Optimal number of oral implants for fixed reconstructions: a review of the literature.

BACKGROUND AND AIM So far there is little evidence from randomised clinical trials (RCT) or systematic reviews on the preferred or best number of implants to be used for the support of a fixed prosthesis in the edentulous maxilla or mandible, and no consensus has been reached. Therefore, we reviewed articles published in the past 30 years that reported on treatment outcomes for implant-supported fixed prostheses, including survival of implants and survival of prostheses after a minimum observation period of 1 year. MATERIAL AND METHODS MEDLINE and EMBASE were searched to identify eligible studies. Short and long-term clinical studies were included with prospective and retrospective study designs to see if relevant information could be obtained on the number of implants related to the prosthetic technique. Articles reporting on implant placement combined with advanced surgical techniques such as sinus floor elevation (SFE) or extensive grafting were excluded. Two reviewers extracted the data independently. RESULTS A primary search was broken down to 222 articles. Out of these, 29 studies comprising 26 datasets fulfilled the inclusion criteria. From all studies, the number of planned and placed implants was available. With two exceptions, no RCTs were found, and these two studies did not compare different numbers of implants per prosthesis. Eight studies were retrospective; all the others were prospective. Fourteen studies calculated cumulative survival rates for 5 and more years. From these data, the average survival rate was between 90% and 100%. The analysis of the selected articles revealed a clear tendency to plan 4 to 6 implants per prosthesis. For supporting a cross-arch fixed prosthesis in the maxilla, the variation is slightly greater. CONCLUSIONS In spite of a dispersion of results, similar outcomes are reported with regard to survival and number of implants per jaw. Since the 1990s, it was proven that there is no need to install as many implants as possible in the available jawbone. The overwhelming majority of articles dealing with standard surgical procedures to rehabilitate edentulous jaws uses 4 to 6 implants.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.