Reliability of parameter estimates from models applied to respiratory impedance data

Many previous studies have fit lumped parameter models to respiratory input (Zin) and transfer (Ztr) impedance data. For frequency ranges higher than 4-32 Hz, a six-element model may be required in which an airway branch (with a resistance and inertance) is separated from a tissue branch (with a resistance, inertance, and compliance) by a shunt compliance. A sensitivity analysis is applied to predict the effects of frequency range on the accuracy of parameter estimates in this model obtained from Zin or Ztr data. Using a parameter set estimated from experimental data between 4 and 64 Hz in dogs, both Zin and Ztr were simulated from 4 to 200 Hz. Impedance sensitivity to each parameter was also calculated over this frequency range. The simulation predicted that for Zin a second resonance occurs near 80 Hz and that the impedance is considerably more sensitive to several of the parameters at frequencies surrounding this resonance than at any other frequencies. Also, unless data is obtained at very high frequencies (where the model is suspect), Zin data provides more accurate estimates than Ztr data. After adding random noise to the simulated Zin data, we attempted to extract the original parameters by using a nonlinear regression applied to three frequency ranges: 4-32, 4-64, and 4-110 Hz. Estimated parameters were substantially incorrect when using only 4- to 32-Hz or 4- to 64-Hz data, but nearly correct when fitting 4- to 110-Hz data. These results indicate that respiratory system parameters can be more accurately extracted from Zin than Ztr, and to make physiological inferences from parameter estimates based on Zin impedance data in dogs, the data must include frequencies surrounding the second resonance.     

Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate δ, the viral plasma clearance rate c, and the time delay τ between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.     

Results of antiretroviral treatment interruption and intensification in advanced multi-drug resistant HIV infection from the OPTIMA trial

Background

Guidance is needed on best medical management for advanced HIV disease with multidrug resistance (MDR) and limited retreatment options. We assessed two novel antiretroviral (ARV) treatment approaches in this setting.

Methods and Findings

We conducted a 2×2 factorial randomized open label controlled trial in patients with a CD4 count ≤300 cells/µl who had ARV treatment (ART) failure requiring retreatment, to two options (a) re-treatment with either standard (≤4 ARVs) or intensive (≥5 ARVs) ART and b) either treatment starting immediately or after a 12-week monitored ART interruption. Primary outcome was time to developing a first AIDS-defining event (ADE) or death from any cause. Analysis was by intention to treat. From 2001 to 2006, 368 patients were randomized. At baseline, mean age was 48 years, 2% were women, median CD4 count was 106/µl, mean viral load was 4.74 log₁₀ copies/ml, and 59% had a prior AIDS diagnosis. Median follow-up was 4.0 years in 1249 person-years of observation. There were no statistically significant differences in the primary composite outcome of ADE or death between re-treatment options of standard versus intensive ART (hazard ratio 1.17; CI 0.86–1.59), or between immediate retreatment initiation versus interruption before re-treatment (hazard ratio 0.93; CI 0.68–1.30), or in the rate of non-HIV associated serious adverse events between re-treatment options.

Conclusions

We did not observe clinical benefit or harm assessed by the primary outcome in this largest and longest trial exploring both ART interruption and intensification in advanced MDR HIV infection with poor retreatment options.

Trial Registration

Clinicaltrials.gov {"type":"clinical-trial","attrs":{"text":"NCT00050089","term_id":"NCT00050089"}}NCT00050089     

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log₁₀-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate α(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize α(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.      

Correlation of in vitro chemopreventive efficacy data from the human epidermal cell assay with animal efficacy data and clinical trial plasma levels

The human epidermal cell (HEC) assay, which uses carcinogen exposed normal skin keratinocytes to screen for cancer prevention efficacy, was used to screen possible preventive agents. The endpoints measured were inhibition of carcinogen-induced growth and induction of involucrin, an early marker of differentiation. Sixteen of twenty agents (apigenin, apomine, budesonide, N-(2-carboxyphenyl)retinamide, ellagic acid, ibuprofen, indomethacin, melatonin, (-)-2-oxo-4-thiazolidine carboxylic acid, polyphenon E, resveratrol, beta-sitosterol, sulfasalazine, vitamin E acetate, and zileuton) were positive in at least one of the two assay endpoints. Four agents (4-methoxyphenol, naringenin, palmitoylcarnitine chloride, and silymarin) were negative in the assay. Nine of the sixteen agents were positive for both endpoints. Agents that showed the greatest response included: ellagic acid > budesonide, ibuprofen > apigenin, and quinicrine dihydrochloride. Fifty-eight of sixty-five agents that have been evaluated in the HEC assay have also been evaluated in one or more rodent bioassays for cancer prevention and several are in clinical trials for cancer prevention. The assay has an overall predictive accuracy of approximately 91.4% for efficacy in rodent cancer prevention irrespective of the species used, the tissue model, or the carcinogen used. Comparison of the efficacious concentrations in vitro to plasma levels in clinical trials show that concentrations that produced efficacy in the HEC assay were achieved in clinical studies for 31 of 33 agents for which plasma levels and/or C(max) levels were available. For two agents, 9-cis-retinoic acid (RA) and dehydroepiandrosterone (DHEA), the plasma levels greatly exceeded the highest concentration (HC) found to have efficacy in vitro. Thus, the HEC assay has an excellent predictive potential for animal efficacy and is responsive at clinically achievable concentrations.     

A simple model of pathogen-immune dynamics including specific and non-specific immunity

We present and analyze a model for the dynamics of the interactions between a pathogen and its host's immune response. The model consists of two differential equations, one for pathogen load, the other one for an index of specific immunity. Differently from other simple models in the literature, this model exhibits, according to the hosts' or pathogen's parameter values, or to the initial infection size, a rich repertoire of behaviours: immediate clearing of the pathogen through aspecific immune response; or acute infection followed by clearing of the pathogen through specific immune response; or uncontrolled infections; or acute infection followed by convergence to a stable state of chronic infection; or periodic solutions with intermittent acute infections. The model can also mimic some features of immune response after vaccination. This model could be a basis on which to build epidemic models including immunological features.     

Modeling hepatitis C virus dynamics: liver regeneration and critical drug efficacy

Mathematical models for hepatitis C viral (HCV) RNA kinetics have provided a means of evaluating the antiviral effectiveness of therapy, of estimating parameters such as the rate of HCV RNA clearance, and they have suggested mechanism of action against HCV for both interferon and ribavirin. Nevertheless, the model that was originally formulated by Neumann et al. [1998. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 282 (5386), 103-107] is unable to explain all of the observed HCV RNA profiles under treatment e.g., a triphasic viral decay and a viral rebound to baseline values after the cessation of therapy. Further, the half-life of productively HCV-infected cells, estimated from the second phase HCV RNA decline slope, is very variable and sometimes zero with no clear understanding of why. We show that extending the original model by including hepatocyte proliferation yields a more realistic model without any of these deficiencies. Further, we define and characterize a critical drug efficacy, such that for efficacies above the critical value HCV is ultimately cleared, while for efficacies below it, a new chronically infected viral steady-state level is reached.     

The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels

The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (²_g) and specific combining ability variance (²_s) had a large positive skewness. For ²_g and ²_s, a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121–128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Halls transformation methods (Zhou and Gao, Am Stat 54:100–104, 2000) had poor coverages. Coverage accuracy of Fiellers interval endpoint(J R Stat Soc Ser B 16:175–185, 1954) and t-interval endpoint were similar for both h² and r_B for sample sizes n10, but for n=30 the Fiellers method is much better.     

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.     

Implications of empirical data quality to metapopulation model parameter estimation and application

Parameter estimation is a critical step in the use of any metapopulation model for predictive purposes. Typically metapopulation studies assume that empirical data are of good quality and any errors are so insignificant that they can be ignored. However, three types of errors occur commonly in metapopulation data sets. First, patch areas can be mis-estimated. Second, unknown habitat patches may be located within or around the study area. Third, there may be false zeros in the data set, that is, some patches were observed to be empty while there truly was a population in the patch. This study investigates biases induced into metapopulation model parameter estimates by these three types of errors. It was found that mis-estimated areas influence the scaling of extinction risk with patch area; extinction probabilities for large patches become overestimated. Missing patches cause overestimation of migration distances and colonization ability of the species. False zeros can affect very strongly all model components, the extinction risk in large patches, intrinsic extinction rates in general, migration distances and colonization ability may become all overestimated. Biases in parameter estimates translate into corresponding biases in model predictions, which are serious particularly if metapopulation persistence becomes overestimated. This happens for example when the migration capability of the species is overestimated. Awareness of these biases helps in understanding seemingly anomalous parameter estimation results. There are also implications for field work: it may be reasonable to allocate effort so that serious errors in data are minimized. It is particularly important to avoid observing false zeros for large and/or isolated patches.     

A simple model of pathogen–immune dynamics including specific and non-specific immunity

We present and analyze a model for the dynamics of the interactions between a pathogen and its host’s immune response. The model consists of two differential equations, one for pathogen load, the other one for an index of specific immunity. Differently from other simple models in the literature, this model exhibits, according to the hosts’ or pathogen’s parameter values, or to the initial infection size, a rich repertoire of behaviours: immediate clearing of the pathogen through aspecific immune response; or acute infection followed by clearing of the pathogen through specific immune response; or uncontrolled infections; or acute infection followed by convergence to a stable state of chronic infection; or periodic solutions with intermittent acute infections. The model can also mimic some features of immune response after vaccination. This model could be a basis on which to build epidemic models including immunological features.     

Stochastic modeling of the neuronal activity in the subthalamic nucleus and model parameter identification from Parkinson patient data

Several stochastic models, with various degrees of complexity, have been proposed to model the neuronal activity from different parts of the human brain. In this article, we use a simple Ornstein–Uhlenbeck process (OUP) to model the spike activity recorded from the subthalamic nucleus of patients suffering from Parkinson’s disease at the time of implantation of the electrodes for deep brain stimulation. From the recorded data, which contains information about the spike times of a single neuron, we identify and extract the model parameters of the OUP. We then use these parameters to numerically simulate the inter-spike intervals and the voltage across the neuron membrane. We finally assess how well the proposed mathematical model fits to the measured data and compare it with other commonly adopted stochastic models. We show an excellent agreement between the computer-generated data according to the OUP model and the measured one, as well as the superiority of the OUP model when compared to the Poisson process model and the random walk model; thus, establishing the validity of the OUP as a simple yet biologically plausible model of the neuronal activity recorded from the subthalamic nucleus of Parkinson’s disease patients.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

Wolbachia and cytoplasmic incompatibility in the California Culex pipiens mosquito species complex: parameter estimates and infection dynamics in natural populations

Before maternally inherited bacterial symbionts like Wolbachia, which cause cytoplasmic incompatibility (CI; reduced hatch rate) when infected males mate with uninfected females, can be used in a program to control vector-borne diseases it is essential to understand their dynamics of infection in natural arthropod vector populations. Our study had four goals: (1) quantify the number of Wolbachia strains circulating in the California Culex pipiens species complex, (2) investigate Wolbachia infection frequencies and distribution in natural California populations, (3) estimate the parameters that govern Wolbachia spread among Cx. pipiens under laboratory and field conditions, and (4) use these values to estimate equilibrium levels and compare predicted infection prevalence levels to those observed in nature. Strain-specific PCR, wsp gene sequencing, and crossing experiments indicated that a single Wolbachia strain infects Californian Cx. pipiens. Infection frequency was near or at fixation in all populations sampled for 2 years along a >1000-km north-south transect. The combined statewide infection frequency was 99.4%. Incompatible crosses were 100% sterile under laboratory and field conditions. Sterility decreased negligibly with male age in the laboratory. Infection had no significant effect on female fecundity under laboratory or field conditions. Vertical transmission was >99% in the laboratory and approximately 98.6% in the field. Using field data, models predicted that Wolbachia will spread to fixation if infection exceeds an unstable equilibrium point above 1.4%. Our estimates accurately predicted infection frequencies in natural populations. If certain technical hurdles can be overcome, our data indicate that Wolbachia can invade vector populations as part of an applied transgenic strategy for vector-borne disease reduction.