心电激励下的人体左心室力学响应分析

人体心脏通过电兴奋引起的心肌收缩实现泵血功能 ,而心肌的力学特性高度依赖于肌纤维结构。本文根据肌纤维旋向和复合材料理论以及电生理心脏模型建立了左心室的有限元机械模型 ,仿真研究了左心室在心电兴奋力作用下的力学响应。结果表明左心室的收缩过程是十分复杂的 ,包括轴向和径向的收缩及绕长轴的不同程度的旋转扭曲。从总体趋势上看 ,心尖处变形最为严重。此外 ,仿真结果还表明 ,心壁应力分布不均匀 ,从内壁到外壁有所减少 ;在心尖和心底部应力较大 ,其中内壁心尖处应力最大。这些结果说明了心脏的力学特性与心肌纤维结构、左心室的几何形状以及电兴奋刺激密切相关。作者将本文的仿真结果与医学图像及其它模型进行了对比分析 ,结果表明了该模型用于分析心肌力学功能特性的可行性     

A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload

Adult cardiac muscle adapts to mechanical changes in the environment by growth and remodeling (G&R) via a variety of mechanisms. Hypertrophy develops when the heart is subjected to chronic mechanical overload. In ventricular pressure overload (e.g. due to aortic stenosis) the heart typically reacts by concentric hypertrophic growth, characterized by wall thickening due to myocyte radial growth when sarcomeres are added in parallel. In ventricular volume overload, an increase in filling pressure (e.g. due to mitral regurgitation) leads to eccentric hypertrophy as myocytes grow axially by adding sarcomeres in series leading to ventricular cavity enlargement that is typically accompanied by some wall thickening. The specific biomechanical stimuli that stimulate different modes of ventricular hypertrophy are still poorly understood. In a recent study, based on in vitro studies in micropatterned myocyte cell cultures subjected to stretch, we proposed that cardiac myocytes grow longer to maintain a preferred sarcomere length in response to increased fiber strain and grow thicker to maintain interfilament lattice spacing in response to increased cross-fiber strain. Here, we test whether this growth law is able to predict concentric and eccentric hypertrophy in response to aortic stenosis and mitral valve regurgitation, respectively, in a computational model of the adult canine heart coupled to a closed loop model of circulatory hemodynamics. A non-linear finite element model of the beating canine ventricles coupled to the circulation was used. After inducing valve alterations, the ventricles were allowed to adapt in shape in response to mechanical stimuli over time. The proposed growth law was able to reproduce major acute and chronic physiological responses (structural and functional) when integrated with comprehensive models of the pressure-overloaded and volume-overloaded canine heart, coupled to a closed-loop circulation. We conclude that strain-based biomechanical stimuli can drive cardiac growth, including wall thickening during pressure overload.     

Left Ventricular Geometry,Tissue Composition,and Residual Stress in High Fat Diet Dahl-Salt Sensitive Rats

Background

Hypertension drives myocardial remodeling, leading to changes in structure, composition and mechanical behavior, including residual stress, which are linked to heart disease progression in a gender-specific manner. Emerging therapies are also targeting constituent-specific pathological features. All previous studies, however, have characterized remodeling in the intact tissue, rather than isolated tissue constituents, and did not include sex as a biological variable.

Objective

In this study we first identified the contribution of collagen fiber network and myocytes to the myocardial residual stress/strain in Dahl-Salt sensitive rats fed with high fat diet. Then, we quantified the effect of hypertension on the remodeling of the left ventricle (LV), as well as the existence of sex-specific remodeling features.

Methods

We performed mechanical tests (opening angle, ring-test) and histological analysis on isolated constituents and intact tissue of the LV. Based on the measurements from the tests, we performed a stress analysis to evaluate the residual stress distribution. Statistical analysis was performed to identify the effects of constituent isolation, elevated blood pressure, and sex of the animal on the experimental measurements and modeling results.

Results

Hypertension leads to reduced residual stress/strain in the intact tissue, isolated collagen fibers, and isolated myocytes in male and female rats. Collagen remains the largest contributor to myocardial residual stress in both normotensive and hypertensive animals. We identified sex-differences in both hypertensive and normotensive animals.

Conclusions

We observed both constituent- and sex-specific remodeling features in the LV of an animal model of hypertension.

     

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.     

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.     

Multi-scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia

The sclera uses unknown mechanisms to match the eye’s axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye’s refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macro-scale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.     

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.     

Effect of trabeculae and papillary muscles on the hemodynamics of the left ventricle

The impact of surface trabeculae and papillary muscles on the hemodynamics of the left ventricle (LV) is investigated using numerical simulations. Simulations of ventricular flow are conducted for two different models of the LV derived from high-resolution cardiac computed tomography (CT) scans using an immersed boundary method-based flow solver. One model comprises a trabeculated left ventricle (TLV) that includes both trabeculae and papillary muscles, while the second model has a smooth left ventricle that is devoid of any of these surface features. Results indicate that the trabeculae and papillary muscles significantly disrupt the vortices that develop during early filling in the TLV model. Large recirculation zones are found to form in the wake of the papillary muscles; these zones enhance the blockage provided by the papillary muscles and create a path for the mitral jet to penetrate deeper into the ventricular apex during diastole. During systole, the trabeculae enhance the apical washout by ‘squeezing’ the flow from the apical region. Finally, the trabeculae enhance viscous dissipation rate of the ventricular flow, but this effect is not significant in the overall power budget.     

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.     

Vortex dynamics in a model left ventricle during filling

Analysis of the properties of the left ventricle flow during filling (diastole) is known to allow early detection of potential malfunctions during the fundamental heart pumping phase (systole). Diagnoses are now usually based on Doppler measurement of the flow velocity for which interpretative schemes and quantitative references are sought. The flow inside an ideal model of the left ventricle is here studied numerically by a finite difference method in prolate spheroid moving coordinates. The axisymmetric assumption is employed in this first study. The vortex dynamics is characterised by the formation of a wake vortex attached at the valvular edge which is shed at the end of the ventricle expansion. Major features are its translation by self-induced velocity and vortex-induced separations from the ventricle internal wall. Results are represented as, and compared with, clinical data showing a good general agreement and allowing an improved physical interpretation of the latter.     

A numerical model of left ventricle and aortic valve function of its afterload (I)

Due to the study of the function of heart and aortic valve, we set up a physical model of left ventricle, aortic valve and afterload and derive theoretical equation of each part from the model. Then we calculate the basic equations within physiology and impair parameters. Based on this, we will discuss fully in the next paper the effect of left ventricular afterload on valve opening, ejection and valve function, etc.     

Adaptive Remodeling in the Elastase-Induced Rabbit Aneurysms

Background

Rupture of brain aneurysms is associated with high fatality and morbidity rates. Through remodeling of the collagen matrix, many aneurysms can remain unruptured for decades, despite an enlarging and evolving geometry.

Objective

Our objective was to explore this adaptive remodeling for the first time in an elastase induced aneurysm model in rabbits.

Methods

Saccular aneurysms were created in 22 New Zealand white rabbits and remodeling was assessed in tissue harvested 2, 4, 8 and 12 weeks after creation.

Results

The intramural principal stress ratio doubled after aneurysm creation due to increased longitudinal loads, triggering a remodeling response. A distinct wall layer with multi-directional collagen fibers developed between the media and adventitia as early as 2 weeks, and in all cases by 4 weeks with an average thickness of 50.6?±?14.3 μm. Collagen fibers in this layer were multi-directional (AI?=?0.56?±?0.15) with low tortuosity (1.08?±?0.02) compared with adjacent circumferentially aligned medial fibers (AI?=?0.78?±?0.12) and highly tortuous adventitial fibers (1.22?±?0.03). A second phase of remodeling replaced circumferentially aligned fibers in the inner media with longitudinal fibers. A structurally motivated constitutive model with both remodeling modes was introduced along with methodology for determining material parameters from mechanical testing and multiphoton imaging.

Conclusions

A new mechanism was identified by which aneurysm walls can rapidly adapt to changes in load, ensuring the structural integrity of the aneurysm until a slower process of medial reorganization occurs. The rabbit model can be used to evaluate therapies to increase aneurysm wall stability.

     

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.

     

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.     

In vivo mechanical study of helical cardiac pacing electrode interacting with canine myocardium

Cardiac pacing is a medical device to help human to overcome arrhythmia and to recover the regular beats of heart. A helical configuration of electrode tip is a new type of cardiac pacing lead distal tip. The helical electrode attaches itself to the desired site of heart by screwing its helical tip into the myocardium. In vivo experiments on anesthetized dogs were carried out to measure the acute interactions between helical electrode and myocardium during screw-in and pull-out processes. These data would be helpful for electrode tip design and electrode/myocardium adherence safety evaluation. They also provide reliability data for clinical site choice of human heart to implant and to fix the pacing lead. A special design of the helical tip using strain gauges is instrumented for the measurement of the screw-in and pull-out forces. We obtained the data of screw-in torques and pull-out forces for five different types of helical electrodes at nine designed sites on ten canine hearts. The results indicate that the screw-in torques increased steplike while the torque–time curves presente saw-tooth fashion. The maximum torque has a range of 0.3–1.9 N mm. Obvious differences are observed for different types of helical tips and for different test sites. Large pull-out forces are frequently obtained at epicardium of left ventricle and right ventricle lateral wall, and the forces obtained at right ventricle apex and outflow tract of right ventricle are normally small. The differences in pull-out forces are dictated by the geometrical configuration of helix and regional structures of heart muscle.     

Nonlinear Dynamics Modeling of Mechanical Periodicity of End Diastolic Volume of Left Ventricle

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Growth,mass transfer,and remodeling in fiber-reinforced,multi-constituent materials

We represent a biological tissue by a multi-constituent, fiber-reinforced material, in which we consider two phases: fluid, and a fiber-reinforced solid. Among the various processes that may occur in such a system, we study growth, mass transfer, and remodeling. To us, mass transfer is the reciprocal exchange of constituents between the phases, growth is the variation of mass of the system in response to interactions with the surrounding environment, and remodeling is the evolution of its internal structure. We embrace the theory according to which these events, which lead to a structural reorganization of the system and anelastic deformations, require the introduction of balance laws, which complete the physical picture offered by the standard ones. The former are said to be non-standard. Our purposes are to determine the rates of anelastic deformation related to mass transfer and growth, and to study fiber reorientation in the case of a statistical distribution of fibers. In particular, we discuss the use of the non-standard balance laws in modeling transfer of mass, and compare our results with a formulation in which such balance laws are not introduced.     

A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus

A bone cell population dynamics model for cortical bone remodeling under mechanical stimulus is developed in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these experimental results such as the increase percentage of final values of bone mineral content (BMC) and bone fracture energy (BFE) among different loading schemes (which proves the validity of the model), but also predict the realtime development pattern of BMC and BFE, as well as the dynamics of osteoblasts (OBA), osteoclasts (OCA), nitric oxide (NO) and prostaglandin E₂ (PGE₂) for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an insight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechanical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foundation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimulus can be investigated. The to-be identified control mechanism will help to develop effective drugs and combined nonpharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering.     

Analysis of self-sustained oscillation sources in segmented flows

The analysis of self-sustained oscillations in segmented flow generated through porous walls has been carried out over a wide range of velocity levels; in fact, we studied a cold gas flow induced by injection through different wall injecting blocks. We have attempted in this study to analyse the potential unstable development occurring in solid propellant rocket motors. We lay emphasis upon the phenomenon of wall vortex shedding insofar as it conduces to acoustic mode resonance in the whole chamber, within whose confines impingement of such structures generates a source of noise. It is on account of segmented flow that the thin shear layer develops and that the aforementioned vortex shedding comes to induce aero-acoustic coupling. Subsequent experimental results highlight a link in such flows between these two noise sources - they also allow one to observe a pronounced form of selectivity in the energy transfer, i.e. in longitudinal acoustic mode amplification, which has an attested effect upon all of the pressure oscillations in the chamber.