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Cardiovascular modeling and the Fourier series and transform

Cardiovascular modeling and the Fourier series and transform.

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Cardiovascular modeling and the Fourier series and transform

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  1. Cardiovascular modeling and the Fourier series and transform Adapted from Roberto Burattini, “Chapter 8 - Identification and Physiological Interpretation of Aortic Impedance in Modelling,” In: Ewart Carson and Claudio Cobelli, Editor(s), Modeling Methodology for Physiology and Medicine, Academic Press, San Diego, 2001, Pages 213-252. (http://www.sciencedirect.com/science/article/pii/B978012160245150009X) 298KLG-32

  2. 298KLG-32

  3. Flow through a tube p(t), pressure difference q(t), flow r, radius Ohm’s Law for flow x, length 298KLG-32

  4. Assume pressure and flow are periodic 298KLG-32

  5. Impedance of the vasculature 298KLG-32

  6. Where Z is modeled impedance for dashed and dotted lines Impedance is not merely resistive Top shows flow measured in dog’s aorta Bottom shows pressure measured in dog’s aorta (solid) and modeled pressures (dashed and dotted) 298KLG-32

  7. Impedance Z(ω) Because the pressure and flow are periodic, the impedance only has value at the fundamental frequency (~2 Hz) and harmonics (big dots). The heart can be paced at other fundamental frequencies to fill in the gaps. (There is no way to use an impulse input to find the impulse response.) 298KLG-32

  8. Arteries are compliant They expand under pressure to accept the volume of each pulse. As people age, arteries stiffen and become less compliant 298KLG-32

  9. Two-element Windkessel (Ger. ‘air chamber’) – W2 298KLG-32

  10. W2 does not suffice Top shows flow measured in dog’s aorta Bottom shows pressure measured in dog’s aorta (solid) and pressure modeled by the W2 (dotted) 298KLG-32

  11. Impedance Z(ω) Again the dotted line shows us that the W2 does not suffice 298KLG-32

  12. Three-element Windkessel – W3 An additional resistance to account for high frequency impedance 298KLG-32

  13. W3 fits the data well Top shows flow measured in dog’s aorta Bottom shows pressure measured in dog’s aorta (solid) and pressure modeled by the W3 (dashed) 298KLG-32

  14. Impedance Z(ω) The dashed line matches the data fairly well. 298KLG-32

  15. Viscoelastic Windkessel Rd accounts for viscous losses at the arterial walls 298KLG-32

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