Optimal cell transport in straight channels and networks

Results are encouraging

Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example of blood is explored in detail, by adopting the commonly used modeling of red blood cells dynamics.

We highlight the complexity of optimization at the level of a network, due to the antagonist evolution of local volume fraction and optimal volume fraction with the channels diameter. In the case of the blood network, the most recent results on the size evolution of vessels along the circulatory network of healthy organs suggest that the red blood cell volume fraction (hematocrit) of healthy subjects is close to optimality, as far as transport only is concerned. However, the hematocrit value of patients suffering from diverse red blood cell pathologies may strongly deviate from optimality.

A positive result

2D and 3D numerical simulations provided information on the behavior of cell flow rate as a function of cell volume fraction in a straight channel. Based on a minimal model we highlight the cell-free layer as a key element to understand the variation of the transport capacity of channels with diameter. This leads to the conclusion that the transport capacity of a whole network depends on its precise architecture, since two antagonist effects enter into play when traversing channels from large to small ones: (i) when the diameter of a channel decreases, the cell volume fraction decreases; (ii) at the same time, the value of the optimal cell volume fraction increases.

For red blood cells, the cell flux is directly linked to the oxygen transport capacity. Interestingly, the values obtained for the optimal hematocrit for vessel sizes corresponding to macrocirculation and intermediate microcirculation (arterioles) are close enough to the corresponding physiologically admitted values. Our analysis on a network where the weight of the contribution of each vessel has been extracted from in vivo data shows that this range of vessels also determines the RBC flow rate, indicating that the physiological values for the hematocrit are close to a kind of optimum in that sense. Our analysis also indicates the locations where active regulation processes like vasodilation or vasoconstriction are more likely to influence oxygen delivery.

Strong alterations are reported if the reduced volume of RBCs is increased, as is known for elliptocytosis and spherocytosis diseases. Not only is the flow rate of RBCs reduced in this case compared to the flow of healthy RBCs at the same hematocrit but also the optimal hematocrit is observed to be significantly lower. The lower value of RBC flow rate within patients suffering these diseases implies a severe collapse of oxygen delivery, which could lead to an increased heart load in order to maintain appropriate perfusion levels. It is known that elliptocytosis and spherocytosis diseases are accompanied by a reduction of the RBC count, a consequence of the spleen filtering. Interestingly, our results show that this decrease of hematocrit probably improves oxygen delivery.

We put forward here the idea that a slightly stretchable encapsulating membrane (like polymerbased capsules) would lead to a significant enhancement of oxygen transport capacity. The information generated by this study may guide the development of new soft materials, such as blood substitutes, and advance the tuning process and optimization of oxygen carriers. This study can also be adopted for more general questions of suspensions transport.

https://hal.archives-ouvertes.fr/hal-01898243

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