A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Individuals with mutations in XPNPEP3, which encodes a mitochondrial protein, develop a nephronophthisis-like nephropathy.

The autosomal recessive kidney disease nephronophthisis (NPHP) constitutes the most frequent genetic cause of terminal renal failure in the first 3 decades of life. Ten causative genes (NPHP1-NPHP9 and NPHP11), whose products localize to the primary cilia-centrosome complex, support the unifying concept that cystic kidney diseases are "ciliopathies". Using genome-wide homozygosity mapping, we report here what we believe to be a new locus (NPHP-like 1 [NPHPL1]) for an NPHP-like nephropathy. In 2 families with an NPHP-like phenotype, we detected homozygous frameshift and splice-site mutations, respectively, in the X-prolyl aminopeptidase 3 (XPNPEP3) gene. In contrast to all known NPHP proteins, XPNPEP3 localizes to mitochondria of renal cells. However, in vivo analyses also revealed a likely cilia-related function; suppression of zebrafish xpnpep3 phenocopied the developmental phenotypes of ciliopathy morphants, and this effect was rescued by human XPNPEP3 that was devoid of a mitochondrial localization signal. Consistent with a role for XPNPEP3 in ciliary function, several ciliary cystogenic proteins were found to be XPNPEP3 substrates, for which resistance to N-terminal proline cleavage resulted in attenuated protein function in vivo in zebrafish. Our data highlight an emerging link between mitochondria and ciliary dysfunction, and suggest that further understanding the enzymatic activity and substrates of XPNPEP3 will illuminate novel cystogenic pathways.

Between two fern genomes.

Ferns are the only major lineage of vascular plants not represented by a sequenced nuclear genome. This lack of genome sequence information significantly impedes our ability to understand and reconstruct genome evolution not only in ferns, but across all land plants. Azolla and Ceratopteris are ideal and complementary candidates to be the first ferns to have their nuclear genomes sequenced. They differ dramatically in genome size, life history, and habit, and thus represent the immense diversity of extant ferns. Together, this pair of genomes will facilitate myriad large-scale comparative analyses across ferns and all land plants. Here we review the unique biological characteristics of ferns and describe a number of outstanding questions in plant biology that will benefit from the addition of ferns to the set of taxa with sequenced nuclear genomes. We explain why the fern clade is pivotal for understanding genome evolution across land plants, and we provide a rationale for how knowledge of fern genomes will enable progress in research beyond the ferns themselves.

Intracardiac acoustic radiation force impulse imaging: a novel imaging method for intraprocedural evaluation of radiofrequency ablation lesions.

BACKGROUND: Arrhythmia recurrence after cardiac radiofrequency ablation (RFA) for atrial fibrillation has been linked to conduction through discontinuous lesion lines. Intraprocedural visualization and corrective ablation of lesion line discontinuities could decrease postprocedure atrial fibrillation recurrence. Intracardiac acoustic radiation force impulse (ARFI) imaging is a new imaging technique that visualizes RFA lesions by mapping the relative elasticity contrast between compliant-unablated and stiff RFA-treated myocardium. OBJECTIVE: To determine whether intraprocedure ARFI images can identify RFA-treated myocardium in vivo. METHODS: In 8 canines, an electroanatomical mapping-guided intracardiac echo catheter was used to acquire 2-dimensional ARFI images along right atrial ablation lines before and after RFA. ARFI images were acquired during diastole with the myocardium positioned at the ARFI focus (1.5 cm) and parallel to the intracardiac echo transducer for maximal and uniform energy delivery to the tissue. Three reviewers categorized each ARFI image as depicting no lesion, noncontiguous lesion, or contiguous lesion. For comparison, 3 separate reviewers confirmed RFA lesion presence and contiguity on the basis of functional conduction block at the imaging plane location on electroanatomical activation maps. RESULTS: Ten percent of ARFI images were discarded because of motion artifacts. Reviewers of the ARFI images detected RFA-treated sites with high sensitivity (95.7%) and specificity (91.5%). Reviewer identification of contiguous lesions had 75.3% specificity and 47.1% sensitivity. CONCLUSIONS: Intracardiac ARFI imaging was successful in identifying endocardial RFA treatment when specific imaging conditions were maintained. Further advances in ARFI imaging technology would facilitate a wider range of imaging opportunities for clinical lesion evaluation.

Intracardiac acoustic radiation force impulse (ARFI) and shear wave imaging in pigs with focal infarctions.

Four pigs, three with focal infarctions in the apical intraventricular septum (IVS) and/or left ventricular free wall (LVFW), were imaged with an intracardiac echocardiography (ICE) transducer. Custom beam sequences were used to excite the myocardium with focused acoustic radiation force (ARF) impulses and image the subsequent tissue response. Tissue displacement in response to the ARF excitation was calculated with a phase-based estimator, and transverse wave magnitude and velocity were each estimated at every depth. The excitation sequence was repeated rapidly, either in the same location to generate 40 Hz M-modes at a single steering angle, or with a modulated steering angle to synthesize 2-D displacement magnitude and shear wave velocity images at 17 points in the cardiac cycle. Both types of images were acquired from various views in the right and left ventricles, in and out of infarcted regions. In all animals, acoustic radiation force impulse (ARFI) and shear wave elasticity imaging (SWEI) estimates indicated diastolic relaxation and systolic contraction in noninfarcted tissues. The M-mode sequences showed high beat-to-beat spatio-temporal repeatability of the measurements for each imaging plane. In views of noninfarcted tissue in the diseased animals, no significant elastic remodeling was indicated when compared with the control. Where available, views of infarcted tissue were compared with similar views from the control animal. In views of the LVFW, the infarcted tissue presented as stiff and non-contractile compared with the control. In a view of the IVS, no significant difference was seen between infarcted and healthy tissue, whereas in another view, a heterogeneous infarction was seen to be presenting itself as non-contractile in systole.

Contrast in intracardiac acoustic radiation force impulse images of radiofrequency ablation lesions.

We have previously shown that intracardiac acoustic radiation force impulse (ARFI) imaging visualizes tissue stiffness changes caused by radiofrequency ablation (RFA). The objectives of this in vivo study were to (1) quantify measured ARFI-induced displacements in RFA lesion and unablated myocardium and (2) calculate the lesion contrast (C) and contrast-to-noise ratio (CNR) in two-dimensional ARFI and conventional intracardiac echo images. In eight canine subjects, an ARFI imaging-electroanatomical mapping system was used to map right atrial ablation lesion sites and guide the acquisition of ARFI images at these sites before and after ablation. Readers of the ARFI images identified lesion sites with high sensitivity (90.2%) and specificity (94.3%) and the average measured ARFI-induced displacements were higher at unablated sites (11.23 ± 1.71 µm) than at ablated sites (6.06 ± 0.94 µm). The average lesion C (0.29 ± 0.33) and CNR (1.83 ± 1.75) were significantly higher for ARFI images than for spatially registered conventional B-mode images (C = -0.03 ± 0.28, CNR = 0.74 ± 0.68).

An Exploration into Fern Genome Space.

Ferns are one of the few remaining major clades of land plants for which a complete genome sequence is lacking. Knowledge of genome space in ferns will enable broad-scale comparative analyses of land plant genes and genomes, provide insights into genome evolution across green plants, and shed light on genetic and genomic features that characterize ferns, such as their high chromosome numbers and large genome sizes. As part of an initial exploration into fern genome space, we used a whole genome shotgun sequencing approach to obtain low-density coverage (∼0.4X to 2X) for six fern species from the Polypodiales (Ceratopteris, Pteridium, Polypodium, Cystopteris), Cyatheales (Plagiogyria), and Gleicheniales (Dipteris). We explore these data to characterize the proportion of the nuclear genome represented by repetitive sequences (including DNA transposons, retrotransposons, ribosomal DNA, and simple repeats) and protein-coding genes, and to extract chloroplast and mitochondrial genome sequences. Such initial sweeps of fern genomes can provide information useful for selecting a promising candidate fern species for whole genome sequencing. We also describe variation of genomic traits across our sample and highlight some differences and similarities in repeat structure between ferns and seed plants.