1. What is Mathematical Biology and how useful is it? Avner Friedman

2.  What is life?  What is mathematical biology?  Wound healing  Hemodialysis  Tuberculosis (aging)  Glioblastoma

3. What is life? Unit of life is a cell. Processes of living. (according to F. Harold, “The Way of the Cell,” 2001) Flux of matter and energy Chemical activities: absorb nutrients, produce biomass, eliminate waste products Adaptation Structure and function evolve to promote organism survival Organization A bacterial cell consists of 300 million molecules, assembled non-randomly DNA  RNA  Protein is strategically planned and executed Self-reproduction Autonomously, not by external forces

4. What is Mathematical Biology?  Talking to biologists and getting familiar with their experiments and data with respect to a biological process.  Developing a mathematical model that describes the biological process (e.g., by differential equations).  Simulating and comparing the numerical results with experimental results – and keep revising until the fit is satisfactory.  Using the model to make a new hypothesis and suggest new experiments.

5. Mathematical model Parameters estimation Simulation Experiments, data

6. Wound healing as a function of tissue oxygen tension: A mathematical model R. Schugart, A. Friedman, R. Zao, C.K. Sen PNAS  Chronic wounds represent a substantial public health problem; treating these wounds costs an estimated $5-10 billion each year. Need to develop tools to study genetic signature of wounds under various conditions, and develop mathematical models.  Wound healing represents a well-orchestrated reparative response that occurs after all surgical procedures or traumatic injuries. Angiogenesis plays a central role in wound healing. In this work the role of oxygen is investigated, and the use of oxygen intervention (hyperbaric chamber) is considered.

10. (2.1) (2.3) (2.4) (2.2) (2.5) (2.6) (2.7)

13. A mathematical model of venous neointimal hyperplasia formation P. Budu-Grajdeanu, R. Schugart, A. Friedman, C. Valentine, B.H. Rovin Theoretical Biology & Medical Modeling In hemodialysis the most common cause of vascular failure is neointimal hyperplasia of vascular smooth muscle cells at the venous anastomosis of fistulas or grafts.

14. Fistula and Graft in Hemodialysis

19. A model on the influence of age on immunity to infection with Mycobacterium tuberculosis A. Friedman, J. Turner, B. Szomolay Experimental Gerontology Increasing susceptibility to many infectious diseases is highly associated with the loss or delay in the generation of antigen specific CD4 + T cells mediated immunity. For tuberculosis, where antigen specific CD4 + T cell derived IFN-  is essential, such a loss is associated with aging, and it can lead to a significant failure to control infection.

24. Virotherapy in Glioblastoma A. Friedman, J.J. Tian, G. Fulci, E.A. Chiocca, and J. Wang Cancer Research, 2006 Glioblastoma is a brain tumor, very invasive, life expectancy 1 year glioblastoma

25. cell virus When the cell dies, a swarm of virus particles burst out b = burst size = replication number

26. Idea: Use virus to destroy tumor cells Oncolytic virus: Genetically altered virus which is  Replication – competent  Infects tumor cells and reproduces in them  Does not harm normal healthy cells Virotherapy: Actively tested in clinical trials on various types of cancer Two important factors:  Safety  Efficacy

27. Factors to be considered:  The immune system: cells which detect virus and virus-infected cells, and destroy them  Cyclophasphamide (CPA) suppresses the innate immune response  During infection, the population of immune cells increases dramatically. When the infection is gone, the population of immune cells returns to its normal size (quadratic clearance).

30. uninfected cell infected cell necrotic cells immune cells (1) (2) (3) (4)

31. virus particles radial velocity (5) (6) (7)

32. Tumor Radius

33. b large infected (uninfected ) immune and kills infected and virus - then: immune cells kill themselves immune In the meantime uninfected cells Remaining virus renew attack infected

35. Conclusions  OV hrR3 cannot eradicate glioma.  If however b can be increased to ≥ 150 then the radius will shrink and become very small (even without CPA)  CPA will help a little bit in decreasing the radius, but its primary effect is decreasing the density of uninfected tumor cells – thus reducing the risk of secondary tumor.  Protocols of CPA treatment (weekly, or double-dose biweekly) do not make a significant difference. Problem  Provide vigorous mathematical proof to the numerical results.