# Microwave Measurement Systems for In-line 3D Monitoring of Pharmaceutical Processes

[Doktorsavhandling]

The monitoring and understanding of pharmaceutical processes are important in order to achieve high-quality products at a low-production cost. The presence of water, e.g. as moisture content in the solid-state pharmaceutical material, is ofparticular interest and importance. In this thesis, we treat microwave based permittivity measurements of mixtures of water and solid state pharmaceutical materials, e.g., microcrystalline cellulose (MCC). In particular, we consider a range of volume fractions from densely packed pellets to very dilute mixtures. For sufficiently dilute mixtures, we solve the inverse problem using a linear method with the aid of a regularization technique that also incorporates a priori information. For the case of densely packed pellets, we solve a nonlinear problem by means of a gradient-based optimization method, where the gradient is computed by means of a continuum sensitivity analysis. These two approaches can also be combined with a database of the measurement-system response for different measurement situations, where the aim is to provide a robust method for the permittivity estimation. The electromagnetic problem is accurately modeled by means of the finite element method and a calibration procedure based on reference measurements is used in order to achieve a small residual between the model and the experimental data. First, we present a technique for in-line measurement of the effective permittivity in pharmaceutical processes hosted by metal vessels. We measure the resonance frequencies of the metal vessel and estimate the effective permittivity of the particle-air mixture inside the vessel. In a post-processing step, we use a density-independent formulation based on the effective permittivity to estimate the losses associated with the dielectric particles in the vessel. The second method involves a microwave tomography system used for the estimation of the effective permittivity of densely packed MCC pellets. The effective permittivity is approximated by a Debye model. Measurements on moisturized MCC pellets show that the effective permittivity depends on the moisture content of the MCC. In addition, we have performed extensive computational studies for the microwave tomography system and we conclude that it can also provide useful spatial information, such as detection of bubbles and other inhomogeneities.

**Nyckelord: **Pharmaceutical processes, microwave measurements, permittivity, moisture content, dispersive media, finite element method, microcrystalline cellulose

Denna post skapades 2013-10-11.

CPL Pubid: 185162