Regional timing of myocardial shortening is related to prestretch from atrial contraction: assessment by high temporal resolution MRI tagging in humans

Earlier studies have shown substantial nonuniformity in normal left ventricular (LV) myocardial function concerning both the degree of shortening and timing of shortening. We hypothesized that nonuniform LV function may be related to nonuniform prestretch induced by atrial contraction. Eleven healthy human subjects were studied using MRI myocardial tagging and strain analysis. The amount of circumferential prestretch was assessed in 30 LV segments. Prestretch was defined as the difference in strain between end diastole (at ECG R wave) and diastasis. Furthermore, both the degree of shortening (quantified as peak circumferential shortening, peak systolic shortening rate, and amount of postsystolic shortening) and timing of shortening (quantified as the onset time of shortening and time to peak shortening) were assessed. LV prestretch was found to be nonuniform, with the highest values in the lateral wall. The amount of segmental prestretch correlated significantly with peak shortening (r = 0.79), peak shortening rate (r = 0.50), amount of postsystolic shortening (r = 0.67), onset time of shortening (r = -0.57), and time to peak shortening (r = 0.71) (P < 0.001 for each of these relations). These relations may be explained by regional differences in wall stress or by a regional Frank-Starling effect. The correlation between timing of shortening and prestretch demonstrates that mechanical timing is not determined by electrical phenomena alone. In conclusion, regional variation in LV function correlates with the nonuniform prestretch from atrial contraction.     

Effects of nonuniform column packing in analytical gel chromatography. II. Associating solutes

Effects of nonuniform column packing on boundary profiles for selfassociating systems have been investigated by computer simulation. Migration rate of each of the interconverting solute species changes along the column as a result of nonuniform packing, and the difference in velocity of monomer and n-mer is not constant as the sample moves down the column. A greater amount of overall axial dispersion results, as compared to the constant-column case. Procedures developed in this study can be applied to any experimentally measured column nonuniformity.     

Analysis of the structure of magnetic fields that induced inhibition of stimulated neurite outgrowth

The important experiments showing nonlinear amplitude dependences of the neurite outgrowth in pheochromocytoma nerve cells due to ELF magnetic field exposure had been carried out in a nonuniform ac magnetic field. The nonuniformity entailed larger than expected variances in magnetic field magnitudes associated with specific levels of biological effects, thereby evoking a question about validity of the interpretations formulated for the case of a uniform field. In this work, we calculate the relative value of nonuniformity and deviations in ac magnetic field. It is shown that these factors do not affect the main conclusion in the original papers about the form of the amplitude dependence of the observed biological effect.     

Effect of degree of uniformity on predicted visual cortical response tuning curves

 The different cortical visual cells exhibit a large repertoire of responses to sinusoidal gratings, depending on their receptive field structure and the stimulation parameters. It has been shown previously that the tuning curves and histogram shapes of cell responses are affected by subunit distances. One receptive field model (Spitzer and Hochstein 1985b) incorporated subunit distance but assigned it as a constant parameter, for ease of calculation. Here we investigate different tuning curve properties of various primary cortical cell types during testing of 10 deg of nonuniform distances of the receptive fields’ subunits. The effect of nonuniformity was compared for average responses, tuning curve shapes, maximum peak responses, and bandwidths across four cell types of different sizes. The shapes and other properties of tuning curves are usually found to be retained also when the degree of uniformity is not very high for most of the cell types. In addition, the effect of uniformity is compared across these different response properties. The maximum peak responses of the tuning curve are found to display a lower coefficient of variation than the bandwidth, for all cell types, for most degrees of uniformity. Received: 15 June 1993/Accepted in revised form: 5 August 1994     

A mathematical model of tumor growth. III. comparison with experiment

In this paper a model of nonuniform inhibitor production is used to discuss some experimental results obtained by Folkman and Hochberg for multicellular spheroids (of V-79 Chinese hamster lung tissue). Built into the mathematical model is a parameter b which is a measure of the degree of nonuniformity of the inhibitor production rate. The “inverse problem” is solved by finding the value of b necessary to account for results with which the uniform model is incompatible [6]. The resulting value of b enables a good estimate to be made for the observed width of peripheral mitotic zones in the V-79 spheroids, and the resulting stability parameters lie in appropriate ranges for the model to be a significant improvement over uniform models. Further improvements are discussed, including a heuristic model for estimating the destabilizing effect of vascularization on tissue growth.     

Impact of Nonuniform Electron Density on Plasmonic Properties of Metal Nanoparticles

The interfacial nonuniformity of the electron density that occurs in metals as a result of atomic imperfections can strongly affect the plasmonic properties of metallic nanostructures. Under certain conditions, it induces the bulk plasmon resonance in the transition area and can significantly change scattering and absorption of light by metallic nanostructures in a broad frequency range. This effect is numerically demonstrated for radially nonuniform spherical silver nanoparticles and analytically investigated with respect to the resonant coupling with the dipolar surface plasmons of the metal core.     

Nonuniformity of the chemical composition of a capillary discharge plasma

A steady-state distribution of the concentration of two ion species in a capillary discharge plasma is studied using MHD equations for a plasma with a spatially nonuniform, time-dependent chemical composition. In our case, the set of equations is significantly simplified because of the steady-state character and symmetry of the problem. Even with such simplification, however, some results could be obtained only by numerical integration. The factors affecting the distribution of heavy ions are studied. It is shown that the distribution of the heavy impurity over the discharge cross section can be much more nonuniform than the distribution of the main component (hydrogen). A simple criterion for such a nonuniformity is obtained.     

A 3D model of the Achilles tendon to determine the mechanisms underlying nonuniform tendon displacements

The Achilles is the thickest tendon in the body and is the primary elastic energy-storing component during running. The form and function of the human Achilles is complex: twisted structure, intratendinous interactions, and differential motor control from the triceps surae muscles make Achilles behavior difficult to intuit. Recent in vivo imaging of the Achilles has revealed nonuniform displacement patterns that are not fully understood and may result from complex architecture and musculotendon interactions. In order to understand which features of the Achilles tendon give rise to the nonuniform deformations observed in vivo, we used computational modeling to predict the mechanical contributions from different features of the tendon. The aims of this study are to: (i) build a novel computational model of the Achilles tendon based on ultrashort echo time MRI, (ii) compare simulated displacements with published in vivo ultrasound measures of displacement, and (iii) use the model to elucidate the effects of tendon twisting, intratendon sliding, retrocalcaneal insertion, and differential muscle forces on tendon deformation. Intratendon sliding and differential muscle forces were found to be the largest factors contributing to displacement nonuniformity between tendon regions. Elimination of intratendon sliding or muscle forces reduced displacement nonuniformity by 96% and 85%, respectively, while elimination of tendon twist and the retrocalcaneal insertion reduced displacement nonuniformity by only 35% and 3%. These results suggest that changes in the complex internal structure of the tendon alter the interaction between muscle forces and tendon behavior and therefore may have important implications on muscle function during movement.     

Developmental signals do not further accentuate nonuniform postpneumonectomy compensatory lung growth.

Mechanical forces imposed on lung tissue constitute major stimuli for normal lung development and postpneumonectomy (PNX) compensatory growth and remodeling. Superimposing developmental signals on PNX signals augments compensatory alveolar growth but exaggerates airway-parenchymal dissociation (i.e., dysanaptic lung growth); the latter tends to offset benefits derived from the former. In adult dogs after PNX, lobar expansion and growth of the remaining lobes were markedly non-uniform (Ravikumar et al. J Appl Physiol 97:1567-1574, 2004). We hypothesized that superimposing developmental and post-PNX signals further accentuates nonuniformity of lobar growth. We used high-resolution computed tomography (HRCT) to follow regional lung expansion and growth in foxhounds undergoing right PNX at 2.5 mo of age compared with litter-matched control (Sham) animals; scans were performed 4 and 10 mo following surgery, i.e., before and after somatic maturity. Air and tissue volumes were measured in each lobe; tissue volume estimated by HRCT includes air-free tissue and blood in small vessels <1 mm. Interlobar nonuniformity of tissue volume was absent at 4 mo but evident 10 mo after PNX; growth of the remaining left lower lobe gradually lagged behind other lobes. At maturity, nonuniformity of lobar growth in pneumonectomized puppies was similar to that previously reported in pneumonectomized adults. We conclude that superimposing developmental and post-PNX signals enhances some aspects of compensatory lung growth and remodeling without altering its nonuniform spatial distribution.     

Endonuclease activity in the blood serum of rats undergoing nonuniform gamma irradiation

During the first hours following nonuniform gamma-irradiation (the nonuniformity coefficient was 3:1 and 5:1 with a dose change along the axis directed cranio-caudally and caudo-cranially), endonuclease activity (pH 5.75) in the blood serum increased with the dose which was estimated with a reference to total utilization of the substrate. Supercoiled plasmid DNA served as the substrate. The transformation of a supercoiled form of plasmid DNA into an open circular form was the criterion of estimation of nuclease activity. It was shown that the increase in the nuclease activity correlated with the increase in the nonuniformity coefficient.     

General continuum analysis of transport through pores. II. Nonuniform pores.

A general continuum derivation of the nonelectrolyte (Js) and volume (Jv) flux through a pore whose cross section is a function of axial position (nonuniform) is given. In general, the flux equations cannot be reduced to the same form as for a uniform pore and it is not possible to characterize the pore kinetics by three constants as in the uniform pore case. However, it is shown that under certain conditions, the nonuniform pore equations can be approximated by the uniform pore form and can be characterized by three constants (omega, sigma, Lp). The only condition needed to reduce the Jv equation to the uniform form is that the solution be dilute. The deviation of the Js equation from the uniform form is characterized by an asymmetrical function of Jv whose maximum value is estimated. It is shown that the maximum posible fractional deviation of the Js equation from the uniform form is given by the parameter: 0:5sigmaJv/omegaRT. Since this parameter is less then 0.15 for most membrane studies, the nonuniform Js equation can usually be approximated by the uniform pore form. The general results are illustrated by explicit calculations on several models of nonuniform pores. It is shown, for example, that the "equivalent pore radius" defined in the usual way is a function of the experimental parameter that is measured and is not unique.     

Nonuniform size distribution of nascent peptides: The role of messenger RNA

The origin of the nonuniform size distribution of nascent rabbit globin peptides has been investigated in the reticulocyte lysate and wheat germ cell-free protein synthesis systems. Increasing the concentrations of the cellular components involved in protein synthesis failed to alter the elution pattern observed upon chromatographic analysis of reticulocyte lysate nascent chains. Nascent chains isolated from a globin messenger RNA-directed wheat germ cell-free system showed a nonuniform size distribution of nascent peptides similar to that of the rabbit reticulocyte nascent chains. These observations indicate that the nonuniformity of the globin nascent chains arises from a unique property of the messenger RNA being translated and not from limiting concentrations of a component or components of the reticulocyte protein synthesis system.     

Pulsatile flow in a constricted channel.

A nonuniform channel is used as a simple model of a constricted arterial vessel. Flow patterns have been calculated for pulsatile flow with both sinusoidal and nonsinusoidal flow rates for a range of Reynolds number, Re, and Strouhal number, St. The results show that even for relatively low frequency flows a strong vortex wave will be generated with a complex wall shear stress distribution and peak values much greater than those found in steady or unsteady parallel flow. The vortex wave increases in strength with increasing Re and St, with its total length and wavelength independent of Re but inversely proportional to St. The form of the imposed flow rate is found to have an important effect on the flow and the shear stress distribution.     

Heterogeneity of the spatial distribution of the primordial organic substance as an initial stage of biological evolution

An approach to describe the emergence of dynamics of polymerization/depolymerization of some spatially distributed prebiological structures has been analyzed, and two phases of the development of the system have been identified. In the first phase, polymerization of organic monomers occurs under the influence of external factors, and in the second one depolymerization takes place. Both processes are accompanied by “diffusive mixing” of reaction products. The dynamic equations of the system are presented. Numerical examination of the space nonuniform solution of model equations has shown that, in conditions of low stability of uniform space distribution, these solutions resolve into a number of discrete peaks of nonzero density, which are isolated from each other by free space. Such nonuniform distributions are stable when close to the bifurcation point; yet in other conditions, they can lose their stability, which entails a more pronounced nonuniformity of space dynamics. Thus, interaction of polymerization/depolymerization processes results in chaotic self-organization and leads to origination of complex and inhomogeneous (patchy) spatial structures. These structures in physical space can reflect the emergence of the spatial nonuniformity in prebiological associations, while in the distributive space of characters they can correspond to the initial steps of emergence of the first discrete domains fixed in biological evolution.     

Description of an XRF system for multielemental analysis

An X-ray fluorescence (XRF) system that uses radioisotopes in an orthogonal configuration between the source, sample, and detector is described. The advantage of such a system is that for large (bulk) samples or in vivo measurements, the background caused by Compton scattering in the sample is minimized. High reproducibility for nonuniform samples is obtained by reducing the sample size and thus the effects of nonuniformity in the spatial response of such a system. Germane to any accurate analytical method is the use of proper mathematical algorithms for data evaluation. The problem is acute, in particular, when photopeaks with low counting statistics are to be analyzed. In the case of a single photopeak on flat background, optimal energy window size, which maximizes the signal-to-noise ratio, for trapezoidal intergration is described. The sensitivity and minimum detection limit at different energies together with background considerations are discussed.     

Nonuniform irradiation of the canine intestine. II. Dosimetry

An experimental model has been developed for quantitative studies of radiobiological damage to the canine small intestine following partial-body nonuniform irradiation. Animals were irradiated with 60Co gamma rays to simulate the nonuniform irradiation which do occur in victims of radiation accidents. The model used a short source-to-surface distance for unilateral irradiations to produce a dose gradient of a factor of two laterally across the canine intestinal region. The remainder of the animal's body was shielded to prevent lethal damage to the bone marrow. In situ dosimetry measurements were made using thermoluminescent dosimeters to determine the radiation dose delivered as a function of position along a segment of the small intestine. This system made it possible to correlate the radiation dose delivered at a specific point along the small intestine with the macroscopic and microscopic appearance of the intestinal mucosa at that point, as determined by direct observation and biopsy using a fiberoptic endoscope. A key feature of this model is that dosimetry data for multiple sites, which receive a graded range of radiation doses, can be correlated with biological measurements to obtain a dose-response curve. This model is being used to evaluate the efficacy of new therapeutic procedures to improve survival following nonuniform irradiation.     

Influence of mutual arrangement of the electric dipole and the spatial nonuniformity of brain electrical conductivity on the solution of the direct task of electroencephalography using the method of finite elements

The results of comparing the solutions of the direct task of electroencephalography on a spherical model and a spherical model with one nonuniformity are discussed. The nonuniformity was simulated by two parabolas situated on the same axis of symmetry and crossing the boundary of the gray and the white matter. The region between the larger and the smaller parabolas had the physical characteristics of the gray matter, and the region inside the smaller parabola had the characteristics of the cerebrospinal fluid. The task was to find a combination of parameters (distance between the dipole and the nonuniformity, angle of rotation of the dipole relative to the nonuniformity, sizes of the dipole and the nonuniformity, etc.) that provides the maximum effect of the difference of potentials on the outer surface of the scalp in the spherical model with one nonuniformity and the spherical model. The influence of the points of grounding on the value of the effect was analyzed (ground only at the right ear and ground at both ears). The data obtained show that a maximum difference of potentials is reached at the positions of dipoles close to tangential relative to the scalp surface.     

Nonuniform recombination within the human beta-globin gene cluster.

Population genetic analysis of 15 restriction site polymorphisms demonstrates nonuniform recombination within the human beta-globin gene cluster. These DNA polymorphisms show two clusters of high nonrandom associations, one 5' and another 3' to the beta-globin structural gene, with no significant linkage disequilibrium between the two clusters. The 5'- and 3'-association clusters are 34.6 kilobases (kb) and 19.4 kb long, respectively, and are separated by 9.1 kb of DNA immediately 5' to the beta-globin gene. For each of these three DNA regions, we have observed a relationship between nonrandom associations and physical distance between the polymorphisms. However, this relationship differed for each of these regions. On the assumption that the effective population size (Ne) is 5,000-50,000, we estimate the total recombination rate to be 0.0017%-0.0002% in the 5' cluster, 0.0931%-0.0093% in the 3' cluster, and 0.2912%-0.0219% in the 9.1-kb region between them. The beta cluster thus shows nonuniformity in recombination. Moreover, the recombination rate in the 9.1-kb DNA segment is 3-30 times greater than expected and is thus a hot spot for meiotic recombination.     

Ventilation heterogeneity in excised lobes: effect of tidal volume.

Although several factors are known to influence nonuniformity of ventilation, including lung mechanical properties (regional structure and compliance), external factors (chest wall, pleural pressure, heart), and ventilatory parameters (tidal and preinspiratory volume, flow rate), their relative contributions are poorly understood. We studied five excised, unperfused, canine right-middle lobes under varied levels of tidal volume (VT), thus eliminating many factors affecting heterogeneity. Multiple-breath washouts of N(2) were analyzed for anatomic dead space volume (VD(anat)), nonuniformity of N(2) washout, and nonuniformity between joined acinar regions vs. that occurring between larger joined regions. Approximately 80% of ventilation heterogeneity was found among joined acinar regions at resting levels of VT, but increasing VT reduced intra-acinar heterogeneity to about 25% of that found at resting levels. Increasing VT had essentially no effect on VD(anat) and heterogeneity among larger joined regions. The results indicate that the magnitude of VT is a major influence on the dominant intra-acinar component of ventilation heterogeneity and that VT effects on VD(anat) are likely due to perfusion and/or influences normally external to the lobar structure.