Uniform Contractions Research Articles

P.58 MRI muscle segmentation in Duchenne muscular dystrophy (DMD): Stepwise region of interest (ROI) contractions to minimize fat fraction variability

MRI proton density fat fraction (MRI-PDFF) to quantify fatty infiltration is a key efficacy endpoint in DMD and other neuromuscular clinical trials. We have previously shown that fat fraction variability can be reduced by contracting the ROI to eliminate noise from non-muscle tissue due to small segmentation errors. Multiple muscles are of interest due to progressive involvement in DMD, and the ideal contraction may vary depending on the muscle size or location. We tested a strategy for optimizing the segmentation of muscles of varying sizes and depths, designed to minimize the variability of fat fraction measurements while maximizing the volume of the contracted ROI. The vastus lateralis (VL) and soleus muscle bellies were segmented by two technologists from T1-weighted images and the center 3 slices were computed for the MRI-PDFF ROI (VL: N=13; soleus: N=14). Uniform axial contractions between 0 mm to 2 mm (in steps of 0.2 mm) were applied to the ROI and the resulting segmentations were registered to PDFF maps to obtain the fat fraction at every step. The minimal detectable change (MDC) for each contracted ROI was computed from the appropriate intraclass correlation coefficient (2-way or 1-way, random-effects, single-rating, absolute agreement) and pooled standard deviation. The Dice coefficient was used to record how much of the original volume is represented at each contraction. The variability approached a minimum as the Dice coefficient neared 0.9 for both muscles. The fat fraction MDC was reduced by 75% in the VL when a 1.2 mm contraction was applied (MDC=1.0%; Dice 0.91) and by 29% in the soleus when a 1.0 mm contraction was applied (MDC=1.3%; Dice 0.90). Further contracting the muscles had minimal effects on MDC. Therefore, we conclude that an axial contraction of the central ROI that represents 90% of the segmented muscle area is optimal for maximizing the interrogated muscle volume and the ability to demonstrate efficacy of disease-modifying therapeutics.

Calculating the k-Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC

Geometric sensitivity analyses of the -eigenvalue have many applications in analyses of geometric uncertainty, calculations of differential control rod worth, and searches for critical geometry. The adjoint-weighted first-order geometric sensitivity theory is widely used and has continuously evolved with the Monte Carlo methods. However, the existing adjoint-weighted algorithm can do only uniform isotropic expansions or contractions of surfaces. The adjoint-weighted algorithm also requires computation of adjoint-weighted scattering and fission reaction rates exactly at material interfaces, which has an infinitesimal probability in reality. This paper presents an improved geometry adjoint-weighted perturbation algorithm that is incorporated into the continuous-energy Reactor Monte Carlo (RMC) code. The improvement of the adjoint-weighted algorithm is decomposed into three steps for constructing a cross-section function of geometric parameters using logical expressions, calculating the derivative of the cross-section function, and estimating the adjoint-weighted surface reaction rates. The improved algorithm can accommodate common one-parameter geometric perturbations of internal interfaces or boundary surfaces as well as those of cells as long as the perturbed cells can be described by logical expressions of spatial surface equations. The perturbation algorithm is compared with a direct difference method, the linear least-squares fitting method with central differences, for several typical geometric perturbations including translation, fixed-axis rotation, and uniform isotropic/anisotropic expansion transformations of planar, spherical, cylindrical, and conical surfaces. The differences between the two methods are not more than 3% and not more than 3 for the majority of the test examples. Even though the perturbation algorithm has higher figures of merit than the direct difference method for the majority of the test examples, there is no guarantee that the former can always be more efficient than the latter. The limitation in the efficiency of the perturbation algorithm was demonstrated by the totally reflecting light water reactor pin model.

On the intrinsic volumes of intersections of congruent balls

Let Ed denote the d-dimensional Euclidean space. The r-ball body generated by a given set in Ed is the intersection of balls of radius r centered at the points of the given set. In this paper we prove the following Blaschke–Santaló-type inequalities for r-ball bodies: for all 1≤k≤d and for any set of given volume in Ed the kth intrinsic volume of the r-ball body generated by the set becomes maximal if the set is a ball. As an application we investigate the Gromov–Klee–Wagon problem for congruent balls in Ed, which is a question on proving or disproving that if the centers of a family of N congruent balls in Ed are contracted, then the volume of the intersection does not decrease. In particular, we investigate this problem for uniform contractions, which are contractions where all the pairwise distances in the first set of centers are larger than all the pairwise distances in the second set of centers, that is, when the pairwise distances of the two sets are separated by some positive real number. Bezdek and Naszódi (2018), proved that the intrinsic volumes of the intersection of N congruent balls in Ed, d>1 increase under any uniform contraction of the center points when N≥1+2d. We give a short proof of this result using the Blaschke–Santaló-type inequalities of r-ball bodies and improve it for d≥42.

Pilot study evaluating the efficacy of exergaming for the prevention of deep venous thrombosis.

Current prophylactic protocols fail to prevent deep venous thrombosis (DVT) in a significant minority of patients, and it remains one of the leading causes of preventable death. We therefore quantified the efficacy of novel game-based exercises (exergaming) to augment femoral venous parameters relative to ankle movement and muscle flexion. Healthy volunteers were recruited to perform a series of ankle and foot exercises using a wireless foot sensor (LEGSys; BioSensics LLC, Watertown, Mass) to navigate a computer cursor sequentially on a screen to the center of 200 circular targets. A single ultrasound technician (W.A.M.) measured each patient's mean flow volume, peak flow velocity, mean flow velocity, and cross-sectional area of the right femoral vein at baseline and obtained immediate postexercise (PEX), 5-minute PEX, and 15-minute PEX measurements. Electromyography (EMG) was performed at baseline and during the exercise. Baseline demographics and medical and surgical comorbidities were also recorded. The primary end point was the difference between baseline and immediate PEX mean flow volume estimates. We secondarily explored the association of baseline characteristics and EMG measurements with femoral vein parameters. Fifteen healthy subjects (53% male; 28.1± 4.6years) completed the exergaming task within a mean of 4minutes, 2± 21seconds. Immediately after exercise, the femoral vein mean flow volume, mean velocity, and peak systolic velocity increased by 49%, 53%, and 48%, respectively (P< .02 for each). Mean flow volume and velocity remained significantly elevated 5minutes after exercise (P< .04 for each). Plantar flexion and dorsiflexion velocities and EMG frequency and intensity were not significantly correlated with PEX mean flow volume estimates (P > .05). Subgroup analysis revealed that women (P< .01) and Hispanics (P< .01) exhibited significantly slower PEX responses. Subjects with the largest improvements in mean flow volume had lower peak plantar flexion velocities (P< .01). Exergaming increases mean flow volume, mean flow velocity, and peak systolic velocity within the femoral vein by approximately 50% above baseline. Exergaming represents a novel and potentially attractive method of DVT prevention by augmenting femoral vein mean volume flow and capitalizing on biofeedback. Less forceful but more uniform contractions were found to be most effective at augmenting venous blood flow. Exergaming will require further validation in larger study bases, among patients at higher risk of DVT.

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and of reference solutions obtained using direct perturbations with central differences for the majority of test problems.

From r-dual sets to uniform contractions

Let $$\mathbb {M}^d$$ denote the d-dimensional Euclidean, hyperbolic, or spherical space. The r-dual set of a given set in $$\mathbb {M}^d$$ is the intersection of balls of radii r centered at the points of the a given set. In this paper we prove that for any set of given volume in $$\mathbb {M}^d$$ the volume of the r-dual set becomes maximal if the set is a ball. As an application we prove the following. The Kneser–Poulsen Conjecture states that if the centers of a family of N congruent balls in Euclidean d-space is contracted, then the volume of the intersection does not decrease. A uniform contraction is a contraction where all the pairwise distances in the first set of centers are larger than all the pairwise distances in the second set of centers, that is, when the pairwise distances of the two sets are separated by some positive real number. We prove a special case of the Kneser–Poulsen conjecture namely, we prove the conjecture for uniform contractions (with sufficiently large N) in $$\mathbb {M}^d$$ .

Stable disarrangement phases arising from expansion/contraction or from simple shearing of a model granular medium

A principal challenge in modeling granular media is to connect the macroscopic deformation of the aggregate of grains with the average deformation of a small number of individual grains. We used in previous research the two-scale geometry of structured deformations (g,G) and the theory of elastic bodies undergoing disarrangements (non-smooth submacroscopic geometrical changes) and dissipation to obtain, in terms of the free-energy response Ψ of the body, an algebraic tensorial consistency relation between the macroscopic deformation F=∇g and the grain deformation G, as well as an accommodation inequality detF⩾detG>0 that guarantees that the aggregate provides enough room at each point for the deformation of the grains. These two relations determine all of the disarrangement phases G corresponding to a given F. We use the term stable disarrangement phase to denote a grain deformation G that minimizes the stored energy density for the aggregate Ψ(G′) among all the disarrangement phases G′ corresponding to F. Stability in this sense is determined solely by the constitutive response function Ψ and, therefore, may be described as a notion of material stability with respect to changes in microstructure. In this article we determine for a model aggregate and for two familiar families of macroscopic deformation – simple shears and uniform expansions or contractions – all of the stable as well as all of the unstable disarrangement phases of the model aggregate. For the stable disarrangement phases, we determine the connections between aggregate deformation and grain deformation. We showed in an earlier article that each stable disarrangement phase of this model aggregate cannot support tensile tractions, and our present results confirm that no-tension property of stable disarrangement phases for the model granular medium. Consequently, the appearance of tensile tractions in the present model granular medium would entail the loss of the material stability that we consider. This loss of stability is expected to be the rule, rather than the exception, because only special boundary conditions turn out to be compatible with one or more of the stable disarrangement phases at the disposal of the material.

Delineating the inner bladder surface using uniform contractions from the outer surface under variable bladder filling conditions.

To evaluate the methods to delineate the inner bladder (IB) surface using a uniform contraction from the outer bladder (OB) surface, assuming the bladder wall (BW) is either of constant thickness, constant volume or variable volume. 14 prostate intensity-modulated radiotherapy patients with 2 planning CTs were identified. For both CTs, OB was delineated using model-based segmentation. IB was delineated manually. Then, using uniform contractions from OB, the position of IB was approximated using a: 2.5-mm contraction, patient-specific contraction, patient-specific constant wall volume method and variable wall volume method. The structures created using those strategies were compared against the manual IB contours using geometric and dosimetric indices. In the presence of variable bladder filling, use of a generic or patient-specific constant contraction resulted in a significant overestimation of IB volume (+12 and +13 cm(3), respectively; p < 0.001) that was inversely correlated with the difference in urine volume between the scans (R(2) > 0.86). Mean differences across 95% of IB surfaces were ≤2 mm for methods using either constant or variable wall volume. Mean dose-volume histogram (DVH) differences were <1 cm(3) across the whole BW DVH when using the method that assumed a variable wall volume. The variable volume BW model provided the best approximation of the IB surface position under varying filling conditions, based on geometric and dosimetric indices. Use of the equation derived in this research provides a quick and accurate method to delineate the hollow BW on serial imaging for the purposes of dose reconstruction.

Anterolateral papillary muscle ventricular tachycardia

A 61-year-old woman presented 1 year earlier with complaints of increasing dyspnea on exertion and “butterfly” palpitations in her chest. Frequent uniform premature ventricular contractions (PVCs) were seen on her 12-lead electrocardiogram (Figure 1A), with no evidence of ischemia on nuclear myocardial perfusion imaging. Twenty-four-hour Holter monitoring revealed 58,612 monomorphic ectopic ventricular beats (50.8% of all beats), with series of ventricular tachycardia up to 91 beats in duration.

Extensions of contractions and uniform contractions on dense subspaces

We give two extension theorems, which state conditions under which a (uniform) contraction from a dense subspace of a convergence approach space (approach uniform convergence space) to a convergence approach space (approach uniform convergence space) can be extended to a (uniform) contraction defined on the whole space. In order to derive these extension theorems we define and study certain diagonal axioms and the concept of uniform regularity for approach uniform convergence spaces.

Stability of nonautonomous equations and Lyapunov functions

We consider nonautonomous linear equations $x'=A(t)x$ in a Banach space, and we give a complete characterization of those admitting nonuniform exponential contractions in terms of strict Lyapunov functions. The uniform contractions are a very particular case of nonuniform exponential contractions. In addition, we establish ``inverse theorems'' that give explicitly a strict Lyapunov function for each nonuniform contraction. These functions are constructed in terms of Lyapunov norms, which transform the nonuniform behavior of the contraction into a uniform exponential behavior. Moreover, we use the characterization of nonuniformexponential contractions in terms of strict Lyapunov functions to establish in a very simple manner, in comparison with former works,the persistence of the asymptotic stability under sufficiently smalllinear and nonlinear perturbations.

Video Force Microscopy (VFM): A New Technique that Allows Cell-Level Driving Forces to Be Determined from Time-Lapse Images

For purposes of video force microscopy (VFM), the forces in the cells of an embryonic epithelium are assumed to consist of active forces, which can be mathematically resolved into equivalent forces along cell boundaries, and passive forces associated with deformation of the cytoplasm and its contained organelles and intermediate filament network, which are represented by an equivalent viscosity, mu. All triple junctions in the time-lapse images are tracked over time and finite element techniques are used to estimate the forces that must act on the passive components of each cell to deform them as observed. A mathematical inverse method is then used to determine the forces that must act along each cell edge in order to produce the net forces needed at each triple junction to drive the observed deformations. The technique has been successfully applied to multi-photon cross-sections of Drosophila embryos undergoing ventral furrow formation. There, it revealed that the ventral furrow is produced by contractions that vary smoothly with time and position in the apical surface of the presumptive mesoderm, by apical-basal contractions in the cells of this tissue and, surprisingly, by spatially more uniform basal contractions in the ectoderm. It was also able to quantify the sometimes subtle force modifications present in mutants that generate abnormal phenotypes. The indicated force alterations are consistent with known genotype-specific structural protein changes. When applied to wound healing in embryonic epithelia, it was able to quantify the forces generated in the purse string that closes the wound and the surrounding cells. It both of these contexts, VFM was able to quantify the forces that drive observed morphogenetic movements and to do so with sub-cellular spatial detail and sub-minute temporal resolution.

Robustness of Discrete Dynamics via Lyapunov Sequences

For a nonautonomous dynamics with discrete time defined by a sequence of matrices, we give a complete characterization of nonuniform exponential contractions and nonuniform exponential dichotomies in terms of Lyapunov sequences. We note that these include as very special cases uniform exponential contractions and uniform exponential dichotomies. Due to the central role played by these properties in a substantial part of the theory of dynamical systems, in particular in connection with the study of stable and unstable invariant manifolds, it is important to have available optimal characterizations that are more amenable to check whether a given dynamics has such a property. We also obtain inverse theorems that give explicitly Lyapunov sequences for a given contraction or dichotomy. As a nontrivial application, we establish the robustness under sufficiently small linear perturbations both of nonuniform exponential contractions and nonuniform exponential dichotomies. We emphasize that when compared to former work, our proof of the robustness property is much simpler.

Nonuniform exponential contractions and Lyapunov sequences

For a nonautonomous dynamics with discrete time obtained from the product of linear operators, we show that a nonuniform exponential contraction can be completely characterized in terms of what we call strict Lyapunov sequences. We note that nonuniform exponential contractions include as a very particular case the uniform exponential contractions that correspond to have a uniform asymptotic stability of the dynamics. We also obtain “inverse theorems” that give explicitly strict Lyapunov sequences for each nonuniform exponential contraction. Essentially, the Lyapunov sequences are obtained in terms of what are usually called Lyapunov norms, that is, norms with respect to which the behavior of a nonuniform exponential contraction becomes uniform. We also show how the characterization of nonuniform exponential contractions in terms of quadratic Lyapunov sequences can be used to establish in a very simple manner the persistence of the asymptotic stability of a nonuniform exponential contraction under sufficiently small linear or nonlinear perturbations. Moreover, we describe an appropriate version of our results in the context of ergodic theory showing that the existence of an eventually strict Lyapunov function implies that all Lyapunov exponents are negative almost everywhere.

Magnetic trends in Mn n nanoclusters effects of uniform relaxations on the magnetic properties

We have computed minimum energy magnetic structure configurations of Mn nanoclusters ranging from 10 to 55 atoms in size. Spin-polarized electronic properties are calculated by solving an spd tight-binding Hubbard like Hamiltonian in the unrestricted Hartree–Fock approximation by using a bulk-like parametrization. Uniform expansions and contractions are done to follow the dependence of magnetization on interatomic distance. The obtained results allow us to infer that close shell icosahedral structures are competitive with bcc-like ones for N=13, 19, 32, and 42, whereas for other N values the bcc (with and without central atom) are the ones with lowest electronic energy reproducing the general experimental behaviour.

Power series and the open set condition of Hutchinson

We give a sufficient condition for a uniformly contracting self-similar set to have the separation property. For uniform contractions of the real line: fi(x) = cx + ai, i = 1, 2, ..., r, with 0 < c < 1 and 0 = a1 < a2 < ⋅⋅⋅ < ar = 1 − c < 1, we prove that the open set condition of Hutchinson holds if q(c) ≠ 0 for all power series q(x) = ∑∞k=0dkxk, where dk = ai − aj, for some i, j = 1, 2, ..., r, for all k = 0, 1, 2, ..., and d0 ≠ 0. Finally, we give two examples.

On the multitude of monoidal closed structures on [formula omitted

In this note, we prove that all compact Hausdorff topological spaces are exponential objects in the category UAP of uniform approach spaces and contractions as introduced in R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, 1997. As a consequence, we show that UAP admits at least as many monoidal closed structures as there are infinite cardinals. We also prove that under the assumption that no measurable cardinals exist, there exists a proper conglomerate of these monoidal closed structures on UAP .

The Cartesian Closed Topological Hull of the Category of Approach Uniform Spaces

The category AUnif of approach uniform spaces and uniform contractions properly combines uniform spaces and extended pseudo-metric spaces but (like Unif) lacks convenience, such as cartesian closedness. This paper therefore considers its cartesian closed topological hull, which is first described as a subcategory of SAULim, the category of semi-approach uniform limit spaces and uniform contractions. This hull is then also given a description inside the topological universe hull of AUnif and is shown to be a reasonable generalization of the corresponding hull of Unif. Furthermore, some referencing notes are provided with respect to similar results that can be obtained when starting from qAUnif (where symmetry assumptions are omitted).

Some Cartesian Closed Topological Constructs in the Category of Semi-Approach Uniform Limit Spaces

We first introduce a "family" of cartesian closed topological subconstructs in SAULim, the category of semi-approach uniform limit spaces and uniform contractions. We then provide some examples to illustrate a linkage to notions of "regularity".

Ventricular Fibrillation During Anesthetic Induction in a Child With Undiagnosed Mitral Valve Prolapse

Ventricular Fibrillation During Anesthetic Induction in a Child With Undiagnosed Mitral Valve Prolapse