Is the indicator dilution theory really the adequate base of many blood flow measurement techniques?

The indicator dilution theory is the underlying model of many blood flow measurement techniques used daily in hospitals, for instance in cardiac catheterization laboratories. The basic version of this theory applies to a "stationary" flow system with one inlet and one outlet, into which a small amount M of indicator is injected "suddenly" at time t = 0 at the inlet. The quintessence of the theory consists in three equations, which themselves result from some apparently simple assumptions about the considered flow systems. The first equation states that the (constant) flow Q through the system can be calculated by use of the known amount of indicator, M, and of the indicator concentration-time curve c(t) recorded at the outlet. The second one allows the calculation of the "mean transit time" t* of fluid and indicator particles through the system from the curve c(t). The third equation, V = Qt*, yields the system volume V. It is generally believed that these three equations would be absolutely valid if the assumptions of the theory could be perfectly fulfilled. We show, by considering a simple model, that all three equations are actually incorrect for most flow systems when the detector used to record the curve c(t) is of the "trans-illumination" type, as is the case for instance in dye dilution methods and in many angiographic or CT techniques. A further consequence is that t*, which is truly the "center of mass" of the concentration-time curve c(t), does not have the well known property of being the adequate parameter for flow determinations. Many flow measurement techniques thus appear to have no theoretical base.