Blood Glucose Monitoring in the Intensive Care Unit: Toward Defining Bias and Imprecision Thresholds for (Near) Continuous Sensors

status: publishe

Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics

Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behaviour of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss some techniques that yield uniform approximation over the whole eigenvalue spectrum and can take large steps even for high eigenvalues. In particular, we will focus on methods based on coefficient approximation which replace the coefficient functions of the Sturm-Liouville problem by simpler approximations and then solve the approximating problem. The use of (modified) Magnus or Neumann integrators allows to extend the coefficient approximation idea to higher order methods

Critical illness-induced bone loss is related to deficient autophagy and histone hypomethylation

BACKGROUND Survivors of critical illness are at increased risk of fractures. This may be due to increased osteoclast formation during critical illness, leading to trabecular bone loss. Such bone loss has also been observed in Paget's disease, and has been related to deficient autophagy. Deficient autophagy has also been documented in vital organs and skeletal muscle of critically ill patients. The objective of this study was to investigate whether deficient autophagy can be linked to critical illness-induced bone loss. METHODS Osteoclasts grown in vitro and their precursor cells isolated from peripheral blood of critically ill patients and from matched healthy volunteers were analysed for the expression of autophagy genes (SQSTM1, Atg3 and Atg7), and proteins (p62, Atg-5, and microtubule-associated protein light chain 3-II (LC3-II)) and for autophagy and epigenetic signalling factors via PCR arrays and were treated with the autophagy inducer rapamycin. The effect of rapamycin was also investigated at the tissue level in an in vivo rabbit model of critical illness. RESULTS Many more osteoclasts formed in vitro from the blood precursor cells isolated from critically ill patients, which accumulated p62, and displayed reduced expression of Atg5, Atg7, and LC3-II compared to healthy controls, suggesting deficient autophagy, whilst addition of rapamycin reduced osteoclast formation. PCR arrays revealed a down-regulation of histone methyltransferases coupled with an up-regulation of negative regulators of autophagy. Critically ill rabbits displayed a reduction in trabecular and cortical bone, which was rescued with rapamycin. CONCLUSIONS Deficient autophagy in osteoclasts and their blood precursor cells at least partially explained aberrant osteoclast formation during critical illness and was linked to global histone hypomethylation. Treatment with the autophagy activator Rapamycin reduced patient osteoclast formation in vitro and reduced the amount of bone loss in critically ill rabbits in vivo. These findings may help to develop novel therapeutic targets to prevent critical illness-induced bone loss

Comment on: a two-stage fourth-order “almost” P-stable method for oscillatory problems

AbstractIn Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118) a fourth-order “almost” P-stable method for y″=f(x,y) is proposed. We claim that it is possible to retrieve this combination of multistep methods by means of the theory of parameterized Runge-Kutta-Nyström (RKN) methods and moreover to generalize the method discussed by Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118)