Time-to-Event Analysis of Polatuzumab Vedotin-Induced Peripheral Neuropathy to Assist in the Comparison of Clinical Dosing Regimens.

Polatuzumab vedotin, an antibody-drug conjugate containing monomethyl auristatin E, was associated with an incidence of grade ≥2 peripheral neuropathy (PN) of 55-72% in patients with indolent non-Hodgkin lymphoma in a phase II study, when dosed 1.8-2.4 mg/kg every 3 weeks until progression or for a maximum of 17 cycles. To quantify the correlation of conjugate exposure and treatment duration with PN risk, a time-to-event model was developed using data from phase I and II studies. The model suggested that PN risk increased with conjugate exposure and treatment cycles, and a trend for increased risk with body weight and albumin concentration. When capping the treatment duration to six to eight cycles, the risk ratio of a dose of 2.4 mg/kg vs. 1.8 mg/kg was ≥1.29; the predicted incidence of grade ≥2 PN at 1.8-2.4 mg/kg dose levels was 17.8-37.2%, which is comparable with other antimicrotubule agents for lymphoma treatment.

The effect of in vivo dissolution, gastric emptying rate, and intestinal transit time on the peak concentration and area-under-the-curve of drugs with different gastrointestinal permeabilities.

PURPOSE: To theoretically investigate the impact of gastric emptying half-time, intestinal transit time and the time for 85% in vivo dissolution on the peak concentration and area-under-the curve of model drugs. METHODS: Simulations were performed using mathematical models of gastrointestinal physiology and pharmacokinetics of model drugs with different gastrointestinal permeability. They were used to investigate the effect of different permutations of gastric emptying times, intestinal transit times, dissolution rates and effective permeabilities on the maximum plasma drug concentration and the area-under-the-curve of immediate release tablets relative to an oral solution (i.e., Cmax(tablet)/Cmax(solution) and AUC(tablet)/AUC(solution)). RESULTS: The higher the permeability of the drug, the more sensitive the Cmax ratio is to dissolution rate and gastric emptying rate. As the intestinal transit time becomes more rapid, the sensitivity to T85% dissolution time and gastric emptying half-time increases. There is less dependence for the AUC ratio on the gastric emptying time and dissolution rate. CONCLUSIONS: Under the assumptions of the models, the criterion of 85% dissolution in 15 minutes (T85%) for classifying a rapidly dissolving drug product is relatively conservative since the Cmax ratio exceeded 0.8 for a T85% dissolution time of one hour and a gastric emptying half-time faster than 0.2 hour over a wide range of permeabilities.

New mathematical implementation of generalized pharmacodynamic models: method and clinical evaluation.

A new method and experimental design are presented to unambiguously estimate the transduction function (phi) and the conduction function (psi) of the generalized pharmacodynamic model: E = phi (psi * r), when measured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. phi relates the observed pharmacologic effect E to the concentration at the effect site: ce = (psi * r), psi defines transfer of drug from plasma site to effect site or from input site to effect site, and * represents the convolution integral. The model functions psi and phi were expressed as cubic splines giving a very flexible description of those processes which is not biased by the structured assumptions of more conventional models, e.g., effect compartment models. The experimental design proposed addresses the problem of ambiguous identification of the model functions typical of these models; that is, there is more than one pair of very different functions describing the effect data collected after a single drug administration. We tested the hypothesis that the simultaneous fitting of at least two administrations allows the unambiguous identification of the model functions without the need for unlikely or cumbersome constraints. The performance of the mathematical implementation and the robustness of the methods with respect to measurement noise and possible failure of some assumptions, such as intraindividual variability, were tested by computer simulations. The method was then applied to the results of a clinical study of verapamil pharmacodynamics in 6 healthy subjects. Results of these studies demonstrated that the mathematical implementation does not introduce bias or artifact into the estimated functions and that the models and the proposed methods are suitable for application to clinical research. Two drug administrations were sufficient to unambiguously describe verapamil pharmacodynamics in the 6 human subjects studied.

Bioavailability assessment from pharmacologic data: method and clinical evaluation.

A novel method is described for assessing drug bioavailability from pharmacologic data. The method is based upon a generalized model for the relationship between the observed effect (E) and the input rate (f): E = phi (ce delta * f), where * denotes convolution, ce delta is effect site unit impulse response ("amount" of drug at the effect site resulting from the instantaneous input of a unit amount of drug) and phi is transduction function (relates "amount" of drug at the effect site to E). The functions phi and ce delta are expressed as cubic splines for maximum versatility. Pharmacologic data collected after the administration of two different doses by i.v. infusion are analyzed simultaneously to estimate the function parameters. This experimental design addresses the fact that phi and ce delta cannot be uniquely estimated from the results of a single dose experiment. The unknown f from a test treatment is then estimated by applying an implicit deconvolution method to the pharmacologic data collected during that treatment. The method was tested with stimulated data. The method and the model were further evaluated by application to a clinical study of verapamil (V) pharmacodynamics in 6 healthy volunteers. Simulations showed that the method is accurate and precise in the presence of a high degree of measurement error, but large intrasubject variability in the model functions can result in biased estimates of the amount absorbed. The method produced reasonably accurate estimates of the V input rate and systemic availability (F) in the 6 human volunteers though there was a trend towards underestimation (estimated total F% = 93.6 +/- 14 vs. the true F% of 100).

Convolution-based approaches for in vivo-in vitro correlation modeling.

One approach to in vivo-in vitro correlation (IVIVC) for extended release (ER) oral dosage forms is to directly model the relationship between the time courses of in vitro release and plasma drug concentrations. For drugs that exhibit linear, time-invariant disposition this can be done using models based on the convolution integral. Advantages of this approach relative to deconvolution-based IVIVC approaches include the following: The relationship between measured quantities (in vitro release and plasma drug concentrations) is modeled directly in a single stage rather than via an indirect two stage approach. The model directly predicts the plasma concentration time course. As a result: The modeling focuses on the ability to predict measured quantities (not indirectly calculated quantities such as the cumulative amount absorbed). The results are more readily interpreted in terms of the effect of in vitro release on conventional bioequivalence metrics. It is easier to construct methods that do not require the administration of an IV, oral solution, or IR reference dose. A variety of convolution-based IVIVC models and modeling strategies are possible depending on the relationship between in vivo and in vitro release, the existence of nonlinear absorption or presystemic biotransformation, and the in vivo study design. The simplest approach is applicable to the case where the in vitro release rate equals the in vivo release (or absorption) rate and the study design includes the administration of an IV, oral solution, or IR dose. That basic convolution-based method can be extended to adjust for differences between the in vitro and in vivo release rates. This is accomplished by formally modeling those differences. Potential models include time-scaling and convolution. The extent of drug absorption may sometimes depend upon the release rate. This may be due to phenomena such as saturable presystemic biotransformation or truncated absorption due to intestinal transit past the sites of absorption. The relationship between the in vitro release rate and extent of absorption may be modeled empirically or mechanistically. Such models may be coupled with convolution to construct an overall IVIVC model for the relationship between in vitro release and plasma drug concentrations. It is also possible to apply convolution-based IVIVC models to study designs in which no IV, oral solution, or IR dose has been administered. Details of the various modeling approaches listed above are presented. Selected approaches are illustrated by examples of their application to real data.

Volumes of distribution and mean residence time of drugs with linear tissue distribution and binding and nonlinear protein binding.

Based on a generalized model, equations for calculating the mean residence time in the body at single dose (MRT) and at steady state (MRTss), apparent steady-state volume of distribution (Vss), and steady-state volume of distribution (Vss) are derived for a drug exhibiting nonlinear protein binding. Interrelationships between Vss and Vss as well as between MRT and MRTss are also discussed and illustrated with simulated data. In addition, a method for estimating the central volume of distribution of the bound drug and the sum of the central volume of distribution of the unbound drug and the area under the first moment curve of distribution function for drugs with nonlinear protein binding is proposed and illustrated with both simulated and published data.

Simultaneous analysis of verapamil and norverapamil enantiomers in human plasma by high-performance liquid chromatography.

An improved HPLC method for the simultaneous determination of the enantiomers of verapamil (V) and its major metabolite norverapamil (NV) in human plasma samples is presented. NV is acetylated immediately to N-acetylnorverapamil (ANV) in the extraction solvent (2% butanol in hexane). Acetylation is so rapid that it does not delay sample processing. ANV and V enantiomers are then separated on an alpha 1-acid glycoprotein chiral column with a mobile phase of phosphate buffer (0.01 M, pH 6.65) and acetonitrile. The fluorescence detector wavelengths are set at 227 nm for excitation and 308 nm for emission. Introduction of the internal standard (I.S.) (+)-glaucine improves accuracy, precision and robustness of the method. The assay is sensitive and specific. Baseline separation is achieved for both V and ANV. Limits of quantitation are 3 ng/ml for V and 2 ng/ml for NV (single enantiomer) with precision and accuracy better than 15% at those levels. Detector response is linear in the range tested (3-200 ng/ml for V and 2-100 ng/ml for NV, single enantiomer). This assay has been applied to a clinical study of the pharmacodynamics of V involving six healthy volunteers.

A multidimensional deconvolution method for evaluating the absorption of drugs undergoing reversible metabolism and presystemic metabolite formation.

A general multidimensional deconvolution method is developed primarily for application to the bioavailability assessment of drugs with reversible metabolism. The proposed approach involves fitting continuous functions to the experimental data and then applying a numerical deconvolution algorithm to the fitted curves. It is shown how the method may be used to determine the rates and extends of drug absorption and presystemic formation of interconversion metabolites. The proposed method is implemented as a FORTRAN subroutine called DCVSYS for the general multidimensional deconvolution problem involving any continuous functions and as a user-friendly PC-compatible program called NDCREV for evaluating the absorption of drugs undergoing reversible metabolism. The methods and computer programs are demonstrated by application to simulated drug and metabolite concentrations for a drug with reversible metabolism.

A physiological and system analysis hybrid pharmacokinetic model to characterize carbon tetrachloride blood concentrations following administration in different oral vehicles.

Oral absorption of chemicals can be influenced significantly by the administration vehicle or diluent. It has been observed that the oral absorption of carbon tetrachloride (CCl4) and other volatile organic chemicals is markedly affected by the dosing vehicle, with administration in oils producing erratic blood concentration-time profiles with multiple peaks. Analysis of this type of data by a compartmental modeling approach can be difficult, and requires numerous assumptions about the absorption processes. Alternatively, a system analysis method with few assumptions may provide a more accurate description of the observed data. In the current investigations, a nonlinear system analysis approach was applied to blood CCl4 concentration-time data obtained following iv and oral administration. The oral regimens consisted of 25 mg CCl4/kg body wt given as an aqueous emulsion, in water, as pure chemicals, and in corn oil. The system analysis procedure, based upon a disposition decomposition method, provided an absorption input rate function, F, for each regimen. A physiological pharmacokinetic model, based primarily on parameters available in the literature, and the F input functions, formed a hybrid model that adequately described the observed blood CCl4 concentration-time data. The same physiological pharmacokinetic model, employing conventional first-order absorption input schemes, did not predict the data as well. Overall, the system analysis approach allowed the oral absorption of CCl4 to be characterized accurately, regardless of the vehicle. Though system analysis is based on general mathematical properties of a system's behavior rather than on its causal mechanisms, this work demonstrates that it can be a useful adjunct to physiological pharmacokinetic models.

Generalized pharmacokinetic modeling for drugs with nonlinear binding: I. Theoretical framework.

The following integrodifferential equation is proposed as the basis for a generalized treatment of pharmacokinetic systems in which nonlinear binding occurs phi'(cu)c'u = -q(cu)+g * cu+f where cu identical to unbound plasma drug concentration, f identical to drug input rate, ' indicates the derivative of a function, and * indicates the convolution operation: (g * cu) (t) = integral of t0 g(t-u)cu(u) du. Possible physical interpretations of the functions q, g and f are: q(cu) identical to rate at which drug leaves the sampling compartment, g * cu identical to rate at which drug returns to the sampling compartment from the peripheral system (tissues that are kinetically distinct from the sampling compartment), and phi(cu) identical to amount of drug in the sampling compartment. The approach assumes that drug binding is sufficiently rapid that it may be treated as an equilibrium process. It may be applied to systems in which nonlinear binding occurs within the sampling compartment, i.e., in the systemic circulation or in tissues to which drug is rapidly distributed. The proposed relationship is a generalization of most existing models for drugs with nonlinear binding. It can serve as a general theoretical framework for such models or as the basis for "model-independent" methods for analyzing the pharmacokinetics of drugs with nonlinear binding. Computer programs for the numerical solution of the integrodifferential equation are presented. Methods for pharmacokinetic system characterization, prediction and bioavailability are presented and demonstrated.

Simple methods for estimation of mean residence time and steady-state volume of distribution from continuous-infusion data.

The following equations are derived for amount of drug in the body (xbss), volume of distribution (vss), and mean residence time in the body (tb) at steady state during a continuous constant rate infusion of drug. (formula; see text) where c(t) identical to drug concentration in the systemic circulation at time t following the start of a constant-rate infusion, css identical to steady-state systemic drug concentration, and R identical to infusion rate. The equations are based on the assumption that the rate of drug elimination is proportional to the systemic drug concentration. The equations provide the basis for simple methods that are presented for estimating xbss, vss, and tb directly from experimental data. More general relationships are also derived for cases where the continuous infusion is preceded by other modes of administration, e.g., a bolus loading dose followed by a constant-rate infusion.

Estimation of theophylline clearance during continuous arteriovenous hemofiltration.

Pharmacologic agents and other non-protein-bound compounds smaller than 5,000 daltons have the potential to be removed by continuous arteriovenous hemofiltration (CAVH). A proposed method for estimating drug clearance by CAVH (ClCAVH) equates ultrafiltrate clearance to the product of the sieving coefficient and the average ultrafiltration rate. This simplified approach for estimating ClCAVH would be a clinically useful method for calculating replacement doses, as it economizes on the sampling and analytical requirements associated with the conventional method. Presented are some theoretical considerations and a brief evaluation of the accuracy of this proposed method. The evaluation was conducted using an animal model whereby CAVH was performed in four male beagles. During the hemofiltration period, an i.v. bolus of theophylline, 6 mg/kg, was administered over 15 s. Samples for analysis of theophylline were collected from the arterial, venous, and ultrafiltrate ports at 0, 5, 15, 30, 45, 60, 90, 120, 180, 240, 360, and 480 min following dosage administration. The volume of ultrafiltrate produced during each collection interval was measured. Theophylline serum concentrations were determined by a high performance liquid chromatography assay. Statistically, the simplified method was found to result in significantly (p less than 0.05) larger estimates of ultrafiltrate clearance when compared to the conventional method. However, the average magnitude of difference was only 9% and does not constitute a clinically significant margin between the two methods.

A system approach to pharmacodynamics. I: Theoretical framework.

A general theoretical framework is constructed for the relationship between a pharmacokinetic response r (e.g., systemic drug concentration or input rate), and an observed pharmacologic effect response E. The overall relationship may be described mathematically by E = omega(r) = omega p(omega b(omega r(r))) where omega is an operator that describes the overall relationship, and omega r, omega b, and omega p are operators that describe the contributions of components of the pharmacodynamic system. The kinetic basis for applying certain general mathematical properties such as linearity are discussed. The result is the introduction of various specific mathematical structures that may be applied to pharmacodynamic systems [e.g., E = phi t(r), E = phi t(psi r*r), E = phi p(psi p*phi b(r)), and E = phi p(psi p*phi b(psi r*r))].

A system approach to pharmacodynamics. II: Glyburide pharmacodynamics and estimation of optimal drug delivery.

A system approach to the analysis of pharmacodynamic systems is applied to the relationship between the glyburide serum concentration (Cd) and a resulting pharmacologic effect response, that is, the C-peptide serum concentration (Cc) in patients with non-insulin dependent diabetes mellitus (NIDDM). Glyburide, glucose, and C-peptide serum concentrations were measured in eight patients with NIDDM following each of five treatments: Treatment A: one glyburide 5-mg tablet (formulation 1); Treatment B: one glyburide 5-mg tablet (formulation 2); Treatment C: glyburide solution as an intragastric infusion (4.67 mg over 12 h); Treatment D: glyburide solution as an intragastric infusion (9.33 mg over 12 h); and Treatment E: no glyburide. The overall relationship between the C-peptide (Cc), glyburide (Cd), and glucose (Cg) serum concentrations is successfully described by operator equations of the form, Cc(t) = t-infinity psi p(t-u)phi t(Cd(u), Cg(u)) du or Cc(t) = t-infinity psi p(t-u)phi t(Cd(u), Cg(u),u) du. The forms of the individual functions are selected empirically based on the results of the present study and those of previous investigations, and are estimated by conventional curve-fitting procedures. The resulting operator equations are used to describe glyburide pharmacodynamics in NIDDM patients and to estimate the optimal glyburide systemic concentration and delivery rate profiles for such patients based on pharmacodynamic response.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. III. Peripheral bioavailability and distribution time concepts applied to the evaluation of distribution kinetics.

Disposition decomposition analysis (DDA) is applied to evaluate the rate and extent of drug delivery from the sampling compartment to the peripheral system, i.e., peripheral bioavailability. Four parameters are introduced which are useful in quantifying peripheral bioavailability. The compounded peripheral bioavailability, F comp, is the ratio between the total compounded amount of drug transferred to the peripheral system and the injected dose, D. The AUC peripheral bioavailability, FAUC, is the ratio between the area under the amount vs. time curves for the peripheral system and the sampling compartment. The distribution time td, is the time following an i.v. bolus at which the net transfer of drug to the peripheral system reverses in direction. The maximum peripheral bioavailability, Fmax, is the maximum fraction of an i.v. bolus dose that is present in the peripheral system at any one time. Equations are derived which permit estimation of those parameters from drug concentrations in the sampling compartment. Simple algorithms and a computer program are provided for estimating Fcomp, FAUC, td, Fmax, and other parameters relevant to DDA for drugs that exhibit a linear polyexponential bolus response. Estimates of Ecomp, FAUC, td, and Fmax are presented for several drugs.