High performance additive manufactured scaffolds for bone tissue engineering application

This study demonstrates the feasibility of additive manufactured poly(3-caprolactone)/silanized tricalcium phosphate (PCL/TCP(Si)) scaffolds coated with carbonated hydroxyapatite (CHA)-gelatin composite for bone tissue engineering. In order to reinforce PCL/TCP scaffolds to match the mechanical properties of cancellous bone, TCP has been modified with 3-glycidoxypropyl trimethoxysilane (GPTMS) and incorporated into PCL to synthesize a PCL/TCP(Si) composite. The successful modification is confirmed by X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR) analysis. Additive manufactured PCL/TCP(Si) scaffolds have been fabricated using a screw extrusion system (SES). Compression testing demonstrates that both the compressive modulus and compressive yield strength of the developed PCL/TCP(Si) scaffolds fall within the lower ranges of mechanical properties for cancellous bone, with a compressive modulus and compressive yield strength of 6.0 times and 2.3 times of those of PCL/TCP scaffolds, respectively. To enhance the osteoconductive property of the developed PCL/TCP(Si) scaffolds, a CHA-gelatin composite has been coated onto the scaffolds via a biomimetic co-precipitation process, which is verified by using scanning electron microscopy (SEM) and XPS. Confocal laser microscopy and SEM images reveal a most uniform distribution of porcine bone marrow stromal cells (BMSCs) and cellsheet accumulation on the CHA-gelatin composite coated PCL/TCP(Si) scaffolds. The proliferation rate of BMSCs on the CHA-gelatin composite coated PCL/TCP(Si) scaffolds is 2.0 and 1.4 times higher compared to PCL/TCP(Si) and CHA coated PCL/TCP(Si) scaffolds, respectively, by day 10. Furthermore, the reverse transcription polymerase chain reaction (RT-PCR) and western blot analyses reveal that CHA-gelatin composite coated PCL/TCP(Si) scaffolds stimulate osteogenic differentiation of BMSCs the most compared to the other scaffolds. In vitro results of SEM, confocal microscopy and proliferation rate also show that there is no detrimental effect of GPTMS modification on biocompatibility of the scaffolds.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.