Towards a biomechanics-based technique for assessing myocardial contractility: an inverse problem approach

This work presents the initial development and implementation of a novel 3D biomechanics-based approach to measure the mechanical activity of myocardial tissue, as a potential non-invasive tool to assess myocardial function. This technique quantifies the myocardial contraction forces developed within the ventricular myofibers in response to electro-physiological stimuli. We provide a 3D finite element formulation of a contraction force reconstruction algorithm, along with its implementation using magnetic resonance (MR) data. Our algorithm is based on an inverse problem solution governed by the fundamental continuum mechanics principle of conservation of linear momentum, under a first-order approximation of elastic and isotropic material conditions. We implemented our technique using a subject-specific ventricle model obtained by extracting the left ventricular anatomical features from a set of high-resolution cardiac MR images acquired throughout the cardiac cycle using prospective electrocardiographic gating. Cardiac motion information was extracted by non-rigid registration of the mid-diastole reference image to the remaining images of a 4D dataset. Using our technique, we reconstructed dynamic maps that show the contraction force distribution superimposed onto the deformed ventricle model at each acquired frame in the cardiac cycle. Our next objective will consist of validating this technique by showing the correlation between the presence of low contraction force patterns and poor myocardial functionality.     

Ventricular motion during the ejection phase: a computational analysis.

In the present paper, the study of the ventricular motion during systole was addressed by means of a computational model of ventricular ejection. In particular, the implications of ventricular motion on blood acceleration and velocity measurements at the valvular plane (VP) were evaluated. An algorithm was developed to assess the force exchange between the ventricle and the surrounding tissue, i.e., the inflow and outflow vessels of the heart. The algorithm, based on the momentum equation for a transitory flowing system, was used in a fluid-structure model of the ventricle that includes the contractile behavior of the fibers and the viscous and inertial forces of the intraventricular fluid. The model calculates the ventricular center of mass motion, the VP motion, and intraventricular pressure gradients. Results indicate that the motion of the ventricle affects the noninvasive estimation of the transvalvular pressure gradient using Doppler ultrasound. The VP motion can lead to an underestimation equal to 12.4 +/- 6.6%.     

Active and passive stresses in the myocardium

A mathematical approach that can be used to calculate the passive stress in the ventricular wall is presented. The active fiber stress (force/unit area) generated by the muscular fibers in the ventricular wall is expressed by means of body force (force/unit volume of the myocardium). It is shown that the total intramyocardial passive stress induced in the passive medium of the myocardium can be expressed as the sum of a passive stress induced by the left ventricular pressure and a passive stress induced by the active fiber stress. Applications to experimental data published in the literature are given. New results are presented that show the relation among those two components of the intramyocardial passive stress. New relations between the intramyocardial passive stress, the slope (elastance) of the pressure-volume relation, and the residual volume are also derived. The results obtained give a better understanding of some aspects of the mechanics of cardiac contraction and can provide a more detailed interpretation of clinical conditions.     

Assessment of systolic and diastolic ventricular properties via pressure-volume analysis: a guide for clinical, translational, and basic researchers

Assessment of left ventricular systolic and diastolic pump properties is fundamental to advancing the understanding of cardiovascular pathophysiology and therapeutics, especially for heart failure. The use of end-systolic and end-diastolic pressure-volume relationships derived from measurements of instantaneous left ventricular pressure-volume loops emerged in the 1970s as a comprehensive approach for this purpose. As invasive and noninvasive techniques for measuring ventricular volume improved over the past decades, these relations have become commonly used by basic, translational, and clinical researchers. This review summarizes 1) the basic concepts underlying pressure-volume analysis of ventricular and myocardial systolic and diastolic properties, 2) deviations from ideal conditions typically encountered in real-life applications, 3) how these relationships are appropriately analyzed, including statistical analyses, and 4) the most common problems encountered by investigators and the appropriate remedies. The goal is to provide practical information and simple guidelines for accurate application and interpretation of pressure-volume data as they pertain to characterization of ventricular and myocardial properties in health and disease.     

Troponin and titin coordinately regulate length-dependent activation in skinned porcine ventricular muscle

We investigated the molecular mechanism by which troponin (Tn) regulates the Frank-Starling mechanism of the heart. Quasi-complete reconstitution of thin filaments with rabbit fast skeletal Tn (sTn) attenuated length-dependent activation in skinned porcine left ventricular muscle, to a magnitude similar to that observed in rabbit fast skeletal muscle. The rate of force redevelopment increased upon sTn reconstitution at submaximal levels, coupled with an increase in Ca2+ sensitivity of force, suggesting the acceleration of cross-bridge formation and, accordingly, a reduction in the fraction of resting cross-bridges that can potentially produce additional active force. An increase in titin-based passive force, induced by manipulating the prehistory of stretch, enhanced length-dependent activation, in both control and sTn-reconstituted muscles. Furthermore, reconstitution of rabbit fast skeletal muscle with porcine left ventricular Tn enhanced length-dependent activation, accompanied by a decrease in Ca2+ sensitivity of force. These findings demonstrate that Tn plays an important role in the Frank-Starling mechanism of the heart via on-off switching of the thin filament state, in concert with titin-based regulation.     

An anatomic basis for fetal right ventricular dominance and arterial pressure sensitivity

Fetal right ventricular dominance of flow and arterial pressure sensitivity were recently recognized but controversial findings. We investigated ventricular volumes, weights and dimensions in order to understand if there were anatomic differences between the ventricles which might explain these differential functional findings in the fetal sheep. Forty-four near term lambs and their hearts were weighed. Right and left ventricular free wall weights were not different. Volumes were measured by generating in vitro pressure-volume relations and by casting the two ventricles after fixation at equal, physiologic pressures. Right ventricular volume was greater than left ventricular volume by both techniques. Ventricular interaction and a restraining effect of the pericardium were present. Measurements of the fixed ventricles and their casts revealed the following: left ventricular wall thickness was slightly greater than right ventricular wall thickness; lateral ventricular diameters were not different but anteroposterior ventricular diameters were much greater in the right than left ventricle. Because of these findings, the right ventricular circumferential radii of curvature were greater than for the left ventricle as was the radius to wall thickness ratio. Greater right ventricular volume and radius to wall thickness ratio may be important factors in right ventricular flow dominance and greater sensitivity to arterial pressure.     

Single-beat estimation of end-diastolic pressure-volume relationship: a novel method with potential for noninvasive application

Whereas end-systolic and end-diastolic pressure-volume relations (ESPVR, EDPVR) characterize left ventricular (LV) pump properties, clinical utility of these relations has been hampered by the need for invasive measurements over a range of pressure and volumes. We propose a single-beat approach to estimate the whole EDPVR from one measured volume-pressure (Vm and Pm) point. Ex vivo EDPVRs were measured from 80 human hearts of different etiologies (normal, congestive heart failure, left ventricular assist device support). Independent of etiology, when EDPVRs were normalized (EDPVRn) by appropriate scaling of LV volumes, EDPVRns were nearly identical and were optimally described by the relation EDP = An.EDV (Bn), with An = 28.2 mmHg and Bn = 2.79. V0 (the volume at the pressure of approximately 0 mmHg) was predicted by using the relation V0 = Vm.(0.6 - 0.006.Pm) and V30 by V30 = V0 + (Vm,n - V0)/(Pm/An) (1/Bn). The entire EDPVR of an individual heart was then predicted by forcing the curve through Vm, Pm, and the predicted V0 and V30. This technique was applied prospectively to the ex vivo human EDPVRs not used in determining optimal An and Bn values and to 36 in vivo human, 12 acute and 14 chronic canine, and 80 in vivo and ex vivo rat studies. The root-mean-square error (RMSE) in pressure between measured and predicted EDPVRs over the range of 0-40 mmHg was < 3 mmHg of measured EDPVR in all settings, indicating a good predictive value of this approach. Volume-normalized EDPVRs have a common shape, despite different etiology and species. This allows the entire curve to be predicted by a new method with a potential for noninvasive application. The results are most accurate when applied to groups of hearts rather than to individual hearts.     

Natural history of coronary artery disease in relation to angiographic, hemodynamic and clinical factors

Studying the natural history of coronary artery disease could provide a frame of reference for prognosis and appraisal of treatment for patients having this disease. We studied a total of 465 consecutive patients with angiographically significant coronary artery disease, defined as greater than 50% stenosis in at least one principal artery, who were followed with medical treatment only from 1 to 7 years. Excluding patients with left main coronary disease, there were 73 deaths, of whom 63 were cardiac. The 5-year cumulative survival rates were 72% for the entire group, 87% for single vessel disease, 73% for double vessel disease and 51% for triple vessel disease. In single vessel disease, patients with left anterior descending artery involvement tended to have higher mortality. In double vessel disease, survival was worse with the combination of left anterior descending and right coronary artery involvements than the other 2 combinations. A history of myocardial infarction was not significantly different from angina in 5-year survival rate. Nevertheless, an abnormal Q-wave in ECG was associated with lower survival. History of hypertension and electrocardiographic left ventricular hypertrophy did not affect survival. While congestive heart failure, abnormal resting LVEDP and left ventricular asynergy were all associated with reduced survival. The left ventricular ejection fraction had highly prognostic value, only 42% of patients survived with ejection fraction less than 0.3 at the end of 5 years after angiography.     

A mathematical derivation of the P-V relation at end-systole

A dynamical model of the left ventricle as a thick-walled cylinder contracting radially is used to derive the P-V (pressure-volume) relation in the left ventricular cavity during contraction. It is shown how the mathematical results derived could apply to experimental results.     

应激性心肌病临床表现和诊断及发病机制研究进展

应激性心肌病(SCM)属于临床上较为常见的一种急性心血管病事件,其中心理因素、疾病因素、药物因素以及躯体应激因素等均可诱发该病。SCM患者的主要表现为胸痛,且伴有可逆性左心室功能障碍、心肌损伤标志物水平异常以及心电图异常等,与急性心肌梗死存在高度相似。SCM患者心室造影可见左室心尖部收缩力明显下降,心底部代偿性收缩增强,从而导致患者左室于收缩末期主要形态为圆底窄颈。由于SCM患者的收缩期左室造影形状和日本渔民用以捕捉章鱼的鱼篓相似,因此SCM又被称之为章鱼篓心肌病。本研究主要是通过患者的临床表现、诊断以及发病机制三个方面对SCM的研究进展进行综述,旨在为临床SCM的防治提供参考依据。     

Applications and limitations of end-systolic measures of ventricular performance

The usefulness of end-systolic measures of left ventricular performance as a load-independent method of assessing of ventricular contractility has been studied in intact, conscious dogs. The end-systolic pressure-chamber diameter (P-D) relation was shown to be linear, unaltered by preload changes, and shifted in a parallel fashion by inotropic stimulation, whereas the end-systolic pressure-volume relation appeared to increase in slope with increased contractility. A simplified measure of end-systolic relations that does not require measurement of chamber volume or diameter, the end-systolic pressure-wall thickness ( WTh ) relation, was also linear and shifted with acute changes in inotropic state. During regional ischemia, the regional end-systolic WTh relation also may provide a relatively load-independent means of detecting regional depression of myocardial contractility. With chronic pressure overload hypertrophy in dogs, the end-systolic P-D relation was markedly shifted upward and to the left, which indicates hyperfunction of the left ventricle; however, end-systolic wall stress-diameter relations were identical before and after the development of hypertrophy, which suggests that myocardial contractility was unaltered. These findings and clinical studies of mitral regurgitation imply that for assessing resting left ventricular contractility in certain chronic conditions, the use of wall stress rather than pressure may be appropriate in the end-systolic framework. Further experimental studies are needed in the intact circulation to better characterize end-systolic relations before their full potential in the clinical setting can be realized.     

Effects of external pressures on the pressure-volume relation of the left ventricle

The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.     

Mechanisms of oxygen demand/supply balance in the right ventricle

Few studies have investigated factors responsible for the O2 demand/supply balance in the right ventricle. Resting right coronary blood flow is lower than left coronary blood flow, which is consistent with the lesser work of the right ventricle. Because right and left coronary artery perfusion pressures are identical, right coronary conductance is less than left coronary conductance, but the signal relating this conductance to the lower right ventricular O2 demand has not been defined. At rest, the left ventricle extracts approximately 75% of the O2 delivered by coronary blood flow, whereas right ventricular O2 extraction is only ~50%. As a result, resting right coronary venous PO2 is approximately 30 mm Hg, whereas left coronary venous PO2 is approximately 20 mm Hg. Right coronary conductance does not sufficiently restrict flow to force the right ventricle to extract the same percentage of O2 as the left ventricle. Endogenous nitric oxide impacts the right ventricular O2 demand/supply balance by increasing the right coronary blood flow at rest and during acute pulmonary hypertension, systemic hypoxia, norepinephrine infusion, and coronary hypoperfusion. The substantial right ventricular O2 extraction reserve is used preferentially during exercise-induced increases in right ventricular myocardial O2 consumption. An augmented, sympathetic-mediated vasoconstrictor tone blunts metabolically mediated dilator mechanisms during exercise and forces the right ventricle to mobilize its O2 extraction reserve, but this tone does not limit resting right coronary flow. During exercise, right coronary vasodilation does not occur until right coronary venous PO2 decreases to approximately 20 mm Hg. The mechanism responsible for right coronary vasodilation at low PO2 has not been delineated. In the poorly autoregulating right coronary circulation, reduced coronary pressure unloads the coronary hydraulic skeleton and reduces right ventricular systolic stiffness. Thus, normal right ventricular external work and O2 demand/supply balance can be maintained during moderate coronary hypoperfusion.     

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.     

激动乙醛脱氢酶2对抗糖尿病大鼠心肌缺血/再灌注损伤的作用

目的:探讨激动乙醛脱氢酶2(ALDH2)在糖尿病大鼠心肌损伤中的作用。方法:腹腔注射55 mg/kg链脲佐菌素复制糖尿病大鼠模型,分为糖尿病组和乙醇+糖尿病组(n=8)。8周后行离体心肌缺血/再灌注(I/R),测定心室动力学指标和复灌期间冠脉流出液中乳酸脱氢酶(LDH)含量。测定空腹血糖、糖化血红蛋白(HbA1c)水平。RT-PCR和Western blot测定左心室前壁心尖组织线粒体ALDH2 mRNA和蛋白表达。结果:与正常大鼠心肌I/R相比,糖尿病大鼠左室发展压、左心室最大上升和下降速率、左室做功进一步下降,左室舒张末压抬高,复灌期冠脉流出液中LDH释放增多,心室ALDH2 mRNA和蛋白表达降低;与糖尿病大鼠心肌I/R相比,ALDH2激动剂乙醇明显促进左室发展压、左心室最大上升和下降速率、左室做功的恢复,降低左室舒张末压,同时降低HbA1c水平和LDH的释放,ALDH2 mRNA和蛋白表达增高。结论:糖尿病大鼠心肌缺血/再灌注时,心肌ALDH2表达降低;增强ALDH2在糖尿病大鼠心肌中的表达可发挥保护作用。     

An estimation of center of gravity from force platform data

A general, dynamic relationship between the data obtained from a force platform, center of gravity of the body on the platform and the time rate of change of moment of momentum of the body about its center of gravity was derived from principles of dynamics for a system of particles. The derived equations are useful for processing and interpreting the force platform data. Displacement and path of center of gravity of human body during standing on one foot and level walking were estimated by using the derived equations. An estimation of the time rate of change of moment of momentum of the body was also obtained. A biomechanical interpretation of point of application of the resultant of ground reactions was presented.     

Computational modeling of left heart diastolic function: examination of ventricular dysfunction

A computational model that accounts for blood-tissue interaction under physiological flow conditions was developed and applied to a thin-walled model of the left heart. This model consisted of the left ventricle, left atrium, and pulmonary vein flow. The input functions for the model included the pulmonary vein driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The Immersed Boundary Method was used for the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology, and the fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). This model was used to examine the flow fields in the left heart under abnormal diastolic conditions of delayed ventricular relaxation, delayed ventricular relaxation with increased ventricular stiffness, and delayed ventricular relaxation with an increased atrial contraction. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions, and to the results from simulations of normal diastolic function in this model [1]. Cases involving impairment of diastolic function were modeled with changes to the input functions for fiber relaxation/contraction of the chambers. The three cases of diastolic dysfunction investigated agreed with the changes in diastolic flow fields seen clinically. The effect of delayed relaxation was to decrease the early filling magnitude, and this decrease was larger when the stiffness of the ventricle was increased. Also, increasing the contraction of the atrium during atrial systole resulted in a higher late filling velocity and atrial pressure. The results show that dysfunction can be modeled by changing the relationships for fiber resting-length and/or stiffness. This provides confidence in future modeling of disease, especially changes to chamber properties to examine the effect of local dysfunction on global flow fields.     

The time-varying elastic properties of the left ventricular muscle

We combine two techniques in order to discuss the time-varying elastic properties of the left ventricular muscle. An analytic model for the shape and forces in the left ventricle is combined with the Fourier series representations of certain of the ventricular dimensions and pressure to derive expressions for the stress and strain in the left ventricle. The strain is thus a function of the elastic material properties, which are then expressed as functions of time by using Fourier series. The only data needed for a numerical study using these techniques are closed-chest determinations of the ventricular dimensions and the ventricular pressure.     

Mechanics of left ventricular relaxation, early diastolic lengthening, and suction investigated in a mathematical model

We investigated the determinants of ventricular early diastolic lengthening and mechanics of suction using a mathematical model of the left ventricle (LV). The model was based on a force balance between the force represented by LV pressure (LVP) and active and passive myocardial forces. The predicted lengthening velocity (e') from the model agreed well with measurements from 10 dogs during 5 different interventions (R = 0.69, P < 0.001). The model showed that e' was increased when relaxation rate and systolic shortening increased, when passive stiffness was decreased, and when the rate of fall of LVP during early filling was decreased relative to the rate of fall of active stress. We first defined suction as the work the myocardium performed to pull blood into the ventricle. This occurred when contractile active forces decayed below and became weaker than restoring forces, producing a negative LVP. An alternative definition of suction is filling during falling pressure, commonly believed to be caused by release of restoring forces. However, the model showed that this phenomenon also occurred when there had been no systolic compression below unstressed length and therefore in the absence of restoring forces. In conclusion, relaxation rate, LVP, systolic shortening, and passive stiffness were all independent determinants of e'. The model generated a suction effect seen as lengthening occurring during falling pressure. However, this was not equivalent with the myocardium performing pulling work on the blood, which was performed only when restoring forces were higher than remaining active fiber force, corresponding to a negative transmural pressure.     

Phosphorylation of titin modulates passive stiffness of cardiac muscle in a titin isoform-dependent manner

We investigated the effect of protein kinase A (PKA) on passive force in skinned cardiac tissues that express different isoforms of titin, i.e., stiff (N2B) and more compliant (N2BA) titins, at different levels. We used rat ventricular (RV), bovine left ventricular (BLV), and bovine left atrial (BLA) muscles (passive force: RV > BLV > BLA, with the ratio of N2B to N2BA titin, approximately 90:10, approximately 40:60, and approximately 10:90%, respectively) and found that N2B and N2BA isoforms can both be phosphorylated by PKA. Under the relaxed condition, sarcomere length was increased and then held constant for 30 min and the peak passive force, stress-relaxation, and steady-state passive force were determined. Following PKA treatment, passive force was significantly decreased in all muscle types with the effect greatest in RV, lowest in BLA, and intermediate in BLV. Fitting the stress-relaxation data to the sum of three exponential decay functions revealed that PKA blunts the magnitude of stress-relaxation and accelerates its time constants. To investigate whether or not PKA-induced decreases in passive force result from possible alteration of titin-thin filament interaction (e.g., via troponin I phosphorylation), we conducted the same experiments using RV preparations that had been treated with gelsolin to extract thin filaments. PKA decreased passive force in gelsolin-treated RV preparations with a magnitude similar to that observed in control preparations. PKA was also found to decrease restoring force in skinned ventricular myocytes of the rat that had been shortened to below the slack length. Finally, we investigated the effect of the beta-adrenergic receptor agonist isoprenaline on diastolic force in intact rat ventricular trabeculae. We found that isoprenaline phosphorylated titin and that it reduced diastolic force to a degree similar to that found in skinned RV preparations. Taken together, these results suggest that during beta-adrenergic stimulation, PKA increases ventricular compliance in a titin isoform-dependent manner.