UC San Diego

Cerebrospinal fluid (CSF) is a water-like fluid that surrounds the brain and the spinal cord, together known as the central nervous system (CNS). CSF provides a physical cushion for the CNS and also plays an important physiological role by maintaining the electrolytic environment, transporting hormones, circulating nutrients and chemicals filtered from the blood, and removing waste products from cell metabolism of the CNS. It is generally accepted that the absence of CSF circulation may compromise the normal physiological functions of the CNS. CSF circulation also provides a mechanism for the delivery of potent analgesics and chemotherapy to the CNS, a drug delivery procedure often referred to as intrathecal drug delivery (ITDD). Despite significant efforts, most of these processes remain poorly understood.

This dissertation analyzes CSF flow and solute transport along the spinal canal by using asymptotic methods based on the disparity of length and time scales associated with this problem. In addition to the oscillatory flow induced by the cardiac and respiratory cycles, with zero time- averaged velocity at any location, it is found that small corrections associated with the convective acceleration and canal deformation lead to a nonzero steady-streaming velocity. This small steady velocity, together with Stokes drift caused by the non-uniform oscillatory flow, determines the slow time-averaged Lagrangian motion of the CSF, which is found to be responsible for the transport of solutes along the canal. A key outcome of the analysis is a time-averaged transport equation that describes solute dispersion in the long-time scale. The use of this simplified equation circumvents the need to compute concentration fluctuations resulting from the fast oscillatory motion in the short-time scale, drastically reducing the associated computational times. The accuracy and limitations of the time-averaged description are tested by comparison to the results of direct numerical simulations spanning hundreds of oscillation cycles, as needed to generate significant dispersion of the solute. The analysis is extended to study effects of buoyancy-induced motion, arising when the injected solute has a density that differs from that of the CSF. For the small density differences that characterize ITDD drugs, buoyancy is found to have a significant effect on the convective transport, leading to large changes in the resulting solute-dispersion patterns. Finally, the classical problem of oscillatory flow past a circular cylinder is extended to the case of a streamwise periodic array of cylinders, providing insight regarding the effects of spinal-canal micro-anatomical features, such as trabeculae, ligaments, and nerve roots, on the flow and transport in the spinal canal.