Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte

Xenoestrogenic activity in blood of European and Inuit populations.

Human exposure to persistent organic pollutants (POPs) is ubiquitous and found in all individuals. Studies have documented endocrine disrupting effects and impact on reproduction. The aim of the present study was to compare the level of xenoestrogenic activity in serum of groups with varying POP exposure, and to evaluate correlations to the POP biomarkers, 2,2',4,4',5,5'-hexachlorobiphenyl (CB-153) and 1,1-dichloro-2,2-bis (p-chlorophenyl)-ethylene (p,p'-DDE). No strong consistent association between xenoestrogenic net activity and the two POP markers was found. The results showed that the selected POP markers alone can not predict the integrated xenoestrogenic serum activity. Correlations to the POP markers were found at the extreme edge; the Inuit's and Warsaw study groups eliciting high frequency of samples with ER antagonistic and agonistic activity, respectively. We suggest that the variation in xenoestrogenic serum activity reflects differences in POP exposure mixture, genetic factors and/or life style factors

Long-term recurrence and complication rates after incisional hernia repair with the open onlay technique

<p>Abstract</p> <p>Background</p> <p>Incisional hernia after abdominal surgery is a well-known complication. Controversy still exists with respect to the choice of hernia repair technique. The objective of this study was to evaluate the long-term recurrence rate as well as surgical complications in a consecutive group of patients undergoing open repair using an onlay mesh technique.</p> <p>Methods</p> <p>Consecutive patients undergoing open incisional hernia repair with onlay-technique between 01/05/1995 and 01/09/2007 at a single institution were included in the study. For follow-up patients were contacted by telephone, and answered a questionnaire containing questions related to the primary operation, the hernia and general risk factors. Patients were examined by a consultant surgeon in the outpatient clinic or in the patient's home if there was suspicion of an incisional hernia recurrence.</p> <p>Results</p> <p>The study included 56 patients with 100% follow-up. The median follow-up was 35 months (range 4–151). Recurrent incisional hernia was found in 8 of 56 patients (15%, 95% CI: 6–24). The overall complication rate was 13% (95% CI, 4–22). All complications were minor and needed no hospital admission.</p> <p>Conclusion</p> <p>This study with a long follow-up showed low recurrence and complication rates in patients undergoing incisional hernia repair with the open onlay technique.</p

An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect

Background: Most randomized controlled trials with a time-to-event outcome are designed and analysed under the proportional hazards assumption, with a target hazard ratio for the treatment effect in mind. However, the hazards may be non-proportional. We address how to design a trial under such conditions, and how to analyse the results. Methods: We propose to extend the usual approach, a logrank test, to also include the Grambsch-Therneau test of proportional hazards. We test the resulting composite null hypothesis using a joint test for the hazard ratio and for time-dependent behaviour of the hazard ratio. We compute the power and sample size for the logrank test under proportional hazards, and from that we compute the power of the joint test. For the estimation of relevant quantities from the trial data, various models could be used; we advocate adopting a pre-specified flexible parametric survival model that supports time-dependent behaviour of the hazard ratio. Results: We present the mathematics for calculating the power and sample size for the joint test. We illustrate the methodology in real data from two randomized trials, one in ovarian cancer and the other in treating cellulitis. We show selected estimates and their uncertainty derived from the advocated flexible parametric model. We demonstrate in a small simulation study that when a treatment effect either increases or decreases over time, the joint test can outperform the logrank test in the presence of both patterns of non-proportional hazards. Conclusions: Those designing and analysing trials in the era of non-proportional hazards need to acknowledge that a more complex type of treatment effect is becoming more common. Our method for the design of the trial retains the tools familiar in the standard methodology based on the logrank test, and extends it to incorporate a joint test of the null hypothesis with power against non-proportional hazards. For the analysis of trial data, we propose the use of a pre-specified flexible parametric model that can represent a time-dependent hazard ratio if one is present

Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of $\xi$, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.Comment: Latex (11pt) 43 pages, 22 figures (Feynman diagrams). The reader interested in the technical details of the calculations presented in the paper may want to visit: http://www.math.helsinki.fi/mathphys/paolo_files/passive_scalar/passcal.htm

Atypical audiovisual speech integration in infants at risk for autism

The language difficulties often seen in individuals with autism might stem from an inability to integrate audiovisual information, a skill important for language development. We investigated whether 9-month-old siblings of older children with autism, who are at an increased risk of developing autism, are able to integrate audiovisual speech cues. We used an eye-tracker to record where infants looked when shown a screen displaying two faces of the same model, where one face is articulating/ba/and the other/ga/, with one face congruent with the syllable sound being presented simultaneously, the other face incongruent. This method was successful in showing that infants at low risk can integrate audiovisual speech: they looked for the same amount of time at the mouths in both the fusible visual/ga/− audio/ba/and the congruent visual/ba/− audio/ba/displays, indicating that the auditory and visual streams fuse into a McGurk-type of syllabic percept in the incongruent condition. It also showed that low-risk infants could perceive a mismatch between auditory and visual cues: they looked longer at the mouth in the mismatched, non-fusible visual/ba/− audio/ga/display compared with the congruent visual/ga/− audio/ga/display, demonstrating that they perceive an uncommon, and therefore interesting, speech-like percept when looking at the incongruent mouth (repeated ANOVA: displays x fusion/mismatch conditions interaction: F(1,16) = 17.153, p = 0.001). The looking behaviour of high-risk infants did not differ according to the type of display, suggesting difficulties in matching auditory and visual information (repeated ANOVA, displays x conditions interaction: F(1,25) = 0.09, p = 0.767), in contrast to low-risk infants (repeated ANOVA: displays x conditions x low/high-risk groups interaction: F(1,41) = 4.466, p = 0.041). In some cases this reduced ability might lead to the poor communication skills characteristic of autism

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy

A global perspective on marine photosynthetic picoeukaryote community structure

A central goal in ecology is to understand the factors affecting the temporal dynamics and spatial distribution of microorganisms and the underlying processes causing differences in community structure and composition. However, little is known in this respect for photosynthetic picoeukaryotes (PPEs), algae that are now recognised as major players in marine CO2 fixation. Here, we analysed dot blot hybridisation and cloning–sequencing data, using the plastid-encoded 16S rRNA gene, from seven research cruises that encompassed all four ocean biomes. We provide insights into global abundance, α- and β-diversity distribution and the environmental factors shaping PPE community structure and composition. At the class level, the most commonly encountered PPEs were Prymnesiophyceae and Chrysophyceae. These taxa displayed complementary distribution patterns, with peak abundances of Prymnesiophyceae and Chrysophyceae in waters of high (25:1) or low (12:1) nitrogen:phosphorus (N:P) ratio, respectively. Significant differences in phylogenetic composition of PPEs were demonstrated for higher taxonomic levels between ocean basins, using Unifrac analyses of clone library sequence data. Differences in composition were generally greater between basins (interbasins) than within a basin (intrabasin). These differences were primarily linked to taxonomic variation in the composition of Prymnesiophyceae and Prasinophyceae whereas Chrysophyceae were phylogenetically similar in all libraries. These data provide better knowledge of PPE community structure across the world ocean and are crucial in assessing their evolution and contribution to CO2 fixation, especially in the context of global climate change