Section: Application Domains

Applicative axis 2: Growth, evolution and regeneration in populations and tissues


Luis Almeida, Pierre-Alexandre Bliman, Marie Doumic, Dirk Drasdo, Benoît Perthame, Diane Peurichard, Nastassia Pouradier Duteil, Philippe Robert

Project-team positioning

The applications in this category span very different subjects from amyloid diseases, dengue fever, wound healing, liver regeneration and toxicity, up to bacterial growth and development of organisms. As the applications, the methods span a wide range. Those concerning identification of models and parameters with regard to data have partially been outlined in axis 3. Focus in this axis is on the model contribution to the biologically and/or medically relevant insights and aspects.

Liver-related modeling is partially performed within the Inria team MIMESIS (Strasbourg) with the focus on real-time, patient-specific biomechanical liver models to guide surgery and surgeons. Internationally, spatial temporal liver related models are developed in Fraunhofer MEVIS (Bremen), by T. Ricken (University of Stuttgart), and P. Segers group (Leuven). Different from these, Mamba has a strong focus on spatial-temporal modeling on the histological scale, integration of molecular processes in each individual cell, and single-cell (agent) based models [32], [30], [143]. Works by Schliess  [139], [101] have been highlighted in editorials.

Mathematical modeling of protein aggregation is a relatively recent domain, only a few other groups have emerged yet; among them we can cite the Inria team Dracula, with whom we are in close contact, and e.g., the work by Jean-Michel Coron (Sorbonne Université) and Monique Chyba (Hawaii, USA) in control, and Suzanne Sindi (USA) for the modeling of the yeast prion. We have interactions with all these groups and organized a workshop in June 2017, gathering both the biophysics and applied mathematics communities.

Scientific achievements

Amyloid disease

Application to protein aggregation in amyloid diseases is a long-standing interest of Mamba, dating back to 2010  [85], and developed through the collaboration with Human Rezaei's team at Inra. More recently, with Wei-Feng Xue in Canterbury, we investigated the intrinsic variability among identical experiments of nucleation  [93], [100], Sarah Eugène's Ph.D subject (co-supervised by Philippe Robert)  [99].

In collaboration with Tom Banks first  [69], [70] and then Philippe Moireau, we developed quantitative comparisons between model and data. Through data assimilation and statistical methods  [63], we proposed new models and mechanisms.

Biological control of arboviroses

Sterile Insect Technique (SIT) [98] is a biological control method relying on massive releases of sterile male insects into the wild. The latter compete with wild males to mate with the females, and induce no offspring to the latter, thus reducing the next generation's population. This can result in a progressive reduction, or even disparition, of the target population.

A related technique is based on the infection by Wolbachia [104]. This symbiotic bacterium is maternally transmitted from infected females to their offspring, but induces cytoplasmic incompatibility [141], [80]: mating between infected males and uninfected females gives no offspring. Releases of Wolbachia infected males alone is thus comparable to classical SIT.

On the other hand, releasing both infected males and females in sufficient quantity may result in infection of the wild population. This gives rise to an interesting new control principle, as Wolbachia has been shown to severely reduce the insect vectorial ability to transmit dengue, zika or chikungunya, indirectly by lifespan and fertility reduction, and directly by reducing the ability of the viruses to proliferate within the organism [121].

We proposed new insights on the practical and theoretical issues raised by the implementation of the previous methods.

Wound healing 1: epithelial tissues

We studied cell motion in epithelial gap closure, a form of collective cell migration that is a very widespread phenomenon both during development and adult life - it is essential for both the formation and for the maintenance of epithelial layers. Due to their importance, in vivo wound healing and morphogenetic movements involving closure of holes in epithelia have been the object of many studies. In our works  (ravasio:hal-01245750, vedula:hal-01298859) we considered wound healing and epithelial gap closure in both in vivo (in particular drosophila pupa) and in vitro (MDCK cell and human keratinocytes). We found some similarities in the geometry dependence of the wound closure strategies between these two situations, indicating the existence of conserved mechanisms that should be widespread across living beings. We are concentrating on the study of actin cable formation.

Wound healing 2: adipose tissues

After injury, if regeneration can be observed in hydra, planaria and some vertebrates, regeneration is rare in mammals and particularly in humans. In this research axis, we investigated the mechanisms by which biological tissues recover after injury. We explored this question on adipose tissue, using the mathematical framework recently developed in [134]. Our assumption is that simple mechanical cues between the Extra-Cellular Matrix (ECM) and differentiated cells can explain adipose tissue morphogenesis and that regeneration requires after injury the same mechanisms. We validated this hypothesis by means of a two-dimensional Individual Based Model (IBM) of interacting adipocytes and ECM fiber elements [135]. The model successfully generated regeneration or scar formation as functions of few key parameters, and seemed to indicate that the fate of injury outcome could be mainly due to ECM rigidity.

Modeling of morphogen diffusion in Drosophila oogenesis

In collaboration with a team of developmental biologists of Rutgers University (Camden, New Jersey), we have built a model for the diffusion of the Gurken morphogen during Drosophila oogenesis, taking into account a wide variety of biological mechanisms such as diffusion of the morphogen, reactions of components of the EGFR signaling pathway, movement of the source of morphogen, shift of the overlying follicle cells and growth of the egg chamber. This model, together with a complete numerical code developed in Matlab, provides a tool to understand how each mechanism influences the signal distribution. The overall aim of the project is to use this tool to guide future experiments, and to understand what mechanisms contribute to the different distributions of signal among species.

Bacterial population growth

We exploited all the methods developed to estimate the division rate of a population (see axis 3) to address a seminal question of biology: is it a size-sensing or a timing mechanism which triggers bacterial growth? In  [138], we showed that a sizer model is robust and fits the data well. Several studies from other groups came at the same time, showing a renewed interest on a question dated back to Jacques Monod's PhD thesis (1941). Of special interest is the “adder” model, for which we are currently developing new estimation methods.

A quantitative high resolution computational mechanics cell model for growing and regenerating tissues

Mathematical models are increasingly designed to guide experiments in biology, biotechnology, as well as to assist in medical decision-making. They are in particular important to understand emergent collective cell behavior. For this purpose, the models, despite still abstractions of reality, need to be quantitative in all aspects relevant for the question of interest. During the regeneration of liver after drug-induced depletion of hepatocytes surviving dividing and migrating hepatocytes must squeeze through a blood vessel network to fill the emerged lesions. Here, the cells' response to mechanical stress might significantly impact on the regeneration process. We developed a 3D high-resolution cell-based model integrating information from measurements in order to obtain a refined quantitative understanding of the cell-biomechanical impact on the closure of drug-induced lesions in liver. Our model represents each cell individually, constructed as a physically scalable network of viscoelastic elements, capable of mimicking realistic cell deformation and supplying information at subcellular scales. The cells have the capability to migrate, grow and divide, and infer the nature of their mechanical elements and their parameters from comparisons with optical stretcher experiments. Due to triangulation of the cell surface, interactions of cells with arbitrarily shaped (triangulated) structures such as blood vessels can be captured naturally. Comparing our simulations with those of so-called center-based models, in which cells have a rigid shape and forces are exerted between cell centers, we find that the migration forces a cell needs to exert on its environment to close a tissue lesion, is much smaller than predicted by center-based models. This effect is expected to be even more present in chronic liver disease, where tissue stiffens and excess collagen narrows pores for cells to squeeze through [44].

Main collaborators: Stefan Höhme, Univ. Leipzig; Josef Käs, Univ. Leipzig.

Modeling the extracellular matrix in multicellular organization and liver regeneration:

An important step has been undertaken to integrate an explicit model of collagen networks in liver and other tissues. The mechanical model of collagen fibers uses linear and rotational springs to represent collagen fibers and collagen network taking into account the stretching and bending energy of the collagen network. The model has been validated by direct comparison to experiments where a force has been excerted on a single collagen fiber, as well as to shear experiments. In a next step, this collagen model has been incorporated into the previous lobule model to simulate spatio-temporal pattern of the ECM in the lobule. One key objective is a model of fibrosis development, whereby fibrotic streets form. So far, not coherent model exist but a number of hypotheses that will be implemented and tested versus data.

Main collaborators: Steven Dooley, Seddik Hammad, Univ. Mannheim; JG Hengstler, IfADo.

Models of flow in liver

Also for the liver, a model for bile salts transport has been developed. The current hypothesis is that bile salt excreted by hepatocytes into bile canaliculi, are transported within canaliculi by convection through the canal of hering to the bilary ducts. In close iterations with experiments and by image based modeling runing simulations directly in reconstructed 3D volume data sets, we test different alternative mechanisms of bile transport.

The blood flow model of the individual liver lobule, the smallest anatomical and functional repetitive unit of liver has been embedded in an electrical analogue model for the whole model hemodynamics to compute the impact of architectural changes at the lobule level as they occur after partial hepatectomy on the whole body hemodynamics. At the lobule level, the impact of capillary diameters on the flow have been studied under consideration of the hematocrit value (the volume fraction of red blood cells).

Collaborators: Chloé Aubert, UPMC, I. Vignon-Clementel, REO, Jan G. Henstler and Natiket Vartak, IfADo, Eric Vibert, Hopital Paul Brousse, Villejuif

Liver development

The deformable cell model is being used to establish a model of bile duct formation. Bile ducts from at the portal veins as a consequence of an interaction of cholagiocytes, aligning the mesenchyme of the portal vein, and hepatoblasts surrounding the portal veins. Hepatoblasts are a pre-stage of hepatocytes. Current biological hypotheses speculate that bile ducts may either emerge from proliferation of the hepatoblast layer that is in contact to cholangiocytes, leading to formation of a lumen by buckling, by attraction of water a positions where cholangiocytes secret mucin, or by apical contraction of hepatoblasts within the layer in contact to the cholangiocytes. The simulations are performed with the deformable cell model.

Collaborators: Frederic Lemaigre, De Duve Institut, Brussels, Anne Dubart-Kupperschmitt, Hopital Paul Brousse.

Image processing, analysis and quantification of tissue microarchitecture

At the interface between experiment and modeling we pursue a number of projects on image analysis and quantification. Such information in the past often served to generate hypotheses of the mechanisms underlying image sequences in time, which then could be turned in a mathematical model to verify, which hypotheses are sufficient to explain the image data. Several image analysis projects focus on the liver. (1.) Bile microinfacts have been found to be initiated by rupture of the apical hepatocyte membrane leading to shunting from bile canaliculi to the blood capillaries. This is followed by massive increase of the immune cells as could be quantified by analysis of intravital micrographs. For every frame in the video, a binary mask that most likely resemble detected immune cells were obtained. The process started by applying suitable linear and non-linear filters to highlight structure of interest and remove noise. Morphological operations and blob analysis was finally utilized to locate and count the cells. With the help of an expert, the confusion matrix was finally established to assess the quality of the segmentation and the obtained results (Ghallab et. al., J. Hepat. 2018; https://aasldpubs.onlinelibrary.wiley.com/doi/full/10.1002/hep.30213. [14]) (2.) In a second project, the CYP – enzyme distribution is quantified after repetitive administration of CCl4. After single overdose of CCl4, the liver shows a peri-central liver lobule (smallest repetitive anatomical unit of liver) necrosis. This pattern changes in repetitive dosing and leads to chronic disease stages and sometimes eventually to either hepatocellular carcinoma [15] or acute-on-chronic liver failure (ACLF), a disease condition with often-lethal outcome. Data from whole-slide scans is analyzed to serve to develop a mathematical model of ACLF. (3.) A similar strategy is pursued for fibrosis formation through high fat diet both by image analysis of mouse and human data, aiming at a mathematical lobule model based on a deformable cell model. Here currently images are analyzed to quantify microarchitectural modifications as a consequence of Western Diet (a high fat diet generating a disease condition reminiscent of NAFLD in human. (4.) TiQuant-algorithms have been used to analyze micro-and macrovascular alterations in cirrhosis  [125] and (5.) tissue modifications after PHx  [82].

Main collaborators: Ahmed Ghallab, Jan G. Hengstler, IfADo; Ursula Klingmüller, DKFZ Heidelberg; Steven Dooley, Univ. Hospital Mannheim; Percy Knolle, Helmholz Inst. Munich, Joachim Bode, Univ. Hospital Düsseldorf, Christian Trautwein, Univ. Hosp. Aachen; P. Seegers (Ghent University); Eric Vibert (Hopital Paul Brousse).

Relating imaging on microscopic scales with imaging on macroscopic scales: From Diffusion-Weighted MRI Calibrated With Histological Data: an Example From Lung Cancer

Diffusion-weighted magnetic resonance imaging (DWI) is a key non-invasive imaging technique for cancer diagnosis and tumor treatment assessment, reflecting Brownian movement of water molecules in tissues. Since densely packed cells restrict molecule mobility, tumor tissues produce usually higher signal (less attenuated signal) on isotropic maps compared with normal tissues. However, no general quantitative relation between DWI data and the cell density has been established. In order to link low-resolution clinical cross-sectional data with high resolution histological information, we developed an image processing and analysis chain, which was used to study the correlation between the diffusion coefficient (D value) estimated from DWI and tumor cellularity from serial histological slides of a resected non-small cell lung cancer tumor. Color deconvolution followed by cell nuclei segmentation was performed on digitized histological images to determine local and cell-type specific 2d (two-dimensional) densities. From these, the 3d cell density was inferred by a model-based sampling technique, which is necessary for the calculation of local and global 3d tumor cell count. Next, DWI sequence information was overlaid with high resolution CT data and the resected histology using prominent anatomical hallmarks for co-registration of histology tissue blocks and non-invasive imaging modalities’ data. The integration of cell numbers information and DWI data derived from different tumor areas revealed a clear negative correlation between cell density and D value. Importantly, spatial tumor cell density can be calculated based on DWI data. In summary, our results demonstrate that tumor cell count and heterogeneity can be predicted from DWI data, which may open new opportunities for personalized diagnosis and therapy optimization  [145]. The work of that paper has been further advanced to adapt the procedures for clinical use (in preparation).


  • Biological control of arboviroses: Nicolas Vauchelet (Université Paris 13); Grégoire Nadin (LJLL, Sorbonne Université); Yannick Privat (Université de Strasbourg); D. Villela, C. Struchiner (Fiocruz, Brazil); Jorge Zubelli (IMPA, Brazil); Alain Rapaport (INRA-Montpellier), Y. Dumont (CIRAD-Montpellier); Ch. Schaerer, P. Pérez-Estigarribia (UNA, Paraguay), O. Vasilieva (Universidad del Valle, Cali, Colombia), D. Cardona-Salgado (Universidad Autónoma de Occidente, Cali, Colombia).

  • Protein aggregation in amyloid diseases: Human Rezaei's team at Inra Jouy-en-Josas (France) and W-F Xue's team in at university of Kent (Great Britain); Tom Banks at the North Carolina State University (USA) and Philippe Moireau (M3DISIM)

  • Bacterial growth and division: Lydia Robert, Sorbonne Université (France)

  • Liver research & toxicology: JG. Hengstler group (IfADo, Dortmund, Germany); R. Gebhardt (Univ. Leipzig); U. Klingmueller (DKFZ, Heidelberg); Irène Vignon-Clementel (Inria, REO)

  • Wound healing: Patrizia Bagnerini (Genova, Numerical methods), Benoît Ladoux (Institut Jacques Monod et Mechanobiology Institute Singapore, Biophysics) and Antonio Jacinto (CEDOC, Lisbon, Biology and Medicine). (Adipose tissue regeneration) team of L. Casteilla (StromaLab, Toulouse)

  • Diffusion of morphogen: Center for Computational and Integrative Biology, Rutgers University (Camden, New Jersey), joint work with Professor Nir Yakoby's Drosophila Laboratory

  • Linking micro and macro-image information: Oliver Sedlaczek, Univ. and DKFZ Heidelberg, Kai Breuhahn, Univ. Heidelberg.