A Comparison of Phenomenologic Growth Laws for Myocardial Hypertrophy

The heart grows in response to changes in hemodynamic loading during normal development and in response to valve disease, hypertension, and other pathologies. In general, a left ventricle subjected to increased afterload (pressure overloading) exhibits concentric growth characterized by thickening of individual myocytes and the heart wall, while one experiencing increased preload (volume overloading) exhibits eccentric growth characterized by lengthening of myocytes and dilation of the cavity. Predictive models of cardiac growth could be important tools in evaluating treatments, guiding clinical decision making, and designing novel therapies for a range of diseases. Thus, in the past 20 years there has been considerable effort to simulate growth within the left ventricle. While a number of published equations or systems of equations (often termed “growth laws”) can capture some aspects of experimentally observed growth patterns, no direct comparisons of the various published models have been performed. Here we examine eight of these laws and compare them in a simple test-bed in which we imposed stretches measured during in vivo pressure and volume overload. Laws were compared based on their ability to predict experimentally measured patterns of growth in the myocardial fiber and radial directions as well as the ratio of fiber-to-radial growth. Three of the eight laws were able to reproduce most key aspects of growth following both pressure and volume overload. Although these three growth laws utilized different approaches to predict hypertrophy, they all employed multiple inputs that were weakly correlated during in vivo overload and therefore provided independent information about mechanics.     

A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening

The objective of this work is to establish a generic continuum-based computational concept for finite growth of living biological tissues. The underlying idea is the introduction of an incompatible growth configuration which naturally introduces a multiplicative decomposition of the deformation gradient into an elastic and a growth part. The two major challenges of finite growth are the kinematic characterization of the growth tensor and the identification of mechanical driving forces for its evolution. Motivated by morphological changes in cell geometry, we illustrate a micromechanically motivated ansatz for the growth tensor for cardiac tissue that can capture both strain-driven ventricular dilation and stress-driven wall thickening. Guided by clinical observations, we explore three distinct pathophysiological cases: athlete's heart, cardiac dilation, and cardiac wall thickening. We demonstrate the computational solution of finite growth within a fully implicit incremental iterative Newton-Raphson based finite element solution scheme. The features of the proposed approach are illustrated and compared for the three different growth pathologies in terms of a generic bi-ventricular heart model.     

Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration

Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations.     

心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法. 在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性. 本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应. 基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比. 结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.      

Mechanical Stimuli for Left Ventricular Growth During Pressure Overload

Background

The mechanical stimulus (i.e., stress or stretch) for growth occurring in the pressure-overloaded left ventricle (LV) is not exactly known.

Objective

To address this issue, we investigate the correlation between local ventricular growth (indexed by local wall thickness) and the local acute changes in mechanical stimuli after aortic banding.

Methods

LV geometric data were extracted from 3D echo measurements at baseline and 2 weeks in the aortic banding swine model (n?=?4). We developed and calibrated animal-specific finite element (FE) model of LV mechanics against pressure and volume waveforms measured at baseline. After simulation of the acute effects of pressure-overload, the local changes of maximum, mean and minimum myocardial stretches and stresses in three orthogonal material directions (i.e., fiber, sheet and sheet-normal) over a cardiac cycle were quantified. Correlation between mechanical quantities and the corresponding measured local changes in wall thickness was quantified using the Pearson correlation number (PCN) and Spearman rank correlation number (SCN).

Results

At 2 weeks after banding, the average septum thickness decreased from 10.6?±?2.92 mm to 9.49?±?2.02 mm, whereas the LV free-wall thickness increased from 8.69?±?1.64 mm to 9.4?±?1.22 mm. The FE results show strong correlation of growth with the changes in maximum fiber stress (PCN?=?0.5471, SCN?=?0.5111) and changes in the mean sheet-normal stress (PCN?=?0.5266, SCN?=?0.5256). Myocardial stretches, however, do not have good correlation with growth.

Conclusion

These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

     

A theoretical model for tissue growth in confined geometries

It is known that cells proliferate and produce extracellular matrix in response to biochemical and mechanical stimuli. Constitutive models considering these phenomena are needed to quantitatively describe the process of tissue growth in the context of tissue engineering and regenerative medicine. In this paper we re-examine the theoretical framework provided by Ambrosi and Guana (2007) and Ambrosi and Guillou (2007). We show how a volumetric growth rate term can be obtained (both in a large and small strain setting), which is consistent with the laws of thermodynamics and then apply the model to a simple geometry of tissue growth within a circular pore. The model, despite its simplicity, is comparable with experimental measurements of tissue growth and highlights the contribution of the mechanical stresses produced during tissue growth on the growth rate itself.     

Regulation of the lumen of a resistance blood vessel by mechanical stimuli

The flow in a vessel able to regulate its lumen under the action of mechanical stimuli, the variation of the pressure difference between the inner and outer surfaces of the vessel wall and the blood flow velocity, is described. This ability is determined by the effect of the mechanical stimuli on the degree of activation of smooth muscle cells in the vessel wall. In order to describe the active properties of the wall, two controlling parameters which have the sense of the concentration of free calcium ions in the cytoplasm of smooth muscle cells and the average concentration of nitric oxide in the smooth muscle layer, are introduced. The approach proposed makes it possible to estimate both the degree of participation of each mechanical stimulus in vessel lumen regulation and the result of interaction of two differently directed vascular responses. The calculations show that both the magnitude and direction of the radius response to a mechanical stimulus depend on the initial state of the vessel wall. The role of the vessel wall sensitivity to mechanical stimuli in the stabilization of the blood flow-rate and the variation of the radius along the vessel is considered.     

Perspectives on biomechanical growth and remodeling mechanisms in glaucoma

Glaucoma is a blinding diseases in which damage to the axons results in loss of retinal ganglion cells. Experimental evidence indicates that chronic intraocular pressure elevation initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa is a porous collagen structure through which the axons pass on their path from the retina to the brain. Recent experimental studies revealed the extensive structural changes of the lamina cribrosa and its surrounding tissues during the development and progression of glaucoma. In this perspective paper we review the experimental evidence for growth and remodeling mechanisms in glaucoma including adaptation of tissue anisotropy, tissue thickening/thinning, tissue elongation/shortening and tissue migration. We discuss the existing predictive computational approaches that try to elucidate the potential biomechanical basis of theses growth and remodeling mechanisms and highlight open questions, challenges, and avenues for further development.     

Modeling of growth and remodeling in soft biological tissues with multiple constituents

Among the various important characteristics of biological tissues is their ability to grow and remodel. It is well-known that one of the primary triggers behind the growth and remodeling process is changes in the mechanical environment, for instance changes in stress, strain, etc. These mechanisms of mechanotransduction are the driving force behind many changes in structure and function including growth and remodeling. The purpose of this article is to formulate better constitutive equations for the stress in tissues with multiple constituents undergoing growth and remodeling. This is a very complex problem and is of tremendous importance. Here, we do the modeling from a mechanics point of view, utilizing the theory of natural configurations coupled with population dynamics to accurately model the production and removal of the different constituents that comprise the tissue. This is accomplished by deriving a generalized McKendrick equation for growth and remodeling and has the advantage of directly including the age distribution of constituents into the model. The population distribution function is then used to determine the stress in the tissue.     

Adaptive reorientation of cardiac myofibers: The long-term effect of initial and boundary conditions

On the basis of results from modeling and experimental studies it has been hypothesized that myocytes adapt their orientation to achieve a preferred mechanical load. In a previous computational model study in which fiber reorientation was considered as a local response to local fiber cross-fiber shear strain, we have shown that predicted left ventricular (LV) myofiber orientations agreed well with experimental data. In this study, we investigated in the latter model the effect of initial and boundary conditions on predicted fiber orientations on the long term. After adaptation, predicted fiber orientation and deformation became more realistic, irrespective of initial and boundary conditions. As adaptation proceeded, the effect of initial conditions was found to disappear, suggesting that one single optimal fiber orientation field exists for the heart. In contrast, the effect of the boundary conditions persisted, indicating that modeling of in particular the interaction between myocardium and valvular annulus is relevant for predicting LV myofiber reorientation.     

An investigation on lateral and torsional coupled vibrations of high power density PMSM rotor caused by electromagnetic excitation

Electromagnetic excitation in high power density permanent magnet synchronous motors (PMSMs) due to eccentricity is a significant concern in industry; however, the treatment of lateral and torsional coupled vibrations caused by electromagnetic excitation is rarely addressed, yet it is very important for evaluating the stability of dynamic rotor vibrations. This study focuses on an analytical method for analyzing the stability of coupled lateral/torsional vibrations in rotor systems caused by electromagnetic excitation in a PMSM. An electromechanically coupled lateral/torsional dynamic model of a PMSM Jeffcott rotor is derived using a Lagrange–Maxwell approach. Equilibrium stability was analyzed using a linearized matrix of the equation describing the system. The stability criteria of coupled torsional–lateral motions are provided, and the influences of the electromagnetic and mechanical parameters on mechanical vibration stability and nonlinear behavior were investigated. These results provide better understanding of the nonlinear response of an eccentric PMSM rotor system and are beneficial for controlling and diagnosing eccentricity.     

A simple model for myocardial changes in a failing heart

In a simplified setting, a multi-network model for remodeling in the left ventricle (LV) is developed that can mimic various pathologies of the heart. The model is an extension of the simple model introduced by Nardinocchi and Teresi [9], Nardinocchi et al. [10], [11] that results in an algebraic relation for LV pressure–volume–contraction. We considered two networks, the original tissue and a new tissue, each of which has its own volume fraction, stress-free reference configuration, elastic properties, and contractility. This is used to explore the consequences of microstructural changes in the muscle tissue on LV function in terms of the pressure–volume loop during a single cardiac cycle. Special attention is paid to the stroke volume, which is directly related to cardiac output, and changes in LV wall stress caused by various disease states, including wall thinning (dilated cardiomyopathy), wall thickening (hypertrophic cardiomyopathy), contractility degradation, and stiffness changes (scarring). Various scenarios are considered that are of clinical relevance, and the extent and nature of remodeling that could lead to heart failure are identified.     

Competition Between Radial Expansion and Thickening in the Enlargement of an Intracranial Saccular Aneurysm

Rupture of intracranial saccular aneurysms is the leading cause of spontaneous subarachnoid hemorrhage, which results in significant morbidity and mortality. Although many have suggested that saccular aneurysms enlarge and rupture due to mechanical instabilities, our recent nonlinear analyses suggest that at least certain classes of aneurysms do not exhibit a quasi-static limit point instability or dynamic instabilities in response to periodic loading. Based on an increased understanding of the ubiquitous role of growth and remodeling within the vasculature and recent histopathological data on saccular aneurysms, it is hypothesized that a stress-mediated regulation of collagen turnover causes their enlargement. There is a need, however, for a theoretical framework to explore this and competing hypotheses. In this paper, we present a 2-D constrained mixture model for growth and remodeling of an ellipsoidally shaped saccular aneurysm and numerically simulate enlargement and changes in material symmetry in the aneurysmal wall. Results suggest that ellipsoidal aneurysms tend toward spherical shapes, and a competition between radial expansion and wall thickening plays a critical role in determining the stability of an enlarging lesion.     

Corrosion fatigue of welded offshore steels and tubular connections

This work is concerned with subcritical crack growth in rail-end bolt hole caused by fatigue. Included in the analysis are the mechanical wheel loads and thermal fluctuations experienced by the rail. The interaction of cyclic loading with the rail geometry is considered to be essential. Finite element stress analysis is coupled with the strain energy density criterion for determining the subcritical crack growth steps. The crack can grow and follow any arbitrary surface in the three-dimensional space depending on the symmetry or antisymmetry conditions of the load and geometry. Results on crack shapes and growth rates compare favorably with those observed experimentally.     

Coupled modeling of tumour angiogenesis,tumour growth,and blood perfusion

This paper proposes a more realistic mathematical simulation method to investigate the dynamic process of tumour angio-genesis by fully coupling the vessel growth, tumour growth and associated blood perfusion. The tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the new vasculature, and an estimation of vessel collapse is made according to the wall shear stress criterion. The results are consistent with physiological observations, and further confirm the application of the coupled model feedback mechanism. The model is available to examine the interactions between angiogenesis and tumour growth, to study the change in the dynamic process of chemical environment and the vessel remodeling.     

A laboratory investigation of the flow in the left ventricle of a human heart with prosthetic, tilting-disk valves

The understanding of the phenomena involved in ventricular flow is becoming more and more important because of two main reasons: the continuous improvements in the field of diagnostic techniques and the increasing popularity of prosthetic devices. On one hand, more accurate investigation techniques gives the chance to better diagnose diseases before they become dangerous to the health of the patient. On the other hand, the diffusion of prosthetic devices requires very detailed assessment of the modifications that they introduce in the functioning of the heart. The present work is focussed on the experimental investigation of the flow in the left ventricle of the human heart with the presence of a tilting-disk valve in the mitral position, as this kind of valve is known to change deeply the structure of such a flow. A laboratory model has been built up, which consists of a cavity able to change its volume, representing the ventricle, on which two prosthetic valves are mounted. The facility is designed to be able to reproduce any arbitrarily assigned law of variation of the ventricular volume with time. In the present experiment, a physiologically shaped curve has been used. Velocity was measured using a feature-tracking (FT) algorithm; as a consequence, the particle trajectories are known. The flow has been studied by changing both the beat rate and the stroke volume. The flow was studied both kinematically, examining velocity and vorticity fields, and dynamically, evaluating turbulent and viscous shear stresses, and inertial forces exerted on fluid elements. The analysis of the results allows the identification of the main features of the ventricular flow, generated by a mitral, tilting-disk valve, during the whole cardiac cycle and its dependence on the frequency and the stroke volume.     

Dynamic void nucleation and growth in solids: A self-consistent statistical theory

We present a framework for a self-consistent theory of spall fracture in ductile materials, based on the dynamics of void nucleation and growth. The constitutive model for the material is divided into elastic and “plastic” parts, where the elastic part represents the volumetric response of a porous elastic material, and the “plastic” part is generated by a collection of representative volume elements (RVEs) of incompressible material. Each RVE is a thick-walled spherical shell, whose average porosity is the same as that of the surrounding porous continuum, thus simulating void interaction through the resulting lowered resistance to further void growth. All voids nucleate and grow according to the appropriate dynamics for a thick-walled sphere made of incompressible material. The macroscopic spherical stress in the material drives the response in all volume elements, which have a distribution of critical stresses for void nucleation, and the statistically weighted sum of the void volumes of all RVEs generates the global porosity. Thus, macroscopic pressure, porosity, and a distribution of growing microscopic voids are fully coupled dynamically. An example is given for a rate-independent, perfectly plastic material. The dynamics of void growth gives rise to a rate effect in the macroscopic material even though the parent material is rate independent.     

Changes in Intracellular Calcium during Compression of C2C12 Myotubes

In recent years, damage directly due to tissue deformation has gained interest in deep pressure ulcer aetiology research. It has been shown that deformation causes muscle cell damage, though the pathway is unclear. Mechanically induced skeletal muscle damage has often been associated with an increased intracellular Ca²⁺ concentration, e.g. in eccentric exercise (Allen et al., J Physiol 567(3):723–735, 2005). Therefore, the hypothesis was that compression leads to membrane disruptions, causing an increased Ca²⁺-influx, eventually leading to Ca²⁺ overload and cell death. Monolayers of differentiated C2C12 myocytes, stained with a calcium-sensitive probe (fluo-4), were individually subjected to compression while monitoring the fluo-4 intensity. Approximately 50% of the cells exhibited brief calcium transients in response to compression, while the rest did not react. However, all cells demonstrated a prolonged Ca²⁺ up-regulation upon necrosis, which induced similar up-regulations in some of the surrounding cells. Population heterogeneity is a possible explanation for the observed differences in response, and it might also become important in tissue damage development. It did not become clear however whether Ca²⁺-influxes were the initiators of damage.