Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

A case study of product usability of a pelvic device used by children with neuromotor impairments

On assistive technology targeted for people with activity limitations and participation, usability issues becomes an essential tool to ensure that the product has the appropriate ergonomics characteristics, in other words, ensure that it fits the specific user´s needs. The aim of this study was to analyze the usability of an adaptive seating device for children with neuromotor impairments, by using kinematic indicators of the reaching movement. The study sample consisted of 13 children with associated neurologic conditions. The tests were developed by using a wooden bench height adjustable, integrated with the adaptive seating device under study, and a system to capture three-dimensional image, called Qualisys Track Manager. The following reaching kinematics variables were measured: maximum reaching velocity, movement duration, index of curvature, and unit movements. It was found that the use of the adaptive seating device had a positive impact on upper limb function in children with neuromotor impairments. It was also noticed an improvement in the reaching movement kinematics, which was statistical significant for the index of curvature and unit movements. As main conclusions, it is possible to point out some positive effects that the product under study seems to have on users' movements, such as the improved movement quality of the upper limb, which could mean a better postural adjustments and higher trunk postural control. By identifying new measures of usability in terms of effectiveness and efficiency for the analyzeddevice, the results obtained may serve also as performance indicators, providing new data that may help to improve the product and eventually modifying it, in order to turn it more compatible with the needs of the considered target population.

Adolescent parents’ values: the role played by retrospective perceptions of the family-of-origin

Family-of-origin is an important system in individual’s lives, and its influence is extensive over the life cycle. The aim of this study was to investigate, in a sample of adolescents’ parents, whether their retrospective perceptions of parenting and relationship qualities within their families-of-origin during adolescence predicted their current collectivist and individualist values. Participants included 110 Portuguese adults with a mean age of 46.86 years old. The results of structural equation modeling supported that retrospective perceptions of parenting and relationship qualities in the family-of-origin predicted the adults’ collectivist values but not their individualist values. This study highlights the importance of retrospective perceptions of supporting and non-rejecting parenting for value acquisition. The results also suggest that values that preserve and protect family connections and collaborations are more likely to be socialized by families. Implications for practice and for the theories on parenting, values, family-of-origin influences and family intergenerational transmission are discussed.

Short-term corneal changes with gas-permeable contact lens wear in keratoconus subjects: a comparison of two fitting approaches

Purpose: To evaluate changes in anterior corneal topography and higher-order aberrations (HOA) after 14-days of rigid gas-permeable (RGP) contact lens (CL) wear in keratoconus subjects comparing two different fitting approaches. Methods: Thirty-one keratoconus subjects (50 eyes) without previous history of CL wear were recruited for the study. Subjects were randomly fitted to either an apical-touch or three-pointtouch fitting approach. The lens’ back optic zone radius (BOZR) was 0.4 mm and 0.1 mm flatter than the first definite apical clearance lens, respectively. Differences between the baseline and post-CL wear for steepest, flattest and average corneal power (ACP) readings, central corneal astigmatism (CCA), maximum tangential curvature (KTag), anterior corneal surface asphericity, anterior corneal surface HOA and thinnest corneal thickness measured with Pentacam were compared. Results: A statistically significant flattening was found over time on the flattest and steepest simulated keratometry and ACP in apical-touch group (all p < 0.01). A statistically significant reduction in KTag was found in both groups after contact lens wear (all p < 0.05). Significant reduction was found over time in CCA (p = 0.001) and anterior corneal asphericity in both groups (p < 0.001). Thickness at the thinnest corneal point increased significantly after CL wear (p < 0.0001). Coma-like and total HOA root mean square (RMS) error were significantly reduced following CL wearing in both fitting approaches (all p < 0.05). Conclusion: Short-term rigid gas-permeable CL wear flattens the anterior cornea, increases the thinnest corneal thickness and reduces anterior surface HOA in keratoconus subjects. Apicaltouch was associated with greater corneal flattening in comparison to three-point-touch lens wear.

Changes in peripheral refractive profile after orthokeratology for different degrees of myopia

Purpose: The purpose of this study was to evaluate the effect of orthokeratology for different degrees of myopia correction in the relative location of tangential (FT) and sagittal (FS) power errors across the central 70 of the visual field in the horizontal meridian. Methods: Thirty-four right eyes of 34 patients with a mean age of 25.2 ± 6.4 years were fitted with Paragon CRT (Mesa, AZ) rigid gas permeable contact lenses to treat myopia (2.15 ± 1.26D, range: 0.88 to 5.25D). Axial and peripheral refraction were measured along the central 70 of the horizontal visual field with the Grand Seiko WAM5500 open-field auto-refractor. Spherical equivalent (M), as well as tangential (FT) and sagittal power errors (FS) were obtained. Analysis was stratified in three groups according to baseline spherical equivalent: Group 1 [MBaseline = 0.88 to 1.50D; n = 11], Group 2 [MBaseline = 1.51 to 2.49D; n = 11], and Group 3 [MBaseline = 2.50 to 5.25D; n = 12]. Results: Spherical equivalent was significantly more myopic after treatment beyond the central 40 of the visual field (p50.001). FT became significantly more myopic for all groups in the nasal and temporal retina with 25 (p 0.017), 30 (p 0.007) and 35 (p 0.004) of eye rotation. Myopic change in FS was less consistent, achieving only statistical significance for all groups at 35 in the nasal and temporal retina (p 0.045). Conclusions: Orthokeratology changes significantly FT in the myopic direction beyond the central 40 of the visual field for all degrees of myopia. Changes induced by orthokeratology in relative peripheral M, FT and FS with 35 of eye rotation were significantly correlated with axial myopia at baseline. Keywords: Field