| Tissue characterization is a broad field that encompasses forward modeling and inverse problems for microstructured biological materials. It aims at finding and quantifying the complex relations between observable and measurable properties at the macroscale, constituents' properties at the microscale, and morphological parameters of clinical relevance. Knowledge of these relationships is crucial for clinical evaluation and treatment monitoring.;Bone quality represents a summary of all characteristics of bone that affect its ability to resist fracture. Measurements of bone mineral density (BMD) are the standard to address osteoporosis or the ability of bone to withstand fracture. Although these measurements have strong correlations with bone mechanical performance and fracture risk, they do not completely explain fracture incidence. Some patients diagnosed with osteoporotic fracture presented the same or even slightly greater BMD values than normal patients. Besides, it has been reported that over half of those who experience fragility fractures do not have BMD levels below the threshold used to identify osteoporosis. As a consequence, there has been an increased interest in other aspects of bone such as its size, shape, and material properties to explain bone fracture. Quantitative ultrasound (QUS) and electric spectroscopy (ES) are relatively cheap and safe techniques being studied for their potential in noninvasive assessment of bone quality. However, most of the studies in the literature are based on correlation analysis between wave parameters and BMD measurements, mechanical, or morphological properties without a mathematical model behind it. The complexity and fine scale of the biological tissue micro-architecture creates a major technical difficulty for prediction of structural and morphological parameters of medical relevance from either QUS or ES measurements. The length of the applied waves is much larger than the variations of the structure, so that only effective or homogenized response of the structure is present in ultrasound or impedance electric data. The goal of this dissertation is to study analytical relations between measured effective or homogenized response and microstructural and morphological parameters. As an application of the results, we derive exact interrelations between dielectric and viscoelastic properties. The proposed approach does not assume any a priori geometrical or idealized microstructure. Applications to bone microstructure will be presented. The obtained results can provide an insight for improvement in existing tissue characterization techniques. |
