What is Mathematical Biology and how useful is it?

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

2. What is life? • What is mathematical biology? • The role of oxygen in wound healing and tissue transfer • The immune response to infection in the lung • Cancer virotherapy • Summary

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 new biologically testable hypotheses.

5. Experiments, data Simulation Mathematical model Parameters estimation

6. Wound healing as a function of tissue oxygen tension: A mathematical model R. Schugart, A. Friedman, R. Zao, C.K. Sen PNAS (2008) • Chronic wounds represent a major public health problem worldwide; affecting 6.5 million individuals in the U.S., with cost of $5-10 billion each year. • 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.

7. Hyperbaric Chamber • Topical Oxygen Treatment

11. (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (2.7)

13. Role of Oxygen Ga w hypoxic normoxic hyperoxic Moderate hypoxia and hyperoxia improve healing.

15. A Mathematical Model of Ischemic Cutaneous Wounds C. Xue, A. Friedman, and C. Sen PNAS (2009) Experiment:

16. A more refined model is needed. • Separating chemoattractant between VEGF and PDGF. • Considering the partially healed tissue as viscoelastic material. • Modeling ischemia in a circular geometry.

17. Experimental and Simulation Results C. Xue, A. Friedman, and C. Sen (2009)

18. Modeling Oxygen Transport in Surgical Tissue Transfer A. Matzavinos, C.Y. Kao, J.E.F. Green, A. Sutradhar, M. Miller, and A. Friedman PNAS (2009) • During surgery, a plastic surgeon must decide how large a flap (with one artery) can be lifted and transferred to another location, without developing fat necrosis.

19. arterial pressure venous pressure oxygen diffusion and transport (tissue) oxygen diffusion and transport (artery) oxygen diffusion and transport (vein)

21. The model represents initial step. Subsequent work will proceed jointly with animal experiments, in order to refine the model by including heterogeneity of the vasculature. • The model will be coupled to that of ischemic cutaneous wounds. Future Work

22. 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-g is essential, such a loss is associated with aging, and it can lead to a significant failure to control infection.

24. Infected macrophages: infected by ~10 bacteria in the absence of IFN-γ; cannot control bacterial growth; they burst releasing many bacteria. • Activated macrophages: infected by ~5 bacteria in the presence of IFN-γ; they present antigen to T cells. • Resting macrophages – do not contain bacteria. Macrophages

25. The Model Variables

28. Modeling the Immune Rheostat of Macrophages in the Lung in Response to Infection J. Day, A. Friedman, and L. Schlesinger (PNAS, 2009) • Alveolar macrophages are also called Alternatively Activated Macrophages (AAM). AAM form the first line of cellular defense. • The macrophages in the lymph nodes are called Classically Activated Macrophages (CAM). • CAM are more effective than AAM in combating infection. • When infection in the lung occurs, there is time delay until CAM arrive and become more dominant than AAM: “switching time.”

31. Using IFN-γ as drug: It decreases the switching time, the maximum bacterial load, and the residual bacteria.

32. 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

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

34. 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

35. 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).

38. Model Equations uninfected cell infected cell necrotic cells immune cells

39. virus particles radial velocity

40. Tumor Radius

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

43. 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 primary effect is in 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.

44. Summary • Mathematical models should relate to experiments. • In PDE or ODE models the choice of parameters is crucial – use experimental results as much as possible. • Use sensitivity analysis. • Simulations of the model must fit with experimental results. • The model should then be used to suggest new hypotheses that are biologically testable.