The preload of individual myocardial fibers

The preload of the indiviuual myocardial fibers of the left ventricle, that is, the stress exerted upon the myocardial fibers at end-diastole, is calculated by means of a set of equations. The development of the equations was based on anatomical data referring to the shape of the left ventricle and the orientation of the myocardial fibers, as well as some assumptions of minor importance. Numerical solution of the equations shows that in general, the preload increases as one advances from the apex to the equator of the left ventricle and then it decreases as one advances toward the base. The preload also changes as one advances from the epicardium to the endocardium in such a way that one can distinguish three zones: one outer, or epicardial, with low preloads, one middle with high preloads and one inner, or endocardial, with low preloads. The physiological significance of the findings as well as the validity of the assumptions on which the theory was based are discussed.     

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.     

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.     

Adaptation of cardiac structure by mechanical feedback in the environment of the cell: a model study.

In the cardiac left ventricle during systole mechanical load of the myocardial fibers is distributed uniformly. A mechanism is proposed by which control of mechanical load is distributed over many individual control units acting in the environment of the cell. The mechanics of the equatorial region of the left ventricle was modeled by a thick-walled cylinder composed of 6-1500 shells of myocardial fiber material. In each shell a separate control unit was simulated. The direction of the cells was varied so that systolic fiber shortening approached a given optimum of 15%. End-diastolic sarcomere length was maintained at 2.1 microns. Regional early-systolic stretch and global contractility stimulated growth of cellular mass. If systolic shortening was more than normal the passive extracellular matrix stretched. The design of the load-controlling mechanism was derived from biological experiments showing that cellular processes are sensitive to mechanical deformation. After simulating a few hundred adaptation cycles, the macroscopic anatomical arrangement of helical pathways of the myocardial fibers formed automatically. If pump load of the ventricle was changed, wall thickness and cavity volume adapted physiologically. We propose that the cardiac anatomy may be defined and maintained by a multitude of control units for mechanical load, each acting in the cellular environment. Interestingly, feedback through fiber stress is not a compelling condition for such control.     

The myocardium as a composite material: Analysis

As a further attempt to determine the stresses and strains of the individual myocardial fibers, the heart muscle is considered as an orthotropic material. A theory is presented which leads to the expression of the equilibrium conditions for the left ventricle in the form of three simultaneous differential equations. Solution of these equations would give the changes in shape of the left ventricle throughout the cardiac cycle, and, in addition, the stresses and strains of the individual myocardial fibers. It is pointed out, however, that meaningful solutions of the equations cannot be obtained at the present time because of difficulties in experimental determination of certain parameters.     

Adrenergic innervation of various sections of the heart in laboratory animals and man

By means of incubating slices in 2% glyoxylic acid solution, distribution of adrenergic fibers in the myocardium of various cardiac parts has been studied in the white rat, rabbit, cat, guinea pig and in the man. Both in the animals and in the man the distribution density of the adrenergic fibers of the myocardial plexuses in the auricle is higher than in the ventricle, and in the left half of the heart it is lower than in the right one. There are certain species differences in distribution of the adrenergic fibers. The density of the adrenergic fibers in the guinea pig myocardium is the highest, and in the white rat is is the lowest.     

Structural finite deformation model of the left ventricle during diastole and systole

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.     

Variability of the cardiomyocyte ploidy in normal human hearts.

We have performed cytophotometry for DNA in isolated myocytes of the left ventricle from 16 men, aged 19-39 years, who died from various non-cardiac or pulmonary causes. The mean ploidy of myocytes varied from 3.2-3.9 c to 6.6-7.3 c in different layers of the anterior wall of the left ventricle (where c is the haploid DNA content measured by cytophotometry in Feulgen-stained preparations). There was no correlation between the layers. The percentage of binuclear cells varied from 25 to 86% and correlated in every layer with the mean ploidy value of the whole myocyte population. Approximate calculation of total ploidy revealed low values in the ventricles of some individuals, and high values in others. Averaging the values for all the hearts studied obscures this variation. Mean myocyte ploidy in different layers of the anterior wall was similar: in the external layer it was 5.1 +/- 0.3 c, in the middle layer 5.5 +/- 0.3 c and in the inner layer 4.8 +/- 0.4 c. The mean percentage of binuclear myocytes in these three layers was also similar, being 61 +/- 3%, 63 +/- 4% and 54 +/- 5%, respectively. Myocyte ploidy in tissue from the posterior wall of the left ventricle also varied, but was always higher than for the same layer of the anterior wall in the same ventricle. We propose that high or low myocyte ploidy, as well as different proportions of mono- and binucleate cells, can be a factor affecting the course and result of cardiac pathology in the absence of any changes of myocyte genome determined during early ontogenesis and representing a stable characteristic of the individual.     

Repolarization of canine ventricular myocardium under the supraventricular rhythm

The ventricular myocardium is characterized by heterogeneity of activation-recovery interval durations. The transmural ARI gradients are present in the right ventricular apex (ARIs monotonically decreased as one moved from the endocardium to the epicardium), and in the left ventricular base (repolarization in the subepicardial layers was significantly shorter than that in the midmyo cardial layers whereas subendocardial ARIs did not differ from the others). The repolarization pattern of these myocardial regions is governed by the distribution of ARIs. In the apical left ventricular and basal right ventricular areas, no significant transmural differences in the repolarization durations were found. The repolarization pattern of these myocardial regions is governed by the activation sequence. In the right ventricle, ARIs were significantly longer at the base and shorter at the apex. In contrast, in the left ventricle, the apical ARIs were prolonged whereas the basal ARIs were abbreviated. The apex-to-base sequence of myocardial repolarization seems to depend on apex-to-base gradient of activation-recovery intervals durations.     

Discrimination of Recent Ischemic Myocardial Changes in WHHLMI Rabbits from the Findings of Postmortem Degeneration.

To distinguish recent ischemic myocardial changes in myocardial infarction-prone Watanabe heritable hyperlipidemic (WHHLMI) rabbits from general postmortem myocardial degeneration, we examined hearts of WHHLMI rabbits after sudden death and postmortem hearts of non-atherogenic rabbits. Hearts of 8 WHHLMI rabbits were excised within 30 min of sudden death and hearts of 27 non-atherosclerotic rabbits were excised at designated periods after sacrifice. A large number of myocardial cells from WHHLMI rabbits exhibited features characteristic of ischemia (intercellular gap, intracellular edema, eosinophilia, disappearance of myocardial cells, indistinct nuclei, wavy myocardial fibers) simultaneously at regions close to proximal occluded coronary arteries. Although postmortem hearts of non-atherosclerotic rabbits exhibited similar characteristics, several features characteristic of autolyzed myocytes were also randomly observed in the left ventricle wall. Each feature was detected independently in myocardial cells or regions of the ventricle wall. In conclusion, we found several unique characteristics associated with myocardial infarction which enable discrimination between recent ischemic myocardial changes and myocardial degeneration following death.     

The Continuity of Right and Left Ventricular Myocardial Sinusoidal Spaces and its Relation to Right Ventricular Implants

Evidence is presented which indicates that blood leaving side branches of an internal mammary artery implanted into the anterior wall of the right ventricle flows from the tunnel in which it lies through myocardial sinusoidal spaces of the anterior right ventricular wall across the midline to fill corresponding spaces in the anterior wall of the left ventricle and thence is carried to the left coronary sinus. The myocardial sinusoidal spaces of right and left ventricles have been well outlined, using injections of polyvinyl acetate and the technique of digestion casts. We have been able to show that there is no barrier between the myocardial sinusoids of the right circulation and those related to the anterior descending branch of the left coronary artery. In structure, these myocardial sinusoidal spaces are quite different from the intramyocardial coronary arteriolar zones which, in 93% of human hearts, are separated from one another without collateral communication.The continuity of the right and left ventricular myocardial sinusoids explains why implantation of a right internal mammary artery into the anterior wall of the right ventricle combined with a corresponding left implant, epicardiectomy and free omental graft, has been so effective in our hands in the treatment of far-advanced human coronary artery insufficiency.     

Variability of the cardiomyocyte ploidy in normal human hearts

We have performed cytophotometry for DNA in isolated myocytes of the left ventricle from 16 men, aged 19–39 years, who died from various non-cardiac or pulmonary causes. The mean ploidy of myocytes varied from 3.2–3.9 c to 6.6–7.3 c in different layers of the anterior wall of the left ventricle (where c is the haploid DNA content measured by cytophotometry in Feulgenstained preparations). There was no correlation between the layers. The percentage of binuclear cells varied from 25 to 86% and correlated in every layer with the mean ploidy value of the whole myocyte population. Approximate calculation of total ploidy revealed low values in the ventricles of some individuals, and high values in others. Averaging the values for all the hearts studied obscures this variation. Mean myocyte ploidy in different layers of the anterior wall was similar: in the external layer it was 5.1±0.3 c, in the middle layer 5.5±0.3 c and in the inner layer 4.8±0.4 c. The mean percentage of binuclear myocytes in these three layers was also similar, being 61±3%, 63±4% and 54±5%, respectively. Myocyte ploidy in tissue from the posterior wall of the left ventricle also varied, but was always higher than for the same layer of the anterior wall in the same ventricle. We propose that high or low myocyte ploidy, as well as different proportions of mono- and binucleate cells, can be a factor affecting the course and result of cardiac pathology in the absence of any changes of myocyte genome determined during early ontogenesis and representing a stable characteristic of the individual.     

Adrenergic innervation of the myocardium in rats with toxic exposures

Chronic intraperitoneal injection of cadmium and copper salts produces cardiotoxic effects of various degree. The degree of the muscular tissue lesion in the ventricles and atria is inverse to the number of luminescent nervous terminals. Changes in the adrenergic fibers are accompanied with certain metabolic shifts in the muscular tissue of the heart; this is evident from decreasing succinate dehydrogenase activity in cardiomyocytes and accumulation of lipids. Certain disorders are also revealed in cardiomyocytes, in vessels and in interstitial connective tissue demonstrated as: plethora, phenomena of stasis in the capillary bed, moderate perivascular edema, myocardial dystrophy. The foci of lesions are found more often in the left ventricle in myocardial tissue and under epicardium, sometimes near plethoric vessels and less often in the right ventricle and in the atria. The dependence between location of the myocardial lesions and vascular disorders is not always noted. This is observed more often under effect of cadmium sulfate and, evidently, is dependent not only on hypoxia, connected with congestive plethora, but with neurohumoral influences, too.     

Myoglobin content and citrate synthase activity in different parts of the normal human heart

Myoglobin (Mb) content and citrate synthase (CS) activity were determined in myocardial samples from nine human brain-dead organ donors with normal hearts. Six regions of each heart were analyzed: right and left atria, right ventricle, left ventricular subepicardium, subendocardium, and anterior papillary muscle. The Mb content was similar, whereas the CS activity was higher in the left than in the right heart at both atrial and ventricular levels. Mb content and CS activity were higher in ventricles than in atria. The subendocardial layer and papillary muscle of the left ventricle had a higher Mb content than the subepicardial layer, whereas CS activity was similar in these three locations. The results suggested a closer relationship between CS activity (oxidative potential) and work load than between Mb content and work load. Mb content may, instead, be related to intramuscular oxygen tension (PO2) on the basis of a comparison between our Mb data and those of others on regional variations in myocardial PO2.     

Horseradish peroxidase localization of sympathetic postganglionic and parasympathetic preganglionic neurons innervating the monkey heart

The localization of the sympathetic postganglionic and parasympathetic preganglionic neurons innervating the monkey heart were investigated through retrograde axonal transport with horseradish peroxidase (HRP). HRP (4 mg or 30 mg) was injected into the subepicardial and myocardial layers in four different cardiac regions. The animals were euthanized 84-96 hours later and fixed by paraformaldehyde perfusion via the left ventricle. The brain stem and the paravertebral sympathetic ganglia from the superior cervical, middle cervical, and stellate ganglia down to the T9 ganglia were removed and processed for HRP identification. Following injection of HRP into the apex of the heart, the sinoatrial nodal region, or the right ventricle, HRP-labeled sympathetic neurons were found exclusively in the right superior cervical ganglion (64.8%) or in the left superior cervical ganglion (35%). Fewer labeled cells were found in the right stellate ganglia. After HRP injection into the left ventricle, labeled sympathetic cells were found chiefly in the left superior cervical ganglion (51%) or in the right superior cervical ganglion (38.6%); a few labeled cells were seen in the stellate ganglion bilaterally and in the left middle cervical ganglion. Also, in response to administration of HRP into the anterior part of the apex, anterior middle part of the right ventricle, posterior upper part of the left ventricle, or sinoatrial nodal region, HRP-labeled parasympathetic neurons were found in the nucleus ambiguus on both the right (74.8%) and left (25.2%) sides. No HRP-labeled cells were found in the dorsal motor nucleus of the vagus on either side.     

Functional and anatomical variability of canine cardiac sympathetic efferent pathways: implications for regional denervation of the left ventricle

To further elucidate the functional anatomy of canine cardiac innervation as well as to assess the feasibility of producing regional left ventricular sympathetic denervation, the chronotropic and (or) regional left ventricular inotropic responses produced by stellate or middle cervical ganglion stimulation were investigated in 22 dogs before and after sectioning of individual major cardiopulmonary or cardiac nerves. Sectioning the right or left subclavian ansae abolished all cardiac responses produced by ipsilateral stellate ganglion stimulation. Sectioning a major sympathetic cardiopulmonary nerve, other than the right interganglionic nerve, usually reduced, but seldom abolished, regional inotropic responses elicited by ipsilateral middle cervical ganglion stimulation. Sectioning the dorsal mediastinal cardiac nerves consistently abolished the left ventricular inotropic responses elicited by right middle cervical ganglion stimulation but minimally affected those elicited by left middle cervical ganglion stimulation. In contrast, cutting the left lateral cardiac nerve decreased the inotropic responses in lateral and posterior left ventricular segments elicited by left middle cervical ganglion stimulation but had little effect on the inotropic responses produced by right middle cervical ganglion stimulation. In addition, the ventral mediastinal cardiac nerve was found to be a significant sympathetic efferent pathway from the left-sided ganglia to the left ventricle. These results indicate that the stellate ganglia project axons to the heart via the subclavian ansae and thus effective sympathetic decentralization can be produced by cutting the subclavian ansae; the right-sided cardiac sympathetic efferent innervation of the left ventricle converges intrapericardially in the dorsal mediastinal cardiac nerves; and the left-sided cardiac sympathetic efferent innervation of the left ventricle diverges to innervate the left ventricle by a number of nerves including the dorsal mediastinal, ventral mediastinal, and left lateral cardiac nerves. Thus consistent denervation of a region of the left ventricle can not be accomplished by sectioning an individual cardiopulmonary or cardiac nerve because of the functional and anatomical variability of the neural components in each nerve, as well as the fact that overlapping regions of the left ventricle are innervated by these different nerves.     

The motion of the left ventricle—III

We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.     

Forced vibrations of a circular muscle ring

We consider the small radial displacement of a circular ring of cardiac muscle subjected to periodic forcing. The ring in question is that in the middle layer, at the transverse midsection, of the left ventricle. We show that the ring reacts in a periodic manner when forced in a periodic manner. This is accomplished by writing the differential equation for the ring and solving it for two cases-one for constant and one for variable ring thickness.