Avner Friedman

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  Rheumatoid Arthritis: a Mathematical Model
  Avner Friedman
  A joint is a structure that connects two parts of the skeleton; in particular, the synovial joint is a joint where two bones are connected. This joint consists of cartilage (as cushion) at each bone-end, synovial fluid (as shock absorber when bones are rotated) and synovial membranes between the cartilages and the fluid. Rheumatoid arthritis (RA) is an autoimmune inflammatory degenerative disease of the synovial joints. The inflammations begins in the synovial membrane by immune cells, and it leads to the destruction of the cartilage. There are two million Americans with RA.
  
  In this talk, I will present a novel mathematical model of RA. The model is presented as a system of PDEs in the three compartments of the synovial joint. As the cartilage layer degrades it becomes thinner, and its boundary that is in contact with the synovial membrane is moving in time as a "free boundary" There is no cure to RA, but drugs are used to try slow the progression of the disease. I shall use the model to evaluate the efficacy of several approved drugs, combination of drugs, and experimental drugs. This a joint work with Nicola Moise from the medical school in Bucharest, Romania.
  
  Finally, I will present rigorous mathematical results, joint with K. Y. Lam, for a simplified model, on the behavior of the free boundary, which is the interface the synovial membrane and the cartilage.
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  Using Mathematical Models to Conduct Cancer Clinical Trials
  Avner Friedman

  Most cancer clinical trials with combination therapy in phase II have failed in phase III. One of the reasons for this failure is that no sufficient forethought was given to the interactions between the two (or more) agents.  Before embarking on a clinical trial with (say) two agents, one should address the following questions:

  
  

  
  
  1. If the two drugs are positively correlated at any dose amounts, how to achieve the same tumor volume reduction with minimal negative side-effects?
  
  
  2. If the two drugs are antagonistic at certain ranges of the doses, how to avoid these zones of antagonism?
  
  
  3. What schedule is most effective in reducing tumor burden? e.g. in which order to give the drugs?
  
  
  4. How to reduce drug resistance by the tumor cells?
  
  

  
  

  We use mathematical models to address these questions, and give several examples with different drugs.

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  An Overview of Cancer and the Immune System
  Avner Friedman

  This is tutorial talk, in which I will introduce the main components of the immune system in the context of cancer. I will introduce the different phenotypes of macrophages, the four classes of CD4+ T cells, and the cytotoxic T cells (CTL) or CD8+ T cell. As will be explained, the tumor may be recognized by macrophages and dendritic cells, and these cells will then activate 'effective' T cells to kill cancer cells. However, the tumor can fight back against the immune system, and in fact it can even use the system to its own advantage, by "educating" macrophages so that they will actually enhance tumor growth by increasing VEGF production. Another factor that works in favor of a tumor are the T regulatory cells, enhanced by the tumor, which inhibit the activities of the effective T cells.