Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Connexin 43 expression in human hypertrophied heart due to pressure and volume overload.

Left ventricular hypertrophy (LVH) is due to pressure overload or mechanical stretch and is thought to be associated with remodeling of gap-junctions. We investigated whether the expression of connexin 43 (Cx43) is altered in humans in response to different degrees of LVH. The expression of Cx43 was analyzed by quantitative polymerase chain reaction, Western blot analysis and immunohistochemistry on left ventricular biopsies from patients undergoing aortic or mitral valve replacement. Three groups were analyzed: patients with aortic stenosis with severe LVH (n=9) versus only mild LVH (n=7), and patients with LVH caused by mitral regurgitation (n=5). Cx43 mRNA expression and protein expression were similar in the three groups studied. Furthermore, immunohistochemistry revealed no change in Cx43 distribution. We can conclude that when compared with mild LVH or with LVH due to volume overload, severe LVH due to chronic pressure overload is not accompanied by detectable changes of Cx43 expression or spatial distribution.

Variation in performance in low-volume mammography screening programmes: experience from Switzerland.

BACKGROUND: Reading volume and mammography screening performance appear positively correlated. Quality and effectiveness were compared across low-volume screening programmes targeting relatively small populations and operating under the same decentralised healthcare system. Except for accreditation of 2nd readers (restrictive vs non-restrictive strategy), these organised programmes had similar screening regimen/procedures and duration, which maximises comparability. Variation in performance and its determinants were explored in order to improve mammography practice and optimise screening performance. METHODS: Circa 200,000 screens performed between 1999 and 2006 (4 rounds) in 3 longest standing Swiss cantonal programmes (of Vaud, Geneva and Valais) were assessed. Indicators of quality and effectiveness were assessed according to European standards. Interval cancers were identified through linkage with cancer registries records. RESULTS: Swiss programmes met most European standards of performance with a substantial, favourable cancer stage shift. Up to a two-fold variation occurred for several performance indicators. In subsequent rounds, compared with programmes (Vaud and Geneva) that applied a restrictive selection strategy for 2nd readers, proportions of in situ lesions and of small cancers (≤1cm) were one third lower and halved, respectively, and the proportion of advanced lesions (stage II+) nearly 50% higher in the programme without a restrictive selection strategy. Discrepancy in second-year proportional incidence of interval cancers appears to be multicausal. CONCLUSION: Differences in performance could partly be explained by a selective strategy for second readers and a prior experience in service screening, but not by the levels of opportunistic screening and programme attendance. This study provides clues for enhancing mammography screening performance in low-volume programmes.

Chirurgie de réduction de volume pulmonaire: Suivi des 26 premiers patients à Lausanne

Ce travail concerne les 26 premiers patients opérés à Lausanne de juillet 1995 à avril 1998 d?une gie de réduction de volume pulmonaire pour un emphysème sévère. Il présente leurs actéristiques préopératoires générales, leur évaluation radiologique et cardiologique, ainsi que mesures fonctionnelles pulmonaires. Il examine ensuite la technique opératoire, la période ériopératoire, ainsi que les résultats fonctionnels postopératoires des patients. De plus il présente les entretiens ayant eu lieu avec chaque patient pour connaître son évaluation de l?opération et de ges résultats. Ces informations sont ensuite comparées avec les résultats présents dans la littérature. Le profil préopératoire, la technique opératoire, la période péripopératoire, et les résultats fonctionnels postopératoires sont comparés. Un groupe de patients qui n?a pas répondu au point de vue fonctionnel A la chirurgie est ensuite examiné afin de tenter de définir des critères préopératoires de bonne ou mauvaise réponse, et ceux-ci sont mis en relation avec les données de la littérature. On compare ensuite le groupe de mauvais répondeurs fonctionnels avec le groupe des patients ne s?estimant pas améliorés par l?opération. En faisant une étude statistiques des valeurs fonctionnelles pré et postopératoire, on observe une amélioration significative du VEMS, du volume résiduel, de la PaC02, de la distance parcounie au test de marche de six minutes et de la dyspnée engendrée par le test sur une échelle de Borg. L?amélioration de la Pa02 postopératoire et de la saturation en oxygène pendant le test de marche n?était pas significative statistiquement. On peut voir que ce collectif de patients lausannois est comparable aux autres séries au niveau du profil préopératoire et de la gravité de l?atteinte fonctionnelle, au niveau de la technique opératoire, de la mortalité et morbidité, et des résultats fonctionnels postopératoires. On observe comme différence un volume résiduel moyen préopératoire plus élevé et davantage amélioré en postopératoire que dans la littérature. Cette étude ne met pas en évidence - et c?est également le cas dans la littérature - de critères clairs préopératoires prédictifs d?une bonne réponse à la chirurgie. De même elle n?a pas mis en évidence de concordance entre l?amélioration de la symptomatologie des patients et les résultats fonctionnels postopératoires. 11 serait donc intéressant de poursuivre ce travail par une évaluation prospective plus systématique des patients opérés et de pouvoir la comparer avec les résultats des patients récusés ou refusant la chirurgie de réduction de volume pulmonaire, afin de pouvoir mieux en évaluer les bénéfices à long terme.

Single breath-hold 3D measurement of left atrial volume using compressed sensing cardiovascular magnetic resonance and a non-model-based reconstruction approach.

BACKGROUND: Left atrial (LA) dilatation is associated with a large variety of cardiac diseases. Current cardiovascular magnetic resonance (CMR) strategies to measure LA volumes are based on multi-breath-hold multi-slice acquisitions, which are time-consuming and susceptible to misregistration. AIM: To develop a time-efficient single breath-hold 3D CMR acquisition and reconstruction method to precisely measure LA volumes and function. METHODS: A highly accelerated compressed-sensing multi-slice cine sequence (CS-cineCMR) was combined with a non-model-based 3D reconstruction method to measure LA volumes with high temporal and spatial resolution during a single breath-hold. This approach was validated in LA phantoms of different shapes and applied in 3 patients. In addition, the influence of slice orientations on accuracy was evaluated in the LA phantoms for the new approach in comparison with a conventional model-based biplane area-length reconstruction. As a reference in patients, a self-navigated high-resolution whole-heart 3D dataset (3D-HR-CMR) was acquired during mid-diastole to yield accurate LA volumes. RESULTS: Phantom studies. LA volumes were accurately measured by CS-cineCMR with a mean difference of -4.73 ± 1.75 ml (-8.67 ± 3.54%, r2 = 0.94). For the new method the calculated volumes were not significantly different when different orientations of the CS-cineCMR slices were applied to cover the LA phantoms. Long-axis "aligned" vs "not aligned" with the phantom long-axis yielded similar differences vs the reference volume (-4.87 ± 1.73 ml vs. -4.45 ± 1.97 ml, p = 0.67) and short-axis "perpendicular" vs. "not-perpendicular" with the LA long-axis (-4.72 ± 1.66 ml vs. -4.75 ± 2.13 ml; p = 0.98). The conventional bi-plane area-length method was susceptible for slice orientations (p = 0.0085 for the interaction of "slice orientation" and "reconstruction technique", 2-way ANOVA for repeated measures). To use the 3D-HR-CMR as the reference for LA volumes in patients, it was validated in the LA phantoms (mean difference: -1.37 ± 1.35 ml, -2.38 ± 2.44%, r2 = 0.97). Patient study: The CS-cineCMR LA volumes of the mid-diastolic frame matched closely with the reference LA volume (measured by 3D-HR-CMR) with a difference of -2.66 ± 6.5 ml (3.0% underestimation; true LA volumes: 63 ml, 62 ml, and 395 ml). Finally, a high intra- and inter-observer agreement for maximal and minimal LA volume measurement is also shown. CONCLUSIONS: The proposed method combines a highly accelerated single-breathhold compressed-sensing multi-slice CMR technique with a non-model-based 3D reconstruction to accurately and reproducibly measure LA volumes and function.

Combined T2 -preparation and two-dimensional pencil-beam inner volume selection.

PURPOSE: To improve coronary magnetic resonance angiography (MRA) by combining a two-dimensional (2D) spatially selective radiofrequency (RF) pulse with a T2 -preparation module ("2D-T2 -Prep"). METHODS: An adiabatic T2 -Prep was modified so that the first and last pulses were of differing spatial selectivity. The first RF pulse was replaced by a 2D pulse, such that a pencil-beam volume is excited. The last RF pulse remains nonselective, thus restoring the T2 -prepared pencil-beam, while tipping the (formerly longitudinal) magnetization outside of the pencil-beam into the transverse plane, where it is then spoiled. Thus, only a cylinder of T2 -prepared tissue remains for imaging. Numerical simulations were followed by phantom validation and in vivo coronary MRA, where the technique was quantitatively evaluated. Reduced field-of-view (rFoV) images were similarly studied. RESULTS: In vivo, full field-of-view 2D-T2 -Prep significantly improved vessel sharpness as compared to conventional T2 -Prep, without adversely affecting signal-to-noise (SNR) or contrast-to-noise ratios (CNR). It also reduced respiratory motion artifacts. In rFoV images, the SNR, CNR, and vessel sharpness decreased, although scan time reduction was 60%. CONCLUSION: When compared with conventional T2 -Prep, the 2D-T2 -Prep improves vessel sharpness and decreases respiratory ghosting while preserving both SNR and CNR. It may also acquire rFoV images for accelerated data acquisition.

Radiographic volume analysis as a novel tool to determine nasopalatine duct cyst dimensions and its association with presenting symptoms and postoperative complications.

OBJECTIVES: The aims of the study were to use cone beam computed tomography (CBCT) images of nasopalatine duct cysts (NPDC) and to calculate the diameter, surface area, and 3D-volume using a custom-made software program. Furthermore, any associations of dimensions of NPDC with age, gender, presence/absence of maxillary incisors/canines (MI/MC), endodontic treatment of MI/MC, presenting symptoms, and postoperative complications were evaluated. MATERIAL AND METHODS: The study comprised 40 patients with a histopathologically confirmed NPDC. On preoperative CBCT scans, curves delineating the cystic borders were drawn in all planes and the widest diameter (in millimeter), surface area (in square millimeter), and volume (in cubic millimeter) were calculated. RESULTS: The overall mean cyst diameter was 15 mm (range 7-47 mm), the mean cyst surface area 566 mm(2) (84-4,516 mm(2)), and the mean cyst volume 1,735 mm(3) (65-25,350 mm(3)). For 22 randomly allocated cases, a second measurement resulted in a mean absolute aberration of ±4.2 % for the volume, ±2.8 % for the surface, and ±4.9 % for the diameter. A statistically significant association was found for the CBCT determined cyst measurements and the need for preoperative endodontic treatment to MI/MC and for postoperative complications. CONCLUSION: In the hands of a single experienced operator, the novel software exhibited high repeatability for measurements of cyst dimensions. Further studies are needed to assess the application of this tool for dimensional analysis of different jaw cysts and lesions including treatment planning. CLINICAL RELEVANCE: Accurate radiographic information of the bone volume lost (osteolysis) due to expansion of a cystic lesion in three dimensions could help in personalized treatment planning.