Characterising neovascularisation in fracture healing with laser Doppler and micro-CT scanning

Vascularity of the soft tissues around a bone fracture is critical for successful healing, particularly when the vessels in the medullary canal are ruptured. The objective of this work was to use laser Doppler and micro-computer tomography (micro-CT) scanning to characterise neovascularisation of the soft tissues surrounding the fracture during healing. Thirty-two Sprague–Dawley rats underwent mid-shaft osteotomy of the left femur, stabilised with a custom-designed external fixator. Five animals were killed at each of 2, 4 days, 1, 2, 4 and 6 weeks post-operatively. Femoral blood perfusion in the fractured and intact contralateral limbs was measured using laser Doppler scanning pre- and post-operatively and throughout the healing period. At sacrifice, the common iliac artery was cannulated and infused with silicone contrast agent. Micro-CT scans of the femur and adjacent soft tissues revealed vessel characteristics and distribution in relation to the fracture zone. Blood perfusion dropped immediately after surgery and then recovered to greater than the pre-operative level by proliferation of small vessels around the fracture zone. Multi-modal imaging allowed both longitudinal functional and detailed structural analysis of the neovascularisation process

Certification of Breadth-First Algorithms by Extraction

International audienceBy using pointers, breadth-first algorithms are very easy to implement efficiently in imperative languages. Implementing them with the same bounds on execution time in purely functional style can be challenging, as explained in Okasaki’s paper at ICFP 2000 that even restricts the problem to binary trees but considers numbering instead of just traversal. Okasaki’s solution is modular and factors out the problem of implementing queues (FIFOs) with worst-case constant time operations. We certify those FIFO-based breadth-first algorithms on binary trees by extracting them from fully specified Coq terms, given an axiomatic description of FIFOs. In addition, we axiomatically characterize the strict and total order on branches that captures the nature of breadth-first traversal and propose alternative characterizations of breadth-first traversal of forests. We also propose efficient certified implementations of FIFOs by extraction, either with pairs of lists (with amortized constant time operations) or triples of lazy lists (with worst-case constant time operations), thus getting from extraction certified breadth-first algorithms with the optimal bounds on execution time