Lung cancerLung cancer, also known as lung carcinoma, is a malignant tumor that begins in the lung. Lung cancer is caused by genetic damage to the DNA of cells in the airways, often caused by cigarette smoking or inhaling damaging chemicals. Damaged airway cells gain the ability to multiply unchecked, causing the growth of a tumor. Without treatment, tumors spread throughout the lung, damaging lung function. Eventually lung tumors metastasize, spreading to other parts of the body.
CT scanA computed tomography scan (usually abbreviated to CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use a rotating X-ray tube and a row of detectors placed in a gantry to measure X-ray attenuations by different tissues inside the body.
Testicular cancerTesticular cancer is cancer that develops in the testicles, a part of the male reproductive system. Symptoms may include a lump in the testicle or swelling or pain in the scrotum. Treatment may result in infertility. Risk factors include an undescended testis, family history of the disease, and previous history of testicular cancer. More than 95% are germ cell tumors which are divided into seminomas and non-seminomas. Other types include sex-cord stromal tumors and lymphomas.
Medical imagingMedical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities.
Squamous-cell carcinomaSquamous-cell carcinoma (SCC), also known as epidermoid carcinoma, comprises a number of different types of cancer that begin in squamous cells. These cells form on the surface of the skin, on the lining of hollow organs in the body, and on the lining of the respiratory and digestive tracts.
Cancer stagingCancer staging is the process of determining the extent to which a cancer has grown and spread. A number from I to IV is assigned, with I being an isolated cancer and IV being a cancer that has metastasized and spread from its origin. The stage generally takes into account the size of a tumor, whether it has invaded adjacent organs, how many regional (nearby) lymph nodes it has spread to (if any), and whether it has appeared in more distant locations (metastasized).
Riemannian manifoldIn differential geometry, a Riemannian manifold or Riemannian space (M, g), so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p. The family gp of inner products is called a Riemannian metric (or Riemannian metric tensor). Riemannian geometry is the study of Riemannian manifolds. A common convention is to take g to be smooth, which means that for any smooth coordinate chart (U, x) on M, the n2 functions are smooth functions.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Ricci curvatureIn differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space.
CarcinomaCarcinoma is a malignancy that develops from epithelial cells. Specifically, a carcinoma is a cancer that begins in a tissue that lines the inner or outer surfaces of the body, and that arises from cells originating in the endodermal, mesodermal or ectodermal germ layer during embryogenesis. Carcinomas occur when the DNA of a cell is damaged or altered and the cell begins to grow uncontrollably and become malignant. It is from the καρκίνωμα (itself derived from karkinos meaning crab).Oxford English Dictionary, 3rd edition, s.
PET-CTPositron emission tomography–computed tomography (better known as PET-CT or PET/CT) is a nuclear medicine technique which combines, in a single gantry, a positron emission tomography (PET) scanner and an x-ray computed tomography (CT) scanner, to acquire sequential images from both devices in the same session, which are combined into a single superposed () image. Thus, functional imaging obtained by PET, which depicts the spatial distribution of metabolic or biochemical activity in the body can be more precisely aligned or correlated with anatomic imaging obtained by CT scanning.
Symplectic geometrySymplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. The term "symplectic", introduced by Weyl, is a calque of "complex"; previously, the "symplectic group" had been called the "line complex group".
LungThe lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side of the heart. Their function in the respiratory system is to extract oxygen from the air and transfer it into the bloodstream, and to release carbon dioxide from the bloodstream into the atmosphere, in a process of gas exchange.
Ovarian cancerOvarian cancer is a cancerous tumor of an ovary. It may originate from the ovary itself or more commonly from communicating nearby structures such as fallopian tubes or the inner lining of the abdomen. The ovary is made up of three different cell types including epithelial cells, germ cells, and stromal cells. When these cells become abnormal, they have the ability to divide and form tumors. These cells can also invade or spread to other parts of the body. When this process begins, there may be no or only vague symptoms.
Christoffel symbolsIn mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without reference to a metric, and many additional concepts follow: parallel transport, covariant derivatives, geodesics, etc. also do not require the concept of a metric.
Bladder cancerBladder cancer is any of several types of cancer arising from the tissues of the urinary bladder. Symptoms include blood in the urine, pain with urination, and low back pain. It is caused when epithelial cells that line the bladder become malignant. Risk factors for bladder cancer include smoking, family history, prior radiation therapy, frequent bladder infections, and exposure to certain chemicals. The most common type is transitional cell carcinoma. Other types include squamous cell carcinoma and adenocarcinoma.
Predictive modellingPredictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases, the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.
Lung noduleA lung nodule or pulmonary nodule is a relatively small focal density in the lung. A solitary pulmonary nodule (SPN) or coin lesion, is a mass in the lung smaller than three centimeters in diameter. A pulmonary micronodule has a diameter of less than three millimetres. There may also be multiple nodules. One or more lung nodules can be an incidental finding found in up to 0.2% of chest X-rays and around 1% of CT scans.
Machine learningMachine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.
Predictive analyticsPredictive analytics is a form of business analytics applying machine learning to generate a predictive model for certain business applications. As such, it encompasses a variety of statistical techniques from predictive modeling and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. It represents a major subset of machine learning applications; in some contexts, it is synonymous with machine learning.
