Bassingthwaighte, James B.

Abstract A method for controlling the plasma creatinine concentration is described. This method uses continuous determination of the plasma creatinine concentration and a servomechanism which drives an infusion pump at a rate proportional to the difference between the actual and desired creatinine concentrations. The rate and volume of creatinine infusion necessary to maintain the desired plasma concentration provide information related to kidney function and the accumulation of creatinine in the body. Experiments using this technic and the method of data analysis are described. It has been shown that under certain conditions this technic may be used to estimate the renal clearance of creatinine and the size and nature of the space into which creatinine is distributed in the dog.

The inapplicability of Beer's law to densitometry of dyes in whole blood or other nonhomogeneous media has been long known. When using a densitometer whose output is directly proportional to the light transmitted, a simple transformation— log X = log (x – x0)—can be employed to allow rapid, accurate estimation of dye concentration. This is facilitated by use of an optical density ruler. The transformation, X = x – x0, can be made mechanically, by shifting the infinity position of the ruler with reference to the zero light transmission position, or electrically, by appropriate use of zero suppression in the densitometer circuit. The transformation results in an exponential (logarithmic) relationship between light transmitted and concentration of the dye (indocyanine green). Readings of relative optical density obtained by use of the ruler are multiplied by a calibration constant to calculate dye concentration. The principles of the transformation have been applied to the determination of the optimal zero suppression required for maintenance of constant sensitivity of the densitometer in the presence of various levels of background dye. densitometer calibration; indocyanine green densitometer; calibration of dye-dilution curves; correction of dye-dilution curves Submitted on September 13, 1963

The assumption that the rate of blood flow past the sampling site is constant is basic to the Stewart-Hamilton estimation of cardiac output. Pulsatile flow might be expected to cause random and systematic errors. In this study dye-dilution curves were recorded simultaneously from two or three sites (pulmonary artery, aortic root, thoracic aorta, femoral artery) after injections of dye into the inferior vena cava, right ventricle, pulmonary artery, or left atrium of anesthetized dogs. The color of the indocyanine-protein complex formed after injection of the dye stabilized rapidly. Such stabilization is required for continuous photometric quantitation of dilution curves with juxtaposed injection and sampling sites. Areas of curves from the central circulation did not differ significantly from each other; they averaged 2.5% less than areas of curves recorded simultaneously from the femoral artery. Heart rate had no consistent influence. The large variability in estimates of cardiac output from curves recorded from the pulmonary artery after injection into the right ventricle was diminished with injection farther upstream. Submitted on May 29, 1961

Blood is nonhomogeneous; hence, the relationship between light transmission and increasing concentration of dye in whole blood is never the perfect exponential curve predicted by Beer's law. Instead, as the concentration of indocyanine green is increased to high levels (40 mg/liter) the light transmission decreases exponentially toward an asymptote at 6–8% transmission for nearly monochromatic densitometers (half-band width: 13–20 mμ), but at 30–40% for densitometers using light of wide-band width. Consequently, following recording of a dilution curve, circulating background dye reduces the change in transmission per unit increase in dye concentration in subsequent curves. This decrease in sensitivity cannot be compensated for by a simple increase in the sensitivity of the densitometer or in the intensity of its light source. Compensation can be attained, however, if increasing densitometer sensitivity is associated with the automatic scale expansion provided when a suppressed zero point is used. At correct zero suppression, the deflection for zero output of the densitometer coincides with the asymptotic transmission value mentioned above. indicator-dilution in circulation; blood flow measurement; blood optical density; dye dilution technic; cardiac output measurement Submitted on April 15, 1963

In 13 canine hearts, 158 disappearance curves for 133 Xe and antipyrine-1 125 I, given by intra-arterial slug injection, were recorded at a wide range of perfusion rates. Flow rates (ml/100 g/min) calculated from these curves by a variety of methods were compared with measured flow rates (F a ) per weight of perfused tissue. Perfusion of isolated, supported hearts and of anterior descending coronary arteries in open-chest dogs provided similar data. The semilogarithmic slope of curves from apex or whole heart decreased with time, particularly at high flow rates. There was a small, consistent difference in shape between antipyrine and xenon curves, suggesting that radioactivity in fat contributed somewhat to this tailing. Estimation of flow rate from the steepest semilog slope yielded an average value of 1.1 F a for all rates; estimation from slope at 30% of peak radioactivity gave 0.9F a . The curves were closely described by a two-exponential equation which gave flow estimates of 0.95F a when collimation limited the observations to the heart apex, and lower values when the whole heart was observed. Peak height/area methods gave values of approximately 0.75F a in spite of various compensations for the impossibility of recording the curve until radioactivity = 0.

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.

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.

Microspheres of different sizes, 125 I-labeled antipyrine (I-Ap), and 42 KCl or 86 RbCl 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 42 K 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 42 K 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 42 K.

The exchanges of 125 I-labeled 4-iodoantipyrine (I-Ap), 14 C-labeled antipyrine ( 14 C-Ap), and tritiated water (THO) were studied in isolated blood-perfused, beating, nonworking dog hearts. From a first set of experiments, analysis of externally monitored myocardial clearance curves of I-Ap after its injection into coronary artery blood showed its washout to be flow limited at flows ranging from 0.8 to 3.8 ml. g -1 . min -1 . Therefore, these curves can be used for estimating coronary blood flow. In a second set of experiments, coronary sinus dilution curves of simultaneously injected I-Ap and THO were found to be indistinguishable in shape at high coronary flows. At low flows (<1.8 ml. g -1 . min -1 ), THO curves showed an earlier upslope and higher peak than antipyrine, indicating either a diffusional shunt for water or a larger volume of distribution for antipyrine. 14 C-Ap had a slightly faster washout than I-Ap. The differences are partially attributable either to differences in solubility of I-Ap, 14 C-Ap, and THO in erythrocytes or to differences in their volumes of distribution, and partially to diffusional shunting of water.

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.