Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Characterization and evaluation of melibiose as novel excipient in tablet compaction

Lactose is probably the most used tablet excipient in the field of pharmacy. Although lactose is thoroughly characterized and available in many different forms there is a need to find a replacer for lactose as a filler/binder in tablet formulations because it has some downsides. Melibiose is a relatively unknown disaccharide that has not been thoroughly characterized and not previously used as an excipient in tablets. Structurally melibiose is close to lactose as it is also formed from the same two monosaccharides, glucose and galactose. Aim of this research is to characterize and to study physicochemical properties of melibiose. Also the potential of melibiose to be used as pharmaceutical tablet excipient, even as a substitute for lactose is evaluated. Current knowledge about fundamentals of tableting and methods for determinating of deformation behavior and tabletability are reviewed. In this research Raman spectroscopy, X-ray powder diffraction (XRPD), near-infrared spectroscopy (NIR) and Fourier-transform infrared spectroscopy (FT-IR) were used to study differences between two melibiose batches purchased from two suppliers. In NIR and FT-IR measurements no difference between materials could be observed. XPRD and Raman however found differences between the two melibiose batches. Also the effects of moisture content and heating to material properties were studied and moisture content of materials seems to cause some differences. Thermal analytical methods, differential scanning calorimetry (DSC) and thermogravimetry (TG) were used to study thermal behaviour of melibiose and difference between materials was found. Other melibiose batch contains residual water which evaporates at higher temperatures causing the differences in thermal behaviour. Scanning electron microscopy images were used to evaluate particle size, particle shape and morphology. Bulk, tapped and true densities and flow properties of melibiose was measured. Particle size of the melibiose batches are quite different resulting causing differences in the flowability. Instrumented tableting machine and compression simulator were used to evaluate tableting properties of melbiose compared to α-lactose monohydrate. Heckel analysis and strain-rate sensitivity index were used to determine deformation mechanism of melibiose monohydrate in relation to α–lactose monohydrate during compaction. Melibiose seems to have similar deformation behaviour than α-lactose monohydrate. Melibiose is most likely fragmenting material. Melibiose has better compactibility than α – lactose monohydrate as it produces tablets with higher tensile strength with similar compression pressures. More compression studies are however needed to confirm these results because limitations of this study.