Computational models of heart pumping efficiencies based on contraction waves in spiral elastic bands

Elastohydrodynamic Scaling Law for Heart Rates

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Torsional motion of the left ventricle does not affect ventricular fluid dynamics of both foetal and adult hearts

Left ventricular torsion is caused by shortening and relaxation of the helical fibres in the myocardium, and is thought to be an optimal configuration for minimizing myocardial tissue strains. Characteristics of torsional motion has also been proposed to be markers for cardiac dysfunction. However, its effects on fluid and energy dynamics in the left ventricle have not been comprehensively investigated. To investigate this, we performed image-based flow simulations on five healthy adult porcine and two healthy human foetal left ventricles (representing two different length scales) at different degrees of torsional motions. In the adult porcine ventricles, cardiac features such as papillary muscles and mitral valves, and cardiac conditions such as myocardial infarctions, were also included to investigate the effect of twist. The results showed that, for all conditions investigated, ventricular torsional motion caused minimal changes to flow patterns, and consistently accounted for less than 2% of the energy losses, wall shear stresses, and ejection momentum energy. In contrast, physiological characteristics such as chamber size, stroke volume and heart rate had a much greater influence on flow patterns and energy dynamics. The results thus suggested that it might not be necessary to model the torsional motion to study the flow and energy dynamics in left ventricles.

Traction force microscopy of engineered cardiac tissues

Cardiac tissue development and pathology have been shown to depend sensitively on microenvironmental mechanical factors, such as extracellular matrix stiffness, in both in vivo and in vitro systems. We present a novel quantitative approach to assess cardiac structure and function by extending the classical traction force microscopy technique to tissue-level preparations. Using this system, we investigated the relationship between contractile proficiency and metabolism in neonate rat ventricular myocytes (NRVM) cultured on gels with stiffness mimicking soft immature (1 kPa), normal healthy (13 kPa), and stiff diseased (90 kPa) cardiac microenvironments. We found that tissues engineered on the softest gels generated the least amount of stress and had the smallest work output. Conversely, cardiomyocytes in tissues engineered on healthy- and disease-mimicking gels generated significantly higher stresses, with the maximal contractile work measured in NRVM engineered on gels of normal stiffness. Interestingly, although tissues on soft gels exhibited poor stress generation and work production, their basal metabolic respiration rate was significantly more elevated than in other groups, suggesting a highly ineffective coupling between energy production and contractile work output. Our novel platform can thus be utilized to quantitatively assess the mechanotransduction pathways that initiate tissue-level structural and functional remodeling in response to substrate stiffness.

A mathematical model of the carp heart ventricle during the cardiac cycle

The poikilothermic heart has been suggested as a model for studying some of the mechanisms of early postnatal mammalian heart adaptations. We assessed morphological parameters of the carp heart (Cyprinus carpio L.) with diastolic dimensions: heart radius (5.73mm), thickness of the compact (0.50mm) and spongy myocardium (4.34mm), in two conditions (systole, diastole): volume fraction of the compact myocardium (20.7% systole, 19.6% diastole), spongy myocardium (58.9% systole, 62.8% diastole), trabeculae (37.8% systole, 28.6% diastole), and cavities (41.5% systole, 51.9% diastole) within the ventricle; volume fraction of the trabeculae (64.1% systole, 45.5% diastole) and sinuses (35.9% systole, 54.5% diastole) within the spongy myocardium; ratio between the volume of compact and spongy myocardium (0.35 systole, 0.31 diastole); ratio between compact myocardium and trabeculae (0.55 systole, 0.69 diastole); and surface density of the trabeculae (0.095μm(-1) systole, 0.147μm(-1) diastole). We created a mathematical model of the carp heart based on actual morphometric data to simulate how the compact/spongy myocardium ratio, the permeability of the spongy myocardium, and sinus-trabeculae volume fractions within the spongy myocardium influence stroke volume, stroke work, ejection fraction and p-V diagram. Increasing permeability led to increasing and then decreasing stroke volume and work, and increasing ejection fraction. An increased amount of spongy myocardium led to an increased stroke volume, work, and ejection fraction. Varying sinus-trabeculae volume fractions within the spongy myocardium showed that an increased sinus volume fraction led to an increased stroke volume and work, and a decreased ejection fraction.

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.

A dynamic double helical band as a model for cardiac pumping

We address here, by means of finite-element computational modeling, two features of heart mechanics and, most importantly, their timing relationship: one of them is the ejected volume and the other is the twist of the heart. The corner stone of our approach is to take the double helical muscle fiber band as the dominant active macrostructure behind the pumping function. We show that this double helical model easily reproduces a physiological maximal ejection fraction of up to 60% without exceeding the limit on local muscle fiber contraction of 15%. Moreover, a physiological ejection fraction can be achieved independently of the excitation pattern. The left ventricular twist is also largely independent of the type of excitation. However, the physiological relationship between the ejection fraction and twist can only be reproduced with Purkinje-type excitation schemes. Our results indicate that the proper timing coordination between twist and ejection dynamics can be reproduced only if the excitation front originates in the septum region near the apex. This shows that the timing of the excitation is directly related to the productive pumping operation of the heart and illustrates the direction for possible bioinspired pump design.