Development Of Transport Phenomena Mathematical Models For Linear And Concentric Microdialysis Probes With Diffusion Limited And Convection Enhanced Operational Features - Kho, Chun Min (2018)
Microdialysis is a well-known sampling technique in medical researches, most commonly used to measure the concentration of chemicals in the extracellular space of tissues. However, despite being a well-established technique, microdialysis often gives inconsistent amounts of chemicals collected from the sampling site (i.e. recovery). This would give rise to other complications, such as the requirement of pre-runs and calibrations. In order to resolve this issue, it is necessary to understand the mass transport limitations of microdialysis set-up, by scrutinizing how each operational and design parameters of the microdialysis set-up affect the recovery. One common approach is through mathematical modelling. Although there are already several mathematical modelling works on microdialysis, those works would focus only on providing accurate estimations of the recovery, while other features such as fluid flows are neglected. The main objective of this research work is to develop finite element mathematical models that could provide accurate simulations of concentration and fluid flow profiles for microdialysis. These models were constructed based on linear and concentric microdialysis probes. Modelling domain of these mathematical models would focus on the microdialysis probes, the membrane attached to the probes, and the probe surrounding area (PSA). The PSA for this research work is a quiescent medium filled with the analyte to be recovered, which is glucose. Mass transport properties in the models are represented by convection-diffusion equations, while fluid flows are represented by Navier-Stokes equations. It is shown that the developed mathematical models could produce simulated recoveries that are comparable to experimental recoveries. Regression analysis between the simulated recoveries and experimental recovery gives R-squared values of ≥ 98.5% for each model. Using these mathematical models, the advantages and drawbacks of altering the operational and design parameters for microdialysis set-up were scrutinized. For instance, microdialysis sampling of glucose under perfused solution flow rate of 1.0 μL min-1 using commercially available liner probe and concentric probe (10 mm membrane length, 30 kDa molecular weight cut-off) yield recovery of 30.98% and 36.67%, respectively. Reducing the perfused solution flow rate to 0.5 μL min-1 would increase the recovery to 55.77% and 60.72%, respectively. However, at the same time, the temporal resolution of the microdialysis samplings was also greatly increased. In addition, although microdialysis is traditionally defined as a diffusion-limited process, it is shown in this work that under combinations of high perfused solution flow rate in the probe, high membrane porosity, and large membrane pore diameter, the influence of convective flux on the recovery of microdialysis sampling would be significant. In this case, convection-enhanced diffusion equations are necessary to represent the mass transport phenomena across the membrane attached to microdialysis probes.