Relation between torsion and cross-sectional area change in the human left ventricle

Aelen, F.W.L.; Arts, Theo; Sanders, D.G.M.; Thelissen, G. R. P.; Muijtjens, Arno M. M.; Prinzen, Frits W.; Reneman, Robert S.

doi:10.1016/s0021-9290(96)00147-9

Cited by 48 publications

(55 citation statements)

References 18 publications

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“…This property suggests that shortening fibers along their length in the direction given by θ could contribute to an efficient shrinkage of volume by yielding a displacement in the direction normal to the heart wall. It has in fact been established that a helical orientation of myofibers is essential to achieve a transmurally homogeneous workload for all myocytes within the healthy myocardium (32)(33)(34). More globally, the helicoidal myofiber architecture induces torsion of the left ventricle during contraction.…”

Section: Discussionmentioning

confidence: 99%

Heart wall myofibers are arranged in minimal surfaces to optimize organ function

Savadjiev

Strijkers

Bakermans

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Heart wall myofibers wind as helices around the ventricles, strengthening them in a manner analogous to the reinforcement of concrete cylindrical columns by spiral steel cables [Richart FE, et al. (1929) Univ of Illinois, Eng Exp Stn Bull 190]. A multitude of such fibers, arranged smoothly and regularly, contract and relax as an integrated functional unit as the heart beats. To orchestrate this motion, fiber tangling must be avoided and pumping should be efficient. Current models of myofiber orientation across the heart wall suggest groupings into sheets or bands, but the precise geometry of bundles of myofibers is unknown. Here we show that this arrangement takes the form of a special minimal surface, the generalized helicoid [Blair DE, Vanstone JR (1978) Minimal Submanifolds and Geodesics 13–16], closing the gap between individual myofibers and their collective wall structure. The model holds across species, with a smooth variation in its three curvature parameters within the myocardial wall providing tight fits to diffusion magnetic resonance images from the rat, the dog, and the human. Mathematically it explains how myofibers are bundled in the heart wall while economizing fiber length and optimizing ventricular ejection volume as they contract. The generalized helicoid provides a unique foundation for analyzing the fibrous composite of the heart wall and should therefore find applications in heart tissue engineering and in the study of heart muscle diseases.

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Section: Discussionmentioning

confidence: 99%

Heart wall myofibers are arranged in minimal surfaces to optimize organ function

Savadjiev

Strijkers

Bakermans

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…Furthermore, the torsion-to-shortening ratio (TSR) parameter was calculated for both rats and humans. TSR indicates the transmural distribution of contractile myofibers and their function (2,5,29). For example, it has been found that TSR is different for aortic stenosis patients than for normal subjects due to the change in the transmural distribution of the myocardial fibers resulting from a remodeling process (29).…”

mentioning

confidence: 99%

Layer-specific strain analysis by speckle tracking echocardiography reveals differences in left ventricular function between rats and humans

Bachner-Hinenzon¹,

Ertracht

Leitman

et al. 2010

American Journal of Physiology-Heart and Circulatory Physiology

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-specific strain analysis by speckle tracking echocardiography reveals differences in left ventricular function between rats and humans. Am J Physiol Heart Circ Physiol 299: H664 -H672, 2010. First published July 2, 2010; doi:10.1152/ajpheart.00017.2010.-The rat heart is commonly used as an experimental model of the human heart in both health and disease states, assuming that heart function of rats and humans is alike. When studying a rat model, echocardiography is usually performed on sedated rats, whereas standard echocardiography on adult humans does not require any sedation. Since echocardiography results of sedated rats are usually inferred to alert humans, in the present study, we tested the hypothesis that differences in left ventricular (LV) function may be present between rats sedated by a low dose of ketamine-xylazine and alert humans. Echocardiography was applied to 110 healthy sedated rats and 120 healthy alert humans. Strain parameters were calculated from the scans using a layer-specific speckle tracking echocardiography program. The results showed that layer longitudinal strain is equal in rats and humans, whereas segmental strain is heterogeneous (P Ͻ 0.05) in a different way in rats and humans (P Ͻ 0.05). Furthermore, layer circumferential strain is larger in humans (P Ͻ 0.001), and the segmental results showed different segmental heterogeneity in rats and humans (P Ͻ 0.05). Radial strain was found to be homogeneous at the apex and papillary muscle levels in humans and heterogeneous in rats (P Ͻ 0.001). Additionally, whereas LV twist was equal in rats and humans, in rats the rotation was larger at the apex (P Ͻ 0.01) and smaller at the base (P Ͻ 0.001). The torsion-to-shortening ratio parameter, which indicates the transmural distribution of contractile myofibers, was found to be equal in rats and humans. Thus, when evaluating LV function of sedated rats under ketamine-xylazine, it is recommended to measure the global longitudinal strain, LV twist, and torsion-to-shortening ratio, since no scaling is required when converting these parameters and inferring them to humans. speckle training; strain imaging; contractility RATS PLAY AN IMPORTANT ROLE in modeling human left ventricular (LV) function, and thus a variety of pathologies, such as myocardial infarction (20, 30) and cardiomyopathy (17, 19), are commonly induced in rats, so that their effect on LV function can be analyzed under controlled conditions. Consequently, the pertinent questions are 1) does the similarity in LV structure between rats and humans (4, 10) result in similar LV function? and 2) is the rat LV an appropriate model for studying human LV function?To evaluate the properties that quantify LV function, a method known as speckle tracking echocardiography (STE) has been recently developed (1, 3 , 9, 11, 13, 14, 18, 20, 23). The STE method uses standard two-dimensional (2-D) echocardiography cines and tracks the speckles in the ultrasound B-mode image sequence of the myocardium, and, subsequently, the parameters of local function ...

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“…Given a certain amount of volume decrease, an amount of torsion can be selected so that the transmural difference in myofiber shortening is zero. In the normal healthy heart this condition is satisfied accurately [1], as shown by a fixed ratio of torsion and the relative decrease in cross-sectional area of the cavity. In the present analysis we have quantified torsion as the axial gradient of rotation during the ejection phase, multiplied by the epicardial radius ( Fig.…”

Section: Methods Of Analysismentioning

confidence: 88%

“…In the group of controls, the transmural course of myofiber shortening is close to zero [1,2]. Using the cylindrical model of cardiac mechanics with known myofiber direction in the wall, the transmural difference ∆e f,(epi-endo) of myofiber shortening, relative to mean myofiber shortening e f,mean was calculated as a function of TSR.…”

Section: Methods Of Analysismentioning

confidence: 99%

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Quantification of transmural differences in myocardial function with MRI tagging

Arts

Toorn

Barenbrug³

et al.

2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-Many cardiac diseases cause transmural differences in myofiber function. With the Magnetic Resonance Imaging Tagging technique a grid of magnetic tags was attached to the heart. Using a model of cardiac mechanics the motion of these tags was analyzed to deduct the transmural gradient of myofiber shortening. In normal, young healthy subjects (n=9), the transmural difference in myofiber shortening varies little, about ± ± ± ±4% (sd) of mean shortening. In patients with aortic stenosis subendocardial function is at risk. In a group of such patients (n=5) fiber shortening in the subendocardial layers was found to be decreased by 23± ± ± ±20% relative to the subepicardial layers. This finding indicates that a model of cardiac mechanics can be used as a tool to convert MRItagging motion data to clinically useful information on a transmural gradient in contractile function. Presently, no other methods are available to detect such transmural gradient noninvasively.

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Relation between torsion and cross-sectional area change in the human left ventricle

Cited by 48 publications

References 18 publications

Heart wall myofibers are arranged in minimal surfaces to optimize organ function

Heart wall myofibers are arranged in minimal surfaces to optimize organ function

Layer-specific strain analysis by speckle tracking echocardiography reveals differences in left ventricular function between rats and humans

Quantification of transmural differences in myocardial function with MRI tagging

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