Identifiability and online estimation of diagnostic parameters with in the glucose insulin homeostasis

Today, diagnostic decisions about pre-diabetes or diabetes are made using static threshold rules for the measured plasma glucose. In order to develop an alternative diagnostic approach, dynamic models as the Minimal Model may be deployed. We present a novel method to analyze the identifiability of model parameters based on the interpretation of the empirical observability Gramian. This allows a unifying view of both, the observability of the system's states (with dynamics) and the identifiability of the system's parameters (without dynamics). We give an iterative algorithm, in order to find an optimized set of states and parameters to be estimated. For this set, estimation results using an Unscented Kalman Filter (UKF) are presented. Two parameters are of special interest for diagnostic purposes: the glucose effectiveness S(G) characterizes the ability of plasma glucose clearance, and the insulin sensitivity S(I) quantifies the impact from the plasma insulin to the interstitial insulin subsystem. Applying the identifiability analysis to the trajectories of the insulin glucose system during an intravenous glucose tolerance test (IVGTT) shows the following result: (1) if only plasma glucose G(t) is measured, plasma insulin I(t) and S(G) can be estimated, but not S(I). (2) If plasma insulin I(t) is captured additionally, identifiability is improved significantly such that up to four model parameters can be estimated including S(I). (3) The situation of the first case can be improved, if a controlled external dosage of insulin is applied. Then, parameters of the insulin subsystem can be identified approximately from measurement of plasma glucose G(t) only.     

The oculomotor system--simulation of physiologic and pathologic horizontal saccadic eye movements

Horizontal saccadic eye movements were analyzed by way of the input- and output-functions of the oculomotor system. On the basis of the parameters of the model, it was possible to simulate both physiological and pathological saccades. In this paper we present the results of simulation experiments that were performed to study the influence of various ocular motor disorders. The parameters of the model proved a useful diagnostic aid.     

Minimum‐Norm Estimation for Binormal Receiver Operating Characteristic (ROC) Curves

The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi‐parametric ROC model, called the binormal model. Our method is based on minimization of the functional distance between two estimators of an unknown transformation postulated by the model, and has a simple, closed‐form solution. We study the asymptotics of our estimators, show via simulation that they compare favorably with existing estimators, and illustrate how covariates may be incorporated into the norm minimization framework.     

A population‐averaged approach to diagnostic test meta‐analysis

The meta‐analysis of diagnostic accuracy studies is often of interest in screening programs for many diseases. The typical summary statistics for studies chosen for a diagnostic accuracy meta‐analysis are often two dimensional: sensitivities and specificities. The common statistical analysis approach for the meta‐analysis of diagnostic studies is based on the bivariate generalized linear‐mixed model (BGLMM), which has study‐specific interpretations. In this article, we present a population‐averaged (PA) model using generalized estimating equations (GEE) for making inference on mean specificity and sensitivity of a diagnostic test in the population represented by the meta‐analytic studies. We also derive the marginalized counterparts of the regression parameters from the BGLMM. We illustrate the proposed PA approach through two dataset examples and compare performance of estimators of the marginal regression parameters from the PA model with those of the marginalized regression parameters from the BGLMM through Monte Carlo simulation studies. Overall, both marginalized BGLMM and GEE with sandwich standard errors maintained nominal 95% confidence interval coverage levels for mean specificity and mean sensitivity in meta‐analysis of 25 of more studies even under misspecification of the covariance structure of the bivariate positive test counts for diseased and nondiseased subjects.     

On-line two-dimensional evaluation of ultrasonic integrated backscatter

We describe an apparatus for the on-line evaluation of integrated backscatter from areas of tissue. The equipment is fully integrated into a B-mode ultrasonic system: there are therefore no new operating procedures to be learned. It provides a simultaneous display of conventional information, together with parameters of tissue characterization. The apparatus is fast and, over a broad diagnostic frequency range, may be used in conjunction with conventional equipment employing transducers.     

Comparisons of predictive values of binary medical diagnostic tests for paired designs

Positive and negative predictive values of a diagnostic test are key clinically relevant measures of test accuracy. Surprisingly, statistical methods for comparing tests with regard to these parameters have not been available for the most common study design in which each test is applied to each study individual. In this paper, we propose a statistic for comparing the predictive values of two diagnostic tests using this paired study design. The proposed statistic is a score statistic derived from a marginal regression model and bears some relation to McNemar's statistic. As McNemar's statistic can be used to compare sensitivities and specificities of diagnostic tests, parameters that condition on disease status, our statistic can be considered as an analog of McNemar's test for the problem of comparing predictive values, parameters that condition on test outcome. We report on the results of a simulation study designed to examine the properties of this test under a variety of conditions. The method is illustrated with data from a study of methods for diagnosis of coronary artery disease.     

Influence of arterial wall-stenosis compliance on the coronary diagnostic parameters

Functional diagnostic parameters such as Fractional Flow Reserve (FFR), which is calculated from pressure measurements across stenosed arteries, are often used to determine the functional severity of coronary artery stenosis. This study evaluated the effect of arterial wall-stenosis compliance, with limiting scenarios of stenosis severity, on the diagnostic parameters. The diagnostic parameters considered in this study include an established index, FFR and two recently developed parameters: Pressure Drop Coefficient (CDP) and Lesion Flow Coefficient (LFC). The parameters were assessed for rigid artery (RR; signifying high plaque elasticity), compliant artery with calcified plaque (CC; intermediate plaque elasticity) and compliant artery with smooth muscle cell proliferation (CS; low plaque elasticity), with varying degrees of epicardial stenosis. A hyperelastic Mooney-Rivlin model was used to model the arterial wall and plaque materials. Blood was modeled as a shear thinning, non-Newtonian fluid using the Carreau model. The arterial wall compliance was evaluated using the finite element method. The present study found that, with an increase in stenosis severity, FFR decreased whereas CDP and LFC increased. The cutoff value of 0.75 for FFR was observed at 78.7% area stenosis for RR, whereas for CC and CS the cutoff values were obtained at higher stenosis severities of 81.3% and 82.7%, respectively. For a fixed stenosis, CDP value decreased and LFC value increased with a decrease in plaque elasticity (RR to CS). We conclude that the differences in diagnostic parameters with compliance at intermediate stenosis (78.7-82.7% area blockage) could lead to misinterpretation of the stenosis severity.     

A preliminary diagnosis and recommendation integrated system (DRIS) model for diagnosing the nutrient status of sweet potato (Ipomoea batatas)

Critical leaf nutrient concentrations have often been used to diagnose the nutritional causes of crop underperformance. Unfortunately, these diagnostic criteria are not available for mature, tuber-bearing sweet potato plants (the word ‘tuber’ being used to describe a swollen root rather than a swollen stem). The Diagnosis and Recommendation Integrated System (DRIS), however, provides a reliable means of linking leaf nutrient concentrations to the yield of sweet potato tubers, and may be developed for this crop using existing data from regional crop surveys. In the present study, tuber yield and leaf nutrient concentration data from a survey of sweet potato gardens conducted in the Papua New Guinea (PNG) highlands in 2005 were used to establish DRIS N, P, K, and S norms and statistical parameters for sweet potato. Although the database was relatively small, the norms derived for nutrient ratios of key biological significance, i.e. N/S and K/N, were within the expected narrow ranges for higher plants, giving credibility to both the database and the DRIS model. Data from future surveys and field trials may subsequently be used to enlarge the database allowing the refinement of model parameters and hopefully an expansion of diagnostic scope to include other macro and micro-nutrients. As it stands, though, this preliminary DRIS model for sweet potato is possibly the best diagnostic tool currently available for evaluating the N, P, K and S statuses of sweet potato crops in the pacific region.     

A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease

This work presents a new model for the linking of within- and between-host dynamics. We use this as a conceptual model for the dynamics of Toxoplasma gondii, in which the parasite’s life cycle includes interactions with the environment. We postulate the infection process to depend on the size of the infective inoculum that susceptible hosts may acquire by interacting with a contaminated environment. Because the dynamical processes associated with the within- and between-host occur on different time scales, the model behaviors can be analyzed by using a singular perturbation argument, which allows us to decouple the full model by separating the fast- and slow-systems. We define new reproductive numbers for the within-host and between host dynamics for both the isolated systems and the coupled system. Particularly, the reproduction number for the between-host (slow) system dependent on the parameters associated with the within-host (fast) system in a very natural way. We show that these reproduction numbers determine the stability of the infection-free and the endemic equilibrium points. Our model may present a so-called backward bifurcation.     

Family tree analysis of a transformed cell line and the transition probability model for the cell cycle

Variation in intermitotic time between individual cells in culture can be ascribed to the occurrence of random transitions in the cell cycle. We have analysed a family tree of mouse neuroblastoma cells, and observed that variation in difference in intermitotic time between sister cells is smaller than between cousin cells, and this difference is again smaller than between second-cousin and unrelated cells. This observation is incompatible with all transition probability models presented so far. We propose a model for the cell cycle with a single random transition, but with the additional assumption that the (two) system parameters may show variability within the population such that the closer cells are in their relation to each other, the closer their values of the system parameters will be. This model describes correctly the behaviour of the family tree of the cell line and in addition is able to explain why differences in intermitotic time between sister cells are exponentially distributed, while intermitotic times themselves are more or less normally distributed. Methods have been described to quantify the various system parameters.     

Diagnostic accuracy and applicability of a PCR system for the detection of Schistosoma mansoni DNA in human urine samples from an endemic area

Schistosomiasis caused by Schistosoma mansoni, one of the most neglected human parasitoses in Latin America and Africa, is routinely confirmed by microscopic visualization of eggs in stool. The main limitation of this diagnostic approach is its lack of sensitivity in detecting individual low worm burdens and consequently data on infection rates in low transmission settings are little reliable. According to the scientific literature, PCR assays are characterized by high sensitivity and specificity in detecting parasite DNA in biological samples. A simple and cost effective extraction method for DNA of Schistosoma mansoni from urine samples in combination with a conventional PCR assay was developed and applied in an endemic area. This urine based PCR system was tested for diagnostic accuracy among a population of a small village in an endemic area, comparing it to a reference test composed of three different parasitological techniques. The diagnostic parameters revealed a sensitivity of 100%, a specificity of 91.20%, positive and negative predictive values of 86.25% and 100%, respectively, and a test accuracy of 94.33%. Further statistical analysis showed a k index of 0.8806, indicating an excellent agreement between the reference test and the PCR system. Data obtained from the mouse model indicate the infection can be detected one week after cercariae penetration, opening a new perspective for early detection and patient management during this stage of the disease. The data indicate that this innovative PCR system provides a simple to handle and robust diagnostic tool for the detection of S. mansoni DNA from urine samples and a promising approach to overcome the diagnostic obstacles in low transmission settings. Furthermore the principals of this molecular technique, based on the examination of human urine samples may be useful for the diagnosis of other neglected tropical diseases that can be detected by trans-renal DNA.     

Highly sensitive detection of Staphylococcus aureus directly from patient blood

BackgroundRapid detection of bloodstream infections (BSIs) can be lifesaving. We investigated the sample processing and assay parameters necessary for highly-sensitive detection of bloodstream bacteria, using Staphylococcus aureus as a model pathogen and an automated fluidic sample processing – polymerase chain reaction (PCR) platform as a model diagnostic system.ConclusionsWe have demonstrated a highly sensitive two-hour assay for detection of sepsis causing bacteria like S. aureus directly in 1 ml of whole blood, without the need for blood culture.     

When the optimal is not the best: parameter estimation in complex biological models

Background

The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values.

Results

We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit.

Conclusions

The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system and point to the need of a theory that addresses this problem more generally.     

The spatiotemporal transfer function of the Limulus lateral eye

The dynamics of the Limulus retina may be well described by the spatiotemporal transfer function, which measures the response of the eye to moving sinusoidal gratings. We consider a model for this system, which incorporates an excitatory generator potential, and self- and lateral inhibitory processes. Procedures are described which allow estimation of parameters for the model consistent with the empirical transfer function data. Transfer functions calculated from the model show good agreement with laboratory measurements, and may be used to predict accurately the response of the eye to arbitrary moving stimuli. The model allows convenient interpretation of the transfer function measurements in terms of physiological processes which underly the response of the Limulus retina.     

High-resolution computed tomography of single breast cancer microcalcifications in vivo

Microcalcification is a hallmark of breast cancer and a key diagnostic feature for mammography. We recently described the first robust animal model of breast cancer microcalcification. In this study, we hypothesized that high-resolution computed tomography (CT) could potentially detect the genesis of a single microcalcification in vivo and quantify its growth over time. Using a commercial CT scanner, we systematically optimized acquisition and reconstruction parameters. Two ray-tracing image reconstruction algorithms were tested: a voxel-driven "fast" cone beam algorithm (FCBA) and a detector-driven "exact" cone beam algorithm (ECBA). By optimizing acquisition and reconstruction parameters, we were able to achieve a resolution of 104 μm full width at half-maximum (FWHM). At an optimal detector sampling frequency, the ECBA provided a 28 μm (21%) FWHM improvement in resolution over the FCBA. In vitro, we were able to image a single 300 μm × 100 μm hydroxyapatite crystal. In a syngeneic rat model of breast cancer, we were able to detect the genesis of a single microcalcification in vivo and follow its growth longitudinally over weeks. Taken together, this study provides an in vivo "gold standard" for the development of calcification-specific contrast agents and a model system for studying the mechanism of breast cancer microcalcification.     

Protease-sensitive fluorescent nanofibers

We report the design and synthesis of enzyme-responsive nanofibers. The fibers are composed of self-assembled hydrophobic beta-sheet peptides incorporating protease-sensitive domains, fluorescent reporters, and hydrophilic poly(ethylene glycol) (PEG) units. Using urokinase plasminogen activator (uPA) as a model system, nanofibers were developed to release fluorescent fragments upon uPA incubation. These protease-sensitive nanofibers may have considerable biomedical applications as diagnostic sensors or for protease-assisted drug deliveries.     

From inverse problems in mathematical physiology to quantitative differential diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information.     

Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study

MOTIVATION: In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. RESULTS: We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.     

Spectral methods for parametric sensitivity in stochastic dynamical systems

Stochastic dynamical systems governed by the chemical master equation find use in the modeling of biological phenomena in cells, where they provide more accurate representations than their deterministic counterparts, particularly when the levels of molecular population are small. The analysis of parametric sensitivity in such systems requires appropriate methods to capture the sensitivity of the system dynamics with respect to variations of the parameters amid the noise from inherent internal stochastic effects. We use spectral polynomial chaos expansions to represent statistics of the system dynamics as polynomial functions of the model parameters. These expansions capture the nonlinear behavior of the system statistics as a result of finite-sized parametric perturbations. We obtain the normalized sensitivity coefficients by taking the derivative of this functional representation with respect to the parameters. We apply this method in two stochastic dynamical systems exhibiting bimodal behavior, including a biologically relevant viral infection model.     

A computational modeling for the detection of diabetic retinopathy severity

Prolonged diabetes ultimately leads to Diabetic Retinopathy (DR) which is one of the leading causes of preventable blindness in the world. Through advanced image analysis techniques are used for abnormalities detection in retina that define and correlate the severity of DR. A thorough study is done in this area in recent past years and on the basis of these studies we have developed a computer based prediction model that is used to determine the severity of DR. To identify severity DR, we have analyzed the human eye image. We have extracted some important features from human eye image i.e. Blood Artery, Optical disc, Exudates. Based on these image and data we have designed an automated system for the determination of DR severity. This automated DR severity assessment methods can be used to predict the clinical case and conditions when young clinicians would agree or disagree with their more experienced fellow members. The algorithms described in this study may be used in clinical practice to validate or invalidate the diagnoses. Algorithms or method developed here may also be used for pooling diagnostic knowledge for serving mankind. Here we have described a computational based low cost retinal diagnostic approach which can aid an ophthalmologist to quickly diagnose the various stages of DR. This system can accept retinal images and can successfully detect any pathological condition associated with DR.