James B. Bassingthwaighte

Regional distribution of diffusible tracers and carbonized microspheres in the left ventricle of isolated dog hearts

Microspheres of different sizes, 125I-labeled antipyrine (I-Ap), and 42KCl or 86RbCl were injected into the aortic inflow of isolated, Langendorff, perfused, nonworking dogs hearts at blood flows of 1.3–4.8 ml/min g−1. After 15 seconds to 5 minutes, the left ventricle was sectioned into about 300 ordered pieces, and the amount of each tracer was determined. For all tracers, the relative density of deposition was generally higher in the endocardial region, except in one heart in which the aortic pressure and the total coronary flow were low. The deposition of 42K and that of I-Ap were essentially similar in three hearts over a large range of regional variation. This finding suggests either that both tracers were distributed in proportion to flow or that a small diminution in relative density of deposition of 42K in high-flow regions due to lower transcapillary extraction was quantitatively similar to a decrease in the residual fraction of I-Ap in these same regions due to faster washout in the first 15–30 seconds after injection. Large microspheres were deposited preferentially in regions of high flow, exaggerating the apparent heterogeneity of regional flows. The distribution of the smaller microspheres was closer to that for I-Ap or 42K.

Applications of the Lagged Normal Density Curve as a Model for Arterial Dilution Curves

1. Indicator dilution curves (concentration versus time) were recorded from the femoral and dorsalis pedis arteries of normal men after injections of indocyanine green into the superior vena cava or thoracic aorta. A four-parameter mathematical model, the lagged normal density curve, adequately described the form of the portion of these curves representing indicator passing by the sampling site for the first time. 2. The curves were observed to be of constant shape, the spread of the curve being approximately linearly related to the mean transit time t¯. The spread was dependent on the injection site; dispersion was shown to be greatest in the central circulation, less in the aorta, and still less in the arteries of the leg. For the latter segment, the mean transit time t¯. The spread was dependent 0.3 t¯, the square root of the variance was 0.18 t¯, and the parameters of the lagged normal density curve, σ and τ, were 0.09 t¯ and 0.16 t¯, respectively. 3. The linear relationships between parameters of the recorded curves and the mean transit times indicate that the effect of rate of flow, over a range from resting values to four to six times above resting values, has almost no influence on the dispersion. This suggests that the flow characteristics are essentially unchanged over this range. Such linear relationships always occur with laminar flow but cannot prove its existence because turbulent flow can also produce this result. The similarity of the linear relationships at low flow rates to those at high flow rates, where turbulence almost certainly is present, suggests that arterial flow is usually turbulent. Turbulence may be expected at relatively low flow rates in nonhomogeneous fluids driven by a pulsatile head of pressure through elastic, branched, tapering, curved tubes.

Fluid spaces in canine bone and marrow.

In order to provide a firm basis for the analysis of experiments on the kinetics of ion and solute exchange in bone, the total water space, extracellular space, and vascular (plasma plus erythrocyte) space in the tibial diaphysis in adult dogs were estimated. Tracers were injected intravenously into 40 dogs after ligation of the renal pedicles. Estimates were made of the volumes of distribution of radioactive tracers of varying characteristics (molecular weight, solubility, and charge), by taking samples of blood, plasma, and bone 3 hr after injection. The volumes of distribution (milliliters per milliliter of cortical bone) were: for tritiated water (a total water marker) 0.245 ± 0.003 (mean ± SD); for [14C]sucrose (an extracellular marker) 0.043 ± 0.001; for 111In-labeled transferrin (a plasma marker) 0.008 ± 0.003; and for red blood cells 0.005 ± 0.002. Interstitial fluid space was estimated by subtracting the estimated plasma space from the estimated extracellular space and it was 0.034 ml/ml of bone. Estimates of haversian canal volumes, obtained morphometrically, were 0.015 ml/ml bone and were compatible with the estimates of the vascular space.

Plasma Indicator Dispersion in Arteries of the Human Leg

Indicator-dilution curves were recorded from the femoral and dorsalis pedis arteries of five normal men after injections of indocyanine green into the superior vena cava or thoracic aorta. By considering the femoral curves as inputs to a mathematically linear system and the dorsalis pedis curves as outputs, transfer functions (the distribution of transit times) for the arterial segment between these sites were obtained in terms of a four-parameter model, the lagged normal density curve, over a sixfold range of flow rates. The parameters of the spread (dispersion) of 57 transfer functions were proportional to the mean transit time. The mean difference between transit time and appearance time was 0.30 t¯; the square root of the variances was 0.18 t¯. These linear relationships suggest that flow rate has no significant influence on dispersion and that, since no transition from laminar to turbulent flow was apparent, arterial flow characteristics were not significantly changed over a wide range of flow rates. The secondary implication is that the rate of spatial longitudinal spreading of indicator with distance traveled is primarily a function of the geometry of the arterial system, not of the rate of flow, and, therefore, that the spatial distribution at any instant is a function of this rate and of the distance traveled through the system.

Flow estimation by indicator dilution (bolus injection).

Indicator dilution techniques used for the estimation of flow (F), mean transit time (t), dispersion (σ), and mean transit time volume (V) in the circulation are subject to error when (1) flow is not steady and (2) concentrations are obtained by sampling at a constant rate (time averaging) rather than at rates proportional to the instantaneous flow past the sampling site (volume averaging). Using a simple descriptive model for indicator transport, the effects of simulated aortic flow or of sinusoidal flow of widely variable frequency were assessed. Errors in estimates of F, t, σ, and V are greater with bolus injections than with constant-rate injections. Errors are roughly proportional to the amplitude of variation in flow. They are maximal when the period of flow fluctuation is similar to the passage time of the dilution curve, which, for the human central circulation, is about the time for one respiratory cycle. With sinusoidal flow between 50% and 150% of the mean flow, errors were at worst up to 60% in F, 30% in t, 50% in σ, and 70% in V, with a bimodal distribution. Errors are minimal at cardiac frequencies. The troublesome lower frequencies can be avoided. Preliminary tests of a method for converting time- to volume-averaged concentrations gave encouraging results.

Anatomy of the microvasculature of the tibial diaphysis of the adult dog.

UNLABELLED The microvasculature in the cortex and marrow of the adult canine tibial diaphysis was filled with the silicone elastomer Microfil, the bone was decalcified, and the water was replaced with methylsalicylate to permit three-dimensional visualization of the microvascular arrangements. The tibial nutrient artery was seen to supply the marrow and the cortex via parallel, independent sets of arterioles and terminal capillary beds. No arteriolar or capillary anastomoses were observed linking these separate beds. The major portion of the venous drainage was found to be via small venules through the cortex into periosteal veins. Many small venules draining the medullary capillaries penetrated the cortex, and there were a few larger emissary veins, including the nutrient vein. Because the marrow and cortex have separate capillary beds in parallel, microsphere deposition should be appropriate for estimating the regional blood flows. CLINICAL RELEVANCE The results of this study should be of concern to surgeons who perform whole diaphyseal bone replacements, as the effluent venous vessels are important in re-establishing the circulation by microsurgical methods.

Transcoronary intravascular transport functions obtained via a stable deconvolution technique.

AbstractFollowing left atrial injection of indocyanine green in closed-chest, anesthetized dogs, 60 simultaneous input-output pairs of dilution curves were sampled via identical catheter sampling systems from the aortic root,Cin(t), and the coronary sinus,Cout(t). Assuming thatCout(t) was the convolution of a transport function,h(t), andCin(t), a new deconvolution technique was used to solve for theh(t)s which was not sensitive to noise, recirculation, or the form ofh(t).The 60 transcoronaryh(t)s were observed to be unimodal, right-skewed frequency distribution functions with mean transit times,

Density and Water Content of Dog Ventricular Myocardium

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