Indicator-dilution theory

Indicator-dilution theory (Axel 1980 Rosen et al. 1989) leads to the formula for calculation of the relative regional cerebral blood volume (rrCBV)... 

Meier, P. and K. Zieler, On the theory of the indicator-dilution method for measurement of blood flow and volume. J Appl Physiol, 1954. 6 p. 731-44. 

Gonzales-Fernandez, J. M. Theory of the Measurement of the Dispersion of an Indicator in Indicator-Dilution Studies. Circulation Research 10 (1962) 409. 

Sherman, H. On the Theory of Indicator-Dilution Methods Under Varying Blood-Flow Conditions. Bull. Math. Biphysics 22 (1960) 417. 

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60]. 

It will be observed that entropies of dilution (as indicated by i) are highly variable from one system to another. This is contrary to the theory developed from consideration of lattice arrangements, according to which pi should be approximately 1/2 and nearly independent of the system. For polystyrene in methyl ethyl ketone, the entropy of dilution is nearly zero i.e., this solvent is a poor one not because of an adverse energy of interaction but because of the low entropy. First neighbor interactions apparently contribute to the entropy as well as to the energy, a point which was emphasized in Chapter XII. It will be noted also that cyclic solvents almost without exception are more favorable from the standpoint of the entropy than acyclic ones. 

Determination of Effective Functionalities from Gelation Data. Gelation data from reactions at various dilutions are sometimes used to determine chemical functionalities of reactants(30,31). Such a procedure should be viewed with caution as it assumes that the functional form of the dependence of ring-forming parameter upon dilution which is predicted by theory is that obtained in practice, and, as Figure 6 indicates, this assumption is not always justified. 

A vast amount of data based on dielectric constant measurements of substances in dilute solution in nonpolar solvents indicate that the theory is correct, but it looses validity and breaks down completely in the case of strongly polar media. It is interesting to notice that such a breakdown can be shown by the concept of the Curie point, introduced in connection with studies of magnetism but directly applicable to the case of dielectric constants. The dielectric constant can be related to the molar polarizability P and the molar concentration c by q. (21) and the value of P itself is given by Eq. (22). It is obvious that P increases as T dimin-... 

Aspler and Gray (65.69) used gas chromatography and static methods at 25 C to measure the activity of water vapor over concentrated solutions of HPC. Their results indicated that the entropy of mixing in dilute solutions is mven by the Flory-Huggins theory and by Flory s lattice theory for roddike molecules at very nigh concentrations. 

Since the dilute solution theory is considered as the basis for the indicated treatment, it will receive considerable attention. Influences of several parameters as molecular weight, molecular weight distribution, thermodynamic and kinetic chain stiffness, intramolecular hydrodynamic inter-action, optical properties of the chain and solvent power will be considered. 

In this connection, a procedure is of interest, which has been followed in the treatment of dilute polymer solutions. In this theory a convective coordinate system is used which moves with the chain molecule under consideration. In this way, the indicated difficulty is overcome when a certain simplified model is used for the chain molecule. The set of coordinates of this model, as related to the convective coordinate system, is then transformed into a set of normal coordinates which behave independently. For a more detailed treatment and discussion of this matter the reader is referred to Chapters 3 and 5 of this review. 

According to modem theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not indicate complete dissociation. For NaCl, the depression is not quite twice the amount calculated on the basis of the number of moles of NaCl added. In the solution, the ions attract one another to some extent therefore they do not behave as completely independent particles, as they would if they were nonelectrolytes. From the colligative properties, therefore, we can compute only the "apparent degree of dissociation" of a strong electrolyte in solution. 

The two mass action equilibria previously indicated have been used in conjunction with a modified form of the Shedlovsky conductance function to analyze the data in each of the cases listed in Table I. Where the data were precise enough, both K2 and K were calculated. As mentioned previously, the K s so evaluated are practically the same as those obtained for ion pairing in solutions of electrolytes in ammonia and amines. This is encouraging since it implies a fairly normal behavior (in the electrolyte sense) for dilute solutions of metals. Further support of the proposed mass action equilibria can be found in the conductance measurements of sodium in NH8 solutions with added salt. Bems, Lepoutre, Bockelman, and Patterson (4) assumed an additional equilibrium between sodium and chloride ions, associated to form NaCl, to compute the concentration of ionic species, monomers, and dimers when the common ion electrolyte is added. Calculated concentrations of conducting species are employed in the Onsager-Kim extension of the conductance theory for low-field conductance of a mixture of ions. Values of [Na]totai ranging from 5 X 10 4 to 6 X 10 2 and of the ratio of NaCl to [Na]totai ranging from zero to 28.5 are included in the calculations. 

---