Dirichlet-to-Neumann Maps, Abstract Weyl-Titchmarsh MM-Functions, and a Generalized Index of Unbounded Meromorphic Operator-Valued Functions

We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter dependent Dirichlet-to-Neumann maps associated to uniformly elliptic partial differential operators, particularly, non-self-adjoint Schr\"odinger operators, on bounded Lipschitz domains, and abstract operator-valued Weyl-Titchmarsh $M$-functions and Donoghue-type $M$-functions corresponding to closed extensions of symmetric operators belong to it. The principal purpose of this paper is to prove index formulas that relate the difference of the algebraic multiplicities of the discrete eigenvalues of Robin realizations of non-self-adjoint Schr\"{o}dinger operators, and more abstract pairs of closed operators in Hilbert spaces with the generalized index of the corresponding energy dependent Dirichlet-to-Neumann maps and abstract Weyl-Titchmarsh $M$-functions, respectively.Comment: A natural continuation of our arXiv:1512.06962 submissio

Modeling Physiological Processes That Relate Toxicant Exposure and Bacterial Population Dynamics

Quantifying effects of toxicant exposure on metabolic processes is crucial to predicting microbial growth patterns in different environments. Mechanistic models, such as those based on Dynamic Energy Budget (DEB) theory, can link physiological processes to microbial growth. Here we expand the DEB framework to include explicit consideration of the role of reactive oxygen species (ROS). Extensions considered are: (i) additional terms in the equation for the ‘‘hazard rate’’ that quantifies mortality risk ; (ii) a variable representing environmental degradation ; (iii) a mechanistic description of toxic effects linked to increase in ROS production and aging acceleration, and to non-competitive inhibition of transport channels ; (iv) a new representation of the ‘‘lag time’’ based on energy required for acclimation. We estimate model parameters using calibrated Pseudomonas aeruginosa optical density growth data for seven levels of cadmium exposure. The model reproduces growth patterns for all treatments with a single common parameter set, and bacterial growth for treatments of up to 150 mg(Cd)/L can be predicted reasonably well using parameters estimated from cadmium treatments of 20 mg(Cd)/L and lower. Our approach is an important step towards connecting levels of biological organization in ecotoxicology. The presented model reveals possible connections between processes that are not obvious from purely empirical considerations, enables validation and hypothesis testing by creating testable predictions, and identifies research required to further develop the theory

Systemic effects of Optos versus indirect ophthalmoscopy for retinopathy of prematurity screening

Many regions of the world have a relative shortage of ophthalmologists trained and willing to screen for retinopathy of prematurity (ROP).1 As a result, many regions have turned to retinal imaging and telemedicine.2 Optos ultrawide-field retinal imaging (Optos PLC, Dunfermline, UK) has recently been used as a screening tool for ROP.3,4 However, there are no data available regarding the systemic effects or stress induced by a ROP screening examination with the Optos. In this prospective, randomized, crossover study, we determined the effects of Optos ultrawide-field screening examination on cardiorespiratory indices, as a measure of stress, and compared the stress response with that of conventional binocular indirect ophthalmoscopy (BIO) examination

Combinatorial pharmacodynamics of polymyxin B and tigecycline against heteroresistant Acinetobacter baumannii

The prevalence of heteroresistant Acinetobacter baumannii is increasing. Infections due to these resistant pathogens pose a global treatment challenge. Here, the pharmacodynamic activities of polymyxin B (PMB) (2–20 mg/L) and tigecycline (0.15–4 mg/L) were evaluated as monotherapy and in combination using a 4 × 4 concentration array against two carbapenem-resistant and polymyxin-heteroresistant A. baumannii isolates. Time Kill Experiments was employed at starting inocula of 106 and 108 CFU/mL over 48 h. Clinically relevant combinations of PMB (2 mg/L) and tigecycline (0.90 mg/L) resulted in greater reductions in the bacterial population compared with polymyxin alone by 8 h (ATCC 19606, −6.38 vs. −3.43 log10 CFU/mL; FADDI AB115, −1.38 vs. 2.08 log10 CFU/mL). At 10× the clinically achievable concentration (PMB 20 mg/L in combination with tigecycline 0.90 mg/L), there was bactericidal activity against FADDI AB115 by 4 h that was sustained until 32 h, and against ATCC 19606 that was sustained for 48 h. These studies show that aggressive polymyxin-based dosing in combination with clinically achievable tigecycline concentrations results in early synergistic activity that is not sustained beyond 8 h, whereas combinations with higher tigecycline concentrations result in sustained bactericidal activity against both isolates at both inocula. These results indicate a need for optimised front-loaded polymyxin-based combination regimens that utilise high polymyxin doses at the onset of treatment to achieve good pharmacodynamic activity whilst minimising adverse events

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

New Polymyxin B Dosing Strategies To Fortify Old Allies in the War against KPC-2-Producing Klebsiella pneumoniae

ABSTRACT Pharmacodynamics of a polymyxin B, meropenem, and rifampin triple combination were examined against Klebsiella pneumoniae carbapenemase-producing Klebsiella pneumoniae (KPC-Kp) ST258. In time-kill experiments against three KPC-Kp isolates, triple combination generated 8.14, 8.19, and 8.29 log 10 CFU/ml reductions within 24 h. In the hollow-fiber infection model, the triple combination caused maximal killing of 5.16 log 10 CFU/ml at 78 h and the time required for regrowth was more than doubled versus the 2-drug combinations. Remarkably, combinations with a high single-dose polymyxin B burst plus rifampin preserved KPC-Kp polymyxin susceptibility (MIC 240 h = 0.5 mg/liter) versus the same combination with traditionally dosed polymyxin B, where resistance was amplified (MIC 240 h = 32 mg/liter)

Paradoxical Effect of Polymyxin B: High Drug Exposure Amplifies Resistance in Acinetobacter baumannii

ABSTRACT Administering polymyxin antibiotics in a traditional fashion may be ineffective against Gram-negative ESKAPE ( Enterococcus faecium , Staphylococcus aureus , Klebsiella pneumoniae , Acinetobacter baumannii , Pseudomonas aeruginosa , and Enterobacter species) pathogens. Here, we explored increasing the dose intensity of polymyxin B against two strains of Acinetobacter baumannii in the hollow-fiber infection model. The following dosage regimens were simulated for polymyxin B ( t 1/2 = 8 h): non-loading dose (1.43 mg/kg of body weight every 12 h [q12h]), loading dose (2.22 mg/kg q12h for 1 dose and then 1.43 mg/kg q12h), front-loading dose (3.33 mg/kg q12h for 1 dose followed by 1.43 mg/kg q12h), burst (5.53 mg/kg for 1 dose), and supraburst (18.4 mg/kg for 1 dose). Against both A. baumannii isolates, a rapid initial decline in the total population was observed within the first 6 h of polymyxin exposure, whereby greater polymyxin B exposure resulted in greater maximal killing of −1.25, −1.43, −2.84, −2.84, and −3.40 log 10 CFU/ml within the first 6 h. Unexpectedly, we observed a paradoxical effect whereby higher polymyxin B exposures dramatically increased resistant subpopulations that grew on agar containing up to 10 mg/liter of polymyxin B over 336 h. High drug exposure also proliferated polymyxin-dependent growth. A cost-benefit pharmacokinetic/pharmacodynamic relationship between 24-h killing and 336-h resistance was explored. The intersecting point, where the benefit of bacterial killing was equal to the cost of resistance, was an f AUC 0–24 (area under the concentration-time curve from 0 to 24 h for the free, unbound fraction of drug) of 38.5 mg · h/liter for polymyxin B. Increasing the dose intensity of polymyxin B resulted in amplification of resistance, highlighting the need to utilize polymyxins as part of a combination against high-bacterial-density A. baumannii infections

Polymyxin B in combination with doripenem against heteroresistant Acinetobacter baumannii : pharmacodynamics of new dosing strategies

Polymyxin B is being increasingly utilized as a last resort against resistant Gram-negative bacteria. We examined the pharmacodynamics of novel dosing strategies for polymyxin B combinations to maximize efficacy and minimize the emergence of resistance and drug exposure against Acinetobacter baumannii