Movies of erythrocyte deformation in plasma flow. This work is the result of my collaboration with Philippe Dantan and has been performed with COMSOL Multiphysics 3.2b and 3.3. The numerical simulations comes from a time-dependant coupling : ALE equations (Winslow model), Navier-Stokes equations and structural mechanics model of red blood cells membrane (Navier equations for non zero thickness membrane or shell deformation for "zero" thickness membrane). Each movie is in MPEG format.
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| Two dimensional red blood cell moving in a plasma flow (Stokes). Erythrocyte membranes are modelised with a thick elastic membrane. Inside structure is filled with fluid and is reinforced with links between front and rear of the red blood cell avoiding large folds. |
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| Three dimensional red blood cell which membrane is modelised as a thick elastic medium and which interior is a Stokes fluid. Its movement and deformation are due to the action of the flow onto the erythrocyte membrane. |
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| Initial red blood cell, modelled as a vesicle with a 0.2 micrometer thick membrane and a "Stokes" cytosol. The membrane is considered as an hyperelastic material. |
| A Neo-Hookean material has been chosen for membrane behavior. The red blood cell moves in a capillary which radius is decreasing. Plasma flows from right to left in the capillary. The camera follows the red blood cell. |
| The membrane has been modelled as an hyperelastic Yeoh material fitted for red blood cells behavior. The capillary geometry comes from measurements of rat capillaries. |
| Same simulation as the preceding one but with three red blood cells in the capillary. |
| Red blood cell in a bottle like geometry consisting in a large cylinder and a small cylinder. Flow concentration into the small cylinder implies a skewing of the erythrocyte. At the end of the second cylinder, the red blood cell deformation can be important, depending on the Young's modulus. The erythrocyte membrane has been modelised thanks to a shell model while inside is solved a Stokes driven fluid. Different values of Young's modulus have been tested : | |
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| movie 3 |
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| Red blood cell "crashing" onto an intersection. Wall interaction has been modelised with a potential force calculated with a distance function. |
| Red blood cell attached from one extremity and stretched from the other simulating optical tweezers action. |
| Red blood cell in Stokes flow attached from one extremity imitating optical tweezers action. |
The referential chosen is that of moving blood. Oxygen is diffusing from the alveoli into plasma crossing a membrane and from the plasma inside red blood cells crossing erythrocite membrane. Inside the red blood cell, a realistic chemical model of oxygen / hemoglobin exchange has been used along with diffusion of the different species inside red blood cells. This work has been performed with COMSOL Multiphysics 3.2b and 3.3.
| Diffusion of oxygen from alveoly into a capillary filled with red blood cells. It is assumed the capillary is large enough not to deform erythrocytes (this is a first approximation). The cells and plasma are moving into the capillary at a velocity of 2 mm/s (exercise regime), |
| Oxygen saturation in the case of deformed red blood cells (from preceding calculations) at mid-length of a pulmonary capillary one millimeter long. Two different capillary radii are shown : the capacity to capture oxygen depends on the geometry of both red blood cells and capillary. |