(567bx) On Starling's Law Being Not Universal
AIChE Annual Meeting
Wednesday, November 10, 2010 - 6:00pm to 8:00pm
The three important developments that gave impetus to the development of the field of Biofluid Dynamics are;
(i) Discovery of Osmosis (ii) Permeability of a Solvent across a Membrane and Starling's Law (iii) Diffusion of a solute across a membrane.
Sharma (2007) has given eight reasons on why Fourier's law of heat conduction is not a universal law. Some of the citations are from the nobel prize winners literature. This is applicable to the following laws that are linear;
(i) Fourier's Law of Heat Conduction (ii) Fick's Law of Mass Diffusion (iii) Newton's Law of Viscosity (iv) Ohm's Law of Electrical Conuction (v) Starling's Law for Fluid Transport (Katz, 2002) (vi) Darcy's Law of Fluid Transport through Porous Media (vii) Hooke's Law of Elasticity
All of these laws imply a infinite spped of propagation. This is not feasible as pointed out by Einstein. This study focuses on the non-universality of Starling's law during short times, high solvent fluxes and nanoscale domains. The acceleration of the molecule can be taken into account and a ballistic term added to the linear Starling's law. This law can be combined with the equation of continuity. Direct closed form analytical solutions can be obtained to the damped wave transport equation using the method of relativistic transformation of coordinates. The solution is within the predictions of second law of thermodynamics. At steady state, starling's law has been used to give reliable predictions when membranes are comprised of uniform macrostructures. Microvessel walls are non-uniform. This is evident in the glycocalyx, endothelium and the basement membrane. Endothelial cells, interendothelial cleft and junction protein strands are not uniform. Experimental observations have been made that are inconsistent with the predictions of Starling's law. Blood in capillary, for example, with a hydrostatic pressure difference of about 15 mm Hg in the arterial end and an osmotic pressure of 26 mm Hg would be expected to filter water into the interstitial space and out of the artery. The reflection coefficient may be taken as 1. With the osmotic pressure difference remaining the same, the net pressure drop would be 17-1(27) ~-10 mm Hg at the veins. The driving force has changed in direction and the water can be expected to filter from interstitial space into veins. Experimental observations of Michel and Phillips (1987) provide a counterexample to the filtration/reabsorption prediction. Hu and Weinbaum (Fournier, 1999) modified the Starling's law by subtracting out the osmotic pressure difference. They discuss three cases such as convection dominated; higher solvent flux, decrease in arterial blood pressure.