Mathematical modelling of mass transport in linear, shunt and concentric microdialysis probes - Siti Kartini, Enche Ab Rahim
Microdialysis is a technique for both recovering and administering substances at a target site (which may be tissues, organs, etc.), using a small equipment termed as probe. There are many types of microdialysis probes such as the linear probe, the shunt probe and the concentric probe, and the probe choices are depended on the site of implantation, whether it is for the tissue (different type of tissue for different probe design) or in the quiescent medium. Although the probe needs to be physically inserted into the site, the microdialysis probe is relatively small and is minimally-invasive (i.e., causing minimal changes or injuries to the target site). This along with many other features of microdialysis (e.g., can be performed on almost every organ and tissue, can be used on living, awake and even moving patients, etc.) make this technique very popular. Nonetheless, poor recovery, doubts related to temporal resolution, and tedious preparations plus the need of pre-runs for calibration, limits the application of this technique. These constraints are generally attributed to mass transfer limitations. In this thesis, a mathematical framework incorporating convection and diffusion equations have been proposed to represent transport phenomena in microdialysis probes. This mathematical framework is then used to analyse the possible influence of various relevant parameters on glucose (i.e., analyte) recovery. In this work, it is defined that within the probe’s membrane and probe surrounding area (PSA), the transport process is solely driven by diffusion. The model parameters and operating conditions have been obtained from literature. In the first part, a mathematical framework was constructed to represent mass transport in two primitive microdialysis probes, namely the linear and shunt probes. Using the respective mathematical frameworks, glucose recoveries under various operating conditions were compared between the two probes, which were defined to operate under similar conditions. As there is no mathematical work that has been done to evaluate these both probes, it would be interesting to see how these two microdialysis probes may perform under similar operating conditions. It is clearly seen that the frameworks were sensitive enough to show concentration changes when parameters were varied. These results were comparable to what was discussed in literature. Comparing the two probe’s performance under similar conditions, the shunt probe displayed higher glucose recoveries, which reflect better performance. The mathematical approach from the more primitive linear and shunt microdialysis probe frameworks was expanded to represent mass transport in the more complex concentric microdialysis probe. This probe is arguably the more popular and is the most commonly referred to in microdialysis literature. The framework is then used to evaluate mass transport within the probe and its surrounding area. Results on percentage recovery and overall mass transfer coefficient under various operating conditions have been discussed. Comparisons were made with the Bungay’s microdialysis framework (BMF) on mass transport performance under different design and operating parameters. The results suggested that the concentric probe framework is sensitive to parameter changes, and the concentration profiles obtained are comparable to the widely accepted BMF. This is one indication that the proposed concentric probe framework can be used to represent mass transport phenomena in such probes. The results from the numerical efforts were then compared to experimental work. It was shown that the simulated data fits well with experimental data using a 5 mm concentric probe, for membrane © This item is protected by original copyright xxvii hindrance factor, α, of 10. The comparison was done again using a similar probe, with a different length (10 mm) and fitting was also found best with α of approximately 10. It is justified that the concentric mathematical framework can be used to represent mass transport phenomena in those probes, and in one way, justifies the validity of the mathematical frameworks for the more primitive probes, beforehand.