Symptomatic epiphyseal sprains and stress fractures of the finger phalanges in adolescent sport climbers

The purpose of this study was to document and evaluate patient characteristics, injury mechanisms and clinical outcomes of epiphyseal stress fractures of the finger phalanges in adolescent rock climbers to identify contributing factors to this injury. Twenty-eight climbers with epiphyseal pain treated at our clinic between 2006 and 2018 were included in the study. Sixteen patients completed a questionnaire addressing injury details as well as training regimen before and after the injury. The mean age at the time of injury was 13.7 years (± 1.9 years) with the injury occurring predominantly in male athletes. Middle (58%) and ring (30%) fingers were the most commonly affected sites out of a total of 67 fingers affected; 54% had a radiologically documented epiphyseal fracture (Salter Harris type II/III) while 46% suffered from a symptomatic sprain, which could potentially lead to a stress fracture. Mean time for radiological union of a fracture was 35 weeks. Recovery time for a symptomatic sprain was on average slightly shorter at 24 weeks. All patients were treated conservatively with load reduction for 3-12 months until the symptoms disappeared. Although most patients had a positive outcome when treated correctly, this injury can damage the growth plate when left untreated, resulting in articular surface incongruency (1 severe, 1 moderate, 6 mild) with permanent impairment of the affected finger. Therefore, pain on the dorsal aspect of the proximal interphalangeal joint in adolescent climbers must be assessed carefully

Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving