An Improvement on the Mechanic Eccentric Punch Power

7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
Real-time Tumor Tracking – Modeling and Simulating the Process
MUHAMMAD ALI YOUSUF, ALEJANDRO STAINES SANDERS, ANA ISABEL SALGUEIRO
OCHOA AND ROSA MARIA FERRADAS SOMOZA
Robotics, Automation and Educational Technology Research Group (GIRATE)
Monterrey Institute of Technology and Higher Education, Santa Fe Campus,
Avenida Carlos Lazo 100, Colonia Santa Fe, Delegacion Alvaro Obregon, CP 01389, México DF,
MEXICO.
Abstract: Real-time motion tracking and compensation in surgeries has been investigated by various researchers
using different methods. We look at the problem from control point of view and try to solve it using a simple
mechanical prototype of the treatment couch and an electronic circuitry to feed the signal from the sensor to correct
for the random movements of the tumor. Our physical model shows stable response under the given conditions. We
also present a simple mathematical model of the lung-tumor system needed to guide the control system at
intermediate points. The project was developed as an undergraduate design project.
Key-Words: Cancer, Innovation, Tumor irradiation, automatic couch, engineering design, mathematical modeling.
Different groups have tried various approaches to
follow the tumor movement, using a mixture of
experimental measurements and some sort of
mathematical modeling [5-8]. Suh et.al. [9] study the
accuracy of 2D projecting imaging for tumor motion
monitoring. Obviously in this projection we loose the
information along the beam axis. Hence the
movement along this axis cannot be resolved. Weiss
et. al. [10] explores the temporospatial variations of
tumor during respiration in lung cancer. Other
methods using robotic arms to control the therapeutic
beams have also been investigated [11-12]. These
rely on infrared tracking and synchronized x-ray
imaging to locate the tumor. Finite state models for
respiratory motion analysis in image guided
radiotherapy have been explored and provide a tool
to quantify respiratory motion characteristics [13].
Low et. al., [14] have developed a mathematical
model for the lung tumor movement based on five
degrees of freedom, including the tidal volume rate
of change. This variable plays an important role in
the simple mathematical model we have presented in
this paper. For the purpose of this paper we have
followed the approach taken by the D’Souza, et. al.
[15-16].
1 Introduction
According to the American Cancer Society [1],
Cancer is the second most common cause of death in
US (after heart attack) with over one million people
getting cancer each year. Out of all types, lung
Cancer [2] is the most frequent form of Cancer.
Hence developing technologies for the accurate
treatment of lung cancer is of paramount importance
for the health of humanity. Cancer develops when
cells in a part of the body begin to grow out of
control. The root cause of this is a defect in the gene
structure of the cell. When that happens, generally a
tumor is formed. A tumor can be of two types, benign
or malignant. Benign tumors can generally be
removed and do not spread to other parts of the body.
On the other hand, malignant tumors grow rapidly
and may travel to the other parts of the body via
blood circulation and hence must be cured early. The
process of cancer spreading is called metastasis.
Depending upon the tumor location and extent, a
surgical removal, or chemotherapy, or a radiation
therapy may be recommended for treatment. Various
other methods are available for this purpose
including direct surgery and minimally-invasive
surgery. A combination of these has also been used.
We are currently interested in variants of
radiotherapy [3-4].
ISBN: 978-960-6766-80-0
The paper is divided into following sections. In
section 2 we discuss the main problem in tumor
localization and our proposal to solve it. In section 3
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7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
we discuss the mathematical models of the lungtumor system and that of the breathing cycle. In
section 4 we describe our experimental setup and
comment on the results. We conclude in section 5.
therefore left with 4-degrees of freedom. Out of
these, the two rotations along x- and y-axis may also
be ignored as a first approximation as that would
mean the beam falling at an angle on the tumor. Part
of this can be compensated for by movements along
x and/ or y-axis as the ultimate objective is to keep
the tumor directly under the beam (which must be
switched off when we are off tumor). Although these
two dimensions will be important at a more advanced
level due to the non-spherical nature of the tumor
where the bottom may need different treatment, we
ignore them for now. Hence we are finally left with
only two translations along x- and y-axis which need
to be controlled. In the first model, we use just one
rotation to understand how things work.
2 Problem Formulation
We want to control the movements of a treatment
couch while keeping an eye on the tumor and
adjusting the couch as soon as the tumor moves from
its position. Since all mechanical and electrical
systems have a time lag, we need a mathematical
model to follow the couch during “dead times” when
there is no fresh data from the sensors tracking the
tumor and the couch has to be moved towards the
next “expected” position of the tumor.
The second part of the project is simulating the
breathing of a patient. For that we have developed a
small doll fitted with a servo mechanism which is
under the control of a PICAXE microcontroller and
provides various movement cycles not known to the
control system and hence are completely random
from the control point of view. The details of the doll
are given in section 4.
In order to solve this problem with the available
resources we had to make various approximations
and adjustments in the design. We first discuss the
“ideal” solution and then, one by one we will show
how to approximate the problem to a more tractable
level where simple microcontrollers can be used to
control the system autonomously.
The control system uses the inclination of the chest
(tumor) as a measure of the position. For this part we
have developed a tachometer which helps the photo
sensor in identifying the rotation angle of the chest
and hence the feedback control system can be
initiated to correct the body movement.
Ideally, the couch should be lying on a 6 degrees of
freedom (three translations and three rotations which
can be taken as the roll, yaw and pitch) robot of any
generic type (an hexapod [17] would be a good
choice). The patient can have any of the previously
mentioned movements. Part of this movement (the
breathing cycle) can be approximated as a sinusoidal
movement for a small period of time t. After that
time, either the breathing pattern breaks due to
normal human behavior or due any other unexpected
circumstance (sudden jerk in the body, reflex action,
vibrations, etc). Hence the movements of a 6-degree
of freedom system (the patient) has to be
compensated by another 6-degree of freedom robotic
couch.
3 Problem Solution
Here we discuss a simple mathematical to predict the
movements of the tumor. As mentioned earlier, the
motivation for this type of modeling comes from the
fact that all control systems have inherent latencies
due to motor inductance, circuit delays, etc. Hence
we need a mathematical model to guide the control
system in intermediate points where no control signal
is present. In order to do that we make a simplistic
model of a lung-tumor system which allows us to
predict the next position of the lung given the current
position, the rate of the air flowing in, and the time
interval.
However, if we look at the problem closely, some of
the degrees of freedom are really not necessary and
one can look for approximations. First, the
translational movement along z-axis (perpendicular
to the base frame, or in the vertical direction of the
room) can be eliminated as the beam energy will
remain more or less the same even if the height
changes. Hence we can eliminate one degree. Also
note that the beam is circularly symmetric and hence
rotation along the z-axis is also unnecessary. We are
ISBN: 978-960-6766-80-0
3.1 A Simple Mathematical Model
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7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
Thus if we know the current values of xi , yi and the
time rate of change of volume, we can find the next
values after a time ∆t as follows:
2sin θ
lc cos 2θ
2cosθ
y f = yi +
lc cos 2θ
x f = xi −
Fig. 1: A simplified model of a lung
And
dy
2cosθ dVL
=
dt lc cos 2θ dt
(5)
ISBN: 978-960-6766-80-0
(9)
2.500
2.000
1.500
1.000
0.500
0.000
0.000
0.500
1.000
1.500
2.000
2.500
Fig. 2: A graph of y versus x.
3.2 A comment on singularities:
(3)
(4)
2
dVL
∆t
l c cos 2θ dt
2
These equations allow us to predict a value of
coordinates after a time ∆t provided we know the
amount of air entering the lung per unit time. As
expected, a plot of these values (Fig. 2) gives us an
arc, showing the variations in the location of point on
the inclined plane.
To estimate the time derivative of the angle, we
assume that the air flowing into the lung increases the
volume (area) of the lung by increasing the angle.
First we write the volume as:
1
(2)
VL = l 2c sin 2θ
4
Where l is the length of the inclined distance to the
point ( x, y, z ) on the triangle, and c is the width of the
lung. These variable would be difficult to measure in
a real system (human lung) but we prefer to use them
as in our prototype system these are measurable. The
subscript L for the volume V has been used to
identify the lung volume. Calculating the derivative
of the above:
dx
2sin θ dVL
=−
dt
lc cos 2θ dt
(8)
θ f = θi +
dx
dθ
= −l sin θ
dt
dt
(1)
dy
dθ
y = l sin θ ⇒
= l cosθ
dt
dt
dz
z=c⇒
=0
dt
x, y
(7)
Similarly,
x = l cosθ ⇒
Hence we can write the derivatives of
(6)
z f = zi
We assume that the lung is a triangular shaped object
with an inclination angle of θ . To make it three
dimensional, we add the z-axis where there will be no
changes. Now the derivatives of the x and y
coordinates can be written as:
dθ
2
dVL
= 2
dt l c cos 2θ dt
dVL
∆t
dt
dVL
∆t
dt
Notice that the above equations become singular
when θ = 45o . The origin of this singularity is
physical. As we approach this value, the area of the
triangle stops increasing and beyond this angle it
actually starts decreasing. Hence exactly at this point
the time rate of change of the volume of air going in
becomes zero. Hence our model functions only in the
range: 0 < θ < 45o . Within this range the air can flow
in or out, as we’ll see shortly.
as
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7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
We assume that the change in the lung volume is
directly proportional to the volume of the air flowing
in (the air inside the lung may be compressed). Hence
dVL
dV
=α
dt
dt
3.4 The Experimental Setup
To test the mathematical model developed and to
gain familiarity with the problems involved in the
experimental setup, we developed a prototype system
with similar parameters as the model. The
schematics, of the lung-tumor system are in Fig. 3.
Although we were supposed to develop an artificial
lung with air flowing in and out randomly, we
noticed the effect will be the same if we program the
microcontroller controlling the tumor for similar
random behavior. Hence we opted for a direct tumor
controller using a stepper motor, which changes its
behavior between various choices, “mimicking” a
random behavior from the point of view of couch
controller.
(10)
This quantity has to be modeled and we will
comment on it later.
The above equation assumes we can measure the
time rate of change of air flowing into the lung. On
the other hand, if we know the pressure difference
between the air inside and outside, we can also
estimate the time derivative of volume using the
equation:
dV
= Av
dt
(11)
Where A is the area of the tube and v is the air flow
velocity.
Using Bernoulli’s equation (subscript 1 indicates
outside system and 2 show the variables inside the
lung):
p1 + ρ gy1 +
1 2
1
ρ v1 = p2 + ρ gy2 + ρ v22
2
2
(12)
Hence, assuming that the air velocity below the
tumor is zero, we get
1
(13)
p2 − p1 = ρ v12
2
Thus we can write
2 ( p2 − p1 )
dV
(14)
=A
dt
ρ
The above equation is useful only if we can measure
the inside and outside pressures accurately.
Fig. 3: A schematics of the lung-tumor system
Fig. 4 shows the complete system with stepper motor
still outside the body. The chest of the doll was cut to
be able to see the tumor moving up and down due to
lung motion.
3.3 Modeling of breathing:
Finally, as pointed out earlier, we need a
mathematical model of the breathing. The simplest
thing to do is to use a cosine form for the rate of
change of volume of air, as follows:
dVL
= α cos(ωt + φ )
dt
(15)
This model obviously is predictive in nature.
However, the idea is to keep this behavior (the values
of α , and ω ) a secret for the control electronics and
let it follow the tumor using a feedback control loop.
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7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
Fig. 4: The control circuitry for the vibrating
tumor
The PICAXE chip used in this project has been
programmed in variant of BASIC that comes with the
microcontroller [18]. It generates the “random”
movements of the lung-tumor system. PICAXE-18 is
a simple to use microcontroller selected for its
educational value. Essentially it is a PIC
microcontroller with bootstrap software that allows
programming in BASIC. Obviously this process
reduces the amount of free space available. Hence the
PICAXE 18, for example, has only 40 lines of
programming memory. The software can be
downloaded freely from the web site [18]. The chip
has a total of 13 I/O pins, which is definitely more
than what we need but offers opportunities for further
expansion with more motors and/or sensors. The pin
layout of PICAXE 18 is given in Fig. 5.
Fig. 6: The “tumor” mounted on a stepper motor.
The Fig. 7 shows the final completed system as used
in further experimentation with the mathematical
model and the control algorithms.
Fig. 5: The Pin Layout of the PICAXE-18
microcontroller [18].
Fig. 7: The complete system
We use two chips in two different circuits. First is the
tumor itself with no input utilized in the circuit. The
second chip has a senor to detect the position of the
tumor and to counter the effect of rotation by a
contra-rotation of the couch. The remaining circuits,
for example the stepper and servo motor controllers,
sensors, etc can be found at [18,19] and will not be
reproduced here. The Fig. 6 shows the “bare” lungtumor system which in turn is controlled by a servo
mechanism attached with the rotation sensor based
feedback system.
4 Conclusion
A simulation of the mathematical model of the lungtumor system together with a breathing cycle has
been shown to model the behavior of our prototype
pretty well. However the movement frequency of the
tumor was much higher than the capability of the
control circuitry, keeping in view the meager
resources available for the project. To avoid that, a
“pause” was introduced into the system so that the
tumor stops after moving to a new position so that the
control system can take actions. We are currently
working on an improved model and will report the
development soon.
In short we have shown that a real-time tracking of a
moving tumor is possible using rotation sensors.
ISBN: 978-960-6766-80-0
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ISSN 1790-5117
7th WSEAS International Conference on Application of Electrical Engineering (AEE’08), Trondheim, Norway, July 2-4, 2008
Keeping in view the timidity of the electronics
involved, the results are quite promising.
tracking in radiosurgery,” Med Phys. 2004
Oct;31(10):2738-41.
[13] Wu H, Sharp GC, Salzberg B, Kaeli D, Shirato
H, Jiang SB., “A finite state model for respiratory
motion analysis in image guided radiation
therapy,” Phys Med Biol. 2004 Dec
7;49(23):5357-72.
[14] Low DA, Parikh PJ, Lu W, Dempsey JF, Wahab
SH, Hubenschmidt JP, Nystrom MM, Handoko
M, Bradley JD., “Novel breathing motion model
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[16] D'Souza WD, McAvoy TJ., “An analysis of the
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[17] See for example, http://www.hexapods.net/
[18] http://www.rev-ed.co.uk/
[19] David Lincoln, "Programming and Customizing
the PICAXE Microcontroller," McGraw-Hill,
2005.
Our preliminary results show that a better system,
incorporating more degrees of freedom may be
developed. The final system will have implications
for the health where lung tumor tracking is a major
research problem.
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[1] American Cancer Society, http://www.cancer.org/
[2] Frank V. Fossella, Joe B. Jr. Putnam, Ritsuko
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[3] James D. Cox, Joe Y. Chang, and Ritsuko
Komaki, "Image-Guided Radiotherapy of Lung
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[4] Madelein Kane, "Biology of Lung Cancer (Lung
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[5] S. S. Vedam, P. J. Keall, A. Docef, D. Todor, V.
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[6] M. Isaksson, J. Jalden, and M. J. Murphy, “On
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[8] T. Neicu, H. Shirato, Y. Seppenwoolde, and S. B.
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[10] Weiss E, Wijesooriya K, Dill SV, Keall PJ.,
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[11] Schweikard A, Glosser G, Bodduluri M, Murphy
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[12] Schweikard A, Shiomi H, Adler J., “Respiration
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