Traction forces exerted by cells on soft elastic substrates are important for characterizing the types of mechanisms used for cell migration. Classical tools for the determination of traction forces ...include the knowledge of the displacement field thanks to fluorescent beads embedded into the substrate. Then, from the discrete beads displacements, an inverse problem is solved to obtain the stress field. Two currently used methods in the literature are the well-known Fourier Transform Traction Cytometry (FTTC) method and the adjoint method (AM), which are compared here. A real case is presented where the displacement field is known from cancer cell migration study. The two methods allow the recovery of the traction stresses and their results are compared. Similar results are seen as long as an adequate projection technique is used (zero force imposed outside the cell). It is found that the AM allows a finer resolution of the traction forces, in particular at the cell edge. This is a strong incentive to use this method for the investigation of cancer cell migration on soft substrates.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
We illustrate a three-dimensional mathematical model for the prediction of biological processes that typically occur in a sea region with minor water exchange. The model accounts for particle ...transport due to water motion, turbulent diffusion and reaction processes and we use a fractional-step approach for discretizing the related different terms.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Over the last twenty years major advancements have taken place in the design of medical devices and personalized therapies. They have paralleled the impressive evolution of three-dimensional, non ...invasive, medical imaging techniques and have been continuously fuelled by increasing computing power and the emergence of novel and sophisticated software tools. This paper aims to showcase a number of major contributions to the advancements of modeling of surgical and interventional procedures and to the design of life support systems. The selected examples will span from pediatric cardiac surgery procedures to valve and ventricle repair techniques, from stent design and endovascular procedures to life support systems and innovative ventilation techniques.
This paper deals with the Traction Force Microscopy (TFM) problem. It consists in obtaining stresses by solving an inverse problem in an elastic medium, from known experimentally measured ...displacements. In this article, the application is the determination of the stresses exerted by a living cell at the surface of an elastic gel. We propose an abstract framework which formulates this inverse problem as a constrained minimization one. The mathematical constraints express the biomechanical conditions that the stress field must satisfy. From this framework, two methods currently used can be derived, the adjoint method (AM) and the Fourier Transform Traction Cytometry (FTTC) method. An improvement of the FTTC method is also derived using this framework. The numerical results are compared and show the advantage of the AM, in particular its ability to capture details more accurately.
Cet article est consacré au problème de la Microscopie à Force de Traction (TFM). Ce problème consiste à déterminer les contraintes exercées par une cellule lors de sa migration sur un substrat élastique à partir d’une mesure expérimentale des déplacements induits dans ce substrat. Mathématiquement, il s’agit de résoudre un problème inverse pour lequel nous proposons une formulation abstraite de type optimisation sous contraintes. Les contraintes mathématiques expriment les constraintes biomécaniques que doit satisfaire le champ de contraintes exercé par la cellule. Ce cadre abstrait permet de retrouver deux des méthodes de résolution utilisées en pratique, à savoir la méthode adjointe (AM) et la méthode de Cytométrie de Traction par Transformée de Fourier (FTTC). Il permet aussi d’ameliorer la méthode FTTC. Les résultats numériques obtenus sont ensuite comparés et démontrent l’avantage de la méthode adjointe, en particulier par sa capacité à capturer des détails avec une meilleure précision.
Numerical simulation of fluid flow for a variety of practical applications is a major activity of the Computational Mechanics Group of CRS4 (Center for Advanced Studies, Research and Development). ...CRS4 develops computer simulation techniques to solve problems in applied science and engineering. The Computational Mechanics Group's work includes codes for CFD applications on parallel computers. The paper describes a selection of their projects, including: aerodynamic flow, coastal circulation and oil recovery processes.
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