Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

A bone-thickness map as a guide for bone-anchored port implantation surgery in the temporal bone

The bone-anchored port (BAP) is an investigational implant, which is intended to be fixed on the temporal bone and provide vascular access. There are a number of implants taking advantage of the stability and available room in the temporal bone. These devices range from implantable hearing aids to percutaneous ports. During temporal bone surgery, injuring critical anatomical structures must be avoided. Several methods for computer-assisted temporal bone surgery are reported, which typically add an additional procedure for the patient. We propose a surgical guide in the form of a bone-thickness map displaying anatomical landmarks that can be used for planning of the surgery, and for the intra-operative decision of the implant’s location. The retro-auricular region of the temporal and parietal bone was marked on cone-beam computed tomography scans and tridimensional surfaces displaying the bone thickness were created from this space. We compared this method using a thickness map (n = 10) with conventional surgery without assistance (n = 5) in isolated human anatomical whole head specimens. The use of the thickness map reduced the rate of Dura Mater exposition from 100% to 20% and OPEN ACCESS Materials 2013, 6 5292 suppressed sigmoid sinus exposures. The study shows that a bone-thickness map can be used as a low-complexity method to improve patient’s safety during BAP surgery in the temporal bone.

Human intervertebral disc stiffness correlates better with the Otsu threshold computed from axial T2 map of its posterior annulus fibrosus than with clinical classifications

Degeneration of the intervertebral disc, sometimes associated with low back pain and abnormal spinal motions, represents a major health issue with high costs. A non-invasive degeneration assessment via qualitative or quantitative MRI (magnetic resonance imaging) is possible, yet, no relation between mechanical properties and T2 maps of the intervertebral disc (IVD) has been considered, albeit T2 relaxation time values quantify the degree of degeneration. Therefore, MRI scans and mechanical tests were performed on 14 human lumbar intervertebral segments freed from posterior elements and all soft tissues excluding the IVD. Degeneration was evaluated in each specimen using morphological criteria, qualitative T2 weighted images and quantitative axial T2 map data and stiffness was calculated from the load-deflection curves of in vitro compression, torsion, lateral bending and flexion/extension tests. In addition to mean T2, the OTSU threshold of T2 (TOTSU), a robust and automatic histogram-based method that computes the optimal threshold maximizing the distinction of two classes of values, was calculated for anterior, posterior, left and right regions of each annulus fibrosus (AF). While mean T2 and degeneration schemes were not related to the IVDs' mechanical properties, TOTSU computed in the posterior AF correlated significantly with those classifications as well as with all stiffness values. TOTSU should therefore be included in future degeneration grading schemes.