Post-infarct evolution of ventricular and myocardial function.

Adverse ventricular remodeling following acute myocardial infarction (MI) may induce ventricular dilation, fibrosis, and loss of global contractile function, possibly resulting in heart failure (HF). Understanding the relation between the time-dependent changes in material properties of the myocardium and the contractile function of the heart may further our understanding of the development of HF post-MI and guide the development of novel therapies. A finite element model of cardiac mechanics was used to model MI in a thick-walled truncated ellipsoidal geometry. Infarct core and border zone comprised 9.6 and 8.1% of the LV wall volume, respectively. Acute MI was modeled by inhibiting active stress generation. Chronic MI was modeled by the additional effect of infarct material stiffening, wall thinning and fiber reorientation. In acute MI, stroke work decreased by 25%. In the infarct core, fiber stress was reduced but fiber strain was increased, depending on the degree of infarct stiffening. Fiber work density was equal to zero. Healthy tissue adjacent to the infarct showed decreased work density depending on the degree of infarct stiffness and the orientation of the myofibers with respect to the infarct region. Thinning of the wall partially restored this loss in work density while the effects of fiber reorientation were minimal. We found that the relative loss in pump function in the infarcted heart exceeds the relative loss in healthy myocardial tissue due to impaired mechanical function in healthy tissue adjacent to the infarct. Infarct stiffening, wall thinning and fiber reorientation did not affect pump function but did affect the distribution of work density in tissue adjacent to the infarct.

A method for the quantification of the pressure dependent 3D collagen configuration in the arterial adventitia.

Collagen plays an important role in the response of the arterial wall to mechanical loading and presumably has a load-bearing function preventing overdistension. Collagen configuration is important for understanding this role, in particular in mathematical models of arterial wall mechanics. In this study a new method is presented to image and quantify this configuration. Collagen in the arterial adventitia is stained with CNA35, and imaged in situ at high resolution with confocal microscopy at luminal pressures from 0 to 140mm Hg. The images are processed with a new automatic approach, utilizing techniques intended for MRI-DTI data. Collagen configuration is quantified through three parameters: the waviness, the transmural angle and the helical angle. The method is demonstrated for the case of carotid arteries of the white New Zealand rabbit. The waviness indicated a gradual straightening between 40 and 80mm Hg. The transmural angle was about zero indicating that the fibers stayed within an axial-circumferential plane at all pressures. The helical angle was characterized by a symmetrical distribution around the axial direction, indicating a double symmetrical helix. The method is the first to combine high resolution imaging with a new automatic image processing approach to quantify the 3D configuration of collagen in the adventitia as a function of pressure.

A model for arterial adaptation combining microstructural collagen remodeling and 3D tissue growth.

Long-term adaptation of soft tissues is realized through growth and remodeling (G&R). Mathematical models are powerful tools in testing hypotheses on G&R and supporting the design and interpretation of experiments. Most theoretical G&R studies concentrate on description of either growth or remodeling. Our model combines concepts of remodeling of collagen recruitment stretch and orientation suggested by other authors with a novel model of general 3D growth. We translate a growth-induced volume change into a change in shape due to the interaction of the growing tissue with its environment. Our G&R model is implemented in a finite element package in 3D, but applied to two rotationally symmetric cases, i.e., the adaptation towards the homeostatic state of the human aorta and the development of a fusiform aneurysm. Starting from a guessed non-homeostatic state, the model is able to reproduce a homeostatic state of an artery with realistic parameters. We investigate the sensitivity of this state to settings of initial parameters. In addition, we simulate G&R of a fusiform aneurysm, initiated by a localized degradation of the matrix of the healthy artery. The aneurysm stabilizes in size soon after the degradation stops.

Towards model-based analysis of cardiac MR tagging data: relation between left ventricular shear strain and myofiber orientation.

Many cardiac pathologies are reflected in abnormal myocardial deformation, accessible through magnetic resonance tagging (MRT). Interpretation of the MRT data is difficult, since the relation between pathology and deformation is not straightforward. Mathematical models of cardiac mechanics could be used to translate measured abnormalities into the underlying pathology, but, so far, they even fail to correctly simulate myocardial deformation in the healthy heart. In this study we investigated to what extent (1) our previously published three-dimensional finite element model of cardiac mechanics [Kerckhoffs, R.C.P., Bovendeerd, P.H.M., Kotte, J.C.S., Prinzen, F.W., Smits, K., Arts, T., 2003. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study. Ann. Biomed. Eng. 31, 536-547] can simulate measured cardiac deformation, and (2) discrepancies between strains in model and experiment are related to the choice of the myofiber orientation in the model. To this end, we measured midwall circumferential strain E(cc) and circumferential-radial shear strain E(cr) in three healthy subjects using MRT. E(cc) as computed in the model agreed well with measured E(cc). Computed E(cr) differed significantly from measured E(cr). The time course of E(cr) was found to be very sensitive to the choice of the myofiber orientation, in particular to the choice of the transverse angle. Discrepancies between circumferential-radial shear strain in model and experiment were reduced strongly by increasing the transverse angle in the original model by 25%.

Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments.

Intraventricular synchrony of cardiac activation is important for efficient pump function. Ventricular pacing restores the beating frequency but induces more asynchronous depolarization and more inhomogeneous contraction than in the normal heart. We investigated whether the increased inhomogeneity in the left ventricle can be described by a relatively simple mathematical model of cardiac electromechanics, containing normal mechanical and impulse conduction properties. Simulations of a normal heartbeat and of pacing at the right ventricular apex (RVA) were performed. All properties in the two simulations were equal, except for the depolarization sequence. Simulation results of RVA pacing on local depolarization time and systolic midwall circumferential strain were compared with those measured in dogs, using an epicardial sock electrode and MRI tagging, respectively. We used the same methods for data processing for simulation and experiment. Model and experiment agreed in the following aspects. 1) Ventricular pacing decreased systolic pressure and ejection fraction relative to natural sinus rhythm. 2) Shortening during ejection and stroke work declined in early depolarized regions and increased in late depolarized regions. 3) The relation between epicardial depolarization time and systolic midwall circumferential strain was linear and similar for the simulation (slope = -3.80 +/- 0.28 s(-1), R2 = 0.87) and the experiments [slopes for 3 animals -2.62 +/- 0.43 s(-1) (R2 = 0.59), -2.97 +/- 0.38 s(-1) (R2 = 0.69), and -4.44 +/- 0.51 s(-1) (R2 = 0.76)]. We conclude that our model of electromechanics is suitable to simulate ventricular pacing and that the apparently complex events observed during pacing are caused by well-known basic physiological processes.

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact.

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. Current FE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model for brain tissue and implemented it in an explicit FE code. To obtain sufficient numerical accuracy for modeling the nearly incompressible brain tissue, deviatoric and volumetric stress contributions are separated. Deviatoric stress is modeled in a non-linear viscoelastic differential form. Volumetric behavior is assumed linearly elastic. Linear viscoelastic material parameters were derived from published data on oscillatory experiments, and from ultrasonic experiments. Additionally, non-linear parameters were derived from stress relaxation (SR) experiments at shear strains up to 20%. The model was tested by simulating the transient phase in the SR experiments not used in parameter determination (strains up to 20%, strain rates up to 8s(-1)). Both time- and strain-dependent behavior were predicted accurately (R2>0.96) for strain and strain rates applied. However, the stress was overestimated systematically by approximately 31% independent of strain(rate) applied. This is probably caused by limitations of the experimental data at hand.

Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study.

The use of mathematical models combining wave propagation and wall mechanics may provide new insights in the interpretation of cardiac deformation toward various forms of cardiac pathology. In the present study we investigated whether combining accepted mechanisms on propagation of the depolarization wave, time variant mechanical properties of cardiac tissue after depolarization, and hemodynamic load of the left ventricle (LV) by the aortic impedance in a three-dimensional finite element model results in a physiological pattern of cardiac contraction. We assumed that the delay between depolarization for all myocytes and the onset of crossbridge formation was constant. Two simulations were performed, one in which contraction was initiated according to the regular depolarization pattern (NORM simulation), and another in which contraction was initiated after synchronous depolarization (SYNC simulation). In the NORM simulation propagation of depolarization was physiological, but wall strain was unphysiologically inhomogeneous. When simulating LV mechanics with unphysiological synchronous depolarization (SYNC) myofiber strain was more homogeneous and more physiologic. Apparently, the assumption of a constant delay between depolarization and onset of crossbridge formation results in an unrealistic contraction pattern. The present finding may indicate that electromechanical delay times are heterogeneously distributed, such that a contraction in a normal heart is more synchronous than depolarization.

A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction.

The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.