a b s t r a c tInhaled aerosol dose models play critical roles in medicine, the regulation of air pollutants and basic research. The models fall into several categories: traditional, computational fluid dynamical (CFD), physiologically based pharmacokinetic (PBPK), empirical, semi-empirical, and "reference". Each type of model has its strengths and weaknesses, so multiple models are commonly used for practical applications. Aerosol dose models combine information on aerosol behavior and the anatomy and physiology of exposed human and laboratory animal subjects. Similar models are used for in-vitro studies. Several notable advances have been made in aerosol dose modeling in the past 80 years. The pioneers include Walter Findeisen, who in 1935 published the first traditional model and established the structure of modern models. His model combined aerosol behavior with simplified respiratory tract structures. Ewald Weibel established morphometric techniques for the lung in 1963 that are still used to develop data for modeling today. Advances in scanning techniques have similarly contributed to the knowledge of respiratory tract structure and its use in aerosol dose modeling. Several scientists and research groups have developed and advanced traditional, CFD, and PBPK models. Current issues under study include understanding individual and species differences; examining localized particle deposition; modeling non-ideal aerosols and nanoparticle behavior; linking the regions of the respiratory tract airways from nasal-oral to alveolar; and developing sophisticated supporting software. Although a complete history of inhaled aerosol dose modeling is far too extensive to cover here, selected highlights are described in this paper.

These results show that silicates and other solutes are present at micromolar levels in all glass-exposed solutions, whether pharmaceutical or homeopathic in nature. Even though silicates are known to have biological activity at higher concentrations, the silicate concentrations we measured in homeopathic preparations were too low to account for any purported in vivo efficacy, but could potentially influence in vitro biological assays reporting homeopathic effects.

Researchers are increasingly focused on the nanoscale level of organization where biological processes take place in living systems. Nanoparticles (NPs, e.g., 1-100 nm diameter) are small forms of natural or manufactured source material whose properties differ markedly from those of the respective bulk forms of the "same" material. Certain NPs have diagnostic and therapeutic uses; some NPs exhibit low-dose toxicity; other NPs show ability to stimulate low-dose adaptive responses (hormesis). Beyond dose, size, shape, and surface charge variations of NPs evoke nonlinear responses in complex adaptive systems. NPs acquire unique size-dependent biological, chemical, thermal, optical, electromagnetic, and atom-like quantum properties. Nanoparticles exhibit high surface adsorptive capacity for other substances, enhanced bioavailability, and ability to cross otherwise impermeable cell membranes including the blood-brain barrier. With super-potent effects, nano-forms can evoke cellular stress responses or therapeutic effects not only at lower doses than their bulk forms, but also for longer periods of time. Interactions of initial effects and compensatory systemic responses can alter the impact of NPs over time. Taken together, the data suggest the need to downshift the dose-response curve of NPs from that for bulk forms in order to identify the necessarily decreased no-observed-adverse-effect-level and hormetic dose range for nanoparticles.

In this paper, we review research on homeopathy from four perspectives, focusing on reviews and some landmark studies. These perspectives are laboratory studies, clinical trials, observational studies, and theoretical work. In laboratory models, numerous effects and anomalies have been reported. However, no single model has been sufficiently widely replicated. Instead, researchers have focused on ever-new models and experiments, leaving the picture of scattered anomalies without coherence. Basic research, trying to elucidate a purported difference between homeopathic remedies and control solutions has also produced some encouraging results, but again, series of independent replications are missing. While there are nearly 200 reports on clinical trials, few series have been conducted for single conditions. Some of these series document clinically useful effects and differences against placebo and some series do not. Observational research into uncontrolled homeopathic practice documents consistently strong therapeutic effects and sustained satisfaction in patients. We suggest that this scattered picture has to do with the fourth line of research: lack of a good theory. Some of the extant theoretical models are reviewed, including placebo, water structure, silica contamination, energy models, and entanglement models. It emerges that local models, suggesting some change in structure in the solvent, are far from convincing. The nonlocal models proposed would predict that it is impossible to nail down homeopathic effects with direct experimental testing and this places homeopathy in a scientific dilemma. We close with some suggestions for potentially fruitful research.

The 'silica hypothesis' is one of several frameworks that have been put forward to explain how homeopathic remedies, which often are diluted beyond the point where any of the original substance remains, might still be clinically effective. We describe here what the silica hypothesis says. From a physical chemistry viewpoint, we explore three challenges that the hypothesis would have to meet in order to explain homeopathy: thermodynamic stability of a large number of distinct structures, pattern initiation at low potencies, and pattern maintenance or gradual evolution at higher potencies. We juxtapose current knowledge about silicates with some of the conventional wisdom about homeopathic remedies, to see how well the latter might be a consequence of the former. We explore variants of the hypothesis including some speculations about mechanisms. We outline laboratory experiments that could help to decide it.