Computational modelling of cellular blood flow in complex vascular networks.
Microcirculatory disorders are associated with some of the most prevailing medical conditions in modern society, e.g., cancer and cardiovascular disease (CVD). Early detection and effective treatment of these diseases require an in-depth knowledge of the changes in the haemodynamic environment preceding fatal deteriorating conditions. However, such a knowledge is difficult to obtain merely relying on experiments, on account of the overwhelming complexity of blood flow at the microscale that is sometimes beyond the capability of contemporary experimental techniques. Alternatively, computational modelling provides a potent tool to uncover the missing details of haemodynamics at the microcirculation level. Thanks to the advent of information era which fosters growingly powerful computing facilities and architectures, the progress that has been made on blood flow modelling over recent years is unprecedented. Notwithstanding, exhaustive modelling of blood flow at the microcirculation level incorporating all blood constituents remains daunting. Existing studies employing a range of models are only possible via invoking simplifications justified under different assumptions. However, one important assumption for many modelling studies, namely that blood in the microcirculation can be approximated by a homogeneous non-Newtonian fluid, has been increasingly challenged. The reason is that the microscopic behaviour of red blood cells (RBCs) as the primary blood constituent is found to non-trivially modify key rheological properties of blood flow at the microscale, such as its effective viscosity, cell-free layer (CFL) and wall shear stress (WSS). To ultimately facilitate the translation of scientific investigations to real medical applications, the cellular character of microcirculatory blood flow has to be properly considered by computational models. Bearing the above challenges in mind, the present PhD embarks on a venture to research the complex behaviour of cellular blood flow under microcirculatory conditions, capitalising on a recently developed computational tool equipped with high-level parallelisation. This computational thesis sets out to answer several important questions, ranging from the rich dynamics of individual RBCs to the collective phenomena of RBC suspensions in either microvascular networks or microfluidic mimicries. The current three-dimensional (3D) computational model is based on the lattice Boltzmann method (LBM) coupled with the immersed boundary method (IBM) for high-level resolution of discrete RBCs, which are modelled as Lagrangian membranes using the finite-element method (FEM). In the thesis, an concise introduction of the computational model is given in Chapter 4. Before applied to research projects, the model has been systematically validated against existing numerical or experimental observations. Three benchmark tests of close relevance to the scope of microscale blood flow are selected for demonstration and discussion in Chapter 5. The main body of this thesis (Chapters 6–8) reports several novel aspects of blood flow at the microscale including, but not limited to, the non-inertial focusing of RBCs under low Reynolds number as revealed in Chapter 6, the excessive haemodilution induced by CFL asymmetry as revealed in Chapter 7, and the strong association between RBC perfusion and vascular patterning as revealed in Chapter 8. Some confusion about or misinterpretation of well-known effects in the community has also been clarified, such as the spatial scaling of hydrodynamic lift in non-circular channels, the development length of CFL in typical microfluidic flows, and the existence of high- /low-flow attraction near bifurcating geometries. Quantitative or qualitative agreement has been achieved through elaborated comparison with supplementary experiments from my collaborators or with established empirical models in the literature. Starting from blood flow in a single microchannel, Chapter 6 highlights an exceedingly large CFL development length even under low inertia, which is greater than 28 times channel hydraulic diameter (Dh) in simulation and 46Dh in experiment (experimental data from my collaborator in Glasgow, UK). This finding suggests that microfluidic designs need to be longer if their purpose is to investigate localised microscopic behaviour of a dilute suspension without interference from entrance effects or upstream disturbances. On a network level where the RBCs flow through bifurcating microchannels arranged biomimetically following Murray’s law, Chapter 7 identifies ideal partitioning of RBCs at symmetric bifurcations (agreeing with predictions of a classic empirical model derived from in vivo data), but biased partitioning when significant CFL asymmetry arises in inter-bifurcation branches. Furthermore, the breakdown of CFL symmetry leads to severe haemo-dilution/concentration in the bifurcating network. In Chapter 8, the computational framework is applied to model blood flow in realistic microvasculatures of developmental mouse retina and demonstrates an unreported highly heterogeneous distribution of RBCs in the post-sprouting vascular network. Remarkably, a strong association between vessel regression and RBC depletion is uncovered, driven by the effect of plasma skimming. The association is further confirmed by in vivo observation of simultaneous vascular remodelling alongside blood perfusion using a developmental zebrafish model (experimental data from my collaborator in Berlin, Germany). In summary, this thesis provides insights for the design of improved microfluidic devices and the conception of haemodynamic mechanisms governing the onset and progression of microcirculatory disorders. Additionally, the computational model successfully applied to various biological or biomimetic scenarios in this thesis justifies itself as a feasible and reliable tool for practical simulation of microcirculatory blood flows and may seek wider applications of its own accord.