Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging

We propose a self-regularized pseudo-time marching strategy for ill-posed, nonlinear inverse problems involving recovery of system parameters given partial and noisy measurements of system response. While various regularized Newton methods are popularly employed to solve these problems, resulting solutions are known to sensitively depend upon the noise intensity in the data and on regularization parameters, an optimal choice for which remains a tricky issue. Through limited numerical experiments on a couple of parameter re-construction problems, one involving the identification of a truss bridge and the other related to imaging soft-tissue organs for early detection of cancer, we demonstrate the superior features of the pseudo-time marching schemes.

Acute fluid shifts influence the assessment of serum vitamin D status in critically ill patients

Introduction Recent reports have highlighted the prevalence of vitamin D deficiency and suggested an association with excess mortality in critically ill patients. Serum vitamin D concentrations in these studies were measured following resuscitation. It is unclear whether aggressive fluid resuscitation independently influences serum vitamin D. Methods Nineteen patients undergoing cardiopulmonary bypass were studied. Serum 25(OH)D3, 1α,25(OH)2D3, parathyroid hormone, C-reactive protein (CRP), and ionised calcium were measured at five defined timepoints: T1 - baseline, T2 - 5 minutes after onset of cardiopulmonary bypass (CPB) (time of maximal fluid effect), T3 - on return to the intensive care unit, T4 - 24 hrs after surgery and T5 - 5 days after surgery. Linear mixed models were used to compare measures at T2-T5 with baseline measures. Results Acute fluid loading resulted in a 35% reduction in 25(OH)D3 (59 ± 16 to 38 ± 14 nmol/L, P < 0.0001) and a 45% reduction in 1α,25(OH)2D3 (99 ± 40 to 54 ± 22 pmol/L P < 0.0001) and i(Ca) (P < 0.01), with elevation in parathyroid hormone (P < 0.0001). Serum 25(OH)D3 returned to baseline only at T5 while 1α,25(OH)2D3 demonstrated an overshoot above baseline at T5 (P < 0.0001). There was a delayed rise in CRP at T4 and T5; this was not associated with a reduction in vitamin D levels at these time points. Conclusions Hemodilution significantly lowers serum 25(OH)D3 and 1α,25(OH)2D3, which may take up to 24 hours to resolve. Moreover, delayed overshoot of 1α,25(OH)2D3 needs consideration. We urge caution in interpreting serum vitamin D in critically ill patients in the context of major resuscitation, and would advocate repeating the measurement once the effects of the resuscitation have abated.