Blood Flow:
Do we have a proper momentum conservation equation for characterizing blood flow?
1. Whether the dimensionless Womersley (Wo) number can be used to describe the transient nature of blood flow in response to a transient local pressure gradient - when the internal cross section of blood flow remains to be different from circular cylinder?
For varying cross sections, when Wo remains to be less than unity, whether the velocity profile still exhibits the parabolic shape such that the fluid oscillating with the greatest amplitude remains to be farthest from the artery walls?
Similarly, when Wo remains to be greater than unity (where, the velocity profiles are no longer parabolic), how exactly the blood remains to be phase-shifted in time relative to the oscillating pressure gradient?
If blood flow is characterized by hyperbolic PDEs (rather than parabolic PDEs), then, why not the pressure pulse of our body is no more conserved throughout our life time? Why does it follow a typical parabolic PDE pattern, where the pressure pulse keeps decaying with time, and finally, reaching a steady-state (last breathe, where the pulse becomes flattened) upon reaching a larger time level?
2. What is the scale at which we got to look at the problem of blood flow in our body?
Will it be microscopic-scale; or, macroscopic-scale?
If so, would it remain feasible to deduce a representative blood concentration over a definite REV (Representative Elementary Volume)?
For that matter, can we deduce a reliable REV in a blood circulation system?
If not, how could we apply the conventional PDEs that remain applicable for a function that is supposed to remain continuous and smooth?
If blood flow has its importance over various scales, then, how could we characterize the blood flow using a single-continuum?
If multiple-continuum needs to be followed, then, how many continuum would be required to characterize the blood flow?
If multiple-continuum exists, then, how could we ensure the continuity of blood fluxes at the interfaces between any two continua?
Feasible to deduce proper boundary conditions for blood flow through arteries, capillaries and veins?
If both Navier-Stokes equation (momentum conservation to characterize flow through pipes) and Darcy’s equation (momentum conservation to characterize flow through a porous medium) cannot be applied to characterize this non-Newtonian blood flow; then, is there a new momentum conservation equation used to characterize blood flow through human body?
3. Survival after a diagnosis of HF hangs around less than 7% now. Why is it so?
4. 20 or 30 years back, HFrEF – the incidence of heart failure with reduced ejection fraction (primary myocardial injury) was dominant. However, now, HFrEF – the incidence of preserved ejection fraction (induced by comorbidities) has become dominant. Complex origin of heart failure resulting from structural, mechanical or electrical dysfunction of the heart?
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