A note on the mathematical theory of the effect of nervous stress on coronary thrombosis

Abstract

The “classical” view of formation of blood clots is that the disintegration of platelets releases thrombokinase which activates prothrombin into thrombin. The latter combining with fibrinogen produces fibrin, the substance of the clot. There is, however, ample evidence of hormonal and other biochemical factors as playing a role in the process of clotting. Through the necessity of a breakdown of platelets has been challenged, yet theirpresence is considered as necessary for clotting. Thefirst part of this paper is based on the assumption that either a breakdown or even an injury of a platelet produces thrombokinase. An injury is likely to occur due to collisions between platelets, between platelets and erythrocytes or between platelets and leukocytes. A probability is ascribed to the production of thrombokinase by a collision. Thus not every collision is effective. The frequency of those collisions is calculated according to classical physics. Inasmuch as mental stress usually causes vasoconstriction and therefore an increase of concentration of the formed elements of blood, the frequency of collisions and therefore the production of small amounts of thrombokinase increases with stress. If thrombokinase formed by the collision remains preserved and therefore accumulates in the blood, we arrive at an expression which gives us the necessary total duration of stress to produce thrombosis. According to that equation, even in the absence of stress, any individual if he lives long enough should eventually develop a thrombosis. If, however the thrombokinase is destroyed, then it is necessary that during a sufficiently short time enough effective collisions occur to increase the amount of thrombokinase to a danger level. With this picture we find only theprobability of a formation of a thrombus as a function of the intensity of stress and its duration. The probability remains finite event for zero stress, showing that even individuals who are always relaxed may develop thrombi.

In the second part of the paper an outline of a biochemical approach is given. Inasmuch as we know very little about the biochemical mechanism involved, it is simply assumed that during a stress of intensityS and duration Δ there is a probability of a thrombosis occurring. Then by applying the theory of probabilities, an expression is derived giving the probability of occurrence of a thrombus after a given number of stress incidences. The expressions are different from those obtained from the first approach but lead basically to the same results. A comparison of both or of their combination, with available data may give indications as to which of the factors plays a preponderant part.