The validity of the sigmoid Emax model and efficiency concept in diuretic studies

Acute Effects of High-Dose Furosemide on Residual Renal Function in CAPD Patients

♦ Background

High doses of furosemide can increase urine volume in chronic peritoneal dialysis (CAPD) patients. However, no information is available about effects on urinary solute excretion in relation to residual glomerular filtration rate (GFR), urinary furosemide excretion, and peritoneal solute kinetics.

♦ Methods

Diuretic response and the effect on peritoneal fluid and solute transport parameters were investigated in 7 stable CAPD patients with residual renal function (median urine volume 350 mL/24 hours, range 140–1900 mL/24 hours). Comparisons were made during two clearance periods of 24 hours: one without (P1) and one during 2 g furosemide (P2).

♦ Results

The median increase in urine volume was 400 mL (range 270 – 910 mL, p < 0.02) and the increase in sodium excretion was 54 mmol (range 25 –118 mmol, p < 0.02). No change in GFR was found between P1 (2.4 mL/minute, range 0.6 – 5.7 mL/min) and P2 (2.0 mL/min, range 1.0 – 4.8 mL/min). An increase in fractional clearance was found for volume, sodium, potassium, and osmolality ( p < 0.02). No change was found in the fractional clearance of urea and electrolyte-free water. Furosemide excretion in urine was 8.7 mg/24 hours (range 2.1 – 38 mg/24 hours) and in dialysate 4.9 mg/24 hours (range 1.9 – 7.8 mg/24 hours). Plasma furosemide concentration was 29.5 mg/L (range 6.2 – 43.9 mg/L). A positive correlation was found between residual GFR and total urine furosemide excretion ( r=0.93, p < 0.005). Efficiency, expressed as the increase in fractional sodium clearance (percent) per milligram of furosemide excreted per 24 hours, was 1.2%/mg (range 0.3%–11.3%/mg).

♦ Conclusion

High-dose furosemide is effective in CAPD patients in increasing urine volume and electrolyte excretion without affecting urea and creatinine clearance. In CAPD patients, the individual response to an identical high dose of furosemide is dependent on the magnitude of residual GFR.

The efficiency concept in pharmacodynamics

The classic approach to describe the pharmacological response to a drug is to analyse its concentration-effect relationship, using a variety of possible models such as maximum effect (Emax) models or sigmoid Emax models. The aim of this review is to discuss an alternative way of describing the pharmacological effect in terms of effect per unit of drug concentration, instead of simple effect. This variable is called efficiency, analogous with concepts used in other fields. The pharmacodynamic model for efficiency is derived from the sigmoid Emax model and is dependent on the same parameters. Since the sigmoid Emax model incorporates 'the law of diminishing returns', requiring ever higher concentrations to increase the effect by a given percentage, efficiency is bound to decrease with increasing concentrations. However, as a mathematical consequence of its derivation from the sigmoid Emax model, efficiency also has a maximum value, which can be expressed as a function of the slope factor (s) and drug concentration associated with half the maximum effect (C50), provided that the slope factor is greater than 1. The efficiency concept is potentially applicable to all drugs and particularly useful for those that follow concentration-effect relationships according to Emax or sigmoid Emax models. Most experience has been obtained with loop diuretics, especially with furosemide (frusemide). Slow administration of furosemide, leading to slow excretion of the drug, has been shown, in many studies, to significantly increase the total diuretic effect per amount of drug recovered in urine. In this review, some examples of the applicability of the efficiency concept to other drugs, such as antibacterials, opioids and antineoplastics, are discussed. In addition to pharmacodynamically varying efficiency, other saturable processes, such as the formation of active metabolites and saturable transport, may form a basis for the application of the efficiency concept. The efficiency of a drug dosage may also be influenced by tolerance and counter-regulation produced by the drug. All these factors contribute to schedule dependency. It is concluded that the shape of the time course of drug presentation to its site of action is an independent determinant of overall response. The possibility of adjusting the drug input profile to maximise therapeutic effect per dose and to separate cumulated therapeutic from cumulated adverse effects should be considered in designing administration schedules and in drug development.

The influence of food intake on the effect of two controlled release formulations of furosemide

Differences in the urinary excretion rate of furosemide may explain discrepancies observed between the bioavailability and the total diuretic effect of different formulations of this drug. Furosemide was given at a dose of 60 mg as two oral controlled release (CR) formulations (FR and LR), with and without breakfast, in a randomized, four-treatment, four-period, crossover design to 28 healthy volunteers. Urinary volume, and contents of furosemide and sodium, were measured in samples taken over 24 h. The extent and rate of absorption of furosemide from FR were decreased after breakfast as compared to fasting: the mean (SD) of total furosemide excreted decreased from 11.38 (3.12) to 7.73 (1.67) mg, p < 0.0001, and the median (range) mean residence time increased from 6.3 (4.1-9.3) to 9.5 (5.9-11.8) h, p < 0.001. On the other hand, the extent of absorption of LR was increased after breakfast, from 8.04 (3.32) to 9.45 (1.83) mg, p < 0.05, without a significant change in MRT. FR had a higher extent and rate of absorption than LR during fasting, but its extent of absorption was lower than that of LR in the postprandial state. Interestingly, the total fraction of furosemide absorbed, as estimated from total furosemide excretion, was not correlated with the total diuresis (r2 = 0.079) and the differences in drug response compared among the four periods were much smaller than would be expected from the differences in amount absorbed. This discrepancy may be explained by differences in urinary excretion rate of furosemide and, related to this, differences in efficiency profiles between the four treatments. Therefore, the urinary excretion profile of a formulation of furosemide may be more important for the cumulated drug effect than the amount absorbed.

Sensitivity of residual nephrons to high dose furosemide described by diuretic efficiency

Ten haemodialysis (HD) patients with a median residual creatinine clearance (CLCR) of 1.9 ml.min-1 x 1.73 m-2 (range 0.6-5.3) were treated with oral furosemide (F) 2.0 g. Overall-efficiency (O-E, daily sodium excretion/total urinary F) and total-efficiency (delta-E, increase in daily sodium excretion/total urinary F) were measured on the last 24 hours of each interdialysis interval. In addition, O-E was measured during the complete interdialysis interval in 10 HD patients with a median CLCR of 5.6 ml.min-1 x 1.73 m-2 (range 0.7-6.8) treated for 1 year with a fixed oral dose of F between 250-1000 mg (median 625 mg). In the short study the median O-E was 10.6 mmol.mg-1 (range 1.9-22.0) and delta-E 6.2 mmol.mg-1 (range 1.3-11.2). The fractional excretion of sodium FENa was significantly increased from 9.6% (range 4.1-22.9) to 27% (range 14.6-56.2) during F treatment. A positive correlation was found between the basal FENa and delta-E. In the long-term study median O-E was 6.4 mmol.mg-1. O-E and FENa showed no change over time although median RCC decreased from 5.6 to 1.9 ml.min-1 x 1.73 m-2 and median F excretion from 11.8 to 7.5 mg per day. It can be concluded that diuretic efficiency in haemodialysis patients is dependent on FENa and the state of hydration during the interdialysis interval.

Discrepancy between bioavailability as estimated from urinary recovery of frusemide and total diuretic effect

1. Frusemide was given at a dose of 60 mg as two oral controlled release (CR) formulations and as plain tablets in a randomised, balanced, three way cross over design to 26 healthy volunteers. Urinary volume, and contents of frusemide, sodium, chloride and potassium were measured in samples taken over 24 h. 2. There was a marked difference between the CR formulations on one hand and the plain tablets on the other, in excretion of frusemide and diuresis vs time. The total diuretic/saluretic effect was only marginally lower (19 and 28% respectively, P less than 0.05) after CR compared with plain tablets although the fraction absorbed was markedly decreased (39 and 51% lower, respectively, P less than 0.05), estimated as urinary recovery of frusemide. The total diuresis of the two CR formulations did not differ although the urinary recovery was significantly different (P less than 0.05). 3. The diuretic effect vs frusemide excretion rate showed minimal counter-clockwise hysteresis after plain tablets while the CR formulations produced clockwise hysteresis indicating tolerance. 4. In agreement with the concept of efficiency, the higher diuretic/saluretic effect per amount of excreted frusemide may be a consequence of the slower output of frusemide in urine with the CR formulations compared with plain tablets. The major part of the pharmacological effect was produced with a higher efficiency after CR compared with plain tablets. It should be noted that the pharmacokinetics of a drug and its pharmacodynamic potency independently determine the total response.(ABSTRACT TRUNCATED AT 250 WORDS)