ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive diviso

Patency of direct revascularisation of the hypogastric arteries in patients with aortoiliac occlusive disease

OBJECTIVES: Various indications for internal iliac artery (IIA) revascularisation have been reported. Revascularisations for gluteal ischaemia and buttock claudication remain controversial and uncommon. The objective of the study was to assess the patency of direct conventional revascularisations (CRs) of the IIA in patients with aortoiliac occlusive disease because few studies have focussed on this specific topic. MATERIALS AND METHODS: The charts of all patients who underwent CR of the IIA, between August 2000 and January 2009, were retrospectively reviewed. We recorded for each patient preoperative vascular work-up. All patients were tested for patency on January 2009. A computed tomography (CT) scan was requested if the duplex scan casts any doubt with regard to patency. If non-patent, the last date for confirmed patency was kept for the analysis. Functional outcomes at the proximal level were also collected. RESULTS: We studied 40 patients with occlusive disease. Buttock claudication was observed in 27 patients (66%), including eight (20%) in whom these symptoms were isolated. The 13 other patients had distal claudication or rest pain and documented proximal ischaemia, justifying the IIA revascularisations. We performed 44 conventional direct revascularisations of the IIA concomitant to aorto- or iliofemoral bypasses in these patients. The overall postoperative patency rate was 89%. Five early occlusions of the IIA remained asymptomatic. The median duration of follow-up was 39 months (3-86 months). The survival rate was 95% at 1 year and 86% at 5 years. The primary patency rate of the IIA was 89% at 1 year and 72.5% at 5 years. Buttock claudication disappeared in 23 of the 27 patients (85%), who were symptomatic at the proximal level prior to surgery. CONCLUSION: Direct IIA concomitant revascularisation has an acceptable patency rate in patients undergoing aorto- or iliofemoral bypasses for occlusive disease. When feasible, this technique appears to be safe for the treatment and prevention of buttock claudication

Functional outcome of hypogastric revascularisation for prevention of buttock claudication in patients with peripheral artery occlusive disease

We have defined proximal lower limb ischaemia as a decrease in Exercise-transcutaneous oxygen pressure (TcPO(2)) lower than minus 15mmHg at the buttock level in patients with peripheral artery occlusive disease. The purpose of this study was to objectively evaluate the benefits of direct versus indirect revascularisation of internal iliac arteries (IIAs) for prevention of buttock claudication in this population. We retrospectively reviewed the charts of proximal ischaemia patients who underwent revascularisation and both preoperative and postoperative stress TcPO(2) testing. Revascularisation procedures were classified as either direct revascularisation, including percutaneous transluminal angioplasty and internal iliac artery bypass, resulting in a direct inflow in a patent IIA (group 1) or indirect revascularisation, including aortobifemoral bypass and recanalisation of the femoral junction on the ischaemic side, resulting in indirect inflow from collateral arteries in the hypogastric territory (group 2). Patency was checked 3 months after revascularisation in all cases. Treadmill exercise stress tests were performed before and after revascularisation using the same protocol designed to assess pain, determine maximum walking distance (MWD) and measure TcPO(2) during exercise. In addition, ankle-brachial indices (ABIs) were calculated. Between May 2001 and March 2008, a total of 93 patients with objectively documented proximal ischaemia underwent 145 proximal revascularisation procedures using conventional open techniques in 109 cases and endovascular techniques in 36. Direct revascularisation was performed on 50 limbs (35%) (group 1) and indirect revascularisation on 95 limbs (65%) (group 2). The mean interval between revascularisation and stress testing was 60+/-74 days preoperatively and 149+/-142 days postoperatively. No postoperative thrombosis was observed. Buttock claudication following revascularisation was more common in group 2 (p<0.001). No difference was observed between the two groups with regard to improvement in MWD (365 / 294 m) and ABI (0.20/0.22). Disappearance of proximal ischaemia was more common after direct revascularisation (p<0.01). The extent of lesions graded according to the TASC II classification appeared not to be predictive of improvement in assessment criteria following revascularisation. Conversely, patency of the superficial femoral artery was correlated with improvement (p<0.01). This study indicates that direct revascularisation, if feasible, provides the best functional outcome for prevention of buttock claudication

Relevance of laser Doppler and laser speckle techniques for assessing vascular function: state of the art and future trends.

In clinical and research applications, the assessment of vascular function has become of major importance to evaluate and follow the evolution of cardiovascular pathologies, diabetes, hypertension, or foot ulcers. Therefore, the development of engineering methodologies able to monitor noninvasively blood vessel activities-such as endothelial function-is a significant and emerging challenge. Laser-based techniques have been used to respond-as much as possible-to these requirements. Among them, laser Doppler flowmetry (LDF) and laser Doppler imaging (LDI) were proposed a few decades ago. They provide interesting vascular information but possess drawbacks that prevent an easy use in some clinical situations. Recently, the laser speckle contrast imaging (LSCI) technique, a noninvasive camera-based tool, was commercialized and overcomes some of the LDF and LDI weaknesses. Our paper describes how-using engineering methodologies-LDF, LDI, and LSCI can meet the challenging clinician needs in assessing vascular function, with a special focus on the state of the art and future trends

Complexity quantification of signals from the heart, the macrocirculation and the microcirculation through a multiscale entropy analysis

Quantifying and modelling the cardiovascular system (CVS) represent a challenge to improve our understanding of the CVS. To describe and quantify the CVS, several physiological signals have been analyzed through various signal processing methods. Recently, a quantitative descriptor – the multiscale entropy (MSE) – has been proposed to quantify time series complexity (i.e. the degree of regularity of signal fluctuations) over multiple time scales. Heart rate variability (HRV) signals (i.e. data from the heart) have largely been studied through MSE. By contrast, complexities of signals from the macrocirculation (i.e. elastic and muscular arteries) and the microcirculation (i.e. arterioles and capillaries), two other main components of the CVS, have rarely been investigated simultaneously with MSE. We therefore propose to quantify and compare complexity of signals from these three CVS subsystems: the heart, the macrocirculation and the microcirculation, using MSE. Electrocardiograms, electrical bio-impedance signals (macrocirculation), as well as laser Doppler flowmetry (LDF) signals from finger and forearm (microcirculation) have been recorded simultaneously in nine healthy subjects. The MSE values from these data have been computed and compared. We note a significant lower complexity on scales τ = 1, 2 and 3 (i.e. around 1.08 Hz, 0.54 Hz and 0.36 Hz respectively) for LDF signals from the finger compared to the ones of signals from the heart and the macrocirculation. On scale τ = 5 (i.e. 0.21 Hz), complexity value of signals from the macrocirculation is significantly lower than the ones of HRV and data from the microvascular blood flow in forearm. The three CVS subsystems present different complexity values depending on scales. It could now be of interest to investigate if these complexity differences are due to physiological activities. Moreover, our results could be compared with those obtained from data recorded on patients with vascular diseases

Algebraic divisibility sequences over function fields

We study the existence of primes and of primitive divisors in classical divisibility sequences defined over function fields. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.Comment: 28 page