The sum of the distances between the leaves of a tree and the 'semi-regular' property.

Various topological indices have been put forward in different studies from bio-chemistry to pure mathematics. Among them the Wiener index, the number of subtrees and the Randic index have received great attention from mathematicians. While studying the extremal problems regarding these indices among trees, one interesting phenomenon is that they share the same extremal tree structures. Much effort was devoted to the study of the correlations between these various indices. In this note we provide a common characteristic (the 'semi-regular' property) of these extremal structures with respect to the above mentioned indices, among trees with a given maximum degree. This observation leads to a more unified approach for characterizing these extremal structures. As an application/example, we illustrate the idea by studying the extremal trees regarding the sum of distances between all pairs of leaves of a tree, a new index, which recently appeared in phylogenetic tree reconstruction and the study of the neighborhood of trees.

Reconstructing trees when sequence sites evolve at variable rates.

For a sequence of colors independently evolving on a tree under a simple Markov model, we consider conditions under which the tree can be uniquely recovered from the "sequence spectrum"-the expected frequencies of the various leaf colorations. This is relevant for phylogenetic analysis (where colors represent nucleotides or amino acids; leaves represent extant taxa) as the sequence spectrum is estimated directly from a collection of aligned sequences. Allowing the rate of the evolutionary process to vary across sites is an important extension over most previous studies-we show that, given suitable restrictions on the rate distribution, the true tree (up to the placement of its root) is uniquely identified by its sequence spectrum. However, if the rate distribution is unknown and arbitrary, then, for simple models, it is possible for every tree to produce the same sequence spectrum. Hence there is a logical barrier to accurate, consistent phylogenetic inference for these models when assumptions about the rate distribution are not made. This result exploits a novel theorem on the action of polynomials with non-negative coefficients on sequences.

Preoperative predictors of operative morbidity and mortality in COPD patients undergoing bilateral lung volume reduction surgery.

Bilateral volume reduction surgery (VRS) improves lung function for selected patients with emphysema. However, predictors of outcome are not well defined. We reviewed the preoperative characteristics of the first 47 consecutive patients who underwent bilateral VRS at the Massachusetts General Hospital in order to define potential predictors of unacceptable outcome. Preoperative data included spirometry, plethysmography, diffusion of carbon monoxide (Dco), maximum inspiratory pressure (MIP), maximum expiratory pressure, resting arterial blood gases (ABG), cardiopulmonary exercise testing with ABG and lactate sampling, and radionuclide ventriculography. Prepulmonary and postpulmonary rehabilitation 6-min walk tets (6MWT), and preoperative chest CT scans were also obtained. Twenty-two subjects were male and 17 of the subjects were on the lung transplant list. Patient characteristics included age of 60.5 +/- 7.5 years, FEV1 of 0.67 +/- 0.20 L, total lung capacity of 7.56 +/- 1.7 L, Dco of 7.40 +/- 4.1 mL/min/mm Hg, and PaCO2 of 41.6 +/- 6.4 mm Hg (mean +/- SD). The FEV1, vital capacity, MIP, resting room air PaCO2, prepulmonary and postpulmonary rehabilitation 6MWT, and PaCO2 at maximum oxygen consumption correlated with length of hospitalization (p < 0.05). Based on analysis of 41 of 47 patients for whom there were complete data, the inability to walk more than 200 m on the 6MWT before or after preoperative pulmonary rehabilitation, and resting PaCO2 > or = 45 mm Hg were the best predictors of an unacceptable outcome. If either of these characteristics was present, six of 16 vs zero of 25 died (Fisher's Exact Test, p = 0.0025, one-tailed) and 11 of 16 vs four of 25 had hospital courses > 21 days (p < 0.002). Both the 6MWT < 200 m and resting PaCO2 > or = 45 mm Hg alone correlated with death (p = 0.004 and p = 0.012, respectively) and the resting PaCO2 > or = 45 mm Hg correlated with hospital days > 21 (p = 0.0002). In conclusion, the data suggest that the inability to walk at least 200 m in 6 min before or after pulmonary rehabilitation and a resting room air PaCO2 > or = 45 mm Hg are excellent preoperative predictors of unacceptable postoperative outcomes.

Use of partial liquid ventilation to manage pulmonary complications of acute verapamil-sustained release poisoning.

INTRODUCTION: Verapamil is a papaverine-derived calcium channel blocker widely used for the treatment of hypertension and supraventricular tachyarrhythmias. It is one of the leading agents involved in pharmaceutical poisoning-related deaths among adults. CASE REPORT: We report a case of severe sustained-release verapamil poisoning associated with respiratory failure in an adult man who survived after receiving 4 days of partial liquid ventilation as a part of his medical management.