Nonaxisymmetric mathematical model of the cardiac left ventricle anatomy

We describe a mathematical model of the shape and fibre direction field of the cardiac left ventricle. The ventricle is composed of surfaces which model myocardial sheets. On each surface, we construct a set of curves corresponding to myocardial fibres. Tangents to these curves form the myofibres direction field. The fibres are made as images of semicircle chords parallel to its diameter. To specify the left ventricle shape, we use a special coordinate system where the left ventricle boundaries are coordinate surfaces. We propose an analytic mapping from the semicircle to the special coordinate system. The model is correlated with Torrent-Guasp’s concept of the unique muscular band and with Pettigrew’s idea of nested surfaces. Subsequently, two models of concrete normal canine and human left ventricles are constructed based on experimental Diffusion Tensor Magnetic Resonance Imaging data. The input data for the models is only the left ventricle shape. In a local coordinate system connected with the left ventricle meridional section, we calculate two fibre inclination angles, i.e. true fibre angle and helix angle. We obtained the angles found from the Diffusion Tensor Magnetic Resonance Imaging data and compared them with the model angles. We give the angle plots and show that the model adequately reproduces the fibre architecture in the majority of the left ventricle wall. Based on the mathematical model proposed, one can construct a numerical mesh that makes it possible to solve electrophysiological and mechanical left ventricle activity problems in norm and pathology. In the special coordinate system mentioned, the numerical scheme is written in a rectangular area and the boundary conditions can simply be written. By changing the model parameters, one can set a general or regional ventricular wall thickening or the left ventricle shape change, which is typical for certain cardiac pathologies

Estimating prognosis in patients with acute myocardial infarction using personalized computational heart models

Biomechanical computational models have potential prognostic utility in patients after an acute ST-segment–elevation myocardial infarction (STEMI). In a proof-of-concept study, we defined two groups (1) an acute STEMI group (n = 6, 83% male, age 54 ± 12 years) complicated by left ventricular (LV) systolic dysfunction; (2) an age- and sex- matched hyper-control group (n = 6, 83% male, age 46 ± 14 years), no prior history of cardiovascular disease and normal systolic blood pressure (SBP < 130 mmHg). Cardiac MRI was performed in the patients (2 days & 6 months post-STEMI) and the volunteers, and biomechanical heart models were synthesized for each subject. The candidate parameters included normalized active tension (ATnorm) and active tension at the resting sarcomere length (Treq, reflecting required contractility). Myocardial contractility was inversely determined from personalized heart models by matching CMR-imaged LV dynamics. Compared with controls, patients with recent STEMI exhibited increased LV wall active tension when normalized by SBP. We observed a linear relationship between Treq 2 days post-MI and global longitudinal strain 6 months later (r = 0.86; p = 0.03). Treq may be associated with changes in LV function in the longer term in STEMI patients complicated by LV dysfunction. Further studies seem warranted

Advances in computational modelling for personalised medicine after myocardial infarction

Myocardial infarction (MI) is a leading cause of premature morbidity and mortality worldwide. Determining which patients will experience heart failure and sudden cardiac death after an acute MI is notoriously difficult for clinicians. The extent of heart damage after an acute MI is informed by cardiac imaging, typically using echocardiography or sometimes, cardiac magnetic resonance (CMR). These scans provide complex data sets that are only partially exploited by clinicians in daily practice, implying potential for improved risk assessment. Computational modelling of left ventricular (LV) function can bridge the gap towards personalised medicine using cardiac imaging in patients with post-MI. Several novel biomechanical parameters have theoretical prognostic value and may be useful to reflect the biomechanical effects of novel preventive therapy for adverse remodelling post-MI. These parameters include myocardial contractility (regional and global), stiffness and stress. Further, the parameters can be delineated spatially to correspond with infarct pathology and the remote zone. While these parameters hold promise, there are challenges for translating MI modelling into clinical practice, including model uncertainty, validation and verification, as well as time-efficient processing. More research is needed to (1) simplify imaging with CMR in patients with post-MI, while preserving diagnostic accuracy and patient tolerance (2) to assess and validate novel biomechanical parameters against established prognostic biomarkers, such as LV ejection fraction and infarct size. Accessible software packages with minimal user interaction are also needed. Translating benefits to patients will be achieved through a multidisciplinary approach including clinicians, mathematicians, statisticians and industry partners

Validation of Immersed Boundary Simulations of Heart Valve Hemodynamics against In Vitro 4D Flow MRI Data

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Validation of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results validate our design-based valve model construction, the IB solvers used and the immersed boundary method for flows around heart valves

A finite strain nonlinear human mitral valve model with fluid structure interaction

A simulated human mitral valve under a physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used for characterizing the mechanical behaviour of the mitral valve tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with the measurements from the magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet, and concentrated around the annulus trigons and free edges of the valve leaflets. Those areas are located where the leaflet has the highest curvature. Effects of the chordae tendineae in the material model are studied and the results show that these chordae play an important role in providing a secondary orifice for the flow when valve opens. Although there are some discrepancies to be overcome in future works, our simulations show that the developed computational model is promising in mimicking the in vivo mitral valve dynamics and providing important information that are not obtainable by in vivo measurements. This article is protected by copyright. All rights reserved