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Exponential Terms (exponential + term)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

The relationships between half-life (t1/2) and mean residence time (MRT) in the two-compartment open body model

BIOPHARMACEUTICS AND DRUG DISPOSITION, Issue 4 2004
Eyal Sobol
Abstract Rationale. In the one-compartment model following i.v. administration the mean residence time (MRT) of a drug is always greater than its half-life (t1/2). However, following i.v. administration, drug plasma concentration (C) versus time (t) is best described by a two-compartment model or a two exponential equation: C=Ae,,t+Be,,t, where A and B are concentration unit-coefficients and , and , are exponential coefficients. The relationships between t1/2 and MRT in the two-compartment model have not been explored and it is not clear whether in this model too MRT is always greater than t1/2. Methods. In the current paper new equations have been developed that describe the relationships between the terminal t1/2 (or t1/2,) and MRT in the two-compartment model following administration of i.v. bolus, i.v. infusion (zero order input) and oral administration (first order input). Results. A critical value (CV) equals to the quotient of (1,ln2) and (1,,/,) (CV=(1,ln2)/(1,,/,)=0.307/(1,,/,)) has been derived and was compared with the fraction (f1) of drug elimination or AUC (AUC-area under C vs t curve) associated with the first exponential term of the two-compartment equation (f1=A/,/AUC). Following i.v. bolus, CV ranges between a minimal value of 0.307 (1,ln2) and infinity. As long as f1t1/2 and vice versa, and when f1=CV, then MRT=t1/2. Following i.v. infusion and oral administration the denominator of the CV equation does not change but its numerator increases to (0.307+,T/2) (T-infusion duration) and (0.307+,/ka) (ka-absorption rate constant), respectively. Examples of various drugs are provided. Conclusions. For every drug that after i.v. bolus shows two-compartment disposition kinetics the following conclusions can be drawn (a) When f1<0.307, then f1t1/2. (b) When ,/,>ln2, then CV>1>f1 and thus, MRT>t1/2. (c) When ln2>,/,>(ln4,1), then 1>CV>0.5 and thus, in order for t1/2>MRT, f1 has to be greater than its complementary fraction f2 (f1>f2). (d) When ,/,<(ln4,1), it is possible that t1/2>MRT even when f2>f1, as long as f1>CV. (e) As , gets closer to ,, CV approaches its maximal value (infinity) and therefore, the chances of MRT>t1/2 are growing. (f) As , becomes smaller compared with ,, ,/, approaches zero, the denominator approaches unity and consequently, CV gets its minimal value and thus, the chances of t1/2>MRT are growing. (g) Following zero and first order input MRT increases compared with i.v. bolus and so does CV and thus, the chances of MRT>t1/2 are growing. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Interpretation of Spring Recession Curves

GROUND WATER, Issue 5 2002
H. Amit
Recession curves contain information on storage properties and different types of media such as porous, fractured, cracked lithologies and karst. Recession curve analysis provides a function that quantitatively describes the temporal discharge decay and expresses the drained volume between specific time limits (Hall 1968). This analysis also allows estimating the hydrological significance of the discharge function parameters and the hydrological properties of the aquifer. In this study, we analyze data from perennial springs in the Judean Mountains and from others in the Galilee Mountains, northern Israel. All the springs drain perched carbonate aquifers. Eight of the studied springs discharge from a karst dolomite sequence, whereas one flows out from a fractured, slumped block of chalk. We show that all the recession curves can be well fitted by a function that consists of two exponential terms with exponential coefficients ,1 and ,2. These coefficients are approximately constant for each spring, reflecting the hydraulic conductivity of different media through which the ground water flows to the spring. The highest coefficient represents the fast flow, probably through cracks, or quickflow, whereas the lower one reflects the slow flow through the porous medium, or baseflow. The comparison of recession curves from different springs and different years leads to the conclusion that the main factors that affect the recession curve exponential coefficients are the aquifer lithology and the geometry of the water conduits therein. In normal years of rainy winter and dry summer, ,1 is constant in time. However, when the dry period is longer than usual because of a dry winter, ,1 slightly decreases with time. [source]

Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulation

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2009
A. Mesgouez
Abstract The authors propose a semi-analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Improved exponential estimates for neutral systems

ASIAN JOURNAL OF CONTROL, Issue 3 2009
Zhan Shu
Abstract Improved exponential estimates and a new sufficient condition for the exponential stability of neutral type time-delay systems are established in terms of linear matrix inequalities (LMIs). A new Lyapunov-Krasovskii functional candidate with appropriately constructed exponential terms is introduced to prove the exponential stability and to reduce the conservatism. For the uncertain case, a corresponding condition for the robust exponential stability is also given. It is shown by numerical examples that the proposed conditions are less conservative than existing results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]