A Bayesian functional data model for surveys collected under informative sampling with application to mortality estimation using NHANES.

Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.

Photoacoustic discrimination of vascular and pigmented lesions using classical and Bayesian methods.

Discrimination of pigmented and vascular lesions in skin can be difficult due to factors such as size, subungual location, and the nature of lesions containing both melanin and vascularity. Misdiagnosis may lead to precancerous or cancerous lesions not receiving proper medical care. To aid in the rapid and accurate diagnosis of such pathologies, we develop a photoacoustic system to determine the nature of skin lesions in vivo. By irradiating skin with two laser wavelengths, 422 and 530 nm, we induce photoacoustic responses, and the relative response at these two wavelengths indicates whether the lesion is pigmented or vascular. This response is due to the distinct absorption spectrum of melanin and hemoglobin. In particular, pigmented lesions have ratios of photoacoustic amplitudes of approximately 1.4 to 1 at the two wavelengths, while vascular lesions have ratios of about 4.0 to 1. Furthermore, we consider two statistical methods for conducting classification of lesions: standard multivariate analysis classification techniques and a Bayesian-model-based approach. We study 15 human subjects with eight vascular and seven pigmented lesions. Using the classical method, we achieve a perfect classification rate, while the Bayesian approach has an error rate of 20%.

Modeling complex phenotypes: generalized linear models using spectrogram predictors of animal communication signals.

A major goal of evolutionary biology is to understand the dynamics of natural selection within populations. The strength and direction of selection can be described by regressing relative fitness measurements on organismal traits of ecological significance. However, many important evolutionary characteristics of organisms are complex, and have correspondingly complex relationships to fitness. Secondary sexual characteristics such as mating displays are prime examples of complex traits with important consequences for reproductive success. Typically, researchers atomize sexual traits such as mating signals into a set of measurements including pitch and duration, in order to include them in a statistical analysis. However, these researcher-defined measurements are unlikely to capture all of the relevant phenotypic variation, especially when the sources of selection are incompletely known. In order to accommodate this complexity we propose a Bayesian dimension-reduced spectrogram generalized linear model that directly incorporates representations of the entire phenotype (one-dimensional acoustic signal) into the model as a predictor while accounting for multiple sources of uncertainty. The first stage of dimension reduction is achieved by treating the spectrogram as an "image" and finding its corresponding empirical orthogonal functions. Subsequently, further dimension reduction is accomplished through model selection using stochastic search variable selection. Thus, the model we develop characterizes key aspects of the acoustic signal that influence sexual selection while alleviating the need to extract higher-level signal traits a priori. This facet of our approach is fundamental and has the potential to provide additional biological insight, as is illustrated in our analysis.

Automated wavelet denoising of photoacoustic signals for circulating melanoma cell detection and burn image reconstruction.

Photoacoustic image reconstruction may involve hundreds of point measurements, each of which contributes unique information about the subsurface absorbing structures under study. For backprojection imaging, two or more point measurements of photoacoustic waves induced by irradiating a biological sample with laser light are used to produce an image of the acoustic source. Each of these measurements must undergo some signal processing, such as denoising or system deconvolution. In order to process the numerous signals, we have developed an automated wavelet algorithm for denoising signals. We appeal to the discrete wavelet transform for denoising photoacoustic signals generated in a dilute melanoma cell suspension and in thermally coagulated blood. We used 5, 9, 45 and 270 melanoma cells in the laser beam path as test concentrations. For the burn phantom, we used coagulated blood in 1.6 mm silicon tube submerged in Intralipid. Although these two targets were chosen as typical applications for photoacoustic detection and imaging, they are of independent interest. The denoising employs level-independent universal thresholding. In order to accommodate nonradix-2 signals, we considered a maximal overlap discrete wavelet transform (MODWT). For the lower melanoma cell concentrations, as the signal-to-noise ratio approached 1, denoising allowed better peak finding. For coagulated blood, the signals were denoised to yield a clean photoacoustic resulting in an improvement of 22% in the reconstructed image. The entire signal processing technique was automated so that minimal user intervention was needed to reconstruct the images. Such an algorithm may be used for image reconstruction and signal extraction for applications such as burn depth imaging, depth profiling of vascular lesions in skin and the detection of single cancer cells in blood samples.

Photoacoustic discrimination of viable and thermally coagulated blood using a two-wavelength method for burn injury monitoring.

Discriminating viable from thermally coagulated blood in a burn wound can be used to profile burn depth, thus aiding the removal of necrotic tissue. In this study, we used a two-wavelength photoacoustic imaging method to discriminate coagulated and non-coagulated blood in a dermal burn phantom. Differences in the optical absorption spectra of coagulated and non-coagulated blood produce different values of the ratio of peak photoacoustic amplitude at 543 and 633 nm. The absorption values obtained from spectroscopic measurements indicate that the ratio of photoacoustic pressure for 543 and 633 nm for non-coagulated blood was 15.7:1 and 1.6:1 for coagulated blood. Using planar blood layers, we found the photoacoustic ratios to be 13.5:1 and 1.6:1, respectively. Using the differences in the ratios of coagulated and non-coagulated blood, we propose a scheme using statistical classification analysis to identify the different blood samples. Based upon these distinctly different ratios, we identified the planar blood samples with an error rate of 0%. Using a burn phantom with cylindrical vessels containing coagulated and non-coagulated blood, we achieved an error rate of 11.4%. These results have shown that photoacoustic imaging could prove to be a valuable tool in the diagnosis of burns.