Diffusion pathways in oxygen supply of cardiac muscle.
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Biomedical subjects
Publications and source records attributed to L Hoofd.
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The effect of long term administration of nifedipine on myocardial capillarity was studied in spontaneously hypertensive rats. Nifedipine was given for 20 weeks, mixed into commercial rat chow (0.3 g per 1 kg). Untreated spontaneously hypertensive rats had higher arterial blood pressure and developed cardiomegaly when compared with Wistar-Kyoto rats used as controls. Nifedipine administration in spontaneously hypertensive rats lowered the arterial blood pressure and reduced cardiac weight; however, both values remained far above those for controls. Myocardial capillarity was determined using the recently introduced method of capillary domains. Hearts from untreated spontaneously hypertensive rats were characterised by greater and more variable intercapillary spacing than those from controls. The treatment of spontaneously hypertensive rats with nifedipine resulted in normalisation of morphometric indices characterising capillary spacing, probably as a result of stimulation of capillary growth as indicated by a significant decrease in myocyte to capillary ratio. Thus, despite persistent hypertension and cardiomegaly the treatment of spontaneously hypertensive rats with nifedipine restored mean intercapillary distance and index of heterogeneity of capillary spacing to normal values.
When a flexible diffusion layer separates two closed gas chambers containing different mixtures of several gases, the different permeabilities of the layer for these gases lead to differences in the total gas pressures of the two chambers resulting in bulging of the layer and consequent changes in the chamber volumes. Application of the gas laws to binary gas mixtures provides two equations relating the partial pressure changes of one gas in any of the two chambers to the partial pressure difference between the two chambers across the layer. This permits the calculation of the two unknown factors, permeability (or Krogh's diffusion coefficient) of the layer for the measured gas and the permeability ratio of the two gases. Thus the permeabilities of both gases can be determined from recording the partial pressure of one of the gases only. We filled the gas chambers with different mixtures of oxygen and a second gas (nitrogen or carbon dioxide) at atmospheric pressure, closed the chambers, and measured the diffusion of the gases across thin (12-500 microns) layers of various materials by recording the oxygen partial pressure in both chambers with polarographic oxygen electrodes. Permeabilities of these layers for oxygen and the other gas were determined for plastic layers (MEM213, Silastic, Teflon), as well as water and methemoglobin solutions either in a fluid layer or soaked in Millipore filters. The data agreed well with those obtained from other studies in most cases.
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The passage of CO2 through water layers is attended by concurrent transport of (bi)carbonate. Since both bicarbonate and carbonate are charged molecules, their diffusion may evoke electric potentials and thus there will be interaction with all other ions present in the solution. Such effects have been described in the literature for weak acids and protein solutions of hemoglobin and albumin (Stroeve et al., 1985). Here, we present measurements of electric potential difference across layers containing 1.5 mmol/l myoglobin at 25 degrees C and various amounts of Na+ ions, where chemical equilibrium for the hydration reaction of CO2 was achieved by adding carbonic anhydrase. Voltages measured ranged from up to 5 mV at zero cation concentration to 0.7 mV around 100-150 mmol/l [Na+]. Contrary to hemoglobin and albumin, these voltages are lower, and even much lower, than theoretical predictions.
For the measurement of gas diffusion through liquids, Millipore filters are an interesting and easy tool. They keep the fluid in place, and layer thickness can be determined precisely and easily. We soaked Millipore type SM filters with solutions containing 1.66 mmol/l methemoglobin to measure the oxygen permeability at 25 degrees C, and compared the results with former measurements in liquid layers. Data scattered between 1.0 and 1.5 10(-11) mol X m-1 X kPa-1 X sec-1 and a decrease with increasing KCl concentration, as found for liquid layers, could neither be confirmed nor rejected. Nitrogen/oxygen permeability ratio of 0.465 +/- 0.016 SE was in agreement with literature data.
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Recently, we collected basic morphometric data from normal and hypertrophic rat hearts: median and mean values of the cell diameter and of the intercapillary distance as well as their variabilities. In the present communication we used these data, first for analysis of the effect of the heterogeneity of capillary spacing on the myocardial tissue PO2. Comparison of tissue PO2 histograms calculated for a situation in which the capillaries are evenly distributed as in the Krogh model, with a situation based on the same capillary but variable intercapillary distances clearly demonstrates the importance of heterogeneity of the capillary spacing as a separate oxygen determinant. This is even more important in the hypertrophic hearts which are characterized by longer and more variable intercapillary distances. In the second part, we compared the classical Krogh model with a model of concentric diffusion in which the oxygen consumption was either uniform or divided into two zones of distinctive rates. Oxygen profiles calculated for the Krogh model with excentric diffusion were similar to those derived for the two models of concentric diffusion.
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The oxygenation of layers of hemoglobin solutions thick enough to ensure chemical equilibrium between oxygen and hemoglobin has been analyzed theoretically assuming simultaneous diffusion of oxygen and oxyhemoglobin. The dimensionless transfer equation was solved for the finite and semi-infinite situation, the parameters being 1) the ratio of bound to physically dissolved oxygen after equilibration (H), 2) the ratio of carrier-mediated to free oxygen flux at steady state (D), and 3) the dimensionless saturation curve (characterized by phi 50). A parametric analysis provided plots of the dimensionless oxygenation time against these three dimensionless parameters. In this way, from the oxygenation times plotted as a function of the reciprocal oxygen driving pressure in any particular hemoglobin solution, the values of the oxygen permeability (or, knowing oxygen solubility, of the oxygen diffusion coefficient) and of the hemoglobin diffusion coefficient can be derived simultaneously.
A new mathematical treatment is presented which simplifies the solution of carrier-diffusion problems. The method is generally applicable and is illustrated and tested for a specific, commonly occurring situation: facilitated diffusion of a single substrate through flat layers. Results predicted for total substrate flux are in excellent agreement with control computer calculations. The method also can be used to obtain concentration profiles for each species; here the results are good only if conditions at the boundaries are predicted correctly.
The force-velocity relationship of maximal contractions with the handgrip muscles is established in a group of subjects. The effect of different muscle temperatures is studied. The parameters vo (maximal velocity), Fo (maximal force), Pmax (maximal power), a/Fo and H (both parameters describing the shape of the curve), and Ft/Fo (the value of the force at which power is maximal) are established. It is shown that 1) in repeated measurements the coefficient of variation in general is less than 10% for all the parameters except a/Fo; 2) the parameter a/Fo should be discarded in comparative measurements since it is not linearly related to the course of the curve. A parameter called H should be used instead to describe the curvature; 3) an increase in muscle temperature is accompanied by an increase in magnitude of all parameters except Fo. The temperature effect expressed as Q10 in the range 22-38 degrees C is in the order of 1.2.
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The classical tissue model of August Krogh remains the cornerstone in the modeling of tissue PO2. However, heterogeneities of O2 determinants can profoundly affect the calculated oxygen fields. One of them is the heterogeneity in capillary spacing. At the present time there are two methods available for the estimation of capillary spacing: the method of capillary domains and the closest-individual method. The former estimates the distribution of the surface areas surrounding each capillary while the latter derives the distribution of distances of tissue points to the nearest capillary. Both can be transformed into the distribution of the radii of tissue cylinders according to the model of Krogh. Their distribution is approximately lognormal and is characterized by the mean (or median) value and the logarithmic standard deviation (log SD), which serves as the heterogeneity index. When applied to the same photomicrographs, both methods give similar values of the mean but the domain method yields a smaller log SD than does the closest-individual method. Subsequently, the calculated tissue PO2 histograms are also more uniform with the domain method. This difference is caused by the asymmetry of the domains. The shape of the domains is not circular and the capillary is not situated in the center as suggested by the model of Krogh. The method of capillary domains, however, is more direct and less time-consuming and thus more suitable for routine work. Nevertheless, the goal of future research is to develop a method that would characterize not only the distribution of the surface area of the domains but also their asymmetry.