The role of the vasculature and the immune system in optimal protocols for cancer therapies Heinz Sch Heinz Sch ättler ättler Dept. of Electr. and Systems Dept. of Electr. and Systems Engr. Engr. Washington University Washington University St. Louis, USA St. Louis, USA Urszula Ledzewicz Urszula Ledzewicz Dept. of Mathematics and Dept. of Mathematics and Statistics Statistics Southern Illinois University Southern Illinois University Edwardsville Edwardsville UT Austin – Portugal Workshop on Modeling and Simulation of Physiological Systems December 6-8, 2012 Lisbon, Portugal
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The role of the vasculature and the immune system in optimal protocols for cancer therapies
Heinz Sch ättler Dept. of Electr. and Systems Engr. Washington University St. Louis, USA. The role of the vasculature and the immune system in optimal protocols for cancer therapies. UT Austin – Portugal Workshop on Modeling and Simulation of Physiological Systems December 6-8, 2012 - PowerPoint PPT Presentation
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The role of the vasculature and the immune system in optimal
protocols for cancer therapies
Heinz SchHeinz SchättlerättlerDept. of Electr. and Systems Engr.Dept. of Electr. and Systems Engr.
Washington University Washington University St. Louis, USASt. Louis, USA
Urszula LedzewiczUrszula LedzewiczDept. of Mathematics and StatisticsDept. of Mathematics and StatisticsSouthern Illinois University Edwardsville Southern Illinois University Edwardsville Edwardsville, USAEdwardsville, USA
UT Austin – Portugal Workshop onModeling and Simulation of Physiological Systems
December 6-8, 2012 Lisbon, Portugal
• Heinz Schättler and Urszula Ledzewicz,
Geometric Optimal Control – Theory, Methods, ExamplesGeometric Optimal Control – Theory, Methods, Examples
Springer Verlag, July 2012Springer Verlag, July 2012
• Urszula Ledzewicz and Heinz Schättler,
Geometric Optimal Control Applied to Biomedical ModelsGeometric Optimal Control Applied to Biomedical Models
Springer Verlag, 2013Springer Verlag, 2013
• Mathematical Methods and Models in BiomedicineMathematical Methods and Models in Biomedicine
Urszula Ledzewicz, Heinz Schättler, Avner Friedman and Eugene Kashdan, Eds.
Springer Verlag, November 2012Springer Verlag, November 2012
Forthcoming Books
Main Collaborators and ContactsAlberto d’OnofrioEuropean Institute for Oncology, Milano, Italy
Helmut MaurerRheinisch Westfälische Wilhelms-Universität Münster, Münster, Germany
Andrzej SwierniakSilesian University of Technology, Gliwice, Poland
Avner FriedmanMBI, The Ohio State University, Columbus, Oh
Research supported by collaborative research Research supported by collaborative research NSF grantsNSF grants
DMS 0405827/0405848DMS 0405827/0405848
DMS 0707404/0707410DMS 0707404/0707410
DMS 1008209/1008221DMS 1008209/1008221
External Grant Support
Components of Optimal Control Problems
dynamics
(model)
min or max
objective
control
response
disturbance
(unmodelled dynamics)
• model for drug resistance under chemotherapy
• a model for antiangiogenic treatment
• a model for combination of antiangiogenic treatment with chemotherapy
• a model for tumor-immune interactions under
chemotherapy and immune boost
• conclusion and future work: model for tumor microenvironment and
metronomic chemotherapymetronomic chemotherapy
Outline – An Optimal Control Approach to …
Optimal Drug Treatment Protocols
Main QuestionsMain QuestionsQUESTION 1:QUESTION 1: HOW MUCH? (dosage)HOW MUCH? (dosage)
QUESTION 2:QUESTION 2: HOW OFTEN? (timing)HOW OFTEN? (timing)
QUESTION 3:QUESTION 3: IN WHAT ORDER? IN WHAT ORDER? (sequencing) (sequencing)
Heterogeneity andHeterogeneity and
Tumor MicroenvironmentTumor Microenvironment
Tumor stimulating myeloid cell
Surveillance T-cell
Fibroblast
EndotheliaChemo-resistant tumor cell
Chemo-sensitivetumor cell
Tumors are same size but contain different composition of chemo-resistant and –sensitive cells.
aS(t),aS(t), cR(t) cR(t) outflow of sensitive/resistance cellsu – cytotoxic drug dose rate, 0≤u≤1
Tumor Anti-angiogenesis• suppress tumor growth bypreventing the recruitment of newblood vessels that supply the tumor with nutrients
(indirect approach)
• done by inhibiting the growth of the endothelial cellsendothelial cells that form the lining of the new blood vesselstherapy “resistant to resistance”
Judah Folkman, 1972
• anti-angiogenic agents are biological drugs (enzyme inhibitors like endostatin) – very expensive and with side effects
Model [Hahnfeldt,Panigrahy,Folkman,Hlatky],Cancer Research, 1999
A Model for a Combination Therapy [d’OLMSch, Mathematical Biosciences, 2009]
with d’Onofrio and H. Maurer
angiogenic inhibitors
cytotoxic agent or other killing term
Questions: Dosage and Sequencing
• Chemotherapy needs the vasculature to deliver the drugs
• Anti-angiogenic therapy destroys this vasculature
• In what dosages?
• Which should come first ?Which should come first ?
Optimal Protocols
4000 6000 8000 10000 12000 14000 16000
7000
8000
9000
10000
11000
12000
13000
carrying capacity of the vasculature, q
tum
or v
olum
e, p
optimal angiogenic monotherapy
Controls and Trajectory [for dynamics from Hahnfeldt et al.]
0 1 2 3 4 5 6 7
0
10
20
30
40
50
60
70
time (in days)
dosa
ge a
ngio
4000 6000 8000 10000 12000 14000 16000
7000
8000
9000
10000
11000
12000
13000
carrying capacity of the vasculature, q
tum
or v
olum
e, p
0 1 2 3 4 5 6 7-0.2
0
0.2
0.4
0.6
0.8
1
dosa
ge c
hem
o
time (in days)
Medical Connection
Rakesh Jain, Steele Lab, Harvard Medical School,
“there exists a therapeutic windowtherapeutic window when changes in the tumor in response to anti-angiogenic treatment may allow chemotherapy to be particularly effective”