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

Bone Marrow Alterations and Lower Endothelial Progenitor Cell Numbers in Critical Limb Ischemia Patients

<div><h3>Background</h3><p>Critical limb ischemia (CLI) is characterized by lower extremity artery obstruction and a largely unexplained impaired ischemic neovascularization response. Bone marrow (BM) derived endothelial progenitor cells (EPC) contribute to neovascularization. We hypothesize that reduced levels and function of circulating progenitor cells and alterations in the BM contribute to impaired neovascularization in CLI.</p> <h3>Methods</h3><p>Levels of primitive (CD34⁺ and CD133⁺) progenitors and CD34⁺KDR⁺ EPC were analyzed using flow cytometry in blood and BM from 101 CLI patients in the JUVENTAS-trial (NCT00371371) and healthy controls. Blood levels of markers for endothelial injury (sE-selectin, sICAM-1, sVCAM-1, and thrombomodulin), and progenitor cell mobilizing and inflammatory factors were assessed by conventional and multiplex ELISA. BM levels and activity of the EPC mobilizing protease MMP-9 were assessed by ELISA and zymography. Circulating angiogenic cells (CAC) were cultured and their paracrine function was assessed.</p> <h3>Results</h3><p>Endothelial injury markers were higher in CLI (P<0.01). CLI patients had higher levels of VEGF, SDF-1α, SCF, G-CSF (P<0.05) and of IL-6, IL-8 and IP-10 (P<0.05). Circulating EPC and BM CD34⁺ cells (P<0.05), lymphocytic expression of CXCR4 and CD26 in BM (P<0.05), and BM levels and activity of MMP-9 (P<0.01) were lower in CLI. Multivariate regression analysis showed an inverse association between IL-6 and BM CD34⁺ cell levels (P = 0.007). CAC from CLI patients had reduced paracrine function (P<0.0001).</p> <h3>Conclusion</h3><p>CLI patients have reduced levels of circulating EPC, despite profound endothelial injury and an EPC mobilizing response. Moreover, CLI patients have lower BM CD34⁺-cell levels, which were inversely associated with the inflammatory marker IL-6, and lower BM MMP-9 levels and activity. The results of this study suggest that inflammation-induced BM exhaustion and a disturbed progenitor cell mobilization response due to reduced levels and activity of MMP-9 in the BM and alterations in the SDF-1α/CXCR4 interaction contribute to the attenuated neovascularization in CLI patients.</p> </div

Lower circulating progenitor cell levels in CLI patients.

<p>Data represent median and P75. Circulating progenitor cell numbers in CLI patients (n = 101) and healthy controls (HC; n = 37). The number of circulating CD133⁺ and CD34⁺KDR⁺ EPC was significantly reduced in CLI patients (* P<0.05). No significant (ns) differences in circulating numbers were observed for CD34⁺ cells.</p

Conditioned medium obtained from CAC cultured from CLI patients has impaired paracrine effects.

<p>Data represent median and P75. Percentage of scratch wound closure stimulated with conditioned medium (CM) obtained from CLI derived CAC (n = 33) was significantly reduced (P<0.0001) compared to CM obtained from healthy control (HC; n = 25) derived CAC. Wound closure after stimulation with HC derived CM was equal to stimulation with a positive control (PC; n = 4). CAC serum free culture medium served as a negative control (NC; n = 4). * P<0.05, ** P<0.01.</p

Subject characteristics.

<p>Values are presented as absolute numbers and percentage (n [%]) for categorical variables and mean ± SD or medians and P25–P75, unless otherwise specified.</p><p>Presence of hypertension, hypercholesterolemia, and hyperhomocysteinemia were determined at the time of inclusion. Hypertension was defined as having a systolic blood pressure >140 mmHg or taking antihypertensive medication. Hypercholesterolemia was defined as having a total cholesterol level >6.5 mmol/l or taking cholesterol reducing medication. Hyperhomocysteinemia was defined as having a homocysteine level >19 µmol/l for men or >17 µmol/l for women.</p>*<p>P<0.05 compared to JUVENTAS patients,</p>†<p>data not available.</p

Endothelial dysfunction markers, chemokines and MMPs.

<p>Data represent means ± SD or medians and P25–P75.</p>*<p>P<0.05 and</p>**<p>P<0.01 compared to control subjects. Endothelial markers were assessed in a subgroup of 54 CLI-patients and 22 controls.</p

BM CD34⁺ progenitor cell are reduced in CLI patients.

<p>Data represent median and P75. BM progenitor cell numbers in CLI patients (n = 101) and healthy controls (HC; n = 12). CD34⁺ cells were significantly reduced (* P<0.05) in CLI patients compared to health controls. No significant (ns) differences in CD133⁺-cells and CD34⁺KDR⁺ EPC in the BM.</p

Arginine analogues.

<p>Data represent medians and P25–P75.</p>**<p>P<0.01 compared to control subjects. Arginine analogues were measured in the blood of 74 CLI patients and in 23 healthy controls.</p

Progenitor cells.

<p>Data represent medians and P25–P75.</p>*<p>P<0.05 compared to control subjects. Progenitor cells were assessed in 101 CLI patients and in 37 and 12 healthy controls for PB and BM, respectively.</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