Determining the most important cellular characteristics for fracture healing, using design of experiments methods

Computational models are employed as tools to investigate possible mechanoregulation pathways fortissue differentiation and bone healing. However, current models do not account for the uncertainty ininput parameters, and often include assumptions about parameter values that are not yet established.The objective of this study was to determine the most important cellular characteristics of amechanoregulatory model describing both cell phenotype-specific and mechanobiological processesthat are active during bone healing using a statistical approach. The computational model included anadaptive two-dimensional finite element model of a fractured long bone. Three different outcomecriteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation atearly, mid and late stages of healing and (3) the total time until complete healing. For the statisticalanalysis, first a resolution IV fractional factorial design (L64) was used to identify the most significantfactors. Thereafter, a three-level Taguchi orthogonal array (L27) was employed to study the curvature(non-linearity) of the 10 identified most important parameters. The results show that the ability of themodel to predict the sequences of normal fracture healing was predominantly influenced by the rate ofmatrix production of bone, followed by cartilage degradation (replacement). The amount of boneformation at early stages was solely dependent on matrix production of bone and the proliferation rateof osteoblasts. However, the amount of bone formation at mid and late phases had the rate of matrixproduction of cartilage as the most influential parameter. The time to complete healing was primarilydependent on the rate of cartilage degradation during endochondral ossification, followed by the rate ofcartilage formation. The analyses of the curvature revealed a linear response for parameters relatedto bone, where higher rates of formation were more beneficial to healing. In contrast, parametersrelated to fibrous tissue and cartilage showed optimum levels. Some fibrous connective tissue- andcartilage formation was beneficial to bone healing, but too much of either tissue delayed boneformation. The identified significant parameters and processes are further confirmed by in vivo animalexperiments in the literature. This study illustrates the potential of design of experiments methods forevaluating computational mechanobiological model parameters and suggests that further experimentsshould preferably focus at establishing values of parameters related to cartilage formation anddegradation.