Linear and Piecewise Functions

This morning Dr. Battle will review basic concepts of linear functions and piecewise functions and how they can be used as models for real-world applications. She will also introduce techniques for using a spreadsheet to analyze data.

Traditional and novel methods for occlusal caries detection: performance on primary teeth

This study aimed to assess the performance of International Caries Detection and Assessment System (ICDAS), radiographic examination, and fluorescence-based methods for detecting occlusal caries in primary teeth. One occlusal site on each of 79 primary molars was assessed twice by two examiners using ICDAS, bitewing radiography (BW), DIAGNOdent 2095 (LF), DIAGNOdent 2190 (LFpen), and VistaProof fluorescence camera (FC). The teeth were histologically prepared and assessed for caries extent. Optimal cutoff limits were calculated for LF, LFpen, and FC. At the D (1) threshold (enamel and dentin lesions), ICDAS and FC presented higher sensitivity values (0.75 and 0.73, respectively), while BW showed higher specificity (1.00). At the D (2) threshold (inner enamel and dentin lesions), ICDAS presented higher sensitivity (0.83) and statistically significantly lower specificity (0.70). At the D(3) threshold (dentin lesions), LFpen and FC showed higher sensitivity (1.00 and 0.91, respectively), while higher specificity was presented by FC (0.95), ICDAS (0.94), BW (0.94), and LF (0.92). The area under the receiver operating characteristic (ROC) curve (Az) varied from 0.780 (BW) to 0.941 (LF). Spearman correlation coefficients with histology were 0.72 (ICDAS), 0.64 (BW), 0.71 (LF), 0.65 (LFpen), and 0.74 (FC). Inter- and intraexaminer intraclass correlation values varied from 0.772 to 0.963 and unweighted kappa values ranged from 0.462 to 0.750. In conclusion, ICDAS and FC exhibited better accuracy in detecting enamel and dentin caries lesions, whereas ICDAS, LF, LFpen, and FC were more appropriate for detecting dentin lesions on occlusal surfaces in primary teeth, with no statistically significant difference among them. All methods presented good to excellent reproducibility.

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Combining qualitative and quantitative methods to analyze serious games outcomes: A pilot study for a new cognitive screening tool

Computer games for a serious purpose - so called serious games can provide additional information for the screening and diagnosis of cognitive impairment. Moreover, they have the advantage of being an ecological tool by involving daily living tasks. However, there is a need for better comprehensive designs regarding the acceptance of this technology, as the target population is older adults that are not used to interact with novel technologies. Moreover given the complexity of the diagnosis and the need for precise assessment, an evaluation of the best approach to analyze the performance data is required. The present study examines the usability of a new screening tool and proposes several new outlines for data analysis.

Macromolecular interaction studies on FF1-3 of human CA150 and STAT1-importin alpha5 using biophysical and biochemical methods

Macromolecular interactions, such as protein-protein interactions and protein-DNA interactions, play important roles in executing biological functions in cells. However the complexity of such interactions often makes it very challenging to elucidate the structural details of these subjects. In this thesis, two different research strategies were applied on two different two macromolecular systems: X-ray crystallography on three tandem FF domains of transcription regulator CA150 and electron microscopy on STAT1-importin α5 complex. The results from these studies provide novel insights into the function-structure relationships of transcription coupled RNA splicing mediated by CA150 and the nuclear import process of the JAK-STAT signaling pathway. ^ The first project aimed at the protein-protein interaction module FF domain, which often occurs as tandem repeats. Crystallographic structure of the first three FF domains of human CA150 was determined to 2.7 Å resolution. This is the only crystal structure of an FF domain and the only structure on tandem FF domains to date. It revealed a striking connectivity between an FF domain and the next. Peptide binding assay with the potential binding ligand of FF domains was performed using fluorescence polarization. Furthermore, for the first time, FF domains were found to potentially interact with DNA. DNA binding assays were also performed and the results were supportive to this newly proposed functionality of an FF domain. ^ The second project aimed at understanding the molecular mechanism of the nuclear import process of transcription factor STAT1. The first structural model of pSTAT1-importin α5 complex in solution was built from the images of negative staining electron microscopy. Two STAT1 molecules were observed to interact with one molecule of importin α5 in an asymmetric manner. This seems to imply that STAT1 interacts with importin α5 with a novel mechanism that is different from canonical importin α-cargo interactions. Further in vitro binding assays were performed to obtain more details on the pSTAT1-importin α5 interaction. ^