What is Mathematical Biology and how useful is it

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What is Mathematical Biology and how useful is it?

• Avner Friedman

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• What is life?
• What is mathematical biology?
• Wound healing
• Hemodialysis
• Tuberculosis (aging)
• Glioblastoma

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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

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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.

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Experiments, data
Simulation
Mathematical model
Parameters estimation
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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.

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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.

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Fistula and Graft in Hemodialysis
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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.
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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
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virus
cell
When the cell dies, a swarm of virus particles
burst out
b burst size replication number
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• 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

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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).

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uninfected cell
(1)
infected cell
(2)
necrotic cells
(3)
immune cells
(4)
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virus particles
(5)
(6)
radial velocity
(7)
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Tumor Radius
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• 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

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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.