Wound healingWound healing refers to a living organism's replacement of destroyed or damaged tissue by newly produced tissue. In undamaged skin, the epidermis (surface, epithelial layer) and dermis (deeper, connective layer) form a protective barrier against the external environment. When the barrier is broken, a regulated sequence of biochemical events is set into motion to repair the damage. This process is divided into predictable phases: blood clotting (hemostasis), inflammation, tissue growth (cell proliferation), and tissue remodeling (maturation and cell differentiation).
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Chronic woundA chronic wound is a wound that does not heal in an orderly set of stages and in a predictable amount of time the way most wounds do; wounds that do not heal within three months are often considered chronic. Chronic wounds seem to be detained in one or more of the phases of wound healing. For example, chronic wounds often remain in the inflammatory stage for too long. To overcome that stage and jump-start the healing process, a number of factors need to be addressed such as bacterial burden, necrotic tissue, and moisture balance of the whole wound.
WoundA wound is a rapid onset of injury that involves lacerated or punctured skin (an open wound), or a contusion (a closed wound) from blunt force trauma or compression. In pathology, a wound is an acute injury that damages the epidermis of the skin. To heal a wound, the body undertakes a series of actions collectively known as the wound healing process. According to the level of contamination, a wound can be classified as: Clean wound – made under sterile conditions where there are no organisms present, and the skin is likely to heal without complications.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
KeratinocyteKeratinocytes are the primary type of cell found in the epidermis, the outermost layer of the skin. In humans, they constitute 90% of epidermal skin cells. Basal cells in the basal layer (stratum basale) of the skin are sometimes referred to as basal keratinocytes. Keratinocytes form a barrier against environmental damage by heat, UV radiation, water loss, pathogenic bacteria, fungi, parasites, and viruses. A number of structural proteins, enzymes, lipids, and antimicrobial peptides contribute to maintain the important barrier function of the skin.
Skin graftingSkin grafting, a type of graft surgery, involves the transplantation of skin. The transplanted tissue is called a skin graft. Surgeons may use skin grafting to treat: extensive wounding or trauma burns areas of extensive skin loss due to infection such as necrotizing fasciitis or purpura fulminans specific surgeries that may require skin grafts for healing to occur – most commonly removal of skin cancers Skin grafting often takes place after serious injuries when some of the body's skin is damaged.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
EpidermisThe epidermis is the outermost of the three layers that comprise the skin, the inner layers being the dermis and hypodermis. The epidermis layer provides a barrier to infection from environmental pathogens and regulates the amount of water released from the body into the atmosphere through transepidermal water loss. The epidermis is composed of multiple layers of flattened cells that overlie a base layer (stratum basale) composed of columnar cells arranged perpendicularly. The layers of cells develop from stem cells in the basal layer.
Integumentary systemThe integumentary system is the set of organs forming the outermost layer of an animal's body. It comprises the skin and its appendages, which act as a physical barrier between the external environment and the internal environment that it serves to protect and maintain the body of the animal. Mainly it is the body's outer skin. The integumentary system includes hair, scales, feathers, hooves, and nails.
Wound bed preparationWound bed preparation (WBP) is a systematic approach to wound management by identifying and removing barriers to healing. The concept was originally developed in plastic surgery. During the year 2000, the concept was applied to systematizing the treatment of chronic wounds. The 2000 proposals recommended that wound management address the identifiable impediments to healing in order to achieve more successful outcomes. Three publications appeared that year that focused on the concept of managing the healing processes of a wound exudate, bioburden and devitalized tissue.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
HealingWith physical trauma or disease suffered by an organism, healing involves the repairing of damaged tissue(s), organs and the biological system as a whole and resumption of (normal) functioning. Medicine includes the process by which the cells in the body regenerate and repair to reduce the size of a damaged or necrotic area and replace it with new living tissue. The replacement can happen in two ways: by regeneration in which the necrotic cells are replaced by new cells that form "like" tissue as was originally there; or by repair in which injured tissue is replaced with scar tissue.
DermisThe dermis or corium is a layer of skin between the epidermis (with which it makes up the cutis) and subcutaneous tissues, that primarily consists of dense irregular connective tissue and cushions the body from stress and strain. It is divided into two layers, the superficial area adjacent to the epidermis called the papillary region and a deep thicker area known as the reticular dermis. The dermis is tightly connected to the epidermis through a basement membrane.
SkinSkin is the layer of usually soft, flexible outer tissue covering the body of a vertebrate animal, with three main functions: protection, regulation, and sensation. Other animal coverings, such as the arthropod exoskeleton, have different developmental origin, structure and chemical composition. The adjective cutaneous means "of the skin" (from Latin cutis 'skin'). In mammals, the skin is an organ of the integumentary system made up of multiple layers of ectodermal tissue and guards the underlying muscles, bones, ligaments, and internal organs.
Actinic keratosisActinic keratosis (AK), sometimes called solar keratosis or senile keratosis, is a pre-cancerous area of thick, scaly, or crusty skin. Actinic keratosis is a disorder (-osis) of epidermal keratinocytes that is induced by ultraviolet (UV) light exposure (actin-). These growths are more common in fair-skinned people and those who are frequently in the sun. They are believed to form when skin gets damaged by UV radiation from the sun or indoor tanning beds, usually over the course of decades.
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
