Click on a project to learn more.


Modeling the effect of electroporation-based therapies

Inria Bordeaux-Sud-Ouest, team MONC (C. Poignard) - University of Santa Barbara (USCB), USA (F. Gibou).

Funded by Inria@SiliconValley

  • Back to top
  • Abstract

    Existing cancer treatments, such as radiotherapy and cryotherapy, can be restricted by the risk of dramatic damages on the nearby blood vessels and vital organs. A new alternative, called Electroporation-based therapy (EPT), aims to kill the tumors with short electric pulses, whose side effects are moderate. While the use of this treatment is currently restricted to (sub)cutaneous cancers, the team NUM4SEP, a collaboration between MONC (Inria Bordeaux-Sud-Ouest, France) and the UCSB (University of Santa Barbara, USA), respectively expert in mathematical cancer modelling and in high-performance computing, aims to develop a cost-effective simulation tool of the effect of EPT on tumors to broaden the scope of this new technique. The aim of the project is to develop a mathematical electroporation model and to calibrate the numerical simulations with experimental data provided by the IPBS (France). The model will subsequently help surgeons at the Jean-Verdier hospital (Bondy, France) to a-priori evaluate and optimise the action of EPT on targeted tumors.







    Main achievements

    From cell to tissue electroporation models: an homogenization approach

    Abstract submitted to the World Congress of electroporation 2019

    Electroporation-based therapies (EPT) consist in applying short electric pulses to tumour cells in order to permeabilize their membranes, thus allowing introduction of DNA or drugs into the cytoplasm (reversible electroporation) or leading to cell death by apoptosis (irreversible electroporation). This non-thermal treatment enables to reach deeply-located tumours without damaging surrounding organs or blood vessels. In addition, the limited side effects of electroporation allow treatment of patients that would be too weak to receive usual therapies such as chemotherapy or radiofrequence. On the other hand, due to the deep location of the tumour, real-time observation of the electric-field effect cannot be performed by the surgeons. Providing mathematical models and numerical tools able to indicate whether the electrode settings made by the clinicians led to reversible or irreversible electroporation is therefore necessary to optimize the use of this promising treatment. Over the last decades, studies of in vivo and in vitro data have led to a good understanding of the effect of electroporation at the microscopic scale. However, the use of electroporation-based therapies for clinical applications is still limited due to the lack of knowledge concerning the electroporation of tissues. In this work, the well-understood static and linear model of cell electroporation is extended to a multicellular model by means of a homogenization approach, inspired by the work of Deville [1] and Collin and Imperiale [2] for cardiac electrophysiology. As a first step, circular cells that are periodically spread into the extracellular medium are considered. We show that the conductivity of the tissue and the solution of the bidomain macroscopic model, obtained from an asymptotic development of the cellular and extracellular potentials, only depend on the leading-order homogeneous potential and on the geometry of cells. Cost-effective simulations of cells subjected to an electric field can therefore be obtained in the homogenized macroscopic domain. In addition, a direct relationship between the homogenized transmembrane potential and the electric field applied by the electrodes is derived, thus providing new information to clinicians about electric-pulse settings required to permeabilize tumour-cell membranes. Finally, convergence of the homogenized potentials is verified with a finite-element method. Future objectives include verification of the homogenized conductivity against the nonlinear model tested at UCSB (Santa Barbara, USA) on 40000 cells, as well as validation against experimental data provided by the IPBS (Toulouse, France). Once validated, we hope that the homogenized model will fill the gap between the cell-electroporation and tissue-electroporation knowledge, therefore broadening the scope of clinical applications of electroporation-based therapies.

    [1] M. Deville, Mathematical modeling of enhanced drug delivery by mean of electroporation or enzymatic tratment, Thèse à l’Université de Bordeaux et l’Université de Tor Vergata, 2017.
    [2] A. Collin and S. Imperiale, Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, In press., 2018.

    Main collaborators

    Clair Poignard - Team MONC (Inria Bordeaux Sud-Ouest, France)
    Frédéric Gibou - Team CASL (UCSB, Santa Barbara, USA)
    Marie-Pierre Rols - IPBS (Toulous, France)


    The SURFs'UP project

    University of Leeds, UK (O. Bokhove and M. Kelmanson);
    Maritime Research Institute Netherlands, NL (T. Bunnik and G. Kapseenberg).

    Funded by Marie Sklodowska Curie Actions

  • Back to top

  • Variational water-wave models and pyramidal freak waves

    A little-known fact is that, every week, two ships weighing over 100 tonnes sink in oceans, sometimes with tragic consequences. This alarming observation suggests that maritime structures may be struck by stronger waves than those they were designed to withstand. These are the legendary rogue (or freak) waves, i.e., suddenly appearing huge waves that have traumatised mariners for centuries and currently remain an unavoidable threat to ships, and to their crews and passengers. Thus motivated, an EU-funded collaboration between the Department of Applied Mathematics (Leeds University) and the Maritime Research Institute Netherlands (MARIN) supported this project, in which the ultimate goal, of importance to the international maritime sector, is to develop reliable damage-prediction tools, leading to beneficial impact in terms of both safety and costs. To understand the behaviour of rogue waves, cost-effective water-wave models are derived in both deep and shallow water. Novel mathematical and numerical strategies are introduced to capture the dynamic air-water interface and to ensure conservation of important properties. Specifically, advanced variational Galerkin finite-element methods are used to provide stable simulations of potential-flow water waves in a basin with wavemakers and seabed topography, which allows reliable simulations of rogue waves in a target area. For optimised computational speed, wave absorption is considered with a beach on which waves break and dissipate energy. Robust integrators are therefore introduced to couple the potential-flow model to shallow-water wave dynamics at the beach. Experimental validation of the numerical tank is conducted at Delft University of Technology to ensure accuracy of the simulations from the wavemaker to the beach. The numerical tank is designed for subsequent use by MARIN to investigate the damage caused by rogue waves on structures in order to update maritime design practice and to ensure safety of ships, therefore leading to a competitive commercial advantage across Europe.

    Short presentation


    Related Publications

    2018. Gidel, F. Variational water-wave models and pyramidal freak waves, PhD thesis, University of Leeds.

    2017. Gidel, F., Bokhove, O., and Kelmanson, M. Driven nonlinear potential flow with wave breaking at shallow-water beaches, Proceedings of the ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 1.

    2017. Gidel, F., Bokhove, O., and Kalogirou, A.: Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection, Nonlin. Processes Geophys., 24, 43-60, doi:10.5194/npg-24-43-2017

    In progress

    Gidel, F., Bokhove, O., and Kelmanson, M.: Variational and numerical water-wave and surf-zone hydrodynamics, Water Waves.

    Gidel, F., Kelmanson, M., and Bokhove, O.: Dynamic interactions between driven potential-flow water waves and shallow-water breaking waves on a sloping beach: numerical strategy and experimental validation, Journal of Fluids Mechanics.

    Gidel, F., Bokhove, O., and Kelmanson, M.: Variational and numerical modelling strategies for cost-effective simulations of driven free-surface waves,Wave Motion.


    Modelling rogue waves in shallow water

    Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection

    In this work, we model extreme waves occurring due to the intersection of two solitons. Studies from Miles (1977) and Kodama et al. (2009-2011) indeed showed that when a soliton collides with a wall, a three-shocks reflection pattern occurs, consisting in the incident wave, the reflected wave, and a Mach stem wave (cf. Figure 2). For a given range of incident angles, this stem wave grows linearly in amplitude and length, reaching up to four times the amplitude of the incident wave. If the wall is modelled by the deck of a boat, an obliquely incident wave can impact the deck and thus propagate along it with a growing amplitude, leading in the end to a phenomenum called green water (cf. Figure 1). The wall can also be virtual when two solitary waves interact with same amplitudes and opposite angles of incidence. In that case, the resulting wave can be considered as a freak wave since its amplitude is at least twice higher than those of the incident solitons. These two phenomena are a real threat for offshore structures such as ships, platforms and wind turbines. Modelling these extreme waves thus enables to predict loads and stresses applied on the structures in order to limit damage. A variational approach is used to derive the Benney-Luke equations, which are solved with the Finite Element Methode using Firedrake. The numerical results for the amplification of the stem wave are compared to theory using an asymptotically-exact solution and the corresponding interaction parameter.


    Find more in:
    2017. Gidel, F., Bokhove, O., and Kalogirou, A.: Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection, Nonlin. Processes Geophys., 24, 43-60, doi:10.5194/npg-24-43-2017




    Modelling rogue waves in deep water

    Variational and numerical modelling strategies for cost-effective simulations of driven free-surface waves

    We model nonlinear potential-flow waves in a deep-water domain with seabed topography. Waves are generated by a piston wavemaker on the left-hand side of the basin and reflected on a vertical wall on the right-hand side of the basin. Spatial discretisation strategies are used to deal with moving boundaries at the wavemaker and at the nonlinear free surface, as well as to update the vertical structure of the potential velocity. The obtained numerical simulations are compared to experimental measurements conducted in the wave tank of the Maritime Research Institute Netherlands (MARIN) in the case of a focussed wave.



    Find more in: 2018. Gidel, F. Variational water-wave models and pyramidal freak waves, PhD thesis, University of Leeds.



    Numerical tank: coupling deep- and shallow-water models

    Dynamic interactions between driven potential-flow water waves and shallow-water breaking waves on a sloping beach: numerical strategy

    With the goal of improving the cost-effectiveness of maritime-industry modelling of wave interactions, a "numerical wavetank" is presented herein whose distinctive feature is its novel ability to couple both deep-water potential-flow and shallow-water models to controllable, prespecified wavemaker dynamics and beach topography. The coupling is obtained via a variational-principle approach (discretised as finite elements and finite volumes) that guarantees important conservation properties and numerical stability; it also reveals that the correct location and nature of the coupling follow from the elimination of deep-water disturbances caused by spurious wave reflection from the beach. The model presented here is the first fully nonlinear model to couple deep- and shallow-water equations. Resulting simulations of wave generation, wave propagation and wave absorption by wave breaking are presented and analysed, and a discussion is presented on the efficacy of the novel approach.

    Find more in:
    2017. Gidel, F., Bokhove, O., and Kelmanson, M.: Driven nonlinear potential flow with wave breaking at shallow-water beaches. Proceedings of the ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 1.





    Numerical tank: experimental validation

    Validation of the novel simulations is conducted through measurements gleaned from purpose-built wave-tank experiments in marine-engineering laboratories at the Delft University of Technology. Both regular and irregular wave forms are considered, each being generated by a wave-maker at one end of a laboratory wave channel and dissipated via wave breaking on a 1:10-sloping beach at the other end. Numerical and experimental results are demonstrated to be in impressive (quantitative and qualitative) agreement, particularly those relating to minimal (long-wave) reflection at the beach, with numerical dissipation occurring in only shallow waters and, most dominantly, in the hydraulic bores. Comparison between simulations and experiments show that our new numerical coupling method is remarkably robust and accurate, and effective in damping the (shorter) incoming waves via wavebreaking at the beach.

    Find more in:
    2018. Gidel, F. Variational water-wave models and pyramidal freak waves, PhD thesis, University of Leeds.


    Master thesis

    Dräger, Germany.

  • Back to top

  • Real-time estimation of lung mechanics during breath under ventilation support

    Objective: Implementation of the Extended Kalman Filter to estimate Lung Mechanics continuously for a patient under ventilation support. Validation of the models against real data.

    Description: Despite remarkable progress in the field of respiratory care in the last years, bad or too slow recovery of the patient still occurs because of inadequate settings of the ventilation support. As a first step in improving the patient recovery, I derived continuous estimation of the respiratory capacity of a patient under ventilation support, based on a mechanistic model of the lung mechanics. Obtained by analogy with electrical circuit laws, the continuous estimation of the lung characteristics was improved by the implementation of an extended Kalman filter in which real-time clinical data were incorporated.

    Key words : Processing and signal analysis, modelling, (extended) Kalman filter, Lung mechanics, electrical engineering.

    Programming : Python.





    Bachelor thesis

    Université de Lausanne, Switzerland (D. Roubinet, P. Pehme and B. Parker).

  • Back to top

  • Modeling of heat conduction in fractured rocks

    Objective: Modelling of heat conduction in fractured rocks to determine their properties (conductivity, thermal diffusivity, porosity, dimension and location of the fractures...) and predict the outcome of pollution in these rocks.

    Description: Fractured rocks are an ideal hide for pollutants, that accumulate in the fractures over years. One method to localize the fractures in view of extracting the pollutants, consists in heating a borehole in the matrix and analyze heat diffusion; due to the different properties in water and rock, a change in heat diffusion indicates a change of medium. With this in mind, my objective was to derive an analytical solution of heat diffusion in a two-composite medium (e.g. water/rock) to facilitate the analysis of field measurements. This solution was built from the thermal and physical properties of the two media (namely, their conductivity and diffusivity) and was able to capture the continous change in heat-diffusion velocity across the two-media interface.

    Key words : Semi-analytical modelling, heat conduction, fractured rocks, fluid dynamics.

    Programming : Matlab.

    Publication : 2016. L.G. Moscoso Lembcke, D. Roubinet, F. Gidel, J. Irving, P. Pehme, and B.L. Parker. Analytical analysis of borehole experiments for the estimation of subsurface thermal properties, Advances in Water Resources, Vol. 91, Pages 88–103.


    ONERA

    Automatic sectorization of airspace

  • Back to top


  • Diadolab

    3D modelling of the tongue and its position for the speech-therapist software Diadolab

  • Back to top