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Optimal control in medicine and biology

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This is a seminar I have given to the students of prof. De Santis. I have presented optimal control in life science and medicine.

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Optimal control in medicine and biology

  1. 1. Optimal control in medicine and biology Jorge Guerra Pires Internal Seminar (DISIM): prof. Elena De Santis DIPARTIMENTO DI INGEGNERIA E SCIENZE DELL'INFORMAZIONE E MATEMATICA (DISIM), Università degli Studi dell'Aquila (UNIVAQ) 20th March 2017, L’Aquila, Italy
  2. 2. 2 Pires J. Pharmacokinetic/Pharmacodynamic modeling, evolutionary Algorithms, and optimal control theory: A numerical-based approach. August 2015. doi:http//dx..org/10.13140/RG.2.1.4599.2800. https://www.researchgate.net/publication/280877647_ PharmacokineticPharmacodynamic_Modeling_Evolut ionary_Algorithms_and_Optimal_Control_Theory_a_ numerical-based_approach. Accessed November 30, 2016.
  3. 3. Introduction 3 Life Sciences (i.e., medical and biological sciences) might be seen as the connections between medicine, biology, mathematics, physics, and computer sciences. Furthermore, optimal control might be defined as the extension of static optimization, or even as some comments, the new face of Variational Calculus. A straightforward definition of life sciences is no longer simple, since it is an inter- and multi- disciplinar field. It might be said that in the past, this scientific domain comprised of a set of united field such as medicine and biology that rarely interfered with each other (in fact, the name seems to be originated in the last decades); nonetheless, in the present it is a “unique” branch comprised of researches from a variety of field such as mathematics, medicine, and biology. The inclusion of mathematics and other fields such as computer science (and information sciences) came as a “rebirth” of the field.
  4. 4. 1. Introduction Source: J G Pires. "On the mathematical modeling in gene expression estimation: an initial discussion on PBM and BM". September 24th 2014, Como Lake (Poster Session). 4
  5. 5. 1. Introduction Source: J G Pires. "On the mathematical modeling in gene expression estimation: an initial discussion on PBM and BM". September 24th 2014, Como Lake (Poster Session). Physical System modeling. A) the dichotomy ‘measure-analysis’; b) the dilemma of controlled and noisy state variables Basically, one have a system, then we created a model for this system. The system generates data for our model, and our model generate possible analytical analysis for our physical system Figure a. Furthermore, Figure b, in most of the cases when we model a system, we apply a stimulus, an input, that supposes to trigger dormant properties of our system under question. 5
  6. 6. 6 1. Introduction
  7. 7. Introduction 7
  8. 8. Introduction 8
  9. 9. Introduction 9
  10. 10. Introduction 10 The Forward-Backward Sweep Method
  11. 11. Optimal control applied to cancer therapy 11
  12. 12. Optimal control applied to cancer therapy 12
  13. 13. Cancer treatment (toy model) 13r=0.3; a=3; δ=0.45; N0 =0.975; T=20;
  14. 14. Cancer treatment (toy model) 14 r=0.3; a=3; δ=0.45; N0 =0.3; T=20;
  15. 15. Optimal control applied to cancer therapy (two drugs) 15
  16. 16. Cancer treatment (two-drug dynamics) 16 r=0.3; a=3; δ=0.45; N0 =0.3; T=20; x0=[0.0 0.0]; ε=[1 1 1]; β=[0.1 0.2]; K=[0.1 0.2]
  17. 17. Optimal control applied to cancer therapy (two drugs, intermitent infusion) 17 You may need to make intermitent infusions, repeated infusions in a period of time.
  18. 18. Cancer treatment (two-drug dynamics, intermitent infusions ) 18 r=0.3; a=3; δ=0.45; N0 =0.3; T=20; x0=[0.0 0.0]; ε=[1 1 1]; β=[0.1 0.2]; K=[0.1 0.2]; I =10
  19. 19. 19
  20. 20. Thank you for your attention, Muito obrigado pela atenção, Grazie mille per l'attenzione, 20 jorge.guerrapires@graduate.univaq.it

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