An integral is a mathematical object that can be interpreted as an area or a generalization of an area. A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed (summation in the limit). In CT, for example this mathematical function is used in the Fourier transformation.

Coulomb is the SI unit of electric charge. One coulomb is the amount of charge accumulated in one second by a current of one ampere.
The charge of a proton is 1.6 x 10^-19 coulombs. The charge of an electron is - 1.6 x 10^-19 coulombs. An atomic particle has a charge which is an integral multiple of 1.6 x 10^-19 coulombs.

Imaging refers to the visual representation of an object. Today, diagnostic imaging uses radiology and other techniques, mostly noninvasive, to create pictures of the human body. Diagnostic radiography studies the anatomy and physiology to diagnose an array of medical conditions. The history of medical diagnostic imaging is in many ways the history of radiology. Many imaging techniques also have scientific and industrial applications. Diagnostic imaging in its widest sense is part of biological science and may include medical photography, microscopy and techniques which are not primarily designed to produce images (e.g., electroencephalography and magnetoencephalography).
Brief overview about important developments:
Imaging used for medical purposes, began after the discovery of x-rays by Konrad Roentgen 1896. The first fifty years of radiological imaging, pictures have been created by focusing x-rays on the examined body part and direct depiction onto a single piece of film inside a special cassette.
In the 1950s, first nuclear medicine studies showed the up-take of very low-level radioactive chemicals in organs, using special gamma cameras. This diagnostic imaging technology allows information of biologic processes in vivo. Today, single photon emission computed tomography (SPECT) and positron emission tomography (PET) play an important role in both clinical research and diagnosis of biochemical and physiologic processes.
In the 1960s, the principals of sonar were applied to diagnostic imaging. Ultrasound has been imported into practically every area of medicine as an important diagnostic tool, and there are great opportunities for its further development. Looking into the future, the grand challenges include targeted contrast imaging, real-time 3D or 4D ultrasound, and molecular imaging. The earliest use of ultrasound contrast agents (USCA) was in 1968.
The introduction of computed tomography (CT/CAT) in the 1970s revolutionized medical imaging with cross sectional images of the human body and high contrast between different types of soft tissues. These developments were made possible by analog to digital converters and computers. First, spiral CT (also called helical), then multislice CT (or multi-detector row CT) technology expanded the clinical applications dramatically.
The first magnetic resonance imaging (MRI) devices were tested on clinical patients in 1980. With technological improvements including higher field strength, more open MRI magnets, faster gradient systems, and novel data-acquisition techniques, MRI is a real-time interactive imaging modality that provides both detailed structural and functional information of the body.

Today, imaging in medicine has been developed to a stage that was inconceivable a century ago, with growing modalities:
x-ray projection imaging, including conventional radiography and digital radiography;
All these types of scans are an integral part of modern healthcare. Usually, a radiologist interprets the images. Most clinical studies are acquired by a radiographer or radiologic technologist. In filmless, digital radiology departments all images are acquired and stored on computers. Because of the rapid development of digital imaging modalities, the increasing need for an efficient management leads to the widening of radiology information systems (RIS) and archival of images in digital form in a picture archiving and communication system (PACS). In telemedicine, medical images of MRI scans, x-ray examinations, CT scans and ultrasound pictures are transmitted in real time.

See also Interventional Radiology, Image Quality and CT Scanner.

A logarithm is the exponent to which the base must be raised to produce a given number.
Logarithms are used to express dynamic processes, also in diagnostic imaging processes.



See also Algorithm, Integral, and Differential.

Tomography is imaging by sections or sectioning to obtain images of slices through objects like the human body. Tomography is derived from the Greek words 'to cut or section' (tomos) and 'to write' (graphein). A device used in tomography is called a tomograph, while the image produced is a tomogram.
The first medical applications utilized x-rays for images of tissues based on their x-ray attenuation coefficient. The mathematical basis for tomographic imaging was laid down by Johann Radon. This type of imaging is used in different medical applications as for example computed tomography, ultrasound imaging, positron emission tomography and magnetic resonance imaging (MRI) also called magnetic resonance tomography (MRT).
Conventional x-ray tomographic techniques show organ structures lying in a predetermined plane (the focal plane), while blurring the tissue structures in planes above and below by linear or complex geometrical motion of the x-ray tube and film cassette.
Basically, computed tomography is the reconstruction of an image from its projections. In the strict sense of the word, a projection at a given angle is the integral of the image in the direction specified by that angle. The CT images (slices) are created in the axial plane, while coronal and sagittal images can be rendered by computer reconstruction.

See also Zonography, Computed or Computerized Axial Tomography, Resolution Element, Radiographic Noise, Intravenous Pyelogram.