Multiscale modelling of cells adhesion
In many biological processes it is critical to predict accurately the cellular transport and deposition close to vessel walls in presence of a complex, unsteady flow. This is important to control drug delivery but also for the understanding of several cardiovascular diseases. Atherosclerosis, for example, is a degenerative disease of the arterial wall that is thought to be initiated due to inflammation of the arterial endothelium, promoting the over-deposition of white blood cells (WBCs). This anomalous WBC accumulation is site-specific and can lead to initial stage lesions or, on a long-term timescale, atherosclerotic plaques. To study these problems, we have developed a multiscale transport model for leukocytes [1] and coupled it to an endothelial cell receptor binding model in order to link the transport and surface biology [2]. The large scale separation existing between biological components (order of microns) and typical vessel size in the macrovascular network (order of cm) prevents the use of detailed mesoscopic particle methods. The multiscale Lagrangian Particle Tracking (LPT) strategy proposed in [1] is based on a continuum viewpoint coupled with a discrete representation of the leukocytes as “test particles” rather than real cells. Leukocyte dynamics is handled based on a continuum advection-diffusion equation for a concentration field in the bulk domain, whereas discrete cells interacting with hydrodynamic and biological adhesion-mediated forces are considered in proximity of the vessel walls. The reduced number of tracked test particles which can be achieved by distributing them within a thin near-wall region only (Fig. 4 top) allow considerable speed-up of simulation for these systems, preserving the accuracy of the deposition profiles [2].
Fig. 1: Top: demonstration of the tracer–particle coupling method – SPH particles are depicted as spheres coloured with velocity magnitudes. Tracers are shown with black dots and are located uniquely in the near-wall region. Bottom: comparison of cell adhesion data between simulation and the experimental data at different Reynolds numbers. Contours of cell adhesion on walls are presented.
References
[1] Gholami, B., A. Comerford, and M. Ellero (2014). ”A SPH multiscale particle model of the near-wall dynamics of leukocites in flow”. Int. J. Num. Meth. Biomed. Engng. 30, 83–102.
[2] Gholami, B., A. Comerford, and M. Ellero (2015). SPH simulations of WBC adhesion to the endothelium: the role of haemodynamics and endothelial binding kinetics. Biomechanics and Modeling in Mechanobiology 14(6), 1317–1333.