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.     

The effect of distension of the left ventricle of the heart on the length of the individual myocardial fibers

Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.     

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.     

Modeling the kinematics of the canine midcostal diaphragm

The hypotheses that the chest wall insertion (CW) is displaced laterally during inspiration and that this displacement is essential in maintaining muscle curvature of the costal diaphragmatic muscle fibers were tested. With the use of data from three dogs, caudal, lateral, and ventral displacements of CW during both quiet, spontaneous inspiration and during inspiratory efforts against an occluded airway were observed and recorded. We have developed a kinematic model of the diaphragm that incorporates these displacements. This model describes the motions of the muscle fibers and central tendon; the displacements of the midplane, muscle-tendon junction (MTJ), CW, and center of the muscle fiber-central tendon arcs are modeled as functions of muscle fiber length. In the model, the center of the fiber arcs and MTJ both move caudally parallel to the midplane during inspiration, whereas CW moves both caudally and laterally. The observed lateral displacement of CW and the observed caudal displacement of MTJ, as functions of muscle fiber length, both approximate well the theoretical displacements that would be necessary to maintain curvature of the fiber arcs. In confirming our hypotheses, we have found that lateral displacement of CW is a mechanism by which changes in the shape of the costal diaphragm, as described by its curvature, are limited.     

Regional stress in a noncircular cylinder.

Several mathematical formulas are presented for estimating regional average circumferential stress and shear stress in a thick-wall, noncircular cylinder with a plane of symmetry. The formulas require images of exterior and interior chamber silhouettes plus surface pressures. The formulas are primarily intended for application to the left ventricle in the short axis plane near the base (where the meridional radius of curvature is normally much larger than the circumferential radius of curvature) and to blood vessels. The formulas predict stresses in a variety of chambers to within 3% of finite element values determined from a large-scale structural analysis computer program called ANSYS.     

Locomotion of free-swimming ghost knifefish: anal fin kinematics during four behaviors

The maneuverability demonstrated by the weakly electric ghost knifefish (Apteronotus albifrons) is a result of its highly flexible ribbon-like anal fin, which extends nearly three-quarters the length of its body and is composed of approximately 150 individual fin rays. To understand how movement of the anal fin controls locomotion we examined kinematics of the whole fin, as well as selected individual fin rays, during four locomotor behaviors executed by free-swimming ghost knifefish: forward swimming, backward swimming, heave (vertical) motion, and hovering. We used high-speed video (1000 fps) to examine the motion of the entire anal fin and we measured the three-dimensional curvature of four adjacent fin rays in the middle of the fin during each behavior to determine how individual fin rays bend along their length during swimming. Canonical discriminant analysis separated all four behaviors on anal fin kinematic variables and showed that forward and backward swimming behaviors contrasted the most: forward behaviors exhibited a large anterior wavelength and posterior amplitude while during backward locomotion the anal fin exhibited both a large posterior wavelength and anterior amplitude. Heave and hover behaviors were defined by similar kinematic variables; however, for each variable, the mean values for heave motions were generally greater than for hovering. Individual fin rays in the middle of the anal fin curved substantially along their length during swimming, and the magnitude of this curvature was nearly twice the previously measured maximum curvature for ray-finned fish fin rays during locomotion. Fin rays were often curved into the direction of motion, indicating active control of fin ray curvature, and not just passive bending in response to fluid loading.     

Potential errors in fiber length measurements resulting from lever arm rotation during mechanical testing of muscle cells

In single muscle cell preparations fibers are often suspended between connectors, extending perpendicularly from a force transducer, and the lever arm of a torque motor. The fiber does not move along a horizontal plane when shortened or lengthened by lever arm rotation. An error from the true length (TL) is introduced if the expected length (EL) is calibrated along this horizontal optical plane. Lever arm length (LAL), initial fiber length (FL(i)), connector length (CL), and the magnitude of EL all contribute to this error. A mathematical model was used to determine the TL during shortening (0.96-0.80 FL(i)) and lengthening (1.10-1.50 FL(i)) at a constant LAL of 13.6mm. CL had the greatest impact on error. For FL(i) = 2mm at the longest CL modeled (15 mm), an expected shortening of 0.20 FL(i) produced a true shortening of ～ 0.17 FL(i), and an expected stretch to 1.50 FL(i) resulted in a true stretch to almost 1.60 FL(i). Under these conditions, the true sarcomere length would be 4% and 6% longer than expected during shortening and lengthening, respectively. Because of their non-linear nature, length errors at long CL's may result in an over-estimation of unloaded shortening velocity during slack tests and a left-ward shift in the passive tension-fiber length relationship at long fiber lengths. Measurement errors decreased dramatically with shorter CL's, becoming negligible (<1%) at CL = 3mm. We recommend that investigators keep CL as short as possible. Alternatively, we provide a method for adjusting the magnitude of the EL to yield a desired TL.     

Structure,crystallography, and morphogenesis of the cryptic shell of the terrestrial slug Limax maximus (Mollusca,gastropoda)

The structure and crystallography of the internal shell of the pulmonate gastropod slug Limax maximus were studied at the levels of light and scanning electron microscopy, revealing patterns of shell ontogeny and morphogenesis. The calcified portion of the slightly convex ovoid shell is composed of a single palisade layer of calcitic crystals. Numerous projections, 100 μm in width at the dorsal tip, are found on the dorsal surface of the shell and coincide with local nucleation sites of primordial calcium salt deposition onto the periostracum. With continued calcification these projections coalesce ventrally, forming the single crystalline shell layer. The organic portion of the shell includes the periostracum and an extensive PAS-staining conchiolin. In EDTA-etched preparations, conchiolin appears as a spongy network of fibers throughout the shell. Both horizontal and vertical components of the conchiolin are present, the former of variable thickness and occurring in an intercrystalline manner, the latter always occurring normal to the horizontal set. Macromorphogenic growth is characterized by three distinct temporal stages. Primary growth occurs radially from the umbonal region. Secondary growth is synonymous with shell thickening. Tertiary growth is characterized by both a lateral component, in which the shell extends beyond the primary growth boundaries, and a ventral component, in which the shell continues to grow in thickness. SEM of the ventral shell surface reveals a pattern of growth at the crystalmatrix interface. Proteinaceous fibers of the conchiolin occur unidirectionally in horizontal rows. Zones of incipient calcitic crystallization onto these hypostracal fiber bundles are contrasted by zones of increasing crystallization until the fibrous template (reduced hypostracum) is completely covered by crystals.     

Oblique alignment of hemoglobin S fibers in sickled cells

Thin sections of embedded, sickled erythrocytes reveal oblique alignment of parallel sheets of single fibers of hemoglobin S, with adjacent layers rotated by about 26 °. The oblique alignment pattern is consistent with the interlocking of helical grooves present in the 14-filament structure determined for individual fibers and could be related to the curvature in cell shape characteristic of the sickling process.     

双源CT 冠状动脉血管成像诊断心肌桥的价值探讨

目的：研究双源CT 冠状动脉血管成像诊断心肌桥的临床价值。方法：选择260 例具有典型心前区不适的患者进行双源CT 冠脉血管成像检查,观察其发生部位,测量其长度和深度并进行分析。结果：260 例受检患者中,62例共70 段存在心肌桥,检出率 达20.76%,高于文献报道的检出率18.2%。所有心肌桥均发生于左前降支,其中近段17 段(24.4%),中段43 段(61.4%),远段10 段 (14.2%)。心肌桥平均长度为15.8± 6.4mm,深度为1.4± 0.85mm。结论：双源CT 冠状动脉血管成像因其便捷无创,不受心率严格 限制且价格低廉可作为心肌桥筛查的理想检查手段。     

Orientation of non-blue cupric complexes on DNA fibers.

Three different orientations of non-blue, type 2 cupric complexes on DNA fibers are obtained from EPR data. The cupric complex of bleomycin, CuBlm, binds as described previously (Shields, H., McGlumphy,C., and Hamrick, P., J., Jr. (1982) Biochim. Biophys. Acta 697, 113-120), except possibly with more restricted motion. The square plane of CuBlm makes an angle of about 65 degrees with the fiber axis. The tridentate complex 2-formylpyridine monothiosemicarbazonato Cu2+ binds with its planar structure perpendicular to the fiber axis. In contrast, other tridentate cupric complexes of tripeptides, CuGHK and CuGHG, bind with the square plane parallel to the fiber axis. The bound forms of Cu(GHK) and Cu(GHG) are determined mostly by the GH moiety in the complex; the contribution of lysine in defining the orientation of the copper moiety is minimal. Thus, the structure of the ligand determines the orientation of these complexes on DNA.     

The distribution of membrane-glycogen complexes in the orbital surface layer of rabbit superior rectus

The distribution of membrane-glycogen complexes along the length of individual muscle fibers was compared among three fiber populations in the orbital surface layer of rabbit superior rectus. These three populations were (a) 61 singly innervated fibers (SIFs), (b) 10 multiply innervated fibers of relatively constant 10 μm diameter (10 μm MIFs), and (c) 22 multiply innervated fibers which are of about 5 μm diameter toward the middle of their length and of about 15 μm diameter toward their proximal and distal segments (5–15 μn MIFs). The orbital surface layer was sampled by electron microscopy at 68 sequential locations. Membrane-glycogen complexes were not seen in any of the 1738 samples of the SIFs. In the MIFs, such complexes were observed in 14% of the 1541 samples. However, both the 10 μm MIFs and 5–15 μm MIFs displayed a preferential concentration of membrane-glycogen complexes toward their distal fiber portions, and such complexes were seen in about 50% of the MIF samples near the beginning of the muscle's distal third. In the distal portion of 5–15 μm MIFs, there was a direct relationship between their increasing fiber diameter and their increasing frequency of occurrence of membrane-glycogen complexes.     

Intraspecific variation in fiber properties inYucca elata andHesperaloe funifera (Agavaceae)

Yucca elata andHesperaloe funifera possess long, thin fibers that have potential for making specialty papers. The objective of this study is to examine patterns ofintraspecific variation in fiber properties in these two species. InYucca elata most of the variation in fiber length is found within populations where fiber length is highly correlated with leaf length. In contrast, inHesperaloe funifera there is significant variation between populations and random variation in fiber lengths within most populations. Within-plant variation inHesperaloe was also examined. Fiber length does not vary between leaves of different ages but does vary within leaves. Fibers from the base of the leaf are shorter and wider than those from the middle and distal sections; fibers from distal sections are narrowest.     

Comparative aspects of cerebellar organization. From mormyrids to mammals.

Recent progress in the comparative analysis of the vertebrate cerebellar organization shows that the cerebella of different tetrapods have a basically similar intrinsic organization, whereas the cerebellum of fishes displays a number of fundamental differences in this respect. Clear examples of teleostean cerebellar specializations are present in the gigantocerebellum of mormyrids, including a valvula cerebelli, the absence of a parasagittal zonal organization, the presence of eurydendroid projection neurons instead of deep cerebellar nuclei, a precerebellar nucleus lateralis valvulae, olivocerebellar fibers that do not climb into the molecular layer, uni- and bilateral locations of granule cells, parallel fibers without a T-shaped bifurcation and with a coextensive distribution in the transverse plane, and different Purkinje cell arrangements including a dendritic palisade pattern. A theoretical exploration of the possible significance of these configurations suggests that they all might be involved in a single main cerebellar function, i.e. coincidence detection of parallel fiber activity by Purkinje cells.     

Changes in force and stiffness during stretch of skeletal muscle fibers, effects of hypertonicity.

Slow stretch ramps (velocity: 0.17 fiber lengths s-1) were imposed during fused tetanic contractions of intact muscle fibers of the frog (1.4-3.0 degrees C; sarcomere length: 2.12-2.21 microns). Instantaneous force-extension relations were derived both under isometric conditions and during slow stretch by applying fast (0.2 ms) length steps to the fiber. An increase in tonicity (98 mM sucrose added to control Ringer solution) led to significant reduction of the maximum isometric tension but at the same time to marked increase in the force enhancement during slow stretch. The maximum force level reached during the stretch was affected very little. Experiments on relaxed fibers showed that recruitment of passive parallel elastic components were of no relevance for these effects. Hypertonicity slightly increased the instantaneous stiffness of the active fiber both in the presence and in the absence of stretch. The total extension of the undamped fiber elasticity was considerably reduced by increased tonicity under isometric conditions but was only slightly affected during slow stretch. The change in length of the undamped cross-bride elasticity upon stretch was thus greater in the hypertonic than in the normotonic solution suggesting a greater increase in force per cross-bridge in the hypertonic medium. The contractile effects are consistent with the assumptions that hypertonicity reduces the capability of the individual cross-bridge to produce active force and, furthermore, that hypertonicity has only minor effects on the number of attached cross-bridges and the maximum load-bearing capacity of the individual bridge.     

Theoretical models in mechanics of the left ventricle

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.     

THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

The fundamental theorem of natural selection was a valiant attempt by R. A. Fisher to fit a quart into a pint pot
The present author reviewing Population Genetics by Ewens, 1969 a (Edwards, 1969).
Many authors have maintained that the theorem holds only under very special conditions, while only a few (e.g. Edwards, 1967) have thought that Fisher may have been correct – if only we could understand what he meant! It will be shown here that this latter view is correct
Price, 1972.
My own reason for not including a planned chapter on the fundamental theorem is… [ that ] in spite of many efforts I am still not satisfied that I am able to provide an account that does the theorem justice
The present author in the Epilogue to Foundations of Mathematical Genetics (Edwards, 1977).     

Optic methods for measurements of muscle fiber birefringence

An optical method for measuring the birefringence of muscle fibers was developed, which is realized on an automated Linnick interferometer microscope equipped with a laser. It was shown that the method has some advantages over the methods based on measurements of the intensity of light passing through a crossed polarizer, an analyzer, and a fiber (light polarized microscopy). The method involves direct phase measurements of optical path length at the parallel and perpendicular orientations of the polarization plane of probing radiation. The phase image is reconstructed automatically from interferograms with the use of the four-frame phase-shifting algorithm. The phase images of one and the same central part of the fiber at different orientations of the polarization plane represent two-dimensional numerical maps of the optical path length. The subtraction of these images gives a two-dimensional map of the phase shift, which includes information about the birefringence of the fiber. A formula for birefringence measurements was deduced, which has a certain advantage in comparison to that used earlier in that it does not take into account the thickness of a fiber that depends on the measurement point. The birefringence is normalized to a value of the half sum of phases, which are measured separately in the course of the experiment.     

Motor nerve topology reflects myocyte morphology in hamster retractor and epitrochlearis muscles

Neuromuscular activation is a primary determinant of metabolic demand and oxygen transport. The m. retractor and m. epitrochlearis are model systems for studying metabolic control and oxygen transport; however, the organization of muscle fibers and motor nerves in these muscles is unknown. We tested whether the topology of motor innervation was related to the morphology of muscle fibers in m. retractor and m. epitrochlearis of male hamsters ( approximately 100 g). Respective muscles averaged 47 and 12 mm in length 100 and 35 mg in mass. Staining for acetylcholinesterase revealed neuromuscular junctions arranged in clusters throughout m. retractor and as a central band across m. epitrochlearis, suggesting differences in fiber morphology. For both muscles, complete cross-sections contained approximately 1,700 fibers. Fiber cross-sectional areas were distributed nearly normal in m. epitrochlearis (mean = 1,559 +/- 17 microm(2)) and skewed left (P < 0.05) in m. retractor (mean = 973 +/- 15 microm(2)). Single fiber length (Lf) spanned muscle length (Lm) in m. epitrochlearis, while fibers tapered to terminate within m. retractor (Lf/Lm = 0.43 +/- 0. 02). With myelin staining, a single branch of ulnar nerve projected axons across the midregion of m. epitrochlearis. For m. retractor, the spinal accessory nerve branched to give rise to proximal and distal regions of innervation, with intermingling of axons between nerve branches. Nerve bundle cross-sections stained for acetylcholinesterase indicate that each motor axon projects to an average of 65 muscle fibers in m. epitrochlearis and 100 in m. retractor. Differences in fiber morphology, innervation topology, and neuromuscular organization may contribute to the heterogeneity of metabolic demand and oxygen supply in skeletal muscle.