Kinetics of intravenous radiographic contrast medium injections as used on CT: simulation with time delay differential equations in a basic human cardiovascular multicompartment model

Abstract

Objectives: To develop a multicompartment model of only essential human body components that predicts the contrast medium concentration vs time curve in a chosen compartment after an intravenous injection. Also to show that the model can be used to time adequately contrast-enhanced CT series.

Methods: A system of linked time delay instead of ordinary differential equations described the model and was solved with a Matlab program (Matlab v. 6.5; The Mathworks, Inc., Natick, MA). All the injection and physiological parameters were modified to cope with normal or pathological situations. In vivo time-concentration curves from the literature were recalculated to validate the model.

Results: The recalculated contrast medium time-concentration curves and parameters are given. The results of the statistical analysis of the study findings are expressed as the median prediction error and the median absolute prediction error values for both the time delay and ordinary differential equation systems; these are situated well below the generally accepted maximum 20% limit.

Conclusion: The presented program correctly predicts the time-concentration curve of an intravenous contrast medium injection and, consequently, allows an individually tailored approach of CT examinations with optimised use of the injected contrast medium volume, as long as time delay instead of ordinary differential equations are used.

Advances in knowledge: The presented program offers good preliminary knowledge of the time-contrast medium concentration curve after any intravenous injection, allowing adequate timing of a CT examination, required by the short scan time of present-day scanners. The injected volume of contrast medium can be tailored to the individual patient with no more contrast medium than is strictly needed.

Figure 1

In a one-compartment model, the quantity of a substance at a given point in time equals the difference between the amount of the substance coming in and the amount going out. C_c, concentration of the considered substance in this compartment; V_c, volume of the considered compartment.

Figure 2

Scheme of the implemented multicompartment model. IV, intravenous; LH, left heart; RH, right heart.

Figure 6

Computed data (continuous curve) and Platt et al [16] measured data (+) with standard deviations (150 ml at 4.0 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 3

Computed data (continuous curve) and Bae et al [3] measured data (+) (125 ml at 2.5 ml s⁻¹ of 320 mgI ml⁻¹).

Figure 4

Computed data (continuous curve) and Knollmann and Coakley [14] measured data (+) (160 ml at 3.5 ml s⁻¹ of 370 mgI ml⁻¹).

Figure 5

Computed data (continuous curve) and Fleischmann et al [15] measured data (+) (120 ml at 4.0 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 7

Computed data (continuous curve) and Kim et al [18] measured data (+) (90 ml at 2.0 ml s⁻¹ or at 5.0 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 8

Computed data (continuous curve) and Awai et al [17] measured data (+) (95 ml at 2.7 ml s⁻¹ or at 3.8 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 9

Computed data (continuous curve) and Tatsugami et al [19] measured data (+) (100 ml at 5.0 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 10

Computed data (continuous curve) and Kim et al [18] measured data (+) (90 ml at 5.0 ml s⁻¹ of 300 mgI ml⁻¹).

Figure 11

Computed data (continuous curve) and Tatsugami et al [19] measured data (+) (100 ml at 5.0 ml s⁻¹ of 300 mgI ml⁻¹).