Three-dimension-printed custom-made prosthetic reconstructions: from revision surgery to oncologic reconstructions

Background The use of custom-made 3D-printed prostheses for reconstruction of severe bone defects in selected cases is increasing. The aims of this study were to evaluate (1) the feasibility of surgical reconstruction with these prostheses in oncologic and non-oncologic settings and (2) the functional results, complications, and outcomes at short-term follow-up. Methods We analyzed 13 prospectively collected patients treated between June 2016 and January 2018. Diagnoses were primary bone tumour (7 patients), metastasis (3 patients), and revision of total hip arthroplasty (3 patients). Pelvis was the most frequent site of reconstruction (7 cases). Functional results were assessed with MSTS score and complications according to Henderson et al. Statistical analysis was performed using Kaplan-Meier and log-rank test curves. Results At a mean follow-up of 13.7 months (range, 6 \u2013 26 months), all patients except one were alive. Oncologic outcomes show seven patients NED (no evidence of disease), one NED after treatment of metastasis, one patient died of disease, and another one was alive with disease. Overall survival was 100% and 80% at one and two years, respectively. Seven complications occurred in five patients (38.5%). Survival to all complications was 62% at two years of follow-up. Functional outcome was good or excellent in all cases with a mean score of 80.3%. Conclusion 3D-printed custom-made prostheses represent a promising reconstructive technique in musculoskeletal oncology and challenging revision surgery. Preliminary results were satisfactory. Further studies are needed to evaluate prosthetic design, fixation methods, and stability of the implants at long-ter

Mutual Dimension

We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We show that these quantities satisfy the main desiderata for a satisfactory measure of mutual algorithmic information. Our main theorem, the data processing inequality for mutual dimension, says that, if $f:\mathbb{R}^m \rightarrow \mathbb{R}^n$ is computable and Lipschitz, then the inequalities $mdim(f(x):y) \leq mdim(x:y)$ and $Mdim(f(x):y) \leq Mdim(x:y)$ hold for all $x \in \mathbb{R}^m$ and $y \in \mathbb{R}^t$. We use this inequality and related inequalities that we prove in like fashion to establish conditions under which various classes of computable functions on Euclidean space preserve or otherwise transform mutual dimensions between points.Comment: This article is 29 pages and has been submitted to ACM Transactions on Computation Theory. A preliminary version of part of this material was reported at the 2013 Symposium on Theoretical Aspects of Computer Science in Kiel, German

Asymptotic Dimension

The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.Comment: Added some remarks about coarse equivalence of finitely generated groups

Dimension expanders

We show that there exists k \in \bbn and 0 < \e \in\bbr such that for every field $F$ of characteristic zero and for every n \in \bbn, there exists explicitly given linear transformations $T_1,..., T_k: F^n \to F^n$ satisfying the following: For every subspace $W$ of $F^n$ of dimension less or equal $\frac n2$, \dim(W+\suml^k_{i=1} T_iW) \ge (1+\e) \dim W. This answers a question of Avi Wigderson [W]. The case of fields of positive characteristic (and in particular finite fields) is left open