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

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Method</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>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.</p

Why can pulmonary vein stenoses created by radiofrequency catheter ablation worsen during and after follow-up ? A potential explanation

<p>Abstract</p> <p>Background</p> <p>Radiofrequency catheter ablation of excitation foci inside pulmonary veins (PV) generates stenoses that can become quite severe during or after the follow-up period. Since severe PV stenoses have most often disastrous consequences, it would be important to know the underlying mechanism of this temporal evolution. The present study proposes a potential explanation based on mechanical considerations.</p> <p>Methods</p> <p>we have used a mathematical-physical model to examine the cyclic increase in axial wall stress induced in the proximal (= upstream), non-stenosed segment of a stenosed pulmonary vein during the forward flow phases. In a representative example, the value of this increase at peak flow was calculated for diameter stenoses (DS) ranging from 1 to 99%.</p> <p>Results</p> <p>The increase becomes appreciable at a DS of roughly 30% and rise then strongly with further increasing DS value. At high DS values (e.g. > 90%) the increase is approximately twice the value of the axial stress present in the PV during the zero-flow phase.</p> <p>Conclusion</p> <p>Since abnormal wall stresses are known to induce damages and abnormal biological processes (e.g., endothelium tears, elastic membrane fragmentations, matrix secretion, myofibroblast generation, etc) in the vessel wall, it seems plausible that the supplementary axial stress experienced cyclically by the stenotic and the proximal segments of the PV is responsible for the often observed progressive reduction of the vessel lumen after healing of the ablation injury. In the light of this model, the only potentially effective therapy in these cases would be to reduce the DS as strongly as possible. This implies most probably stenting or surgery.</p

Schematic representation of a stenosed, non bridged coronary artery: a) When flow is zero, the intravascular pressure p exerts two axial, opposite, equal forces (Fand F) in the constriction and expansion cones, respectively

<p><b>Copyright information:</b></p><p>Taken from "Could increased axial wall stress be responsible for the development of atheroma in the proximal segment of myocardial bridges?"</p><p>http://www.tbiomed.com/content/4/1/29</p><p>Theoretical Biology & Medical Modelling 2007;4():29-29.</p><p>Published online 9 Aug 2007</p><p>PMCID:PMC2020464.</p><p></p> 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 pis greater than the distal pressure p, and the sum of the two forces pulling in downstream direction (Fand F, see Appendix) is greater than the sum of the two forces pulling in upstream direction (Fand F). If flow and proximal pressure do not reach their maximum simultaneously, the net force F = F+ F- F- Fis 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

Axial wall stress (y-axis) at the entrance of the bridge considered in the numerical example versus diameter reduction values (DS; x-axis)

<p><b>Copyright information:</b></p><p>Taken from "Could increased axial wall stress be responsible for the development of atheroma in the proximal segment of myocardial bridges?"</p><p>http://www.tbiomed.com/content/4/1/29</p><p>Theoretical Biology & Medical Modelling 2007;4():29-29.</p><p>Published online 9 Aug 2007</p><p>PMCID:PMC2020464.</p><p></p> 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%

Definition of circumferential, axial, and radial wall stress (perspective view)

<p><b>Copyright information:</b></p><p>Taken from "Could increased axial wall stress be responsible for the development of atheroma in the proximal segment of myocardial bridges?"</p><p>http://www.tbiomed.com/content/4/1/29</p><p>Theoretical Biology & Medical Modelling 2007;4():29-29.</p><p>Published online 9 Aug 2007</p><p>PMCID:PMC2020464.</p><p></p> Division of the circumferential force Fby the area S of the cube face it pulls at yields the circumferential wall stress σ= F/S. Division of the axial force Fby the area S of the cube face it pulls at yields the axial wall stress σ= F/S. Division of the radial force Fby the area S of the cube face it pushes on yields the radial wall stress σ= F/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- R))

The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees

Patient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography (MSCT) imaging. MSCT cannot provide hemodynamic variables, and the outflow through the side branches must be estimated. The impact of two different models to determine flow through the side branches on the wall shear stress (WSS) distribution in patient specific geometries is evaluated. Murray's law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power. The empirical model is based on flow measurements performed by Doriot et al. (2000) in angiographically normal coronary arteries. The fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2.27. The experimental data imply that Murray's law underestimates the flow through the side branches. We applied the two models to study the WSS distribution in 6 coronary artery trees. Under steady flow conditions, the average WSS between the side branches differed significantly for the two models: the average WSS was 8% higher for Murray's law and the relative difference ranged from -5% to +27%. These differences scale with the difference in flow rate. Near the bifurcations, the differences in WSS were more pronounced: the size of the low WSS regions was significantly larger when applying the empirical model (13%), ranging from -12% to +68%. Predicting outflow based on Murray's law underestimates the flow through the side branches. Especially near side branches, the regions where atherosclerotic plaques preferentially develop, the differences are significant and application of Murray's law underestimates the size of the low WSS region

The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees

\u3cp\u3ePatient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography (MSCT) imaging. MSCT cannot provide hemodynamic variables, and the outflow through the side branches must be estimated. The impact of two different models to determine flow through the side branches on the wall shear stress (WSS) distribution in patient specific geometries is evaluated. Murray's law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power. The empirical model is based on flow measurements performed by Doriot et al. (2000) in angiographically normal coronary arteries. The fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2.27. The experimental data imply that Murray's law underestimates the flow through the side branches. We applied the two models to study the WSS distribution in 6 coronary artery trees. Under steady flow conditions, the average WSS between the side branches differed significantly for the two models: the average WSS was 8% higher for Murray's law and the relative difference ranged from -5% to +27%. These differences scale with the difference in flow rate. Near the bifurcations, the differences in WSS were more pronounced: the size of the low WSS regions was significantly larger when applying the empirical model (13%), ranging from -12% to +68%. Predicting outflow based on Murray's law underestimates the flow through the side branches. Especially near side branches, the regions where atherosclerotic plaques preferentially develop, the differences are significant and application of Murray's law underestimates the size of the low WSS region.\u3c/p\u3