I was once a researcher at Princess Margret Hospital (part of
University Health Network) and participated in a research group which
involved photodynamic therapy to treat cancer. I just wanted to share
a tid-bit on what we did there and what came out of it.

What is Photodynamic Therapy?

You can read a detailed description here
, but in a nutshell, it
is a form of cancer treatment which involves injecting a tumor with a
drug that is activated by light. The drug can injected or taken orally
and the light can come from external or internal (via fiber optic
cables) sources.

The Problem

After injecting the drug into the tumor, it does not stay within
the bounds of the tumor and is absorbed by the surrounding
tissue. In prevent damage to the surrounding tissue, the key
is to only “activate” the drug that resides within the tumor. Light is
emitted from the light source in a radial pattern and the “intensity”
of the light dimishes as you travel further from the source. The loss
of “intensity” occurs in a pradicitable manner and thus given a light
source, tissue properties, and distance, one can measure the light and
thus “strength” of the drug at any given position.

Because light is emitted radially outwards like a sphere, it is
difficult to achieve the correct light intensity in irregular shaped
tumors. In particular, it is very difficult to achieve good solutions
for tumors with sharp edges (think about a box full of balls, there is
always some amount of empty space). The key is to try and achieve the
correct dosage within the tumor tissue and no drug activation outside.

Modeling the Problem

Before starting, we had to model the
problem. We used Matlab (with embedded Java) to model the problem in a
3D environment. For our test tumor, we decided to use the sine
function with each point rotated around the axis creating a 3D object.
Within the test space, we picked N number of points (inside and
outside the tumor) for which we computed the expected and actual
dosages. These would be our testing points.

The Computational Problem

Here in lies the computation problem. We have several light
sources and testing points within the tumor. The goal is to set the
intensity of the sources such that we get the correct activation level
of the drug at all of our testing points.

Simulated Annealing

This problem is complex…it is not possible to generate all
possible solutions and choose the best case. However , one could
generate a initial solution and keep tweaking values. Each time we
teak a value, we compare its outcome (cost) with the current outcome
and take the better solution. This will eventually lead to a solution
in winch tweaking of the sources leads to no more better solutions.
This is called a local minimum and unfortunately, finding a local
minimum does not guarantee it is the overall best solution (or global
minimum).

To get around the problem of becoming stuck at local minimums,
we decided to go down the route of using probabilistic algorithms to
determine a “good” solution and in particular, decided to use
Simulated Annealing(SA).

In SA, we start off at some initial solution and teak several
light sources as before but at each step, when determining to accept a
particular solution, we allow for a probability to accept a worse
solution. This allows us to “jump” past local minimums.
Mathematically, this can allow the algorithm to eventually find the
global minimum if we run the program for a very long time.

The Cost Function

For each solution generated, we have to evaluate the quality of
the solution. This is done via the cost function. For our problem, we
looked at each testing point and compared the drug activation at that
point with the required amount. We then took the difference and
applied some multiplier. The multiplier was used to emphasize how
important it was for a testing point to be close to it’s required
dosage. For example, if tumor existed near a vital organ, the
multiplier on points within the organ would have extremely high
values.

In the end, it was determined that SA had a difficult time generating “good” solutions.
If often found solutions that could not be easily manufactured in a optic fiber. We also
found that letting the algorithmic run for a long time did not generate better solutions.
That being said, there was a lot discovered. Researchers learned what factors affected the
algorithm, and what worked and what didn’t. It was also a great learning experience for me
since it was my first time participating in a research group.

You can see the full results from the published paper here:

A. Rendon, J. Okawa, R. Weersink, J.C. Beck and Lothar Lilge, Conformal light delivery using tailored cylindrical diffusers,
Optical Methods for Tumor Treatment and Detection: Mechanisms and Techniques in Photodynamic Therapy XVI, 2007.
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