Vessel Size Research Articles

Bronchial vessel density is correlated with airway smooth muscle cell proliferation in horses with mild and moderate asthma.

In severe equine asthma, structural remodeling of the airways ultimately leads to bronchial wall thickening and airflow obstruction. Increased bronchial vascularization has been described in horses affected by the severe form of the disease, but whether it contributes to bronchial remodeling in milder forms of asthma remains to be determined. In a blinded, retrospective case-control study, we evaluated the presence of bronchial angiogenesis in horses with mild and moderate equine asthma (MEA) and its correlation to airway smooth muscle remodeling. Endobronchial biopsies from the Equine Respiratory Tissue Biobank collected between August 14, 2014, and May 31, 2019, from 9 horses with MEA and 7 healthy controls were studied. The vascular basement membrane was identified by immunohistochemistry, allowing the measurement of the number of bronchial vessels, vascular area, and mean vessel size by histomorphometry. The correlations between angiogenic parameters, airway smooth muscle (ASM) remodeling features, and airway neutrophilia were studied. No differences between groups were observed for the angiogenic parameters evaluated. The number of vessels was correlated to ASM cell proliferation in MEA horses (Spearman r = 0.73) but not in controls. Airway neutrophilia correlated negatively with mean vessel size in horses with MEA (Pearson r = -0.83) but not in control horses. Major changes in bronchial vascularization do not occur in central airways in MEA. Contrary to previous findings in horses with severe equine asthma, angiogenesis is not a prominent feature of MEA, but it might be associated with ASM remodeling.

Usefulness of computed tomography findings for predicting soft tissue sarcoma grades.

Soft tissue sarcomas (STSs) constitute a heterogeneous group of tumors that originate from mesenchymal cells. Imaging plays an important role in the assessment of the oncological stage of STSs. Computed tomography findings facilitate the identification of the tumor location and margins in relation to the surrounding anatomic boundaries and thereby enable preoperative planning of tumor management. The histological grade is among the most important parameters that affect tumor recurrence and metastasis rates. However, the prediction of STS histological grades using CT characteristics has not yet been elucidated. This study retrospectively investigated CT findings of patients with different STS grades for differentiation. Thirty dogs with STSs (12 Grade 1, 10 Grade 2, and 8 Grade 3) were included from three animal hospitals. The investigated CT features included tumor delineation, dysmorphic intratumoral or peritumoral vessels, contrast enhancement patterns, peripheral rim enhancement, intratumoral calcification, degree of intratumoral cystic lesions, peritumoral fat stranding, metastatic regional lymphadenopathy, and lung metastasis. Quantitative findings included tumor size and pre- and postcontrast attenuation. Tumor size, dysmorphic intratumoral or peritumoral vessels, peritumoral fat stranding, and metastatic regional lymphadenopathy significantly differed among tumor grades. On post hoc analysis, Grade 3 tumors were significantly larger, had a higher prevalence of dysmorphic vessels than Grade 1 tumors, and had a significantly higher rate of adjacent metastatic lymphadenopathy than Grade 2 tumors. Predicting STS grades before the histopathological examination could potentially aid in the planning of the STS resection margins.

Multifaceted Responses to Heat Stress in Plants: A Review of the Morpho-physiological, Biochemical and Anatomical Changes

Heat stress, a significant abiotic factor, adversely affects plant growth and productivity by disrupting various physiological and biochemical processes. Plants, being immobile, respond to environmental changes through alterations in gene expression, metabolism, and growth dynamics. Elevated temperatures, exceeding the threshold for heat tolerance, negatively influence critical functions such as photosynthesis, respiration, water balance, and membrane stability. Root development is particularly sensitive to heat stress, resulting in reduced root mass and impaired water and nutrient uptake. Photosynthetic capacity diminishes due to decreased chlorophyll content and impaired photochemical reactions, leading to reduced biomass and yield. Heat stress impacts plant water status by disturbing hydraulic conductivity and increasing membrane permeability, leading to dehydration and a decline in water potential. This stress reduces membrane stability, resulting in electrolyte leakage and cellular damage. It also induces the production of reactive oxygen species (ROS), which requires the activation of antioxidant enzymes to minimize oxidative stress. Also, to maintain osmotic balance and enhance stress tolerance, plants accumulate osmolytes such as proline. Additionally, anatomical adaptations in leaves, stems, and roots, such as changes in stomatal density, xylem vessel size, and gas exchange patterns, highlight the plant's strategies to cope with heat stress. Understanding these varied responses is crucial for developing strategies to enhance crop resilience in the face of increasing global temperatures and climate change.

Lumped parameter simulations of cervical lymphatic vessels: dynamics of murine cerebrospinal fluid efflux from the skull

BackgroundGrowing evidence suggests that for rodents, a substantial fraction of cerebrospinal fluid (CSF) drains by crossing the cribriform plate into the nasopharyngeal lymphatics, eventually reaching the cervical lymphatic vessels (CLVs). Disruption of this drainage pathway is associated with various neurological disorders.MethodsWe employ a lumped parameter method to numerically model CSF drainage across the cribriform plate to CLVs. Our model uses intracranial pressure as an inlet pressure and central venous blood pressure as an outlet pressure. The model incorporates initial lymphatic vessels (modeling those in the nasal region) that absorb the CSF and collecting lymphatic vessels (modeling CLVs) to transport the CSF against an adverse pressure gradient. To determine unknown parameters such as wall stiffness and valve properties, we utilize a Monte Carlo approach and validate our simulation against recent in vivo experimental measurements.ResultsOur parameter analysis reveals the physical characteristics of CLVs. Our results suggest that the stiffness of the vessel wall and the closing state of the valve are crucial for maintaining the vessel size and volume flow rate observed in vivo. We find that a decreased contraction amplitude and frequency leads to a reduction in volume flow rate, and we test the effects of varying the different pressures acting on the CLVs. Finally, we provide evidence that branching of initial lymphatic vessels may deviate from Murray’s law to reduce sensitivity to elevated intracranial pressure.ConclusionsThis is the first numerical study of CSF drainage through CLVs. Our comprehensive parameter analysis offers guidance for future numerical modeling of CLVs. This study also provides a foundation for understanding physiology of CSF drainage, helping guide future experimental studies aimed at identifying causal mechanisms of reduction in CLV transport and potential therapeutic approaches to enhance flow.

Deep learning detected histological differences between invasive and non-invasive areas of early esophageal cancer.

The depth of invasion plays a critical role in predicting the prognosis of early esophageal cancer, but the reasons behind invasion and the changes occurring in invasive areas are still not well understood. This study aimed to explore the morphological differences between invasive and non-invasive areas in early esophageal cancer specimens that have undergone endoscopic submucosal dissection (ESD), using artificial intelligence (AI) to shed light on the underlying mechanisms. In this study, data from 75 patients with esophageal squamous cell carcinoma (ESCC) were analyzed and endoscopic assessments were conducted to determine submucosal (SM) invasion. An AI model, specifically a Clustering-constrained Attention Multiple Instance Learning model (CLAM), was developed to predict the depth of cancer by training on surface histological images taken from both invasive and non-invasive regions. The AI model highlighted specific image portions, or patches, which were further examined to identify morphological differences between the two types of areas. The 256-pixel AI model demonstrated an average area under the receiver operating characteristic curve (AUC) value of 0.869 and an accuracy (ACC) of 0.788. The analysis of the AI-identified patches revealed that regions with invasion (SM) exhibited greater vascularity compared with non-invasive regions (epithelial). The invasive patches were characterized by a significant increase in the number and size of blood vessels, as well as a higher count of red blood cells (all with p-values <0.001). In conclusion, this study demonstrated that AI could identify critical differences in surface histopathology between non-invasive and invasive regions, particularly highlighting a higher number and larger size of blood vessels in invasive areas.

7T MRI as a powerful tool to detect small and medium size vessel CNS vasculitis.

Imaging can help to diagnose CNS vasculitis. Yet so far, no imaging studies of CNS vasculitis at 7T are available. We share our experience of vessel wall imaging (VWI) at 7T in patients with suspected vasculitis. All included patients (n=45) underwent a clinically approved 7T MRI comprising high resolution arterial TOF angiography as well as high resolution VWI with T1SPACE and T1SE acquired pre-and post-contrast. 23 patients showed negative and 22 patients positive VWI at 7T. Ten out of 22 7T VWI positive cases were suggestive of vasculitis with 9 patients showing VWI of large and medium size vessels and one patient VWI of small vessels. Small vessel vasculitis was only depicted with 7T VWI, but not 3T VWI. Our work demonstrates that diagnosing CNS vasculitis, especially small vessel vasculitis, is feasible at 7T and highlights the potential of high field VWI encouraging further studies in this field.ABBREVIATIONS: FS= fat-saturated, SNR= signal-to-noise ratio, VWI= vessel wall imaging.

Assessing diagnostic accuracy of intravascular imaging for functionally significant coronary stenosis: updated findings from a meta-analysis

BackgroundAccurate discrimination of functionally significant coronary stenosis using intravascular imaging remains uncertain, particularly with regard to vessel size. This meta-analysis evaluates the diagnostic performance of intravascular ultrasound (IVUS) and optical...

An Experimental Approach to Minoan Larnakes: Exploring Craft Spaces for Production of Large Ceramic Vessels

ABSTRACT This article aims to explore craft spaces associated with the production of Minoan larnakes. Larnakes are large clay coffins, used mainly on Crete from the beginning to the end of the Minoan Bronze Age (ca. 2650–1050 BCE). Scholars have long given attention to larnakes for their iconographical richness. However, previous research has neglected the context of production and modes of distribution of these artifacts. This study investigates the spatial organization of craft spaces for larnax production, using an experiment conducted in collaboration with traditional potters, and compares the results with the ethnographic and archaeological record. The study offers new insights on the organization of larnax production and the production of large vessels in general, by formulating criteria to identify workshops related to the manufacture of large vessels. Examining the relationship between vessel size and craft spaces offers a better understanding of the organization of this pottery craft in Minoan Crete.

Technical note: Improving orbital atherectomy efficacy for calcified nodules using a curved guide catheter.

Endovascular therapy (EVT) for calcified nodules in patients with peripheral artery disease (PAD) remains challenging in achieving favorable outcomes. This study aims to investigate the effectiveness of orbital atherectomy (OA) for calcified nodules using an IM catheter to precisely control the device and achieve optimal engagement with the target lesion. We performed EVT for a calcified nodule in the right common femoral artery using an OA. Due to the large vessel size, controlling the OA to effectively engage the lesion was challenging. To overcome this, we utilized an IM catheter to guide the OA toward the target lesion. The use of the IM catheter successfully directed the OA to the calcified lesion, resulting in significant lumen enlargement. The procedure was completed without any complications, and the OA achieved effective debulking of the calcified nodule. The combination of OA and IM catheter facilitated effective contact with the target lesion, improving the performance of the debulking device. This approach may enhance the management of calcified lesions in large-diameter arteries during EVT, potentially leading to better clinical outcomes.

Accurate retinal vessel segmentation in OCT-A images based on MsTCG-Net

Optical coherence tomography angiography (OCT-A) is a non-invasive visualization imaging technology with high-resolution that can more clearly image tiny blood vessels. Using OCT-A imaging technology, certain ophthalmic diseases can be better diagnosed by the morphological changes of retinal blood vessels. However, the task of segmenting retinal vessels is still very challenging due to the large variation in vessel size and shape and the presence of noise. In this paper, by introducing a transformer with a self-attention mechanism, we propose a novel multi-scale transformer-based channel and global attention network (MsTCG-Net) for segmentation of blood vessels in retinal OCT-A images. In MsTCG-Net, transformer-based channel joint attention (TC) block and transformer-based global joint attention (TG) block are proposed to capture multi-semantic features from spatial and channel dimension and fuse global contextual semantic features from different layers of encoder. Experimental results show that our proposed method achieves better segmentation performance than other state-of-the-art U-Net-based methods.

Accurate retinal vessel segmentation in OCT-A images based on MsTCG-Net

Optical coherence tomography angiography (OCT-A) is a non-invasive visualization imaging technology with high-resolution that can more clearly image tiny blood vessels. Using OCT-A imaging technology, certain ophthalmic diseases can be better diagnosed by the morphological changes of retinal blood vessels. However, the task of segmenting retinal vessels is still very challenging due to the large variation in vessel size and shape and the presence of noise. In this paper, by introducing a transformer with a self-attention mechanism, we propose a novel multi-scale transformer-based channel and global attention network (MsTCG-Net) for segmentation of blood vessels in retinal OCT-A images. In MsTCG-Net, transformer-based channel joint attention (TC) block and transformer-based global joint attention (TG) block are proposed to capture multi-semantic features from spatial and channel dimension and fuse global contextual semantic features from different layers of encoder. Experimental results show that our proposed method achieves better segmentation performance than other state-of-the-art U-Net-based methods.

Fingertip replantation using artery-only anastomosis: case series

The fingertip is a complex organ compacted with precise functional roles of fine movements and fine touch sensory functions. Fingertip injury commonly occurs in machinery work, and presents as crush injuries or amputations. Even though it is a challenging procedure due to the area of injury relative to the size of vessels for restoration, fingertip replantation has been developing as a newer method for both functional and aesthetic restoration, with better success rates and improved long-term outcomes. Artery-only replant has been emerging as a suitable option in many cases, which allows the blood to flow out of the injury site, allowing the natural venous revascularization, owing to the difficulty in small venous anastomosis. Here, we present two cases with fingertip replantation using artery-only anastomosis who underwent fingertip replantation at Tamai level II without venous anastomosis.

Focal liver lesions: multiparametric microvasculature characterization via super-resolution ultrasound imaging

BackgroundNoninvasive and functional imaging of the focal liver lesion (FLL) vasculature at microscopic scales is clinically challenging. We investigated the feasibility of using super-resolution ultrasound (SR-US) imaging for visualizing and quantifying the microvasculature of intraparenchymal FLLs.MethodsPatients with FLLs between June 2022 and February 2023 were prospectively screened. Following bolus injection of microbubbles at clinical concentration, SR-US was performed using a high frame rate (350–500 Hz) modified ultrasound scanner and a convex array transducer with a central frequency of 3.1 MHz.ResultsIn total, 47 pathologically proven FLLs at a depth of 5.7 ± 1.7 cm (mean ± standard deviation) were included: 30 hepatocellular carcinomas (HCC), 11 liver metastases (LM), and 6 focal nodular hyperplasias (FNH). The smallest detectable vessel size of the hepatic microvasculature was 128.4 ± 18.6 μm (mean ± standard deviation) at a depth of 8 cm. Significant differences were observed among the three types of lesions in terms of pattern categories, vessel density, minimum flow velocity, and perfusion index. We observed higher vessel density for FNH versus liver parenchyma (p < 0.001) as well as fractal dimension and local flow direction entropy value for FNH versus HCC (p = 0.002 and p < 0.001, respectively) and for FNH versus LM (p = 0.006 and p = 0.002, respectively).ConclusionMultiparametric SR-US showed that these three pathological types of FLLs have specific microvascular phenotypes. Vessel density, fractal dimension and local flow direction entropy served as valuable parameters in distinguishing between benign and malignant FLLs.Trial registrationClinicalTrials.gov (NCT06018142).Relevance statementMultiparametric SR-US imaging offers precise morphological and functional assessment of the microvasculature of intraparenchymal focal liver lesions, providing insights into tumor heterogeneity and angiogenesis.Key PointsSuper-resolution (SR)-US imaging allowed morphological and functional evaluation of intraparenchymal hepatic lesion microvasculature.Hepatocellular carcinoma, liver metastasis, and focal nodular hyperplasia exhibit distinct microvascular architectures and hemodynamic profiles.Multiparametric microvasculature characterization via SR-US imaging facilitates the differentiation between benign and malignant microvascular phenotypes.Graphical

Investigating the Impact of Chronical Prenatal Alcohol Exposure on Fetal Vascular Development Across Pregnancy Stages Using Photoacoustic Tomography.

Prenatal alcohol exposure (PAE) is a major contributor to fetal alcohol spectrum disorder (FASD), resulting in neurodevelopmental abnormalities. This study utilizes photoacoustic tomography (PAT) to investigate the effects of PAE on fetal brain vasculature in mice. PAT imaging was conducted from embryonic Day 10 (E10) to Day 20 (E20), aimed to compare two alcohol-exposed groups with a control group. Key vascular parameters, including blood vessel diameter and density, and oxygen saturation (sO2), were analyzed. Results show significant reductions in vessel size and density, as well as reduced sO2 levels, in alcohol-exposed groups, especially from E14 onward, compared to controls. These findings underscore the vulnerability of the fetal brain to alcohol exposure during early development and highlight the potential of PAT as a valuable tool for investigating FASD-related vascular changes.

Response of capillaries and small arterioles to full-field flicker is not dependent on local ganglion cell thickness

To measure the influence of ganglion cell layer (GCL) thickness on the changes in size and red blood cell (RBC) flow in small retinal vessels evoked by full-field flicker. We used a dual-beam adaptive optics scanning laser ophthalmoscope to image 11 healthy young controls in two retinal areas with significantly different GCL thicknesses. All capillaries and arterioles of the superficial vascular plexus were responsive to the flicker stimulation. Average lumen dilation and RBC flow changes were greater in capillaries than in arterioles (vasodilation: 10.9%, 6.7%; RBC flow: 51%, 38%, respectively). No statistically significant differences regarding relative lumen diameter, RBC velocity, or RBC flow were found with respect to GCL thickness, or vessel size.

Ultrasound evaluation of the size of the umbilical cord vessels and Wharton’s jelly and correlation with intrapartum CTG findings

ObjectiveTo compare the sonographic measurement of the umbilical cord between women with or without repetitive decelerations during the first stage of labor. Study designProspective study including a non-consecutive cohort of women at term gestation carrying a normal sized fetus at term in cephalic presentation. The cross-sectional area of the umbilical cord, of its vessels and the amount of the Wharton’s jelly were assessed at 2D ultrasound upon labor admission. The CTG traces recorded in labor were retrospectively evaluated and the biometric parameters of the umbilical cord were compared between women with or without repetitive decelerations during the first stage and their correlation with the total deceleration area/total length (stage I TDA/t) of the first stage of labor (overall and following the rupture of membrane) was assessed. ResultsOverall, 113 women were included, of whom 21 (18.6 %) presented repetitive decelerations during the first stage of labor. In this latter group, the umbilical cord showed a significantly smaller total arterial area (24.4 ± 10.7 vs. 19.6 ± 9.0 mm2; p = 0.02), vein area (46.8 ± 13.6 vs. 34.1 ± 13.3 mm2; p < 0.001) as well Wharton’s Jelly (WJ) area (122.7 ± 32.1 vs. 79.3 ± 11.1 mm2; p < 0.001) compared with fetuses with a normal CTG. At logistic regression analysis the WJ area was associated with the occurrence of repetitive decelerations during the first stage of labor (p < 0.001). The I stage TDA/t overall and after the rupture of membranes was found to be negatively correlated with the WJA (Spearman’s coefficient −0.40; p < 0.001 and −0.45; p < 0.001 respectively). ConclusionIn normal sized infants a reduced umbilical cord thickness is associated with an increased occurrence of repetitive decelerations during the first stage of labor. The severity of these decelerations is negatively correlated to the amount of WJ.

Do gender-specific carotid plaque characteristics and stroke risk prediction suggest different biomarkers for men and women?

There is convincing evidence for sex differences in carotid atherosclerosis although the relation between sex and plaque characteristics needs further insight accessing individual patient data characteristics to perform these analyses. The structure and composition of arterial walls can differ between genders. At every age, most women are of shorter stature and smaller size than most men. Height is related directly to arterial caliber and length as well as cardiac output through effects on stroke volume and heart rate.Statistical comparisons for gender suggest that females appeared more vulnerable to the progression of arterial stiffening [1]. Carotid plaque measurements using maximum wall thickness as 1-dimensional (1D) size, wall area as 2D size, and wall volume as 3D size are larger in men opposed to women [2]. Nevertheless, the normalized wall index, which accounts for the total vessel size, shows no significant difference between males and females. Regarding the number of calcifications, it was found that men have higher calcification volumes than women and accordingly intraplaque hemorrhage is more common in men than in women [3]. Sex differences in stroke incidence, and complication rate have been reported [4].The current study aims a review of recent publications on gender-specific differences regarding carotid plaque characteristics and stroke risk aiming different biomarkers for men and women what may benefit clinical management and specific treatment.[1] Wang Z, Li W, Liu W, Tian J. Gender is a determinant of carotid artery stiffness independent of age and blood pressure. Br J Radiol. 2021 Mar 1;94(1119):20200796. [2] van Dam-Nolen DHK, van Egmond NCM, Dilba K, Nies K, van der Kolk AG, Liem MI, Kooi ME, Hendrikse J, Nederkoorn PJ, Koudstaal PJ, et al. Sex differences in plaque composition and morphology among symptomatic patients with mild-to-moderate carotid artery stenosis. Stroke. 2022; 53:370–378. [3] Scheffler M, Pellaton A, Boto J, Barnaure I, Delattre BM, Remuinan J, Sztajzel R, Lovblad KO, Vargas MI. Hemorrhagic plaques in mild carotid stenosis: the risk of stroke. Can J Neurol Sci. 2021; 48:218–225. [4] Voigt S, van Os H, van Walderveen M, van der Schaaf IC, Kappelle LJ, Broersen A, Velthuis BK, de Jong PA, Kockelkoren R, Kruyt ND, et al; DUST study group. Sex differences in intracranial and extracranial atherosclerosis in patients with acute ischemic stroke. Int J Stroke. 2021;16: 385–391.

A mathematical approach to microvascular anastomosis for beginners and the effectiveness of chicken legs and partial meat from chicken legs and chicken wings as a training model

Purpose: The aim of this study was to use a mathematical approach to understand the exact location and spacing of microvascular anastomosis, and investigate the effectiveness of a practice model using chicken legs and partial meat from chicken wings.Methods: The suture techniques used for microvascular anastomosis were analyzed mathematically. In addition, chickens of various sizes were dissected to measure the size of blood vessels and compared with the size of blood vessels found in partial meat.Results: When using eight- or nine-point sutures, the positions and intervals were different. Larger chickens had larger blood vessels. In the partial meat samples, the average size of the blood vessels was 0.8 mm for the radial artery, 0.45 mm for the ulnar artery, and 1.3 mm for the tibial artery.Conclusion: It is important to understand the location and spacing of sutures through a mathematical analysis of microvascular anastomosis, which enables suturing techniques to be improved. The practice model using chicken legs and partial meat from chicken wings was found to be useful for beginners.

Resolution dependence of vessel size index across various brain regions.

Magnetic resonance imaging (MRI) excels at detecting quantitative changes in microvascular parameters such as cerebral blood volume, cerebral blood flow, and vessel size index (VSI), which are essential for diagnosing and monitoring cerebrovascular diseases. Absolute VSI estimation, often utilizing superparamagnetic iron oxide nanoparticles as contrast agents, relies on measuring transverse relaxation rates (∆R2* and ∆R2). This study systematically investigates the spatial resolution dependence of VSI using Monte Carlo simulations and in vivo rat brain MRI experiments. Monte Carlo simulations modeled randomly oriented vasculatures with various vessel sizes, revealing that ∆R2 values are significantly higher at an in-plane spatial resolution of 125 × 125 µm² compared to lower resolutions, particularly for smaller vessels. In vivo experiments on 13 rats using a 7 T MRI scanner compared VSI measurements at spatial resolutions of 125 µm² and 250 µm² across different brain regions. Results indicated region-specific VSI variations, with smaller vessels showing more pronounced resolution-dependent changes. The corpus callosum and hippocampal formation regions in particular exhibited significant increases in VSI at lower resolutions. The observed variability is attributed to the differing sensitivities of ΔR2* and ΔR2 to vessel size. Corroboration between the experimental data and simulation findings emphasizes the necessity of optimizing spatial resolution to ensure accurate VSI quantification and enhance the precision of neuro-microvascular imaging techniques.

Passage of Pi Since Antiquity Emphasizing Indian Evolution

This research article is an effort to explore the intriguing fact about the Indian evolution of mathematical constant π being ratio between circumference and diameter of any circle whose decimal part is never ending and non-repetitive having transcendental in nature. The Indian evolutionary passage started since ancient past Indus Civilization approximately during 3000 B.C, continued up to the great Ramanujan and still being worked on. Though, it has no constant value but it is an essential integral part in various branches of scientific occurrences and formulae used as constant. Its extreme utility value in daily life made it indispensible. Some examples of its daily uses are: a) Electricians apply it to solve various problems for electrical applications. b) Statisticians use it in track population dynamics c) Its medical benefits are to study the structures of eye d) Physicists uses it while calculating behavior of fluid ripples e) Biotechnologists use it to explain structure/function of DNA. f) It is also used in designing pendulum clocks. g) Aero designers use it to calculate outer surface area of aircraft. h) Used to calculate frequencies in waves used in signal processing (the period of sine waves is 2π. i) Used in GPS for navigation. j) In geometrical problems of circular and spherical designs where circumference of circle is 2πr, area π , volume of spherical structure = π , surface area of it is 4π . k) Used to get Wi-Fi to work on in jet planes through satellite communication system). l) It helps a controller, drive a motor to move an actuator, which controls the flaps on aircraft wings and tails in jet planes. The equation of angular frequency ω= 2πf radians; f= in Hz; where T is time. m) To assess vessels size at refineries, where volume of cylindrical vessels are governed by the formula 2πrh.