Occurrence and Treatment of Bone Atrophic Non-Unions Investigated by an Integrative Approach

Recently developed atrophic non-union models are a good representation of the clinical situation in which many nonunions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures

On the value of conditioning data to reduce conceptual model uncertainty in groundwater modeling

Recent applications of multi-model methods have demonstrated their potential in quantifying conceptual model uncertainty in groundwater modeling applications. To date, however, little is known about the value of conditioning to constrain the ensemble of conceptualizations, to differentiate among retained alternative conceptualizations, and to reduce conceptual model uncertainty. We address these questions by conditioning multi-model simulations on measurements of hydraulic conductivity and observations of system-state variables and evaluating the e ffects on (i) the posterior multi-model statistics and (ii) the contribution of conceptual model uncertainty to the predictive uncertainty. Multi-model aggregation and conditioning is performed by combining the generalized likelihood uncertainty estimation (GLUE) method and Bayesian model averaging (BMA). As an illustrative example we employ a 3-dimensional hypothetical system under steady-state conditions, for which uncertainty about the conceptualization is expressed by an ensemble (M) of 7 models with varying complexity. Results show that conditioning on heads allowed for the exclusion of the two simplest models, but that their information content is limited to further diff erentiate among the retained conceptualizations. Conditioning on increasing numbers of conductivity measurements allowed for a further reffinement of the ensemble M and resulted in an increased precision and accuracy of the multi-model predictions. For some groundwater flow components not included as conditioning data, however, the gain in accuracy and precision was partially o ffset by strongly deviating predictions of a single conceptualization. Identifying the conceptualization producing the most deviating predictions may guide data collection campaigns aimed at acquiring data to further eliminate such conceptualizations. Including groundwater flow and river discharge observations further allowed for a better diff erentiation among alternative conceptualizations and drastic reductions of the predictive variances. Results strongly advocate the use of observations less commonly available than groundwater heads to reduce conceptual model uncertainty in groundwater modeling