ABSTRACT. Bone metastasis is the spread of cancer cells from a primary tumor (e.g. prostate, breast) to the bone tissue. Clinically, it is considered incurable.
AN OPTIMAL CONTROL APPROACH TO STUDY CELL DYNAMICS UNDER BONE METASTASIS TREATMENTS Ariel Camacho, Dr. Silvia Jerez
Centro de Investigación en Matemáticas (Guanajuato, México) OPTIMAL CONTROL TREATMENTS
DENOSUMAB TREATMENT
RADIATION TREATMENT
0.4 0.3 0.2 0.1 0
(+)
100
Time (days)
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Time (days)
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Find a way to introduce specific, explicit cost terms (economical, side-effects). Analyze the case of linear controls or another types of cost functionals.
(OCs) (OBs) (CCs)
[Pivonka2008] B +bone mass, TGF-b from bone resorption, maturation of OCs-OBs
[Wang2011] B +multiple myeloma and other factors such as IL-6
[Komarova2003] [Jerez2016]
assumptions
Model other treatments used on bone metastasis disease.
Cell population 150
Time (days)
200
250
no control B=1e06 B=1e07 B=1e08
50
100
150
Time (days)
200
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250
10 5
0
50
100
150
Time (days)
200
250
Osteoblasts no control B=1e9 B=1e10 B=1e11
1000 500
0
50
100
150
Time (days)
200
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200
250
Cancer cells no control B=1e09 B=1e10 B=1e11
8000
2000
0
Time (days)
200
no control B=1e09 B=1e10 B=1e11
10000
4000
0
150
Osteoclasts
0
Cell population
[Coelho2016] A +bone metastasis, PTH dynamics and chemotherapy
100
1500
Cancer cells
6000
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2000
200
0
0
15
0
250
400
8000
Cell population
[Ayati2010] A +multiple myeloma and also spatial dynamics with
200
no control B=1e9 B=1e10 B=1e11
10000
FUTURE WORK
150
Osteoblasts
600
0
BONE METASTASIS: THE MATHEMATICS
0
20
4
0
B=1e09 B=1e10 B=1e11
25
6
800
Cell population
FORWARD-BACKWARD ALGORITHM
0.005
250
no control B=1e06 B=1e07 B=1e08
1000
EXAMPLE OF OSTEOBLASTIC BM INTERACTION NETWORK
0.01
Osteoclasts
8
0
[Lemaire2004] B OCs-OBs+RANKL, OPG, PTH, TGF-beta (LMA)
200
2
(+)
[Komarova2003] A 2 ODEs describing OCs-OBs dynamics (S-System)
150
10
Cell population
(–)
50
12
PONTRYAGIN'S MAXIMUM PRINCIPLE (+)
0
Optimal solutions
0.015 B=1e06 B=1e07 B=1e08
0.5
EXAMPLE OF OSTEOLYTIC BM INTERACTION NETWORK
(–)
Optimal solutions
0.6
BONE METASTASIS: THE BIOLOGY
RADIATION TREATMENT
Radiation impact
DENOSUMAB TREATMENT
Cell population
Bone metastasis is the spread of cancer cells from a primary tumor (e.g. prostate, breast) to the bone tissue. Clinically, it is considered incurable. Metastatic cells trigger a vicious cycle within the bone microenvironment by manipulating bone cells (osteo-blasts, -clasts, -cytes) in order to sustain its invasion. Using ecological principles, we examine this complex interaction network with mathematical models. Applying optimal control theory we aim to study bone metastasis treatments. The optimal treatment is modeled to minimize side-effects and the cost.
RESULTS
Effectivity
ABSTRACT
6000 4000 2000 0
0
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Time (days)
Parameter estimation/data fit and incorporate into optimal control problem.
REFERENCES
Combine multiple BMUs/regions and study their dynamics under treatments.
[Komarova2003] Komarova, S. V., Smith, R. J., Dixon, S. J., Sims, S. M., & Wahl, L. M. (2003). Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone, 33(2), 206-215. [Lemaire2004] Lemaire, V., Tobin, F. L., Greller, L. D., Cho, C. R., & Suva, L. J. (2004). Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. Journal of theoretical biology, 229(3), 293-309.
Apply optimal control framework for Lemaire-type models. Propose a spatial model for BMU-metastasis interactions + treatments.
