Objective characterization of the course of the parasellar internal carotid artery using mathematical tools

Background Along the internal carotid artery (ICA), atherosclerotic plaques are often located in its cavernous sinus (parasellar) segments (pICA). Studies indicate that the incidence of pre-atherosclerotic lesions is linked with the complexity of the pICA; however, the pICA shape was never objectively characterized. Our study aims at providing objective mathematical characterizations of the pICA shape. Methods and results Three-dimensional (3D) computer models, reconstructed from contrast enhanced computed tomography (CT) data of 30 randomly selected patients (60 pICAs) were analyzed with modern visualization software and new mathematical algorithms. As objective measures for the pICA shape complexity, we provide calculations of curvature energy, torsion energy, and total complexity of 3D skeletons of the pICA lumen. We further measured the posterior knee of the so-called ""carotid siphon"" with a virtual goniometer and performed correlations between the objective mathematical calculations and the subjective angle measurements. Conclusions Firstly, our study provides mathematical characterizations of the pICA shape, which can serve as objective reference data for analyzing connections between pICA shape complexity and vascular diseases. Secondly, we provide an objective method for creating Such data. Thirdly, we evaluate the usefulness of subjective goniometric measurements of the angle of the posterior knee of the carotid siphon.

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

Inside the `cavernous sinus` or `parasellar region` the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.

A practical example of a siphon at work

In this paper, some classroom experiments are described for correcting the common misconception that the operation of a siphon depends on atmospheric pressure. One experiment makes use of a chain model of a siphon and another demonstrates that flow rate is dependent on the height difference between the inflow and outflow of a siphon and not atmospheric pressure. A real-life example of the use of a siphon to refill a lake in South Australia is described, demonstrating that the siphon is not only of academic interest but has practical applications.

Using a siphon to drain floodwaters

This article describes how to use a siphon to drain floodwaters. A siphon is a tube that conveys water to a lower level via point above the upper water level by gravity. A siphon can be set up to drain existing floodwaters more quickly than they would naturally and can also prevent flooding. Siphons are particularly useful in situations where no pump is available, and a drainage point exists lower than the level of the floodwaters. Some case studies are presented.

The Secret Siphon

Although the siphon has been in use since ancient times, the exact mechanism of operation is still under discussion. For example, most dictionaries assert that atmospheric pressure is essential to the operation of a siphon rather than gravity. Although there is general agreement that gravity is the motivating force in a siphon, there is disagreement on how liquid enters a siphon – is it atmospheric push or tensile pull? This paper describes a classroom experiment that can serve as the basis for discussing how a siphon works. The experiment involves the construction of a siphon in which the water level in the upper reservoir is held constant during the operation of the siphon. Since the atmosphere is not doing any work on the water in the upper reservoir only gravity is at work. The special situation of a bubble-in-a-siphon is also discussed in which both atmospheric pressure and gravity are at work.

Exploring the boundary between the siphon and barometer in a hypobaric chamber

Siphons have been used since ancient times, but exactly how they work is still a matter of debate. In order to elucidate the modus operandi of a siphon, a 1.5 m high siphon was set up in a hypobaric chamber to explore siphon behaviour in a low-pressure environment. When the pressure in the chamber was reduced to about 0.18 atmospheres, a curious waterfall-like feature appeared downstream from the apex of the siphon. A hypothesis is presented to explain the waterfall phenomenon. When the pressure was reduced further the siphon broke into two columns - in effect becoming two back-to-back barometers. This experiment demonstrates the role of atmospheric pressure in explaining the hydrostatic characteristics of a siphon and the role of molecular cohesion in explaining the hydrodynamic aspects.

Bottle-feeding and the risk of pyloric stenosis

OBJECTIVES: Bottle-feeding has been suggested to increase the risk of pyloric stenosis (PS). However, large population-based studies are needed. We examined the effect of bottle-feeding during the first 4 months after birth, by using detailed data about the timing of first exposure to bottle-feeding and extensive confounder information. METHODS: We performed a large population-based cohort study based on the Danish National Birth Cohort, which provided information on infants and feeding practice. Information about surgery for PS was obtained from the Danish National Patient Register. The association between bottle-feeding and the risk of PS was evaluated by hazard ratios (HRs) estimated in a Cox regression model, adjusting for possible confounders. RESULTS: Among 70 148 singleton infants, 65 infants had surgery for PS, of which 29 were bottle-fed before PS diagnosis. The overall HR of PS for bottle-fed infants compared with not bottle-fed infants was 4.62 (95% confidence interval [CI]: 2.78–7.65). Among bottle-fed infants, risk increases were similar for infants both breast and bottle-fed (HR: 3.36 [95% CI: 1.60–7.03]), formerly breastfed (HR: 5.38 [95% CI: 2.88–10.06]), and never breastfed (HR: 6.32 [95% CI: 2.45–16.26]) (P = .76). The increased risk of PS among bottle-fed infants was observed even after 30 days since first exposure to bottle-feeding and did not vary with age at first exposure to bottle-feeding. CONCLUSIONS: Bottle-fed infants experienced a 4.6-fold higher risk of PS compared with infants who were not bottle-fed. The result adds to the evidence supporting the advantage of exclusive breastfeeding in the first months after birth.

The hemodynamic effects of in-tandem carotid artery stenosis: Implications for carotid endarterectomy

Objectives: It remains controversial whether patients with severe disease of the internal carotid artery and a coexisting stenotic lesion downstream would benefit from a carotid endarterectomy (CEA) of the proximal lesion. The aim of this study was to simulate the hemodynamic and wall shear effects of in-tandem internal carotid artery stenosis using a computational fluid dynamic (CFD) idealized model to give insight into the possible consequences of CEA on these lesions. Methods: A CFD model of steady viscous flow in a rigid tube with two asymmetric stenoses was introduced to simulate blood flow in arteries with multiple constrictions. The effect of varying the distance between the two stenoses, and the severity of the upstream stenosis on the pressure and wall shear stress (WSS) distributions on the second plaque, was investigated. The influence of the relative positions of the two stenoses was also assessed. Results: The distance between the plaques was found to have minimal influence on the overall hemodynamic effect except for the presence of a zone of low WSS (range -20 to 30 dyne/cm2) adjacent to both lesions when the two stenoses were sufficiently close (<4 times the arterial diameter). The upstream stenosis was protective if it was larger than the downstream stenosis. The relative positions of the stenoses were found to influence the WSS but not the pressure distribution. Conclusions: The geometry and positions of the lesions need to be considered when considering the hemodynamic effects of an in-tandem stenosis. Low WSS is thought to cause endothelial dysfunction and initiate atheroma formation. The fact that there was a flow recirculation zone with low WSS in between the two stenoses may demonstrate how two closely positioned plaques may merge into one larger lesion. Decision making for CEA may need to take into account the hemodynamic situation when an in-tandem stenosis is found. CFD may aid in the risk stratification of patients with this problem.

Invasive and non-invasive modalities of imaging carotid stenosis

Despite recent therapeutic advances, acute ischemic complications of atherosclerosis remain the primary cause of morbidity and mortality in Western countries, with carotid atherosclerotic disease one of the major preventable causes of stroke. As the impact of this disease challenges our healthcare systems, we are becoming aware that factors influencing this disease are more complex than previously realized. In current clinical practice, risk stratification relies primarily on evaluation of the degree of luminal stenosis and patient symptomatology. Adequate investigation and optimal imaging are important factors that affect the quality of a carotid endarterectomy (CEA) service and are fundamental to patient selection. Digital subtraction angiography is still perceived as the most accurate imaging modality for carotid stenosis and historically has been the cornerstone of most of the major CEA trials but concerns regarding potential neurological complications have generated substantial interest in non-invasive modalities, such as contrast-enhanced magnetic resonance angiography. The purpose of this review is to give an overview to the vascular specialist of the current imaging modalities in clinical practice to identify patients with carotid stenosis. Advantages and disadvantages of each technique are outlined. Finally, limitations of assessing luminal stenosis in general are discussed. This article will not cover imaging of carotid atheroma morphology, function and other emerging imaging modalities of assessing plaque risk, which look beyond simple luminal measurements.

Combined PET-FDG and USPIO-enhanced MR imaging in patients with symptomatic moderate carotid artery stenosis

Introduction: PET-FDG and USPIO-enhanced MRI are increasingly being used in depicting carotid atheroma inflammation - a risk factor for the high risk plaque. Their combined use has not been previously reported. Report: Two patients presenting with stroke and identified with 50% carotid stenosis on duplex ultrasonography, underwent PET FDG and USPIO-enhanced MR imaging. Results were concordant and complementary suggesting that both techniques reflect similar metabolic processes. Discussion: The selection of patients for carotid revascularisation has largely been based on the severity of luminal stenosis alone. The two imaging modalities, which identify inflammatory activity, may be potential surrogate risk markers in the selection of patients eligible for carotid surgery, if plaque inflammation can be correlated with risk of developing clinical symptoms.

Correlation of carotid atheromatous plaque inflammation using USPIO-enhanced MR imaging with degree of luminal Stenosis

BACKGROUND AND PURPOSE Inflammation is a recognized risk factor for the vulnerable atherosclerotic plaque. The study explores the relationship between the degree of Magnetic Resonance (MR)"defined inflammation using Ultra Small Super-Paramagnetic Iron Oxide (USPIO) particles and the severity of luminal stenosis in asymptomatic carotid plaques. METHODS Seventy-one patients with an asymptomatic carotid stenosis of ĝ‰¥40% underwent multi-sequence USPIO-enhanced MR imaging. Stenosis severity was measured according to the NASCET and ECST methods. RESULTS No demonstrable relationship between inflammation as measured by USPIO-enhanced signal change and the degree of luminal stenosis was found. CONCLUSIONS Inflammation and stenosis are likely to be independent risk factors, although this needs to be further validated.

Comparison of the inflammatory burden of truly asymptomatic carotid atheroma with atherosclerotic plaques in patients with asymptomatic carotid stenosis undergoing coronary artery bypass grafting: An ultrasmall superparamagnetic iron oxide enhanced magnetic resonance study

Introduction: Inflammation is a recognized risk factor for the vulnerable atherosclerotic plaque. The aim of this study was to explore whether there is a difference in the degree of Magnetic Resonance (MR) defined inflammation using Ultra Small Super-Paramagnetic Iron Oxide (USPIO) particles, within carotid atheroma in completely asymptomatic individuals and the asymptomatic carotid stenosis in a cohort of patients undergoing coronary artery bypass grafting (CABG). Methods: 10 patients awaiting CABG with asymptomatic carotid disease and 10 completely asymptomatic individuals with no documented coronary artery disease underwent multi-sequence MR imaging before and 36 hours post USPIO infusion. Images were manually segmented into quadrants and signal change in each quadrant, normalised to adjacent muscle signal, was calculated following USPIO administration. Results: The mean percentage of quadrants showing signal loss was 94% in the CABG group, compared to 24% in the completely asymptomatic individuals (p < 0.001). The carotid plaques from the CABG patients showed a significant mean signal intensity decrease of 16.4% after USPIO infusion (95% CI 10.6% to 22.2%; p < 0.001). The truly asymptomatic plaques showed a mean signal intensity increase (i.e. enhancement) after USPIO infusion of 8.4% (95% CI 2.6% to 14.2%; p = 0.007). The mean signal difference between the two groups was 24.9% (95% CI 16.7% to 33.0%; p < 0.001). Conclusions: These findings are consistent with the hypothesis that inflammatory atheroma is a systemic disease. The carotid territory is more likely to take up USPIO if another vascular territory is symptomatic.

Correlation of macrophage location and plaque stress distribution using USPIO-enhanced MRI in a patient with symptomatic severe carotid stenosis: A new insight into risk stratification

High resolution, USPIO-enhanced MR imaging can be used to identify inflamed atherosclerotic plaque. We report a case of a 79-year-old man with a symptomatic carotid stenosis of 82%. The plaque was retrieved for histology and finite element analysis (FEA) based on the preoperative MR imaging was used to predict maximal Von Mises stress on the plaque. Macrophage location correlated with maximal predicted stresses on the plaque. This supports the hypothesis that macrophages thin the fibrous cap at points of highest stress, leading to an increased risk of plaque rupture and subsequent stroke.

Assessment of inflammatory burden contralateral to the symptomatic carotid stenosis using high-resolution ultrasmall, superparamagnetic iron oxide-enhanced MRI

BACKGROUND AND PURPOSE It is well known that the vulnerable atheromatous plaque has a thin, fibrous cap and large lipid core with associated inflammation. This inflammation can be detected on MRI with use of a contrast medium, Sinerem, an ultrasmall superparamagnetic iron oxide (USPIO). Although the incidence of macrophage activity in asymptomatic disease appears low, we aimed to explore the incidence of MRI-defined inflammation in asymptomatic plaques in patients with known contralateral symptomatic disease. METHODS Twenty symptomatic patients underwent multisequence MRI before and 36 hours after USPIO infusion. Images were manually segmented into quadrants, and the signal change in each quadrant was calculated after USPIO administration. A mixed mathematical model was developed to compare the mean signal change across all quadrants in the 2 groups. Patients had a mean symptomatic stenosis of 77% compared with 46% on their asymptomatic side, as measured by conventional angiography. RESULTS There were 11 (55%) men, and the median age was 72 years (range, 53 to 84 years). All patients had risk factors consistent with severe atherosclerotic disease. All symptomatic carotid stenoses had inflammation, as evaluated by USPIO-enhanced imaging. On the contralateral sides, inflammatory activity was found in 19 (95%) patients. Contralaterally, there were 163 quadrants (57%) with a signal loss after USPIO when compared with 217 quadrants (71%) on the symptomatic side (P=0.007). CONCLUSIONS - This study adds weight to the argument that atherosclerosis is a truly systemic disease. It suggests that investigation of the contralateral side in patients with symptomatic carotid stenosis can demonstrate inflammation in 95% of plaques, despite a mean stenosis of only 46%. Thus, inflammatory activity may be a significant risk factor in asymptomatic disease in patients who have known contralateral symptomatic disease. Patients with symptomatic carotid disease should have their contralateral carotid artery followed up.

Unsteady flow with attenuation in a fluid filled elastic tube with a stenosis

An equation governing the excess pressure has been derived, for an axially tethered and stenosed elastic tube filled with viscous liquid, by introducing the elasticity of the tube through pressure-area relation. This equation is solved numerically for large Womersley parameter and the results are presented for different types of pressure-radius relations and geometries by prescribing an outgoing wave suffering attenuation at some axial point of the tube. For a locally constricted tube it is observed that the pressure oscillates more and generates sound on the down stream side of the constriction.