Tracer washout

The outflow concentration c(L,t) of the above model describes tracer washout curves from organs that have a tree-like network structure, and it is given by an analytic form reported in [328]. 

Beard, D. and Bassingthwaighte, J., Power-law kinetics of tracer washout from physiological systems, Annals of Biomedical Engineering, Vol. 26, 1998, pp. 775-779. 

A large change in the conductance of the luminal mucosal cell membrane, PS has only a modest effect on tracer washout of tracer preloaded into the intestinal lumen. Fig. 4b. The curve rises more rapidly, but the washout rate is only slightly greater when the conductance is raised 100-fold. 

Figure 5 shows tracer washout when a constant infusion of tracer is made into the plasma (Fig. 5a) or intestinal lumen (Fig. 5b). Flow through the intestinal lumen is 0.05 ml g- min membrane conductances, volumes, and plasma flow are identical to those used for Fig. 4a. The concentration of tracer in the plasma outflow rises more quickly in either case due to its much greater flow. The much higher plasma flow (20-fold greater than intestinal flow) results in nearly equal steady-state concentrations when the tracer is injected into the plasma and in a lower concentration in the plasma than in the intestine when the tracer enters through the intestine.

Negative Step Changes and the Washout Function. Suppose that an inert tracer has been fed to a CSTR for an extended period of time, giving C, = Cout = Co for r < 0. At time r = 0, the tracer supply is suddenly stopped so that = 0 for r > 0. Equation (14.2) governs the transient response of the system. For t > 0,... 

Tracer molecules originally in the system at time t = 0 gradually wash out. The exponential form of Equation (15.1) is specific to a CSTR, but the concept of washout applies to any flow system. Consider some time t > 0 when the fraction of molecules remaining in the system is W(t) = C ut(0ICo- These molecules must necessarily have entered the reactor before time t = 0 since no tracer was fed... 

Washout experiments can be used to measure the residence time distribution in continuous-flow systems. A good step change must be made at the reactor inlet. The concentration of tracer molecules leaving the system must be accurately measured at the outlet. If the tracer has a background concentration, it is subtracted from the experimental measurements. The flow properties of the tracer molecules must be similar to those of the reactant molecules. It is usually possible to meet these requirements in practice. The major theoretical requirement is that the inlet and outlet streams have unidirectional flows so that molecules that once enter the system stay in until they exit, never to return. Systems with unidirectional inlet and outlet streams are closed in the sense of the axial dispersion model i.e., Di = D ut = 0- See Sections 9.3.1 and 15.2.2. Most systems of chemical engineering importance are closed to a reasonable approximation. 

Thus, measurement of one readily gives the other. The washout experiment is generally preferred since IF(oo) = 0 will be known a priori but F(oo) = Cq must usually be measured. The positive step change will also be subject to possible changes in Co during the course of the experiment. However, the positive step change experiment requires a smaller amount of tracer since the experiment will be terminated before the outlet concentration fully reaches Cq. 

The Single CSTR. The washout function for a CSTR is found from its response to a negative step change in tracer concentration from Equation (15.1) ... 

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

A step input of tracer may itself be one of two types a step increase fiom one steady-state value to another (cAin), or a step decrease. Usually, as illustrated in Figure 19.4, tiie step increase is fiom a zoo value, and, as illustrated in Figure 19.5, the step decrease is to a zero value in the latter case it is called a washout. Figures 19.4 and. 5 also show responses (cA out) to a step increase and to a washout-step decrease. In Figure 19.4, note that cAout cA in as 1 °°> similarly in Figure 19.5, cAout — 0. 

A tracer study mas7 use a step increase followed at a later time by a step decrease the transient responses in the two cases are then checked far consistency. When considered separately, the washout technique has advantages less tracer is required, and it avoids having to maintain a steady-state value of cA in for a lengthy period. 

Figure 19.5 Step-decrease (washout) input of tracer (a) and response (b)...

A tracer experiment was conducted in a certain vessel. The following data were obtained from a washout experiment ... 

In practice, it may be more simple to evaluate E(t) either through the washout function or the cumulative RTD F(t) by making a step change in inlet tracer concentration and measuring outlet concentration by the mixing cup average. Such a procedure is advocated by Nauman [4]. 

Several F-labeled fatty acid derivatives have been successfully prepared and evaluated as potential FAO assessing tracers [19-24]. Methyl-branched-chain (w- F-fluorofatty acids, such as 3-methyl-(3-MFHA) and 5-methyl-17-[ F]fluoro-heptadecanoic acid (5-MFHA), have been reported [23]. In a comparative study, it was found that rw-[ F]fluoropalmitic acid (FPA) exhibits the highest myocardial uptake, followed by 5-MFHA and 3-MFHA. FPA possesses the fastest myocardial washout rate, and 3-MFHA the slowest. In lipid analysis studies, 5-MFHA... 

Be should be a useful tracer in detailed studies of atmospheric transport and washout. It is not produced in significant quantities by nuclear tests, and therefore variations in its activity from year to year should reflect variations in atmospheric processes. Several investigators have measured 7Be at different altitudes and latitudes. As the latitude, altitude, and time variations become better known, it should be possible to calculate precisely the rates of vertical and meridional transport and the rates of deposition at the earth s surface. 

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