Experimental and theoretical investigations of the dynamics of collective phenomena in blood II: Towards a physically more realistic model

本项目的目的是通过实验和计算机模拟研究外部施加的剪切流下的红细胞（RBC）的悬浮液，重点是在高浓度下的集体动力学和非线性响应。该项目是在题为“血液中集体现象动态的实验和理论研究一：理想化的囊泡/液滴模型”的同一倡议第一部分的基础上开展的。由于上一个项目的成就（参见），在下文的进展报告中），我们现在能够研究在剪切速率、细胞变形性和体积分数/血细胞比容（由细胞占据的通道体积的部分）方面的感兴趣的参数范围内的RBC的物理上更现实的（与液滴相比）模型。新开发的模型所获得的结果是非常有前途的，值得更详细的调查。特别是，以下公开问题应通过实验和计算机模拟来解决。·剪切诱导扩散率：即使是在一个相当低的体积分数为0.6%，我们的模拟表明，（流动介导的）红细胞之间的碰撞显着改变他们的个人动态。除了流动，红细胞似乎表现出扩散运动在足够大的时间，近似高斯分布的颗粒位移。当监测垂直于流动方向的位移时，这是最明显的。这里一个有趣的问题是，这种剪切诱导的扩散如何随施加的剪切速率而变化，以及这与有效粘度的剪切速率依赖性如何比较。此外，在足够高的血细胞比容下，悬浮液开始形成固体状特征，并且诸如动态屈服和剪切驱动的熔化的问题变得相关。在这种情况下，我们预计在一些典型的时间和长度尺度上会出现与高斯行为的强烈偏离。然后，研究这些长度和时间尺度如何取决于剪切速率和红细胞压积将是非常有趣的。·合作运动：与上述方面密切相关的一个问题涉及动态相关性的可能性。事实上，粒子位移的非高斯分布提供了粒子（这里是红细胞）动力学中存在相关性的暗示。有趣的是，调查是否以及在何种条件下存在动态相关的RBC簇。我们预计这些簇的寿命随着施加的剪切速率而降低，并且在较高的浓度/血细胞比容下增加。类似于上面提出的问题之间的关系剪切诱导扩散和粘度，这是非常有趣的研究是否管理的动态相关的集群的生命时间的物理定律相比，那些描述扩散和粘度。这个问题的答案是远远不是微不足道的，肯定需要一个彻底的研究这些集群的长度规模作为剪切速率和红细胞压积的函数：扩散超过一个距离的颗粒大小可能足以摧毁小集群。然而，在一个较大的规模上的粒子运动可能是必要的动力学相关性的衰变在一个集群，其中包含了大量的粒子。屈服应力：如前所述，在高浓度下，红细胞悬浮液可能会形成固体样特征。除了上面讨论的动态问题，这也可能表现在屈服应力（这里定义为维持流动所需的最小应力）的出现。有限屈服应力的存在可能具有严重的生物学后果，因为如果血管中的粘性应力福尔斯下降到屈服应力以下，它可能导致流动阻塞。正如一个简单的论证所示，如果血管半径低于某个值，这确实可能发生在狭窄的血管中。因此，研究屈服应力及其与红细胞压积和其他系统参数的关系是非常重要的。红细胞变形能力的影响：上述问题通常取决于红细胞的变形能力。例如，如果红细胞的变形性降低，则预期在较低的体积分数下感受到细胞-细胞碰撞的效果和所产生的有效扩散。类似地，随着细胞硬度的增加（例如通过镰状细胞贫血或其他广泛疾病如糖尿病或疟疾引起），人们预期屈服应力可以随着血细胞比容更快地增长，从而导致更高的流动阻塞概率。这里感兴趣的一个问题是剪切速率和变形能力/细胞刚度是否扮演定性独立的角色，或者单个无量纲参数，如剪切能与弹性变形能的比率，足以描述系统的行为在一定的参数范围内。

The aim of the present project is to study via experiments and computer simulations suspensions of red blood cells (RBCs) under externally imposed shear flow with a focus on collective dynamics and non-linear response at high concentrations. This project builds upon the part I of the same initiative entitled “Experimental and theoretical investigations of the dynamics of collective phenomena in blood I: Idealized vesicle/fluid droplet models”. Thanks to the achievements of the previous project (cf. progress report below), we are now able to investigate a physically more realistic –as compared to droplets– model of RBCs in the parameter range of interest in terms of shear rate, cell deformability and volume fraction/ hematocrit (the portion of the channel volume occupied by the cells). Results obtained with the newly developed model are very promising and deserve more elaborate investigations. In particular, the following open issues shall be addressed both experimentally and via computer simulations. • Shear-induced diffusivity: Even at a rather low volume fraction of ≈6%, our simulations show that (flow-mediated) collisions between red blood cells significantly alter their individual dynamics. In addition to the flow, RBCs seem to exhibit a diffusive motion at sufficiently large times with, approximately, a Gaussian distribution of particle displacements. This is best visible when monitoring displacements perpendicular to the flow direction. An interesting question here is how this shear-induced diffusion varies with imposed shear rate and how does this compare to the shear rate dependence of the effective viscosity. Furthermore, at a sufficiently high hematocrit, the suspension starts to develop a solid-like character and issues such as dynamic yielding and shear driven melting become relevant. In this case, we expect strong deviations from Gaussian behavior to develop at some typical time and length scales. It would then be very interesting to study how these length and time scales depend on shear rate and hematocrit. • Cooperative motion: An issue, closely related to the above aspect, concerns the possibility of dynamic correlations. Indeed, a non-Gaussian distribution of particle displacements provides a hint on the presence of correlations in the dynamics of particles (here red blood cells). It is interesting to investigate whether and under which conditions dynamically correlated clusters of RBCs exist. We expect the life time of these clusters to decrease with the imposed shear rate and to increase at higher concentration/hematocrit. Similar to the above raised question on the relation between shear-induced diffusion and viscosity, it is very interesting to study whether physical laws governing the life time of dynamically correlated clusters compare to those describing diffusion and viscosity. Answer to this question is far from being trivial and will certainly require a thorough study of the length scale of these clusters as a function of shear rate and hematocrit: Diffusion over a distance of a particle size may be sufficient to destroy small clusters. However, particle motion on a lager scale may be necessary for a decay of dynamic correlations within a cluster which contains a large number of particles. • Yield stress: As already mentioned, at high concentrations, suspensions of red blood cellsmay develop a solid-like character. In addition to the above discussed dynamic issues, thismay also manifest itself in the emergence of a yield stress (defined here as the minimumstress needed to maintain the flow). The presence of a finite yield stress may have severebiological consequences, since it may lead to a flow blockage if the viscous stress in theblood vessel falls below the yield stress. As can be shown by a simple argument, this may indeed occur in narrow vessels, if the vessel radius is below a certainvalue. Therefore, it is important to study the issue of yield stress and its dependence onhematocrit and other system parameters.• The effect of RBC-deformability: The above issues do in general depend on the deformability of red blood cells. For instance, the effect of cell-cell collision and the resulting effective diffusion is expected to be felt at a lower volume fraction if the deformability of red blood cells is reduced. Similarly, with increasing cell-stiffness (caused e.g. via sickle cell anemia or other widespread diseases such as diabetes mellitus or malaria) one expects that yield stress may grow faster with hematocrit and thus lead to a higher probability of flow blockage. A question of interest here is whether both shear rate and deformability/cell-stiffness play qualitatively independent roles, or a single dimensionless parameter such as the ratio of shear energy to the elastic deformation energy is sufficient to describe the system behavior in a certain parameter-range.