ShoulderThe human shoulder is made up of three bones: the clavicle (collarbone), the scapula (shoulder blade), and the humerus (upper arm bone) as well as associated muscles, ligaments and tendons. The articulations between the bones of the shoulder make up the shoulder joints. The shoulder joint, also known as the glenohumeral joint, is the major joint of the shoulder, but can more broadly include the acromioclavicular joint. In human anatomy, the shoulder joint comprises the part of the body where the humerus attaches to the scapula, and the head sits in the glenoid cavity.
Rotator cuffThe rotator cuff is a group of muscles and their tendons that act to stabilize the human shoulder and allow for its extensive range of motion. Of the seven scapulohumeral muscles, four make up the rotator cuff. The four muscles are: supraspinatus muscle infraspinatus muscle teres minor muscle subscapularis muscle. The supraspinatus muscle spreads out in a horizontal band to insert on the superior facet of the greater tubercle of the humerus. The greater tubercle projects as the most lateral structure of the humeral head.
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.
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.
Shoulder problemShoulder problems including pain, are one of the more common reasons for physician visits for musculoskeletal symptoms. The shoulder is the most movable joint in the body. However, it is an unstable joint because of the range of motion allowed. This instability increases the likelihood of joint injury, often leading to a degenerative process in which tissues break down and no longer function well. Shoulder pain may be localized or may be referred to areas around the shoulder or down the arm.
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.
Dislocated shoulderA dislocated shoulder is a condition in which the head of the humerus is detached from the shoulder joint. Symptoms include shoulder pain and instability. Complications may include a Bankart lesion, Hill-Sachs lesion, rotator cuff tear, or injury to the axillary nerve. A shoulder dislocation often occurs as a result of a fall onto an outstretched arm or onto the shoulder. Diagnosis is typically based on symptoms and confirmed by X-rays. They are classified as anterior, posterior, inferior, and superior with most being anterior.
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.
Shoulder girdleThe shoulder girdle or pectoral girdle is the set of bones in the appendicular skeleton which connects to the arm on each side. In humans it consists of the clavicle and scapula; in those species with three bones in the shoulder, it consists of the clavicle, scapula, and coracoid. Some mammalian species (such as the dog and the horse) have only the scapula. The pectoral girdles are to the upper limbs as the pelvic girdle is to the lower limbs; the girdles are the parts of the appendicular skeleton that anchor the appendages to the axial skeleton.
Rotator cuff tearRotator cuff tendinopathy is a process of senescence. The pathophysiology is mucoid degeneration. Most people develop rotator cuff tendinopathy within their lifetime. As part of rotator cuff tendinopathy, the tendon can thin and develop a defect. This defect is often referred to as a rotator cuff tear. Acute, traumatic rupture of the rotator cuff tendons can also occur, but is less common. Traumatic rupture of the rotator cuff usually involves the tendons of more than one muscle.
Shoulder impingement syndromeShoulder impingement syndrome is a syndrome involving tendonitis (inflammation of tendons) of the rotator cuff muscles as they pass through the subacromial space, the passage beneath the acromion. It is particularly associated with tendonitis of the supraspinatus muscle. This can result in pain, weakness, and loss of movement at the shoulder. The most common symptoms in impingement syndrome are pain, weakness and a loss of movement at the affected shoulder.
Humerus fractureA humerus fracture is a break of the humerus bone in the upper arm. Symptoms may include pain, swelling, and bruising. There may be a decreased ability to move the arm and the person may present holding their elbow. Complications may include injury to an artery or nerve, and compartment syndrome. The cause of a humerus fracture is usually physical trauma such as a fall. Other causes include conditions such as cancer in the bone. Types include proximal humeral fractures, humeral shaft fractures, and distal humeral fractures.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
JointA joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole. They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements.
Anatomical terms of motionMotion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the body parts involved. Anatomists and others use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing unique movements such as those of the hands, feet, and eyes.
Approximation errorThe approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute error divided by the data value). An approximation error can occur for a variety of reasons, among them a computing machine precision or measurement error (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.
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.
HumerusThe humerus (ˈhjuːmərəs; : humeri) is a long bone in the arm that runs from the shoulder to the elbow. It connects the scapula and the two bones of the lower arm, the radius and ulna, and consists of three sections. The humeral upper extremity consists of a rounded head, a narrow neck, and two short processes (tubercles, sometimes called tuberosities). The body is cylindrical in its upper portion, and more prismatic below. The lower extremity consists of 2 epicondyles, 2 processes (trochlea & capitulum), and 3 fossae (radial fossa, coronoid fossa, and olecranon fossa).
Adhesive capsulitis of the shoulderAdhesive capsulitis, also known as frozen shoulder, is a condition associated with shoulder pain and stiffness. It is a common shoulder ailment that is marked by pain and a loss of range of motion, particularly in external rotation. There is a loss of the ability to move the shoulder, both voluntarily and by others, in multiple directions. The shoulder itself, however, does not generally hurt significantly when touched. Muscle loss around the shoulder may also occur. Onset is gradual over weeks to months.
Skeletal muscleSkeletal muscles (commonly referred to as muscles) are organs of the vertebrate muscular system and typically are attached by tendons to bones of a skeleton. The muscle cells of skeletal muscles are much longer than in the other types of muscle tissue, and are often known as muscle fibers. The muscle tissue of a skeletal muscle is striated – having a striped appearance due to the arrangement of the sarcomeres. Skeletal muscles are voluntary muscles under the control of the somatic nervous system.
