Albert Einstein Explains the Causes For Decrease of Capillary Pressure: Increasing Resistance and Rigidity

In an increasingly rare letter of Einstein on a scientific subject, he joins his field of science to the field of medicine; doctors today still rely on this scientific principle.  "Your formula 1 concerning the diastolic phase does show that the logarithmic dekrement of the pressure is increasing with the active pressure."

In 1900, Einstein was granted a teaching diploma by the Federal Polytechnic Institute. Then, even prior to his days as a clerk in the patent office, he submitted his very first paper for publication to the prestigious Annalen der Physik, which published it. Einstein was well versed and interested in thermodynamics, and the article concerned the capillary forces of a drinking straw, and was entitled “Consequences of the observations of capillarity phenomena". Capillary action, or capillarity, is the ability of a liquid to flow against gravity where liquid spontaneously rises in a narrow space such as a thin tube or straw, or in porous materials such as paper. This effect can cause liquids to flow against the force of gravity or the magnetic field induction, and it occurs because of attractive forces between the liquid and solid surrounding surfaces. In his article, Einstein reasoned: "To each atom corresponds a molecular attraction field that is independent of the temperature and of the way in which the atom is chemically bound to other atoms." Later, Einstein worked on similar fields of phyics with his law on viscosity and in developing the Bose-Einstein Constant.

Domingo Mauricio Gómez was a Cuban biomathematician and author of some 70 scientific works. He wrote the first modern treatise on hemodynamics (dynamics of blood flow) and developed the Gomez-Langevin procedure for measuring pressure changes in blood vessels. He also created the Gómez formulae for estimating intrarenal hemodynamics, and showed that blood flow through the kidneys was reduced in patients with hypertension. His work is still relied on and cited today.

Gomez was concerned with the "pressure decrement", which is the difference in pressure between the blood entering, and the blood leaving. The renal system is a highly branched network with lots of capillaries, and there is a difference in pressure because the kidney is filtering things out. Although the capillaries here are literally capillaries in the body, the phenomenon was related to the capillarity that was the subject of Einstein's work. Gomez wrote Einstein on the subject.

Typed letter signed, on his blind-embossed letterhead, Princeton, NJ, April 14, 1943, to Gomez.  "I am very interested in the paper you sent me, but I have not time enough to study it thoroughly. Only one remark: Your formula 1 concerning the diastolic phase does show that the logarithmic dekrement of the pressure is increasing with the active pressure. This can have two causes: 1): A decrease of resistance in the capilars (dilatation of the capilars). 2): The system containing the blood before it comes to the capilars is not ideally elastic but becomes more rigid with increasing pressure. 3): Both causes are acting in combination.

"On the enclosed page I have brought your formula 1 in a different form which will show you what I mean. (Not present). I have thought over carefully the kind invitation of President Batista. To my great regret the poor state of my health does not allow me to accept the invitation. I have to be content if I am able to do my regular work at home. I beg you to transmit to President Batista my sincere thanks for his great kindness." Letters of Einstein on scientific subjects have become very scarce in recent years.

This whole system being discussed here can be modeled like an electrical circuit. The "pressure decrement" is like the voltage of a circuit, the blood flow is the current, and the capillaries act like a resistor. Increase the resistance, you get a bigger voltage drop or a bigger pressure drop. Similarly, increase the current/flow and you get a bigger voltage drop, or pressure drop. Much of Gomez's early work is in French journals, and his original "Equation 1" may lie there. The pressure decrement is greater than zero, as Einstein here states. The active pressure is the pressure entering the kidney. The difference between the two pressures increases as the active pressure increases.

Fulgencio Batista was the president and dictator of Cuba at the time. He was overthrown by Fidel Castro in 1959. It is interesting that he extended this invitation to Einstein.