Biomaterial Database

A probabilistic rule of mixtures for elastic moduli. 1999

A J Rapoff, and D M Heisey, and R Vanderby

Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville 32611-6250, USA. rapoff@aero.ufl.edu

A novel approach is developed for mathematically modeling the variability observed in experimentally determined elastic moduli of longitudinally oriented fibrous tissues such as ligaments and tendons. The elastic modulus of these tissues is modeled with a rule of mixtures (ROM) where each parameter (fibril and matrix moduli and fibril volume fraction) is assumed to be an independent random variable. A joint density function formed from the independent densities results in a probabilistic ROM (pROM). This pROM is used to generate a distribution of moduli which agrees well with moduli determined from tests of rabbit medial collateral ligaments (Woo and Ohland, 1994, Unpublished experimental data as gift). Minimizing the error between the pROM and experimental distributions resulted in an integrated error of 9% for a constrained set of independent distribution parameters derived from the literature. This pROM thus incorporates microstructural observations (fibril and matrix moduli and fibril volume fraction) to partially explain the experimentally observed variability in a macroscopic property (tissue modulus).

UI	MeSH Term	Description	Entries
D007596	Joints	Also known as articulations, these are points of connection between the ends of certain separate bones, or where the borders of other bones are juxtaposed.	Joint
D008023	Ligaments, Articular	Fibrous cords of CONNECTIVE TISSUE that attach bones to each other and hold together the many types of joints in the body. Articular ligaments are strong, elastic, and allow movement in only specific directions, depending on the individual joint.	Articular Ligament,Articular Ligaments,Ligament, Articular
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D003094	Collagen	A polypeptide substance comprising about one third of the total protein in mammalian organisms. It is the main constituent of SKIN; CONNECTIVE TISSUE; and the organic substance of bones (BONE AND BONES) and teeth (TOOTH).	Avicon,Avitene,Collagen Felt,Collagen Fleece,Collagenfleece,Collastat,Dermodress,Microfibril Collagen Hemostat,Pangen,Zyderm,alpha-Collagen,Collagen Hemostat, Microfibril,alpha Collagen
D004548	Elasticity	Resistance and recovery from distortion of shape.
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D013269	Stochastic Processes	Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.	Process, Stochastic,Stochastic Process,Processes, Stochastic
D013710	Tendons	Fibrous bands or cords of CONNECTIVE TISSUE at the ends of SKELETAL MUSCLE FIBERS that serve to attach the MUSCLES to bones and other structures.	Endotenon,Epotenon,Tendons, Para-Articular,Tendons, Paraarticular,Endotenons,Epotenons,Para-Articular Tendon,Para-Articular Tendons,Paraarticular Tendon,Paraarticular Tendons,Tendon,Tendon, Para-Articular,Tendon, Paraarticular,Tendons, Para Articular