Extend The Equation Of Bone Remodeling Form 2D To 3D

As a health problem, osteoporosis has caught all the world's attention and there are more and more people pay more and more attention on it. For the population aged, there is an increasing trend of the incidence of the ostroporosis that is bad to the health of the elderly.But there are a few models of osteoporosis simulation based on the mechanical factors. H.M. Frost give the definition on biomechanical that bone mass and bone strength falls extremely that cause the bone can not fit the muscle strength; physical activity can cause fractures and ache in bone and the fracture always affect extremity bone more than the spine. Frost originally coined the term "activation"to denote the beginning of a new BMU, and the activation frequency was defined as the birthrate of new BMUs in a unit amount of bone. By activation, Frost meant a stimulus to precursor cells to begin dividing to produce the new cells that comprise the new BMU. As calculated by Frost in cortical bone, and as currently calculated by many investigators in cancellous bone, activation frequency is a 2D, not a 3D, concept. The 3D version of this variable is the rate at which new BMUs are generated on internal bone surfaces; thus, the units of this variable would be BMUs created per square millimeter of surface per day. There are three key variables used to describe a population of BMUs in a given volume of bone tissues: the total number of BMUs; their birthrate; and their mean lifespan. The conceptualization of these three variables in the 2D and 3D observational systems has been quite different. Activation frequency is often used as a measure of basic multicellular unit activity in cancellous bone. Huiskes developed a mechanistic model for metabolism of cancellous bone in the year of 2000, and Hazelwood developed a mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload in the year of 2001. These models can simulate the process of remodeling of bone, but these simulations are two-dimensional, not three-dimensional. The main different between two-dimensional simulation and three-dimensional one is the difference of activation frequency. Activation frequency calculated in two-dimensional concept is the best histological index of the overall intensity of bone remodeling, but it is not the birthrate of new BMUs. The explanation of this paradox is that the calculation of activation frequency takes no account of the three-dimensional organization of the BMU, and another fault is that the calculation of activation frequency is not expressed in reference to the amount of bone surface, because all remodeling occurs on bone surface. The two-dimensional activation frequency is the appearance rate and the three-dimensional activation frequency is the birthrate or the origination rate, the latter can more accurately express the activity of bone remodeling and is very useful for the development of BMU-level bone remodeling. The formula of origination rate, the three-dimension activation frequency, of cancellous and cortical bone is different. For cortical bone: f( TB MUs /mm 3/ day )= λ×BfMHU .R fT the true activation or origination frequency (BMU/mm3/day) fH histologic activation or two-dimension frequency (BMU/mm3/day) λthe BMU lifespan (day) BMU.R the rate of BMU progression across the surface (mm/day) For cancellous bone: Or. f (BMUs/ mm 2/day)= .. .DSAc fBMU Wi ×BMU Or. f origination frequency or birthrate (BMUs/mm2/day) Ac.f histologic activation or two-dimension frequency(1/day) BMU.Wi the width of the BMU (mm) The improved remodeling formulas are used in the bone remodeling simulations existed, here we apply the formula in the bone remodeling simulation which developed by Hazelwood. In the simulation we replace the activation frequency with the improved formula of origination frequency, and modify the interrelated variables. The three-dimension activation frequency is equal to the two-dimension activation frequency multiply by a coefficient called X. Known from the three key variables used to describe a population of BMUs in a given volume of bone tissues, there are more BMUs in the three-dimension conception and the BMUs have better activity, the coefficient should be a constant greater...