Computational methods for investigating cell motility with applications to neutrophil cell migration

Cell motility is closely linked to many important physiological and pathological events such as the immune response, wound healing, tissue differentiation, embryogenesis, in ammation, tumour invasion and metastasis. Understanding the ability of cells to alter their shape, deform and migrate is of vital importance in many biological studies. The rapid development in microscopy and imaging techniques has generated a huge amount of discrete data on migrating cells in vivo and in vitro. A key challenge is the use of discrete experimental observations to develop novel methods and algorithms that track cells and construct continuous trajectories of their motion as well as characterising key geometric quantities associated with cell migration. Therefore, in this work using robust numerical tools we focus on proposing and implementing mathematical methodologies for cell movement and apply them to model neutrophil cell migration. We derive and implement a computational framework that encompasses modelling of cell motility and cell tracking based on phase field and optimal control theory. The cell membrane is represented by an evolving curve and approximated by a diffuse interface; while the motion of the cell is driven by a force balance acting normal on the cell membrane. This approach allows us to characterise the locus of the centroid cell-surface position. In addition, we describe a surface partial differential equation framework that can be coupled with the phase-field framework, thereby offering a wholistic approach for modelling biochemical processes and biomechanics properties associated with cell migration.