Mefti Nacim, Ganghoffer Jean François, Haussy Bernard
LEMTA-ENSEM, 2, Avenue de la Fôret de Haye, BP 160, 54054 Vandoeuvre Cedex, France.
Technol Health Care. 2006;14(4-5):349-58.
Cell adhesion plays an important role in biology: essentially with regard to immunizing defence and the transport of medicinal substances toward specific zones. The focus is here on the mechanical description of adhesion kinetics, in terms of the failure and creation of connections during the rolling phenomenon. Hence, we consider the case of a single cell, which is linked to a rigid substratum. A 2D model is established. We consider that the contact zone cell-wall is rectilinear and composed of vertical fibers and two horizontal rigid beams (complex cell membrane- fibers-vein wall). These connections are modeled by elastic springs having identical elastic properties (e.g stiffness), but different failure strengths. The cell is subjected to the flow of plasma, which can generate the rolling phenomenon; we accordingly consider two distinct zones, one associated with the failure of the old fibers and one with the creation of the new fibers (in the direction opposite to the flow). Several interactions are taken into account in this model: van der Waals (attractive) and electrostatic (repulsive) forces and the effects of fluid pressure, assimilated into a periodic point force applied to the interface zone. We also study the vibration induced failure in the contact zone without mechanical damping using the principle of virtual work and a failure criterion to establish the equation of motion and the time evolution of the failure (dynamical approach). Rupture of a fiber can occur if the stress applied to the fiber is above a certain limit. These limits are determinated with using a probabilistic approach by use of a spectral method to simulate a stochastic and Gaussian field. Modeling of the creation of new fibers is also achieved by the combination of a dynamical and probabilistic method and a kinematical criterion. On the basis of these elements, numerical simulations are developed, that elucidate the rupture and rolling phenomena.
主要涉及免疫防御以及药物向特定区域的运输。这里重点关注粘附动力学的力学描述，涉及滚动现象中连接的破坏和形成。因此，我们考虑单个细胞与刚性基质相连的情况。建立了一个二维模型。我们认为细胞壁的接触区域是直线形的，由垂直纤维和两根水平刚性梁组成（复合细胞膜 - 纤维 - 静脉壁）。这些连接由具有相同弹性特性（如刚度）但不同破坏强度的弹性弹簧建模。细胞受到血浆流动的作用，这会产生滚动现象；因此我们考虑两个不同的区域，一个与旧纤维的破坏相关，另一个与新纤维的形成相关（沿与流动相反的方向）。该模型考虑了几种相互作用：范德华力（吸引力）和静电力（排斥力）以及流体压力的影响，流体压力被等效为施加在界面区域的周期性点力。我们还使用虚功原理和破坏准则研究了无机械阻尼时接触区域的振动诱导破坏，以建立运动方程和破坏的时间演化（动态方法）。如果施加在纤维上的应力超过某个极限，纤维就会发生断裂。这些极限通过使用谱方法模拟随机高斯场的概率方法来确定。新纤维形成的建模也通过动态和概率方法以及运动学准则的结合来实现。基于这些要素，开展了数值模拟，阐明了断裂和滚动现象。
