The Funnel: a Screening Technique for Identifying Optimal Two-Drug Combination Chemotherapy Regimens.

The Mycobacterium tuberculosis drug discovery effort has generated a substantial number of new/repurposed drugs for therapy for this pathogen. The arrival of these drugs is welcome, but another layer of difficulty has emerged. Single agent therapy is insufficient for patients with late-stage tuberculosis because of resistance emergence. To achieve our therapeutic ends, it is requisite to identify optimal combination regimens. These regimens go through a lengthy and expensive evaluative process. If we have a modest group of 6 to 8 new or repurposed agents, this translates into 15 to 28 possible 2-drug combinations. There is neither time nor resources to give an extensive evaluation for all combinations. We sought a screening procedure that would identify combinations that had a high likelihood of achieving good bacterial burden decline. We examined pretomanid, moxifloxacin, linezolid, and bedaquiline in log-phase growth, acid-phase growth, and nonreplicative persister (NRP) phase in the Greco interaction model. We employed the interaction term α and the calculated bacterial burden decline as metrics to rank different regimens in different metabolic states. No relationship was found between α and bacterial kill. We chose bacterial kill as the prime metric. The combination of pretomanid plus moxifloxacin emerged as the clear frontrunner, as the largest bacterial declines were seen in log phase and acid phase with this regimen and it was second best in NRP phase. Bedaquiline also produced good kill. This screening process may identify optimal combinations that can be further evaluated in both the hollow-fiber infection model and in animal models of Mycobacterium tuberculosis infection.

Modeling Ribavirin-Induced Anemia in Patients with Chronic Hepatitis C Virus.

Ribavirin remains an important component of hepatitis C treatment in certain clinical scenarios, but it causes hemolytic anemia. A quantitative understanding of the ribavirin exposure-anemia relationship is important in dose individualization/optimization. We developed a model relating ribavirin triphosphate (RTP) exposure in red blood cells (RBCs), RBC lifespan, feedback regulation of RBC production when anemia occurs, and the resulting hemoglobin decline. Inosine triphosphatase (ITPA) and interleukin 28B (IL28B) genetics were found to be significant covariates. Clinical trial simulations predicted that anemia is least severe in IL28B non-CC (rs12979860, CT or TT), ITPA variant subjects, followed by IL28B non-CC, ITPA wild-type, IL28B CC, ITPA variant, and IL28B CC, ITPA wild-type subjects (most severe). Reducing the ribavirin dose from 1,200/1,000 mg to 800/600 mg could reduce the proportions of grade 2 anemia by about half. The resulting model framework will aid the development of dosing strategies that minimize the incidence of anemia in treatment regimens that include ribavirin.

Pharmacodynamic model of topotecan-induced time course of neutropenia.

Pharmacodynamic measures of neutropenia, such as absolute neutrophil count at nadir and neutrophil survival fraction, may not reflect the overall time course of neutropenia. We developed a pharmacokinetic-pharmacodynamic model to describe and quantify the time course of neutropenia after administration of topotecan to children and to compare this with nonhuman primates (NHPs) as a potential preclinical model of neutropenia. Topotecan was administered as a 30-min infusion daily for 5 days, repeated every 21 days. As part of a Phase I Pediatric Oncology Group study, topotecan was administered at 1.4 and 1.7 mg/m(2)/day without filgrastim (POG), and at 1.7, 2, and 2.4 mg/m(2)/day with filgrastim (POG+G). In NHPs, topotecan was administered at 5, 10, and 20 mg/m(2)/day without filgrastim. A pharmacokinetic-pharmacodynamic model was fit to profiles of topotecan lactone plasma concentrations and neutrophil survival fraction from cycle 1 and used to calculate topotecan lactone area under the plasma concentration-versus-time curve from 0 to 120 h (AUC(LAC)) and the area between the baseline and treatment-related neutrophil survival fraction (ABC) from 0 to 700 h. The mean +/- SD neutrophil survival fraction at nadir for the POG, POG+G, and NHP groups was 0.12 +/- 0.09, 0.11 +/- 0.17, and 0.09 +/- 0.08, respectively (P > 0.05). The mean +/- SD for the ratio of ABC to AUC(LAC) for the POG and NHP groups was 1.02 +/- 0.38 and 0.16 +/- 0.09, respectively (P < 0.05). The model estimate of ABC and the ratio of ABC to AUC(LAC) in children and NHPs may better reflect sensitivity to chemotherapy-induced neutropenia.

Use of drug effect interaction modeling with Monte Carlo simulation to examine the impact of dosing interval on the projected antiviral activity of the combination of abacavir and amprenavir.

The delineation of optimal regimens for combinations of agents is a difficult problem, in part because, to address it, one needs to (i) have effect relationships between the pathogen in question and the drugs in the combination, (ii) have knowledge of how the drugs interact (synergy, antagonism, and additivity), and (iii) address the issue of true between-patient variability in pharmacokinetics for the drugs in the population. We have developed an approach which employs a fully parametric assessment of drug interaction using the equation of W. R. Greco, G. Bravo, and J. C. Parsons (Pharmacol. Rev. 47:331-385, 1995) to generate an estimate of effects for the two drugs and have linked this approach to a population simulator, using Monte Carlo methods, which produce concentration-time profiles for the drugs in combination. This software automatically integrates the effect over a steady-state dosing interval and produces an estimate of the mean effect over a steady-state interval for each simulated subject. In this way, doses and schedules can be easily evaluated. This software allows for a rational choice of dose and schedule for evaluation in clinical trials. We evaluated different schedules of administration for the combination of the nucleoside analogue abacavir plus the human immunodeficiency virus type 1 protease inhibitor amprenavir. Amprenavir was simulated as either 800 mg every 8 h (q8h) or 1,200 mg q12h, each along with 300 mg q12h of abacavir. Both regimens produced excellent effects over the simulated population of 500 subjects, with average percentages of maximal effect (as determined from the in vitro assays) of 90.9%+/- 11.4% and 80.9%+/-18.6%, respectively. This difference is statistically significant (P<<0.001). In addition, 68.8 and 46.0% of the population had an average percentage of maximal effect which was greater than or equal to 90% for the two regimens. We can conclude that the combination of abacavir plus amprenavir is a potent combination when it is given on either schedule. However, the more fractionated schedule for the protease inhibitor produced significantly better effects in combination. Clinicians need to explicitly balance the improvement in antiviral effect seen with the more fractionated regimen against the loss of compliance attendant to the use of such a regimen. This approach may be helpful in the preclinical evaluation of multidrug anti-infective regimens.

The triple combination indinavir-zidovudine-lamivudine is highly synergistic.

Administration of the combination of indinavir-zidovudine-lamivudine has been demonstrated to cause a large fraction of treated patients to have a decline in human immunodeficiency virus type 1 (HIV-1) copy number to below the detectability of sensitive assays. A recent investigation (G. L. Drusano, J. A. Bilello, D. S. Stein, M. Nessly, A. Meibohm, E. A. Emini, P. Deutsch, J. Condra, J. Chodakewitz, and D. J. Holder, J. Infect. Dis. 178:360-367, 1998) demonstrated that the durability of the antiviral effect was affected by combination chemotherapy. Zidovudine-lamivudine-indinavir differed significantly from the combination of zidovudine plus indinavir. We hypothesized that the addition of lamivudine might alter the regimen, producing a synergistic anti-HIV effect. In vitro analysis of drug interaction demonstrated that zidovudine-indinavir interacted additively. The addition of lamivudine in concentrations which suppressed viral replication by 20% or less by itself demonstrated marked increases in the synergy volume, increasing the synergy volume 20-fold with the addition of 320 nM lamivudine (which does not suppress HIV by itself) and 40-fold with the addition of 1,000 nM lamivudine (20% viral inhibition as a single agent). A fully parametric analysis with a newly developed model for three-drug interaction confirmed and extended these observations. The interaction term (alpha(IND,AZT, 3TC)) for all three drugs showed the greatest degree of synergy. This marked synergistic interaction among the three agents may explain some of the clinical results which differentiate this regimen from the double-drug regimen of zidovudine plus indinavir.

Nucleoside analog 1592U89 and human immunodeficiency virus protease inhibitor 141W94 are synergistic in vitro.

The use of combinations of anti-human immunodeficiency virus (anti-HIV) agents targeted to different molecular targets will most likely result in increased viral suppression and may also delay or prevent the emergence of resistant HIV strains. The purpose of the present study was to develop information on the in vitro anti-HIV activities of combinations of the reverse transcriptase inhibitor 1592U89 and the protease inhibitor 141W94 to help guide the choice of dosages in clinical trials. Triplicate in vitro dose-response matrices were prepared with MT-2 cells infected with HIV type 1 (HIV-1) strain IIIB. In order to account for the effects of protein binding, tissue culture medium with 10% fetal bovine serum was supplemented with the human serum proteins alpha1 acid glycoprotein (1 mg/ml) and albumin (40 mg/ml). The three-dimensional drug interaction surface for 1592U89 and 141W94 was constructed with the program MacSynergy II. As analyzed relative to a Bliss Independence null reference model, this combination was synergistic, with volumes of synergy exceeding 100 (99% confidence). Analysis of the data set with a fully parametric form of an equation for the quantitation of drug interaction developed by Greco et al. (W. R. Greco, G. Bravo, and J. C. Parsons, Pharmacol. Rev. 47:331-385, 1995) resulted in an interaction term statistically significantly greater than 0.0, indicating true synergy. Both methods concur that this combination is significantly synergistic. These data, with favorable findings from phase I/II trials for each drug alone, suggest that the combination of 1592U89 plus 141W94 should be further evaluated in clinical trials.

Fluid dynamics of a partially collapsible stenosis in a flow model of the coronary circulation.

The influence of passive vasomotion on the pressure drop-flow (delta P-Q) characteristics of a partially compliant stenosis was studied in an in vitro model of the coronary circulation. Twelve stenosis models of different severities (50 to 90 percent area reduction) and degrees of flexible wall (0 to 1/2 of the wall circumference) were inserted into thin-walled latex tubing and pressure and flow data were collected during simulated cardiac cycles. In general, the pressure drop increased with increasing fraction of flexible wall for a given flow rate and stenosis severity. The magnitude of this effect was directly dependent upon the underlying stenosis severity. The diastolic delta P-Q relationship of severe, compliant models exhibited features of partial collapse with an increase in pressure drop at a decreasing flow rate. It is concluded that passive vasomotion of a normal wall segment at an eccentric stenosis in response to periodic changes in intraluminal pressure causes dimensional changes in the residual lumen area which can strongly affect the hemodynamic characteristics of the stenosis during the cardiac cycle. This mechanism may have important implications for the onset of plaque fracture and the prediction of the functional significance of a coronary stenosis based on quantitative angiogram analysis.

On the correction for radioactive decay in pharmacokinetic modeling.

The question of how to include radioactive decay during biological modeling with first-order differential equations was considered. Modeling may involve either experimental data y(t) or decay-corrected data z(t) [identical to exp(lambda t)y(t) where lambda is the decay constant] for each compartment. It is sometimes assumed that the latter are solutions to corresponding purely pharmacokinetic models (no decay). We primarily compared the two analyses in the case where the model did not require simultaneous consideration of both labeled and unlabeled material. A general theorem was found which limits the use of decay-corrected data to pharmacokinetic models containing linear, homogeneous differential equations. By way of verification, an example of this model type was analyzed for a chimeric monoclonal antibody biodistribution in man. Even in this case, statistically significant differences between the two solutions showed that one may find different model parameters depending upon which data set (y or z) was analyzed. For other mathematical forms, the analyst must include the physical decay in all relevant compartments. By analyzing an open, quadratic model, effects of not including decay were seen to be maximized if the biological rate constant was > or = lambda, the physical decay constant. Finally, using monoclonal antibody-antigen reactions, similar discrepancies between the z functions and the pharmacokinetic variables were demonstrated. This result was found to persist even if competitive molecules were included. We conclude that decay-corrected data may be shown, but should not be entered into the modeling equations unless the latter are of the linear, homogeneous form.

Targeting the systemic exposure of teniposide in the population and the individual using a stochastic therapeutic objective.

A stochastic control approach for dose regimen design is developed and applied to the problem of targeting the systemic exposure, defined as the area under the blood concentration-time curve (AUC), of the anticancer drug teniposide in both the population and individual patients. The control objective involves maximizing the probability that AUC is within a selected target interval given either the population distribution for the kinetic model parameters (a priori control) or the posterior distribution for an individual patient (feedback control). Results of a detailed simulation study are presented, illustrating the feasibility of applying stochastic control principles to the design of dose regimens. The predictive ability of the calculated distributions of AUC for the population and for individuals is evaluated in part by determining the percentage coverage of the computed 95% uncertainty intervals using the simulation results. For the a priori control phase, 94% of the simulated subjects had values of systemic exposure within the computed 95% uncertainty interval, while 93.4% of the simulated subjects had feedback control phase systemic exposure values within their computed 95% uncertainty intervals. Similar evaluation of the uncertainty intervals calculated for plasma concentrations further document the ability of the proposed stochastic control method to predict the uncertainty associated with future therapy.

Analysis of segmental phosphate absorption in intact rats. A compartmental analysis approach.

Available information supports the dominance of the proximal intestine in inorganic phosphate (Pi) absorption. However, there is no strategy for analyzing segmental Pi absorption from a spontaneously propelled meal in an intact animal. We propose a solution using compartmental analysis. After intragastric administration of a 32P-labeled Pi liquid meal containing a nonabsorbable marker, [14C]polyethylene glycol (PEG), rats were killed at 2, 10, 20, 30, 60, 120, and 240 min. The gastrointestinal tract was removed and divided into seven segments, from which 32P and [14C]PEG were recovered. Data was expressed as a percentage of the dose fed, i.e., (32P[in segment] divided by 32P[fed]) and [14C]PEG[in segment] divided by [14C]PEG[fed]), respectively. A compartmental model was constructed and the rate constants for intersegmental transit and segmental absorption were estimated. The "goodness of fit" between the simulated model and the actual data indicates the estimated rate constants reflect in vivo events. The duodenum, with the highest transit and absorption rates, accounted for a third of the total absorption. However, the terminal ileum, with a lower absorption rate but a longer transit time, absorbed an equal amount of Pi. This approach allows the analysis of the mechanism and the regulation of Pi absorption under more authentic in vivo conditions.

Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments.

An experiment design procedure is proposed for nonlinear parameter estimation studies that formally incorporates prior parameter uncertainty. The design criterion derives from information theory considerations and involves an asymptotic interpretation of the expected posterior information provided by an experiment. A pharmacokinetic sample schedule design problem is used to illustrate and evaluate this information theoretic design strategy. The model considered is commonly used to describe the plasma concentration of a drug following its oral administration. The limitations and advantages of the proposed design procedure are discussed in relation to other previously reported design techniques for incorporating parameter uncertainty.

A kinetic model for 99mTc-DMSA in the rat.

A pharmacokinetic model was developed for the renal imaging agent 99mTc-DMSA in anesthetized rats, which incorporated data from serial measurements of blood and urine simultaneously with dynamic images obtained over an 8-h period. Animals which received a 10 mg/kg dose of unlabeled DMSA immediately before 99mTc-DMSA injection had a significantly reduced kidney accumulation and greater urinary elimination of 99mTc than animals which received the radiopharmaceutical alone. The kidney clearance was also significantly lower in rats receiving unlabeled DMSA, but no significant difference was determined between the urine clearance estimates of the two animal groups. Because the increase in the amount eliminated in the urine was not coupled with a significant change in urine clearance, it would appear that unlabeled DMSA saturated the kidney uptake mechanism(s) of 99mTc-DMSA without modifying the urinary clearance process. This interpretation is consistent with the hypothesis that renal handling of 99mTc-DMSA is governed by both glomerular filtration and peritubular capillary uptake. The simultaneous acquisition of blood, urine and non invasive image data allows for a comprehensive and informative model of the physiological disposition of 99mTc-DMSA.

A minimal model of liver glycogen metabolism; feasibility for predicting flux rates.

A minimal model of glycogen metabolism can allow the estimation of the flux rates in the glycogen pathway from the time course of the intermediates in the pathway, measured during substrate administration and hormonal stimulation. The comprehensive model of El-Refai & Bergman (Am. J. Physiol. 231, 1608, 1976) consisting of six compartments and 26 non-estimable parameters has successfully accounted for the responses of hepatic glycogenic intermediates in response to a glucose load in hepatocytes (Katz et al., J. biol. Chem. 253, 4530, 1978), in perfused liver (Nordlie et al., J. biol. Chem. 255, 1834, 1980) and during refeeding in vivo (Van DeWerve & Jeanrenaud, Am. J. Physiol. 247, E271, 1984). The comprehensive model is here reduced to a minimal model, consisting of five compartments representing extracellular and intracellular glucose, glucose-phosphate, uridine diphosphate glucose (UDPG), glycogen, and five parameters estimated from the hepatic response to a given stimulus. Estimation of these parameters requires the measurement of the net hepatic glucose balance, the net gluconeogenic flux, and the time course of glycogenic intermediates responding to a hormone or substrate stimulus. The hepatic glycogenolytic response predicted by the comprehensive model in response to an increase in glucagon is closely fitted by the minimal model. When Gaussian distributed random error was added, 0-5% SD in the glucose and glycogen compartments and 0-10% SD in the glucose-phosphate and UDPG compartments, the hepatic response predicted by the minimal model was virtually free of the added error, and the model parameters were found to be within 30% of their true values. When the minimal model was used to interpret the experimental response to an increase in glucose concentration it predicted that: (1) glucokinase can phosphorylate glucose at rates similar to maximal rates of net glycogen synthesis; (2) futile cycling at the glycogen/glucose-1-phosphate level can limit glycogen synthesis; and (3) glucose-6-phosphatase inhibition by glucose has a significant role in net glycogen synthesis.

Simulation of linear compartment models with application to nuclear medicine kinetic modeling.

Several techniques are evaluated for solving the linear ordinary differential equations arising from compartment models. The methods involve approximating the matrix exponential of the state matrix (i.e. the transition matrix). The computational efficiencies of these techniques, together with that of a general purpose differential equation solver, are compared for several models arising from radiopharmacokinetic studies. The matrix exponential calculations are performed using both Ward's Padé approximation method and an eigenvalue-eigenvector decomposition (QR factorization) of the matrix A. These two algorithms have been incorporated as simulation options into the programs of the ADAPT package. ADAPT consists of a set of high-level programs for simulation, parameter estimation and experiment design, developed primarily for basic and clinical research modeling and data analysis applications involving pharmacokinetic and pharmacodynamic processes. The advantages and disadvantages of these simulation strategies for solving linear kinetic models within a parameter estimation setting are illustrated and discussed.

Implementation and evaluation of control strategies for individualizing dosage regimens, with application to the aminoglycoside antibiotics.

Three strategies are implemented for controlling serum concentrations by determining individualized dosage regimens. The methods incorporate, respectively, nonlinear least squares parameter estimation, Bayesian maximum a posteriori probability estimation, and a stochastic control procedure that minimizes the expected value of an appropriate therapeutic cost. The performance of the three dose regimen calculation strategies was evaluated using Monte Carlo simulations of a typical therapeutic protocol for tobramycin.

Noninvasive estimation of bound and mobile platinum compounds in the kidney using a radiopharmacokinetic model.

Nephrotoxicity remains a major limitation in the use of cisplatin [cis-diamminedichloroplatinum(II)]. Although several strategies are in use to limit this serious side effect, none is fully satisfactory. Classical pharmacokinetic studies of cisplatin have been based on blood and urine samples. As nephrotoxicity plays a significant role in the design of the therapeutic strategy, the kidneys should be considered as a separate state in any model formulated for ultimate control purposes. Previous studies of organ pharmacokinetics have relied on population measurements. The authors have developed an organ compartmental model from individual animal data obtained noninvasively. The eight-compartment model used to represent the distribution of cisplatin considers free and bound platinum in plasma, platinum in the erythrocytes, mobile and bound platinum in the kidneys, mobile and bound platinum in the tissues, and platinum in the urine. Data were collected from experiments with anesthetized female rats, after intravenous administration of [195mPt]cisplatin. Both arterial and bladder samples, and multiple images obtained with an Anger camera interfaced to a microcomputer were used. The model was estimated from individual data obtained after injection of a bolus of cisplatin (six animals). The model was validated by using it to predict data obtained from forcing the system with a different input function, a 0.5-h intravenous infusion (three animals). The results of this work show that it is possible to noninvasively study drug kinetics in organs that are not readily accessible to direct measurements in an individual, rather than relying on invasive measurements performed on a population.(ABSTRACT TRUNCATED AT 250 WORDS)

Computer assessment of hemodynamic severity of coronary artery stenosis from angiograms.

A computer-assisted analysis of coronary obstructions from cineangiograms is presented, which includes both the geometric and hemodynamic evaluation of coronary stenosis severity. Single frame images are digitized into a 512 X 512 X 8 bit array after a cine-to-video conversion. Automatic edge tracking is performed using a combination of derivative and threshold methods. Vessel borders from two orthogonal views of the arterial segment are used to create a three-dimensional reconstruction of the stenosis, which serves as a basis for calculation of absolute and relative geometric dimensions, stenotic resistance and trans-stenotic pressure gradient for various given flow rates. A preliminary performance evaluation of this method was made by analysis of x-ray phantoms representing stenoses of known dimensions, which were filmed under quasi-clinical conditions. The results are discussed with respect to their accuracy and reproducibility.

Adaptive control of theophylline therapy: importance of blood sampling times.

A two-observation protocol for estimating theophylline clearance during a constant-rate intravenous infusion is used to examine the importance of blood sampling schedules with regard to the information content of resulting concentration data. Guided by a theory for calculating maximally informative sample times, population simulations are used to assess the effect of specific sampling times on the precision of resulting clearance estimates and subsequent predictions of theophylline plasma concentrations. The simulations incorporated noise terms for intersubject variability, dosing errors, sample collection errors, and assay error. Clearance was estimated using Chiou's method, least squares, and a Bayesian estimation procedure. The results of these simulations suggest that clinically significant estimation and prediction errors may result when using the above two-point protocol for estimating theophylline clearance if the time separating the two blood samples is less than one population mean elimination half-life.

Experimental design for estimating integrals by numerical quadrature, with applications to pharmacokinetic studies.

Many experimental situations, including bioavailability studies, require the estimation of integrals by numerical quadrature applied to dependent variable observations with measurement error. A strategy is described for selecting values for the independent variable (e.g. time). The strategy minimizes the expectation of the square of the difference between the exact integral and the quadrature approximation. This approach was applied to simulated pharmacokinetic problems, including the estimation of bioavailability. Results indicate that the procedure is potentially useful in reducing the variance of resulting estimates and that it appears to be robust with respect to prior assumptions about model parameter values.

Sampling strategies for noncompartmental estimation of mean residence time.

An optimization procedure is presented for selecting sample times for estimating mean residence time using noncompartmental data analysis. Performance of this experimental design strategy is evaluated using Monte Carlo simulations of a model for digoxin kinetics. The contribution of measurement error to the overall expected error in MRT estimates is examined and its importance emphasized. Also, the sensitivity of the proposed experimental design strategy to required assumptions is investigated using the digoxin model, and the importance of accurate estimates of extrapolated areas is noted.