Prediction of Regional Tumor Spread Using Markov Models Megan S. Blackburn Monday, April 14, 2008.
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Transcript of Prediction of Regional Tumor Spread Using Markov Models Megan S. Blackburn Monday, April 14, 2008.
Prediction of Regional Tumor Spread Using Markov Models
Megan S. Blackburn
Monday, April 14, 2008
Background
• 2006 Conference Paper by Benson et al.
• Describes use of Markov Chains to model cancer spread in patients
• Specifically studied head and neck cancers
• Comparisons made to surgical data
• Goal: Try to reproduce model proposed by Benson et al.
Background
• Cancer impacts our society as a whole
• Everyone is affected in some way by cancer in their lifetime
Cancer
• Generalized name describing more than 100 different disorders
• Cancer cells can be considered immortal• Divide many more times than normal cells
thus growing out of control• Do not interact normally with other cells
resulting in invasion of regions of the body other cells could not
Cancer Treatment
• Because of the far-reaching effects, much effort has been put into the treatment of cancer
• Goal of treatments: Kill the maximum cancer cells while killing the minimum normal cells
• Typical Treatments: Radiation Therapy and/or Chemotherapy
Radiation Therapy
• Beam of photons is incident on the patients
• Photons deposit their energy within the body
• Kills both healthy and diseased cells
http://www.srhc.com/services/oncology/image/Clinac.jpg
Radiation Therapy
• Before treatment can begin, CT scan is taken of the patient
• CT scan is used to plan the patient’s treatment
http://asiaonc.com/files/images/H&N%20Lat2.img_assist_custom.jpg
Radiation Therapy
• ICRU 50 describes several definitions for treatment planning
• GTV• CTV• PTV• Treated Volume• Irradiated Volume
Room for Improvement
• In Radiation Therapy, many different margins must be used in order to assure the tumor gets a therapeutic dose
• Margins result in more healthy tissue being dosed• Microscopic disease must also be accounted for• Markov Model could help to determine where the
cancer has spread
Head and Neck Cancers
• Unique compared to other cancers
• Typically very irregular in size
• Early treatment was surgical removal
• Radiation Therapy and Brachytherapy are now useful tools
• Diseased Lymph nodes must be treated as well
Lymph Node Regions
Region Nodal GroupI Submental & SubmandibularII Upper JugularIII Middle JugularIV Lower JugularV Posterior TriangleVI Anterior Compartment
http://www.iscb.org/rocky06/presentations_pdf/29Kalet-rev2.pdf
Cancer Staging
• Tumor-Node-Metastasis (TNM) Staging• T – anatomical description of the primary
tumor site• N – involvement of the lymph nodes• M – metastasis to other regions of the body• Staging is very diverse for cancers of the
head and neck due to varied anatomical regions
Markov Model• Named after Russian Mathematician
Andrey Markov
• Mathematical Model describing a random progression of a system
S1 S5S2 S3 S4
0.5
0.5 0.3
0.7
0.1
0.9 0.8
0.2
Markov Model• Probabilities of transitioning from one state
to another
• Discrete time steps
• Cannot be in more than one state at a time
S1 S5S2 S3 S4
0.5
0.5 0.3
0.7
0.1
0.9 0.8
0.2
Markov Model• Clock – describing number of steps to take
• N States – number of locations in which one could be
• N Events – One event associated with each state
S1 S5S2 S3 S4
0.5
0.5 0.3
0.7
0.1
0.9 0.8
0.2
TTt ,1,...,2,1
NNQ ,1,...,2,1
NN eeeeE ,,...,, 121
Markov Model• Initial Probabilities – probability of starting state
• Transition Probabilities – probability of moving from one state to another
S1 S5S2 S3 S4
0.5
0.5 0.3
0.7
0.1
0.9 0.8
0.2
j P q1 j
iqjqPa ttij 1| Nji ,10ija ji,
11
N
jija i
Applications to Cancer
• Apply Markov Models to the movement of cancer – specifically lymph nodal involvement
• Goal is to determine the lymphatic spread with only the starting location of the cancer and the staging of the cancer
• Used a series of Markov Chains rather than a single Markov Chain
Applications to Cancer
• Single Markov Model represents each nodal region
• Within each Model, there are 5 states –
0 (no cancer), 1, 2, 3, 4 (extensive disease)
• Unique aspect is the linking of the Markov Models
• Links represents future nodal involvement
Applications to Cancer
• s defined states (0,1,2,3,4) in each node region
• Probability qs of each state metastasizing to next nodal region (state 1)
• Probability distribution, pi, of being in a specific state within each lymphatic region
• Probability, p’, of the next nodal region becoming affected by microscopic disease
p' psqss0
4
Applications to Cancer
• Initially, probability distribution for each lymphatic region is set
• For initial tumor region, probability is set to 1 for state 1, 0 in all other states
• For all other lymphatic region, probability is set to 1 for state 0, 0 in all other states
Applications to Cancer
• Initial Tumor Region– Transition Matrix
– Metastasis Vector
• Lymphatic Regions– Transition Matrix
– Metastasis Vector
P'
1 0 0 0 0
0 0.9 0.1 0 0
0 0 0.9 0.1 0
0 0 0 0.9 0.1
0 0 0 0 1
8.0
6.0
4.0
2.0
0
'm
10000
5.05.0000
05.05.000
005.05.00
00001
P
9.0
8.0
7.0
6.0
0
m
Application to Cancer
• Model is iterated on 4*Cancer Staging• Probability of microscopic cancer occuring in each
nodal region uses:• Value must be adjusted against the probability that
metastasis has already occurred• Added to the probability that the downstream
nodal region is already in State 1
p' psqss0
4
Implementation
• Implemented in MATLAB
• Benson et al. used FMA (Foundational Model of Anatomy) for all anatomical regions
• Unable to match the anatomical data that Benson et al. obtained
• Could not directly compare with his results
Results• Assumed 6 nodal regions downstream from primary tumor• Obtained probabilities of cancer spreading to this regions
given an initial cancer stage
Lymph Region
A
Lymph Region
B
Lymph Region
C
Lymph Region
D
Lymph Region
E
Lymph Region
F
Cancer Stage
1 28% 22% 17% 12% 9% 7%
2 36% 30% 25% 21% 17% 13%
3 43% 37% 32% 27% 23% 19%
4 50% 44% 38% 33% 28% 24%
Conclusions
• Much tweaking is needed to the concept
• Too many arbitrarily chosen values
• Interesting idea BUT very unlikely to be accepted by the medical community anytime soon