[The antagonistic function of the heart muscle sustains the autoregulation according to Frank and Starling : Part I: Structure and function of heart muscle]. / Die antagonistische Funktion des Herzmuskels unterstützt die Autoregulation nach Frank-Starling : Teil I: Struktur und Funktion des Herzmuskels.

In the tradition of Harvey and according to Otto Frank the heart muscle structure is arranged in a strictly tangential fashion hence all contractile forces act in the direction of ventricular ejection. In contrast, morphology confirms that the heart consists of a 3-dimensional network of muscle fibers with up to two fifths of the chains of aggregated myocytes deviating from a tangential alignment at variable angles. Accordingly, the myocardial systolic forces contain, in addition to a constrictive also a (albeit smaller) radially acting component. Using needle force probes we have correspondingly measured an unloading type of force in a tangential direction and an auxotonic type in dilatative transversal direction of the ventricular walls to show that the myocardial body contracts actively in a 3-dimensional pattern. This antagonism supports the autoregulation of heart muscle function according to Frank and Starling, preserving ventricular shape, enhances late systolic fast dilation and attenuates systolic constriction of the ventricle wall. Auxotonic dilating forces are particularly sensitive to inotropic medication. Low dose beta-blocker is able to attenuate the antagonistic activity. All myocardial components act against four components of afterload, the hemodynamic, the myostructural, the stromatogenic and the hydraulic component. This complex interplay critically complicates clinical diagnostics. Clinical implications are far-reaching (see Part II, https://doi.org/10.1007/s00059-018-4735-x).

[Antagonistic function of the heart muscle : Part II: Clinical implications]. / Die antagonistische Funktion des Herzmuskels : Teil II: Klinische Auswirkungen.

In the hypertrophic heart the myostructural afterload in the form of endoepicardial networks is predominant, which enhances myocardial hypertrophy. The intrinsic antagonism is derailed. Likewise, the connective tissue scaffold, i.e. the stromatogenic afterload, is enriched in the response to the derailment of antagonism in a hypertrophic heart up to regional captivation of the heart musculature. Due to the selective susceptibility of the auxotonic, contracting oblique transmural myocardial network for low dose negative inotropic medication, this promises to attenuate progress in myocardial hypertrophy. Volume reduction surgery is most effective in reducing wall stress as long as the myocardium is not critically fettered by fibrosis. The use of external mechanical circulatory support is then effective if the heart is supported in its resting mode, which means around a middle width and at minimal amplitude of motion. The takotsubo cardiomyopathy might possibly reflect an isolated, extreme stimulation of the intrinsic antagonism as a response to hormonally induced sensitization of the myocardium to catecholamine. A particular significant conclusion with respect to the diseased heart is that clinical diagnostics need new impulses with a focus on the analysis of local motion patterns and on myocardial stiffness reflecting disease-dependent antagonistic intensity. This would become a relevant diagnostic marker if corresponding (noninvasive) measurement techniques would become available.

A mathematical model of the mechanical link between shortening of the cardiomyocytes and systolic deformation of the left ventricular myocardium.

BACKGROUND: Left ventricular myocytes are arranged in a complex three-dimensional mesh. Since all myocytes contract approximately to the same degree, mechanisms must exist to enable force transfer from each of these onto the framework as a whole, despite the transmural differences in deformation strain. This process has hitherto not been clarified in detail. OBJECTIVE: To present a geometrical model that establishes a mechanical link between the three-dimensional architecture and the function of the left ventricular myocardium. METHODS: The left ventricular equator was modeled as a cylindrical tube of deformable but incompressible material, composed of virtual cardiomyocytes with known diastolic helical and transmural angles. By imposing reference circumferential, longitudinal, and torsional strains onto the model, we created a three-dimensional deformation field to calculate passive shortening of the myocyte surrogates. We tested two diastolic architectures: 1) a simple model with longitudinal myocyte surrogates in the endo- and epicardium, and circular ones in the midwall, and 2) a more accurate architecture, with progressive helical angle distribution varying from -60° in the epicardium to 60° in the endocardium, with or without torsion and transmural cardiomyocyte angulation. RESULTS: The simple model caused great transmural unevenness in cardiomyocyte shortening; longitudinal surrogates shortened by 15% at all depths equal to the imposed longitudinal strain, whereas circular surrogates exhibited a maximum shortening of 23.0%. The accurate model exhibited a smooth transmural distribution of cardiomyocyte shortening, with a mean (range) of 17.0 (13.2-20.8)%. Torsion caused a shortening of 17.0 (15.2-18.9)% and transmural angulation caused a shortening of 15.2 (12.4-18.2)%. Combining the effects of transmural angulation and torsion caused a change of 15.2 (13.2-16.5)%. CONCLUSION: A continuous transmural distribution of the helical angle is obligatory for smooth shortening of the cardiomyocytes, but a combination of torsional and transmural angulation changes is necessary to execute systolic mural thickening whilst keeping shortening of the cardiomyocytes within its physiological range.

Diastolic ventricular aspiration: a mechanism supporting the rapid filling phase of the human ventricles.

During the rapid filling phase of the heart cycle, the internal volumes of the two ventricular cavities approximately double, while the intraventricular pressures rise typically only by an amount of less than 1 kPa. Such a small pressure increase cannot be the sole driving mechanism for the large inflow of blood associated with ventricular expansion during this period. Instead, the rapid filling phase is to be interpreted as being mediated primarily by the heart recoiling elastically from its contracted state, causing blood to be aspirated rapidly into the ventricles. In order to study the role of this mechanism, elastic finite element (FE) simulations of ventricular expansion were performed, taking into account the large deformations occurring during this period and the effective compressibility of the myocardium due to intramural fluid flow. Thereby, a realistic three-dimensional geometry derived from magnetic resonance imaging (MRI) measurements of both human ventricles was used. To validate our FE analyses, the results were compared with published measurements relating to the rapid filling phase of the human left ventricle. Our study shows that, under normal physiological conditions, ventricular aspiration plays a key role in the ventricular filling process.

A finite element model of the human left ventricular systole.

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.

A finite element study relating to the rapid filling phase of the human ventricles.

During the rapid diastolic filling phase at rest, the ventricles of the human heart double approximately in volume. In order to investigate whether the ventricular filling pressures measured under physiological conditions can give rise to such an extensive augmentation in ventricular volumes, a finite element model of the human right and left ventricles has been developed, taking into account the nonlinear mechanical behavior and effective compressibility of the myocardial tissue. The results were compared with the filling phase of the human left ventricle as extrapolated from measurements documented in the literature. We arrived at the conclusion that the ventricular pressures measured during the rapid filling phase cannot be the sole cause of the rise of the observed ventricular volumes. We rather advocate the assumption that further dilating mechanisms might be part of ventricular activity thus heralding a multiple function of the ventricular muscle body. A further result indicates that under normal conditions the influence of the viscoelasticity of the tissue should not be disregarded in ventricular mechanics.

On the significance of fiber branching in the human myocardium.

Myocardial tissue exhibits a high degree of organization in that the cardiac muscle fibers are both systematically aligned and highly branched. In this study, the influence and significance of fiber branching is analyzed mathematically. In order to allow for analytic solutions, a regular geometry and simplified constitutive relations are considered. It is found that branching is necessary to stabilize the ventricular wall.

The forces generated within the musculature of the left ventricular wall.

OBJECTIVES: To test the hypothesis that two populations of myocardial fibres-fibres aligned parallel to the surfaces of the wall and an additional population of fibres that extend obliquely through the wall-when working in concert produce a dualistic, self stabilising arrangement. METHODS: Assessment of tensile forces in the walls of seven porcine hearts by using needle probes. Ventricular diameter was measured with microsonometry and the intracavitary pressure through a fluid filled catheter. Positive inotropism was induced by dopamine, and negative inotropism by thiopental. The preload was raised by volume load and lowered by withdrawal of blood. Afterload was increased by inflation of a balloon in the aortic root. The anatomical orientation of the fibres was established subsequently in histological sections. RESULTS: The forces in the fibres parallel to the surface decreased 20-35% during systolic shrinkage of the ventricle, during negative inotropism, and during ventricular unloading. They increased 10-30% on positive inotropic stimulation and with augmentation in preload and afterload. The forces in the oblique transmural fibres increased 8-65% during systole, on positive inotropic medication, with an increase in afterload and during ventricular shrinkage, and decreased 36% on negative inotropic medication. There was a delay of up to 147 ms in the drop in activity during relaxation in the oblique transmural fibres. CONCLUSION: Although the two populations of myocardial fibres are densely interwoven, it is possible to distinguish their functions with force probes. The delayed drop in force during relaxation in obliquely oriented fibres indicates that they are hindered in their shortening to an extent that parallels any increase in mural thickness. The transmural fibres, therefore, contribute to stiffening of the ventricular wall and hence to confining ventricular compliance.

A critical evaluation of results of partial left ventriculectomy.

BACKGROUND: Because of the variation in the surgical procedures designed to reduce ventricular radius, along with differences in hospital care, it is difficult to disentangle the factors that may contribute to the success or failure of the partial left ventriculectomy. METHODS AND RESULTS: We undertook partial left ventriculectomy in 18 patients, 10 suffering from idiopathic dilated cardiomyopathy and 8 from ischemic heart disease. We assessed the amount of reduction in wall stress, the systolic thickening of the ventricular wall, and the extent of connective tissue in the excised segment of the wall. Of the overall group, six patients died, three from infarction, one of stroke, one with asystole, and one with ventricular fibrillation. The mean decrease in measured mesh tension was 40% (p < 0.001). Most patients exhibited improvements postoperatively in terms of the systolic thickening of the posterior and superior free walls of the left ventricle. In those in whom the events could be monitored, life-threatening arrhythmias posed complications in three of four patients with ischemic heart disease, and in two of six patients suffering from idiopathic dilated cardiomyopathy. In one patient, death was associated with a transmural alignment of fibrous tissue. CONCLUSIONS: Our measured reductions in myocardial mesh tension were in keeping with the anticipated theoretical reduction in wall stress expected from partial ventriculectomy. The basic concept underscoring surgical maneuvers to reduce ventricular radius, therefore, is sound. A potential trap is the resection of the marginal artery. Critical myofibrosis was a rare complication. Arrhythmias, which are common, can successfully be treated by implantation of antitachycardic and defibrillatory devices.

Late ventricular structure after partial left ventriculectomy.

Nine months after partial ventriculectomy, a 53-year-old man died of progressive heart failure. His heart was examined to determine the alignment of the muscle fibers around the ventricular scar, which was 11 cm long, 1.3 cm thick and 4 cm wide. The scar reached 2 to 12 mm beyond the surgical suture line. The fibers in the middle and subendocardial layers were malaligned, resulting in convergence, compression and regional necrosis.

Immediate effects of partial left ventriculectomy on left ventricular function.

BACKGROUND: Attempts to prolong life or to improve the quality of life by partial left ventriculectomy in patients suffering from dilated cardiomyopathy have yielded strikingly variable results in leading surgical centers. HYPOTHESIS: The outcome of patients after partial left ventriculectomy depends on intraoperative myocardial protection together with appropriate long-term pharmacotherapy. We further assume that partial removal of the fibrotic ventricular wall may lead to a particularly inhomogeneous pattern of wall stress, giving rise to the potential of a paradoxical increase in wall stress and the creation of arrhythmogenic foci. METHODS: During surgery in 24 patients, local mesh tension was measured using needle-force probes in up to five sites within the left ventricular wall before and after resection of the interpapillary mural segment. The data were used to calculate regional peak developed force and to identify any differences in the timing of local mechanical activity between the measured regions. RESULTS: Mean decrease in regional wall stress was 42% (76 sites of measurement). However, we discovered a paradoxical increase of 42% in 18 sites of measurement. The time delay in the onset of force development between the measured regions prior to surgery was 0 msec in 10 patients, up to 30 msec in 7 patients, and beyond 80 msec in 7 patients. After resection, the time delay increased considerably in incidence and duration. CONCLUSION: Ventriculectomy is an effective means of reducing wall stress. The unexpectedly high incidence of inhomogeneities in wall stress after asymmetrical surgical ventricular remodeling, currently typical for the classical Batista procedure, together with the asynchronous regional ventricular function that we found to increase after partial left ventriculectomy, needs further elucidation by electrophysiological investigations.

The anisotropic structure of the human left and right ventricles.

An important determinant of cardiac output derives from the structure of the ventricular wall given by the arrangement of the cardiac muscle fibres. A key feature of this arrangement is both a global and local anisotropy. First, a preparation method necessary for analyzing the main aspects of spatial fibre architecture is outlined. Global anisotropy can be described by a gross band-like structure wrapping both left and right ventricles while local anisotropy results from the arrangement of the individual muscle fibres within the band. In pathologic cases this basic structure may be disturbed leading to cardiac failure. Second, a Finite Element model, formulated on the basis of Magnetic Resonance measurements has been devised which is intended to reflect the global as well as the local anisotropy of the ventricles in order to further the understanding of cardiac performance.

The heart muscle's putative "secondary structure'. Functional implications of a band-like anisotropy.

Opinions are divided as to whether the rope-like secondary structure, which Torrent-Guasp dissected out of the myocardial body by the blunt unwinding technique (BUT) reveals some kind of functional compartmentation of the heart muscle. The myocardial fibres are aligned parallel to the fibre disruption (cleavage) plane, along which the band has been prepared but they are not necessarily aligned parallel to the long axis of the band. Inconsistencies in the myocardial rope model arise from the obligatory zones of transmural inflection, which are obvious in the base and the apex of both ventricles. They are, however, merely discernible in the midzone of the left ventricular cone. The investigator experienced in BUT knows that the cleavage plane is not unique. We doubt the assumption that the rope structure is the predominant stress transmission pathway, because the fibre strand peel-off technique (SPOT) delivers irregular fibre disruption planes which are definitely different from those which Torrent-Guasp prepares. The rope-like fibre arrangement could be just a redundant structure, a remnant of past developmental steps without, however, any functional implication to the human heart. On the other hand, peeling-off fibre strands from the ventricular wall produces deeply perforating, i.e., oblique transmurally grooved surfaces. Putative functions of force transmission in an oblique transmural direction are (1) ventricular dilation as a function of the variable inclination angle with respect to the epicardial surface, (2) monitoring of ventricular wall stress and ventricular size and (3) segmental stiffening which could serve other dependent segments as a punctum fixum.

The heart's fibre alignment assessed by comparing two digitizing systems. Methodological investigation into the inclination angle towards wall thickness.

Myocardial contractile pathways which are not aligned strictly parallel to the heart's epicardial surface, give rise to forces which also act in the ventricular dilating direction. We developed a method which allows us to assess any fibre orientation in the three-dimensional myocardial weave. Decollagenized hearts were prepared by peeling-off fibre strands, following their main fibre orientation down to near the endocardium. In the subepicardium the strands followed a course more or less parallel to the epicardium, whereas from the mid-wall on they tended to dive progressively deeper into the wall. The preparation displays more or less rugged surfaces rather than smooth layers. The grooves and crests on the exposed surfaces were sequentially digitized by two methods: (1) Using a magnet tablet (3 Draw Digitizer System, Polhemus, Cochester VTO 5446, USA) on a dilated pig heart we manually followed the crests using a stylus, handling each groove and crest as an individual contractile pathway. (2) A constricted cow heart was digitized using a contact-free optical system (opto TOP, Dr. Breuckmann, Meersburg, Germany), which is based on the principle of imaging triangulation. Using specially developed software the inclination angles of selected crests and grooves with respect to the epicardial surface were calculated. The two digitizing methods yield comparable results. We found a depth- and side-specific weave component inclined to the epi-endocardial direction. This oblique netting component was more pronounced in the inner 1/3 of the wall than in the subepicardium. The inclination angle probably increases with increasing wall thickness during the ejection period. Manual digitizing is an easy and fast method which delivers consistent results comparable with those obtained by the cumbersome high resolution optical method. The rationales for the assessment of transmural fibre inclination are (1) the putative existence of dilating forces inherent in the myocardial weave and (2) the possible overproportional increase in the oblique transmural weave component during myocardial hypertrophy, which would entail a reduction in efficiency of ventricular performance in terms of haemodynamic work.

The assessment of intramural stress alignment on the beating heart in situ using micro-ergometry: functional implications.

The main local stress transmission pathways in the left ventricular base, midportion and apex in up to seven layers have been assessed in normal dog and porcine hearts, in hypertrophied dog hearts, and in three pig hearts having undergone a temporary left ventricular outflow stricture. The rotational sensitivity of needle force probes was used to determine the focal surface-parallel direction of the myocardial tension vector. In all places investigated the orientation of the force transmission pathways differs slightly from the morphologically determined fibre alignment. Vector rotation upon an axis normal to the epicardial surface is definitely tempered as compared to fibre rotation. Alterations in the force transmission pathways assessed in hypertrophied dog hearts by micro-ergometry qualitatively confirm structural remodelling in so far as an irregularity in the transmural rotation of the main stress vector was found. The measured disparities between the alignment of the myocardial fibre weave and the direction of stress transmission both in the normal and the diseased heart is widely individual, and hence, scattering of the data is marked. However, it must also be called into consideration that the measured orientation of force vectors is that at the moment of highest developed force, only. Further investigations will elucidate if discrepancies between that force vector and morphology are less pronounced when the vector is averaged over the entire heart cycle.

Computation of the alignment of myocardial contractile pathways using a magnetic tablet and an optical method.

The computation of the inclination angle of myocardial contractile pathways, based on the data from (1) optically and (2) manually digitized hearts is described. The measured raw data comprised: (1) A list epi of points on an "epicardial' surface S. (2) For each selected contractile pathway f, a list of points along the contractile pathway. For any point p on a contractile pathway f, the angle of inclination alpha p = alpha p (p,f,S) is defined to be the angle (in degrees) between the tangent tp = tp(f) to the contractile pathway f at the point p and the tangent plane Tvp to the surface S at the surface point up = v(p,S) which is nearest to p. Thus alpha p is a generalization of the imbrication angle of Streeter. The angle of inclination was computed using two separate numerical methods: (1) A discrete method, applying finite differences to the raw data, to compute the tangents tp and the tangent planes Tvp, after which the results were smoothed. (2) A smoothing method in which the data was first smoothed to obtain an approximation Scpi to the epicardial surface and spline approximations to the contractual pathways f. We describe the results for two typical hearts: a manually digitized dilated pig heart and an optically digitized constricted cow heart. For each heart we first present the depths and angles of inclination of typical contractual pathways and then summarize the results in the form of histograms. The results are discussed in detail in the accompanying paper of Lunkenheimer. Redmann et al. [5], where the digitization methods are also described.