Biomedical subjects

Wojciech Krzyzanski

Publications and source records attributed to Wojciech Krzyzanski.

15 recordsLinked to original sources

PubMed2006

Mathematical assessment of properties of precursor-dependent indirect pharmacodynamic response models.

Precursor-dependent indirect response (PDIDR) models may describe the tolerance and rebound phenomenon observed for many pharmacodynamic responses where these characteristics are manifested due to the depletion or accumulation of a physiological precursor or cofactor pool responsible for generating drug effects. The purpose of this report is to extend the concepts and applications of these models and to approximate responses and limiting conditions for very large doses of drugs. Asymptotic analysis was performed for qualitative determination of various parameters, such as maximum response (Rmax) and rebound (RBmax), time to maximum response and rebound (TRmax and TRBmax), and area under the effect and rebound curve (ABEC and ABRC) for large doses. Computer simulations were performed to assess the role of dose for both cases where drugs act either by depleting (Model V) or by blocking (Model VI) the endogenous precursor. Simulations showed that Rmax, RBmax, TRBmax, ABEC and ABRC increase with dose, eventually reaching a plateau when Dose/V is very large compared to the efficacy parameters (SC50 or IC50) of the drug. However, TRmax either increased or decreased with dose depending on various system and drug parameters. The limits for these parameters at large doses qualitatively determined by asymptotic analysis closely approximated the plateaus observed from the simulated curves. At large doses, the drug response could be approximated by a Bateman-like function for both Models V and VI. Qualitative analyses along with simulation studies provide a fundamental basis for understanding the temporal aspects of the PDIDR models especially at large doses to describe the tolerance and rebound phenomenon.

Area Under Curve↗

PubMed2006

Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after intravenous and subcutaneous administration in rats.

The pharmacokinetics (PK) and pharmacodynamics (PD) of recombinant human erythropoietin (rHuEPO) were studied in rats after single i.v. and s.c. administration at three dose levels (450, 1350, and 4050 IU/kg). The plasma concentrations of rHuEPO and its erythropoietic effects including reticulocyte (RET), red blood cell (RBC), and hemoglobin (Hb) levels were determined. A two-compartment model with dual input rate and nonlinear disposition was used to characterize the PK of rHuEPO. The catenary indirect response model with several compartments reflecting the bone marrow and circulating erythropoietic cells was applied. The s.c. doses exhibited slow absorption (T(max) = 12 h) and incomplete bioavailability (F = 0.59). In placebo groups, RBC and Hb values gradually increased over time with growth of the rats, and the changes in the baselines monitored from 8 to 32 weeks of age were described by a nonlinear growth function. All doses resulted in dose-dependent increases in RET counts followed by an immediate decline below the baseline at around 6 days and returned to the predose level in 21-24 days after dosing. A subsequent steady increase of RBC and Hb levels followed and reached peaks at 6 days. A tolerance phenomenon observed at all dose levels was modeled by a negative feedback inhibition with the relative change in Hb level. The PK/PD model well described the erythropoietic effects of rHuEPO as well as tolerance, thereby yielding important PD parameters (S(max) = 1.87 and SC(50) = 65.37 mIU/ml) and mean lifespans of major erythropoietic cell populations in rats.

Algorithms↗

PubMed2006

Assessment of dosing impact on intra-individual variability in estimation of parameters for basic indirect response models.

The application of D-optimization and the assessment of bias and precision of parameter estimates for four basic pharmacodynamic (PD) indirect response (IDR) models for ascending doses was examined using simulated data. While D-optimization provided four sampling times, each IDR model was used to generate eight data points per dose level. The PD parameters were: input rate constant (k (in)), disposition rate constant (k (out)), capacity constant (I (max) or S (max)), and sensitivity constant (IC (50) or SC (50)). A monoexponential pharmacokinetic function was applied with single doses increased by a factor of 10 to generate responses that vary from weak to fully saturable. For each dose, 100 replications of response data were simulated using independent normally distributed errors of CV = 20%. The original IDR model was fitted and PD parameters estimated. Histograms and descriptive statistics were generated. All parameters exhibited asymmetric distributions with positive coefficients of skewness except for I (max). Higher doses resulted in unbiased estimates of all PD parameters. The precision of parameter estimates improved with increasing doses except for IC (50) and SC (50) indicating that a single dose experimental design cannot be corrected by increasing dose in order to improve precision of estimates of IC (50) or SC (50). Highest variability was for IC (50) and SC (50) parameters. This study provides new insights into optimum study designs and recovery of parameters for basic IDR models.

Biological Availability↗

PubMed2006

Pharmacodynamic models for agents that alter production of natural cells with various distributions of lifespans.

Indirect pharmacodynamic response (IDR) models were developed for agents which alter the generation of cell populations with arbitrary lifespan distributions. These models extend lifespan based IDR models introduced previously [J. Pharmacokinet. Biopharm. 27: 467, 1999] for cell populations with the same lifespan ("delta" distribution). Considered are cell populations exhibiting time-invariant lifespan distributions described by the probability density function l(tau). It is assumed that cell response (R) is produced at a zero-order rate (kin(t)) and is eliminated from the population when the cell lifespan expires. The cell loss rate is calculated as kin*l(t), where '*' denotes the convolution operator. Therapeutic agents can stimulate or inhibit production rates according to the Hill function: 1 +/- H(C(t)) where H(C(t)) contains the capacity (Smax) and potency (SC50) parameters and C(t) is a pharmacokinetic function. The production rate is kin(t) = kin.[ 1+/-H(C(t))]. The operational model is dR/dt = kin(t)-kin*l(t) with the baseline condition R0 = kin.TR, where TR is the mean lifespan. Single populations as well as populations with precursors were examined by simulation to establish the role of lifespan distribution parameters (mean and standard deviation) in controlling the response vs. time profile. Estimability of parameters was assessed. Numerical techniques of solving differential equations with the convolution integral were proposed. In addition, the models were applied to literature data to describe the stimulatory effects of single doses of recombinant human erythropoietin on reticulocytes in blood. The estimates of Smax and SC50 for these agents were obtained along with means and standard deviations for reticulocyte lifespan distributions. The proposed models can be used to analyze the pharmacodynamics of agents which alter natural cell production yielding parameters describing their efficacy and potency as well as means and standard deviations for cell lifespan distributions.

Algorithms↗

PubMed2006

Assessment of basic indirect pharmacodynamic response models with physiological limits.

Many physiological factors are regulated by homeostatic mechanisms to maintain normal body function. Empirical lower Rl (Model I and IV) or upper Rh limits (Model II and III) were included in current basic indirect response (IDR) models to account for the additional role of physiological limits (IDRPL). Various characteristics of these models were evaluated with simulations and explicit equations. The simulations reveal that the expanded models exhibit most properties of basic indirect response models, such as slow response initiation, lag time between the kinetic and dynamic peaks, a large dose plateau, and shift in Tmax with dose. The proposed models always produce lesser net responses than predicted by basic IDR models. Simulations demonstrate that addition of a parameter limit which is close to the baseline has a great influence on the overall and maximum responses and fitted model parameters. Only stimulatory IDRPL Models III and IV allow resolution of all model parameters in the absence of clear indications or predetermined values of the lower or upper limits. However, all four models are able to resolve model parameters when subgroups with different baselines are simultaneously fitted. These models create new interpretations of the determinants of baseline conditions which can be important in assessing inter-subject variability in responses. The applicability of IDRPL models is demonstrated using several examples from the published literature. Indirect response models with physiological limits will be useful in characterizing drug responses for turnover systems which are maintained within a certain range.

5-alpha Reductase Inhibitors↗

PubMed2005

Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition.

PURPOSE: The aim of this study is to derive and evaluate an equilibrium model of a previously developed general pharmacokinetic model for drugs exhibiting target-mediated drug disposition (TMDD). METHODS: A quasi-equilibrium solution to the system of ordinary differential equations that describe the kinetics of TMDD was obtained. Computer simulations of the equilibrium model were carried out to generate plasma concentration-time profiles resulting from a large range of intravenous bolus doses. Additionally, the final model was fitted to previously published pharmacokinetic profiles of leukemia inhibitory factor (LIF), a cytokine that seems to exhibit TMDD, following intravenous administration of 12.5, 25, 100, 250, 500, or 750 microg/kg in sheep. RESULTS: Simulations show that pharmacokinetic profiles display steeper distribution phases for lower doses and similar terminal disposition phases, but with slight underestimation at early time points as theoretically expected. The final model well-described LIF pharmacokinetics, and the final parameters, which were estimated with relatively good precision, were in good agreement with literature values. CONCLUSIONS: An equilibrium model of TMDD is developed that recapitulates the essential features of the full general model and eliminates the need for estimating drug-binding microconstants that are often difficult or impossible to identify from typical in vivo pharmacokinetic data.

Algorithms↗

PubMed2005

Population cell life span models for effects of drugs following indirect mechanisms of action.

Pharmacokinetic/pharmacodynamic (PK/PD) models for hematological drug effects exist that assume that cells are produced by a zero- or first-order process, survive for a specific duration (cell lifespan), and then are lost. Due to the fact that delay differential equations (DDE) are needed for cell lifespan models, their software implementation is not straightforward. Our objective is to demonstrate methods to implement three different cell lifespan models for dealing with hematological drug effects and to evaluate the performance of NONMEM to estimate the model parameters. For the basic lifespan indirect response (LIDR) model, cells are produced by a zero-order process and removed due to senescence. The modified LIDR model adds a precursor pool. The LIDR model of cytotoxicity assumes a three-pool indirect model to account for the cell proliferation with capacity-limited cytotoxicity followed by maturation, and removal from the circulation. A numerical method (method of steps) implementing DDE in NONMEM was introduced. Simulation followed by estimation was used to evaluate NONMEM performance and the impact of the minimization algorithm (first-order method vs. first-order conditional estimation method) and the model for residual variability on the estimates of the population parameters. The FOCE method combined with log-transformation of data was found to be superior. This report provides methodology that will assist in application of population methods for assessing hematological responses to various types of drugs.

Algorithms↗

PubMed2005

Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after multiple subcutaneous doses in healthy subjects.

A pharmacokinetic and pharmacodynamic (PK/PD) model for recombinant human erythropoietin (Epoetin alfa) in healthy subjects was developed to describe the time profiles of changes in serum Epoetin alfa and the pharmacological responses of percent reticulocytes, total red blood cell counts, and hemoglobin after single and multiple subcutaneous administration of Epoetin alfa. Data used in the development of the model were obtained from a clinical study carried out in healthy volunteers in which Epoetin alfa was administered either as 150 IU/kg three-times-a-week (t.i.w.) or fixed 40,000 IU weekly (q.w.) doses for 4 weeks. A dual-absorption rate model (fast zero-order and slow first-order inputs) with linear disposition kinetics was used to characterize the pharmacokinetics of erythropoietin after subcutaneous administration. A new catenary cell production and lifespan loss model was used to fit the pharmacodynamic data yielding estimates of SC50, Smax, and other pharmacodynamic parameters. Flip-flop kinetics was apparent in the pharmacokinetics as the absorption rate was slower (k(a) = 0.7 day(-1)) than the elimination rate (CL/V(d) = 1.2-9.2 day(-1)). In the pharmacodynamics, an SC50 of 58 mIU/mL was estimated indicating that low serum erythropoietin concentrations were sufficient to produce pharmacological effects. The established PK/PD model predicts similar pharmacological responses of hemoglobin and total red blood cell counts for the 150 IU/kg t.i.w. and 40,000 IU q.w. regimens in healthy subjects.

Adolescent↗

PubMed2004

Pharmacokinetic model of target-mediated disposition of thrombopoietin.

Thrombopoietin, TPO, a 353 amino acid cytokine, is a primary regulator of platelet production that was cloned recently. A target-mediated (platelet receptors) pharmacokinetic model was developed to characterize the disposition of TPO. Receptor-mediated endocytosis was assigned as the major elimination pathway in the model. A nonspecific binding compartment was also incorporated into the model. TPO concentration vs time profiles from a published phase 1 and 2 clinical trial were used to apply this model. Noncompartmental analysis demonstrated that TPO exhibits nonlinear kinetics. The proposed model captured the concentration-time profiles relatively well. The first-order internalization rate constant was estimated as 0.1 h(-1). The endogenous binding capacity was estimated as 164.0 pM. The second-order binding association constant (k(on)) was 0.055 h(-1).pM(-1) and the first-order dissociation constant (k(off)) was estimated as 2.5 h(-1), rendering the equilibrium dissociation constant K(d) as 45.5 pM. This model may be relevant to other therapeutic agents with receptor-mediated endocytotic disposition.

Biological Availability↗

PubMed2004

Assessment of drug interactions relevant to pharmacodynamic indirect response models.

The assessment of drug interactions for a simple turnover system when the basic pharmacodynamic response is governed by indirect mechanisms was explored. This report describes a diverse array of possible in vivo pharmacodynamic effects from a combination of two drugs acting by similar or different indirect mechanisms. Various conditions of pharmacodynamic drug combinations were explored mathematically and by simulation: (a) interactions of two drugs acting simultaneously either on the production (k(in)) or on the dissipation (k(out)) processes controlling the in vivo response by competitive (four cases) or non-competitive interaction (six cases); and (b) combinations of two drugs acting on separate k(in) and k(out) processes simultaneously (four cases). A range of different combinations of drug doses was used. Plasma concentration time profiles were generated according to monoexponential disposition. Pharmacodynamic response profiles were simulated using the above conditions and characterized by descriptors such as Area Between Effect (and Baseline) Curve (ABEC) values. The interaction of agents by competitive mechanisms produced net responses that were additive in nature. Response profiles for non-competitive interactions on the same process were both antagonistic (for two drugs with effects that oppose each other) and synergistic (for two drugs that produce the same response). On the other hand, response signatures for agents acting non-competitively on the production and dissipation factors by opposing mechanisms (e.g. inhibiting k(in) plus stimulating k(out)) showed dramatic changes in net effects and produced apparent drug synergy. Net indirect response profiles for joint use of two or more drugs measured by ABEC values may look "additive", "antagonistic", or "synergistic" depending on doses, their intrinsic potencies, the nature of interaction (competitive or non-competitive) as well as their mechanisms of action. These models may help explain changes in pharmacologic responses to two agents in a more rational and mechanistic fashion than older empirical methods.

Computer Simulation↗

PubMed2003

Methods of estimation of IC50 and SC50 parameters for indirect response models from single dose data.

The basic indirect response models are described by several pharmacodynamic parameters of which IC(50) (drug concentration eliciting 50% of the maximum inhibition) and SC(50) (drug concentration eliciting 50% of the maximum stimulation) are not readily derived from the response versus time or response versus concentration plots. We discuss limitations of existing methods of IC(50) and SC(50) estimation from single dose data. A novel approach to such estimations based on the area between the baseline and effect curve is introduced. The effects of pharmacokinetic profile, dose, data variability, and number of data on the parameter estimation are analyzed for the new and one of the previously described methods. Our analysis is based on reconstruction of true IC(50) and SC(50) values from rich and sparse computer-generated data sets modified by two noise levels. Extensions of these methods to two dose data sets are presented. Both methods yielded IC(50) and SC(50) close to the known true values. Depending on the factors mentioned above, these methods exhibited different levels of accuracy.

Dose-Response Relationship, Drug↗

PubMed2002

A signal transduction pharmacodynamic model of the kinetics of the parasympathomimetic activity of low-dose scopolamine and atropine in rats.

We used a novel pharmacokinetic-pharmacodynamic (PK-PD) approach that had been applied for signal transduction kinetics to investigate the kinetics of the parasympathomimetic effect of scopolamine and atropine in rats. The parasympathetic tone was assessed by continuous measurement of the power of the high frequency band (HF) of electrocardiogram (ECG) R-R intervals obtained by power spectral analysis (PSA) of heart rate variability (HRV). To overcome the inherent noise of the HRV-HF data and to quantitatively identify temporal changes in the autonomic tone, a new approach of stepwise regression of the cumulative HF data was applied. The elevation of the parasympathetic tone occurred after a significant lag time (>70 min) following scopolamine administrations [0.25 and 0.5 mg/kg intravenous (iv) bolus or infusion over 100 min], followed by a gradual return to the baseline levels. A similar lag time in parasympathetic stimulation was observed following iv bolus administration of atropine (0.1 mg/kg). The plasma drug concentration versus time data were linked to the response versus time data using a signal transduction pharmacodynamic model that was fitted simultaneously to all four experimental data sets. This PK-PD model resolved the significant discrepancy between the concentration versus time and the response versus time patterns and successfully described the kinetics of the parasympathetic stimulation obtained for different drugs and different rates of administration. This work paves the way for further PK-PD preclinical investigations in this field.

Animals↗

PubMed2002

Multiple-pool cell lifespan model of hematologic effects of anticancer agents.

The leukopenic effects of anticancer agents are described using a semi-physiologic multiple-pool cell lifespan model. The time course of myelosuppression in relation to the drug concentration vs. time profile was characterized using a three pool indirect model. The proliferation and maturation stages of myeloid cells in the bone marrow and cell removal from the circulation were quantitated with a cell life-span concept. Drug effects were assumed to take place in the bone marrow based on irreversible linear or capacity-limited cytotoxicity. Mathematical derivations and computer simulations (Adapt II) were used to examine the properties of the model. Data from the literature were also analyzed. Cell response profiles after therapy typically exhibit a lag period, reduction to a nadir, and return to baseline. The predicted values of the time periods of granulopoiesis were 10-14 days for proliferation, and 1-6 days for maturation of progenitor cells in the bone marrow. The proposed irreversible mechanism of cell killing by anticancer drugs explains previously observed relationships between leukocyte nadir counts and exposure to the drug and/or duration of drug concentrations above some threshold level. The model was applied to literature data for paclitaxel and etoposide effects on leukocyte counts. The predicted value of KC50 for paclitaxel ranged from 0.004 to 0.2 microgram/mL and for etoposide 2 micrograms/mL. The present model accounts for drug-induced leukopenia using a physiologic cell production and loss model and irreversible cytotoxicity in a precursor pool.

Animals↗

PubMed2002

Neuronal integrative analysis of the "Dumbbell" model for passive neurons.

We analyze the so called "Dumbbell" model of Jackson (J. Neurophysiol. 69 (1993) pp. 464) for a single neuron consisting of a patch-clamped cell body attached to dendritic cable of finite length terminating in an oblique derivative ("natural termination") boundary condition representing a dendritic swelling or a natural ending sealed by a continuous surface of the cell membrane. The model is solved analytically via the Green's function method. Large and small time asymptotic behavior of the membrane potential is developed when there is a somatic voltage-clamp imposed. We discuss the difference in the voltage distribution if a sealed-end (Neumann) termination is used instead of the natural termination boundary condition. If the access resistance is large the differences between the potentials corresponding to the two boundary conditions are small at the soma, but can vary significantly near the dendritic termination. This discrepancy is amplified at the soma if there is a synaptic stimulus introduced between the soma and dendritic tip.

Animals↗

PubMed2002

Pharmacodynamic modeling of thrombopoietin, platelet, and megakaryocyte dynamics in patients with acute myeloid leukemia undergoing dose intensive chemotherapy.

A proposed model of thrombopoietin (TPO) regulation is that of a constitutive production of TPO with circulating levels being predominately regulated by changes in platelet and megackaryocyte mass. Using a pharmacodynamic (PD) approach, the authors examined the validity of this model for patients with acute myeloid leukemia (AML) undergoing dose-intensive postinduction chemotherapy (HDT). TPO and platelet values were assayed weekly in AML patients undergoing HDT. A parsimonious dynamic model was then applied to these experimental data. The results (1) support the proposed model of TPO regulation, (2) model and quantify the effects of HDT on the megakaryocyte compartment, (3) characterize variables not amenable to direct measurement, and (4) have clinical utility as this model predicted that TPO given after HDT would not have a significant effect on platelet recovery, a finding borne out in clinical trials. This model provides information relevant to the interpretation of clinical trials of hematopoietic growth factors.

Adult↗