Doppler ultrasonographyDoppler ultrasonography is medical ultrasonography that employs the Doppler effect to perform imaging of the movement of tissues and body fluids (usually blood), and their relative velocity to the probe. By calculating the frequency shift of a particular sample volume, for example, flow in an artery or a jet of blood flow over a heart valve, its speed and direction can be determined and visualized. Duplex ultrasonography sometimes refers to Doppler ultrasonography or spectral Doppler ultrasonography.
Medical ultrasoundMedical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscles, joints, blood vessels, and internal organs, to measure some characteristics (e.g. distances and velocities) or to generate an informative audible sound. The usage of ultrasound to produce visual images for medicine is called medical ultrasonography or simply sonography, or echography.
Transcranial DopplerTranscranial Doppler (TCD) and transcranial color Doppler (TCCD) are types of Doppler ultrasonography that measure the velocity of blood flow through the brain's blood vessels by measuring the echoes of ultrasound waves moving transcranially (through the cranium). These modes of medical imaging conduct a spectral analysis of the acoustic signals they receive and can therefore be classified as methods of active acoustocerebrography.
Heart failureHeart failure (HF), also known as congestive heart failure (CHF), is a syndrome, a group of signs and symptoms, caused by an impairment of the heart's blood pumping function. Symptoms typically include shortness of breath, excessive fatigue, and leg swelling. The shortness of breath may occur with exertion or while lying down, and may wake people up during the night. Chest pain, including angina, is not usually caused by heart failure, but may occur if the heart failure was caused by a heart attack.
EchocardiographyEchocardiography, also known as cardiac ultrasound, is the use of ultrasound to examine the heart. It is a type of medical imaging, using standard ultrasound or Doppler ultrasound. The visual image formed using this technique is called an echocardiogram, a cardiac echo, or simply an echo. Echocardiography is routinely used in the diagnosis, management, and follow-up of patients with any suspected or known heart diseases. It is one of the most widely used diagnostic imaging modalities in cardiology.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Carotid ultrasonographyCarotid ultrasonography is an ultrasound-based diagnostic imaging technique to evaluate structural details of the carotid arteries. Carotid ultrasound is used to diagnose carotid artery stenosis (CAS) and can assess atherosclerotic plaque morphology and characteristics. Carotid duplex and contrast-enhanced ultrasound are two of the most common imaging techniques used to evaluate carotid artery disease. Carotid ultrasound is a low-cost, noninvasive, and accurate diagnostic imaging modality used to evaluate diseases of the carotid arteries.
Quadratic functionIn mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before the 20th century, the distinction was unclear between a polynomial and its associated polynomial function; so "quadratic polynomial" and "quadratic function" were almost synonymous. This is still the case in many elementary courses, where both terms are often abbreviated as "quadratic".
Quadratic equationIn algebra, a quadratic equation () is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.
Contrast-enhanced ultrasoundContrast-enhanced ultrasound (CEUS) is the application of ultrasound contrast medium to traditional medical sonography. Ultrasound contrast agents rely on the different ways in which sound waves are reflected from interfaces between substances. This may be the surface of a small air bubble or a more complex structure. Commercially available contrast media are gas-filled microbubbles that are administered intravenously to the systemic circulation. Microbubbles have a high degree of echogenicity (the ability of an object to reflect ultrasound waves).
