Identifiability and sensitivity analysis of a Photodynamic Therapy model

International audiencePhotodynamic therapy (PDT) is an alternative treatment for cancer that involves the administration of a photosensitizing agent, which is activated by light at a specific wavelength. The photo-toxic phase of this therapy can be described by a dynamic model composed of six nonlinear differential equations. The model parameters can be used to compare photosensitizing agents in their capability to produce cytotoxic species. The practical issue is their estimation from in vivo experimental data. In this paper, a new approach is proposed to analyze the photophysical parameters estimability through a local practical identifiability study combined with a global sensitivity analysis. Results show that only three parameters can reasonably be estimated in a given and realistic experimental framework. Input design (light signal) and model reduction are currently in progress

Limits of variance-based sensitivity analysis for non- identifiability testing in high dimensional dynamic models

International audienceIn systems biology, a common approach to model biological processes is to use large systems of nonlinear differential equations. The associated parameter estimation problem then requires a prior handling of the global identifiability question in a realistic experimental framework. The lack of a method able to solve this issue has indirectly encouraged the use of global sensitivity analysis to select the subset of parameters to estimate. Nevertheless, the links between these two global analyses are not yet fully explored. The present work reveals new bridges between sensitivity analyses and global non-identifiability, through the use of functions derived from the Sobol' high dimensional representation of the model output. We particularly specify limits of variance-based sensitivity tools to completely conclude on global non-identifiability of parameters in a given experimental context

A system-engineering model to analyze gap-FRAP in multicellular models.

International audienceIntroduction. Developed in the 70s, the Fluorescence Recovery After Photobleaching (FRAP) technique is based on the progressive increase of fluorescence intensity in a photobleaching area obtained after an illumination with a LASER beam. This enhancement corresponds to the gradual arrival (through gap junctions) of intact fluorescent molecules towards the targeted zone. This widely used method is principally dedicated to study fluorescent constituents mobility in cellular membranes and gap junctional intercellular communication (GJIC) at microscopic scale. Purpose. The final addressed question is to assess the relevance to use GJIC characteristics to discriminate different cancer cell lines. With this aim in view, we have proposed a model-based approach in which some parameters could be potentially used as decision statistics. As proof of concept, we have tested the applicability of a compartmental model to describe differences between gap-FRAP responses of two human head and neck carcinoma cell lines (FaDu and KB). . Methods and Materials. Cx43, a protein of the connexin family responsible for GJIC, distribution and intercellular communication of FaDu and KB cells were performed in monolayer cultured cells and spheroids. Six experiments were performed for each case and data were collected through an imaging system composed of a macroscope combined to a fluorescence excitation source (Hg) and a CCD camera. The pixel intensities were measured in three concentric Regions of Interest (ROI) every 15 seconds for 15 minutes on each images. The measured values were assumed to be proportional to the mean amount of photons emitted in each ROI. After normalization with respect to the fluorescence intensity values before photobleaching, the data were plotted across the time. Modeling method. To study gap-Fluorescence Recovery After Photobleaching (gap-FRAP), the perturbation-relaxation kinetic equation is commonly used but is sometimes unable to describe some parts of the fluorescence response. A new behavioral model is proposed to study fluorescence recovery. The latter is based on a three-compartment representation (one compartment for each ROI) and the rates between each compartment represent the flow coefficients of the different gap junctions. This model provides a set of differential equations for which the associated continuous-time second-order transfer function was identified using the Simplified Refined Instrumental Variable in Continuous-time (SRIVC) algorithm. The algorithm returns three estimated parameters (a static gain and two time constants) and their standard deviations. Results. Two model parameters have allowed us to discriminate gap junctions functionalities. Indeed, parameters of KB cells, which is positive for Cx43 expression, are significantly superior to those of FaDu cells in culture 2-D and 3-D. No significant differences were observed for KB cells data independently of culture type confirming negligible contribution from underlying layers during fluorescence restitution in Z plan by confocal microscopy. Conclusions. Our study exemplifies the contributions brought by dynamic models of biological phenomena to diagnostic applications in biomedicine

System identification of the intrabrain tumoral uptake of multifunctional nanoparticles

International audienceRecent developments on multifunctional nano-systems have opened new perspectives for tumor control by proposing new nano-actuators and nano-sensors in in vivo anti-cancer treatments. But the delivery control of these nano-agents into the cancer cells is one of the major factors that directly affect the efficiency of nanotherapies. In this study, we show that system identification methods (CONTSID Matlab toolbox), generally used in control engineering, can bring efficient solutions to help biologists to estimate crucial parameters of the nanoparticles pharmacokinetics from experimental data. The in vivo results presented herein clearly emphasize the relevance of these data-driven modeling approaches associated with magnetic resonance imaging

Identification of Pharmacokinetics Models in the presence of Timing Noise

International audienceThe problem addressed in this paper deals with the parameter estimation of in vitro uptake kinetics of drugs into living cells in presence of timing noise. Effects of the timing noise on the bias and variance of the output error are explicitly determined. A bounded-error parameter estimation approach is proposed as a suited solution to handle this problem. Application results are presented which emphasize the effectiveness of the methodology in such an experimental framework

Parameter estimation of pharmacokinetics models in the presence of timing noise

International audienceWe consider a model of pharmacokinetics which takes into account the presence of timing nois

Vascular-Targeted Photodynamic Therapy (VTP)

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Real-time control of photobleaching trajectory during photodynamic therapy

International audienceIntroduction: obstacles and challenges to the clinical use of the photodynamic therapy (PDT) are numerous: large inter-individual variability, heterogeneity of therapeutic predictability, lack of in vivo monitoring concerning the reactive oxygen species (ROS) production, etc. All of these factors affect in their ways the therapeutic response of the treatment and can lead to a wild uncertainty on its efficiency. Objective: to deal with these variability sources, we have designed and developed an innovative technology able to adapt in realtime the width of light impulses during the photodynamic therapy. The first objective is to accurately control the photobleaching trajectory of the photosensitizer during the treatment with a subsequent goal to improve the efficacy and reproducibility of this therapy.Methods: in this approach, the physician a priori defines the expected trajectory to be tracked by the photosensitizer photobleaching during the treatment. The photobleaching state of the PS is regularly measured during the treatment session and is used to change in real-time the illumination signal. This adaptive scheme of the photodynamic therapy has been implemented, tested and validated during in vitro tests.Results: these tests show that controlling the photobleaching trajectory is possible, confirming the technical feasibility of such an approach to deal with inter-individual variabilities in PDT. These results open new perspectives since the illumination signal can be different from a patient to another according to his individual response.Conclusions: this study has proven its interest by showing promising results in an in vitro context, which has to be confirmed by the current in vivo experiments. However, it is fair to say that in a near future, the proposed solution could lead, in fine, to an optimized and personalized PDT

Phenomenological modeling of tumor diameter growth based on a mixed effects model

International audienceOver the last few years, taking advantage of the linear growth of diameter kinetics, tumor diameter-based rather than tumor volume-based models have been developed for the phenomenological modeling of tumor growth. In this study, we propose a new tumor diameter growth function composed of two linear parts and one exponential term to characterize early, late and steady-state treatment effects. Model parameters consist of growth rates, growth delays and time constants and are meaningful for biologists. Biological experiments provide in vivo longitudinal data. The latter are analyzed using a mixed effects model based on the new diameter growth function, to take into account inter-mouse variability and treatment factors. The relevance of the tumor growth mixed model is firstly assessed by analyzing the effects of three therapeutic strategies for cancer treatment (radiotherapy, concomitant radiochemotherapy and photodynamic therapy) administered on mice. Then, effects of the radiochemotherapy treatment duration are estimated within the mixed model. The results highlight the model suitability for analyzing therapeutic efficiency, comparing treatment responses and optimizing, when used in combination with optimal experiment design, anti-cancer treatment modalities