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The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent results hold for the approximate probability of fixation under the Wright-Fisher process, after an appropriate change of variables). We show that the logarithm of the fixation probability has particularly simple behavior when the selection coefficient is measured as a difference of Malthusian fitnesses, and we exploit this simplicity to derive inequalities and approximations. We also present a comprehensive comparison of both existing and new approximations for the fixation probability, highlighting those approximations that induce a reversible Markov chain when used to describe the dynamics of evolution under weak mutation. To demonstrate the power of these results, we consider the classical problem of determining the total substitution rate across an ensemble of biallelic loci and prove that, at equilibrium, a strict majority of substitutions are due to drift rather than selection., (Copyright © 2014 Elsevier Inc. All rights reserved.)

Studies on the genetics of adaptation from new mutations typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first mutation to fix is most often deleterious, even when fitness is expected to increase in the long term. In particular, we prove that this phenomenon occurs under weak mutation for any house-of-cards model with an equilibrium distribution. We find that the same qualitative results hold under Fisher's geometric model. We also provide a simple intuition for the surprising prevalence of unconditionally deleterious substitutions during early adaptation. Importantly, the phenomenon we describe occurs on fitness landscapes without any local maxima and is therefore distinct from "valley crossing." Our results imply that the common practice of ignoring deleterious substitutions leads to qualitatively incorrect predictions in many regimes. Our results also have implications for the substitution process at equilibrium and for the response to a sudden decrease in population size., (© 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.)

Susceptometry-based MR oximetry has previously been shown suitable for quantifying hemoglobin oxygen saturation in large vessels for studying vascular reactivity and quantification of global cerebral metabolic rate of oxygen utilization. A key assumption underlying this method is that large vessels can be modeled as long paramagnetic cylinders. However, bifurcations, tapering, noncircular cross-section, and curvature of these vessels produce substantial deviations from cylindrical geometry, which may lead to errors in hemoglobin oxygen saturation quantification. Here, the accuracy of the "long cylinder" approximation is evaluated via numerical computation of the induced magnetic field from 3D segmented renditions of three veins of interest (superior sagittal sinus, femoral and jugular vein). At a typical venous oxygen saturation of 65%, the absolute error in hemoglobin oxygen saturation estimated via a closed-form cylinder approximation was 2.6% hemoglobin oxygen saturation averaged over three locations in the three veins studied and did not exceed 5% for vessel tilt angles <30° at any one location. In conclusion, the simulation results provide a significant level of confidence for the validity of the cylinder approximation underlying MR susceptometry-based oximetry of large vessels., (Copyright © 2011 Wiley Periodicals, Inc.)

The Wright-Fisher model of allele dynamics forms the basis for most theoretical and applied research in population genetics. Our understanding of genetic drift, and its role in suppressing the deterministic forces of Darwinian selection has relied on the specific form of sampling inherent to the Wright-Fisher model and its diffusion limit. Here we introduce and analyze a broad class of forward-time population models that share the same mean and variance as the Wright-Fisher model, but may otherwise differ. The proposed class unifies and further generalizes a number of population-genetic processes of recent interest, including the Λ and Cannings processes. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We characterize in detail the behavior of standard population-genetic quantities across this family of generalized models. Some quantities, such as heterozygosity, remain unchanged; but others, such as neutral absorption times and fixation probabilities under selection, deviate by orders of magnitude from the Wright-Fisher model. We show that generalized population models can produce startling phenomena that differ qualitatively from classical behavior - such as assured fixation of a new mutant despite the presence of genetic drift. We derive the forward-time continuum limits of the generalized processes, analogous to Kimura's diffusion limit of the Wright-Fisher process, and we discuss their relationships to the Kingman and non-Kingman coalescents. Finally, we demonstrate that some non-diffusive, generalized models are more likely, in certain respects, than the Wright-Fisher model itself, given empirical data from Drosophila populations., (Copyright © 2011 Elsevier Inc. All rights reserved.)

An accurate noninvasive method to measure the hemoglobin oxygen saturation (%HbO(2)) of deep-lying vessels without catheterization would have many clinical applications. Quantitative MRI may be the only imaging modality that can address this difficult and important problem. MR susceptometry-based oximetry for measuring blood oxygen saturation in large vessels models the vessel as a long paramagnetic cylinder immersed in an external field. The intravascular magnetic susceptibility relative to surrounding muscle tissue is a function of oxygenated hemoglobin (HbO(2)) and can be quantified with a field-mapping pulse sequence. In this work, the method's accuracy and precision was investigated theoretically on the basis of an analytical expression for the arbitrarily oriented cylinder, as well as experimentally in phantoms and in vivo in the femoral artery and vein at 3T field strength. Errors resulting from vessel tilt, noncircularity of vessel cross-section, and induced magnetic field gradients were evaluated and methods for correction were designed and implemented. Hemoglobin saturation was measured at successive vessel segments, differing in geometry, such as eccentricity and vessel tilt, but constant blood oxygen saturation levels, as a means to evaluate measurement consistency. The average standard error and coefficient of variation of measurements in phantoms were <2% with tilt correction alone, in agreement with theory, suggesting that high accuracy and reproducibility can be achieved while ignoring noncircularity for tilt angles up to about 30 degrees . In vivo, repeated measurements of %HbO(2) in the femoral vessels yielded a coefficient of variation of less than 5%. In conclusion, the data suggest that %HbO(2) can be measured reproducibly in vivo in large vessels of the peripheral circulation on the basis of the paramagnetic cylinder approximation of the incremental field., ((c) 2009 Wiley-Liss, Inc.)

One of the most challenging problems in modern neuroimaging is detailed characterization of neurodegeneration. Quantifying spatial and longitudinal atrophy patterns is an important component of this process. These spatiotemporal signals will aid in discriminating between related diseases, such as frontotemporal dementia (FTD) and Alzheimer's disease (AD), which manifest themselves in the same at-risk population. Here, we develop a novel symmetric image normalization method (SyN) for maximizing the cross-correlation within the space of diffeomorphic maps and provide the Euler-Lagrange equations necessary for this optimization. We then turn to a careful evaluation of our method. Our evaluation uses gold standard, human cortical segmentation to contrast SyN's performance with a related elastic method and with the standard ITK implementation of Thirion's Demons algorithm. The new method compares favorably with both approaches, in particular when the distance between the template brain and the target brain is large. We then report the correlation of volumes gained by algorithmic cortical labelings of FTD and control subjects with those gained by the manual rater. This comparison shows that, of the three methods tested, SyN's volume measurements are the most strongly correlated with volume measurements gained by expert labeling. This study indicates that SyN, with cross-correlation, is a reliable method for normalizing and making anatomical measurements in volumetric MRI of patients and at-risk elderly individuals.

We assess the effects of in utero cocaine and polysubstance exposure on the adolescent caudate nucleus through high-resolution magnetic resonance imaging. Cocaine exposure may compromise the developing brain through disruption of neural ontogeny in dopaminergic systems, effects secondary to fetal hypoxemia, or altered cerebrovascular reactivity. Cocaine exposure may also lead to neonatal lesions in the caudate. However, long-term or latent effects of intrauterine cocaine exposure are rarely found. We use T(1)-weighted magnetic resonance imaging to quantify caudate nucleus morphology in matched control and exposed groups. The literature suggests that in utero cocaine exposure consequences in adolescents may be subtle, or masked by other variables. Our comparison focuses on contrasting the control group with high-exposure subjects (mothers who reported 2 median of 117 days of cocaine use during pregnancy; 82% tested positive for cocaine use at term). We use advanced image registration and segmentation tools to quantify left and right caudate morphology. Our results indicate that the caudate is significantly larger in controls versus subjects (P < 0.0025), implying cocaine exposure-related detriments to the dopaminergic system. The right (P < 0.025) and left (P < 0.035) caudate, studied independently, show the same significant trend. Permutation testing and the false discovery rate were used to assess significance.

We introduce a simple, efficient, low-SAR method for magnetic resonance imaging in the presence of a static field with a permanent, and possibly large gradient. The technique, which is called slant-slice imaging is essentially a spin-echo imaging sequence except that the imaging slice is oriented such that the static field gradient can be used in conjunction with applied gradients during readout. Data are collected for 2D slices. Unlike single point imaging techniques, entire lines of k-space are acquired with each readout. The slant-slice pulse sequence is used to obtain high quality images, using a clinical scanner to simulate a static field with a large permanent gradient. The effects of the inhomogeneity are quantified by two parameters nu and q, which are useful for assessing the utility of a magnet design for 3D-MR imaging.

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the Spin-Dirac operator, eth(eo). To study the index of these boundary value problems we introduce a generalization of Fredholm pairs to the "tame" category. In this context, we show that the index of the graph closure of (eth(eo), Reo) equals the tame relative index, on the boundary, between Reo and the Calderon projector. Let X0 and X1 be strictly pseudoconvex, Spin manifolds, as above. Let phi : bX1 --> bX0, be a contact diffeomorphism, S0, S1 denote generalized Szego projectors on bX0, bX1, respectively, and R0(eo), R1(eo), the subelliptic boundary conditions they define. If X1 is the manifold X1 with its orientation reversed, then the glued manifold X = X0 coproduct operator(phi) X1 has a canonical Spin structure and Dirac operator, ethX(eo). Applying these results we obtain a formula for the relative index, R-Ind(S0, phi*S1), [formula: see text]. As a special case, this formula verifies a conjecture of Atiyah and Weinstein [(1997) RIMS Kokyuroku 1014:1-14] for the index of the quantization of a contact transformation between cosphere bundles.

Susceptibility artifacts due to metallic prostheses are a major problem in clinical magnetic resonance imaging. We theoretically and experimentally analyze slice distortion arising from susceptibility differences in a phantom consisting of a stainless steel ball bearing embedded in agarose gel. To relate the observed image artifacts to slice distortion, we simulate images produced by 2D and 3D spin-echo (SE) and a view angle tilting (VAT) sequence. Two-dimensional SE sequences suffer from extreme slice distortion when a metal prosthesis is present, unlike 3D SE sequences for which--since slices are phase-encoded--distortion of the slice profile is minimized, provided the selected slab is larger than the region of interest. In a VAT sequence, artifacts are reduced by the application of a gradient along the slice direction during readout. However, VAT does not correct for the excitation slice profile, which results in the excitation of spins outside the desired slice location and can lead to incorrect anatomical information in MR images. We propose that the best sequences for imaging in the presence of a metal prosthesis utilize 3D acquisition, with phase encoding replacing slice selection to minimize slice distortion, combined with excitation and readout gradient strengths at their maximum values.

This paper provides the practical details required to use the inverse scattering (IST) approach to design selective RF-pulses. As in the Shinnar-Le Roux (SLR) approach, we use a hard pulse approximation to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. We explain how to approximate the reflection coefficient to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, we retain direct control on the phase of the magnetization profile throughout the design process. We give explicit recursive algorithms for computing the hard pulse from the inverse scattering data. These algorithms are quite different from the SLR recursion, being essentially discretizations of the Marchenko equations. We call our approach the discrete inverse scattering transform or DIST. Overall, it is as fast as the SLR approach. When bound states are present, we use both the left and right Marchenko equations to improve the numerical stability of the algorithm. We compute a variety of examples and consider the effect of amplitude errors on the magnetization profile.

In a paper of Nielson et al. it is shown, using the linear approximation, that it might be possible to create a pair of RF-pulses, which, after summation of the unrephased signals achieve a specified transverse magnetization. Such pulses, designed using the linear approximation, show rather poor slice selectivity. Using the inverse scattering transform formalism we give an algorithm to exactly achieve a specified "summed" transverse magnetization profile. Indeed for a constant phase transverse profile, our algorithm produces infinitely many solutions.

This paper considers a variety of problems in the design of selective RF-pulses. We apply a formula of Zakharov and Manakov to directly relate the energy of an RF-envelope to the magnetization profile and certain auxiliary parameters used in the inverse scattering transform (IST) approach to RF-pulse synthesis. This allows a determination of the minimum possible energy for a given magnetization profile. We give an algorithm to construct both the minimum energy RF-envelope as well as any other envelope that produces a given magnetization profile. This includes an algorithm for solving the Gel'fand-Levitan-Marchenko equations with bound states. The SLR method is analyzed in terms of traditional scattering data, and shown to be a special (singular) case of the IST approach. RF-envelopes are computed for a variety of examples.

Purpose: This phase I trial was undertaken to determine the maximum-tolerated dose (MTD) and dose-limiting toxicities (DLTs) of the B-cell-restricted immunotoxin anti-B4-blocked ricin (anti-B4-bR) when it is administered by 7-day continuous infusion., Patients and Methods: Thirty-four patients with relapsed and refractory B-cell neoplasms (26 non-Hodgkin's lymphoma [NHL], four chronic lymphocytic leukemia [CLL], four acute lymphoblastic leukemia [ALL]) received 7-day continuous infusion anti-B4-bR. Successive cohorts of at least three patients were treated at doses of 10 to 70 micrograms/kg/d for 7 days with the dose increased by 10 micrograms/kg/d for each cohort. The initial three cohorts of patients (10, 20, and 30 micrograms/kg/d x 7 days) also received a bolus infusion of 20 micrograms/kg before beginning the continuous infusion., Results: The MTD was reached at 50 micrograms/kg/d x 7 days. The DLTs were National Cancer Institute Common Toxicity Criteria (NCI CTC) grade IV reversible increases in AST and ALT, and grade IV decreases in platelet counts. Adverse reactions included fevers, nausea, headaches, myalgias, hypoalbuminemia, dyspnea, edema, and capillary leak syndrome. Potentially therapeutic serum levels of anti-B4-bR could be sustained for 4 days in patients treated at the MTD. Two complete responses (CRs), three partial responses (PRs), and 11 transient responses (TRs) were observed., Conclusion: Anti-B4-bR can be administered safely by 7-day continuous infusion with tolerable, reversible toxicities to patients with relapsed B-cell neoplasms. Although occasional responses were seen, future trials will use anti-B4-bR in patients with lower tumor burdens to circumvent the obstacle of immunotoxin delivery to bulk disease.