Lecture

Bone Adaptation Modeling

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Description

This lecture covers the modeling of bone adaptation using partial differential equations, focusing on the relationship between bone density and mechanical stimuli. It discusses examples from orthopedic surgery research and numerical simulations using COMSOL Multiphysics software.

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Related concepts (15)

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

Hyperbolic partial differential equation

In mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Numerical methods for partial differential equations

Numerical 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.

Orthopedic surgery

Orthopedic surgery or orthopedics (alternatively spelt orthopaedics) is the branch of surgery concerned with conditions involving the musculoskeletal system. Orthopedic surgeons use both surgical and nonsurgical means to treat musculoskeletal trauma, spine diseases, sports injuries, degenerative diseases, infections, tumors, and congenital disorders. Nicholas Andry coined the word in French as orthopédie, derived from the Ancient Greek words ὀρθός orthos ("correct", "straight") and παιδίον paidion ("child"), and published Orthopedie (translated as Orthopædia: Or the Art of Correcting and Preventing Deformities in Children) in 1741.

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