La trigonometría como herramienta para medir nuestro entorno

En esta experiencia de aula se presenta el trabajo de un grupo de estudiantes de grado décimo que realizaron una actividad en la clase de trigonometría en la que aplicaron conceptos trigonométricos para calcular las medidas de las instalaciones de la institución educativa a la cual pertenecen. El objetivo es mostrar un ejemplo de cómo se puede generar un ambiente de aprendizaje en el que los estudiantes puedan elaborar significados de objetos matemáticos como lo son las razones trigonométricas mediante una labor que permita la aplicación fundamental de la trigonometría realizando mediciones indirectas

Changes in stiffness at low strains as measured with indentation tests.

<p>The stiffness was computed in the belly (A) and commisures (B) (left side: all data points used for correlation analysis with age; at the right side). In the aortic valve, the stiffness in the belly and commissures increase with age, whereas in the pulmonary valve only the commissural stiffness increases with age. In both valves, E-moduli show a steep increase from adolescence to adulthood. Significant differences between groups (p<0.05) are indicated by paired symbols. AV: aortic valve, PV: pulmonary valve.</p

Valve hemodynamics during postnatal life in the aortic and pulmonary valve.

<p>Trend lines for reported data on valve hemodynamics (black) and our measured data on annulus diameter (grey), matrix composition, and stiffness of the belly (red) during postnatal life in the aortic (A) and pulmonary valve (B). Left-sided pressures increase during childhood, while the right-sided pressures decrease to adult values rapidly after birth. Hemodynamic data are collected from several databases, including The National Heart Lung and Blood Institute, MedScape and literature. Trend lines for our experimental data were obtained using the mean values of the data sets depicted in Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149020#pone.0149020.g002" target="_blank">2</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149020#pone.0149020.g004" target="_blank">4</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149020#pone.0149020.g006" target="_blank">6</a>.</p

Changes in DNA-, sGAG-, and hydroxyproline (HYP) content.

<p>Changes in DNA- (A), sGAG- (B), and hydroxyproline (HYP) content (C) in μg/mg dry weight (left side: all data points used for correlation analysis with age; right side: grouped data). DNA content is higher in children, especially in the first years of life (0–4 years), compared to the adolescents and adults. sGAG content decreases with age. Hydroxyproline content increases with age in the aortic valve. Differences between groups (p<0.05) are indicated by paired symbols. AV: aortic valve, PV: pulmonary valve.</p

Averaged stress-strain curves, E-modulus at high strains, and extensibility obtained from biaxial tensile tests.

<p>Averaged stress-strain curves (A, B), E-modulus at high strains (C), and extensibility (D) obtained from biaxial tensile tests. The E-moduli (E) in both circumferential and radial direction increase with age in the aortic valve (p<0.05). In the pulmonary valve the E-modulus does not change with age. The leaflets of the 11 and 20-year-old donors are more extensible than the adult leaflets (F). In addition, in these young donors, the pulmonary leaflets were slightly more extensible than the aortic leaflets. As the data of the 8-month old donor could be considered as an outlier, we also performed linear regression analysis of the data set excluding the 8-month data and added the corresponding linear regression lines to Figs E and F. This reveals that after the age of 11, leaflet extensibility significantly decreases with age in circumferential (AV: p<0.01, PV: p<0.05) and radial direction (PV: p<0.01). AV: aortic valve, PV: pulmonary valve.</p

Representative histological and immunofluorescent stainings on aortic valves.

<p>Figures A-E represent the whole aortic valve (leaflet, hinge region, and wall, while in E-W a representative part of the leaflet is shown. (A, C-F, H-J) Verhoeff-Van Gieson staining for collagen (red) and elastin (black). (B, G) Elastin was observed in the fetal valve using immunofluorescence (red). (K-N) Collagen type I (red) was predominant in the fibrosa. (O-R) Safranin-O staining showed proteoglycan presence (red/orange) mainly in the spongiosa and the hinge region. (S-W) αSMA (immunofluorescence; green) with cell nuclei (in blue). In the leaflets of the fetal (S) and 8-month old donor (T) αSMA-positive cells were observed, while in the older leaflets almost no αSMA-positive cells were observed (U-W). Scale bar: 500 μm. l: leaflet; w: wall; f: fibrosa; s: spongiosa; v: ventricularis.</p

Schematic overview of the leaflet sectioning and assignment to the different experiments.

<p>(A) Schematic overview of sectioning of one heart valve for analyses. Samples for biaxial tensile testing are indicated in green; parts for histology in red. The right coronary cusp (RCC) and right facing cusp (RFC) were used for indentation tests (purple). Afterwards, this leaflet was used for biaxial tensile testing. Leftover tissue (blue) was freeze-dried for biochemical assays. LCC: Left coronary cusp; LFC: Left facing cusp; NCC: non-coronary cusp; AC: anterior cusp. (B) The size of the leaflets was measured in circumferential and radial direction (arrows). (C) Indentation tests were performed in the commissural (c1 –c4) and belly (b1 –b7) region of the RCC/RFC. (D) Schematic cross-section of the postnatal heart valve used for histology, depicting the wall, leaflet and hinge regions.</p

Evolution of valve dimensions.

<p>(A) Increase in annulus diameter in the aortic (grey) and pulmonary (black) valve. The diameter increases rapidly early in life and slowly, but continuously, thereafter. The pulmonary valve is slightly larger compared to the aortic valve. (B) The thickness of the leaflets is heterogenous and larger in the belly compared to the commissures, which is similar for all age groups. Aortic valves are slightly thicker than pulmonary valves, especially in the belly. (C+D) Changes in leaflet geometry (left side: all data points for correlation analysis with age; right side: grouped data). The leaflet size measured in circumferential (C) and radial (D) direction increases with age. Significant differences between groups (p<0.05) are indicated by paired symbols. AV: aortic valve, PV: pulmonary valve.</p