From head micro-motions towards CSF dynamics and non-invasive intracranial pressure monitoring.

Continuous monitoring of the intracranial pressure (ICP) is essential in neurocritical care. There are a variety of ICP monitoring systems currently available, with the intraventricular fluid filled catheter transducer currently representing the "gold standard". As the placement of catheters is associated with the attendant risk of infection, hematoma formation, and seizures, there is a need for a reliable, non-invasive alternative. In the present study we suggest a unique theoretical framework based on differential geometry invariants of cranial micro-motions with the potential for continuous non-invasive ICP monitoring in conservative traumatic brain injury (TBI) treatment. As a proof of this concept, we have developed a pillow with embedded mechanical sensors and collected an extensive dataset (> 550 h on 24 TBI coma patients) of cranial micro-motions and the reference intraparenchymal ICP. From the multidimensional pulsatile curve we calculated the first Cartan curvature and constructed a "fingerprint" image (Cartan map) associated with the cerebrospinal fluid (CSF) dynamics. The Cartan map features maxima bands corresponding to a pressure wave reflection corresponding to a detectable skull tremble. We give evidence for a statistically significant and patient-independent correlation between skull micro-motions and ICP time derivative. Our unique differential geometry-based method yields a broader and global perspective on intracranial CSF dynamics compared to rather local catheter-based measurement and has the potential for wider applications.

Departure of some parameter-dependent spectral statistics of irregular quantum graphs from random matrix theory predictions.

Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c[over ](omega,x) as well as the distributions of level curvatures and avoided crossing gaps are calculated. The numerical results are compared with the predictions of random matrix theory for Gaussian orthogonal ensemble (GOE) and for coupled GOE matrices. The application of coupled GOE matrices was justified by studying localization phenomena in graphs' wave functions Psi(x) using the inverse participation ratio and the amplitude distribution P(Psi(x)) .

Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption.

We present the results of an experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modeled by optical potentials. The distribution of the reflection coefficient P(R) and the distributions of the reaction K matrix were obtained from measurements and numerical calculations of the scattering matrix S of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory.

Force plate monitoring of human hemodynamics.

BACKGROUND: Noninvasive recording of movements caused by the heartbeat and the blood circulation is known as ballistocardiography. Several studies have shown the capability of a force plate to detect cardiac activity in the human body. The aim of this paper is to present a new method based on differential geometry of curves to handle multivariate time series obtained by ballistocardiographic force plate measurements. RESULTS: We show that the recoils of the body caused by cardiac motion and blood circulation provide a noninvasive method of displaying the motions of the heart muscle and the propagation of the pulse wave along the aorta and its branches. The results are compared with the data obtained invasively during a cardiac catheterization. We show that the described noninvasive method is able to determine the moment of a particular heart movement or the time when the pulse wave reaches certain morphological structure. CONCLUSIONS: Monitoring of heart movements and pulse wave propagation may be used e.g. to estimate the aortic pulse wave velocity, which is widely accepted as an index of aortic stiffness with the application of predicting risk of heart disease in individuals. More extended analysis of the method is however needed to assess its possible clinical application.

Physics, stability, and dynamics of supply networks.

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bullwhip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Quantum irregular scattering induced by tunneling.

Irregular behavior in a simple two-dimensional scattering model is investigated in the quantum domain. The scattering potential is composed from Dirac deltas on a stadium shaped curve. The unusual feature of the model is that the irregular patterns disappear in the classical limit because the main mechanism leading to resonances in the cross section data is the quantum tunneling. Calculations for the standard characteristics such as nearest-neighbor distribution of eigenphases of the S-matrix, the distribution of the S-matrix elements and the correlation function of the total cross section are performed. Deviations from the usual predictions for irregular scattering have been found in certain regions, which can be traced back to the fact that the model does not have such a characteristic time like the classical escape rate, which survives the classical limit.