Knee replacementKnee replacement, also known as knee arthroplasty, is a surgical procedure to replace the weight-bearing surfaces of the knee joint to relieve pain and disability, most commonly offered when joint pain is not diminished by conservative sources. It may also be performed for other knee diseases, such as rheumatoid arthritis. In patients with severe deformity from advanced rheumatoid arthritis, trauma, or long-standing osteoarthritis, the surgery may be more complicated and carry higher risk.
KneeIn humans and other primates, the knee joins the thigh with the leg and consists of two joints: one between the femur and tibia (tibiofemoral joint), and one between the femur and patella (patellofemoral joint). It is the largest joint in the human body. The knee is a modified hinge joint, which permits flexion and extension as well as slight internal and external rotation. The knee is vulnerable to injury and to the development of osteoarthritis. It is often termed a compound joint having tibiofemoral and patellofemoral components.
Joint replacementReplacement arthroplasty (from Greek arthron, joint, limb, articulate, + plassein, to form, mould, forge, feign, make an image of), or joint replacement surgery, is a procedure of orthopedic surgery in which an arthritic or dysfunctional joint surface is replaced with an orthopedic prosthesis. Joint replacement is considered as a treatment when severe joint pain or dysfunction is not alleviated by less-invasive therapies. It is a form of arthroplasty, and is often indicated from various joint diseases, including osteoarthritis and rheumatoid arthritis.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
ArthroplastyArthroplasty (literally "[re-]forming of joint") is an orthopedic surgical procedure where the articular surface of a musculoskeletal joint is replaced, remodeled, or realigned by osteotomy or some other procedure. It is an elective procedure that is done to relieve pain and restore function to the joint after damage by arthritis or some other type of trauma. Joint replacement For the last 45 years, the most successful and common form of arthroplasty is the surgical replacement of arthritic or destructive or necrotic joint or joint surface with a prosthesis.
Patellar tendinitisPatellar tendinitis, also known as jumper's knee, is an overuse injury of the tendon that straightens the knee. Symptoms include pain in the front of the knee. Typically the pain and tenderness is at the lower part of the kneecap, though the upper part may also be affected. Generally there is no pain when the person is at rest. Complications may include patellar tendon rupture. Risk factors include being involved in athletics and being overweight. It is particularly common in athletes who are involved in jumping sports such as basketball and volleyball.
BoneA bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and enable mobility. Bones come in a variety of shapes and sizes and have complex internal and external structures. They are lightweight yet strong and hard and serve multiple functions. Bone tissue (osseous tissue), which is also called bone in the uncountable sense of that word, is hard tissue, a type of specialised connective tissue.
Hip replacementHip replacement is a surgical procedure in which the hip joint is replaced by a prosthetic implant, that is, a hip prosthesis. Hip replacement surgery can be performed as a total replacement or a hemi (half) replacement. Such joint replacement orthopaedic surgery is generally conducted to relieve arthritis pain or in some hip fractures. A total hip replacement (total hip arthroplasty or THA) consists of replacing both the acetabulum and the femoral head while hemiarthroplasty generally only replaces the femoral head.
Bone mineralBone mineral (also called inorganic bone phase, bone salt, or bone apatite) is the inorganic component of bone tissue. It gives bones their compressive strength. Bone mineral is formed predominantly from carbonated hydroxyapatite with lower crystallinity. Bone mineral is formed from globular and plate structures distributed among the collagen fibrils of bone and forming yet a larger structure. The bone salt and collagen fibers together constitute the extracellular matrix of bone tissue.
Bone densityBone density, or bone mineral density, is the amount of bone mineral in bone tissue. The concept is of mass of mineral per volume of bone (relating to density in the physics sense), although clinically it is measured by proxy according to optical density per square centimetre of bone surface upon imaging. Bone density measurement is used in clinical medicine as an indirect indicator of osteoporosis and fracture risk. It is measured by a procedure called densitometry, often performed in the radiology or nuclear medicine departments of hospitals or clinics.
OsteopeniaOsteopenia, known as "low bone mass" or "low bone density", is a condition in which bone mineral density is low. Because their bones are weaker, people with osteopenia may have a higher risk of fractures, and some people may go on to develop osteoporosis. In 2010, 43 million older adults in the US had osteopenia. Unlike osteoporosis, osteopenia does not usually cause symptoms, and losing bone density in itself does not cause pain.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
SurgerySurgery is a medical specialty that uses manual and/or instrumental techniques to physically reach into a subject's body in order to investigate or treat pathological conditions such as a disease or injury, to alter bodily functions (e.g. bariatric surgery such as gastric bypass), to improve appearance (cosmetic surgery), or to remove/replace unwanted tissues (body fat, glands, scars or skin tags) or foreign bodies. The subject receiving the surgery is typically a person (i.e. a patient), but can also be a non-human animal (i.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
OsteoporosisOsteoporosis is a systemic skeletal disorder characterized by low bone mass, micro-architectural deterioration of bone tissue leading to bone sterility, and consequent increase in fracture risk. It is the most common reason for a broken bone among the elderly. Bones that commonly break include the vertebrae in the spine, the bones of the forearm, and the hip. Until a broken bone occurs there are typically no symptoms. Bones may weaken to such a degree that a break may occur with minor stress or spontaneously.
BiomechanicsBiomechanics is the study of the structure, function and motion of the mechanical aspects of biological systems, at any level from whole organisms to organs, cells and cell organelles, using the methods of mechanics. Biomechanics is a branch of biophysics. In 2022, computational mechanics goes far beyond pure mechanics, and involves other physical actions: chemistry, heat and mass transfer, electric and magnetic stimuli and many others.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
CorrelationIn statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
