setup.
B. 1D Pulsatile Flow Control Experiment
1. 1D Pulsatile Flow Setup
A ferromagnetic sphere with identical characteristics is
placed in a rigid cylindrical tube of inner diameter of 9.82 mm.
The tube is inserted in a PMMA base that ensures its
horizontality as shown on Fig. 11. Flexible tubes are used to
connect the cardiovascular pump outlet and inlet to the rigid
tube’s ends. Handmade PMMA filters enclosing nylon meshes
are inserted between the rigid tube and the flexible tube to
avoid leakage of the fluid pump and to constrain the bead
inside the rigid tube. For the pump to function adequately, the
fluid consists of a mix of 40% of glycerol and 60% of water
which emulates the blood density. The alignment of the rigid
tube with the x-axis is ensured with the MRI laser beam. A
femoral flow, whose typical rate waveform (see Fig. 12) in
human body is provided by a dedicated programmable pump
[29].
At the beginning of the experiment, the pump would carry
the bead in the positive x-axis along the tube. Upon visual
inspection, once the pump reversed its pumping direction,
causing the bead to drift to the other side of the tube, the
sequence was launched, assigning to the controller a positive
target along the x-axis, and thus acting opposite to the flow.
Fig. 12. Human femoral rate flow waveform with a scale factor of 50.
2. 1D Pulsatile Flow Results
Both waveforms of Fig. 15 reveal periodic oscillations
TBME-00524-2006-R3-preprint 8
induced by the pulsatile flow close to the set point value. In the
simulation, the flow is considered to be directed along the
segment being followed by the bead which is why the
segment’s angle is passed on to the model in Fig. 6 and set to
zero. Experiments were carried out with average flow rate of 6106 and 6101.7 m
3/s which coincides with the stability
limits of the controller shown for both waveforms of Fig. 15.
The same controller gains were used as in Sect. II.A.1 except
for KTP that was increased to 4 to counteract the pulsatile flow.
IV. DISCUSSION
A. 2D Quiescent Flow Control Analysis
The kinetic coefficients obtained for z in Fig. 10 are lower
than those obtained in Fig. 9. On one side, it is most likely that
the relative high magnetic propulsion gradients applied to the
bead will induce vibrations to the phantom, hence diminishing
the effects of friction forces between the bead and the PMMA
plate. On the other side, it could be explained by the fact that
the bead’s motion is not steady as it is rolling and sliding at the
same time.
The oscillations clearly observed in the experimental plots
with intermediate waypoints (Fig. 13) are mainly due to the
large tdelay. Such oscillations appear as the bead approach a
waypoint. It is noted that the oscillations are smaller in
amplitude (Fig. 14) even when the bead is getting closer to
waypoint ( 6 , 6 )w wx cm z cm because it is carried by the
momentum of the high gradients. Despite the friction’s aspect,
correlation does exist between experimental results and
simulation, which validates the chosen model. In the absence
of friction, the normal control main purpose is to act when the
bead changes its course. As it can be noticed in the figures
related to the 2D closed loop control, the bead doesn’t drift
away even when turning with an angle close to 90º. The
derivative element of the normal controller contributes in
canceling the normal velocity vector along the current
segment, which is in fact the tangent velocity vector along the
previous segment, whereas the proportional element acts in
reducing the normal error. The normal PD controller is
therefore useful to avoid the bead being propelled in unwanted
junction at the bifurcation of blood vessels. Another pertinent
observation found in these figures is the significant drift of the
bead along the x direction to the detriment of the z direction as
the bead leaves the current waypoint and set its course towards
the next waypoint along the first segment. Since the first
segment has a slope of 45º, the command signals calculated by
the controller must have equal magnitudes. But the fact that
the frictions along the z-axis are much more significant than
those along the x-axis the controller is unable to compensate
rapidly with a relatively significant tdelay.
A.
B.
Fig. 13. Plot of the position in z versus the position in x of a closed loop
control experiment carried out on the horizontal plane withyB = 30 mT/m
and mT/m 40 maxmax zx BB , along a waypoint track whose xz-
coordinates are [(2,2) ; (4,4) ; (6,6) ; (5,8.8)] cm, with a corresponding
simulation plot considering s
= 0.5, and xk= 0.1,
zk= 0.4 for (A) and
xk = 0.05, zk = 0.3 for (B) respectively, t = 13.5 s.
When moving from a waypoint to another, the bead starts
first by traveling along the x direction and then along the z
direction due to the fact that the friction force is larger in
magnitude along the z direction than in the x direction.
Moreover, when departing from a waypoint, the normal
controller command is not high enough when compared to the
tangent controller command to bring back the bead along the
TBME-00524-2006-R3-preprint 9
track. Besides, based on simulation, if normal PD controller
gains are increased in order to reach a higher command, the
bead will oscillate even more.
The comparison of the experimental results observed along
the first segment between Fig. 13 and Fig. 14 reveals the
advantage of the intermediate waypoints as they prevent the
bead from drifting away from the trajectory.
It is noted that once the MRI system will be equipped with
coils capable of generating high amplitude gradients, the
friction forces won’t be a major issue. Nevertheless, even if the
levitation of the bead is unfeasible for the moment, the friction
that would exist between the bead and endothelial membrane
of the blood vessels would most probably be of viscous type
and hence negligible compared to sliding friction, as a thin
layer of blood would be separating the bead from the vessel’s
wall at all time.
B. 1D Pulsatile Flow Control Analysis
The compliance effect due to the flexible tubes [30] and the
handmade filters bring a strong alteration to the signal. The
programmed waveform — where the femoral waveform is
chosen — signal gets significantly attenuated in amplitude
when it reaches the tube since these have an effect comparative
to low pass filters. Nevertheless, as mentioned in Sect. II.B,
since the pump is adjusted empirically to meet the
controllability limits, the fluid drag force becomes significant
enough to evaluate the controller performance. Based on the
results obtained in Fig. 15, it might be possible, without the
need of measuring the actual flow waveform signal to which
the bead is subdued, to attenuate or remove these oscillations
by applying a feedforward control. This would be performed
first by measuring and registering an early oscillation cycle
based on the first two cycles. Then a command signal whose
waveform is proportional to one oscillation cycle subtracted to
the steady state error is then applied with a 180º phase shift,
i.e. opposite in sign. In order to meet this phase shift,
synchronization between the command signal and the pulsatile
flow is necessary and established mainly by taking into
account tdelay and the duty cycle. For a more reliable approach
destined for in vivo navigation, synchronization could be
attained by the use of a pulse oximeter [15]. It is to be noted
that the feedforward control would find utility mainly for final
waypoints rather than intermediate waypoints as there would
be a necessity to perform the intervention with a maximum
stability.
C. General Analysis
The control experiments conducted in vitro mimic in vivo
behavior. Nevertheless, major aspects need to be taken into
account in order to perform MII efficiently. First and foremost,
the nature of waypoints (intermediates and finals) need in
some cases, to be compensated for motion artifacts such as the
patient breathing and movements using registration techniques
as discussed in [22]. Second, the 2D controller needs to be
tuned in order to prevent the system from exiting the region of
attraction as determined by the formal stability analysis, due to
the variations of physiological parameters such as the ratio of
the diameter of the bead over the vessel’s diameter, blood
viscosity and density. Still, early in vivo experiments without
the improvements of these aspects proved the acceptability of
the current control algorithm [31].
Fig. 14. Plot of the position in z versus the position in x of a closed loop
control experiment carried out on the horizontal plane withyB =30 mT/m
and mT/m 40 maxmax zx BB , along a waypoint track whose xz-
coordinates are [(2,2) ; (4,6)] cm, with a corresponding simulation plot
considering s
= 0.5, and xk
= 0.05 and zk
= 0.3 respectively, t = 20.2 s.
Fig. 15. Plot of the position in x versus time of a closed loop control
experiment carried out withyB = 40 mT/m and
maxxB = 40 mT/m, along
the x-axis with a waveform whose scale factor is adjusted respectively to 50
(with an offset of 3 cm along the x-axis) for waveform (a) and to 60 for
waveform (b) for a common set point wx = 6 cm.
V. CONCLUSION
In this paper, we consider the use of an MRI system for
cardiovascular navigation. Through two complementary
experiments, the PID controller has shown that 2D real-time
control is feasible despite some limitations. As being part of
the trajectory planning, a velocity profile can be envisioned
instead of a positional profile. Due to the existence of a large
range of variation in physiological and physical parameters,
although the initial version of the controller has proven to be
TBME-00524-2006-R3-preprint 10
effective during experiments conducted in the carotid artery of
a living swine [31], an adaptive control algorithm would be
susceptible to improve the robustness to those variations.
Subsequent to such improvements, the system may eventually
be applied to other areas of the biomedical field such as
precise guide wire or needle [32] steering into deformable
tissues which would ensure safer insertions and precise
placements. The technique may also prove to be applicable
within blood vessels as small as capillaries for applications
such as the direct delivery of therapeutic agents to tumor cells.
In such cases, because factors such as inertia, buoyancy and
gravity are not dominant for devices navigating in the
microvasculature, a 3D controller can be envisioned. But
because at such a scale other forces dominate and since the
blood is no more homogeneous, the controller would need to
be adapted accordingly.
ACKNOWLEDGMENT
The authors would like to thank particularly O. Felfoul, and
E. Aboussouan for their active involvement in the experiments
as well as their suggestions, Dr. D. Ménard for providing the
facilities in order to measure the magnetisation of the
ferromagnetic beads, L.-P. Carignan for his help in operating
the VSM, and R. Ouellet from the Montreal Heart Institute for
providing the cardiovascular pump.
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Samer Tamaz received the B.E. degree in
electrical engineering in 2002 from the
Lebanese American University (LAU) and the
M.S. degree in biomedical engineering from
École Polytechnique de Montréal (EPM),
Montreal, QC, Canada, in 2006. He is
currently working as a biomedical engineer at
the healthcare center and community service
of Laval, Qc, Canada.
Richard Gourdeau (S'88-M'91) received is
B.Sc.A and M.Sc. in mechanical engineering
from Laval University (1986, 1988) and his
Ph.D. from Carleton University (1991). He
joined the Department of Mathematics and
Industrial Engineering at the École
Polytechnique de Montréal in 1991 as
assistant professor and then moved to the
Department of Electrical Engineering in 1999
where he is professor since 2005. He is
teaching robotics and automatic control. His
research interests include robotic
manipulators control, control of mechanical
systems and digital control.
Arnaud Chanu received the B.Sc. degree in
computer engineering in 2003 and the
M.S. degree in biomedical engineering from
École Polytechnique de Montréal (EPM),
Montréal, QC, Canada, in 2006. He is
currently working as an embedded system
engineer at iMetrik. His work interests are the
development of embedded system software
architectures and computer hardware design.
Jean-Baptiste Mathieu received the
B.Sc. degree in mechanical engineering in
2002 and the M.S. degree in biomedical
engineering from École Polytechnique de
Montréal (EPM), Montréal, QC, Canada,
in 2004. He is currently with the
NanoRobotics Laboratory in the
department of Computer Engineering at
EPM. His current research interests are in
the development of medical applications of
microdevices propelled in the blood vessels
by magnetic gradients generated by
magnetic resonance imaging (MRI)
systems.
Sylvain Martel (S’95-M’96- SM’07) was
born in Québec City, Canada in 1959. He
received the B.E. degree from the
Université du Québec (UQTR), and the
M.Eng. and Ph.D. degrees from McGill
University, Montréal, Canada in 1989 and
1997 respectively, all in electrical
engineering. Following postdoctoral
studies at MIT, he was Research Scientist
at the BioInstrumentation Laboratory,
Department of Mechanical Engineering at
MIT. He is currently Associate Professor in
the Department of Computer Engineering
and the Institute of Biomedical
Engineering at École Polytechnique de Montréal (EPM), Montréal, Canada,
and Director of the NanoRobotics Laboratory at EPM. Dr. Martel holds the
Canada Research Chair (CRC) in Conception, Fabrication and Validation of
Micro/Nanosystems. He has over 130 refereed publications and participates
in many international committees and organizations Presently, Dr. Martel
leads a multidisciplinary team involved in research and development of new
platforms and nano-factories based on a fleet of scientific instruments
configured as autonomous miniature robots capable of high throughput
autonomous operations at the molecular scale, minimally invasive tools based
on microdevices propelled in the blood vessels by magnetic gradients
generated by Magnetic Resonance Imaging (MRI) systems, Micro-Electro-
Mechanical System (MEMS) and System-on-Chip (SoC)-based miniature
instrumented robots, development if new MEMS/NEMS based on the
integration of bacteria as biological components, and many other related
projects. Dr. Martel’s main expertise is in the field of nanorobotics, micro-
and nano-systems, and the development of novel instrumented platforms
including advanced micromechatronics systems and a variety of related
support technologies. He has also a vast experience in electronics, computer
engineering, and also worked extensively in biomedical and mechanical
engineering.
