Luigi E. Perotti

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Regional segmentation of ventricular models to achieve repolarization dispersion in cardiac electrophysiology modeling

The electrocardiogram (ECG) is one of the most significant outputs of a computational model of cardiac electrophysiology because it relates the numerical results to clinical data and is a universal tool for diagnosing heart diseases. One key features of the ECG is the T-wave, which is caused by longitudinal and transmural heterogeneity of the action potential duration (APD). Thus, in order to model a correct wave of repolarization, different cell properties resulting in different APDs must be assigned across the ventricular wall and longitudinally from apex to base. To achieve this requirement, a regional parametrization of the heart is necessary. We propose a robust approach to obtain the transmural and longitudinal segmentation in a general heart geometry without relying on ad hoc procedures. Our approach is based on auxiliary harmonic lifting analyses, already used in the literature to generate myocardial fiber orientations. Specifically, the solution of a sequence of Laplace boundary value problems allows parametrically controlled segmentation of both heart ventricles. The flexibility and simplicity of the proposed method is demonstrated through several representative examples, varying the locations and extents of the epicardial, midwall, and endocardial layers. Effects of the control parameters on the T-wave morphology are illustrated via computed ECGs.

A viscoactive constitutive modeling framework with variational updates for the myocardium

We present a constitutive modeling framework for contractile cardiac mechanics by formulating a single variational principle from which incremental stress-strain relations and kinetic rate equations for active contraction and relaxation can all be derived. The variational framework seamlessly incorporates the hyperelastic behavior of the relaxed and contracted tissue along with the rate - and length - dependent generation of contractile force. We describe a three-element, Hill-type model that unifies the active tension and active deformation approaches. As in the latter approach, we multiplicatively decompose the total deformation gradient into active and elastic parts, with the active deformation parametrizing the contractile Hill element. We adopt as internal variables the fiber, cross-fiber, and sheet normal stretch ratios. The kinetics of these internal variables are modeled via definition of a kinetic potential function derived from experimental force-velocity relations. Additionally, we account for dissipation during tissue deformation by adding a Newtonian viscous potential. To model the force activation, the kinetic equations are coupled with the calcium transient obtained from a cardiomyocyte electrophysiology model. We first analyze our model at the material point level using stress and strain versus time curves for different viscosity values. Subsequently, we couple our constitutive framework with the finite element method (FEM) and study the deformation of three-dimensional tissue slabs with varying cardiac myocyte orientation. Finally, we simulate the contraction and relaxation of an ellipsoidal left ventricular model and record common kinematic measures, such as ejection fraction, and myocardial tissue volume changes.

Method for the unique identification of hyperelastic material properties using full field measures. Application to the passive myocardium material response

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

Useful scars: Physics of the capsids of archaeal viruses

We propose a physical model for the capsids of tailed archaeal viruses as viscoelastic membranes under tension. The fluidity is generated by thermal motion of scarlike structures that are an intrinsic feature of the ground state of large particle arrays covering surfaces with nonzero Gauss curvature. The tension is generated by a combination of the osmotic pressure of the enclosed genome and an extension force generated by filamentous structure formation that drives the formation of the tails. In continuum theory, the capsid has the shape of a surface of constant mean curvature: an unduloid. Particle arrays covering unduloids are shown to exhibit pronounced subdiffusive and diffusive single-particle transport at temperatures that are well below the melting temperature of defect-free particle arrays on a surface with zero Gauss curvature.

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart’s susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.

Computational Mechanics of Viral Capsids

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

Microstructurally Anchored Cardiac Kinematics by Combining In Vivo DENSE MRI and cDTI

Metrics of regional myocardial function can detect the onset of cardiovascular disease, evaluate the response to therapy, and provide mechanistic insight into cardiac dysfunction. Knowledge of local myocardial microstructure is necessary to distinguish between isotropic and anisotropic contributions of local deformation and to quantify myofiber kinematics, a microstructurally anchored measure of cardiac function. Using a computational model we combine in vivo cardiac displacement and diffusion tensor data to evaluate pointwise the deformation gradient tensor and isotropic and anisotropic deformation invariants. In discussing the imaging methods and the model construction, we identify potential improvements to increase measurement accuracy. We conclude by demonstrating the applicability of our method to compute myofiber strain in five healthy volunteers.