Comparison of the histological structure of the tibial nerve and its terminal branches in the fresh and fresh-frozen cadavers

Background: The aim of this study was to compare the histological structure (cross-sectional area [CSA] and number of nerve fascicles) of the distal part of the tibial nerve (TN) and its terminal branches (medial plantar nerve [MPN], lateral plantar nerve [LPN]) in the fresh and fresh-frozen cadavers using computer assisted image analysis.Materials and methods: The TNs with terminal branches (MPN and LPN) were dissected from the fresh and fresh-frozen cadavers. Each nerve was harvested 5 mm proximally and respectively 5 mm distally from the TN bifurcation, marked, dehydrated, embedded in paraffin, sectioned at 2 μm slices and stained with haematoxylin and eosin. Then the specimens were photographed and analysed using Olympus cellSens software.Results: The fresh cadavers’ group comprised 60 feet (mean age 68.1 ± 15.2 years). The mean CSA and the number of nerve fascicles were respectively 15.25 ± 4.6 mm2, 30.35 ± 8.45 for the TN, 8.76 ± 1.93 mm2, 20.75 ± 7.04 for the MPN and 6.54 ± 2.02 mm2, 13.40 ± 5.22 for the LPN. The fresh-frozen cadavers’ group comprised 21 feet (mean age 75.1 ± 9.0 years). The mean CSA and the number of nerve fascicles were respectively 13.71 ± 5.66 mm2, 28.57 ± 8.00 for the TN, 7.55 ± 3.25 mm2, 18.00 ± 6.72 for the MPN and 4.29 ± 1.93 mm2, 11.33 ± 1.93 for the LPN. Only LPNs showed statistical differences in the CSA and the number of nerve fascicles between examined groups (p = 0.000, p = 0.037, respectively). A positive correlation was found between donors age and tibial nerve CSA in the fresh cadavers group (r = 0.44, p = 0.000). A statistical difference was found between the MPN and LPN both in the CSA and the number of nerve fascicles (p < 0.001, p < 0.001, respectively).Conclusions: The CSA and the number of nerve fascicles of the tibial and medial plantar nerves were similar in the fresh and fresh-frozen cadavers whilst different in the LPN. The TN showed increasing CSA with the advanced age in the fresh cadavers. The MPN had larger CSA and more nerve fascicles than the LPN

Ultrasound-guided topographic anatomy of the medial calcaneal branches of the tibial nerve

Background: The purpose of this study was to evaluate the topographic anatomy of the tibial nerve and its medial calcaneal branches in relation to the tip of the medial malleolus and to the posterior superior tip of the calcaneal tuberosity using the ultrasound examination and to verify its preoperative usefulness in surgical treatment. Materials and methods: Bilateral ultrasound examination was performed on 30 volunteers and the location of the tibial nerve bifurcation and medial calcaneal branches origin were measured. Medial calcaneal branches were analysed in reference to the amount and their respective nerves of origin. Results: In 77% of cases, tibial nerve bifurcation occurred below the tip of the medial malleolus with the average distance of 5.9 mm and in 48% of cases above the posterior superior tip of the calcaneal tuberosity with the average distance of 2.7 mm. In 73% of cases medial calcaneal branches occurred as a single branch originating from the tibial nerve (60%). The average distance of the first, second and third medial calcaneal branch was accordingly 9.3 mm above, 9.5 mm below and 11.6 mm below the tip of the medial malleolus and 17.7 mm above, 1.6 mm below and 4 mm below the posterior superior tip of the calcaneal tuberosity. Conclusions: As the tibial nerve and its branches present a huge variability in the medial ankle area, in order to prevent the iatrogenic injuries, the preoperative or intraoperative ultrasound assessment (sonosurgery) of its localisation should be introduced into the clinic

Multiscale Partition of Unity

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for 'cheap' parameter choices.Comment: Proceedings for Seventh International Workshop on Meshfree Methods for Partial Differential Equations, 18 pages, 3 figure

Solving One Dimensional Scalar Conservation Laws by Particle Management

We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate. The method is TVD, entropy decreasing, exactly conservative, and has no numerical dissipation. Difficulties involving transonic points do not occur, however inflection points of the flux function pose a slight challenge, which can be overcome by a special treatment. Away from shocks the method is second order accurate, while shocks are resolved with first order accuracy. A postprocessing step can recover the second order accuracy. The method is compared to CLAWPACK in test cases and is found to yield an increase in accuracy for comparable resolutions.Comment: 15 pages, 6 figures. Submitted to proceedings of the Fourth International Workshop Meshfree Methods for Partial Differential Equation

Increased levels of type VIII collagen in human brain tumours compared to normal brain tissue and non-neoplastic cerebral disorders.

The expression of type VIII collagen was examined in the normal and diseased human brain. Focal immunoreactivity was seen in histologically abnormal vessels of all four angiomas and 40 of 52 brain tumours (gliomas, meningiomas and schwannomas). An extended staining pattern, as well as a punctate distribution, was frequently observed in affected vessels. Staining was not apparent in nine normal brains and in 15 pathologic brains showing various cerebrovascular abnormalities, including Alzheimer's, Leigh's and Wernicke's diseases. Immunoblotting of glioblastomas revealed two bands at 56 kD and 67 kD which were also present at low levels in normal frontal cortex. The extracellular distribution of type VIII collagen was different from that of the other collagen types which have been described in brain and resembles patterns of expression described for certain tissues during mammalian embryogenesis (Kapoor et al., 1988). Our results provide additional evidence for the participation of type VIII collagen in some types of angiogenesis

Computer-assisted measurements of the histological structure of the tibial nerve and its terminal branches

Background: The aim of this study was to analyse the histological structure (cross-sectional area [CSA] and number of nerve bundles) of the distal part of the tibial nerve and its terminal branches (medial plantar nerve, lateral plantar nerve) using computer-assisted image analysis. Materials and methods: The tibial nerve and its distal branches (medial and lateral plantar nerves) were dissected from the fresh cadavers. Each nerve was harvested 5 mm proximally and respectively 5 mm distally from the tibial nerve bifurcation, marked, dehydrated, embedded in paraffin, sectioned at 2 μm slices and stained with haematoxylin and eosin. Then photographed and analysed using Olympus cellSens software. Results: The studied group comprised 28 female and 32 male feet (mean age 68.1 ± 15.2 years). The mean CSA and the number of nerve bundles were respectively 17.86 ± 4.57 mm2, 33.88 ± 6.31 for the tibial nerve, 9.58 ± 1.95 mm2, 23.41 ± 7.37 for the medial plantar nerve and 7.17 ± 2.36 mm2, 15.06 ± 5.81 for the lateral plantar nerve in males and 12.27 ± 2.45 mm2, 26.32 ± 8.87 for the tibial nerve, 7.81 ± 1.41 mm2, 17.71 ± 5.28 for the medial plantar nerve and 5.83 ± 1.25 mm2, 11.50 ± 3.72 for the lateral plantar nerve in females. Both CSA and number of nerve bundles of the tibial, medial plantar and lateral plantar nerves revealed no statistical differences when comparing foot side of the individual. The statistical difference was related to the gender, showing significantly bigger CSA and number of nerve bundles in males (CSA: p = 0.000, p = 0.000, p = 0.016; number of nerve bundles: p = 0.01, p = 0.003, p = 0.004, respectively). A positive correlation was found between the donor age and the tibial nerve CSA (r = 0.44, p = 0.000). A significant statistical difference was found between the medial and lateral plantar nerves both in CSA and number of nerve bundles (p < 0.001, p < 0.001, respectively). Conclusions: The CSA and the number of nerve bundles in the distal part of the tibial nerve and its branches are significantly larger in males with no differences between right and left foot of the individual. The tibial nerve shows increasing CSA with advanced age. The medial plantar nerve has larger CSA and more nerve bundles than the lateral plantar nerve

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure