Clearance equation

Digoxin is not extensively metabolized in humans almost two thirds is excreted unchanged by the kidneys. Its renal clearance is proportional to creatinine clearance. Equations and nomograms are available for adjusting digoxin dosage in patients with renal impairment. 

In Chapter 1/ we pointed out that the creatinine clearance equation... 

Liquid head loss through downcomer clearance (Equation 14.14),... 

By substituting this equation for E, the clearance equation becomes... 

This equation is the mathematical expression of the definition of a half-life, specifically, the time required for plasma concentrations to be divided by 2 after reaching pseudoequilibrium as X3 is a hybrid parameter related to Varea (the volume of distribution associated with the terminal phase) and plasma clearance. Equation (2.3) can be re-written in a more mechanistically useful way as follows ... 

The value of the constant, c, is approximated for this study by 160 (mm)(W/m K.) However, references are available to help calculate it for other conditions [1-3.] Also, a more complex relationship between the heat transfer coefficient and the clearance (equation 5) could be developed if enough data are available to determine it. 

For close-clearance impellers the correlations in Figure 35b apply to installations without scrapers. If scrapers are used, the values given by the equations should be multiphed by a factor of 1.3. 

The clinical performance of a hemodialy2er is usually described in terms of clearance, a term having its roots in renal physiology, which is defined as the rate of solute removal divided by the inlet flow concentration as shown in equation 7, where Cl is clearance in ml,/min and all other terms are as defined previously except that, in deference to convention, flow rates are now expressed in minutes rather than seconds and feed side (/) is now synonymous with blood flow on the luminal side. 

Note that the numerator in each of the ratios in equation 7 represents the rate of solute removal from the patient. By mass balance, clearance is related to mass-transfer coefficient Kq as defined eadier in equations 3, 4, and 5, and where each of the three expressions equal rate of mass removal in g/s. 

For consistency, clearance here is expressed in cm /s although the more common clinical units, and those used later in this chapter, are ml,/min. Combination and rearrangement of equations 6—8 allows clearance to be estimated from mass-transfer coefficient and vice versa the conditions of countercurrent flow with no dialysate recycling are shown below. 

Fig. 6. Solute transport in hemodialysis. Clearance vs solute mol wt for dialy2ers prepared from the two different membranes illustrated in Figure 5. Numbers next to points represent in min /cm calculated from equations 10 and 5. Data is in vitro at 37°C with saline as the perfusion fluid. Lumen flow, dialysate flow, and transmembrane pressure were 200 ml,/min, 500 mL/min, and 13.3 kPa (100 mm Hg) area = 1.6. Inulin clearance of the SPAN...

A 3.5 h treatment of a 70 kg patient (V = 40.6 liters) with a urea clearance of 200 ml,/min should result in a 64% reduction in urea concentration or a value of 0.36 for the ratio d (f this parameter almost always falls between 0.30 and 0.45. The increase in urea concentration between hemodialysis treatments is obtained from equation 13, again assuming a constant V, where (f is the urea concentration in the patient s blood at the end of the hemodialysis, and d the concentration at time t during the intradialytic interval. 

Earlier in the chapter, when the compression cycle was described, a portion of the indicator. Path 3-4, was referred to as the expansion portion of the cycle. The gas trapped in the clearance area expands and partly refills the cylinder taking away some of the capacity. The following equation reflects the expansion effect on capacity and is referred to as the theoretical volumetric efficiency Ev,. 

The second reason for modification of the displaced volume is that in real world application, the cylinder will not achieve the volumetric performance predicted by Equation 3.4. It is modified, therefore, to include empirical data. The equation used here is the one recommended by the Compressed Air and Gas Institute [1], but it is somewhat arbitrary as there is no universal equation. Practically speaking, however, there is enough flexibility in guidelines for the equation to produce reasonable results. The 1.00 in the theoretical equation is replaced with. 97 to reflect that even with zero clearance the cylinder will not fill perfectly. Term L is added at the end to allow for gas slippage past the piston rings in the various types of construction. If, in the course of making an estimate, a specific value is desired, use, 03 for lubricated compressors and. 07 for nonlubricated machines. These are approximations, and the exact value may vary by as much as an additional. 02 to. 03... 

It can be seen from Equation 11-7 that as R is increased, and as clearance is incre ised, volumetric efficiency is reduced. The relationship of volumetric efficiency and clearance is important, because it allows variable clearances (both fixed volume and adjustable volume pockets) to be used to control capacity and obtain the maximum use of available driver horsepower. 

Cheng-Prasoff relationship, 65-66, 214 Cholecystokinin receptor antagonists, 80 Cimetidine, 9-10 Clark, Alfred J., 3, 3f, 12, 41 Clark plot, 114 Clearance, 165—166 Clinical pharmacokinetics, 165 Cocaine, 149, 150f Competitive antagonism description of, 114 Gaddum equation for, 101-102, 113,... 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

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