Modeling of therapeutic dialysis of cerebrospinal fluid by epidural cooling in spinal cord injuries

Paraplegias of traumatic origin may be classified as primary or secondary. Secondary traumatic paraplegia (STP) is believed to result from an autodestructive process. Different authors have published results supporting or contradicting the therapeutic effects of durotomy alone or associated with exposed spinal cord and perfusion with a saline solution at normal or cold temperatures. It appears that although decompression and open dialysis might be beneficial, the surgical trauma over the injured region is detrimental. A method of local epidural spinal cord cooling has been developed and successfully used to treat STP. With this method, no surgical injury or damage is imposed on the dura, cerebrospinal fluid (CSF), or spinal cord. Furthermore, several of the beneficial effects attributed to hypothermia in the traumatized area are evident, including reduction of metabolic demands, edema, swelling, vasospasm, and blood pressure. Aware of the benefits that dialysis may have in STP, as well as of the encouraging results obtainable with local epidural spinal cord cooling, we hypothesized that this method of hypothermia may in some way trigger CSF dialysis. Based on this hypothesis, a model was developed approximating the behavior of the CSF in the situation where a cold source is applied to the dura. Using dimensionless analysis techniques, we predict that CSF under the cooled region of the dura undergoes convective motion, even in adverse situations where the spinal cord has swollen. Under steady-state conditions, the moving fluid forms several Bénard cells directly under the cold source. The size of these Bénard cells was estimated. The range of probe temperatures at which convective flow is generated was considered, as well as the relative benefits of hypothermia versus flow. Results of more rigorous analysis are discussed.