Viralbased Gene Therapy of Tumours

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Viral-based Gene Therapy of Tumours

• Andy, Andy, Kim, Liya, Quin Raf
• Dr. Radek Erban Dr. Kerry Fisher

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• What our problem was and why
  we wanted to model it?
• How Tumours Work
• Modelling Virus Kinetics
• Experimental Data
• Predictions from our Model
• Diffusion of the Virus
• Conclusion Further Work

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Modelling of Viral-based Gene Therapy of Tumours

• Many medical conditions have faulty, mutant
  genes, as an underlying cause
• Tumours dont stay in one place, but spread
  around the body making operating difficult
• Reintroducing healthygenes is difficult

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Modelling of Viral-based Gene Therapy of Tumours

• Viruses can be used to carry healthy genes
• Oxfords Gene Therapy group aim to administer
  viruses via the blood stream
• Find and destroy all tumours in the body
• Ideal treatmentfor later stagesof cancer

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Modelling of Viral-based Gene Therapy of Tumours

• Problems
• The Liver removes virus particles quickly
• Tumours take in the virus slowly
• Solutions
• Modify the virus
• Modify liver clearance efficiency

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Adenovirus
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(No Transcript)
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Experiments

• Gene therapy group Clinical Pharmacology
• Test subjects Mice (Mus Musculus)
• Two types of tumour
• Different levels of Clodronate administered
• Tumours removed
• Tested for virus particles

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Zero-order and first-order kinetics
Zero-order kinetics
Rate of removal of virus in the blood is
independent of the amount of virus particles
present.
First-order kinetics
Rate of removal of virus is proportional to the
amount of virus particles.
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How realistic is the model?
LIVER
BLOOD
TUMOUR

• First-order kinetics is not enough
• Multi-compartment model
• Virus particles absorbed by liver and tumour
• Liver can be saturated with virus particles

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Developed model with saturation
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Dosing schedule

• Solve analytically using first-order kinetics
• V Kexp(-rt)

• New dose is to be given at time td where
• Td log(C0/K) / r

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Exploratory Data Analysis
LoVo blood counts (24h)
HT29 blood counts (24h)
24h tumour counts
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The Blood Counts
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The Blood Counts
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The Tumour Counts
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Diffusion of Virus

• If the virus gets into capillaries, does it get
  into the tumour?
• How fast do virus particles diffuse?

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Random Walk Model

• Simulation with 500 virus particles
• Estimated diffusion coefficient D 0.93397
  µm2/s
• Diameter of a virus particle a 90 nm (90?10-9
  m)
• Diameter of a capillary d 8 µm (8?10-6 m)

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Deterministic Model
Concentration of Particles in a Capillary
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Comparing the two models
1'000 particles
100'000 particles
0
0
4µm
4µm
-4µm
-4µm
Distribution of particles in the cross-section of
a capillary
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Summary

• ODE model of virus concentration.
• Data analysis to find parameters.

• Diffusion model for virus in blood stream.

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Extensions

• Virus diffusion model
• Allow for non-homogeneous tissue
• Model blood flow in capillaries
• Replicant competent virus
• Virus capable of multiplying within a tumour
• Which grows fastest, the tumour or the virus?

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Conclusion

• Viral based gene therapy is an exciting
  development in the battle against cancer.
• Research is still required.
• Mathematicians can help!

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Acknowledgements

• Dr Radek Erban
• Dr Kerry Fisher