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Cerebral Vasculature and Fractals

Cerebral Vasculature and Fractals. Week 8. Smit Naik Advisor: Brian Sweetman Director: Andreas Linninger LPPD UIC Spring 2009. Purpose and Motivation. Define cerebral vasculature quantitatively. Arteries ArteriolesCapillariesVenulesVeins

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Cerebral Vasculature and Fractals

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  1. Cerebral Vasculature and Fractals Week 8 Smit Naik Advisor: Brian Sweetman Director: Andreas Linninger LPPD UIC Spring 2009

  2. Purpose and Motivation • Define cerebral vasculature quantitatively. • ArteriesArteriolesCapillariesVenulesVeins • Simulate fluid flow through vasculature given quantified parameters and constraints. • Predict vasculature response.

  3. Goals • Smooth current cerebral vasculature model to eliminate mathematical artifacts. • Further understand and create fractals using programming software (Matlab). • Create various fractal trees as a precursor to a model for microvasculature.

  4. Fractals • Repeating geometric shapes built off one another on an ever diminishing scale. • Are representations of number systems. Pythagorean Theorem: a2 +b2 = c2 Pythagoras Fractal

  5. Results

  6. Pythagoras Tree Depth = 9 α = 45o Depth = 9 α = 60o

  7. Hollowed Pythagoras Tree

  8. Other Pythagoras Trees Inverted Every Branch Inverted Every Depth

  9. Extracerebral Vasculature • Reconstructed using Mimics • Fluid flow simulated in ADINA

  10. Conclusions/Future Work • Simulate fluid flow through fractal model • Converting from 2D to 3D • Answer the following questions: • How can we test/experiment to see if model is accurate? • Which fractal is best for microcirculation?

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