Mechanical behaviour of ventricular aneurysms

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

Regional three-dimensional geometry and function of left ventricles with fibrous aneurysms. A cine-computed tomography study

BACKGROUND

To assess the extent and nature of the dysfunction surrounding aneurysms of the left ventricle (LV), we examined the parameters of local and global three-dimensional shape, size, and function of LVs of eight patients with histologically confirmed anterior fibrous aneurysms.

METHODS AND RESULTS

Three-dimensional reconstructions of each LV were made from 10-12 short-axis fast cine-angiographic computed tomography (cine-CT) slices encompassing the entire heart at end diastole and end systole. Regional three-dimensional wall thickness, thickening, motion, curvature, and stress index were calculated for 84 elements encompassing the entire LV. The aneurysmal border was defined by a sharp decrease in end-diastolic wall thickness and separated the LV into an aneurysmal zone and a normal zone that was further divided into adjacent normal (AN) and remote normal (RN) zones. As expected, thickening was negligible in both the aneurysmal and the border zones. Although both the AN and the RN zones had normal wall thickness (1.05 +/- 0.20 and 1.09 +/- 0.20 cm, respectively), thickening was depressed in the AN (0.22 +/- 0.08 cm) but not the RN (0.44 +/- 0.19 cm) zones. The size of the dysfunction zone (defined as less than 2 mm thickening) was found to be considerably greater than the anatomic size of the aneurysm (60.9 +/- 13.7% versus 33.6 +/- 7.6% of the left ventricular endocardial area, respectively; p less than 0.001). In addition, the AN zone had a smaller curvature and a higher stress index than the RN zone.

CONCLUSIONS

LVs with fibrous aneurysms are characterized by a relatively large region of nonfunction that encompasses the thin aneurysmal area and its transitional border zone, a normally functioning remote zone, and an intermediate region of normal wall thickness but with reduced function, which may be attributed to its low curvature and high stress index.

Mechanics of left ventricular aneurysm

When a coronary artery is significantly occluded, the left ventricular myocardial segment, which is perfused by that coronary artery, will become ischaemic and even irreversibly infarcted. An acute infarct has very low stiffness and if it involves the entire wall there is a risk of rupture; however, in the absence of such a critical situation, fibrous tissue is laid into the infarcted myocardial segment. Such an infarcted fibrotic myocardial segment will not be able to contract, and so generate tensile stress. The surrounding intact myocardium will contract and generate wall stress, thereby developing a high intra-chamber systolic pressure; the chronically infarcted and fibrotic segment will have to sustain this high chamber pressure. Its loss of contractility and the resulting reduced systolic stiffness relative to the intact segment, will cause it to deform into a bulge; this is an aneurysm. When a left ventricular chamber with an aneurysm contracts during the systolic phase, some blood also goes into the aneurysm, and this decreases the stroke volume; since the aneurysm wall is passive, stagnant blood flow prevails in the aneurysm itself, which in turn can give rise to the formation of a mural thrombus. These serious consequences provide a justification for the analysis of an infarcted left ventricular chamber, in order to predict the size of the aneurysmic bulge. Such an analysis is presented in this paper. To determine the left ventricular wall deformation, and the stress arising from infarction of a wall segment (which leads to a ventricular aneurysm) the left ventricle is modelled here as a pressurized ellipsoidal shell. Deformations of infarcted wall segments are computed for several damaged wall-thicknesses in left ventricles of different shapes. The analysis involves a derivation of equations for wall-stress equilibrium with the chamber pressure, and myocardial incompressibility before and after infarct formation. The equations are solved by the Newton-Raphson method (using elliptical integrals of the first and second kind). Of significance are the prognostic implications of the results, presented in the form of graphs, showing the dependence of tensile stress and the bulge of infarcted wall-segments, on the extent of damaged wall-thickness and the angle of infarct. Scaled illustrations of the bulge shapes, for various degrees of infarcts, are provided. The results indicate that for rupture of the ventricle, the percentage of infarcted wall-thickness and the shape of the ellipsoidal left ventricular chamber play more dominant roles than the angle-of-damage, or the extent of the infarct.