in silico simulation of a translational human breast cancer model in mice march 25 th, 2013 mark...
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In Silico Simulation of a Translational Human Breast Cancer Model in Mice
March 25th, 2013
Mark Dawidek
Department of Medical Biophysics
Introduction• Improvements in ultrasound
® Improvements in monitoring angiogenic growth
® Improvements in quantifying tumor-induced angiogenesis
• Yet to unravel tumor-induced angiogenesis
• Multiple feed-back and feed-forward mechanisms
Department of Medical Biophysics
Introduction• In silico model of tumor angiogenesis
• Search for mechanisms to target therapeutically
• Predict treatment effects
• Consists of separate angiogenesis and tumor growth models
• Project focus is tumor growth model
Department of Medical Biophysics
Hahnfeldt Model• Lattice where each point represents a cell
• Cell activity governed by four parameters:
• ps probability of stem cell
• probability of spontaneous death
• proliferation capacity
• max migration distance
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Hahnfeldt Model• “Conglomerates of self-metastases”
• Model algorithm implemented in MATLAB
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Target Curve
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0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
1.2
f(x) = 5.38352452386406E-06 x³ + 0.000246997749071592 x² − 0.00798036766762435 x + 0.0468636664804204
Averaged Experimental Tumor Data
Time (Days)
Nor
mal
ized
Vol
ume
Limitations of MATLAB Code• Additional parameters:
• Size of lattice (3D)
• Number of iterations
• Both can drastically affect computation time
• Both held constant:
• 100x100x100 lattice
• 100 iterations
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Scaling• 50 days / 100 iterations = 0.5 day mitotic cycle
period
• Assumption: volume # of cells
• # of cells in silico << # of cells in vivo
• # of cells after 100 iterations varies with parameters
• Comparing shape of curve, not volume
® Normalize
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Fixing Proliferation Capacity and Spontaneous Death
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0.0250.05
0.0750.1
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
5
10
15
# of
Cel
ls
Optimizing Migration Distance and Stem Cell Probability
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0.01
0.02
0.03
0.04
0.05
0.06
0.07
0
50
100
150
200
250
1
2
3
4
ps
Cost
Trend Along ps
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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080
50
100
150
200
250
300
350
ps Plotted Along Independent Values
ps
Cost
Trend Along
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0.5 1 1.5 2 2.5 3 3.5 4 4.50
50
100
150
200
250
300
Plotted Along Independent ps Values
0.01
0.02
0.03
Cost
Trend Along
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0.5 1 1.5 2 2.5 3 3.5 4 4.50
5
10
15
20
25
30
Plotted Along Independent ps Values
0.04
0.05
0.06
0.07
Cost
ps= 0.02, = 1
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ps= 0.02, = 3
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ps= 0.06, = 1
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ps= 0.06, = 3
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US Image of Actual Tumor
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Limitations and Next Steps• Increase scale
• Angiogenesis simulation ~1/4 of actual cancer size
• Initialized with one cell versus millions
• Improve speed
• Dead cells simply “disappear”
• Effects of surrounding tissue
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Summary• Constant lattice size and fixed number of
iterations
• essentially negligible, ps controls metastatic tumor size, both parameters fixed
• Increasing improves curve fit• Improvements decay predictably, exponentially• Negligible gain for > ~0.4
• No clear effect of on fit• controls shape and size (Hahnfeldt)
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Acknowledgements
Thank You to Dr. James Lacefield & Matthew Lowerison
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