In this article, the use of an SPME technique is reported for the first time for direct measurement of free drug concentration in solid tissue. In our investigations, we considered doxorubicin (DOX) spiked in homogenized tissue matrix at transient and equilibrium extraction conditions, with subsequent assessment of obtained experimental results by an in silico approach using mathematical models developed in COMSOL Multyphysics. In silico studies were performed on the basis of transported diluted species (tds) and reaction engineering (re) modules from COMSOL Multiphysics, using the same conditions as those used to attain experimental results. To determine the apparent binding affinity of DOX to the tissue matrix which contains multiple binding species, the experimentally determined binding affinity of DOX with human serum albumin (HSA) was considered to simplify the mathematical calculations. Here, the value of the binding affinity was considered for a single binding site and adjusted by fitting the experimental results with the mathematical model. Bovine lung tissue homogenate was selected as a surrogate matrix, and a biocompatible C-8 commercial SPME fiber was used for extraction of DOX. In total, four mathematical models were herein developed to describe the mass transfer kinetics of solid coatings: in agar gel at static conditions, in PBS solution with agitated conditions, extraction in PBS solution in the presence of an HSA binding matrix, and static extraction in homogenized lung tissue. For all conditions, simulated results were in good agreement with experimental results. The developed mathematical model allows for measurements of free drug concentrations inside the tissue matrix and facilitates calculations of local depletion of DOX by a solid SPME coating. Results of the investigations indicate that local depletion of the free form of DOX, even at the kinetic stage, is negligible for tissue extraction, as the release of the heavily bound analyte (over 99% binding to tissue matrix) is very rapid, thus easily compensating for the loss of the drug to the SPME coating. This indicates that the dissociation rate constant of DOX from lung tissue components is very rapid; therefore, the mass transfer of drug to the fiber coating via free from is very efficient. Our results also indicate that thin coating SPME fibers provide a good way to measure drug distribution after dosing, as extractions via thin coating SPME fibers do not affect the free concentration of the drug, which is responsible for drug distribution in tissue.

An alternative strategy to increase mass transfer entails geometry optimization of the extraction systems including design of solid-phase microextraction (SPME) probes. In this work, a computational model was employed to elucidate practical aspects such as efficiency and kinetics of extraction by employing several new geometries. Extraction of a model analyte at static conditions with the configurations, such as thin-film, fiber, coated tip, and nanoparticles, was numerically simulated to obtain an in-depth understanding of the advantages and limitations of each geometry in microextraction and exhaustive modes. The attained results associated with the equilibration time dependency on shape were in good agreement with previously reported experimental observations. They demonstrate that the mass-transfer is highly dependent on the size and shape of the coatings and increases with a decrease in size of the devices particularly rapidly below 10 μm caused by radial diffusion effect. Nevertheless, extractions performed using octadecyl-functionalized magnetic nanoparticles demonstrated that higher enrichment factors are achievable with the use of a fewer number of particles in comparison to factors achieved via exhaustive extraction, where a larger number of particles must be employed, confirming theoretical predictions. The conclusions reached are valid for any extraction method. The results obtained herein are very useful toward the design and optimization of future extraction technologies and approaches.