DeMonS--a new deconvolution method for estimating drug absorbed at different time intervals and/or drug disposition model parameters using a monotonic cubic spline

Flip-flop pharmacokinetics--delivering a reversal of disposition: challenges and opportunities during drug development

Flip-flop pharmacokinetics is a phenomenon often encountered with extravascularly administered drugs. Occurrence of flip-flop spans preclinical to human studies. The purpose of this article is to analyze both the pharmacokinetic interpretation errors and opportunities underlying the presence of flip-flop pharmacokinetics during drug development. Flip-flop occurs when the rate of absorption is slower than the rate of elimination. If it is not recognized, it can create difficulties in the acquisition and interpretation of pharmacokinetic parameters. When flip-flop is expected or discovered, a longer duration of sampling may be necessary in order to avoid overestimation of fraction of dose absorbed. Common culprits of flip-flop disposition are modified dosage formulations; however, formulation characteristics such as the drug chemical entities themselves or the incorporated excipients can also cause the phenomenon. Yet another contributing factor is the physiological makeup of the extravascular site of administration. In this article, these causes of flip-flop pharmacokinetics are discussed with incorporation of relevant examples and the implications for drug development outlined.

Phenomenological definition of response times with application to metabolic reactions

The metabolic response time, i.e. the delay the system introduces in the response to an input flux, is considered. A novel phenomenological definition is presented, which is valid for any kind of behavior, including transitory or permanent oscillatory responses. In order to calculate the response time of single-input systems, output fluxes have to be deconvoluted with the input flux. The bases for this are established. The resulting function (unit impulse response in time-invariant linear systems) is transformed by subtracting its final state, taking the absolute value and normalizing by the resulting area, so that a norm can be applied that weights the response at every time. This response time can also be interpreted as an average. It coincides with the transition (characteristic) time of an output flux, provided that the input is performed instantaneously (step function). A strictly non-negative response function is needed for the response time to be interpreted as a mass balance. A simple example is used to study the deviation otherwise. The method is advantageous in that it provides clues on the phenomenological behavior of biochemical systems. For example, deconvolution reveals the intrinsic oscillation-generating mechanism of an allosteric enzyme, which becomes hidden when the input flux increases in a slow way. This is illustrated by means of a model.

The use of a physiologically based pharmacokinetic model to evaluate deconvolution measurements of systemic absorption

BACKGROUND

An unknown input function can be determined by deconvolution using the systemic bolus input function (r) determined using an experimental input of duration ranging from a few seconds to many minutes. The quantitative relation between the duration of the input and the accuracy of r is unknown. Although a large number of deconvolution procedures have been described, these routines are not available in a convenient software package.

METHODS

Four deconvolution methods are implemented in a new, user-friendly software program (PKQuest, http://www.pkquest.com). Three of these methods are characterized by input parameters that are adjusted by the user to provide the "best" fit. A new approach is used to determine these parameters, based on the assumption that the input can be approximated by a gamma distribution. Deconvolution methodologies are evaluated using data generated from a physiologically based pharmacokinetic model (PBPK).

RESULTS AND CONCLUSIONS

The 11-compartment PBPK model is accurately described by either a 2 or 3-exponential function, depending on whether or not there is significant tissue binding. For an accurate estimate of r the first venous sample should be at or before the end of the constant infusion and a long (10 minute) constant infusion is preferable to a bolus injection. For noisy data, a gamma distribution deconvolution provides the best result if the input has the form of a gamma distribution. For other input functions, good results are obtained using deconvolution methods based on modeling the input with either a B-spline or uniform dense set of time points.

An extended point-area deconvolution approach for assessing drug input rates

PURPOSE

To describe an extended point-area deconvolution approach for evaluating drug input rates based on the application of piecewise cubic polynomial functions.

METHODS

Both the nonimpulse response data and the impulse reference data were independently represented by the piecewise cubic polynomials to obtain interpolations, numerical integration, and reduced step size for the staircase input rates. A moving average algorithm was employed to compute the input rate estimates. The method was illustrated using data from preclinical and human studies. Simulations were used to examine the effects of data noise.

RESULTS

In all cases examined, the piecewise cubic interpolation functions combined with the moving average algorithm yielded estimates that were reasonable and acceptable. Compared to the standard point-area approach based on the trapezoidal rule, the present method resulted in estimates that were closer to the expected values.

CONCLUSIONS

The point-area deconvolution analysis is one of the preferred approaches in assessing pharmacokinetic and biopharmaceutic data when it is undesirable to assume the functional forms of the input processes. The present method provides improved performance and greater flexibility of this approach.

Investigation of absorption kinetics by the phase plane method

PURPOSE

To develop a simple approach for investigating absorption kinetics, which does not require modeling assumption or intravenous data.

METHODS

The concentration (C) -time (t) data are plotted as a phase plane plot (dCldt versus C). Errorless C,t data were generated from one and two compartment models employing first-order, zero-order and Michaelis-menten input kinetics, and the phase plane plots were constructed. A simple test based on the ratio of slopes of the separate linear regression analyses of absorption and elimination data of the phase plane plot is proposed to justify or not the presence of zero order input kinetics. Errant data were used to assess the performance of the test developed. Literature data of theophylline and nitroglycerin formulations were analyzed using the phase plane plot. Input rate-time profiles were constructed for one compartment model drugs utilizing the data of the phase plane plot.

RESULTS

The geometric forms of the phase plane plots derived form the errorless data of the various pharmacokinetic models were found to be indicative of the absorption kinetics. Very good resulted were obtained when the test for he discernment of absorption kinetics was applied to errant data. Zero-order absorption kinetics were justified (i) for the transdermal absorption of nitroglycerin and (ii) only for a certain period of time, for the gastrointestinal absorption of theophylline.

CONCLUSIONS

Investigation of absorption kinetics can be accomplished with the phase plane method. The cumulative character of the classical percent absorbed versus time plots can be misleading in justifying the presence of zero-order input kinetics.

Testosterone pharmacokinetics after application of an investigational transdermal system in hypogonadal men

This open-label, randomized, placebo lead-in, three-treatment crossover study in 19 hypogonadal men (27-82 years of age) evaluated dose proportionality of serum testosterone concentrations with application of one or two investigational transdermal testosterone systems for application to the arm or torso. Testosterone in vivo kinetics profiles were determined using DeMonS, a recently developed numerical deconvolution method that estimates drug absorption at different time intervals and/or drug disposition model parameters. After application of the investigational transdermal systems, the mean serum testosterone, dihydrotestosterone, estradiol, and free testosterone concentrations were elevated to normal levels. Treatment allowed approximation of the normal circadian pattern of endogenous testosterone secretion, and the increase in serum testosterone concentrations was proportional to the surface area of systems applied. The investigational transdermal system provided effective testosterone replacement therapy as judged by pharmacokinetic parameters.

Transdermal testosterone administration in hypogonadal men: comparison of pharmacokinetics at different sites of application and at the first and fifth days of application

In this study of 13 hypogonadal men (25-69 years of age), three open-label, randomized treatments were administered to determine the pharmacokinetics of serum testosterone after application of an investigational testosterone transdermal system to the upper buttocks, upper arm, and back. Testosterone in vivo input kinetics profiles were estimated by DeMonS, a recently developed numerical deconvolution method for estimating drug absorption at different time intervals and/or drug disposition model parameters, and compared on the first and fifth days of system application. Area under the concentration-time curve from 0 to 27 hours (AUC0-27) values for testosterone after one-day applications to the upper buttocks, upper arm, and back were 9,560 ng.hr/dL, 8,651 ng.hr/dL, and 8,988 ng.hr/dL, respectively. Maximum observed concentration (Cmax) values were 482 ng/dL, 462 ng/dL, and 499 ng/dL, respectively. Serum testosterone concentrations were equivalent to each other, and Cmax values fell within the normal range. No drug accumulation was seen with repeated dosing over 5 days.