Mircea Dumitru

A Circadian Clock Transcription Model for the Personalization of Cancer Chronotherapy

Circadian timing of anticancer medications has improved treatment tolerability and efficacy several fold, yet with intersubject variability. Using three C57BL/6-based mouse strains of both sexes, we identified three chronotoxicity classes with distinct circadian toxicity patterns of irinotecan, a topoisomerase I inhibitor active against colorectal cancer. Liver and colon circadian 24-hour expression patterns of clock genes Rev-erbα and Bmal1 best discriminated these chronotoxicity classes, among 27 transcriptional 24-hour time series, according to sparse linear discriminant analysis. An 8-hour phase advance was found both for Rev-erbα and Bmal1 mRNA expressions and for irinotecan chronotoxicity in clock-altered Per2(m/m) mice. The application of a maximum-a-posteriori Bayesian inference method identified a linear model based on Rev-erbα and Bmal1 circadian expressions that accurately predicted for optimal irinotecan timing. The assessment of the Rev-erbα and Bmal1 regulatory transcription loop in the molecular clock could critically improve the tolerability of chemotherapy through a mathematical model-based determination of host-specific optimal timing.

Computed tomography reconstruction based on a hierarchical model and variational Bayesian method

In order to improve the quality of X-ray Computed Tomography (CT) reconstruction for Non Destructive Testing (NDT), we propose a hierarchical prior modeling with a Bayesian approach. In this paper we present a new hierarchical structure for the inverse problem of CT by using a multivariate Student-t prior which enforces sparsity and preserves edges. This model can be adapted to the piecewise continuous image reconstruction problems. We demonstrate the feasibility of this method by comparing with some other state of the art methods. In this paper, we show simulation results in 2D where the image is the middle slice of the Shepp-Logan object but the algorithms are adapted to the big data size problem, which is one of the principal difficulties in the 3D CT reconstruction problem.

Model selection in the sparsity context for inverse problems in Bayesian framework

The Bayesian approach is considered for inverse problems with a typical forward model accounting for errors and a priori sparse solutions. Solutions with sparse structure are enforced using heavy-tailed prior distributions. The particular case of such prior expressed via normal variance mixtures with conjugate laws for the mixing distribution is the main interest of this paper. Such a prior is considered in this paper, namely, the Student-t distribution. Iterative algorithms are derived via posterior mean estimation. The mixing distribution parameters appear in updating equations and are also used for the initialization. For the choice of mixing distribution parameters, three model selection strategies are considered: (i) parameters approximating the mixing distribution with Jeffrey law, i.e., keeping the mixing distribution well defined but as close as possible to the Jeffreys priors, (ii) based on the prior distribution form, fixing the parameters corresponding to the form inducing the most sparse solution and (iii) based on the sparsity mechanism, fixing the hyperparameters using the statistical measures of the mixing and prior distribution. For each strategy of model selection, the theoretical advantages and drawbacks are discussed and the corresponding simulations are reported for a 1D direct sparsity application in a biomedical context. We show that the third strategy seems to provide the best parameter selection strategy for this context.

Bayesian sparse solutions to linear inverse problems with non-stationary noise with Student-t priors

Bayesian approach has become a commonly used method for inverse problems arising in signal and image processing. One of the main advantages of the Bayesian approach is the possibility to propose unsupervised methods where the likelihood and prior model parameters can be estimated jointly with the main unknowns. In this paper, we propose to consider linear inverse problems in which the noise may be non-stationary and where we are looking for a sparse solution. To consider both of these requirements, we propose to use Student-t prior model both for the noise of the forward model and the unknown signal or image. The main interest of the Student-t prior model is its Infinite Gaussian Scale Mixture (IGSM) property. Using the resulted hierarchical prior models we obtain a joint posterior probability distribution of the unknowns of interest (input signal or image) and their associated hidden variables. To be able to propose practical methods, we use either a Joint Maximum A Posteriori (JMAP) estimator or an appropriate Variational Bayesian Approximation (VBA) technique to compute the Posterior Mean (PM) values. The proposed method is applied in many inverse problems such as deconvolution, image restoration and computed tomography. In this paper, we show only some results in signal deconvolution and in periodic components estimation of some biological signals related to circadian clock dynamics for cancer studies. Bayesian sparsity enforcing inference for linear inverse problems.Non-stationary noise modelled via Gaussian with unknown varying variances.A generalized Student-t prior model for enforcing sparsity.Application in sparse signal deconvolution.Application in periodic components estimation in biological time series.

Periodic components estimation in chronobiological time series via a Bayesian approach

In chronobiology a periodic components variation analysis for the signals expressing the biological rhythms is needed. Therefore precise estimation of the periodic components is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (non-stationary, short length and noisy). In this paper we propose a new method using inverse problem and Bayesian approach with sparsity enforcing prior. The considered prior law is the Student-t distribution, viewed as a marginal distribution of an Infinite Gaussian Scale Mixture (IGSM) defined via the inverse variances. For modelling the non stationarity of the observed signal and the noise we use a Gaussian model with unknown variances. To infer those variances as well as the variances of the periodic components we use conjugate priors. From the joint posterior law the unknowns are estimated via Posterior Mean (PM) using the Variational Bayesian Approximation (VBA). Finally, we validate the proposed method on synthetic data and present some preliminary results for real chronobiological data.