Dynamics of left ventricular wall and mitral valve mechanics--a model study

The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.     

Fiber stress profiles in the left ventricle of the heart during diastole: Effects of distension and hypertrophy

Pressure-volume and volume-dimensions relationships, obtained from excised dog left ventricles were used for calculating the stresses acting along the longitudinal axis of the individual myocardial fibers. The calculations were based on a set of empirical and theoretical equations. The pressure-volume relationship as well as the volume-dimensions relationships for the excised left ventricle were expressed in the form of empirical equations; the fiber orientation was written as a function of the fiber location within the left ventricular wall; finally, the fiber stress was determined by means of theoretically derived formulas. Simultaneous solutions for the fibers of a meridian cut through the left ventricular myocardial shell were obtained by means of a digital computer and presented in the form of diagrams. The results showed that at low degrees of distension of the left ventricle there are two zones of higher stresses at the equatorial area, one near the epicardium and one near the endocardium. As the distension proceeds under the effect of progressively increasing intraventricular pressure, these two zones become less well defined, whereas a new zone of higher stresses appears near the apex. At high degrees of distension, the ventricle assumes a more spherical shape and the equatorial zones of higher stresses are replaced by zones of lower stresses. Increase in the myocardial mass results in appearance of the equatorial lower stress zones at lower degrees of distension.     

Structure and torsion in the normal and situs inversus totalis cardiac left ventricle. II. Modeling cardiac adaptation to mechanical load

Mathematical models provide a suitable platform to test hypotheses on the relation between local mechanical stimuli and responses to cardiac structure and geometry. In the present model study, we tested hypothesized mechanical stimuli and responses in cardiac adaptation to mechanical load on their ability to estimate a realistic myocardial structure of the normal and situs inversus totalis (SIT) left ventricle (LV). In a cylindrical model of the LV, 1) mass was adapted in response to myofiber strain at the beginning of ejection and to global contractility (average systolic pressure), 2) cavity volume was adapted in response to fiber strain during ejection, and 3) myofiber orientations were adapted in response to myofiber strain during ejection and local misalignment between neighboring tissue parts. The model was able to generate a realistic normal LV geometry and structure. In addition, the model was also able to simulate the instigating situation in the rare SIT LV with opposite torsion and transmural courses in myofiber direction between the apex and base [Delhaas et al. (6)]. These results substantiate the importance of mechanical load in the formation and maintenance of cardiac structure and geometry. Furthermore, in the model, adapted myocardial architecture was found to be insensitive to fiber misalignment in the transmural direction, i.e., myofiber strain during ejection was sufficient to generate a realistic transmural variation in myofiber orientation. In addition, the model estimates that, despite differences in structure, global pump work and the mass of the normal and SIT LV are similar.     

A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

The effect of distension of the left ventricle of the heart on the length of the individual myocardial fibers

Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.     

Energetics of ventricular contraction as traced in the pressure-volume diagram

The pressure-volume (P-V) relationship of the canine left ventricle can reasonably be simulated by a time-varying elastance model. In this model the total mechanical energy generated by a contraction can be determined theoretically from the change in the elastance. Applying this theory to the actual left ventricle, we have found that the area in the P-V diagram circumscribed by the end-systolic P-V relation line, the end-diastolic P-V relation curve, and the systolic segment of the P-V trajectory is equivalent to the total mechanical energy generated by ventricular contraction. We call this area the systolic P-V area (PVA). We have studied experimentally the correlation between the PVA and myocardial oxygen consumption (VO2) in the canine left ventricle. VO2 was linearly correlated with PVA regardless of the contraction mode and loading conditions in a given left ventricle. The VO2-PVA relation parallel shifted upward with positive inotropic agents. This shift comprised a significant increase in VO2 component for the unloaded contraction. We therefore consider that further analyses of the VO2-PVA relationship will greatly promote our understanding of cardiac energetics.     

Transplantation of elastin-secreting myoblast sheets improves cardiac function in infarcted rat heart

Myoblast sheet transplantation for cardiac failure is a promising therapy to enhance cardiac function via paracrine mechanism. However, their efficacies of treatment showed a gradual decline. The gene modification of the implanted myoblast is important in improving the long-term results of the treatment. Elastin fiber enhances the extensibility of the infarcted wall and can prevent left ventricular dilation. We therefore hypothesized that the elastin gene modification of the implanted myoblast could strengthen and maintain the long-term improvement effects of cardiac function. In this study, we evaluated long-term follow-up benefits of functional myoblast sheets that secrete elastin in an infarcted model. The animal models were divided into three groups: a group transplanted with nontransfected, wild-type, skeletal myoblast-type sheets (WT-rSkM); group transplanted with myoblast sheets that secreted elastin fragments (ELN-rSkM); and a control group (ligation only). Cardiac function was examined by echocardiography, and cardiac remodeling after infarction was evaluated by histological examination. The cardiac function was significantly improved and the left ventricle end-diastolic dimensions were significantly reduced in the ELN-rSkM group. Histological analysis showed that left ventricular remodeling was attenuated in the ELN-rSkM group and that elastic fiber was formed in the epicardial area of ELN-rSkM group. The functionalization of myoblast sheet by elastin gene transfer showed the long-term improvement of cardiac function. Expressed recombinant elastin fiber prevented the dilation of the left ventricular chamber after myocardial infarction. The functional myoblast sheet transplantation maintained the treatment effect by the paracrine effect of myoblast and the formed recombinant elastin.     

Mechanics of the left ventricular myocardial interstitium: effects of acute and chronic myocardial edema

Myocardial interstitial edema forms as a result of several disease states and clinical interventions. Acute myocardial interstitial edema is associated with compromised systolic and diastolic cardiac function and increased stiffness of the left ventricular chamber. Formation of chronic myocardial interstitial edema results in deposition of interstitial collagen, which causes interstitial fibrosis. To assess the effect of myocardial interstitial edema on the mechanical properties of the left ventricle and the myocardial interstitium, we induced acute and chronic interstitial edema in dogs. Acute myocardial edema was generated by coronary sinus pressure elevation, while chronic myocardial edema was generated by chronic pulmonary artery banding. The pressure-volume relationships of the left ventricular myocardial interstitium and left ventricular chamber for control animals were compared with acutely and chronically edematous animals. Collagen content of nonedematous and chronically edematous animals was also compared. Generating acute myocardial interstitial edema resulted in decreased left ventricular chamber compliance compared with nonedematous animals. With chronic edema, the primary form of collagen changed from type I to III. Left ventricular chamber compliance in animals made chronically edematous was significantly higher than nonedematous animals. The change in primary collagen type secondary to chronic left ventricular myocardial interstitial edema provides direct evidence for structural remodeling. The resulting functional adaptation allows the chronically edematous heart to maintain left ventricular chamber compliance when challenged with acute edema, thus preserving cardiac function over a wide range of interstitial fluid pressures.     

Transmural heterogeneity of diffusion anisotropy in the sheep myocardium characterized by MR diffusion tensor imaging

The orientation of MRI-measured diffusion tensor in the myocardium has been directly correlated to the tissue fiber direction and widely characterized. However, the scalar anisotropy indexes have mostly been assumed to be uniform throughout the myocardial wall. The present study examines the fractional anisotropy (FA) as a function of transmural depth and circumferential and longitudinal locations in the normal sheep cardiac left ventricle. Results indicate that FA remains relatively constant from the epicardium to the midwall and then decreases (25.7%) steadily toward the endocardium. The decrease of FA corresponds to 7.9% and 12.9% increases in the secondary and tertiary diffusion tensor diffusivities, respectively. The transmural location of the FA transition coincides with the location where myocardial fibers run exactly circumferentially. There is also a significant difference in the midwall-endocardium FA slope between the septum and the posterior or lateral left ventricular free wall. These findings are consistent with the cellular microstructure from histological studies of the myocardium and suggest a role for MR diffusion tensor imaging in characterization of not only fiber orientation but, also, other tissue parameters, such as the extracellular volume fraction.     

Effects of sympathetic stimulation during cooling on hypothermic as well as posthypothermic hemodynamic function

This experimental study was performed to explore hemodynamic effects of a moderate dose epinephrine (Epi) during hypothermia and to test the hypothesis whether sympathetic stimulation during cooling affects myocardial function following rewarming. Two groups of male Wistar rats (each, n=7) were cooled to 15 degrees C, maintained at this temperature for 1 h, and then rewarmed. Group 1 received 1 microg/min Epi, i.v., for 1 h during cooling to 28 degrees C, a dose known to elevate cardiac output (CO) by approximately 25% at 37 degrees C. Group 2 served a saline solution control. At 37 degrees C, Epi infusion elevated CO, left ventricular systolic pressure, maximum rate of left ventricle pressure rise, and mean arterial pressure. During cooling to 28 degrees C, these variables, with the exception of mean arterial pressure, decreased in parallel to those in the saline solution group. In contrast, in the Epi group, mean arterial pressure remained increased and total peripheral resistance was significantly elevated at 28 degrees C. Compared with corresponding prehypothermic values, most hemodynamic variables were lowered after 1 h at 15 degrees C in both groups (except for stroke volume). After rewarming, alterations in hemodynamic variables in the Epi-treated group were more prominent than in saline solution controls. Thus, before cooling, continuous Epi infusion predominantly stimulates myocardial mechanical function, materialized as elevation of CO, left ventricular systolic pressure, and maximum rate of left ventricle pressure rise. Cooling, on the other hand, apparently eradicates central hemodynamic effects of Epi and during stable hypothermia, elevation of peripheral vascular vasopressor effects seem to take over. In contrast to temperature-matched, non-Epi stimulated control rats, a significant depression of myocardial mechanical function occurs during rewarming following a moderate sympathetic stimulus during initial cooling.     

Dynamic geometry of the intact left ventricle

Knowledge of left ventricular chamber dynamics is central to our understanding of cardiac physiology. The complicated changes in left ventricular geometry observed in the dog during various phases of the cardiac cycle can be represented as distinct linear relationships between chamber eccentricity and intracavitary volume during diastole and ejection, and probably represent structural properties of the ventricular wall. Chamber geometry of the left ventricle is a major determinant of overall myocardial function. The slope of the radius of curvature (r) to wall thickness (h) relationship is a geometric constant that determines the mural force at any given transmural pressure. Chronic pressure and volume overload produce changes in this geometric relationship as a result of increased mural force resisting ejection. The adaptive mechanism of ventricular hypertrophy in this setting alters the r/h ratio and returns systolic mural force toward normal. Coronary occlusion induces acute changes in regional geometry characterized by holosystolic wall bulging and systolic wall thinning, which shift the r/h relationship upward and to the left. The geometric alteration during ischemia probably increases systolic mural force and could adversely affect myocardial function. Recent studies with patients have shown the r/h ratio to be of value in distinguishing between reversible and irreversible impairment of myocardial performance. Because most myocardial diseases produce major alterations in the structure of the ventricular wall, analysis of dynamic chamber geometry may prove of prognostic value in assessing patients with cardiac disorders.     

Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.     

A hemodynamic load in vivo induces cardiac expression of the cellular oncogene, c-myc

To establish whether a hemodynamic load that causes cardiac hypertrophy in the intact animal might interact with cellular pathways that are thought to transduce growth signals in model systems, we have analyzed expression of the cellular oncogene, c-myc, after a systolic pressure load. Aortic constriction increased c-myc mRNA abundance in both the atria and left ventricle of 28-day rats, but did not activate a second "competence" gene, r-fos, whose expression by cardiac cells ceases upon termination of mitotic growth. In 80-day rats, c-myc was induced in the atria alone. Induction of c-myc by aortic constriction in vivo may correlate with the respective capacity of atrial and ventricular myocytes to replicate DNA during cardiac hypertrophy. Activation of c-myc was not sufficient to account for inhibition of muscle creatine kinase (mck) mRNA, which was decreased only in 28-day rats.     

Theoretical models in mechanics of the left ventricle

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.     

Theoretical analysis of the effects of a radial activation wave and twisting motion on the mechanics of the left ventricle

The mechanical effects resulting from the normal transmural delay of electrical depolarization of the myocardium are investigated. An activation sequence having a finite radial propagation velocity is introduced into the equations of ventricular mechanics. The resulting system of coupled integral equations is solved using a perturbation method based on the small ratio of transmural propagation time to cardiac period. Numerical calculations are performed using cavity pressure and volume waveforms characteristic of the canine left ventricle (LV), for both simultaneous and delayed activation of fiber layers. The results show that a finite transmural electrical propagation velocity tends to: (i) equalize the transmural distribution of sarcomere length during systole; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) insignificantly affect myocardial tissue pressure. Calculations are also performed to investigate the mechanical effects resulting from the application of an externally applied moment that prevents LV torsion. Those results are highly dependent on the transmural distribution of sarcomere length in the stress-free reference state (unloaded diastole). When we assume a uniform distribution, then normal torsion acting with normal activation delay tends to: (i) increase the magnitude of fiber strain in the subendocardium and decrease it in the subepicardium; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) lower myocardial tissue pressure. The normally occurring transmural delay of activation tends to lessen endocardial O2 demand, while the normally occurring torsion further lessens that demand and improves O2 supply.     

骨髓基质干细胞移植对扩张型心肌病心衰大鼠心功能改善作用机制的研究

通过对心肌胶原纤维、微血管生成、血管内皮生长因子(VEGF)及其受体表达的研究,探讨骨髓基质干细胞(BMSSCs)心肌内移植对扩张型心肌病心衰大鼠心功能的保护机制．应用阿霉素注射法建立扩张型心肌病心衰大鼠模型,成功建模后移植4', 6-二乙酰基-2-苯基吲哚(DAPI)标记的BMSSCs．分别于术后1、2、3、4周进行血流动力学检测,利用免疫组化、RT-PCR技术分析心肌胶原纤维、血管内皮生长因子(VEGF)及其受体Flt-1、Flk-1表达的改变,以及微血管密度．结果显示,移植细胞于术后4周通过免疫荧光可检测到存活．于术后2周开始,移植组心功能较对照组改善,表现为移植组收缩压(LVSP)、左心室内压最大上升或下降速率(?dp/dt)较对照组显著升高,舒张压(LVDP)显著下降,P < 0.05．移植组心肌胶原纤维沉积减少,光密度值比较P < 0.05．移植组VEGF、Flt-1、Flk-1表达较同期对照组增加,并张且与其受体达峰时间不同步．4周时移植组微血管密度明显高于对照组．上述结果表明,BMSSCs移植后可通过上调受体内VEGF、Flt-1、Flk-1的表达,促进血管新生,减少胶原纤维沉积,从而改善受体心脏的功能．     

肾性高血压大鼠肥大心肌的力速关系和收缩末...

Renovascular hypertension was induced in rats by left renal artery constriction. Force-velocity relation, end systolic tension-length relation (ESTLR) and responses to high extracellular calcium were investigated in hypertrophied myocardium with 4-week hypertension. The results showed that: (1) The myocardial hypertrophy was accompanied by increased peak active tension, decreased maximal velocity of shortening and prolonged contraction duration (P less than 0.01). (2) The ESTLR in hypertrophied myocardium was similar to that in the control, fitted well by an exponential curve and did not show significant alterations in all its regression parameters (P greater than 0.05). (3) No significant difference about the responses to high extracellular calcium (4 mmol/L) was observed between the control and the hypertrophied myocardium (P greater than 0.05). It is concluded that the mechanical properties of hypertrophied myocardium were characterized by a dissociation between force development and velocity of shortening and possibly these contractile abnormalities at the early stage of cardiac hypertrophy are not related to ability of calcium transport in cardiac plasma membrane. The indexes of myocardial mechanics are more sensitive to changes in contractility of hypertrophied myocardium as compared with the parameters of ESTLR.     

Effect of endurance running on cardiac and skeletal muscle in rats

We studied the effect of resistance running on left cardiac ventricle size and rectus femoris muscle fiber composition. Ten male Wistar rats were trained on a treadmill 6 days per week for 12 weeks. Ten rats remained sedentary and served as controls. A higher endurance time (40%) and cardiac hypertrophy in the trained animals were indicators of training efficiency. Morphometric analysis of the left ventricle cross-sectional area, left ventricular wall, and left ventricular cavity were evaluated. The endurance-running group demonstrated a hypertrophy of the ventricular wall (22%) and an increase in the ventricular cavity (25%); (p<0.0001). Semi-quantitative analysis of rectus femoris fiber-type composition and of the oxidative and glycolytic capacity was histochemically performed. Endurance running demonstrated a significant (p<0.01) increase in the relative frequency of Type I (24%), Type IIA (8%) and Type IIX (16%) oxidative fibers, and a decrease in Type IIB (20%) glycolytic fibers. There was a hypertrophy of both oxidative and glycolytic fiber types. The relative cross-sectional area analysis demonstrated an increase in oxidative fibers and a decrease in glycolytic fibers (p<0.0001). Changes were especially evident for Type IIX oxidative-glycolytic fibers. The results of this study indicate that the left ventricle adapts to endurance running by increasing wall thickness and enlargement of the ventricular cavity. Skeletal muscle adapts to training by increasing oxidative fiber Type. This increase may be related to fiber transformation from Type IIB glycolytic to Type IIX oxidative fibers. These results open the possibility for the use of this type of exercise to prevent muscular atrophy associated with age or post-immobilization.     

肾性高血压大鼠肥大心肌的力速关系和收缩末期张力长度关系

左肾动脉部分狭窄造成大鼠肾血管性高血压,研究高血压四周肥大心肌的力速关系,收缩末期张力长度关系(ESTLR)以及对细胞外高钙的反应。结果表明:(1)肥大心肌主动峰张力 PT 轻度增大,零负荷最大缩短速度 V_(max)明显减小,收缩时程 TPT 延长(P<0.01),力速曲线向下移位;(2)高血压组心肌 ESTLR 与对照相似,亦为非线性的指数曲线。回归参数a(总张力)、k(静息张力)、b(曲线曲率)和 L。(最大缩短程度)均无明显改变(P>0.05),(3)高钙灌流时,肥大心肌的反应(△PT,△V_(max)和△TPT)与对照间无显著差异(P>0.05)。上述结果提示:高血压心肌肥大早期基础力学性能的变化以力速分离现象为特征,此时心肌功能的异常可能与肌膜钙转运系统的功能状态无关;对于心肌收缩能力的这种慢性改变,心肌力学指标比 ESTLR 类参数更敏感。     

Abnormal cardiac wall motion and early matrix metalloproteinase activity

Activation of matrix metalloproteinases (MMPs) in the heart is known to facilitate cardiac remodeling and progression to failure. We hypothesized that regional dyskinetic wall motion of the left ventricle would stimulate activation of MMPs. Abnormal wall motion at a target site on the anterior lateral wall of the left ventricle was induced by pacing atrial and ventricular sites of five open-chest anesthetized dogs. Changes in shortening at the left ventricular (LV) pacing site and at a remote site at the anterior base of the left ventricle were monitored with piezoelectric crystals. Simultaneous atrial and ventricular pacing resulted in abnormal motion at the LV pacing site, yielding early shortening and late systolic lengthening, whereas the shortening pattern at the remote site remained unaffected. Assessment of global myocardial MMP activity showed a sevenfold increase in substrate cleavage (P < 0.02) at the LV pacing site relative to the remote site. Gelatin zymography revealed increases in 92-kDa MMP-9 activity and 86-kDa MMP-9 activity at the LV pacing site relative to the remote site, whereas MMP-2 activity was unaffected. Abnormal wall motion was associated with increases in collagen degradation (approximately 2-fold; P < 0.03), plasmin activity (approximately 1.5-fold; P < 0.05), nitrotyrosine levels (approximately 20-fold; P = 0.05), and inflammatory infiltrate (approximately 2-fold; P < 0.02) relative to the remote site. Results indicate that regional dyskinesis induced by epicardial activation is sufficient to stimulate significant MMP activity in the heart, suggesting that abnormal wall motion is a stimulus for MMP activation.