Numerical deconvolution by least squares: Use of polynomials to represent the input function

A new method for numerical deconvolution is described, for use in calculating drug input rates. The method is based on the least-squares criterion and approximates the input rate by a polynomial function. Ill-conditioning of the normal equations is avoided by using orthogonal functions. The use of the method is illustrated by means of examples, using simulated data.     

Numerical deconvolution using system identification methods

A deconvolution method is presented for use in pharmacokinetic applications involving continuous models and small samples of discrete observations. The method is based on the continuous-time counterpart of discrete-time least squares system identification, well established in control engineering. The same technique, requiring only the solution of a linear regression problem, is used both in system identification and input identification steps. The deconvolution requires no a prioriinformation, since the proposed procedure performs system identification (including optimal selection of model order), selects the form of the input function and calculates its parametric representation and its values at specified time points.On leave from Eötvös Lorand University, Budapest, Hungary.     

A note on appropriate constraints on the initial input response when applying deconvolution

When deconvolution is employed to estimate cumulative input profiles, nonzero initial values may result unless certain constraints are imposed on the function used to approximate the input response c(t).It is shown that the initial value of the response to a nonimpulse input is zero, i.e., c(t₀)=0,where t₀ is the input lag time. If, in addition, the initial value of the impulse response is zero, i.e.,c (0)=0,then c(t₀)=0.Therefore, it is appropriate to impose the constraint c(t₀)=0in general and c(t₀)=0when c (0)=0if c(t)is the response to a nonimpulse input. The use of such constraints is demonstrated in an example where the cumulative in vivodissolution profile is estimated by deconvolution.     

Linear systems analysis in pharmacokinetics

The application of certain aspects of linear systems analysis to pharmacokinetic-problems is described. Topics covered include the evaluation of in vivodissolution rates, absorption rates, and metabolic rates, and the use of pharmacological data. Relevant numerical procedures are also discussed.This work was partly supported by a Commonwealth Scholarship from the British Council.     

Comparative bioavailability: A new type ofin vitro-in vivo correlation exemplified by prednisone

The average time to reach half-maximal plasma concentration of prednisolone and the average plasma concentrations of prednisolone at 0.5 and 1 hr obtained from three crossover bioavailability studies, involving testing of commercially available 5-mg prednisone tablets, were highly correlated (r0.88) with parameters derived from in vitrotablet dissolution rates performed in the spin filter apparatus of Shah. The in vitroparameters were the times to dissolve 16% or 50% of the labeled amount of prednisone or the percent of the labeled amount of prednisone dissolved in 20 min in water at 37C. Such correlations may be useful in the setting of in vitrodissolution rate specifications for commencal prednisone tablets.Supported by Contract FDA 69-22, Food and Drug Administration, Washington, D.C., and in part by Public Health Service Grant 5-P11-GM15559.     

Multiple Oral Administration of a Ketoprofen–Dextran Ester Prodrug in Pigs: Assessment of Gastrointestinal Unavailability by Deconvolution

Deconvolution has been applied to estimate the in vivo dissolution/ release process of ketoprofen from a ketoprofen–dextran ester pro-drug in pigs. The prodrug was given to three pigs at intervals of 12 hr and in seven doses corresponding to 4 mg ketoprofen/kg body weight. Frequent blood sampling was carried out at the first, third, and seventh intervals. Plasma steady-state concentrations of ketoprofen following the prodrug administration were between 2 and 4 µg/ml. The reference consisted of a single p.o. dose of parent ketoprofen (4 mg/kg body weight). For each pig the response following the multiple dosing was deconvolved with the reference response using an algebraic deconvolution procedure adopted from the literature. The obtained cumulated in vivo dissolution/release profiles revealed similar release rates for the three pigs and similar extents of release (59, 70, and 65%). The mean in vivo dissolution/release times (MDT) were calculated to be 5.4, 6.1, and 5.7 hr, respectively. In conclusion, following administration of the dextran prodrug the plasma concentration curves and the dissolution/release profiles are uniform, with small interindividual variations.     

Fat Emulsions Based on Structured Lipids (1,3-specific triglycerides): An Investigation of the in Vivo Fate

Purpose. Structured lipids (1,3-specific triglycerides) are new chemical entities made by enzymatic transesterification of the fatty acids in the 1,3 positions of the triglyceride. The purpose of this study is to characterize structured lipids with either short chain fatty acids or medium chain fatty acids in the 1,3 positions with regard to their hydrophobicity, and investigate the in vivo fate in order to evaluate the potential of structured lipids as core material in fat emulsions used as parenteral drug delivery system. Methods. The lipids were characterized by employing reversed phase high performance liquid chromatography. The biodistribution of radio-actively labeled emulsions was studied in rats. Results. By employing high performance liquid chromatography a rank order of the hydrophobicities of the lipids could be given, with the triglycerides containing long chain fatty acids being the most hydrophobic and the structured lipid with short chain fatty acids in the 1,3 positions the least. When formulated as fat emulsions, the emulsion based on structured lipids with short fatty acids in the 1,3 positions was removed slower from the general blood circulation compared to emulsions based on lipids with long chain fatty acids in the 1,3 positions. Conclusions. The type of core material influences the in vivo circulation time of fat emulsions.     

In Vitro/In Vivo Comparison of Drug Release and Polymer Erosion from Biodegradable P(FAD-SA) Polyanhydrides—A Noninvasive Approach by the Combined Use of Electron Paramagnetic Resonance Spectroscopy and Nuclear Magnetic Resonance Imaging

Purpose. The purpose of this study was to compare drug release and polymer erosion from biodegradable P(FAD-SA) polyanhydrides in vitro and in vivoin real time and with minimal disturbance of the investigated system. Methods. P(FAD-SA) 20:80 and P(FAD-SA) 50:50 polymer tablets were loaded with the spin probe 3-carboxy-2,2,5,5-tetramethyl-pyrrollidine-1-oxyl (PCA) and implanted subcutaneously in the neck of rats or placed in 0.1 M phosphate buffer. 1.1 GHz EPR spectroscopy experiments and 7T MRI studies (Tl and T2 weighted) were performed. Results. A front of water penetration was visible by MRI in vitro in the case of P(FAD-SA) 20:80, but not for P(FAD-SA) 50:50. For both polymers, the thickness of the tablets decreased with time and a insoluble, easy deformable residue remained. Important processes such as edema, deformation of the implant, encapsulation and bioresorption were observable by MRIin vivo. P(FAD-SA) 50:50 was almost entirely absorbed by day 44, whereas an encapsulated residue was found for P(FAD-SA) 20:80 after 65 days. The EPR studies gave direct evidence of a water penetration induced changes of the microenvironment inside the tablet. EPR signals were still detectable in P(FAD-SA) 20:80 implants after 65 days, while the nitroxide was released in vitro within 16 days. Conclusions. Important parameters and processes such as edema, deformation of the tablet, micro viscosity inside the tablet and encapsulation can be monitored in real time by the combined use of the noninvasive techniques MRI and EPR leading to better understanding of the differences between the in vitroandin vivo situation.     

Controlled release of tetracycline—III: A physiological pharmacokinetic model of the pregnant rat

A controlled tetracycline delivery device, consisting of a membrane enclosed trilaminate disc fabricated from a series of 2-hydroxyethylmethacrylate/methylmethacrylate copolymers, demonstrated the ability to deliver tetracycline at zero-order rates in vitro and in vivo in rats and was applied to study the pharmacokinetics of tetracycline in the pregnant rat. The trilaminate discs containing tetracycline were implanted in pregnant Sprague-Dawley rats on the eighth day of gestation. The animals were sacrificed on days 19, 20, and 21 of gestation in order to measure the distribution of the controlled release tetracycline in the maternal, fetal, and placental tissues. Constant plasma tetracycline levels were attained in both the maternal and fetal circulations after 4 to 5 days postimplantation of the trilaminate discs. Placental transfer of tetracycline appeared rapid and no partitioning of the drug was observed between the maternal and fetal plasma. Tetracycline levels did not differ significantly in the maternal and fetal soft tissues (liver, kidney, G. I. tract, muscle, placenta) as measured over the last 3 to 4 days of the animal's gestational period. Highest tetracycline concentrations were determined in the fetal bone samples. In addition, some accumulation of the drug occurred in the amniotic fluid. A flow-limited pharmacokinetic model was constructed to simulate the distribution of tetracycline, delivered at a constant rate from the trilaminate device, in the pregnant rats. Predictions of fetal growth and maternal and fetal tissue tetracycline concentrations were in good agreement with the experimental measurements. The ability of these copolymer systems to deliver tetracycline at zero-order rates over extended periods offers numerous potential therapeutic and investigational applications, especially where such drug delivery characteristics are beneficial to the elucidation of physiological rate mechanisms, as in the pregnant animal.     

A theoretical consideration of percutaneous drug absorption

The percutaneous drug absorption process and its clinical significance are not fully known. In this article we propose a theoretical method to obtain two parameters (k _d and k_c) of percutaneous drug absorption from in vivodata. These parameters are related to diffusion of a drug through the skin and removal process at the skin-capillary boundary, respectively, characterizing several pharmacokinetic aspects of the drug applied to the skin. Moreover, by employing these two kinetic constants, a simulation of percutaneous drug absorption can be theoretically generated. On the basis of our theoretical considerations on the percutaneous drug absorption process described herein, we conclude that the percutaneous drug absorption process is better understood by employing two kinetic constants in a mathematical model and that its clinical application would be highly possible.