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Figure 3.8 – Left image:Mean square displacement measured in the RBC-rich layer. Thet0 corresponds to 300 ms from the beginning of the simulations. The linear fitting on the MSD gives a slope that is traditionally linked to 2D, where D is the diffusion coefficient of platelets.

Right image:Average distance of platelets from the walls, showing that platelets move towards the walls.

3.3.3 Platelet Transport for Larger Geometries

Most studies are bounded by domains of few micrometers and low hematocrit due to the high computational cost. Nevertheless, interesting phenomena can amplify as sizes increase [103]. Given our HPC-capable framework, we are interested on quantifying the diffusivity of platelets as the channel height varies. Here, a flow field with constant shear rate 100s−1 and 35% hematocrit is considered. The wall-bounded direction takes three different sizes H={50, 100, 500} µm, while the other periodic directions remain at 50µm(see table 3.1). The dimensionless numbers that describe the dynamics of the problem are the capsule Reynolds numberRec apsul e=γ˙r


ν with ˙γthe shear rate,rthe characteristic length of the capsule, and the capillary numberC a=BSkal akµγr˙ withµthe dynamic viscosity of blood plasma andBSkal ak the membrane shear modulus (see Appendix B and [73]). Figure 3.8 shows the mean square displacement in the RBC-RL, and the average platelet distance from the walls, qualitatively validating experimental findings on platelet transport and deposition [29]. The diffusion coefficients for all the different experiments are about two to three orders of magnitude higher than the Brownian diffusivity [140, 162], while the increasing diffusivity with the problem size (see slopes in Figure 3.8) is an indication of platelet anomalous diffusion. For a thorough analysis on platelet anomalous diffusion, the reader could consult our follow-up research project [74] and chapter 5. Figure 3.9 summarises some of the simulations conducted for the varying channel case study.

3.4 Conclusions

In this chapter, we provided a computational framework for digital blood, freely available under Palabos library (for more see chapter 6). The full resolution of the particulate nature of

blood is a challenging venture, especially when it is compiled into a framework that is based on generality, modularity, performance without compromising robustness and accuracy. The individual numerical techniques used for the simulation of blood constituents (LBM for the fluid and FEM for the solid phase) are characterised by their high fidelity for capturing physical phenomena, and their coupling has shown to sufficiently resolve the complex interaction between the blood cells.

This kind of computational tool complements the toolset for a digital lab. More precisely, the present project complements another research activity based on a coarse-grained approxima-tion of blood using stochastic methods and random walks (see chapter 5). The fully resolved models, apart from providing in-depth investigations on various case studies, are used to fine-tune the coarse-grained models, e.g. providing diffusion coefficients of various particles, thus constituting a critical component in this integrative approach towards digital blood/lab.

Figure 3.9 –Shear flow generated by our computational framework for fully resolved blood flow simulations. The left image shows two different viewpoints of the 503µm3domain at 35% hematocrit. The right image depicts a domain 50x100x50µm3at 35 % hematocrit.

3.4. Conclusions


This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 823712 (CompBioMed2 project).


We acknowledge support from the PASC project 2017-2020, Virtual Physiological Blood: an HPC framework for blood flow simulations in vasculature and in medical devices.

4 Spherization of red blood cells and platelet margina-tion in COPD patients

Red blood cells (RBCs) in pathological situations undergo biochemical and conformational changes leading to alterations in rheology involved in cardiovascular events. RBCs shape in volunteers (n=21), stable (n=42) and exacerbated (n=31) COPD (Chronic Obstructive Pul-monary Disease) patients was analysed. Effects of the RBCs spherization on platelet transport (displacements in the flow field due to their interaction with RBCs) were studied,in vitro, and by numerical simulations (based on the tools presented in chapters 2 & 3).

RBC spherization was observed in COPD patients compared to volunteers ( p<0.0001).In vitro experiments, at shear rate of 100 s-1, the RBCs treated with neuraminidase inducing greater sphericity, mainly affect platelet aggregates (p = 0.004) without change in the aggregates size.

At 400 s-1neuraminidase treatment changes both the size of the aggregates (p = 0.009) and the number of platelet aggregates (p = 0.008). Numerical simulations indicated that RBCs spherization induces an increase of the platelet Mean Square Displacement (MSD), which is traditionally linked to platelet diffusion coefficient.

Conclusion:RBCs of COPD patients are more spherical than healthy volunteers. Experimen-tally, the RBCs spherization induces an increased platelet transport to the wall. Additional studies are needed to understand the link between the RBCs effect on platelet transport and the increased cardiovascular events observed in COPD patients.

4.1 Introduction

Chronic obstructive pulmonary disease (COPD) is an important cause of mortality worldwide, associated with the development of cardiovascular events [33, 45]. Donaldsonet al. [38]

reported that the risk of acute cardiovascular events increases during an exacerbation of COPD (ECOPD). According to their study, the risk of myocardial infarction 1 to 5 days after an ECOPD episode would increase 2.3-fold (95% confidence interval (CI): 1.1 to 4.7; probability value

This chapter is based on the article entitled “Spherization of red blood cells and platelet margination in COPD patients.” by Boudjeltia, Kotsalos et al. [21].

(p) = 0.03) and the risk of stroke 1 to 49 days after ECOPD would increase 1.3-fold (95% CI:

1.0 to 1.06; p=0.05). Another study showed that for ECOPD patients who die within 24h of hospitalisation, the death would be mostly due to a cardiac failure or thromboembolism [161].

Chronic inflammation is considered as a determinant factor of multimorbidities in COPD pa-tients. Indeed, for example, extensive crosstalk exists between inflammation and coagulation, which is linked to the development of cardiovascular diseases (CVD) [6]. Platelets, monocytes and their interaction play a pivotal role in chronic inflammation. Activated platelets secrete numerous substances such as chemokines, cytokines and molecules involved in haemosta-sis. Platelet degranulation leads to an increased expression of P-selectin on platelet surface membrane, whereas a conformational change in the integrinαIIβ3 results in increasing fib-rinogen binding. Finally, fibfib-rinogen binding results in platelet aggregation, clot formation and adhesion of platelets to the endothelial cell surface.

Moreover, various works demonstrated significant interactions between red blood cells (RBCs) and platelets in the bloodstream. These interactions lead, among others, to the phenomenon of platelet margination: in the blood flow, platelets globally migrate towards the wall of the blood vessel. Therefore, the distribution of platelet concentration is not uniform in the vessel:

platelet concentration is higher near the walls than in the centre [86, 29]. This imbalance is interpreted from a teleological point of view as being a need for platelets at the vascular wall in case of injury, in order to efficiently limit bleeding. However, an abnormal increase in this margination process may also modify platelet–vascular wall interactions, leading to uncontrolled platelet aggregation and dysfunctional endothelial responses.

Furthermore, in pathological situations, RBCs may undergo biochemical and conformational changes, altering blood rheology [23]. Spherization of RBCs has been demonstrated in sepsis and in other pathologies inducing chronic or acute systemic inflammation [113].

In COPD patients, some reports of constitutional changes in the composition of membrane lipids in RBCs exist but, to the best of our knowledge, no systematic study of the form of the RBCs and its consequences has been performed.

In the present work/chapter, we first propose an analysis of the shape of RBCs in stable and exacerbated COPD patients, compared with healthy volunteers. Secondly, we analyse the effect of the spherization of red blood cells on platelet margination experimentally, bothin vitroandin silico.

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