Progressive Contractions Research Articles

Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions

We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply the method of progressive contractions, which belongs to T.A. Burton, to Caputo fractional-order differential equation, including multiple variable delays, which has not yet appeared in the relevant literature by this time. The significant point of the method of progressive contractions consists of a very flexible idea to discuss the uniqueness of solutions for various mathematical models. Lastly, we provide two examples to demonstrate how this paper’s primary outcome can be applied.

Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions

In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature.

Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations

The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.

Functional differential equations with maxima, via step by step contraction principle

T. A. Burton presented in some examples of integral equations a notion of progressive contractions on C([a,\infty \lbrack). In 2019, I. A. Rus formalized this notion (I. A. Rus, Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle, Advances in the Theory of Nonlinear Analysis and its Applications, 3 (2019) No. 3, 111–120), put “step by step” instead of “progressive” in this notion, and give some variant of step by step contraction principle in the case of operators with Volterra property on C([a,b],\mathbb{B)} and C([a,\infty \lbrack,\mathbb{B}) where \mathbb{B} is a Banach space. In this paper we use the abstract result given by I. A. Rus, to study some classes of functional differential equations with maxima.

Amniotic fluid lactate level as a diagnostic tool for prolonged labour.

Prolonged labour can lead to postpartum complications and adverse outcomes for both mother and baby. Measurable parameters can help in the active management of labour, timely diagnosis of dystocia and in the choice of the method of delivery. Progressive uterine contractions are necessary to complete labour successfully. Myometrial fatigue during prolonged labour causes a change from aerobic to anaerobic metabolism, resulting in an accumulation of intramuscular lactic acid and probably a subsequent increase in amniotic fluid lactate concentration. High amniotic fluid lactate level has been associated with ineffective uterine contractions leading to labour arrest. A considerable number of studies conducted so far indicate that the level of lactate in amniotic fluid may be a new non-invasive diagnostic tool for early prediction of prolonged labour and the need for immediate obstetric intervention. Low amniotic fluid lactate level may facilitate a decision to continue vaginal labour by oxytocin augmentation. A high level of amniotic fluid lactate is associated with surgical obstetric procedures. Measuring amniotic fluid lactate level might simplify the patient’s allocation to a group, which will benefit from the administration of oxytocin and to a group that will not benefit from further prolongation of labour. This study aimed to briefly review current knowledge on amniotic fluid lactate concentrations measured using standard biochemical methods during the first stage of labour following normal pregnancy, as a possible diagnostic tool for prolonged labour. For this purpose, PubMed, EMBASE, Medline (1990 to July 2020) trials register and reference lists of relevant articles were searched.

Anaesthesia and orphan disease: A patient with neuromyotonia undergoing single lung ventilation.

Anaesthesia and orphan disease: A patient with neuromyotonia undergoing single lung ventilation.

On the Burton method of progressive contractions for Volterra integral equations

On the Burton method of progressive contractions for Volterra integral equations

Central Activation Ratio Is a Reliable Measure for Gluteal Neuromuscular Function.

Central activation ratio (CAR) is a common outcome measure used to quantify gross neuromuscular function of the quadriceps using the superimposed burst technique, yet this outcome measure has not been validated in the gluteal musculature. To quantify gluteus medius (GMed) and gluteus maximus (GMax) CAR in a healthy population and evaluate its validity and reliability over a 1-week period. Descriptive. Laboratory. A total of 20 healthy participants (9 males and 11 females; age 22.2 [1.4]y, height 173.4 [11.1]cm, mass 84.8 [25.8]kg) were enrolled in this study. Participants were assessed at 2 sessions, separated by 1 week. Progressive electrical stimuli (25%, 50%, 75%, and 100%) were delivered to the GMed and GMax at rest, and 100% stimuli were delivered during progressive hip abduction and extension contractions (25%, 50%, 75%, and 100% maximal voluntary isometric contraction). GMed and GMax CAR, and hip abduction and hip extension maximal voluntary isometric contraction torque. Line of best fit and coefficient of determination (r2) were used to assess the relationship between torque output and CAR at varying levels of stimuli. Intraclass correlation coefficients, ICCs(3,k), were used to assess the between-session reliability. GMed CAR was 96.1% (3.4%) and 96.6% (3.2%), on visits 1 and 2, respectively, whereas GMax CAR was 86.5% (7.5%) and 87.2% (10.7%) over the 2 sessions. A third-order polynomial demonstrated the best line of fit between varying superimposed burst intensities at rest for both GMed (r2 = .156) and GMax (r2 = .602). Linear relationships were observed in the CAR during progressive contractions with a maximal superimposed burst, GMed (r2 = .409) and GMax (r2 = .639). Between-session reliability was excellent for GMed CAR, ICC(3,k) = .911, and moderate for GMax CAR, ICC(3,k) = .704. CAR appears to be an acceptable measure of GMed and GMax neuromuscular function in healthy individuals. Gluteal CAR measurements are reliable measures over a 1-week test period.

Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle

Following the idea of T.A. Burton, of progressive contractions, presented in some examples (T.A. Burton, \emph{A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions}, Fixed Point Theory, 20 (2019), No. 1, 107-113) and the forward step method (I.A. Rus, \emph{Abstract models of step method which imply the convergence of successive approximations}, Fixed Point Theory, 9 (2008), No. 1, 293-307), in this paper we give some variants of contraction principle in the case of operators with Volterra property. The basic ingredient in the theory of step by step contraction is $G$-contraction (I.A. Rus, \emph{Cyclic representations and fixed points}, Ann. T. Popoviciu Seminar of Functional Eq. Approxim. Convexity, 3 (2005), 171-178). The relevance of step by step contraction principle is illustrated by applications in the theory of differential and integral equations.

A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions

A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions

Progressive contractions, product contractions, quadratic integro-differential equations

Fixed point theory has been used very successfully to obtain properties of solutions of integral and integro-differential equations of the form $ x(t) = g(t) +\int^t_0 A(t-s) v(t, s, x(s))ds $ because under general conditions the integral term may map bounded sets of continuous functions into equi-continuous sets. But quadratic integral equations have a coefficient of the integral terms of the form $ f(t, x(t))\int^t_0 A(t-s)v(t, s, x(s))ds $ which destroys the compactness of the map. Investigators have resorted to deep solutions often involving measures of non-compactness and Darbo's fixed point theorem. In an effort to obtain some elementary approaches, in this paper we develop an apparently new technique by showing that by using progressive contractions we can show conditions under which the product of two contractions is a contraction. We focus on integro-differential equations and use direct fixed point mappings which convert Lipschitz conditions into progressive contraction conditions.

Progressive contractions, measures of non-compactness and quadratic integral equations

Progressive contractions, measures of non-compactness and quadratic integral equations

Global existence of solutions of integral equations with delay: progressive contractions

Global existence of solutions of integral equations with delay: progressive contractions

Activation Patterns In Muscles With Different Fiber Ratios

Background: Surface electromyography (sEMG) can be used to provide real-time muscle performance data and desirable feedback to patients and clinicians in rehabilitation or sports injury settings. However, a comparison of electrical activity patterns of muscles with different fiber type compositions has not been conducted, and the relationship between electrical outputs with muscles of different sizes is relatively unexplored. PURPOSE: This study was designed to evaluate and compare the recruitment and activation patterns of large and small muscles with different fiber type combinations (proportion of type I and II fibers) during isometric contractions using sEMG. METHODS: Participants (n=10, mean age: 24.4 ± 2.5 years) with no history of musculoskeletal injuries or cardiovascular problems were asked to perform progressive isometric contractions at 25%, 50%, 75%, and 100% of their maximal voluntary contraction (MVC) level. sEMG data was collected from the abductor pollicis brevis (APB) of the thumb and vastus lateralis (VL) of the upper leg. Raw force output, mean integrated EMG (iEMG), normalized electrical activity output, and median frequency were compared between these two muscles and four contraction levels. RESULTS: APB, which consists of a higher percentage of Type I fibers, generated more electrical activity (mean iEMG: APB = 1187.57 ± 117.41 uV·s, VL = 175.93 ± 18.00 uV·s, p<0.001), but less force output at maximal contraction (p<0.001). Normalized electrical activity showed significantly different recruitment patterns between the two muscles (p<0.001), and the power spectra indicated a higher median frequency for APB (mean MDF: APB = 100.45 ± 3.30 Hz, VL = 77.24 ± 1.22 Hz, p<0.001). CONCLUSION: sEMG has been used as a biofeedback tool to help both patients and clinicians in documenting muscle recovery following sports injuries. However, it is important to realize there are muscle differences based on size and type of fiber. Changes in electrical activity used as an indication for strength improvement cannot be generalized across muscles. Smaller, predominately Type I muscles may require a higher muscle performance target during rehabilitation. Supported by NSF EFRI 1332329.

Adult Colonic Intussusception Mimicking Renal Colic

Intestinal intussusception is defined as the telescoping of one segment of bowel into the immediately distal segment. The proximal segment, or intussusceptum, is constricted by peristalsis and is invaginated by progressive smooth muscle contractions into the distal segment, or intussuscipiens. The condition is rare in adults, accounting for about 1% of patients with bowel obstruction; to the best of our knowledge, it has rarely been considered in the context of differential diagnosis of flank pain (1,2).

Is Functional MR Imaging of Skeletal Muscle the Ultimate Tool for Assessment of Peripheral Arterial Occlusive Disease?

HomeRadiologyVol. 241, No. 2 Next Science to PracticeIs Functional MR Imaging of Skeletal Muscle the Ultimate Tool for Assessment of Peripheral Arterial Occlusive Disease?Bruce B. ForsterBruce B. ForsterAuthor AffiliationsDepartment of Radiology, University of British Columbia Hospital, 2211 Wesbrook Mall, Vancouver, BC, Canada V6T 2B5, [email protected]Bruce B. ForsterPublished Online:Nov 1 2006https://doi.org/10.1148/radiol.2412060952MoreSectionsFull textPDF ToolsImage ViewerAdd to favoritesCiteTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked In References1 Forster BB, Johnstone RD, Shannon HM, et al. Technical innovation: quantification of hemodynamic improvement after superficial femoral artery angioplasty by cine phase-contrast MR angiography. AJR Am J Roentgenol 1999;173:1564–1566. Crossref, Medline, Google Scholar2 Ledermann HP, Heidecker HG, Schulte AC, et al. Calf muscles imaged at BOLD MR: correlation with TcPo2 and flowmetry measurements during ischemia and reactive hyperemia—initial experience. Radiology 2006;241(2):477–484. Link, Google Scholar3 Lutz AM, Weisthaupt D, Amann-Vesti BR, et al. Assessment of skeletal muscle perfusion by contrast medium first-pass MRI: technical feasibility and preliminary experience in healthy volunteers. J Magn Reson Imaging 2004;20:111–121. Crossref, Medline, Google Scholar4 Wigmore DM, Damon BM, Pober DM, Kent-Braun JA. MRI measure of perfusion-related changes in human skeletal muscle during progressive contractions. J Appl Physiol 2004;97:2385–2394. Crossref, Medline, Google Scholar5 Lebon V, Brillault-Salvat C, Bloch G, Leroy-Willig A, Carlier PG. Evidence of muscle BOLD effect revealed by simultaneous interleaved gradient-echo NMRI and myoglobin NMRS during leg ischemia. Magn Reson Med 1998;40:551–558. Crossref, Medline, Google ScholarArticle HistoryPublished in print: 2006 FiguresReferencesRelatedDetailsCited ByNuclear Medicine Communications, Vol. 29, No. 9Magnetic Resonance Imaging Clinics of North America, Vol. 15, No. 3European Radiology, Vol. 17, No. 10Recommended Articles Exercise Oximetry and Exercise Near-infrared Spectroscopy to Assess Peripheral Artery DiseaseRadioGraphics2017Volume: 37Issue: 1pp. 363-364MR Imaging of Muscle Trauma: Anatomy, Biomechanics, Pathophysiology, and Imaging AppearanceRadioGraphics2017Volume: 38Issue: 1pp. 124-148Acute Effects of Electronic Cigarette Aerosol Inhalation on Vascular Function Detected at Quantitative MRIRadiology2019Volume: 293Issue: 1pp. 97-106Use of Caval Subtraction 2D Phase-Contrast MR Imaging to Measure Total Liver and Hepatic Arterial Blood Flow: Preclinical Validation and Initial Clinical TranslationRadiology2016Volume: 280Issue: 3pp. 916-923Noninvasive Physiologic Vascular Studies: A Guide to Diagnosing Peripheral Arterial DiseaseRadioGraphics2016Volume: 37Issue: 1pp. 346-357See More RSNA Education Exhibits State-of-the-art Noninvasive Imaging of Peripheral Arterial Disease of Lower ExtremitiesDigital Posters2020Painful if Provocated: The Role of Provocative Computed Tomography Angiography Protocol in the Workup and Surgical Management of Functional Popliteal Entrapment Syndrome Digital Posters2020Collateral FlowDigital Posters2020 RSNA Case Collection Renal Transplant Vein Thrombosis RSNA Case Collection2020Ovarian TorsionRSNA Case Collection2020Acute Aortoiliac Occlusion RSNA Case Collection2021 Vol. 241, No. 2 Metrics Downloaded 83 times Altmetric Score PDF download

Unilateral pallidotomy for hemidystonia

Hemidystonia is a clinical presentation of many pathological conditions that can affect the basal ganglia. It is usually a refractory condition to current medical treatment. Recently, stereotactic procedures such as radiofrequency lesioning or deep brain stimulation provided hope for patients with dystonia; we are reporting the clinical outcome of a patient with hemidystonia treated with unilateral pallidotomy. A 15-year-old boy with no family history of movement disorders and normal perinatal history is presented. He started to have progressive dystonic contractions in the right hand and extended to involve both the upper and lower extremities in the right side over a period of 3 years. He was subjected to a left-sided posteroventral pallidotomy. Postoperatively, his hemidystonia improved over a period of a few weeks. The Unified Dystonia Rating Scale improved by 84%. He maintained the improvements for the 2-year postoperative follow-up period. No complications were encountered. Clinical presentation, surgical techniques, and surgical results are presented. In conclusion, hemidystonia may significantly respond to a contralateral posteroventral pallidotomy.

Missense mutation in theN-acetylglucosamine-1-phosphotransferase gene (GNPTA) in a patient with mucolipidosis II induces changes in the size and cellular distribution of GNPTG

Mucolipidosis type II (ML II; I-cell disease) and mucolipidosis III (ML III; pseudo Hurler polydystrophy) are autosomal recessively inherited disorders caused by a defective N-acetylglucosamine 1-phosphotransferase (phosphotransferase). The formation of mannose 6-phosphate markers in soluble lysosomal enzymes is impeded leading to their increased excretion into the serum, to cellular deficiency of multiple hydrolases, and lysosomal storage of non-digested material. Phosphotransferase deficiency is caused by mutations in GNPTA and GNPTG encoding phosphotransferase subunits. Here we report on an adolescent with progressive joint contractions and other signs of mucolipidosis II who survived to the age of 14 years. Impaired trafficking of lysosomal enzymes cathepsin D and -hexosaminidase in metabolically labeled fibroblasts was documented. Mutations in the GNPTG gene and alterations in the GNPTG mRNA level were not detected. A different electrophoretic mobility of the 97 kDa GNPTG dimer suggested posttranslational modification abrogating the compartmentalization of GNPTG in the Golgi apparatus. A nucleotide substitution in the GNPTA gene (c.3707A>T) was identified altering the predicted C-terminal transmembrane anchor of the phosphotransferase subunit. The data demonstrate that defective GNPTA not only impairs lysosomal enzyme targeting but also the availability of intact GNPTG required for phosphotransferase activity and assembly of subunits.

MRI measures of perfusion-related changes in human skeletal muscle during progressive contractions.

Although skeletal muscle perfusion is fundamental to proper muscle function, in vivo measurements are typically limited to those of limb or arterial blood flow, rather than flow within the muscle bed itself. We present a noninvasive functional MRI (fMRI) technique for measuring perfusion-related signal intensity (SI) changes in human skeletal muscle during and after contractions and demonstrate its application to the question of occlusion during a range of contraction intensities. Eight healthy men (aged 20-31 yr) performed a series of isometric ankle dorsiflexor contractions from 10 to 100% maximal voluntary contraction. Axial gradient-echo echo-planar images (repetition time = 500 ms, echo time = 18.6 ms) were acquired continuously before, during, and following each 10-s contraction, with 4.5-min rest between contractions. Average SI in the dorsiflexor muscles was calculated for all 240 images in each contraction series. Postcontraction hyperemia for each force level was determined as peak change in SI after contraction, which was then scaled to that obtained following a 5-min cuff occlusion of the thigh (i.e., maximal hyperemia). A subset of subjects (n = 4) performed parallel studies using venous occlusion plethysmography to measure limb blood flow. Hyperemia measured by fMRI and plethysmography demonstrated good agreement. Postcontraction hyperemia measured by fMRI scaled with contraction intensity up to approximately 60% maximal voluntary contraction. fMRI provides a noninvasive means of quantifying perfusion-related changes during and following skeletal muscle contractions in humans. Temporal changes in perfusion can be observed, as can the heterogeneity of perfusion across the muscle bed.

Hirschsprung's disease: a review.

Because it is now more than 50 years since both the discovery of the cause and a treatment for Hirschsprung’s disease, it seems appropriate to assess outcomes for those unfortunate children who have this previously lethal disease. In 1948, the discovery of the cause of this disease was based on a series of clinical observations indicating that there was a defective segment of distal colon producing a partial bowel obstruction.1 Peristaltic tracings of the dilated proximal colon recorded progressive contractions; however, this peristaltic wave did not enter the more distal narrow segment. This was suggestive evidence of a physiologic defect in that distal segment. Therefore, removing this segment would prove the validity of these observations. An operative technique was devised and tested in the laboratory, and when it proved feasible, a patient’s distal narrow segment was removed and his intestinal continuity was restored with a pull-down and reanastomosis. Soon thereafter, the patient’s gastrointestinal system began to function normally. We concluded that this operation provided experimental evidence that proved our assumptions were correct.2 It is possible to suspect the presence of Hirschsprung’s disease in the newborn by clinical criteria if the infant does not pass meconium in the first 48 hours or by the presence of vomiting and abdominal distention.3 In the older child, clinical criteria for diagnosis includes a history of severe constipation from birth, failure to thrive, abdominal distension and often an empty rectal ampulla on rectal examination. The disease occurs about once in 5000 live births.4 The incidence of this disease being transmitted to offspring is about 3%. In specific instances in females where the length of the aganglionic lesion is extensive, the percentage increases.4 As part of our investigation into the cause of this disease, a radiographic enema using a small amount …