Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

A Framework for the Automation of Discrete-Event Simulation Experiments

Simulation is an important resource for researchers in diverse fields. However, many researchers have found flaws in the methodology of published simulation studies and have described the state of the simulation community as being in a crisis of credibility. This work describes the project of the Simulation Automation Framework for Experiments (SAFE), which addresses the issues that undermine credibility by automating the workflow in the execution of simulation studies. Automation reduces the number of opportunities for users to introduce error in the scientific process thereby improvingthe credibility of the final results. Automation also eases the job of simulation users and allows them to focus on the design of models and the analysis of results rather than on the complexities of the workflow.

Surveillance and simulation of bovine spongiform encephalopathy and scrapie in small ruminants in Switzerland

BACKGROUND: After bovine spongiform encephalopathy (BSE) emerged in European cattle livestock in 1986 a fundamental question was whether the agent established also in the small ruminants' population. In Switzerland transmissible spongiform encephalopathies (TSEs) in small ruminants have been monitored since 1990. While in the most recent TSE cases a BSE infection could be excluded, for historical cases techniques to discriminate scrapie from BSE had not been available at the time of diagnosis and thus their status remained unclear. We herein applied state-of-the-art techniques to retrospectively classify these animals and to re-analyze the affected flocks for secondary cases. These results were the basis for models, simulating the course of TSEs over a period of 70 years. The aim was to come to a statistically based overall assessment of the TSE situation in the domestic small ruminant population in Switzerland. RESULTS: In sum 16 TSE cases were identified in small ruminants in Switzerland since 1981, of which eight were atypical and six were classical scrapie. In two animals retrospective analysis did not allow any further classification due to the lack of appropriate tissue samples. We found no evidence for an infection with the BSE agent in the cases under investigation. In none of the affected flocks, secondary cases were identified. A Bayesian prevalence calculation resulted in most likely estimates of one case of BSE, five cases of classical scrapie and 21 cases of atypical scrapie per 100'000 small ruminants. According to our models none of the TSEs is considered to cause a broader epidemic in Switzerland. In a closed population, they are rather expected to fade out in the next decades or, in case of a sporadic origin, may remain at a very low level. CONCLUSIONS: In summary, these data indicate that despite a significant epidemic of BSE in cattle, there is no evidence that BSE established in the small ruminant population in Switzerland. Classical and atypical scrapie both occur at a very low level and are not expected to escalate into an epidemic. In this situation the extent of TSE surveillance in small ruminants requires reevaluation based on cost-benefit analysis.

Fitting ACE Structural Equation Models to Case-Control Family Data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). To this end, we describe a ACE model for binary family data and then introduce an approach to fitting the model to case-control family data. The structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. Our likelihood-based approach to fitting involves conditioning on the proband’s disease status, as well as setting prevalence equal to a pre-specified value that can be estimated from the data themselves if necessary. Simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly-made assumptions hold. These assumptions include: the usual assumptions for the classic ACE and liability-threshold models; assumptions about shared family environment for relative pairs; and assumptions about the case-control family sampling, including single ascertainment. When our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are illustrated with two examples and their validity for cases with practical sample sizes is demonstrated via a simulation study.

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study.

Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Additive Hazards Models with Latent Treatment Effectiveness Lag Time

In many clinical trials to evaluate treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical procedure or chemical compound would be in full effect. In this article, semiparametric regression models are proposed and studied to estimate the treatment effect accounting for such latent lag times. The new models take advantage of the invariance property of the additive hazards model in marginalizing over random effects, so parameters in the models are easy to be estimated and interpreted, while the flexibility without specifying baseline hazard function is kept. Monte Carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure. Data collected in the actual randomized clinical trial, which evaluates the effectiveness of biodegradable carmustine polymers for treatment of recurrent brain tumors, are analyzed.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Reduced Bayesian Hierarchical Models: Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants

Quantifying the health effects associated with simultaneous exposure to many air pollutants is now a research priority of the US EPA. Bayesian hierarchical models (BHM) have been extensively used in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for potential confounding of other pollutants and other time-varying factors. However, when the scientific goal is to estimate the impacts of many pollutants jointly, a straightforward application of BHM is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters, which often do not have an easy interpretation. In this paper we introduce a new BHM formulation, which we call "reduced BHM", aimed at analyzing clustered data sets in the presence of a large number of random effects that are not of primary scientific interest. At the first stage of the reduced BHM, we calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants). At the second stage, we specify a flexible random-effect distribution directly on the parameter of interest. The reduced BHM overcomes many of the challenges in the specification and implementation of full BHM in the context of a large number of nuisance parameters. In simulation studies we show that the reduced BHM performs comparably to the full BHM in many scenarios, and even performs better in some cases. Methods are applied to estimate location-specific and overall relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during the period 1999-2005.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Reynolds-stress turbulence model in the KIVA code for engine simulation

A Reynolds-Stress Turbulence Model has been incorporated with success into the KIVA code, a computational fluid dynamics hydrocode for three-dimensional simulation of fluid flow in engines. The newly implemented Reynolds-stress turbulence model greatly improves the robustness of KIVA, which in its original version has only eddy-viscosity turbulence models. Validation of the Reynolds-stress turbulence model is accomplished by conducting pipe-flow and channel-flow simulations, and comparing the computed results with experimental and direct numerical simulation data. Flows in engines of various geometry and operating conditions are calculated using the model, to study the complex flow fields as well as confirm the model’s validity. Results show that the Reynolds-stress turbulence model is able to resolve flow details such as swirl and recirculation bubbles. The model is proven to be an appropriate choice for engine simulations, with consistency and robustness, while requiring relatively low computational effort.

Time-domain models for power system stability and unbalance

It is an important and difficult challenge to protect modern interconnected power system from blackouts. Applying advanced power system protection techniques and increasing power system stability are ways to improve the reliability and security of power systems. Phasor-domain software packages such as Power System Simulator for Engineers (PSS/E) can be used to study large power systems but cannot be used for transient analysis. In order to observe both power system stability and transient behavior of the system during disturbances, modeling has to be done in the time-domain. This work focuses on modeling of power systems and various control systems in the Alternative Transients Program (ATP). ATP is a time-domain power system modeling software in which all the power system components can be modeled in detail. Models are implemented with attention to component representation and parameters. The synchronous machine model includes the saturation characteristics and control interface. Transient Analysis Control System is used to model the excitation control system, power system stabilizer and the turbine governor system of the synchronous machine. Several base cases of a single machine system are modeled and benchmarked against PSS/E. A two area system is modeled and inter-area and intra-area oscillations are observed. The two area system is reduced to a two machine system using reduced dynamic equivalencing. The original and the reduced systems are benchmarked against PSS/E. This work also includes the simulation of single-pole tripping using one of the base case models. Advantages of single-pole tripping and comparison of system behavior against three-pole tripping are studied. Results indicate that the built-in control system models in PSS/E can be effectively reproduced in ATP. The benchmarked models correctly simulate the power system dynamics. The successful implementation of a dynamically reduced system in ATP shows promise for studying a small sub-system of a large system without losing the dynamic behaviors. Other aspects such as relaying can be investigated using the benchmarked models. It is expected that this work will provide guidance in modeling different control systems for the synchronous machine and in representing dynamic equivalents of large power systems.