Angiograms and Ultrasound Are Not Accurate Enough to Measure Improvement Following Chelation

by Elmer M. Cranton, M.D.

It seems counterintuitive but is nonetheless scientifically proven that less than 7 percent increase in the interior diameter of a blood vessel can double the flow of blood. Angiograms and ultrasound imaging are only accurate to within 20 percent and cannot measure such small changes, despite repeated demands by opponents of EDTA chelation therapy that this be the "gold standard" for effectiveness.

A doubling of blood flow can obviously relieve symptoms of blockage and can also reduce the risk a heart attack or stroke. A doubling in size of the opening past a plaque will increase the flow of blood by more than 16 times. An increase of less than 7% will double blood flow. Angiograms are much too inaccurate to provide the  type of evidence demanded by critics, without which  they refuse to accept a large amount of clinical research showing that chelation therapy is truly effective. Objective measurements of functional improvement and increased blood flow, well documented before and after treatment in published clinical trials should be the "gold standard" for success, not imprecise imaging.

Poiseuille's law corresponds to Ohm's law for electrical circuits (V = I R), where the pressure is analogous to the voltage V and rate of blood flow is analogous to the current I. Then the resistance R=

This concept is useful because the effective resistance in an artery is inversely proportional to the fourth power of the radius or diameter. This means that halving the internal diameter of the vessel increases the resistance to blood flow by 16 times.

By applying Poiseuille's  Equation to the flow of blood through even a healthy, smooth-walled artery with laminar flow, we find that the volume of blood flow increases or decreases relative to Pi divided by 8 times blood pressure, times the fourth power of the artery's interior diameter, divided by the product of the artery's interior diameter times the dynamic viscosity of the blood. In a diseased artery with turbulent flow past plaque, this fourth power equation changes to the fifth power. In other words, coronary blood flow is inversely proportional to the of the interior diameter raised to its fifth power (1/D⁵). To put this another way, doubling the width of an opening through the narrow gap beside a  plaque can potentially increase the flow of blood by 20 times or more. A mere 7% or less increase in the opening of a blocked artery will double the flow of blood.

Blood is noncompressible and only  half liquid. The other half is composed of red and white blood cells. These cells rub along blood vessel walls creating friction and thus move more slowly than more fluid blood in the center of an artery. This means that  blood highly viscous and somewhat sticky as it flows. Because the distance (relative to blood cells) between the outer wall and the center of a vessel is much less in small blood vessels, a small increase in the internal diameter will result in a very large increase in the flow of blood. Blood flow past plaques is turbulent, causing even more resistance. In diseased arteries with plaque an increase in diameter in the range of than 6 percent can double the flow of blood and totally relieve symptoms of blockage.

Both liquid and cell-free portions of blood are more viscous than pure water because of blood's high protein content. Cell-free plasma is about 1.5 times more viscous than water. When blood cells are added, the viscosity increases to more than 3 times that of water.

The cross sectional area in the opening in a blood vessel decreases proportionate to the square of a change in diameter. An artery of half the diameter has only one fourth the cross sectional area.

Combining all of these factors together, as shown by Poiseuille’ Equation, we see that a mere doubling the internal diameter of a coronary artery, for example, can result in a 16-fold increase in the flow of blood (assuming no change in blood pressure, viscosity, or length of the artery). Put another way, a smooth, healthy a blood vessel will carry twice as much blood if the interior increases less than 10% in diameter. A blood vessel with plaque and has turbulent flow and a mere 7 percent or less increase in internal diameter can double the flow of blood.

Angiograms and ultrasound imaging are only accurate to within approximately 20 percent. Even when repeated an hour later on the same patient, using the same technique, readings can vary by more than 20 percent. That amount of disagreement was reported when coronary angiograms were circulated among a large number of leading, academic medical centers and interpreted independently by the best specialists available. This explains why patients whose symptoms have improved dramatically following chelation therapy may not show a significant change on followup angiogram. For the same reason, calcium scores on followup ultra-fast, electron-beam, CT scan (EBCT) are also not a reliable way to measure benefit following chelation therapy.

If a patient feels much better, if symptoms improve, if exercise tolerance increases,   it can be a waste of time, money, and an unnecessary risk to do routine follow-up angiograms merely to document improvement from EDTA chelation therapy. The proof of the pudding is in the eating. If symptoms improve and remain improved, it seems logical to assume that blood flow has increased. Placebo effect rarely lasts for very long, while benefits from chelation therapy persist for years. If that benefit can be maintained over time with periodic chelation treatments, combined with healthy lifestyle and nutritional supplementation, enormous good can be achieved without resorting to surgery, stents or other potentially dangerous procedures.

          References

Poiseuille's  Law

Scientific details on Poiseuille's Law

Cardiovascular Physiology and Poiseuille's Equation