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. 1966 Apr;18(4):398-415.
doi: 10.1161/01.res.18.4.398.

Applications of the lagged normal density curve as a model for arterial dilution curves

J B Bassingthwaighte, F H Ackerman, E H Wood

Applications of the lagged normal density curve as a model for arterial dilution curves

J B Bassingthwaighte et al. Circ Res. 1966 Apr.
No abstract available

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Figures

FIGURE 1
FIGURE 1
Model for indicator dilution curves. Left panel: normal density curve. Middle panel single exponential. Right panel: lagged normal density curve.
FIGURE 2
FIGURE 2
Responses of the sampling systevis to step changes in dye concentration. During sampling at 10 ml/min, the undyed blood at the tip of the sampling system was suddenly replaced by blood containing indocyanine green (10 mg/liter). The response of the system used at the femoral artery was slower than that at the dorsalis pedis artery. The difference in mean transit times was about 0.3 second.
FIGURE 3
FIGURE 3
Calibration of two densitometers for indocyanine green in whole blood. Calibration was done on blood containing no background dye (lines passing through the origin) and on blood having background dye levels of 2.5 or 5.0 mg/liter (lines intercepting the abscissa at 2.5 and 5.0). The increase in calibration constant (decrease in slope) with higher background dye levels indicates a loss in sensitivity.
FIGURE 4
FIGURE 4
The lagged normal density curve fitted to curves recorded after injection of dye into the superior vena cava. Each panel shows the curves recorded (open circles) from the femoral artery and the dorsalis pedis artery of normal men. The parameters, σ, τ, and tc of the model (solid line) fitting each curve, and the coefficient of variation of the fit are given above the curves.
FIGURE 5
FIGURE 5
Lagged normal density curves fitted to curves recorded after injection of dye into the thoracic aorta.
FIGURE 6
FIGURE 6
Curves recorded after two injections in the aorta, a few seconds apart (solid line), approximated by sum of two lagged normal density curves. ΔTinj = time between the two injections. R = ratio of volume of second injection to volume of first injection.
FIGURE 7
FIGURE 7
Parameters of the model simulating recorded dye curves. Left and center panels: the linear relationships (see table 1) between σ or τ and the mean transit time show that the temporal dispersion of indicator is inversely proportional to the average velocity of the blood between the injection and sampling sites. Right panel the correlation of σ and τ indicates that the shape of the curves is fairly constant. In the left and middle panels the points for curves following SVC injection (open triangles for curves sampled at the femoral arteries, closed triangles for those from the dorsalis pedis arteries) are higher than those for aortic injections (plus signs for curves sampled at the femoral arteries, X's for those from the dorsalis pedis arteries) but the slopes of the regression equations (table 1) for the two groups are not significantly different. The positive intercepts indicate that dispersion in the central circulation is greater than in a peripheral artery. In these and subsequent graphs the length of the vertical line through the average point is two standard deviations. The correlation coefficient is r.
FIGURE 8
FIGURE 8
Nonparametric measures of the dispersion. ta (left upper panel), (t̄−ta) (right upper panel), and π21/2 (square root of the variance) (left lower panel) are all linearly related to t̄. The spread, t̄− ta, and π21/2 are closely related to each other, as expected (right lower panel). These linear relationships indicate that temporal disjjersion is related linearly to the lime taken to travel a given distance and suggest that the spatial dispersion is unrelated to the flow rate through the limb. (Symbols as in fig. 7; for regression equations, see table 1.)
FIGURE 9
FIGURE 9
Interrelationships between parameters of model and characteristics of recorded dye curves estimating the dispersion.
FIGURE 10
FIGURE 10
Relationships between recorded curves and the model. Left upper panel: the appearance time for the models fitted to the curves ta Model) were less than the recorded ones, ta, indicating that the earliest recognized indicator had a lower velocity than the equation implied. Right upper panel: the values of T were only slightly smaller than the time constants, TD, showing that a had little effect on the decay slope. Left lower panel: the mean transit times of the models, r + tc, were 1% larger than the first moments, t̄. Right lower panel: The square roots of the second moments of modeh, (σ2 + τ2)½, were almost 2% larger than those of the recorded curves, π2½.
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References

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