Could increased axial wall stress be responsible for the development of atheroma in the proximal segment of myocardial bridges?

Abstract

Background: A recent model describing the mechanical interaction between a stenosis and the vessel wall has shown that axial wall stress can considerably increase in the region immediately proximal to the stenosis during the (forward) flow phases, so that abnormal biological processes and wall damages are likely to be induced in that region. Our objective was to examine what this model predicts when applied to myocardial bridges.

Method: The model was adapted to the hemodynamic particularities of myocardial bridges and used to estimate by means of a numerical example the cyclic increase in axial wall stress in the vessel segment proximal to the bridge. The consistence of the results with reported observations on the presence of atheroma in the proximal, tunneled, and distal vessel segments of bridged coronary arteries was also examined.

Results: 1) Axial wall stress can markedly increase in the entrance region of the bridge during the cardiac cycle. 2) This is consistent with reported observations showing that this region is particularly prone to atherosclerosis.

Conclusion: The proposed mechanical explanation of atherosclerosis in bridged coronary arteries indicates that angioplasty and other similar interventions will not stop the development of atherosclerosis at the bridge entrance and in the proximal epicardial segment if the decrease of the lumen of the tunneled segment during systole is not considerably reduced.

Figure 1

Angiographic images showing a bridge on the left anterior descending coronary artery (LAD) in a male patient of 65 years. A1) Right anterior oblique view taken at end systole. The compressed vessel segment is indicated by the two arrows. B1) Left anterior oblique view taken nearly at the same instant. A2) Same view as in A1, but taken 133 ms later. The tunneled segment is no longer compressed. B2) Same view as in B1 but 133 ms later.

Figure 2

Definition of circumferential, axial, and radial wall stress (perspective view). Division of the circumferential force F_c by the area S of the cube face it pulls at yields the circumferential wall stress σ_c = F_c/S. Division of the axial force F_a by the area S of the cube face it pulls at yields the axial wall stress σ_a = F_a/S. Division of the radial force F_r by the area S of the cube face it pushes on yields the radial wall stress σ_r = F_r/S. These three orthogonal stresses are used to describe the mechanical state of the vessel wall at the considered location. The average axial wall stress over a wall cross-section is equal to the quotient "force pulling axially at that cross-section, divided by the area A of that cross-section" (A = π (R_o² - R_i²)).

Figure 3

Schematic representation of a stenosed, non bridged coronary artery: a) When flow is zero, the intravascular pressure p exerts two axial, opposite, equal forces (F_o and F_o) in the constriction and expansion cones, respectively. The vertical equidistant slashes indicate that the vessel wall does not pull (axially) at the surrounding myocardium. b) When blood flows through the stenosis, the proximal pressure p_p is greater than the distal pressure p_d, and the sum of the two forces pulling in downstream direction (F₁ and F₂, see Appendix) is greater than the sum of the two forces pulling in upstream direction (F₃ and F_tissues). If flow and proximal pressure do not reach their maximum simultaneously, the net force F = F₁ + F₂ - F₃ - F_tissues is not necessarily maximal when flow or proximal pressure are maximal. The oblique slashes show where the vessel wall will elongate axially and pull at the myocardium.

Figure 4

Axial wall stress (y-axis) at the entrance of the bridge considered in the numerical example versus diameter reduction values (DS; x-axis). The stress values are the sum of "normal" axial wall stress (see text) and supplementary axial stress generated cyclically by the pressure drop across the bridge. The flow was set to 1 ml/s as long as the distal pressure did not fall below 10 mmHg. At high DS values (80, 85, 90, and 99%), it was appropriately reduced in order to respect this 10 mmHg limit. Axial stress begins to increase markedly at a DS value of approximately 60%; this corresponds to a lumen area reduction of roughly 80%.