Slow-Fast Model and Therapy Optimization for Oncolytic Treatment of Tumors.

The present work studies models of oncolytic virotherapy without space variable in which virus replication occurs at a faster time scale than tumor growth. We address the questions of the modeling of virus injection in this slow-fast system and of the optimal timing for different treatment strategies. To this aim, we first derive the asymptotic of a three-species slow-fast model and obtain a two-species dynamical system, where the variables are tumor cells and infected tumor cells. We fully characterize the behavior of this system depending on the various biological parameters. In the second part, we address the modeling of virus injection and its expression in the two-species system, where the amount of virus does not appear explicitly. We prove that the injection can be described by an instantaneous jump in the phase plane, where a certain amount of tumors cells are transformed instantly into infected tumor cells. This description allows discussing qualitatively the timing of different injections in the frame of successive treatment strategies. This work is illustrated by numerical simulations. The timing and amount of injected virus may have counterintuitive optimal values; nevertheless, the understanding is clear from the phase space analysis.

Characterization of the physical properties of tumor-derived spheroids reveals critical insights for pre-clinical studies.

Three-dimensional spheroids are widely used as cancer models to study tumor cell proliferation and to evaluate new anticancer drugs. Growth-induced stress (i.e., stress that persists in tumors after external loads removal) influences tumor growth and resistance to treatment. However, it is not clear whether spheroids recapitulate the tumor physical properties. Here, we demonstrated experimentally and with the support of mathematical models that, like tumors, spheroids accumulate growth-induced stress. Moreover, we found that this stress is lower in spheroids made of 5,000 cancer cells and grown for 2 days than in spheroids made of 500 cancer cells and grown for 6 days. These two culture conditions associated with different growth-induced stress levels also had different effects on the spheroid shape (using light sheet microscopy) and surface topography and stiffness (using scanning electron microscopy and atomic force microscopy). Finally, the response to irinotecan was different in the two spheroid types. Taken together, our findings bring new insights into the relationship between the spheroid physical properties and their resistance to antitumor treatment that should be taken into account by the experimenters when assessing new therapeutic agents using in vitro 3D models or when comparing studies from different laboratories.

FitEllipsoid: a fast supervised ellipsoid segmentation plugin.

BACKGROUND: The segmentation of a 3D image is a task that can hardly be automatized in certain situations, notably when the contrast is low and/or the distance between elements is small. The existing supervised methods require a high amount of user input, e.g. delineating the domain in all planar sections. RESULTS: We present FitEllipsoid, a supervised segmentation code that allows fitting ellipsoids to 3D images with a minimal amount of interactions: the user clicks on a few points on the boundary of the object on 3 orthogonal views. The quantitative geometric results of the segmentation of ellipsoids can be exported as a csv file or as a binary image. The core of the code is based on an original computational approach to fit ellipsoids to point clouds in an affine invariant manner. The plugin is validated by segmenting a large number of 3D nuclei in tumor spheroids, allowing to analyze the distribution of their shapes. User experiments show that large collections of nuclei can be segmented with a high accuracy much faster than with more traditional 2D slice by slice delineation approaches. CONCLUSIONS: We designed a user-friendly software FitEllipsoid allowing to segment hundreds of ellipsoidal shapes in a supervised manner. It may be used directly to analyze biological samples, or to generate segmentation databases necessary to train learning algorithms. The algorithm is distributed as an open-source plugin to be used within the image analysis software Icy. We also provide a Matlab toolbox available with GitHub.

Viscoelastic modeling of the fusion of multicellular tumor spheroids in growth phase.

BACKGROUND: Since several decades, the experiments have highlighted the analogy of fusing cell aggregates with liquid droplets. The physical macroscopic models have been derived under incompressible assumptions. The aim of this paper is to provide a 3D model of growing spheroids, which is more relevant regarding embryo cell aggregates or tumor cell spheroids. METHODS: We extend the past approach to a compressible 3D framework in order to account for the tumor spheroid growth. We exhibit the crucial importance of the effective surface tension, and of the inner pressure of the spheroid to describe precisely the fusion. The experimental data were obtained on spheroids of colon carcinoma human cells (HCT116 cell line). After 3 or 6 days of culture, two identical spheroids were transferred in one well and their fusion was monitored by live videomicroscopy acquisition each 2 h during 72 h. From these images the neck radius and the diameter of the assembly of the fusing spheroids are extracted. RESULTS: The numerical model is fitted with the experiments. It is worth noting that the time evolution of both neck radius and spheroid diameter are quantitatively obtained. The interesting feature lies in the fact that such measurements characterise the macroscopic rheological properties of the tumor spheroids. CONCLUSIONS: The experimental determination of the kinetics of neck radius and overall diameter during spheroids fusion characterises the rheological properties of the spheroids. The consistency of the model is shown by fitting the model with two different experiments, enhancing the importance of both surface tension and cell proliferation. GENERAL SIGNIFICANCE: The paper sheds new light on the macroscopic rheological properties of tumor spheroids. It emphasizes the role of the surface tension and the inner pressure in the fusion of growing spheroid. Under geometrical assumptions, the model reduces to a 2-parameter differential equation fit with experimental measurements. The 3-D partial differential system makes it possible to study the fusion of spheroids in non-symmetrical or more general frameworks.

Experimental estimation of stored stress within spherical microtissues : What can and cannot be inferred from cutting experiments.

Biological tissues accumulate mechanical stress during their growth. The mere measurement of the stored stress is not an easy task. We address here the spherical case and our experiments consist in performing an incision of a spherical microtissue (tumor spheroid) grown in vitro. On the theoretical part we derive a compatibility condition on the stored stress in spherical symmetry, which imposes a relation between the circumferential and radial stored stress. The numerical implementation uses the hyperelastic model of Ciarlet and Geymonat. A parametric study is performed to assess the influence of each parameter on the shape of the domain after the incision. As a conclusion, the total radial stored stress can be confidently estimated from the measurement of the opening after incision. We validate the approach with experimental data.

Oxygen Partial Pressure Is a Rate-Limiting Parameter for Cell Proliferation in 3D Spheroids Grown in Physioxic Culture Condition.

The in situ oxygen partial pressure in normal and tumor tissues is in the range of a few percent. Therefore, when studying cell growth in 3D culture systems, it is essential to consider how the physiological oxygen concentration, rather than the one in the ambient air, influences the proliferation parameters. Here, we investigated the effect of reducing oxygen partial pressure from 21% to 5% on cell proliferation rate and regionalization in a 3D tumor spheroid model. We found that 5% oxygen concentration strongly inhibited spheroid growth, changed the proliferation gradient and reduced the 50% In Depth Proliferation index (IDP50), compared with culture at 21% oxygen. We then modeled the oxygen partial pressure profiles using the experimental data generated by culturing spheroids in physioxic and normoxic conditions. Although hypoxia occurred at similar depth in spheroids grown in the two conditions, oxygen partial pressure was a major rate-limiting factor with a critical effect on cell proliferation rate and regionalization only in spheroids grown in physioxic condition and not in spheroids grown at atmospheric normoxia. Our findings strengthen the need to consider conducting experiment in physioxic conditions (i.e., tissue normoxia) for proper understanding of cancer cell biology and the evaluation of anticancer drugs in 3D culture systems.

Structure Tensor Based Analysis of Cells and Nuclei Organization in Tissues.

Extracting geometrical information from large 2D or 3D biomedical images is important to better understand fundamental phenomena such as morphogenesis. We address the problem of automatically analyzing spatial organization of cells or nuclei in 2D or 3D images of tissues. This problem is challenging due to the usually low quality of microscopy images as well as their typically large sizes. The structure tensor is a simple and robust descriptor that was developed to analyze textures orientation. Contrarily to segmentation methods which rely on an object based modeling of images, the structure tensor considers the sample at a macroscopic scale, like a continuous medium. We show that this tool allows quantifying two important features of nuclei in tissues: their privileged orientation as well as the ratio between the length of their main axes. A quantitative evaluation of the method is provided for synthetic and real 2D and 3D images. As an application, we analyze the nuclei orientation and anisotropy on multicellular tumor spheroids cryosections. This analysis reveals that cells are elongated in a privileged direction that is parallel to the spheroid boundary. A MATLAB toolbox and an Icy plugin are available to use the proposed method.

An implicit sliding-motion preserving regularisation via bilateral filtering for deformable image registration.

Several biomedical applications require accurate image registration that can cope effectively with complex organ deformations. This paper addresses this problem by introducing a generic deformable registration algorithm with a new regularization scheme, which is performed through bilateral filtering of the deformation field. The proposed approach is primarily designed to handle smooth deformations both between and within body structures, and also more challenging deformation discontinuities exhibited by sliding organs. The conventional Gaussian smoothing of deformation fields is replaced by a bilateral filtering procedure, which compromises between the spatial smoothness and local intensity similarity kernels, and is further supported by a deformation field similarity kernel. Moreover, the presented framework does not require any explicit prior knowledge about the organ motion properties (e.g. segmentation) and therefore forms a fully automated registration technique. Validation was performed using synthetic phantom data and publicly available clinical 4D CT lung data sets. In both cases, the quantitative analysis shows improved accuracy when compared to conventional Gaussian smoothing. In addition, we provide experimental evidence that masking the lungs in order to avoid the problem of sliding motion during registration performs similarly in terms of the target registration error when compared to the proposed approach, however it requires accurate lung segmentation. Finally, quantification of the level and location of detected sliding motion yields visually plausible results by demonstrating noticeable sliding at the pleural cavity boundaries.

Variational algorithms to remove stationary noise: applications to microscopy imaging.

A framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called variational stationary noise remover. It can be interpreted both as a restoration method in a Bayesian framework and as a cartoon+texture decomposition method. In numerous denoising applications, the white noise assumption fails. For example, structured patterns such as stripes appear in the images. The model described here addresses these cases. Applications are presented with images acquired using different modalities: scanning electron microscope, FIB-nanotomography, and an emerging fluorescence microscopy technique called selective plane illumination microscopy.

Traffic instabilities in self-organized pedestrian crowds.

In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in opposite directions spontaneously segregate into lanes of uniform walking directions. This phenomenon is often referred to as a smart collective pattern, as it increases the traffic efficiency with no need of external control. However, the functional benefits of this emergent organization have never been experimentally measured, and the underlying behavioral mechanisms are poorly understood. In this work, we have studied this phenomenon under controlled laboratory conditions. We found that the traffic segregation exhibits structural instabilities characterized by the alternation of organized and disorganized states, where the lifetime of well-organized clusters of pedestrians follow a stretched exponential relaxation process. Further analysis show that the inter-pedestrian variability of comfortable walking speeds is a key variable at the origin of the observed traffic perturbations. We show that the collective benefit of the emerging pattern is maximized when all pedestrians walk at the average speed of the group. In practice, however, local interactions between slow- and fast-walking pedestrians trigger global breakdowns of organization, which reduce the collective and the individual payoff provided by the traffic segregation. This work is a step ahead toward the understanding of traffic self-organization in crowds, which turns out to be modulated by complex behavioral mechanisms that do not always maximize the group's benefits. The quantitative understanding of crowd behaviors opens the way for designing bottom-up management strategies bound to promote the emergence of efficient collective behaviors in crowds.

Live cell division dynamics monitoring in 3D large spheroid tumor models using light sheet microscopy.

BACKGROUND: Multicellular tumor spheroids are models of increasing interest for cancer and cell biology studies. They allow considering cellular interactions in exploring cell cycle and cell division mechanisms. However, 3D imaging of cell division in living spheroids is technically challenging and has never been reported. RESULTS: Here, we report a major breakthrough based on the engineering of multicellular tumor spheroids expressing an histone H2B fluorescent nuclear reporter protein, and specifically designed sample holders to monitor live cell division dynamics in 3D large spheroids using an home-made selective-plane illumination microscope. CONCLUSIONS: As illustrated using the antimitotic drug, paclitaxel, this technological advance paves the way for studies of the dynamics of cell divion processes in 3D and more generally for the investigation of tumor cell population biology in integrated system as the spheroid model.

Low dimensional optimization for in vivo real-time porcine liver motion estimation using ultrasound imaging.

This study presents a contribution to the tracking of a moving target during high-intensity focused ultrasound (HIFU) treatment. Indeed, HIFU has proved to be highly efficient in inducing homogeneous and reproducible tumor destruction by thermal coagulation necrosis. However, accurate targeting of human abdominal tumors is difficult to maintain due to the motion induced by breathing. An algorithm is presented to track a region of interest of fixed size in a sequence of images. This algorithm was evaluated on synthetic data and on in vivo sequences of ultrasound liver images acquired using 12 MHz ultrasound imaging probe at a rate of 16 frames/s. The algorithm presented here was derived from the non-linear constant brightness assumption. Since the motion was smooth it was possible to reduce the space of admissible displacements; hence the number of unknown parameters was small compared with the size of the data. The optimal displacement was estimated by a Gauss-Newton method, and the matrix required at each step was assembled by reading the data only once. This algorithm was applied to simulated data, where the true displacement was known and a precise evaluation was possible. The relative error was about 2%. The algorithm was also applied to a video sequence of sonograms acquired during in vivo experiments. These trials were conducted on porcine liver since its size and physiology are similar to humans. Movements were induced by breathing and heart-beating. Two particular frequencies representing breathing (0.26 Hz) and heart beat (1.14 Hz) were identified in the estimated displacement and were correlated with the monitored breathing (0.27 Hz) and electrocardiograms (1.28 Hz). In addition, a region of interest (ROI) modeling the focal zone of a HIFU transducer was tracked along time. Therefore this study provides a mean of determining the location of the targeted region in vivo during HIFU treatments. This can be applied to correct the location of the focal zone accordingly. This method can preferentially be applied to the liver or to any other moving organ.