Expulsion rate

Expulsion rates of IUDs - an example of a contingency table... 

The percentage figures included in the table are column percentages. Thus, in the first column, 86.6 per cent of women using the control device did not expel the device and 13.4 per cent did. These indicate an apparentiy lower expulsion rate with the new test design. 

How strong is the contrast between the two outcomes If one sample indicated an expulsion rate only very marginally greater than the other, we would have to accept that such a small difference could be due to sampling error alone. However, a large difference would be difficult to explain away on this basis. 

The proportion of expulsions in one of the groups - literature reports suggest an expulsion rate of about 15 per cent for the control device. 

Newell, S. Y. (2001b). Spore-expulsion rates and extents of blade occupation by ascomycetes of the smooth cordgrass standing decay system. Botanica Marina, 44, 277—85. 

These estimated specific discharges for the buoyancy-driven migration of oil through a carrier rock are about 5 orders of magnitude greater than the estimated expulsion rates for oil from source rocks as given in Chapter 3. 

Using a system of rate equations cmistructed from the above mechanism, Aniansson and Wall showed that in a relaxation experiment close to equilibrium, in the linear regime, the relaxation is determined by two relaxation time constants. The first time constant characterizes the fast relaxation associated with a readjustment of the unimer concentration, without a change in the number density of micelles. As shown by Aniansson and Wall, this contribution depends on the expulsion rate constant, the width of the distribution of the micellar population, a, and the fraction of unimers, X. 

Thus, this simple result suggests that the rate of unimer exchange is governed by the expulsion rate constant. We will see later that this approximation is indeed a good assumption when we compare with the proposed models for unimeric expul-sion/insertion. 

Given the central role of the expulsion rate constant for micellar stability, formation, and dissociation, it is essential to determine the physical governing factors and functional form. Aniansson and Wall based their calculations [54] on a general diffusion in an external potential. In this approach, the diffusion coefficient, D(r) is dependent on the position, r, due to the potential V(r). In a sphero-symmetric system, we can imagine that the diffusion of a unimer only depends on the distance, r, from the origin and this problem can be summarized in a Einstein-Smoluchowski type equation ... 

The theory proposed by Halperin and Alexander (H-A theory) [60] is based on the structural scaling description of polymeric micelles outlined in Sect. 2.1.2. Using a combination of scaling theory and Kramers rate theory for diffusirai in an external potential [61], the expulsion rate for both crew-cut and star-like spherical micelles was derived. Moreover, Halperin and Alexander discussed different scenarios of chain exchange between micelles. 

Hence, the most important process for the equilibrium kinetics is the unimer exchange mechanism which, as expected from the Aniansson-WaU scenario, is mainly governed by the expulsion rate constant. In the model of Halperin and Alexander this release of a single unimer from the micelle is pictured to go through two stages ... 

The expulsion rate can be obtained using k = exp(—F )vdiff sion/ c —... 

Equivalently, the same scenario can be expressed mathematically in terms of the expulsion rate constant, kF, which gives ... 

The rst double-blind, randomized trial was conducted in 1987 by Mukamel et al. on 40 patients with acute renal colic. In the Rowatinex group, there was a sign candy higher expulsion rate of stones >3 mm in diameter in comparison to the placebo (61% and 28%, respectively). There was also a higher overall success rate in terms of spontaneous stone expulsion and/or disappearance of ureteral dilatation in the treatment group compared to placebo (78%-52%), but the difference was not statistically sign cant. 

FIGURE 6.1 Energy diagrams for bimolecular substimtion (a) and (b) involve an intermediate with, respectively, nucleophilic attack and leaving group expulsion rate limiting (c) represents a conceited mechanism with a single transition state. 

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