Mohamed S. Hamid

Effects of cyclic flexion of coronary arteries on progression of atherosclerosis

The purpose of this investigation was to test the hypothesis that cyclic flexion of the coronary arteries contributes to the progression of atherosclerotic plaques. Coronary arteriograms were evaluated in 33 unselected patients who underwent 2 studies over a period of 25 +/- 16 months (mean +/- SD). Among the 33 patients, 103 plaques were identified. Plaques that showed progression were compared with plaques that showed no progression. The angle of flexion that occurred during systole at the site of the plaque was measured on the first arteriogram. In comparing progression versus no progression, the interval between arteriograms was 29 +/- 18 versus 23 +/- 14 months (p = NS) and percent stenosis at the first arteriogram was 42 +/- 28 versus 45 +/- 19% (p = NS). Percent stenosis at the time of the second arteriogram among plaques that progressed was 78 +/- 21%, and by definition, it remained 45 +/- 19% among those that did not progress. Among arteries with plaques that showed a progression of stenosis, the angle of flexion during systole was 19 +/- 13 degrees versus 9 +/- 15 degrees among arteries with plaques that did not progress (p < 0.01). Linear regression showed that the correlation of the angle of flexion with percent change of stenosis was relatively low (r = 0.32) but statistically significant (p < 0.005). Mathematic modeling of flexible and stiff plaques showed stresses approximately 1.5 to 1.9 times greater with 20 degrees than with 10 degrees flexion. Stresses due to flexion were usually greatest proximal and distal to the plaque along the subendothelial layer of the inner wall of the curved vessel. Data show that the angle of cyclic flexion, and consequently the stresses due to cyclic flexion of the artery were greatest in the region of plaques that progressed over the period of observation. Such stresses may have contributed to tissue damage of fatigue resulting in a more rapid progression of the atheromatous plaques.

Estimation of mechanical stresses on closed cusps of porcine bioprosthetic valves: Effects of stiffening, focal calcium and focal thinning☆

The magnitude and distribution of mechanical stresses acting on the closed cusps of porcine bioprosthetic valves (PBVs) were estimated using a finite element model. The effects of leaflet stiffening, focal calcium and focal thinning on leaflet stresses were determined. In a normal closed PBV leaflet, stresses increased as pressure was increased. At a pressure of 80 mm Hg, the maximal normal principal stresses were 11 g/mm2 near the center of the leaflet and increased to 19 g/mm2 at a pressure of 160 mm Hg. These observations suggest that the closed valve in the mitral position would experience higher mechanical stresses than the closed valve in the aortic position. Tissue stiffening increased stresses throughout the leaflet and introduced a site of stress concentration near the center of the leaflet. At a pressure of 80 mm Hg, the maximal principal normal stress increased 55% when the leaflet was stiff in comparison to the normal leaflet. Focal calcium and focal thinning caused marked gradients of stress between the sites of calcium or thinning and the immediate surrounding tissue. The magnitude of these stress gradients increased with increasing pressure. These sites of mechanical stress concentration or stress gradients appear to be compatible with sites of leaflet calcification or disruption. Such stresses may contribute to spontaneous degeneration of PBVs.

Finite element evaluation of stresses on closed leaflets of bioprosthetic heart valves with flexible stents

Abstract The purpose of this study is to evaluate the influence of stent flexibility on the magnitude and distribution of stresses on the closed leaflets of a porcine bioprosthetic valve. The finite element technique which incorporated large deformation theory has been used in the analysis. Nonlinearities due to geometry, material and pressure dependent boundary conditions are included in the model. An incremental method has been employed in determining the stresses. The pressure was incremented from 0 to 21.3 kPa. Three separate stent flexibilities were considered and this was achieved by modifying the Youngs modulus of the stent material. The calculated radial deflections of the tip of the stent post were in agreement with the results of other investigators. The distribution of stresses in the leaflet of a valve mounted on a flexible stent were compared to the stresses in the leaflet of a valve mounted on a rigid stent. Stent flexibility markedly reduced the stresses in the main body of the leaflet in comparison to a rigid stent, but did not affect the magnitude of stresses near commissures.

Comparison of finite element stress analysis of aortic valve leaflet using either membrane elements or solid elements

Abstract A comparison of the stress distribution during diastole in a single aortic valve leaflet was made using either a membrane shell or solid 20 node curved element. A physiological pressure gradient of 100mmHg was used in the analyses. The geometry of the aortic leaflet was approximated as an elliptic-paraboloid. The material of the leaflet was assumed to be isotropic with a Youngs modulus of 500 gm/mm2 and a Poissons ratio of 0.3. The maximal principal stresses predicted by membrane shell elements, in general, were in good agreement with those predicted by 3-dimensional solid elements, although some variations were present.

Determination of left ventricular wall stresses during isovolumic contraction using incompressible finite elements

Abstract Left ventricular wall stresses were determined during isovolumic contraction using triangular incompressible finite elements. The geometry of the left ventricle (LV) was approximated as a thick shell of revolution. Both finite deformation and finite strain theories were used in the analysis. The incompressibility condition was applied by equating the third strain invariant as unity. The strain energy density function for the myocardial muscle was assumed to be that of a Mooney material. Physiological loads encountered by the LV during isovolumic contraction were used in the analysis. The stresses generated by the myocardium during isovolumic contraction were assumed to be equal and opposite to that of the stresses induced due to application of a cavity pressure of 10.66 kPa (80 mm Hg). During isovolumic contraction, the stresses at the midsection of the LV were of the order 40 kPa. Near the apex, the stresses changed from compressive at the endocardial surface to tensile at the epicardial surface. In conclusion, an improved mathematical model was developed for the characterization of left ventricular stresses during isovolumic contraction.

Effect of alcohol upon arrhythmias following nonpenetrating cardiac impact.

The purpose of this study was to determine if alcohol worsens arrhythmias produced by nonpenetrating cardiac impact. Twenty-three dogs were studied. Twelve underwent nonpenetrating cardiac impact alone at 12 m/sec with a contact compression of 2 cm. Eleven underwent cardiac impact after having received intravenous alcohol (blood level of 197 +/- 37 mg/100 ml) (mean +/- SD). Three dogs experienced ventricular fibrillation immediately after impact and died: of these, two underwent impact alone and one underwent impact following ethanol. These three dogs were eliminated from the study. All of the dogs had some form of complex arrhythmia during the first 10 minutes of observation, the average cumulative duration of which during the first 10 minutes following trauma was greater among dogs that received ethanol. No complex arrhythmias other than ventricular premature contractions or ventricular tachycardia were observed after the first 10 minutes following impact. During the first 2 hours of observation following cardiac impact, dogs that received alcohol before trauma showed more single premature ventricular contractions (p less than 0.03), couplets (p less than 0.01), triplets (p less than 0.02), runs of 4-20 beats (p less than 0.05), and total number of premature ventricular contractions (p less than 0.05) than dogs that underwent trauma alone. Following the first 10 minutes, ventricular irritability increased with time until approximately 1 hour, and then there was a gradual reduction of the frequency of arrhythmias in both dogs that received alcohol and those that did not. In conclusion, nonpenetrating cardiac impact in dogs that previously received ethanol was associated with greater ventricular irritability than in dogs that underwent impact alone.

Large-deformation analysis of aortic valve leaflets during diastole

Abstract The stress distribution on the aortic valve leaflet during diastole under increasing loading conditions was calculated using nonlinear large-deformation finite elements. The geometry of the leaflet was derived based upon the actual configuration of the closed aortic valve leaflets obtained from a cast of the root of the aorta. Variability of the leaflet thickness was incorporated in the finite-element model. The leaflet material was assumed to be isotropic and three values of Youngs modulus E were used. The first two E values that were used were assumed constant at 300 and 5000 kPa, which corresponded to pretransition and posttransition values, respectively, in the stress-strain curve. The third E that was used assumed a stress-dependent value according to a trilinearized approximation of the stress-strain curve. The stress distribution on the leaflet at diastolic aortic pressures of 9.33 and 16.00 kPa (70 and 120 mm Hg) are presented. The large-deformation analysis predicted lower maximal principal stresses than linear theory.

Dynamic response of closed bioprosthetic valve leaflets

Abstract The dynamic response of the leaflets of a closed bioprosthetic valve was determined using triangular shell elements. The damping ratio of the system was estimated using a one-dimensional spring-mass system and was found to be 0.02. This damping ratio was used in estimating the transient response of the three-dimensional leaflets that occurs due to the normal pressure gradient during diastole. The maximal deflection with a Youngs modulus of 600 kPa was 3.71 mm. Stiffening of the leaflet was shown to reduce the maximal deflection. A perforation in one of the leaflets (20% area of a single leaflet) did not change the response appreciably.

Evaluation of the influence of leaflet stiffening on leaflet stresses of porcine bioprosthetic valves using a finite element model

Abstract The magnitude and distribution of mechanical stresses acting on the closed cusps of porcine bioprosthetic valves were estimated using a finite element model. Leaflet stresses were calculated using reported stress-strain properties of glutaraldehyde processed normal porcine valves and stress-strain properties of porcine valve leaflets stiffened by fatigue cycling (658 x 10 cycles). In the normal leaflet, at a pressure of 80 mm Hg, stresses were highest near the commissures (140 kPa), decreased near the center of the leaflet (110 kPa) and were lowest near the base of the leaflet (30 kPa). With increased leaflet stiffening, stresses near the commissures remained relatively unchanged (140 kPa). Stresses near the center of the leaflet, however, increased markedly (170 kPa). With increased leaflet stiffening, stresses near the base of the leaflet remained the lowest (60 kPa). The development of a site of stress concentration near the center of the leaflet following leaflet stiffening, may offer a clue to the etiology of leaflet perforations reported to occur in the central region of leaflets of degenerated porcine bioprosthetic valves.

Evaluation of left ventricular wall stresses during ejection using nonlinear finite elements

Abstract Wall stresses in a normal and infarcted left ventricle were calculated during ejection using nonlinear incompressible finite elements. The geometry of the left ventricle was approximated as a thick ellipsoidal shell of revolution. Tissue incompressibility was assumed and was achieved in the model by applying a constraint in each element that equated the third strain invariant as unity. Both large deformation and large strain theories were used in the analysis. A strain energy density function was assumed for the ventricular muscle. A load of 5.33 kPa (40 mm Hg) was applied at the endocardial surface, in the normal direction away from the surface. This allowed the endocardial surface to encroach upon the ventricular cavity and thus simulated ejection. In the normal left ventricle, stresses were highest in the subendocardium and decreased toward the subepicardium. The computed increase of wall thickness at the mid-ventricular level during ejection was comparable to measurements of wall thickness in anesthetized dogs. Introduction of a small simulated axisymmetric infarct into the model near the apex resulted in an appreciable stress gradient between the infarcted tissue and the adjacent normal myocardium. The estimation of the magnitude and distribution of stresses during ejection in the normal and infarcted left ventricle is useful in understanding the principles that govern left ventricular mechanics.