This thesis aims at building high-delity models for the simulation of blood at both the microscopic and the macroscopic scales. Our work focuses on creating a digital replica of human blood through various tools of multi-scale/multi-physics nature, and on contributing novel pieces towards the realisation of a digital lab. We then use these tools for investigating cases that span from fundamental research to problems of clinical relevance.

Regarding the micrometre/microscopic scale, we propose a computational framework (called Palabos-npFEM) for the simulation of blood ow with fully resolved constituents, i.e. red blood cells (RBCs) and platelets (PLTs). Palabos-npFEM deploys a modular approach that consists of a lattice Boltzmann solver for the blood plasma, a novel nite element based solver (npFEM) for the deformable bodies (both trajectories and deformations), and an immersed boundary method for the uid-solid interaction. Palabos-npFEM provides, on top of a CPU-only version, the option to simulate the deformable bodies on GPUs, thus the code is tailored for the fastest supercomputers. The software is integrated in the open-source Palabos library, and it is available on the Git repository https://gitlab.com/unigespc/palabos. Furthermore, we prove that high delity FEM solvers (such as the npFEM solver) can be a viable solution for the simulation of large systems of deformable bodies in comparison to the more simplied mass-spring-systems. Performance-wise, Palabos-npFEM competes closely with other state-of-the-art libraries. Towards the validation/verication of our solver, we have performed an extensive comparison of single-RBC in silico experiments with their in vitro counterparts, while for multiple blood cells test cases, we have performed numerous simulations along specially designed in vitro experiments.

We later use the Palabos-npFEM framework along with in vitro experiments to study the eect of spherized RBCs on PLT transport. RBCs of patients with chronic obstructive pulmonary disease (COPD) are more spherical than healthy volunteers. Both the numerical and the in vitro experiments show an increase of platelet transport towards the blood vessel walls for the COPD patients. However, the in vitro study does not allow us to know if the observed eect is linked to the decrease in the electronegativity of RBCs or to an eect simply linked to the shape of RBCs. This is where the numerical counterpart kicks-in and proves that just the shape-change can explain the increased PLT transport. Therefore, this study shows the excellent complementarity between experimentations and numerical simulations to explore complex dynamic systems.

Inspired by the research of Chopard et al. 2017, we prove that the random part of PLT velocities is governed by a fat-tailed probability distribution, usually referred to as a Levy ight. While the transport of platelets in blood is commonly assumed to obey an advection-diusion equation (Brownian-like random walk), we show that this assumption is not valid, and instead of a Gaussian velocity probability distribution function (pdf), a power law velocity pdf with exponent   2 describes far better the motion of PLTs. This result comes from a careful statistical analysis of 64 direct numerical simulations (DNS) of blood using Palabos-npFEM. Following, we develop stochastic models (macroscopic view of blood) based on the power law velocity pdf (  1:5) and simulate a PLT function analyser (impact-R device), comparing and validating our new models with the in vitro counterpart (Chopard et al. 2017).

To summarise, focal point of this thesis has been the understanding of the underlying mechanisms of platelet transport. For this, we followed a bottom-up approach, i.e. started from fully resolved cellular blood ow simulations (microscopic scale) and moved towards calibrated stochastic models (macroscopic scale) based on the DNS. Our results help clarify platelet transport physics, leading to more accurate modelling and design of PLT function tests, like the impact-R device. Given the limited prognostic capacity of these tests (contradicting results and lack of consensus), we strongly believe that our newly-introduced stochastic models could lead in next generation PLT function tests with higher clinical relevance/readiness.