Experimental Therapeutics
Attenuation of Colistin Bactericidal Activity by High Inoculum of Pseudomonas aeruginosa Characterized by a New Mechanism-Based Population Pharmacodynamic Model
Jürgen B. Bulitta, Jenny C. Yang, Liliana Yohonn, Neang S. Ly, Silvia V. Brown, Rebecca E. D'Hondt, William J. Jusko, Alan Forrest, Brian T. Tsuji
Jürgen B. Bulitta
School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York 14260Ordway Research Institute, Albany, New York 12208
For correspondence: btsuji@buffalo.edu j@bulitta.com
Jenny C. Yang
School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York 14260
Liliana Yohonn
School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York 14260University of Rochester Medical Center, Rochester, New York
Neang S. Ly
Silvia V. Brown
Rebecca E. D'Hondt
Ordway Research Institute, Albany, New York 12208
William J. Jusko
Alan Forrest
Brian T. Tsuji
School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York 14260Departments of Pharmacy and Medicine, Roswell Park Cancer Institute, Buffalo, New York 14260
DOI: 10.1128/AAC.00881-09
Colistin is increasingly being utilized against Gram-negative pathogens, including Pseudomonas aeruginosa, resistant to all other antibiotics. Since limited data exist regarding killing by colistin at different initial inocula (CFUo), we evaluated killing of Pseudomonas aeruginosa by colistin at several CFUo and developed a mechanism-based mathematical model accommodating a range of CFUo. In vitro time-kill experiments were performed using ≥8 concentrations up to 64 × the MIC of colistin against P. aeruginosa PAO1 and two clinical P. aeruginosa isolates at CFUo of 106, 108, and 109 CFU/ml. Serial samples up to 24 h were simultaneously modeled in the NONMEM VI (results shown) and S-ADAPT software programs. The mathematical model was prospectively "validated" by additional time-kill studies assessing the effect of Ca2+ and Mg2+ on killing of PAO1 by colistin. Against PAO1, killing of the susceptible population was 23-fold slower at the 109 CFUo and 6-fold slower at the 108 CFUo than at the 106 CFUo. The model comprised three populations with different second-order killing rate constants (5.72, 0.369, and 0.00210 liters/h/mg). Bacteria were assumed to release signal molecules stimulating a phenotypic change that inhibits killing. The proposed mechanism-based model had a good predictive performance, could describe killing by colistin for all three studied strains and for two literature studies, and performed well in a prospective validation with various concentrations of Ca2+ and Mg2+. The extent and rate of killing of P. aeruginosa by colistin were markedly decreased at high CFUo compared to those at low CFUo. This was well described by a mechanism-based mathematical model, which should be further validated using dynamic in vitro models.
During the last decades, important strides have been made in our understanding of antimicrobial pharmacodynamics (PD) (16, 21). Identification of the pharmacokinetic/pharmacodynamic (PKPD) index that best predicts a successful outcome became a cornerstone of optimization of antimicrobial therapy (2, 16, 21). However, PKPD target values may vary between antibiotics and pathogens (2, 3) and may not be universal for all infections (27) and types of outcomes (44, 59). For example, severe infections, such as endocarditis, infections of prostheses, and ventilator-associated pneumonia are known to have a high density of bacteria, which is associated with a higher mortality (25, 47, 54, 60). Furthermore, an increased density of bacteria represents a greater challenge to the immune system and may result in higher bacterial toxin concentrations. In addition, bacterial killing by antibiotics has been shown to be attenuated at high initial inocula (CFUo) compared to low CFUo (9, 10, 47, 53, 67, 69).
Colistin, also known as polymyxin E, was introduced to the market nearly half a century ago (40). Due to the increasing prevalence of Pseudomonas aeruginosa strains resistant to virtually all other commercially available antibiotics, polymyxins are now being increasingly utilized as salvage therapy against infections due to multidrug-resistant Gram-negative pathogens, including P. aeruginosa (40, 42).
As the initial site of action, the polycationic polymyxin molecules displace Mg2+ and Ca2+ ions that cross-bridge between adjacent negatively charged phosphate groups of lipopolysaccharides (LPS) in the outer membrane of Gram-negative bacteria (19, 33, 39, 48, 61). High concentrations of Mg2+ and Ca2+ can competitively inhibit the effects of polymyxins (48, 55, 56). Changes in the composition of LPS reducing the net negative charge of the outer membrane and modifying the hydrophobic side chain have been proposed as a mechanism of resistance to polymyxins (14, 36). P. aeruginosa can sense certain environmental conditions that cause adaptive resistance to polymyxins (49, 51).
Infections by P. aeruginosa are especially difficult to treat if they are deep seated or sequestered or have a biofilm matrix at high bacterial densities (15, 28, 71), and infections with a high CFUo often carry a high number of resistant mutants. To limit the emergence of resistance, optimizing the PKPD of antimicrobials to combat infections with a high CFUo is therefore of the utmost importance. Adler and Finland (1) reported higher MICs for polymyxin B when tested at high compared CFUo to low CFUo, and Peyret et al. (52) and Tam et al. (65) found a lower rate of killing of P. aeruginosa by polymyxin B against high versus low CFUo. We are not aware of studies on the impact of CFUo on the rate and extent of killing by colistin. To our knowledge, there are no published mathematical models for the rate and extent of killing by polymyxins. We proposed and evaluated the first inoculum effect model studying ceftazidime against P. aeruginosa (10-11; J. B. Bulitta, J. C. Yang, B. T. Tsuji, W. J. Jusko, and A. Forrest, presented at the post-ICAAC symposium of the International Society of Anti-Infective Pharmacology, Chicago, IL, 20 September 2007), and subsequently, Udekwu et al. (70) proposed a simulation model with one subpopulation to describe the inoculum effect.
The objectives of the current study were to evaluate the impact of CFUo on the rate and extent of killing of P. aeruginosa by colistin and to develop and evaluate a mechanism-based mathematical PD model that can describe killing by colistin over a range of CFUo.
(This work was presented in part as a poster [no. A-6] at the 47th Interscience Conference of Antimicrobial Agents and Chemotherapy, Chicago, IL, 2007 [73], in part as an oral presentation at the post-ICAAC meeting of the International Society of Anti-Infective Pharmacology in Chicago, IL, 2007, in part as a poster [abstr. 1829] at the AAPS Annual Meeting, San Diego, CA, 2007 [11], and in part as a poster [no. A-119] at the 109th General Meeting of the American Society for Microbiology, Philadelphia, PA, 2009 (74)).
Bacterial strains, media, and MICs.Three isolates of P. aeruginosa were studied: a genetically characterized clinical isolate, PAO1, obtained from the R.E.W. Hancock Laboratory at the University of British Columbia, Vancouver, Canada (62), and two clinical isolates, URMC1 and URMC2, obtained from the University of Rochester Medical Center, Rochester, NY. Fresh solutions of colistin sulfate (Sigma-Aldrich, St. Louis, MO), dissolved in sterile water, were prepared prior to each experimental run. Luria-Bertani (LB) broth supplemented with Ca2+ (25 mg/liter) and Mg2+ (12.5 mg/liter) was utilized for all time-kill experiments. Bacterial counts were determined on LB agar. Luria-Bertani broth and agar were selected as rich media to facilitate growth at high CFUo in time-kill experiments (30). The MICs were determined by broth microdilution in quadruplicate using colistin sulfate according to Clinical Laboratory Standards Institute guidelines in cation-adjusted Mueller-Hinton broth (MHB) or cation-adjusted LB broth. The MICs in MHB (LB) broth were 2.0 (4.0) mg/liter for PAO1 and 0.5 (1.0) mg/liter for URMC1 and for URMC2.
Time-kill experiments.Fresh bacterial colonies from an overnight growth were added to normal saline and adjusted spectrophotometrically to provide a standard suspension. This suspension was diluted with LB broth to achieve the desired CFUo. Each 20-ml culture was incubated in a water bath at 37°C with constant shaking. Initial inocula were 104, 106, 108, and 109 CFU/ml for PAO1 and 106, 108, and 109 CFU/ml for URMC1 and URMC2. Bacteria were allowed to grow for approximately 45 min in LB broth before colistin was added from a standard antibiotic stock solution to achieve 11 colistin concentrations up to 256 mg/liter colistin (64 × MIC in LB broth) for PAO1 and to achieve nine colistin concentrations up to 64 mg/liter colistin (64 × MIC in LB broth) for strains URMC1 and URMC2 at each CFUo.
Samples were collected for determination of bacterial counts at the following time points: 0, 0.25, 0.5, 1, 2, 3, 4, 8, 12, 16, and 24 h for PAO1 for initial characterization of colistin pharmacodynamics and 0, 0.5, 1, 2, 4, 6, 8, and 24 h for URMC1 and URMC2. Antimicrobial carryover was taken into account by serial dilution (10- to 100,000-fold) and centrifuging the bacterial samples for 5 min, after which they were reconstituted with sterile normal saline to their original volumes. Colony counts were determined as previously described (68) using an automated spiral dispenser. Plates were incubated for 18 to 24 h. To determine quantitative viable counts of less-susceptible cells for PAO1, bacterial suspensions at 24 h were centrifuged and resuspended in saline, and 200 μl of this suspension was manually plated on LB agar containing 0, 2, 4, 8, or 16 mg/liter colistin (MIC of PAO1 on LB agar, 2 mg/liter). Drug-containing plates were incubated for 48 h at 35°C. All time-kill experiments were performed in duplicate.
Time-kill experiments to assess potential drug binding or degradation.Additional experiments were performed to evaluate the potential effect of binding of colistin to LPS or other molecules in spent broth as a potential mechanism to account for the inoculum effect. A CFUo of PAO1 was grown from 106 to 109.4 CFU/ml over 24 h in cation-adjusted LB broth. Then, 16 or 64 mg/liter colistin or no drug was added to this suspension (without filtration of the suspension). After 0.75 or 24 h of coincubation at 37°C, the suspension was centrifuged and filter sterilized (0.22-μm filter). Fresh PAO1 cells in log-growth phase were added to the filtrate to achieve a CFUo of 106.2 CFU/ml. No additional colistin was added to the filtrate. Viable counts were recorded over an additional 24 h.
Time-kill experiments to support the target site model.Time-kill experiments to assess the effect of Ca2+ and Mg2+ on the activity of colistin against PAO1 were performed as described above. For samples with low colony counts, 200 μl of the bacterial suspensions in saline were plated to increase the sensitivity of the viable counts. EDTA (pH adjusted to 7.0) as a chelating agent, Ca2+, or Mg2+ was added to LB broth to achieve the following concentrations of added cations or EDTA: (i) 20 mM EDTA, (ii) 2 mM EDTA, (iii) no cations added, (iv) 10 mg/liter (0.250 mM) Ca2+ and 5 mg/liter (0.206 mM) Mg2+, (v) 20 mg/liter Ca2+ and 10 mg/liter Mg2+, or (vi) 80 mg/liter Ca2+ and 40 mg/liter Mg2+. At these concentrations of EDTA, >95% of Ca2+ and Mg2+ should be bound.
Descriptive data analysis.Initially, an integrated area approach was applied to describe the log ratio area by a Hill-type model as previously described (34).
Development and qualification of the population PD model. (i) Bacterial populations.Models with two, three, or four preexisting bacterial populations were considered as proposed previously (24, 35, 45, 50). Since we had only time-kill data with a constant colistin concentration, the natural death rate constant (kd) from the work of Meagher et al. (45) of 0.3 h−1 was used, since their data were based on a one-compartment in vitro PD model with drug concentrations changing over time.
(ii) Growth model.The growth model comprised a previously described, saturable growth function (45) with a maximal velocity of bacterial growth [VGmax, expressed in CFU/(ml·h)] and the bacterial density that results in 50% of the maximal rate of growth (CFUm, expressed in CFU/ml). We reparameterized this growth function (see the work of Harigaya et al. [34] for equations) and estimated the maximum population size (POPmax) and the fastest growth half-life at low bacterial densities [t1/2(kg,low CFU)], since these two parameters can be more readily interpreted than VGmax and CFUm. To incorporate a slower initial growth phase, a lag compartment that contained the susceptible population at time zero was included and linked by a first-order rate constant (klag) with the compartment of the susceptible population subject to growth (Fig. 1).
Structure of the pharmacodynamic model, including bacterial growth, killing, and the inoculum effect (A) and the receptor occupancy model (B). The bacterial model contains one compartment for the susceptible, intermediate, and least-susceptible ("resistant") population and a lag compartment for the susceptible population. In the lag compartment, bacteria do not replicate and are not subject to natural death but are subject to drug-induced killing and the effect of signal molecules. For the other three bacterial compartments, loss of cells occurs via a first-order natural death and a second-order killing process by colistin. Signal molecules were assumed to inhibit bacterial killing by colistin and the rate of bacterial replication (only the arrow for the effect of signal molecules on the susceptible population is shown). Initial conditions (IC) were estimated (see Methods). The target site model comprised a competitive interaction of colistin with Mg2+ and Ca2+ at the LPS binding sites in the outer membrane. Binding sites occupied by Mg2+ and Ca2+ were assumed to decrease the colistin concentration that is available in the active conformation(s) at the site of action.
(iii) Receptor occupancy model.We assumed that colistin has to competitively displace Mg2+ and Ca2+ from their binding sites on the outer membrane before it can cause killing at the target site. Schindler and Osborn (55) found a similar dissociation constant for Mg2+ and Ca2+ for the binding site on LPS extracted from Salmonella enterica serovar Typhimurium. The approximately four binding sites of LPS extracted from P. aeruginosa were shown to have equivalent affinities for polymyxin B (48). In the present modeling, the dissociation constants were fixed to 200 μmol/liter for Mg2+ and Ca2+ (KdCations) and to 0.3 μmol/liter for colistin (KdColistin) according to data on strain G30A of Salmonella serovar Typhimurium (55). This choice of values for KdColistin and KdCations was assessed in a systematic sensitivity analysis. Under these assumptions, the fractional occupancy (FrCations) of the receptor for these two cations can be expressed as a function of the sum of the molar Mg2+ and Ca2+ concentration (CCations) and the colistin concentration (CColistin in mg/liter): $$mathtex$$\[\mathrm{Fr}_{\mathrm{Cations}}{=}\frac{C_{\mathrm{Cations}}}{K\mathrm{d}_{\mathrm{Cations}}{+}C_{\mathrm{Cations}}{+}\frac{K\mathrm{d}_{\mathrm{Cations}}}{K\mathrm{d}_{\mathrm{Colistin}}}\ {\cdot}\ \frac{C_{\mathrm{Colistin}}}{M_{\mathrm{m}}}}\]$$mathtex$$(1) The average molecular mass (Mm) of the two predominant components of colistin (colistin A and B) is 1,163 g/mol. The fraction of receptors not occupied by Mg2+ or Ca2+ was used in a Hill equation to calculate the effective colistin concentration at the target site (CColistin,eff) as a function of the colistin concentration in broth (CColistin). Binding was assumed to be rapid: $$mathtex$$\[C_{\mathrm{Colistin},\mathrm{eff}}{=}\frac{(1{-}\mathrm{Fr}_{\mathrm{Cations}})^{{\gamma}}}{\mathrm{EC}_{50}^{{\gamma}}{+}(1{-}\mathrm{Fr}_{\mathrm{Cations}})^{{\gamma}}}\ {\cdot}\ C_{\mathrm{Colistin}}\]$$mathtex$$(2)
(iv) Drug effect and inoculum effect.Bacterial killing was specified as second-order processes with a different killing rate constant for each population. The data revealed a substantially slower killing at high CFUo than at low CFUo. To characterize this inoculum effect, all viable bacteria were assumed to synthesize and release freely diffusible signal molecules (57) that cause phenotypic changes inhibiting killing by polymyxins. The maximum inhibition of killing (ImaxKill) and of the replication rate (ImaxRep) and the signal molecule concentration associated with 50% of maximal inhibition (IC50) were estimated.
(v) Composite model.The following equations describe the concentration of all viable bacteria (CFUALL) and inhibition of killing (INHKill) and of replication (INHRep) by signal molecules (concentration, CSign): $$mathtex$$\[\mathrm{CFU}_{\mathrm{ALL}}{=}\mathrm{CFU}_{\mathrm{S},\mathrm{lag}}{+}\mathrm{CFU}_{\mathrm{S}}{+}\mathrm{CFU}_{\mathrm{I}}{+}\mathrm{CFU}_{\mathrm{R}}\]$$mathtex$$(3) $$mathtex$$\[\mathrm{INH}_{\mathrm{Kill}}{=}1{-}\mathrm{Imax}_{\mathrm{Kill}}\ {\cdot}\ \frac{C_{\mathrm{Sign}}}{\mathrm{IC}_{50}{+}\ C_{\mathrm{Sign}}}\]$$mathtex$$(4) $$mathtex$$\[\mathrm{INH}_{\mathrm{Rep}}{=}1{-}\mathrm{Imax}_{\mathrm{Rep}}\ {\cdot}\ \frac{C_{\mathrm{Sign}}}{\mathrm{IC}_{50}{+}C_{\mathrm{Sign}}}\]$$mathtex$$(5) The differential equations for susceptible cells in the lag compartment (CFUS,lag), replicating susceptible cells (CFUS), cells with intermediate susceptibility to colistin (CFUI), and least-susceptible cells (CFUR) are: $$mathtex$$\[\frac{d\mathrm{CFU}_{\mathrm{S},\mathrm{lag}}}{dt}{=}({-}k_{\mathrm{lag}}{-}\mathrm{INH}_{\mathrm{Kill}}\ {\cdot}\ k_{2\mathrm{S}}\ {\cdot}\ C_{\mathrm{Colistin},\mathrm{eff}})\ {\cdot}\ \mathrm{CFU}_{\mathrm{S},\mathrm{lag}}\]$$mathtex$$(6) $$mathtex$$\[\frac{d\mathrm{CFU}_{\mathrm{S}}}{dt}{=}\ \left(\frac{\mathrm{INH}_{\mathrm{Rep}}\ {\cdot}\ \mathrm{VG}_{\mathrm{max},\mathrm{S}}}{\mathrm{CFU}_{m}{+}\mathrm{CFU}_{\mathrm{ALL}}}{-}k_{d}{-}\mathrm{INH}_{\mathrm{Kill}}\ {\cdot}\ k_{2\mathrm{S}}\ {\cdot}\ C_{\mathrm{Colistin},\mathrm{eff}}\right)\ {\cdot}\ \mathrm{CFU}_{\mathrm{S}}{+}k_{\mathrm{lag}}\ {\cdot}\ \mathrm{CFU}_{\mathrm{S},\mathrm{lag}}\]$$mathtex$$(7) $$mathtex$$\[\frac{d\mathrm{CFU}_{\mathrm{I}}}{dt}{=}\ \left(\frac{\mathrm{INH}_{\mathrm{Rep}}\ {\cdot}\ \mathrm{VG}_{\mathrm{max},\mathrm{I}}}{\mathrm{CFU}_{m}{+}\mathrm{CFU}_{\mathrm{ALL}}}{-}k_{d}{-}\mathrm{INH}_{\mathrm{Kill}}\ {\cdot}\ k_{2\mathrm{I}}\ {\cdot}\ C_{\mathrm{Colistin},\mathrm{eff}}\right)\ {\cdot}\ \mathrm{CFU}_{\mathrm{I}}\]$$mathtex$$(8) $$mathtex$$\[\frac{d\mathrm{CFU}_{\mathrm{R}}}{dt}{=}\ \left(\frac{\mathrm{INH}_{\mathrm{Rep}}\ {\cdot}\ \mathrm{VG}_{\mathrm{max},\mathrm{R}}}{\mathrm{CFU}_{\mathrm{m}}{+}\mathrm{CFU}_{\mathrm{ALL}}}{-}k_{d}{-}\mathrm{INH}_{\mathrm{Kill}}\ {\cdot}\ k_{2\mathrm{R}}\ {\cdot}\ C_{\mathrm{Colistin},\mathrm{eff}}\right)\ {\cdot}\ \mathrm{CFU}_{\mathrm{R}}\]$$mathtex$$(9) The CFUo of all populations was estimated. Initial conditions of the intermediate and least-susceptible population were estimated as log10 of the fraction (FrI and FrR) of CFUo (see Table 1 for further explanation of parameters). We considered both models that assume the same FrI and FrR for all CFUo and models that allowed FrI and FrR to differ between CFUo. The initial condition for CFUS,lag was calculated as the difference between the CFUo and the initial condition of the intermediate and least-susceptible populations. The initial condition for CFUS was zero. To consider the potential absence of populations with a low mutation frequency at low CFUo, the initial condition of a bacterial population was set to zero if less than 1 cell would have been expected in 20 ml of broth.
Parameter estimates for population pharmacodynamic modelh
To account for a slower growth of the intermediate and least-susceptible populations than of the susceptible population, different VGmax terms were estimated for each population, and the associated t1/2(kg,low CFU) values were reported. The differential equation for hypothetical signal molecules is as follows (kdeg is the degradation rate constant): $$mathtex$$\[\frac{dC_{\mathrm{Sign}}}{dt}{=}\ \left(\mathrm{CFU}_{\mathrm{ALL}}\ {\cdot}\ \frac{\mathrm{ml}}{\mathrm{CFU}}{-}C_{\mathrm{Sign}}\right)\ {\cdot}\ k_{\mathrm{deg}}\]$$mathtex$$(10) The parameterization of equation 10 yields the same numerical value for the signal molecule concentration as for the bacterial concentration (CFUALL) at steady state.
(vi) Observation model.The residual unidentified variability was described by an additive error model on a log10 scale, and data were fit as log10 (CFU/ml) if the observed bacterial density was 100 CFU/ml or more (equivalent to at least five colonies per plate). The CFUALL,obs is the observed CFU/ml, CFUALL,pred is the individual fitted CFU/ml (without error), and εCFU is a random variable with a mean of zero and standard deviation (SDCFU) describing the additive error on log10 scale: $$mathtex$$\[\mathrm{log}_{10}(\mathrm{CFU}_{\mathrm{ALL},\mathrm{obs}}){=}\mathrm{log}_{10}(\mathrm{CFU}_{\mathrm{ALL},\mathrm{pred}}){+}{\varepsilon}_{\mathrm{CFU}}\]$$mathtex$$(11) For observations from undiluted samples with fewer than five colonies per plate, data were fit as actual colony counts, and the additive error on log scale was transformed to a proportional error on the scale of observed colony counts with the same variance as the additive error on log10 scale. At low colony counts, the random error due to observing only an integer number of colonies is most important compared to other sources of error. Therefore, a Poisson error (εPois) and an additive error (εAdd) were included if fewer than five colonies per plate were observed: $$mathtex$$\[\frac{\mathrm{CFU}_{\mathrm{ALL},\mathrm{obs}}}{20}{=}\frac{\mathrm{CFU}_{\mathrm{ALL},\mathrm{pred}}}{20}\ {\cdot}\ [1{+}\mathrm{ln}(10)\ {\cdot}\ {\varepsilon}_{\mathrm{CFU}}]{+}\ \left(\frac{\mathrm{CFU}_{\mathrm{ALL},\mathrm{pred}}}{20}\right)^{0.5}\ {\cdot}\ {\varepsilon}_{\mathrm{Pois}}{+}{\varepsilon}_{\mathrm{Add}}\]$$mathtex$$(12) Division by 20 converts the CFU/ml data into colony counts on the plate, since 50 μl of undiluted sample was plated for these low colony counts. The εPois and εAdd are random variables with a mean of 0 and fixed standard deviations of 1 for εPois and 0.25 for εAdd. The residual error model was evaluated in an exhaustive simulation-estimation study using a model with two subpopulations of different susceptibilities, first-order growth, logistic plateau function, and 2nd-order killing function.
(vii) Model qualification.Models were assessed via standard diagnostic plots and a leave-one-inoculum-out internal cross-validation as described previously (10). For external model qualification involving two different clinical strains, selected model parameters for growth and killing of P. aeruginosa at low CFUo were reestimated based on data from the work of Gunderson et al. (31) and Li et al. (41). The Beal M3 method (6) was used for data from Gunderson et al. to appropriately handle data below the reported limit of detection.
(viii) Computation.Nonlinear mixed-effects modeling in the NONMEM VI (7) and S-ADAPT (version 1.55 and 1.56) (5) software programs was applied as described previously (10). The first-order conditional estimation method with the interaction estimation option was used in NONMEM, and the importance sampling Monte-Carlo expectation-maximization method (pmethod = 4 or 8) was used in S-ADAPT. Variability of PD parameters between individual profiles was described by an exponential parameter variability model. An additive variability model was used for parameters estimated on log scale. A three-stage hierarchical analysis in S-ADAPT was performed to model the data of the time-kill experiments with various concentrations of Ca2+, Mg2+, or EDTA using methods described previously (37). The population PD results of the inoculum effect modeling in S-ADAPT were used as prior information. Plausible but uninformative priors were used for the maximum population size, initial inoculum, and half-life of growth and of the growth lag, since these parameters could be estimated well from the available data set. The sum of the free concentrations of Ca2+ and Mg2+ and the growth half-life in the presence of EDTA were estimated.
The structural mathematical model (Fig. 1) described the rapid, concentration-dependent killing by colistin (Fig. 2) and the inhibition of killing at high CFUo compared to that at low CFUo. At the 106 CFUo, bacterial killing by colistin was rapid and concentration dependent against all P. aeruginosa isolates. For the 106 CFUo, bactericidal activity within 1 h was achieved at concentrations of 1 to 4 × the MIC, and concentrations of ≥16 × the MIC resulted in bacterial reductions to undetectable concentrations within 30 min. Against the 108 and 109 CFUo, colistin activity was markedly attenuated (Fig. 2). Up to 32-fold-higher concentrations were required at the 109 CFUo than at the 106 CFUo to achieve bactericidal activity. At the 109 CFUo, killing was less pronounced and much slower, with nadir CFU counts at 8 to 12 h for PAO1 (Fig. 2), and regrowth occurred for all three strains. Drug-containing plates (Fig. 3) showed an increased fraction of less-susceptible cells at 2 to 16 mg/liter for the 106 CFUo at 4 to 32 mg/liter for the 108 CFUo and at 4 to 128 mg/liter for the 109 CFUo for PAO1. The overall effect of colistin represented by the log ratio area approach was well described (r2 > 0.97) by Hill-type models (Fig. 4). The maximal effect (Emax) decreased systematically, and the colistin exposure (EC50) associated with 50% of Emax increased systematically with increasing CFUo for all three strains.
Population predicted versus observed log10 (CFU/ml) for three strains of P. aeruginosa at a low (top), intermediate (middle), or high (bottom) initial inoculum (see also Table 1 and Fig. 1; based on results from S-ADAPT). A log10 value of observed colony counts plotted as zero means no colony was on the plate. Given the volume of 50 μl plated, one colony is equivalent to 20 CFU/ml (approximately 1.3 on log10 scale) for an undiluted sample.
Viable counts on drug-free and drug-containing plates at 24 h for P. aeruginosa PAO1 for an initial inoculum of 106 (A), 108 (B), or 109 (C) CFU/ml (agar MIC of PAO1, 2 mg/liter). Colistin concentrations above 16 mg/liter were not studied at the 106-CFU/ml inoculum. Plates with 8 mg/liter colistin showed a log10 CFU/ml between 1.6 and 4.1 for 2 mg/liter at the 106 inoculum and for 2, 4, and 8 mg/liter colistin in broth at the 108-CFU/ml inoculum. The log10 CFU/ml was 2.75 for 16 mg/liter colistin at the 108-CFU/ml inoculum. All other plates with 8 or 16 mg/liter colistin showed no viable growth.
Pharmacodynamic relationship between colistin concentration/MIC and the log ratio area [log10 (area under the CFU curve from 0 to 24 h for colistin/area under the CFU curve from 0 to 24 h for growth control)] at each initial inoculum for three P. aeruginosa strains (all r2 values ranged between 0.978 and 0.999): PAO1 (A), URMC1 (B), and URMC2 (C).
We found the following extent of killing by colistin relative to baseline levels in the filtrate after coincubation for 0.75 or 24 h with 109.4 CFU/ml. For 0.75 h of coincubation, net killing was >5 log10 in the filtrate of the 16-mg/liter and 64-mg/liter suspensions. For 24 h of coincubation, net killing was 5 log10 (>5 log10) in the filtrate of the 16-mg/liter (64-mg/liter) suspension. The growth control in spent broth grew by 1.5 log10 at 4 h and 3.1 log10 at 12 h.
In the mathematical model (Fig. 1), the attenuated effect of colistin at a high CFUo was assumed to be triggered by high concentrations of hypothetical signal molecules. At a signal molecule concentration much larger than the concentration associated with 50% of maximal inhibition (IC50) of 106.17 (Table 1), bacterial killing of all populations by colistin could be almost completely inhibited (ImaxKill = 0.992). The parameter estimates from NONMEM (results shown in the text) and S-ADAPT were well comparable (Table 1) and precise. Relative standard errors of all fixed effects were below 20% in S-ADAPT (results not shown). Parameter estimates for our two clinical strains were comparable to those for PAO1 (Table 1). In agreement with the lower MIC for the clinical isolates, these strains had a faster 2nd-order killing rate constant for the intermediate population (k2I) than PAO1 (Table 1).
Population predictions were reasonably precise and unbiased (Fig. 2 and 5B). The individual fits were more precise (Fig. 5A for PAO1). Slopes (correlation coefficients) of observed versus individual fitted log10 CFU/ml were 0.986 (r = 0.989) for URMC1 and 0.982 (r = 0.991) for URMC2. At the 109 CFUo, the predicted viable population counts showed more killing than observed for the 4 and 8 × MIC profiles. These two profiles primarily caused the mispredictions in panels B and C of Fig. 5. Figure 5C shows predictions for the observations that were not used during the four estimation runs of the cross-validation. Predictions were reasonably precise and unbiased during cross-validation of the three lower inocula. For the 109 CFUo, mispredictions were only slightly more pronounced during cross-validation (Fig. 5C) than during estimation of all data (panel B). The model described the time course of killing for our two clinical strains at three CFUo and the two literature studies (Fig. 6) well. Slopes (correlation coefficients) of observed versus fitted log10 CFU/ml were 1.023 (r = 0.927) for the data from the work of Gunderson et al. (31) and 1.002 (r = 0.985) for the data from the work of Li et al. (41).
Observed versus predicted bacterial counts on log10 scale for P. aeruginosa PAO1 (based on results from NONMEM). (A) Observed versus individual fitted CFU/ml. (B) Observations versus population predictions when all data were used for estimation. (C) Observations versus population predictions from the internal cross-validation. Importantly, none of the observations at the respective inocula were used during cross-validation when data at this inoculum were predicted. A log10 value of observed colony counts plotted as zero means no colony was on the plate.
Fitted and observed bacterial counts versus time for one-compartment in vitro model data from the work of Gunderson et al. (32) (A) (lower limit of detection: log10 CFU/ml of 2.48; observations below this reported lower limit are plotted as 0 log10 [CFU/ml]) and time-kill data from Li et al. (42) (B) (plates with zero colonies are plotted as zero).
The most important model assumptions are discussed in Table 2. Models with a first-order conversion between the susceptible, intermediate, and least-susceptible populations were estimated, but neither significantly improved either the objective function or the curve fits of our static time-kill data (results not shown). Models with four instead of three populations provided no significant benefit, and models with two populations were inadequate to describe the observations (results not shown). Estimating different FrI and FrR values at each CFUo yielded only a small improvement in the objective function and well-comparable estimates for FrI and FrR for each CFUo (results not shown). Therefore, FrI and FrR were assumed to be the same for all CFUo. Models with different relative affinities of colistin relative to Mg2+ and Ca2+ for the susceptible, intermediate, and least-susceptible populations in addition to a different killing rate constant for each population achieved only a slightly lower objective function in S-ADAPT but did not notably improve the diagnostic plots. Thus, we did not implement different relative affinities of colistin and Mg2+ and Ca2+ for each population following the rule of parsimony.
Overview of assumptions and supporting data for proposed model features (see Methods and Discussion for further details)
It was estimated that 53.7% (EC50) of the binding sites for Mg2+ and Ca2+ were required to be unoccupied by Mg2+ or Ca2+ to achieve an effective colistin concentration of 50% of the colistin concentration in broth (Fig. 1). The Hill coefficient of this relationship was initially estimated to fall between 10 and 20, indicating cooperativity, and subsequently fixed to 10 to improve model stability. This choice did not affect curve fits.
Our three-stage hierarchical analysis showed excellent individual curve fits at various concentrations of Ca2+, Mg2+, and EDTA (Fig. 7). All ratios of the population mean parameter estimates from the 3-stage hierarchical analysis divided by their prior estimates from the population PD analysis of the inoculum effect data set in S-ADAPT were within 0.90 to 1.13 (average ± SD: 1.00 ± 0.056). This supported the proposed target site model and indicated consistency between both series of experiments. Compared to LB broth without addition of cations or EDTA (Fig. 7B), addition of cations inhibited killing by colistin (Fig. 7C to E). Addition of 2 mM EDTA to chelate Ca2+ and Mg2+ enhanced killing by colistin (Fig. 7A) but increased the estimated growth half-life of the susceptible population to 48.5 min. The rate and extent of killing were very similar for 2 mM EDTA and 20 mM EDTA (data not shown). However, 20 mM EDTA inhibited net growth of PAO1 substantially, and therefore, these data were not included in the modeling analysis. The sum of the free concentrations of Ca2+ and Mg2+ in LB broth was estimated to be small (0.06 mM).
Observed and individual fitted viable counts of P. aeruginosa PAO1 for various concentrations of Ca2+, Mg2+, or EDTA added to LB broth: 2.0 mM EDTA (A), no cations and no EDTA added (B), 10 mg/liter Ca2+ and 5 mg/liter Mg2+ (C), 20 mg/liter Ca2+ and 10 mg/liter Mg2+ (D), or 80 mg/liter Ca2+ and 40 mg/liter Mg2+ (E). Observed viable counts of zero mean no colony on the plate (using a volume of 200 μl plated manually for samples with low viable counts).
Our simulation-estimation study assessing the proposed residual error model showed that this model was robust and curve fits were unbiased and precise using the cutoff value of 5 colonies per plate applied in this colistin study (equivalent to 100 CFU/ml for a 50-μl plating volume). For fixed-effect parameters, bias was ≤0.07 for estimates on log10 scale and ≤4% for all other estimates. Precision of fixed effects had a standard deviation (SD) of <0.09 for estimates on log10 scale and a coefficient of variation (CV) of <10% for all other estimates. This new residual error model was more robust in NONMEM than the Beal M3 method (6).
The increasing prevalence of Gram-negative bacteria, including P. aeruginosa, that are resistant to almost all commercially available antibiotics is a cause for significant concern (22, 40). The lack of alternative therapeutic options has forced clinicians to use polymyxins due to their activity against these multidrug-resistant pathogens (40, 42). Although colistin has displayed rapid bactericidal activity against low CFUo of P. aeruginosa, it has not yet been determined whether this profile would also be seen against high CFUo. We therefore studied the impact of CFUo on colistin killing activity in vitro for three isolates of P. aeruginosa. In our study, killing by colistin was drastically attenuated at high CFUo, and substantially higher colistin concentrations were necessary to achieve bactericidal activity at high CFUo (Fig. 2). Consistent with the inverted-U concept (64), intermediate concentrations caused resistance at 24 h, whereas low or (very) high concentrations did not increase the fraction of less-susceptible cells (Fig. 3).
Hancock et al. (32, 33, 63) highlighted that it is critical to understand the mechanisms of antibiotic killing to prevent emergence of bacterial resistance. Consequently, we developed a mathematical model that incorporates known features of the mechanism of action of colistin (39). After displacing Mg2+ and Ca2+ from their LPS binding sites, colistin disrupts the outer and cytoplasmic membrane, and leakage of small intracellular molecules and bacterial killing are observed within less than 2 min (39, 48, 56, 61). The proposed model (Fig. 1 and Table 2) incorporates the competitive interaction of colistin with Mg2+ and Ca2+ as a first step of colistin action. After colistin sufficiently destabilized the outer membrane by increasing the fraction of receptors not occupied by Mg2+ or Ca2+ to 53.7% (EC50), colistin reached its target site and caused killing. The assumed relative affinity for LPS binding sites was 670-fold higher for colistin than for Mg2+ and Ca2+ (55), which is consistent with the literature as it relates to P. aeruginosa (13, 43, 48). All model parameters except EC50 were essentially unaffected in a sensitivity analysis (in S-ADAPT) that varied the dissociation constants for colistin and Mg2+ and Ca2+ up to 50-fold in either direction. In agreement with data in the literature (43, 48), the (estimated) Hill coefficient of 10 suggests cooperativity in loss of membrane integrity after sufficient displacement of Ca2+ and Mg2+.
A prospective experimental validation (Fig. 7) coupled with a three-stage hierarchical analysis supported the proposed target site model (Fig. 1B). To our knowledge, this analysis for a mechanism-based model is the first application of a three-stage hierarchical population PD analysis in antibacterial PD. This method is very helpful for borrowing results from other studies in the literature and using these results as prior information with uncertainty.
The mathematical model developed in this study incorporates a second-order killing function and three preexisting populations with different susceptibilities to colistin. This characterization of colistin PD is in agreement with the rapid, concentration-dependent killing of P. aeruginosa by colistin and with the regrowth of resistant cells (4, 8, 31, 41). At high colistin concentrations against low CFUo, 99.9% killing was achieved within 15 min and undetectable levels were maintained until 24 h. The descriptive log ratio area method yielded a robust measure for the average drug effect and indicated a systematic trend toward less killing at high CFUo (Fig. 4).
Our mathematical model could describe the time course of killing and regrowth for a range of CFUo (Fig. 2 and Fig. 5). Initially, the slower killing at high CFUo compared to low CFUo was modeled as different second-order killing rate constants for each population at each CFUo. In this descriptive analysis for strain PAO1, the killing rate constant of the susceptible population was approximately 23-fold (6-fold) smaller for the 109 (108) CFUo than for the 106 CFUo.
Subsequently, the inoculum effect was described as a phenotypic change of bacterial cells. Potential reasons for the inhibition of killing by colistin are a decreased negative charge of LPS and changes in the hydrophobic side chain in the outer membrane of P. aeruginosa in response to cells sensing their environment (14, 36, 49, 51). Parameter estimates from NONMEM and S-ADAPT using notably different estimation algorithms were well comparable (Table 1). The model described the killing by colistin well for clinical strains URMC1 and URMC2 (Fig. 2B and 2C) and for two literature data sets (Fig. 6). The proposed mechanism-based model incorporates certain features of the mode of action of colistin, can predict the time course of bacterial killing by colistin over a wide range of CFUo, and can be extended to describe killing by combinations of antibiotics. The new proposed residual error model was very robust, yielded unbiased and precise estimates in a simulation-estimation study with a simplified PD model, and could account for plates with zero colonies during estimation and for the Poisson error at low viable counts.
Our model is largely simplified, since it contains only one compartment for hypothetical, unmeasured signal molecules that were assumed to cause the phenotypic changes of cells leading to a slower killing by colistin (Table 2). Several signal molecules are known to be involved in cell-to-cell communication (quorum sensing) of P. aeruginosa (20, 57) and to cause a delayed onset of expression of quorum-induced genes (57, 58). The proposed model can account for this delay and had a good predictive performance for interpolation (when leaving out data of the 106 or 108 CFUo) and extrapolation (when leaving out data of the 104 or 109 CFUo) between CFUo (Fig. 5C). Further studies are needed to assess the influence of antibiotics on bacterial signaling, gene expression, proteomics, and bacterial physiology at high and low CFUo in vitro and in vivo.
A potential reason for the inoculum effect of colistin might arise from its antiendotoxin activity in neutralizing bacterial LPS (26, 29, 72). Colistin forms mixed monolayers with phospholipids and is incorporated in micelles in vitro (46). "Binding" of colistin to LPS fragments of killed bacteria might decrease the free colistin concentration in vitro and contribute to the inoculum effect. Our coincubation experiments with colistin added to a CFUo of 109.4 CFU/ml for 0.75 or 24 h suggest that binding to LPS or other molecules in spent broth was not the major reason for the inoculum effect in our study. This coincubation experiment and the slow killing with late nadir CFU counts at 8 to 12 h for PAO1 suggested that a phenotypic change of bacterial cells is the most likely reason for the inoculum effect in our in vitro experiments.
Davis (17) found no inoculum effect for colistin at the two lower dose levels in mouse protection tests with P. aeruginosa, whereas the mean effective dose increased approximately 16-fold for gentamicin or tobramycin with a 100-fold increase in CFUo. Since there was no washout of signal molecules or other substances, a time-kill experiment as in our study may overestimate the inoculum effect in vivo. However, several animal infection model studies showed the significance of the inoculum effect in vivo (25, 38, 47, 60). It is important to note that the clinical relevance of the inoculum effect has rarely been demonstrated, and numerous factors, such as host defense and severity of infection, greatly influence antimicrobial effect and treatment success in patients.
Based on our in vitro time-kill data, our mathematical model predicted (results not shown) that colistin regimens with a large colistin exposure during the first approximately 12 h may be able to achieve enough net killing that the immune system can eradicate the remaining colistin-resistant cells. Further in vitro and animal studies are required to substantiate this model prediction.
Our study has potential limitations. First, the mathematical model of the present study was developed based on data from static time-kill experiments. Our in vitro model also does not account for the complex protein binding of colistin in vivo (23). Second, our study was not designed to assess the mechanism(s) of colistin resistance. To build mathematical models for the time course of colistin resistance, hollow-fiber infection models determining the viable counts of the total and resistant subpopulation(s) and resistance mechanisms will need to be studied for clinically relevant colistin dosage regimens over approximately 10 to 14 days. Finally, other potential limitations of our study are that the resistant subpopulation(s) might have been growing faster in LB broth, which is richer in nutrients than many infection sites in vivo, and that colistin concentrations were not directly measured. However, time-kill experiments in spent broth after coincubating colistin and a high CFUo of PAO1 suggested that drug degradation was not the primary reason for the inoculum effect of colistin in our study.
In summary, the extent and rate of killing of PAO1 and two clinical P. aeruginosa isolates by colistin were markedly inhibited at high CFUo compared to low CFUo. Killing of PAO1 was approximately 23-fold (6-fold) slower for the 109 (108) CFUo than for the 106 CFUo. The proposed mechanism-based mathematical model described bacterial growth and killing of three P. aeruginosa strains across a range of CFUo well, had a good predictive performances for all studied CFUo, and could well describe data from two additional clinical strains from the literature. A prospective experimental "validation" using different concentrations of Ca2+ and Mg2+ in combination with a three-stage hierarchical population PD analysis supported the proposed target site model. The proposed mathematical model should be further validated using dynamic in vitro models with colistin in mono- and combination therapy. Overall, this study emphasizes the potential need for higher colistin exposure or combination regimens to treat deep-seated, difficult-to-treat infections with high CFUo. Further animal studies are warranted to assess the toxicity and inoculum effect of colistin in vivo.
We thank Roger Nation, Jian Li, and Cornelia Landersdorfer for very fruitful discussion and comments on the manuscript. We thank Robert E. Hancock, Joseph McPhee, and Manjeet Bains for their insights and for the gift of PAO1. We thank Dwight Hardy for the gift of URMC1 and URMC2 and Curtis Hass and Ashley-Dodds for their contribution to this project.
This work was supported in part by Public Health Service grant R01AI079330 from the National Institute of Allergy and Infectious Diseases and in part by the University at Buffalo, State University of New York. J.B.B. was supported by a postdoctoral fellowship from Johnson & Johnson, and W.J.J. was supported by NIH grant GM 57980.
We have no conflicts of interest to report.
Received 29 June 2009.
Returned for modification 11 October 2009.
Accepted 19 February 2010.
↵▿ Published ahead of print on 8 March 2010.
American Society for Microbiology
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Warren, H. S., S. A. Kania, and G. R. Siber. 1985. Binding and neutralization of bacterial lipopolysaccharide by colistin nonapeptide. Antimicrob. Agents Chemother. 28:107-112.
Yang, J. C., J. B. Bulitta, A. Forrest, and B. T. Tsuji. 2007. High inocula Pseudomonas aeruginosa (PA) attenuates colistin bactericidal activity and alters pharmacodynamics (PD). Abstr. 47th Annu. Intersci. Conf. Antimicrob. Agents Chemother. (ICAAC), poster A-6. American Society for Microbiology, Washington, DC.
Yohonn, L., S. V. Brown, J. B. Bulitta, A. Forrest, H. Sun, C. McPhee, P. N. Holden, P. A. Kelchlin, E. Dodds Ashley, C. E. Haas, D. Hardy, and B. T. Tsuji. 2007. Bactericidal activity of colistin against clinical isolates of Pseudomonas aeruginosa at high and low bacterial density, abstr. A-119. Abstr. 109th Gen. Meet. Am. Soc. Microbiol. American Society for Microbiology, Washington, DC.
Antimicrobial Agents and Chemotherapy Apr 2010, 54 (5) 2051-2062; DOI: 10.1128/AAC.00881-09
You are going to email the following Attenuation of Colistin Bactericidal Activity by High Inoculum of Pseudomonas aeruginosa Characterized by a New Mechanism-Based Population Pharmacodynamic Model


Pick of the Plots: Monday 16th September
The latest goings on in Coronation Street, EastEnders, Emmerdale, Hollyoaks and Doctors.
Paul's disgusted to hear about Bernie's pregnancy test scam and that she's back with her old boyfriend Kel, who Paul last saw when he was fourteen. Paul resolves to come up with a plan to get rid of them both. Later, an angry man calls at No.5, claiming to have fallen victim to a hoax pregnancy and vowing to go to the police. Chesney orders Bernie to pack her bags with Gemma's support.
Later, Kel catches up with Paul in the Rovers' yard and asserts that what happened between them in the past was special but he's committed to Bernie this time. However, Bernie's gutted when Kel leaves, blaming Paul for making him feel unwelcome. Meanwhile, Billy quizzes Gemma about Paul's feud with Kel, and Paul doesn't appreciate his interest.
Elsewhere, Sinead and Daniel visit a hospice, but Daniel admits that as her husband he wants to care for Sinead at home to the bitter end. Later, chemotherapy takes its toll on Sinead.
Also, Toyah pointedly lets Ali know she's there for when he's ready to talk; Jenny makes a fuss of Adam as he moves into the Rovers to give the Osbourne's space; Nick forces a reluctant Derek to sign the rental agreement for the factory.
Coronation Street, Monday at 7.30pm and 8.30pm on ITV, STV and UTV.
Kathy finds out that Bobby is staying with Max and pleads with her grandson to reconsider. Bobby gets a message from his friend, Imran, and quickly exits. When Jack puts the kibosh on Bobby and his friend staying at the Branning's, Bobby returns home where Kathy is concerned to see how uneasy he is, wrongly assuming it's got something to do with Imran. Wanting to help, Kathy takes matters into her own hands leaving Bobby furious.
Meanwhile, Phil and Sharon notice some unusual withdrawals from the E20's account, with Phil immediately sussing that Mel must be making them to pay for Hunter's funeral. He demands that her access is cut off. Realising what's happened, Mel is distraught at not being able to pay for Hunter's funeral and confronts Sharon.
Elsewhere, Bex tries to distract herself from thoughts of university; Linda takes Ollie to his new school but is put out at the hostility of the other mums; Mitch continues to berate Keegan about leaving school whilst Keegan calms Tiffany's nerves before she starts her course.
EastEnders, Monday at 8pm on BBC One.
Sarah tries to show off in front of her new friend Danny but gets herself into trouble when Vanessa catches them hanging out together instead of doing school work. Later, Sarah is mortified when Charity gives her a ticking off in front of Danny.
Meanwhile, Chas tries to offer a fresh perspective.
Elsewhere, Dan finds himself with an admirer; Will's situation leaves him frustrated.
Emmerdale, Monday at 7pm on ITV, STV and UTV.
Ste gives a speech at Stuart's 'family day' to rapturous applause but Jack is disgusted to stumble on the event at The Teahouse and calls the police. Later, Ste sees Sinead who is upset about Finn's return. It's like old times until talk turns to Ste's beliefs and he finds out that she's engaged to Sami. Back at home, Ste agrees to help with Stuart's big plan…
Meanwhile, Diane is surprised to hear that Sinead is getting married when Azim tries to book The Hutch for the engagement party. Sinead doesn't want anything to do with her mum while Finn is around.
Elsewhere, James thinks Juliet deserves to be punished for what she did to Brooke and suggests she sees a counsellor. Bobby surprises Mercedes with a 'beach' on The Dog patio. Mercedes tells Bobby that she's happiest when she's with him and he asks why she hasn't had a baby with Sylver yet.
Hollyoaks, Monday at 6.30pm on Channel 4 and a 'first look' at 7pm on E4.
It's the day of the court case to decide the fate of Josh: Letherbridge NHS trust are seeking a declaration that continued ventilation is not in the baby's best interests and his parents are protesting this.
The court hears from both sides before the judge retires to her chambers to deliberate. Will the judge give the verdict that Theresa and Phil desperately hope to hear?
At the Mill, Al finds an unexpected confidante, and Valerie obsesses about Daniel and Becky.
Doctors, Monday at 1.45pm on BBC One.


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'There's No Good Dust': What Happens After Quartz Countertops Leave The Factory
By Nell Greenfieldboyce
Published December 2, 2019 at 6:19 AM MST
The Cambria factory in Minnesota manufactures slabs of engineered quartz for kitchen and bathroom countertops. If businesses don't follow worker protection rules, cutting these slabs to fit customers' kitchens can release lung-damaging silica dust.
Every day, 20 to 30 trucks roll into a factory in Minnesota. They're filled with quartz — some of it like a powder, and some of it like sparkling little pebbles, in big white sacks.
"It's about 30 million pounds of quartz a month," says Marty Davis, the CEO of Cambria, a company that manufactures material for kitchen and bathroom countertops. "About a million pounds a day."
All of this quartz gets transformed into a kind of engineered stone that looks like granite and marble, but with more durability and stain resistance. Quartz countertops have really taken off over the past decade, and factories around the world are churning out slabs of the stuff under different brand names.
However, if countertop-making businesses don't follow worker protection rules, cutting these slabs to fit customers' kitchens can release lung-damaging silica dust.
Natural granite contains silica too, but all of the quartz that goes into engineered stone means that it contains about twice as much.
So far, 19 countertop workers in the U.S. are known to have developed severe lung disease after cutting engineered stone along with other stone; two of them died of their illness, and others have been told they will eventually require lung transplants.
Manufacturers such as Cambria say that their slabs of composite stone are completely safe when cut and polished with the proper precautions.
"There's clear regulation and clear guidance and governance on how to process materials safely to control dust and respiratory inhalation of dust," Davis says.
He invited NPR to tour his factory. Above the entrance is a sign that says: "Through these doors walk the finest countertop makers in the world."
Cambria produces around 30,000 slabs of quartz countertop material every month, says Davis, who adds that the company has also spent millions of dollars on air-handling systems to control dust.
"There's no good dust. Zero," says Davis, who gained an appreciation of safe manufacturing practices while working in his family's dairy business.
/ Cambria
Cambria receives raw quartz that is then combined with a binder and pigments to produce engineered quartz slabs, which are then sent out to workshops around the country.
A sign warns of silica at the door to a huge room filled with mechanical mixers. There, workers wear respirators as they combine quartz, pigments and a binder. The mixture gets spread out onto what looks like a giant baking sheet, then goes through a machine that vibrates the material in a vacuum to remove any voids.
This produces a soft, compressed slab that feels almost like cookie dough. It hardens when it gets heated, then cooled and polished. The factory is filled with rows of finished slabs in different colors, ready to be sent out to countertop-makers.
Davis says these slabs go out to thousands of workshops, and he can't follow his product to each one.
"How do you police your customers?" he says, noting that the dangers of silica have been known for decades. "There are many products that we make in our world that, if processed or consumed improperly, are dangerous."
He says the Occupational Safety and Health Administration has clear rules on controlling worker exposure to silica. "If you follow and adhere, your employees will be safe," Davis says.
His company's own countertop fabrication shops prove this, he says. In addition to manufacturing slabs, Cambria runs a network of five shops that cut slabs to order.
"They're clean as a whistle," says Davis, adding that one of his own sons works in the shops.
In these workshops, and at the main factory, Cambria uses devices to do real-time monitoring of silica dust — something that Davis says goes above and beyond what is currently typical for the industry.
But some workers in countertop shops run by other companies say they weren't protected from silica.
Juan (who didn't want to use his last name because of medical privacy) says he had a job making countertops in Washington state, and a lot of what he cut was quartz.
For the first couple of years, his workplace practiced dry cutting — that means no spray of water to keep the dust down. There was so much dust, he says, he couldn't see someone working 20 feet away.
Juan, who is now 38, says he wore a simple face mask that didn't provide enough protection and that no one told him about silica, or the danger.
"At first you don't feel the changes a lot," Juan said in Spanish, speaking through an interpreter. "Then later, with time passing, your body starts telling you that you're missing air, that you're suffocating and you're tired."
In 2016, after four years at the shop, he developed a cough that wouldn't go away, no matter what medicine he took. About a year later, a friend who was a chiropractor advised him to get his lungs tested.
At first, his doctor told him it wasn't necessary. "Then when he did the tests, the doctor almost cried. He said, 'I'm sorry, you're right, your lungs are very damaged,' " says Juan, who has a wife and three children.
He says he can't carry groceries and gets exhausted just walking from his house to his car. He's being evaluated for a lung transplant.
"After this happened, they made lots of changes in the company," Juan says. "Now they don't cut like they used to. They bought a lot of machines and the machines do most of the work."
Dry-cutting methods generally are cheaper because they do not require specialized equipment or water recycling systems. One survey of countertop shops in 2012 found that the majority reported using dry methods all or most of the time in at least one fabrication step.
Margaret Phillips, an occupational health expert at the University of Oklahoma Hudson College of Public Health in Oklahoma City, has done silica sampling in shops to assess worker exposures.
Michael Conroy / AP
Water applied to cutting equipment, like this computer-operated saw, is one method to control silica dust exposure when cutting quartz slabs.
"If workers were doing mostly dry fabrication, so they were grinding, polishing, cutting, without any use of water on their tool to suppress the dust, then exposures tended to be very high," Phillips says. "Like 20 times over the current OSHA limit, maybe even 40 times, or more. Dry fabrication is exposing workers to very, very high levels of silica dust."
Her research has found that even just a few minutes of dry fabrication was enough to put a worker's exposure over the permissible limit. "Any amount of dry fabrication could really be a problem," she says.
Some shops don't do dry cutting, like Capitol Granite near Richmond, Va. There, big computer-controlled machines cut through slabs while dumping up to 35 gallons of water a minute on the blade to keep down the silica dust.
"We do not do any dry work whatsoever. That's the only way that you can eliminate any risk affiliated with silicosis in the shop," says owner Paul Menninger.
He says if it were up to him, dry cutting would be illegal.
In his workplace, machine operators and workers doing touch-ups with handheld tools don't have to wear respirators, because silica is well-controlled. Menninger knows this because he recently invited in an inspector from OSHA, who tested the air.
But he says there are a lot of shops, especially smaller operations, that government inspectors never get to. And the stone cutting industry is unlicensed.
"It's not like plumbing or electrical or HVAC or any of the other trades," he says, "whereby there seems to be a standard or an international code."
Yet consumers rely on the industry and regulators to ensure that products are made safely, says Carolyn Levine, a Washington, D.C., resident who recently replaced her natural granite countertops with engineered quartz.
The lung illnesses found in the countertop industry are alarming, she says.
"Having regulations and precautions is important, and this is a good example of why," Levine says.
She had never heard of engineered quartz before deciding to replace her old granite countertops, which she had for more than 12 years.
"I just wanted something lighter and brighter," Levine says. "I had two guys give me estimates."
They both were emphatic, she says, that compared to granite, the superior product was quartz.
Nell Greenfieldboyce
Nell Greenfieldboyce is a NPR science correspondent.
See stories by Nell Greenfieldboyce
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Reviews Photography Canon Eos 5D Mark Iv Dslr Camera
Canon EOS 5D Mark IV DSLR camera
dfcc7494-9b12-4966-9e1b-3cb8728a91eb
Bird photography has never been more popular, and Canon has emerged as the brand of choice in the DSLR market. The EOS 7D Mark II is a particular favourite in the company's enthusiast line-up, but anyone wanting to immerse themselves more deeply in bird photography needs to look at Canon's professional range, including the latest iteration of the long-serving 5D.
The 5D Mark IV looks and feels like a classic Canon, and the ergonomics and layout of controls are immediately familiar. Constructed from magnesium-alloy and with weatherproofing Canon describes as "resilient", it feels robust and well built. On the rear of the body is a bright, fixed 3.2-inch screen which, unlike in the 5D Mark III, is a touchscreen with a higher resolution of 1,620,000 dots. As with most professional bodies, there is no built-in flash.
At the model's core is its 30.4 MP CMOS sensor, a major step up from the 22.3 MP 5D Mark III. You may not get the 1.6x crop factor with this full-frame camera, but it generates impressively large RAW and JPG files of 6,720x4,480 pixels. The ISO range is 100-25,600, expandable to 50-102,400, maximum video resolution is 4,096x2,160 – double that of the Mark III – and it boasts an advanced, 61-point dual-pixel CMOS autofocus system. GPS and wi-fi capabilities further enhance this camera's performance, and there are advanced in-camera image-processing options.
I tested the 5D Mark IV with multiple lenses in a range of conditions, and it produced hugely impressive results. Coupling it with the EF 300 mm f2.8 L IS USM II lens provided the optimal combination in terms of image quality, but it will deliver top-drawer images with any telephoto lens.
Low-light performance was particularly strong, and I found I could ramp up the ISO to settings normally avoided on other Canon bodies because of noise issues. Its low-light capabilities also extend opportunities at both ends of the day and in dark conditions such as forest. In terms of colour depth and dynamic range, images are exceptional and independent lab tests rate the 5D Mark IV as the best-performing of all Canon DSLRs (see www.dxomark.com).
Battery life is rated at 900 shots, a slight improvement on the Mark III and 50 per cent more than in the 7D Mark II. I usually leave GPS and wi-fi switched off to avoid battery drain, but used the 5D Mark IV's wi-fi to pair it to Canon's Camera Connect app on my iPhone. Through this I was able to view camera images on my phone, download them direct to the phone's own photo app and quickly edit and share them on social media, without needing to do so on my PC at home first – a real plus. The app can also be used as a remote shutter control for shooting in live view and movie modes, and this worked well with the camera set up on a tripod in a hide.
I had just one odd experience when using the 5D Mark IV. In continuous shooting modes, I couldn't initially get the camera to take multiple images while holding down the shutter button, let alone fire at the claimed speed of 7 fps. This was the case with both the review sample and another I tried subsequently. By comparing the settings with another photographer's 5D Mark IV, I discovered that Multiple Exposure and HDR Mode were both disabled and also inactive in the menu, and couldn't immediately be changed. The only way I could find to activate these options was to reset all camera settings, then enable them individually and restore my other settings – no big deal, but a curious anomaly.
Otherwise, the 5D Mark IV performed exceptionally well at all times. It is a joy to use, delivering images of the highest quality in all conditions. Getting to know how to use it fully will be a long process, but in this reviewer's case I look forward to that challenge, as Canon's latest version of a long-term favourite has now become my camera of choice.
SRP: £3,249.99
Size: 150.7x116.4x75.9 mm
Sensor: 30.4 MP full-frame CMOS sensor
ISO: 100-25,600 (expandable to 50-102,400)
FPS: 7.0 continuous shooting
Storage slots: 1xCF, 1xSD
Other features: 61-point AF, 4K video, GPS, wi-fi, Digic 6+
Warranty: two-year guarantee
Exceptional image quality with superb detail
High-definition, 3.2-inch touchscreen
Expensive SRP, but deals are available online
This Bar-tailed Godwit was photographed with the EOS 5D Mark IV in failing light on a grey afternoon in winter. At ISO 1,600, noise is undetectable and overall the 5D's low-light performance is excellent (Dominic Mitchell).
Written by: Dominic Mitchell
18:39 Glossy Ibis


The Truth Be Told (Book 3)
Series: The Truth in Lies Saga
Author: Jeanne McDonald
Cover Design: Jada D'Lee Designs
Expected Release Date: May 18, 2015
Jeanne McDonald is an author, a mother, a wife, a student of knowledge and of life, a coffee addict, a philosophy novice, a pop culture connoisseur, inspired by music, encouraged by words, and a believer in true love. When she's not spending time with her family, she can be found reading, writing, enjoying a great film, chatting with friends or diligently working toward her bachelor's degree in literature. A proud Texan, Jeanne currently resides in the Dallas/Fort Worth area with her family.
Website | Facebook | Twitter | Goodreads | Amazon | Google+ | Smashwords
From the moment Andrew Wise and McKenzie Evans first met, they tried to fight the magnetism that pulled them together. No matter how hard they struggled with their feelings, their love was a force so strong that neither of them could deny it.
The news of Olivia Hamilton's pregnancy, and the understanding that Drew is the father, led McKenzie to flee with the hope of rectifying her secret betrayal of falling in love with her best friend's boyfriend. However, when Drew showed up and declared his undying love for her, McKenzie could no longer deny the truth. She and Drew were destined for each other.
McKenzie now has no choice but to face Olivia in order for her and Drew to move on with their lives together. Secrets and lies may have kept them apart, but now, in the light of the truth, their legacy shines as pure as their love.
For as long as Drew can remember, there has always been tension between him and his father, Jonathan. This time is proving no different. Since sharing the truth of his past with McKenzie, Drew is emboldened by her unwavering love and acceptance of the man he is. He'll do anything necessary to protect the woman he loves and the life he's come to understand she deserves. With Jonathan and Olivia teamed together to rip them apart, Drew and McKenzie, along with the aid of some unexpected allies, must join forces to overcome the obstacles that will inevitably come their way.
In this much anticipated final installment of The Truth in Lies Saga, Drew and McKenzie will unite together to conquer the past, face the future, and uncover the truth in lies that threaten to destroy them. Love brought them together and love will set them free.
"What are you thinking about?" The soft rumble of Drew's voice tickled my ear.
My head rested on his shoulder, caught between reality and the world of dreaming. After everything that had happened, I was mentally and physically drained. Now, thirty-some-odd-thousand feet in the air and for the first time in months, I felt truly happy, which seemed strange since I was heading straight for a hornet's nest.
Boston scared me. Facing Drew's family was bad enough, but coming face to face with one of my oldest and dearest friends, Olivia Hamilton, was even harder. For so long, I'd hidden from her my real reason for my leaving Sarasota. My departure hurt her in the worst sort of way. In her mind, I abandoned her when she needed me most. If she only knew the truth of how terrible of a person I really was, she wouldn't consider me her best friend. Losing her friendship altogether was something I had to prepare myself for once we reached Boston.
Gah, how was I to face her?
Olivia deserved a friend who was there for her, as she had been for me when I lost everything I held dear in my life. She had so much on her plate already with her pregnancy and her job, and I was about to add to her burden by admitting that the father of her child and I were in love. It was because of me that all of her hopes and dreams would soon be destroyed. And while all of that weighed on me, my heart still couldn't bear being another day without Drew. I'd punished myself long enough and suffered more heartache than anyone should have to endure. Losing Evan, then breaking up with Nate, then leaving Drew and abandoning Olivia—I was emotionally drained.
Only hours earlier I was in church begging God for guidance. I was conflicted and needed answers. Drew was about to leave for Boston and wanted me with him, and I wanted to be with him. But the idea of openly admitting our love, not only to his family but to Olivia, while at a wedding, seemed in poor taste to me. My heart struggled with its need to be near Drew and my desire to protect my friend. Even though Drew had confessed time and time again he held no feelings for Olivia, I still felt terrible for the predicament she now found herself in.
By the end of the service, I thought I was prepared to let him leave. Things were different now between Drew and me. All of the lies that held us back were no longer an obstacle. All that weighed between us was his family and my best friend. Those things could wait a week while he celebrated the union of Gavin, his older brother, and Morgan.
It wasn't until Gavin became infuriated with the idea of leaving me behind that I realized I wasn't trying to protect his wedding. I was afraid—terrified, really—of not only being hurt again, but of hurting someone I cared about. By not going to Boston, I was once again running away from my problems. No sooner had the fellas drove off, than I was in my car, barrelling down the E-way back to my apartment to pack. Poor Mackie, my kitten, thought I'd lost my mind as I shoved her little butt in a carryon.
"I know what I'm thinking," Jared piped up. He turned around in his seat, that winning smile of his plastered over his adorable face. I'd missed the shit out of him. Our long conversations on the phone weren't enough. Out of everyone, including Olivia or Drew, I'd say Jared knew me the best. He had a huge heart and a witty, sometimes sadistic, sense of humor. His shaggy blond hair fell into his golden eyes, but that didn't keep me from seeing them bounce with mischief.
"And what's that?" I dared to ask.
Drew slipped his hand into mine. A soft chuckle resounded from his chest. It was strange seeing him laugh at Jared. When I left Sarasota, they could barely be in the same room together without daggers flying. My Neanderthal wasn't too keen on the discovery that my best bud had developed feelings for me that surpassed friendship. If I were to be honest, I'd known Jared's heart long before he revealed his secret. But my heart had been conquered by Drew.
Talk about your messed up quadrangle. Olivia wanted Drew, but he loved me. Jared loved me, but I was in love with Drew. My life was one big soap opera.
Jared drummed his fingers together, the corner of his mouth twitching.
Gavin peered over the plush leather headrest and gave me the cutest little wink. His brown hair was slathered in a thick layer of gel. A thin beard lined his slim jaw. Eyes, blue as the ocean, stared back at me. They weren't quite aquamarine like Drew's, but they were pretty all the same.
"So, what are we talking about?" he buzzed.
"Jared here was just about to fill us in on what he was thinking. As if any of us cared," Drew declared.
Jared gave a dramatic gasp. "If that's how you're going to be…" He started to turn back around in his seat, feigning disappointment.
Me, the ever gullible one, called out, "I care. What were you thinking, Jare?"
Jared sprang back around, his smile flared wide. "I was thinking about the look on the Skanky Ho Momma's face when she sees you." He clapped his hands, flamboyant and giddy.
"Someone better have a cell phone ready to snap a pic of that. I want to plaster it everywhere!" Drew cackled.
"Why do you hate Liv so much?" I questioned.
All of them did, and I couldn't understand why. Okay, so she wasn't Mother Teresa, but she'd always done right by me. She took care of me in college, and came to my rescue when I needed her most. Never once did she turn me away. Olivia might be self-centered and a little ostentatious with her wardrobe, but deep down, I knew she had a good heart.
"I don't hate her…" Jared paused, "…exactly. But I can say if she were ever on fire and I had a bottle of water," his eyes bounced between the three of us as he leaned in closer and stage whispered, "I'd drink it."
Laughter ricocheted from Gavin and Drew throughout the compartment. Jared wore a look of pride at making everyone laugh. Well, almost everyone.
Drew released my hand and nearly buckled over in laughter. "Quack, quack," he snorted.
This caused an even further uproar of laughter that I didn't quite understand.
"What the hell does that mean?" I demanded. It was difficult not to laugh with the three of them howling, but somehow I managed.
"Nothing. Nothing." Drew gasped for breath, holding his gut.
"No! Really. Someone tell me what that means?"
Drew, realizing I was getting a little frustrated, managed to calm down enough to tell me a story about Olivia appearing at his place wearing a bright yellow dress and waddling like a duck. "She's got a baby bump, but she's not big enough to waddle yet," he crooned.
All at once, the weight of everything came crashing back down on me. Olivia was pregnant with Drew's child. Out of everything I would have to endure, that was probably the worst of it. I'd prepared myself for the shitstorm that would ensue the moment Olivia discovered Drew and I were together. Not that I would blame her for hating me. If the roles were reversed, I'd hate me, too. But her pregnancy was a constant reminder that she would always be in his life. Together, they had something I longed for…a baby.
"Wow," I muttered, unable to mask my disappointment. "I guess I missed a lot."
Gavin reached over the seat and patted my cheek. "Nothing you can't get caught up on quickly."
Drew wrapped his arm around my shoulders, drawing me in close to him. "Honestly, Baby, you haven't missed much. I'm happy to have you with us, Mickie. I can't express how much we all missed you."
If he only knew that wasn't what really had me upset. This was my secret to keep. A jealousy I would always have to endure. And maybe one day, Drew and I might start our own family.
I rested my head back on his shoulder and closed my eyes. He smelled so inviting, and his gentle touch was very relaxing. So relaxing, in fact, I fell asleep. I was awakened by the sound of the intercom coming to life.
"Ladies and Gentleman, we are beginning our final descent to Boston Logan International. It's now nine twenty-three P.M. local time, and the temperature is currently eighty-one degrees. We have certainly enjoyed having you aboard today, and we hope to see you again soon. Thank you again for flying Skyway Airlines, and have a wonderful evening."
My stomach lurched as the plane started to descend. I stretched, wiggling my toes inside my sneakers.
"How long was I out?"
"Not too long. You looked so peaceful. I couldn't bring myself to wake you."
"You never could."
"I enjoy watching you sleep. It comforts me." Drew brushed his knuckles across my cheek. "You comfort me."
I leaned into his hand, content to feel the warmth of his skin and the love in his touch.
Drew placed a soft kiss to my lips. A bright smile appeared as he pulled back and glanced out the window. "Look, Baby."
I shifted forward to look out the window. Such beauty and history lay out before me as we lowered closer and closer to the ground. The evening glow of the moon danced over the water, and buildings full of history towered above the trees, beckoning me to explore their mysteries.
"It's gorgeous."
He leaned in and whispered tenderly in my ear, "Welcome to my home, Baby." I turned my head to find the most amazing man staring back at me. His eyes were filled with so much love that it took my breath away. He cupped my face in his hands and kissed me.
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Cambridge, Storbritannien
East Rd, CB1 1PT Cambridge Storbritannien
Anglia Ruskin University is like no other higher education institution. That's a bold statement, but we've plenty of evidence to back this up:
Our research results and innovation in teaching and business development have led to us being named the Entrepreneurial University of the Year (Times Higher Education Awards 2014).
In a number of areas, we're generating world-leading research, as recognised by the UK's Higher Education funding bodies. Results of the Research Excellence Framework (REF) 2014 highlight our research activities as making a significant impact on economies, societies, the environment and culture globally.
39,400 students choose to study with us every year across the world.
From day one, we help our students work towards a career and graduate with confidence. The results speak for themselves: 9 out of 10 of our graduates start their careers within the first six months.
We're the first university to get a Customer Service Excellence Award and our Student Services Team was rated the UK's best (Times Higher Education Awards).
We run EU-funded programmes in our region, worth millions of Euros, which help researchers, businesses and organisations get on.
The Anglia Ruskin Medtech Campus was launched at the House of Commons. This will be one of the world's largest health innovation spaces, creating 12,500 jobs and boosting the UK's medical technology sector by £1.2 billion.
We've five faculties at ARU, each providing students, industry and the academic community with professionally focused and world-leading courses and research.
Our Five Faculties:
Faculty of Arts, Law and Social Sciences
Faculty of Medical Science
Lord Ashcroft International Business School
Our Research Institutes
In the last decade, we've forged ahead with our research work. We've research-active staff across ARU, and a growing reputation in this area.
You'll now find six high-profile research institutes here. The first of these was our Postgraduate Medical Institute, set up in 2008, which carries out ground-breaking medical research and trains healthcare professionals in a range of sophisticated techniques. The Institute for International Management Practice followed in 2009; it's dedicated to researching in the fields of enterprise, innovation and internationalisation.
In 2010, we established the Cultures of the Digital Economy (CoDE) Research Institute to explore the effects of the digital economy on art, culture and society. Next came the Global Sustainability Institute in 2011. It focuses on issues surrounding climate change and sustainability and has quickly gained a reputation for its topical, high-impact research and reports.
Finally, our two newest institutes were set up in 2014. The Veterans and Families Institute is carrying out valuable research into the impact of military experience on veterans and their loved ones; and the Anglia Ruskin IT Research Institute works to enhance IT systems through intelligent modelling and visualisation.
Alongside these six institutes is a range of research units, dedicated to subjects as diverse as music therapy, eye diseases, children's book studies, and political history.
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