Consideration of solutions to the inverse scattering problem for biomedical applications

For many situations in clinical medicine and other areas, knowledge of the interior structure and properties of materials is of great practical value. Imaging schemes which employed high energy sources, such as X-rays, have been the method of choice, in part, because of the high quality images that can be produced. While the undesirable biological effects of ionizing radiation have been known for several decades, it has only been within the past 15-20 years that alternative strategies that evaluate endogenous sources or exogeneous, but non-ionizing, sources have been made available. Endogenous sources include the electrical and magnetic fields produced as a result of synaptic propagation of the chemical signals generated in neuro-muscular tissues. Electroencephalographic (EEG) [1] and magnetoencephalographic (MEG) [2] imaging methods are based on measurement of these signals. Knowledge that body tissues contain ionic species that will conduct electrical current has led to the development of elecirical impedance tomography (EIT) [3]. Within the electromagnetic spectrum, radio and microwave sources are also being explored for their suitability. When performed in the presence of a large external magnetic field, the former, has proven extremely successful in the form of magnetic resonance imaging [4,5]. The observation that mechanical energy will differentially propagate in tissue has led to acoustic imaging methods in the form of ultrasound imaging and more recently as acoustic tomography [6]. More recently, the search for identifying alternative sources for imaging studies has been extended into the near infrared range [7-9]. At these frequencies it is known that whereas light is intensely scattered by tissue, NIR photons will penetrate deeply, allowing measurements through the head of a neonate or an adult female breast [10]. The great sensitivity of optical measurements and the known relationship between tissue function and the oxygen-dependent spectral properties of hemoglobin and other heme proteins has underscored interest in this area.