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When dealing with longitudinal data, linear mixed-effects models (LMMs) are often used by researchers. However, LMMs are not always the most adequate models, especially if we expect a nonlinear relationship between the outcome and a continuous covariate. To allow for more flexibility, we propose the use of a semiparametric mixed-effects model to evaluate the overall treatment effect on the hemodynamic responses during bone graft healing and build a prediction model for the healing process. The model relies on a closed-form expectation–maximization algorithm, where the unknown nonlinear function is estimated using a Lasso-type procedure. Using this model, we were able to estimate the effect of time for individual mice in each group in a nonparametric fashion and the effect of the treatment while accounting for correlation between observations due to the repeated measurements. The treatment effect was found to be statistically significant, with the autograft group having higher total hemoglobin concentration than the allograft group. 

Allograft is the current gold standard for treating critical-sized bone defects. However, allograft healing is usually compromised partially due to poor host-mediated vascularization. In the efforts towards developing new methods to enhance allograft healing, a non-terminal technique for monitoring the vascularization is needed in pre-clinical mouse models. In this study, we developed a non-invasive instrument based on spatial frequency domain imaging (SFDI) for longitudinal monitoring of the mouse femoral graft healing. SFDI technique provided total hemoglobin concentration (THC) and oxygen saturation (StO₂) of the graft and the surrounding soft tissues. SFDI measurements were performed from 1 day before to 44 days after graft transplantation. Autograft, another type of bone graft with higher vascularization potential was also measured as a comparison to allograft. For both grafts, the overall temporal changes of the measured THC agreed with the physiological expectations of vascularization timeline during bone healing. A significantly greater increase in THC was observed in the autograft group compared to the allograft group, which agreed with the expectation that allografts have more compromised vascularization.