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Cardiac output
C.O. = Stroke Volume X Heart Rate
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Blood vessel branching
n=VinAin/VoutAout
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Shear in blood flow
- Assume laminar, steady flow
- tau = -dp/dx*r/2
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Velocity in blood flow
- Assume laminar, steady flow
- Newtonian fluid
- V(r) = (1/4mu)*(dp/dx)*(R^2-r^2)
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Poiseuille's Law
- Assume laminar, steady flow
- Newtonian fluid
- dp/dx = Q(8mu/piR^4)
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Windkessel Analysis
- Assume arteries are pascal chambers
- Pressure is same throughout
- Instantaneous change
- Q(t) = kexp(-t/rc)+Qheart
- P(t) = kRexp(-t/rc)+QRheart
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Pulse propagation
- Distensibility (Inverse of stiffness)
- D = 2r/Et
- c=sqrt(Et/2rrho) (rho of the walls)
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Reflection at junctions
- P = Q(rho*c/A)
- Impedance (z)= (rho*c/A)
- Admittance (a) = 1/z
Pr/Pi = ao-(a1+a2)/(a0+a1+a2)
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