Analytical Modelling of the V-COOL Device and In Vitro Preliminary Evaluation

A simplified, mono-compartmental model describing the thermal balance of brain cooling by means of the extracorporeal recirculation of CSF was considered. The balance involves the internal energy transferred to/from the brain tissue by blood flow, the heat produced by parenchymal brain metabolism, and the internal energy transfer induced by the extracorporeal circulation of CSF. Before initiating the treatment, the brain tissue may be considered at steady state, with a temperature constant in time. As the treatment starts, cool CSF is injected into the ventricular cavity, while warm CSF is withdrawn at an equal flow rate, thus generating a thermal unbalance aimed at reducing brain temperature. Under some reasonable simplifying assumptions (e.g., ideal heat exchange between the CSF and brain parenchyma, uniform specific heat c, and uniform density ρ), the following time course of brain temperature is yielded:

where T₀ is the pre-treatment temperature, T_∞ is the final settling temperature, and τ is the time constant of the process (99% settling time equals 5τ). These quantities, in turn, depend upon the treatment parameters as:

where subscripts b and CSF refer to blood and cerebrospinal fluid, respectively; Q are flow rates, T_i are inlet fluid temperatures, V_t is the total intracranial volume, and Φ is the heat produced by metabolism.

A simplified phantom model was developed for an in vitro preliminary feasibility evaluation of the experimental setting. The brain tissue was modelled as a spherical volume of water of 2 mL, surrounded by a transparent, heat-insulating polymethylmethacrylate (PMMA) capsule. Temperature within the sphere was measured by a thermocouple probe deepened into the fluid, replicating the simulated parenchymal temperature. Two holes in the PMMA wall allowed for water at 37 °C to be injected/withdrawn with a peristaltic pump, thus replicating blood perfusion at a fixed 2.2 mL/min flow. A separate hole in the wall allowed a dual-lumen V-COOL cannula tip to be deepened into the core fluid volume. Water at 15 °C was injected through the inflow lumen of this cannula with a syringe pump and, simultaneously, withdrawn at the same flow rate (0.5, 0.8, 1.0 mL/min) through the outflow lumen, thus representing the circulation of cool CSF.