Estimating diffusion distances in muscle

Models of fibers and capillaries in cross sections of muscle were used to quantify the relationships between diffusion distances and tissue capillarity. The fibers were constructed as square and hexagonal arrays, and the placement of capillaries around the perimeters of the fibers ordered them in similar arrays. Diffusion distances were measured as the percent cumulative frequency of fiber area within a given distance of a capillary when capillary-to-fiber ratio was increased from 0.5 to 4.0. Equations fitted to the data make it possible to estimate diffusion distances in muscle and to correlate changes in diffusion distances with fiber growth, capillary growth, and the geometrical arrangement of capillaries in the muscle bed.     

Effect of fixation protocols on muscle preservation and in situ diffusion distances

In order to examine the effects of various methods for tissue preparation on ultrastructural analyses, and hence standardize reported values, six commonly used fixatives were examined for their quantitative effect on muscle fibre size and capillary dimensions. Both the composition and osmolarity of fixatives affected structural indices significantly, producing a range of values of similar magnitude to that presented in reports of structural adaptations. When comparing data from different studies, therefore, it is essential to establish that dissimilar values reflect different tissue composition, rather than methodologies. The method of choice for quantitative analysis of intracellular diffusion pathways uses a combined aldehyde fixative with a metabolic poison, and an isotonic buffer as vehicle.     

Capillarity and diffusion distances in skeletal muscles in birds

Summary Tissue capillarity and diffusion distances were determined for red and white skeletal muscles of adult birds ranging in mass from 10.8 to 6200 g. In addition, literature values for capillarity and diffusion distances in skeletal muscles of mammals were incorporated into the data set. Muscle mass was closely coupled to body mass. However, no significant allometric relations were found for any of the other variables measured. Number of capillaries per fiber was not correlated with cross sectional area of individual muscle fibers. Thus, capillary density decreased in a hyperbolic manner against fiber area and diffusion distance decreased in a hyperbolic manner against the number of capillaries per muscle fiber. Red muscles had significantly higher numbers of capillaries per fiber and significantly shorter diffusion distances than did white muscles. The patterns for tissue capillarity and diffusion distances in avian muscle reported here are similar to values reported previously for mammalian muscles. In both taxanomic groups capillarity and diffusion distances are independent of body mass. In addition, diffusion distances are characteristic of capillaries distributed in random arrays through the muscle cross section.Abbreviations ALD muscle anterior latissimus dorsi - CD numerical density of capillaries in muscle cross section - C/F number of capillaries per individual muscle fiber - FCSA fiber cross sectional area - GST muscle gastrocnemius - LGST lateral head of muscle gastrocnemius - MGST medial head of muscle gastrocnemius - MM muscle mass - PLD muscle posterior latissimus dorsi     

Capillary growth in relation to blood flow and performance in overloaded rat skeletal muscle

Rat extensor digitorum longus muscleswere overloaded by stretch after removal of the synergist tibialisanterior muscle to determine the relationship between capillary growth,muscle blood flow, and presence of growth factors. After 2 wk,sarcomere length increased from 2.4 to 2.9 µm. Capillary-to-fiberratio, estimated from alkaline phosphatase-stained frozen sections, wasincreased by 33% (P < 0.0001) and60% (P < 0.01), compared withcontrol muscles (1.44 ± 0.06) after 2 and 8 wk, respectively. At 2 wk, the increased capillary-to-fiber ratio was not associated with anychanges in mRNA for basic fibroblast growth factor (FGF-2) or itsprotein distribution. FGF-2 immunoreactivity was present in nerves andlarge blood vessels but was negative in capillaries, whereas theactivity of low-molecular endothelial-cell-stimulating angiogenicfactor (ESAF) was 50% higher in stretched muscles. Muscle blood flowsmeasured by radiolabeled microspheres during contractions were notsignificantly different after 2 or 8 wk (132 ± 37 and 177 ± 22 ml · min¹ · 100 g¹, respectively) fromweight-matched controls (156 ± 12 and 150 ± 10 ml · min¹ · 100 g¹, respectively).Resistance to fatigue during 5-min isometric contractions (final/peaktension × 100) was similar in 2-wk overloaded and contralateralmuscles (85 vs. 80%) and enhanced after 8 wk to 92%, compared with77% in contralateral muscles and 67% in controls. We conclude thatincreased blood flow cannot be responsible for initiating expansion ofthe capillary bed, nor does it explain the reduced fatigue withinoverloaded muscles. However, stretch can present a mechanical stimulusto capillary growth, acting either directly on the capillary abluminalsurface or by upregulating ESAF, but not FGF-2, in the extracellular matrix.

     

Capillarity and oxygen diffusion distances of the soleus muscle of guinea pigs and rats. Effects of hyperthyroidism

The relationship between capillarity and oxidative capacity in the soleus muscle of rats and guinea pigs injected with triiodothyronine (T3) or with saline for up to 4 weeks was studied. The rats' soleus weight and FCSA were not affected by T3, but the guinea pigs that received T3 had smaller muscle weight and FCSA than the controls. The activities of cytochrome c oxidase and citrate synthase were significantly (41 and 65%) higher in the T3 than in the control rats. T3 administration did not affect the activities of these enzymes in the soleus of the guinea pigs. Capillary density (CD) was higher in T3 rats (892 +/- 80 vs 622 +/- 54 caps/mm2), and in T3 guinea pigs (1219 +/- 95 vs 739 +/- 142 caps/mm2). The higher CD in T3 rats was due to growth of new microvessels, while in the T3 guinea pigs it was due to a reduction in FCSA. Mean and maximal diffusion distances evaluated by the closest individual method were reduced by 2.02 and 3.37 microns in rats, and by 3.73 and 6.16 microns in guinea pigs. The magnitude of the reduction in diffusion distances brought about by the increased capillary density was partially offset by a concomitant change in the capillary arrangement from an ordered (hexagonal), towards a random distribution. These results seem to indicate that skeletal muscle capillarity is not necessarily determined by the oxidative capacity of the fibers.     

Using diffusion distances for flexible molecular shape comparison

Background  

Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.     

Capillarization,mitochondrial densities,oxygen diffusion distances and innervation of red and white muscle of the lizard Dipsosaurus dorsalis

Summary The white and red regions of the iliofibularis muscle of the lizard Dipsosaurus dorsalis were analyzed using histologic and morphometric analysis. These regions are composed of fast glycolytic (FG) and both fast oxidative, glycolytic (FOG) and tonic fibers, respectively. Endplate morphology and number of endplates per fiber were estimated from fibers from both areas. Capillary volume densities of the red and white regions were quantified from transverse sections. Mitochondrial volume of fibers from the red and white regions were estimated from electron micrographs.All fibers from the white region of the iliofibularis possessed a single, well defined endplate, as did most red region fibers. The remaining red fibers (28±5%) possessed an average of 14.7±3 endplates each, distributed along the entire length of the fiber at intervals of approximately 1124 m.Red fibers possessed twice the mitochondrial volume of white fibers (7.6±0.4%, red; 3.8±0.3%, white). Mitochondria were distributed uniformly through the fibers from both regions. Capillary anisotropy was low ( = 1.018) in both regions. Capillary densities of the red region (629±35 mm^-2) were much greater than those of the corresponding White region (73±8 mm^-2).The data indicate that capillary densities, mitochondrial volumes and theoretical diffusion distances correlate well with the oxidative capacity of lizard muscle fibers. Tonic fibrs of this species appear oxidative and therefore metabolically capable of functioning during locomotion. The similar mitochondrial volumes and capillary densities of reptilian and mammalian muscles suggest that the greater oxidative capacity of mammalian muscle is due in part to possession of more oxidatively active mitochondria rather than to possession of more mitochondria per se.     

Enhancement of human muscle growth in diffusion chambers by bone marrow cells

Samples of minced human muscle were cultured in millipore diffusion chambers incubated in the peritoneal cavities of mice. In about half the chambers the minced muscle samples were mixed with autogenous bone marrow cells which lead to improved myogenic growth. A similar but less marked effect was produced by mononuclear cells from the patients' blood. No growth enhancement occurred when the muscle and marrow cells were separated by a filter in double chambers. In addition to accelerated myogenesis, the chambers with added bone marrow cells had a much lower incidence of infection. This work may have practical clinical implications for the treatment of muscle injuries. Local implantation of autogenous marrow cells (+/- minced muscle) may prove useful in improving myogenic regeneration.     

Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.     

Capillary density of skeletal muscle in Andean dogs.

High capillary density and small muscle fiber diameters were found in the sternothyroid muscle of dogs native to 4350 m. The number of capillaries per square millimeter was three times greater while the diameter was less than half of those obtained in the same muscle of normoxic dogs. These findings suggest that tissular adaptative mechanisms are important in the process of acclimatization to hypoxia, contributing to the maintenance of adequate levels of PO2 in the tissue in the presence of hypoxemia.     

Calcium diffusion in uterine smooth muscle sheets

The potassium contracture in the longitudinal muscle of estrogen- treated rat uterus was kinetically investigated. The rates of tension development after Ca addition and relaxation after Ca removal were measured under the high-potassium depolarization. Both rates decreased with an increase in preparation thickness. The relaxation rate had only a slight dependence on temperature. On the contrary, both relaxation and contraction rates in a contraction induced by an electrical stimulation strongly depended on temperature, but not on preparation size. These results suggest that the Ca diffusion process in the extracellular space is the rate-limiting step in relaxation of Ca- dependent contracture under potassium depolarization. The diffusion model, in which the effect of the unstirred layer was considered, could quantitatively explain the experimental results. The apparent diffusion coefficient in the muscle sheet was estimated to be approximately 3 x 10(-7) cm2/s. The difference from that in aqueous solution is discussed.     

Capillary zone electrophoresis of insulin and growth hormone

The separation power of capillary zone electrophoresis was examined using highly purified and well-characterized biosynthetic human insulin, growth hormone, their derivatives, and related proteins. Mixtures of proteins were chosen to illustrate practical applications of this technique. Proteins differing slightly in structure, but equivalent in net charge, were not completely separated. Degradation of insulin by dilute acid treatment was followed by capillary zone electrophoresis, native polyacrylamide gel electrophoresis, and reversed-phase liquid chromatography. Excellent correlation was observed between these techniques. Simple equipment requirements and analysis times on the order of 10 min make capillary zone electrophoresis attractive for analytical protein separations.     

Calcium diffusion in transient and steady states in muscle.

Rates of diffusion through the extracellular space of thin sheets of myocardium from the right ventricular outflow tract of kittens were estimated at 23 degrees C for 45Ca2+ and an inert reference tracer, [14C]sucrose. The myocardial sheets were mounted in an Ussing chamber and equilibrated with Tyrode solution with varied calcium concentrations, Cao. The tracers were added to one side and their concentrations on the other side measured at 5-15-min intervals for 6 h. The apparent tracer diffusion coefficient for sucrose was 1.11 +/- 0.06 X 10(-6) cm2s-1 (mean +/- SEM, n = 74), 22% of the free diffusion coefficient; the lag time before reaching a steady state provided estimates of the intratissue volume of distribution or diffusion space of 0.41 +/- 0.15 ml/ml tissue (n = 74), a value compatible with expectations for extracellular fluid space. Over the range of Cao from 0.02 to 9.0 mM, the intratissue apparent diffusion coefficient for Ca, DCa, averaged 1.65 +/- 0.10 X 10(-6) cm2s-1, n = 74, which is 21% of the free DoCa, and was not influenced by Cao. Because transsarcolemmal Ca permeation is slow, DCa is the diffusion coefficient in the extracellular region. The paired ratios DCa/Ds averaged 1.32 +/- 0.05 (n = 67) for all levels of Cao but at physiologic or higher Cao averaged 1.45 +/- 0.07 (n = 39), close to the ratio of free diffusion coefficients, 1.53. Equations distinguishing transient from steady state diffusion were fitted to the data, showing that the apparent distribution volume of "binding sites" external to the diffusion pathway diminished at higher Cao in a fashion suggesting that a least two different Ca2+ binding sites were present.     

Capillary blood perfusion during postischemic reperfusion in striated muscle.

Monitoring of nutritive blood flow in muscle is of particular importance to reconstructive surgeons, since ischemia/reperfusion in striated muscle is known to result in postischemic microvascular perfusion failure. Laser Doppler flowmetry has recently been introduced as an easy-to-use, noninvasive technique for continuous monitoring of microvascular tissue perfusion. Despite its popularity, there exists a great deal of controversy as to what actually generates the laser Doppler signal recorded from a given tissue. Intravital microscopy is a technique for direct visualization of the nutritional circulation in tissue. By using intravital microscopy, direct measurements of blood perfusion in individual segments of the nutritional microcirculation can be made. In 22 Syrian golden hamsters we performed laser Doppler flowmetry and intravital microscopy measurements in muscle tissue prior to and during reperfusion after 4 hours of tourniquet ischemia using the dorsal skinfold chamber model. Intravital microscopy (n = 10) revealed a heterogeneous capillary perfusion during the early reperfusion phase with a decrease (p less than 0.01) in functional capillary density to 49.4 +/- 17.0 percent of control. No recovery was observed after 24 hours of reperfusion. Laser Doppler flowmetry (n = 12) showed a parallel reduction of capillary red blood cell flux during the early perfusion phase to 43.9 +/- 22.6 percent of control values (p less than 0.01), and no recovery was observed after 24 hours of reperfusion. However, the laser Doppler flowmetry technique was not able to detect the capillary perfusion inhomogeneities shown by intravital microscopy. Postischemic reperfusion in striated muscle is characterized by a decrease in functional capillary density and a heterogeneous capillary perfusion. Laser Doppler flowmetry is a useful tool for monitoring microvascular tissue perfusion, although in striated muscle of the hamster it must be considered that accurate nutritional "capillary" flow readings can be grossly overestimated if larger vessels, such as arterioles and collecting venules, are contained in the measuring field of the laser Doppler probe.     

On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.     

Self diffusion of water in frog muscle.

Self diffusion of cell water has been measured at diffusion times ranging form 0.3 ms to 2.4 s for three muscle types of Rana pipiens, using various magnetic field gradient nuclear magnetic resonance methods. Intracellular diffusion coefficients and membrane permeabilities are calculated with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficient is 1.6 x 10-5 cm2/s, in approximate agreement with other literature values for skeletal muscles. The outer membrane permeabilities are estimated at 0.01 cm/s for two of the muscle types, and much higher for the other one.     

Capillary tortuosity in skeletal muscles of mammals depends on muscle contraction

Capillary orientation (anisotropy) was compared in hindlimb muscles of mammals of different size and/or different aerobic capacity (dog, goat, pony, and calf). All muscles were fixed by vascular perfusion at sarcomere lengths ranging from 1.5 to 2.7 micron. The ratios of capillary counts per fiber cross-sectional area on two sets of sections (0 and 90 degrees) to the muscle fiber axis were used to estimate capillary anisotropy and the coefficient c(K,0) relating 1) capillary counts on transverse sections (a commonly used parameter to assess muscle capillarity) and 2) capillary length per volume of fiber (i.e., capillary length density). Capillary orientation parallel to the muscle fiber axis decreased substantially with muscle fiber shortening. In muscles fixed at sarcomere lengths of 2.69 microns (dog vastus intermedius) and 1.52 microns (dog gastrocnemius), capillary tortuosity and branching added 7 and 64%, respectively, to capillary length density. The data obtained in this study are highly consistent with the previously demonstrated relationship between capillary anisotropy and sarcomere length in extended vs. contracted rat muscles, by use of the same method. Capillary anisotropy in mammalian locomotory muscles is curvilinearly related to sarcomere length. No systematic difference was found in capillary tortuosity with either body size, athletic ability, or aerobic capacity. Capillary tortuosity is a consequence of fiber shortening rather than an indicator of the O2 requirements of the tissue.