Mixed-effects modeling of clinical DCE-MRI data: application to colorectal liver metastases treated with bevacizumab.

PURPOSE: Most dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data are evaluated for individual patients with cohorts analyzed to detect significant changes from baseline values, repeating the process at each posttreatment timepoint. Our study aimed to develop a statistically valid model for the complete time course of DCE-MRI data in a patient cohort. MATERIALS AND METHODS: Data from 10 patients with colorectal cancer liver metastases were analyzed, including two baseline scans and four post-bevacizumab scans. Apparent changes in tumor median K(trans) were adjusted for changes in observed enhancing tumor fraction (EnF) by multiplying K(trans) by EnF (KEnF). A mixed-effects model (MEM) was defined to describe the KEnF time course for all patients simultaneously by assuming a three-parameter indirect response model with model parameters lognormally distributed across patients. RESULTS: The typical cohort time course showed a KEnF reduction to 59% of baseline at 24 hours, returning to 65% of baseline values by day 12. Interpatient variability of model parameters ranged from 11% to 307%. CONCLUSION: The MEM approach has potential for comparing responses at a group level in clinical trials with different doses, schedules, or combination regimens. Furthermore, the KEnF biomarker successfully resolved confounds in interpreting K(trans) arising from therapy induced changes in the volume of enhancing tumor.

The power of FDG-PET to detect treatment effects is increased by glucose correction using a Michaelis constant.

BACKGROUND: We recently showed improved between-subject variability in our [18F]fluorodeoxyglucose positron emission tomography (FDG-PET) experiments using a Michaelis-Menten transport model to calculate the metabolic tumor glucose uptake rate extrapolated to the hypothetical condition of glucose saturation: MRglucmax=Ki*(KM+[glc]), where Ki is the image-derived FDG uptake rate constant, KM is the half-saturation Michaelis constant, and [glc] is the blood glucose concentration. Compared to measurements of Ki alone, or calculations of the scan-time metabolic glucose uptake rate (MRgluc = Ki * [glc]) or the glucose-normalized uptake rate (MRgluc = Ki*[glc]/(100 mg/dL), we suggested that MRglucmax could offer increased statistical power in treatment studies; here, we confirm this in theory and practice. METHODS: We compared Ki, MRgluc (both with and without glucose normalization), and MRglucmax as FDG-PET measures of treatment-induced changes in tumor glucose uptake independent of any systemic changes in blood glucose caused either by natural variation or by side effects of drug action. Data from three xenograft models with independent evidence of altered tumor cell glucose uptake were studied and generalized with statistical simulations and mathematical derivations. To obtain representative simulation parameters, we studied the distributions of Ki from FDG-PET scans and blood [glucose] values in 66 cohorts of mice (665 individual mice). Treatment effects were simulated by varying MRglucmax and back-calculating the mean Ki under the Michaelis-Menten model with KM = 130 mg/dL. This was repeated to represent cases of low, average, and high variability in Ki (at a given glucose level) observed among the 66 PET cohorts. RESULTS: There was excellent agreement between derivations, simulations, and experiments. Even modestly different (20%) blood glucose levels caused Ki and especially MRgluc to become unreliable through false positive results while MRglucmax remained unbiased. The greatest benefit occurred when Ki measurements (at a given glucose level) had low variability. Even when the power benefit was negligible, the use of MRglucmax carried no statistical penalty. Congruent with theory and simulations, MRglucmax showed in our experiments an average 21% statistical power improvement with respect to MRgluc and 10% with respect to Ki (approximately 20% savings in sample size). The results were robust in the face of imprecise blood glucose measurements and KM values. CONCLUSIONS: When evaluating the direct effects of treatment on tumor tissue with FDG-PET, employing a Michaelis-Menten glucose correction factor gives the most statistically powerful results. The well-known alternative 'correction', multiplying Ki by blood glucose (or normalized blood glucose), appears to be counter-productive in this setting and should be avoided.

18F-FDG PET as a surrogate biomarker in non-small cell lung cancer treated with erlotinib: newly identified lesions are more informative than standardized uptake value.

UNLABELLED: This study assesses the predictive value of (18)F-FDG PET for overall survival in lung cancer patients treated with a targeted drug. METHODS: (18)F-FDG PET was performed in 125 second- or third-line non-small cell lung cancer (NSCLC) patients with a baseline Eastern Cooperative Oncology Group performance status less than 3 before treatment with erlotinib (150 mg daily) and 2 wk into treatment. The predictive value of (18)F-FDG PET, clinical parameters, and epithelial growth factor receptor (EGFR) mutation status for survival duration was evaluated by fitting accelerated failure time models. RESULTS: New lesions on PET at 2 wk, EGFR mutation status, performance status, and baseline tumor burden were independent and significant predictors of overall survival. Reduction of maximum standardized uptake value by at least 35% was predictive of survival only when EGFR mutation status was not accounted for. CONCLUSION: (18)F-FDG PET in second- or third-line NSCLC patients at 2 wk after starting treatment with erlotinib carries information about overall survival. Parametric survival modeling enables a quantitative assessment of the predictive value of (18)F-FDG PET in the context of clinical and laboratory information. New-lesion status by (18)F-FDG PET at 2 wk is a potential surrogate biomarker for survival in NSCLC.

Quantitation of glucose uptake in tumors by dynamic FDG-PET has less glucose bias and lower variability when adjusted for partial saturation of glucose transport.

BACKGROUND: A retrospective analysis of estimates of tumor glucose uptake from 1,192 dynamic 2-deoxy-2-(18F)fluoro-D-glucose-positron-emission tomography [FDG-PET] scans showed strong correlations between blood glucose and both the uptake rate constant [Ki] and the metabolic rate of glucose [MRGluc], hindering the interpretation of PET scans acquired under conditions of altered blood glucose. We sought a method to reduce this glucose bias without increasing the between-subject or test-retest variability and did this by considering that tissue glucose transport is a saturable yet unsaturated process best described as a nonlinear function of glucose levels. METHODS: Patlak-Gjedde analysis was used to compute Ki from 30-min dynamic PET scans in tumor-bearing mice. MRGluc was calculated by factoring in the blood glucose level and a lumped constant equal to unity. Alternatively, we assumed that glucose consumption is saturable according to Michaelis-Menten kinetics and estimated a hypothetical maximum rate of glucose consumption [MRGlucMAX] by multiplying Ki and (KM + [glucose]), where KM is a half-saturation Michaelis constant for glucose uptake. Results were computed for 112 separate studies of 8 to 12 scans each; test-retest statistics were measured in a suitable subset of 201 mice. RESULTS: A KM value of 130 mg/dL was determined from the data based on minimizing the average correlation between blood glucose and the uptake metric. Using MRGlucMAX resulted in the following benefits compared to using MRGluc: (1) the median correlation with blood glucose was practically zero, and yet (2) the test-retest coefficient of variation [COV] was reduced by 13.4%, and (3) the between-animal COVs were reduced by15.5%. In statistically equivalent terms, achieving the same reduction in between-animal COV while using the traditional MRGluc would require a 40% increase in sample size. CONCLUSIONS: MRGluc appeared to overcorrect tumor FDG data for changing glucose levels. Applying partial saturation correction using MRGlucMAX offered reduced bias, reduced variability, and potentially increased statistical power. We recommend further investigation of MRGlucMAX in quantitative studies of tumor FDG uptake.

Maximizing tumour exposure to anti-neuropilin-1 antibody requires saturation of non-tumour tissue antigenic sinks in mice.

BACKGROUND AND PURPOSE: Neuropilin-1 (NRP1) is a VEGF receptor that is widely expressed in normal tissues and is involved in tumour angiogenesis. MNRP1685A is a rodent and primate cross-binding human monoclonal antibody against NRP1 that exhibits inhibition of tumour growth in NPR1-expressing preclinical models. However, widespread NRP1 expression in normal tissues may affect MNRP1685A tumour uptake. The objective of this study was to assess MNRP1685A biodistribution in tumour-bearing mice to understand the relationships between dose, non-tumour tissue uptake and tumour uptake. EXPERIMENTAL APPROACH: Non-tumour-bearing mice were given unlabelled MNRP1685A at 10 mg·kg(-1) . Tumour-bearing mice were given (111) In-labelled MNRP1685A along with increasing amounts of unlabelled antibody. Blood and tissues were collected from all animals to determine drug concentration (unlabelled) or radioactivity level (radiolabelled). Some animals were imaged using single photon emission computed tomography - X-ray computed tomography. KEY RESULTS: MNRP1685A displayed faster serum clearance than pertuzumab, indicating that target binding affected MNRP1685A clearance. I.v. administration of (111) In-labelled MNRP1685A to tumour-bearing mice yielded minimal radioactivity in the plasma and tumour, but high levels in the lungs and liver. Co-administration of unlabelled MNRP1685A with the radiolabelled antibody was able to competitively block lungs and liver radioactivity uptake in a dose-dependent manner while augmenting plasma and tumour radioactivity levels. CONCLUSIONS AND IMPLICATIONS: These results indicate that saturation of non-tumour tissue uptake is required in order to achieve tumour uptake and acceptable exposure to antibody. Utilization of a rodent and primate cross-binding antibody allows for translation of these results to clinical settings.

Noncompartmental kinetic analysis of DCE-MRI data from malignant tumors: Application to glioblastoma treated with bevacizumab.

Dynamic contrast enhanced MRI contrast agent kinetics in malignant tumors are typically complex, requiring multicompartment tumor models for adequate description. For consistent comparisons among tumors or among successive studies of the same tumor, we propose to estimate the total contrast agent-accessible volume fraction of tumor, including blood plasma, v(pe), and an average transfer rate constant across all tumor compartments, K(trans.av), by fitting a three-compartment tumor model and then calculating the area under the tumor impulse-response function (= v(pe)) and the ratio area under the tumor impulse response function over mean residence time in tumor (= K(trans.av)). If the duration of dynamic contrast enhanced MRI was too short to extrapolate the tumor impulse-response function to infinity with any confidence, then conditional parameters v(pe)(*) and K(trans.av*) should be calculated from the available incomplete impulse response function. Median decreases of 33% were found for both v(pe)(*) and K(trans.av*) in glioblastoma patients (n = 16) 24 hours after the administration of bevacizumab (P < 0.001). Median total contrast-enhancing tumor volume was reduced by 18% (P < 0.0001). The combined changes of tumor volume, v(pe)(*), and K(trans.av*) suggest a reduction of true v(pe), possibly accompanied by a reduction of true K(trans.av). The proposed method provides estimates of a scale and a shape parameter to describe contrast agent kinetics of varying complexity in a uniform way.

An automated method for nonparametric kinetic analysis of clinical DCE-MRI data: application to glioblastoma treated with bevacizumab.

Here, we describe an automated nonparametric method for evaluating gadolinium-diethylene triamine pentaacetic acid (Gd-DTPA) kinetics, based on dynamic contrast-enhanced-MRI scans of glioblastoma patients taken before and after treatment with bevacizumab; no specific model or equation structure is assumed or used. Tumor and venous blood concentration-time profiles are smoothed, using a robust algorithm that removes artifacts due to patient motion, and then deconvolved, yielding an impulse response function. In addition to smoothing, robustness of the deconvolution operation is assured by excluding data that occur prior to the plasma peak; an exhaustive analysis was performed to demonstrate that exclusion of the prepeak plasma data does not significantly affect results. All analysis steps are executed by a single R script that requires blood and tumor curves as the sole input. Statistical moment analysis of the Impulse response function yields the area under the curve (AUC) and mean residence time (MRT). Comparison of deconvolution results to fitted Tofts model parameters suggests that AUCMRT and AUC of the Impulse response function closely approximate fractional clearance from plasma to tissue (K(trans)) and fractional interstitial volume (v(e)). Intervisit variability is shown to be comparable when using the deconvolution method (11% [AUCMRT] and 13%[AUC]) compared to the Tofts model (14%[K(trans)] and 24%[v(e)]). AUC and AUCMRT both exhibit a statistically significant decrease (P < 0.005) 1 day after administration of bevacizumab.

Erythropoietin dosing in children with chronic kidney disease: based on body size or on hemoglobin deficit?

There are no investigations demonstrating that body size-adapted doses of erythropoietin (EPO) are as equally effective in children as in adults. A treatment starting with 150 IU/kg body weight per week leads to an insufficient rise in hemoglobin levels in anemic children with chronic kidney disease (CKD). Nevertheless, this strategy is widely used and seems to be the reason for a high percentage of young anemic children in spite of EPO treatment. In children and in adults, 1,000 IU EPO intravenously increases the hemoglobin level equally by 0.04 g/l. This strongly argues for specifying the EPO dose in the treatment of children with CKD in absolute amounts. A prediction model exists which allows the determination of the EPO dose which is expected to raise hemoglobin from a given pretreatment level to a desired steady state level.

Parametric and nonparametric population methods: their comparative performance in analysing a clinical dataset and two Monte Carlo simulation studies.

BACKGROUND AND OBJECTIVES: This study examined parametric and nonparametric population modelling methods in three different analyses. The first analysis was of a real, although small, clinical dataset from 17 patients receiving intramuscular amikacin. The second analysis was of a Monte Carlo simulation study in which the populations ranged from 25 to 800 subjects, the model parameter distributions were Gaussian and all the simulated parameter values of the subjects were exactly known prior to the analysis. The third analysis was again of a Monte Carlo study in which the exactly known population sample consisted of a unimodal Gaussian distribution for the apparent volume of distribution (V(d)), but a bimodal distribution for the elimination rate constant (k(e)), simulating rapid and slow eliminators of a drug. METHODS: For the clinical dataset, the parametric iterative two-stage Bayesian (IT2B) approach, with the first-order conditional estimation (FOCE) approximation calculation of the conditional likelihoods, was used together with the nonparametric expectation-maximisation (NPEM) and nonparametric adaptive grid (NPAG) approaches, both of which use exact computations of the likelihood. For the first Monte Carlo simulation study, these programs were also used. A one-compartment model with unimodal Gaussian parameters V(d) and k(e) was employed, with a simulated intravenous bolus dose and two simulated serum concentrations per subject. In addition, a newer parametric expectation-maximisation (PEM) program with a Faure low discrepancy computation of the conditional likelihoods, as well as nonlinear mixed-effects modelling software (NONMEM), both the first-order (FO) and the FOCE versions, were used. For the second Monte Carlo study, a one-compartment model with an intravenous bolus dose was again used, with five simulated serum samples obtained from early to late after dosing. A unimodal distribution for V(d) and a bimodal distribution for k(e) were chosen to simulate two subpopulations of 'fast' and 'slow' metabolisers of a drug. NPEM results were compared with that of a unimodal parametric joint density having the true population parameter means and covariance. RESULTS: For the clinical dataset, the interindividual parameter percent coefficients of variation (CV%) were smallest with IT2B, suggesting less diversity in the population parameter distributions. However, the exact likelihood of the results was also smaller with IT2B, and was 14 logs greater with NPEM and NPAG, both of which found a greater and more likely diversity in the population studied. For the first Monte Carlo dataset, NPAG and PEM, both using accurate likelihood computations, showed statistical consistency. Consistency means that the more subjects studied, the closer the estimated parameter values approach the true values. NONMEM FOCE and NONMEM FO, as well as the IT2B FOCE methods, do not have this guarantee. Results obtained by IT2B FOCE, for example, often strayed visibly away from the true values as more subjects were studied. Furthermore, with respect to statistical efficiency (precision of parameter estimates), NPAG and PEM had good efficiency and precise parameter estimates, while precision suffered with NONMEM FOCE and IT2B FOCE, and severely so with NONMEM FO. For the second Monte Carlo dataset, NPEM closely approximated the true bimodal population joint density, while an exact parametric representation of an assumed joint unimodal density having the true population means, standard deviations and correlation gave a totally different picture. CONCLUSIONS: The smaller population interindividual CV% estimates with IT2B on the clinical dataset are probably the result of assuming Gaussian parameter distributions and/or of using the FOCE approximation. NPEM and NPAG, having no constraints on the shape of the population parameter distributions, and which compute the likelihood exactly and estimate parameter values with greater precision, detected the more likely greater diversity in the parameter values in the population studied. In the first Monte Carlo study, NPAG and PEM had more precise parameter estimates than either IT2B FOCE or NONMEM FOCE, as well as much more precise estimates than NONMEM FO. In the second Monte Carlo study, NPEM easily detected the bimodal parameter distribution at this initial step without requiring any further information. Population modelling methods using exact or accurate computations have more precise parameter estimation, better stochastic convergence properties and are, very importantly, statistically consistent. Nonparametric methods are better than parametric methods at analysing populations having unanticipated non-Gaussian or multimodal parameter distributions.

Simultaneous sustained release of fludarabine monophosphate and Gd-DTPA from an interstitial liposome depot in rats: potential for indirect monitoring of drug release by magnetic resonance imaging.

INTRODUCTION: Cytostatic depot preparations are interstitially administered for local chemotherapy and prevention of tumor recurrence. It would be of interest to monitor in patients as to when, to what extent, and exactly where, the drug is actually released. Liposomes containing a hydrophilic cytostatic and a hydrophilic contrast agent might be expected to release both agents simultaneously. If so, then drug release could be indirectly followed by monitoring contrast enhancement at the injection site. METHODS: Multivesicular liposomes containing the antimetabolite fludarabine monophosphate and the magnetic resonance imaging (MRI) contrast agent Gd-DTPA were subcutaneously injected in rats and both agents were monitored at the injection site for 6 weeks by 19F nuclear magnetic resonance spectroscopy (MRS) in vivo and contrast-enhanced 1H MRI (T1w 3D FLASH), respectively, in a 1.5-T whole-body tomograph. The MRS and MRI data were analyzed simultaneously by pharmacokinetic modeling using NONMEM. RESULTS: During an initial lag time, the amount of drug at the injection site stayed constant while the contrast-enhanced depot volume expanded beyond the volume injected. Drug amount and depot volume then decreased in parallel. Lag time and elimination half-life were 9 and 6 days, respectively, in three animals, and were about 50% shorter in another animal where the depot split into sub-depots. CONCLUSION: The preliminary data in rats suggest that simultaneous release of a hydrophilic cytostatic and a hydrophilic contrast agent from an interstitial depot can be achieved by encapsulation in liposomes. Thus, there seems to be a potential for indirect drug monitoring through imaging.

Recombinant human erythropoietin for the treatment of renal anaemia in children: no justification for bodyweight-adjusted dosage.

BACKGROUND: Drug doses for children are usually calculated by reducing adult doses in proportion to bodyweight. The clinically effective dose of recombinant human erythropoietin (epoetin) in children, however, seems to be higher than predicted by this calculation. OBJECTIVE: To determine the quantitative relationship between epoetin dose, bodyweight and response in children with end-stage renal disease. PATIENTS AND METHODS: The time-course of haemoglobin in 52 children during long-term treatment with epoetin beta was analysed by population pharmacodynamic modelling. Patients were 5-20 years old and weighed 16-53kg at the beginning of treatment. Epoetin beta was given intravenously three times per week after haemodialysis. Doses ranged from 110 to 7500IU (3-205 IU/kg). Haemoglobin versus time was described by assuming that the haemoglobin level rises after each dose due to the formation of new red blood cells, which then survive according to a logistic function. The initial rise after each dose was modelled in terms of absolute dose (not dose/kg). A parametric analysis was done with NONMEM, followed by a nonparametric analysis with NPAG. RESULTS: Dose-response was best described by a sigmoid maximum-effect (E(max)) model with median E(max) = 0.29 g/dL, median 50% effective dose (ED(50)) = 2400IU and shape parameter gamma = 2. The estimated median survival time of the epoetin-induced red blood cells, tau, was 76 days. Neither of the dose-response parameters E(max) and ED(50) showed dependence on bodyweight. The median haemoglobin response to a standard dose, 0.042 g/dL for 1000IU, was similar to that reported for adults with intravenous administration. CONCLUSIONS: Doses for children in this age range should be specified as absolute amounts rather than amounts per unit bodyweight. Initial doses can be calculated individually, based on haemoglobin level before treatment, the desired haemoglobin at steady state and the median population parameters E(max), ED(50) and tau.

Noninvasive methods to study drug distribution.

Positron emission tomography (PET) and nuclear magnetic resonance spectroscopy (MRS) are two techniques that allow the noninvasive monitoring of drug distribution in living systems (humans, animals), and dynamic contrast-enhanced magnetic resonance imaging (dMRI) provides noninvasive physiological information relevant for drug distribution. PET yields series of cross-sectional images that can be used to monitor the absolute radioactivity concentrations in tissues pixel-by-pixel, but does not allow direct identification of each of the products present. MRS produces spectra showing changes in the concentration of both the parent drug and of the metabolites separately for a sensitive volume, but does not provide a simple means for measuring absolute concentrations. dMRI, which measures the changes in the rates of relaxation of water, proportional to the concentrations of the contrast agent (usually Gd-DTPA), readily allows the determination of functional changes in cross-sectional images down to a pixel-by-pixel level. All of these methods are of special interest to evaluate the amounts of drug that can reach the target tissue, penetrate it, remain present at such targets for a sufficient length of time, and how they are metabolized at the target site. Such information may be of particular interest in the study of solid malignant tumors and may become very relevant for determining better treatment strategies. This article presents examples of successful studies of tissue pharmacokinetics with MRS and dMRI. The following article is devoted to PET.