Inter-vertebral rotational deformity after endoscopic anterior scoliosis correction may contribute to rib hump recurrence after two years

Introduction. Endoscopic anterior scoliosis correction has been employed recently as a less invasive and level-sparing approach compared with open surgical techniques. We have previously demonstrated that during the two-year post-operative period, there was a mean loss of rib hump correction by 1.4 degrees. The purpose of this study was to determine whether intra- or inter-vertebral rotational deformity during the post-operative period could account for the loss of rib hump correction. Materials and Methods. Ten consecutive patients diagnosed with adolescent idiopathic scoliosis were treated with an endoscopic anterior scoliosis correction. Low-dose computed tomography scans of the instrumented segment were obtained post-operatively at 6 and 24 months following institutional ethical approval and patient consent. Three-dimensional multi-planar reconstruction software (Osirix Imaging Software, Pixmeo, Switzerland) was used to create axial slices of each vertebral level, corrected in both coronal and sagittal planes. Vertebral rotation was measured using Ho’s method for every available superior and inferior endplate at 6 and 24 months. Positive changes in rotation indicate a reduction and improvement in vertebral rotation. Intra-observer variability analysis was performed on a subgroup of images. Results. Mean change in rotation for vertebral endplates between 6 and 24 months post-operatively was -0.26˚ (range -3.5 to 4.9˚) within the fused segment and +1.26˚ (range -7.2 to 15.1˚) for the un-instrumented vertebrae above and below the fusion. Mean change in clinically measured rib hump for the 10 patients was -1.6˚ (range -3 to 0˚). The small change in rotation within the fused segment accounts for only 16.5% of the change in rib hump measured clinically whereas the change in rotation between the un-instrumented vertebrae above and below the construct accounts for 78.8%. There was no clear association between rib hump recurrence and intra- or inter-vertebral rotation in individual patients. Intra-rater variability was ± 3˚. Conclusions. Intra- and inter-vertebral rotation continues post-operatively both within the instrumented and un-instrumented segments of the immature spine. Rotation between the un-instrumented vertebrae above and below the fusion was +1.26˚, suggesting that the un-instrumented vertebrae improved and de-rotated slightly after surgery. This may play a role in rib hump recurrence, however this remains clinically insignificant.

Familial recurrence risks for multiple sclerosis in Australia

BACKGROUND: Genetic susceptibility to multiple sclerosis (MS) has been recognised for many years. Considerable data exist from the northern hemisphere regarding the familial recurrence risks for MS, but there are few data for the southern hemisphere and regions at lower latitude such as Australia. To investigate the interaction between environmental and genetic causative factors in MS, the authors undertook a familial recurrence risk study in three latitudinally distinct regions of Australia. METHODS: Immediate and extended family pedigrees have been collected for three cohorts of people with MS in Queensland, Victoria and Tasmania spanning 15° of latitude. Age of onset data from Queensland were utilised to estimate age-adjusted recurrence rates. RESULTS: Recurrence risks in Australia were significantly lower than in studies from northern hemisphere populations. The age-adjusted risk for siblings across Australia was 2.13% compared with 3.5% for the northern hemisphere. A similar pattern was seen for other relatives. The risks to relatives were proportional to the population risks for each site, and hence the sibling recurrence-risk ratio (λ(s)) was similar across all sites. DISCUSSION: The familial recurrence risk of MS in Australia is lower than in previously reported studies. This is directly related to the lower population prevalence of MS. The overall genetic susceptibility in Australia as measured by the λ(s) is similar to the northern hemisphere, suggesting that the difference in population risk is explained largely by environmental factors rather than by genetic admixture.

Risk factors for ocular surface squamous neoplasia recurrence after treatment with topical mitomycin C and interferon alpha-2b

Purpose To determine the rate of recurrence and associated risk factors following the use of mitomycin C (MMC) and/or interferon alpha-2b (IFN) for management of non-invasive ocular surface squamous neoplasia (OSSN). Design Retrospective non-comparative interventional case series. Methods Clinical practice setting of 135 patients treated consecutively with topical MMC (0.4 mg/mL) and/or IFN (1 million units/mL) for OSSN observed for clinical recurrence. Results Clinical recurrences were diagnosed in 19 of 135 (14.1%) eyes following topical treatment. The mean time to recurrence was 17.2 months (range 4 - 61) with 14 (73.7%) recurring within a two year period. There was no greater risk of recurrence identified for variables including lesion size, lesion location, gender, age, treatment type or duration. Post-hoc log-Rank pairwise comparisons revealed that lesions initially treated using surgery alone had significantly reduced time to recurrence (21.1 ± 5.6 months) compared to previous topical treatment with MMC (with or without surgery) (29.6 ± 4.7 months) (p = 0.04) and primary OSSN (23.2 ± 1.8 months) (p = 0.09). Conclusions Topical MMC and IFN are an effective treatment modality for a wide range of non-invasive OSSN. Topical therapy avoids the morbidity of excisional surgery with equivalent or reduced recurrence rates and should be considered as primary therapy.

Venous leg ulcer recurrence : deciphering long term patient adherence to preventive treatments and activities

To better understand long term adherence to self-care activities to prevent the recurrence of venous leg ulcers, participants (n=80) were recruited to a prospective longitudinal study after experiencing healing of a venous leg ulcer. Data on demographics, health, psychosocial measures and adherence to prevention strategies (compression therapy, leg elevation and lower leg exercise) were collected every three months for one year after healing. Multivariable regression modelling was used to identify the factors that were independently associated with adherence. Over the year, a significant decline in adherence to all three strategies was observed, predominantly between 6–12 months after healing (p<0.01). Several factors were associated with adherence to more than one preventive activity. Regular follow-up care and a history of multiple previous ulcers were related to improved adherence (p<0.05), while scoring at higher risk for depression and restricted mobility were related to decreasing adherence over time (p<0.05). Patients with osteoarthritis had significantly reduced adherence to compression hosiery (p=0.026). These results provide information to assist care providers plan strategies for prevention of recurrent venous leg ulcers; and suggest a need for regular follow-up care which addresses both the physical and mental health of this population.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Development of an evidence-based symptom checklist for symptoms of recurrence in women with endometrial cancer

Objective Women treated for endometrial cancer currently commonly attend clinic-based follow-up examinations for up to five years. This is based on little evidence and alternative models need to be investigated. This study aimed to identify currently available symptom checklists, determine the comprehensiveness of identified checklists, and generate an updated list of symptoms potentially associated with a recurrence of endometrial cancer for future testing within a prospective study. Methods/materials We conducted a systematic review of the literature extracting; routine follow-up schedules; proportion of patients with symptomatic or asymptomatic recurrence; symptoms of recurrence; prevalence of these symptoms at recurrence. Results Overall, three previous checklists, and 12 retrospective studies were identified meeting the selection criteria. The average rate of recurrence across the studies was 13% (range 3%-19%). The proportion of patients identified with a symptomatic recurrence varied widely (overall average 67%;range 41% to 91%). The most commonly reported symptoms were vaginal bleeding (25%), pain [not further described] (16%) and abdominal pain and/or discomfort and swelling (15%) which combined, represented 56% of the total reported symptoms. The three previous checklists listed 14 and this review identified an additional 24 symptoms (e.g. vaginal discharge, leg pain, constipation, headache and self-detected mass) not previously identified. Conclusion The newly developed symptom checklist expands previous ones, by an additional 24 symptoms. It will be used in a prospective cohort study to assess whether it is sensitive and specific enough to identify recurrence compared to current standard follow-up examinations.

Identifying risk factors and protective factors for venous leg ulcer recurrence using a theoretical approach : a longitudinal study

Background The high recurrence rate of chronic venous leg ulcers has a significant impact on an individual’s quality of life and healthcare costs. Objectives This study aimed to identify risk and protective factors for recurrence of venous leg ulcers using a theoretical approach by applying a framework of self and family management of chronic conditions to underpin the study. Design Secondary analysis of combined data collected from three previous prospective longitudinal studies. Setting The contributing studies’ participants were recruited from two metropolitan hospital outpatient wound clinics and three community-based wound clinics. Participants Data were available on a sample of 250 adults, with a leg ulcer of primarily venous aetiology, who were followed after ulcer healing for a median follow-up time of 17 months after healing (range: 3 to 36 months). Methods Data from the three studies were combined. The original participant data were collected through medical records and self-reported questionnaires upon healing and every 3 months thereafter. A Cox proportion-hazards regression analysis was undertaken to determine the influential factors on leg ulcer recurrence based on the proposed conceptual framework. Results The median time to recurrence was 42 weeks (95% CI 31.9–52.0), with an incidence of 22% (54 of 250 participants) recurrence within three months of healing, 39% (91 of 235 participants) for those who were followed for six months, 57% (111 of 193) by 12 months, 73% (53 of 72) by two years and 78% (41 of 52) of those who were followed up for three years. A Cox proportional-hazards regression model revealed that the risk factors for recurrence included a history of deep vein thrombosis (HR 1.7, 95% CI 1.07–2.67, p=0.024), history of multiple previous leg ulcers (HR 4.4, 95% CI 1.84–10.5, p=0.001), and longer duration (in weeks) of previous ulcer (HR 1.01, 95% CI 1.003–1.01, p<0.001); while the protective factors were elevating legs for at least 30 minutes per day (HR 0.33, 95% CI 0.19–0.56, p<0.001), higher levels of self-efficacy (HR 0.95, 95% CI 0.92–0.99, p=0.016), and walking around for at least three hours/day (HR 0.66, 95% CI 0.44–0.98, p=0.040). Conclusions Results from this study provide a comprehensive examination of risk and protective factors associated with leg ulcer recurrence based on the chronic disease self and family management framework. These results in turn provide essential steps towards developing and testing interventions to promote optimal prevention strategies for venous leg ulcer recurrence.

Recurrence risk modelling of the genetic susceptibility to ankylosing spondylitis

Objectives - It has long been suspected that susceptibility to ankylosing spondylitis (AS) is influenced by genes lying distant to the major histocompatibility complex. This study compares genetic models of AS to assess the most likely mode of inheritance, using recurrence risk ratios in relatives of affected subjects. Methods - Recurrence risk ratios in different degrees of relatives were determined using published data from studies specifically designed to address the question. The methods of Risch were used to determine the expected recurrence risk ratios in different degrees of relatives, assuming equal first degree relative recurrence risk between models. Goodness of fit was determined by χ2 comparison of the expected number of affected subjects with the observed number, given equal numbers of each type of relative studied. Results - The recurrence risks in different degrees of relatives were: monozygotic (MZ) twins 63% (17/27), first degree relatives 8.2% (441/5390), second degree relatives 1.0% (8/834), and third degree relatives 0.7% (7/997). Parent-child recurrence risk (7.9%, 37/466) was not significantly different from the sibling recurrence risk (8.2%, 404/4924), excluding a significant dominance genetic component to susceptibility. Poor fitting models included single gene, genetic heterogeneity, additive, two locus multiplicative, and one locus and residual polygenes (χ2 > 32 (two degrees of freedom), p < 10-6 for all models). The best fitting model studied was a five locus model with multiplicative interaction between loci (χ2 = 1.4 (two degrees of freedom), p = 0.5). Oligogenic multiplicative models were the best fitting over a range of population prevalences and first degree recurrence risk rates. Conclusions - This study suggests that of the genetic models tested, the most likely model operating in AS is an oligogenic model with predominantly multiplicative interaction between loci.

Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.