Mathematical modelling of the CSF system: effects of microstructures and posture on optic nerve subarachnoid space dynamics

Background: The pressure difference between the eye and brain in upright postures may be affected by compartmentalization of the optic nerve subarachnoid space (ONSAS). Both pressure and deformation will depend on the microstructures of the ONSAS, and most likely also on ocular glymphatic clearance. Studying these factors could yield important knowledge regarding the translaminar pressure difference, which is suspected to play a role in normal-tension glaucoma. Methods: A compartment model coupling the ONSAS with the craniospinal CSF system was used to investigate the effects of microstructures on the pressure transfer through the ONSAS during a posture change from supine to upright body postures. ONSAS distensibility was based on MRI measurements. We also included ocular glymphatic flow to investigate how local pressure gradients alter this flow with changes in posture. Results: A compartmentalization of the ONSAS occurred in the upright posture, with ONSAS porosity (degree of microstructural content) affecting the ONSAS pressure (varying the supine/baseline porosity from 1.0 to 0.75 yielded pressures between − 5.3 and − 2 mmHg). Restricting the minimum computed porosity (occurring in upright postures) to 0.3 prevented compartmentalization, and the ONSAS pressure could equilibrate with subarachnoid space pressure (− 6.5 mmHg) in ≤ 1 h. The ocular glymphatics analysis predicted that substantial intraocular-CSF flows could occur without substantial changes in the ONSAS pressure. The flow entering the ONSAS in supine position (both from the intraocular system and from the cranial subarachnoid space) exited the ONSAS through the optic nerve sheath, while in upright postures the flow through the ONSAS was redirected towards the cranial subarachnoid space. Conclusions: Microstructures affect pressure transmission along the ONSAS, potentially contributing to ONSAS compartmentalization in upright postures. Different pathways for ocular glymphatic flow were predicted for different postures.publishedVersio

Prediction of cerebral perfusion pressure during carotid surgery – A computational fluid dynamics approach

Background: Maintaining cerebral perfusion pressure in the brain when a carotid artery is closed during vascular surgery is critical for avoiding intraoperative hypoperfusion and risk of ischemic stroke. Here we propose and evaluate a method based on computational fluid dynamics for predicting patient-specific cerebral perfusion pressures at carotid clamping during carotid endarterectomy. Methods: The study consisted of 22 patients with symptomatic carotid stenosis who underwent carotid endarterectomy (73 ± 5 years, 59–80 years, 17 men). The geometry of the circle of Willis was obtained preoperatively from computed tomography angiography and corresponding flow rates from four-dimensional flow magnetic resonance imaging. The patients were also classified as having a present or absent ipsilateral posterior communicating artery based on computed tomography angiography. The predicted mean stump pressures from computational fluid dynamics were compared with intraoperatively measured stump pressures from carotid endarterectomy. Findings: On group level, there was no difference between the predicted and measured stump pressures (−0.5 ± 13 mmHg, P = 0.86) and the pressures were correlated (r = 0.44, P = 0.039). Omitting two outliers, the correlation increased to r = 0.78 (P < 0.001) (−1.4 ± 8.0 mmHg, P = 0.45). Patients with a present ipsilateral posterior communicating artery (n = 8) had a higher measured stump pressure than those with an absent artery (n = 12) (P < 0.001). Interpretation: The stump pressure agreement indicates that the computational fluid dynamics approach was promising in predicting cerebral perfusion pressures during carotid clamping, which may prove useful in the preoperative planning of vascular interventions.publishedVersio

Ubiquitous finite-size scaling features in IV characteristics of various dynamic XY models in two dimensions

Two-dimensional (2D) XY model subject to three different types of dynamics, namely Monte Carlo, resistivity shunted junction (RSJ), and relaxational dynamics, is numerically simulated. From the comparisons of the current-voltage (I-V) characteristics, it is found that up to some constants I-V curves at a given temperature are identical to each other in a broad range of external currents. Simulations of the Villain model and the modified 2D XY model allowing stronger thermal vortex fluctuations are also performed with RSJ type of dynamics. The finite-size scaling suggested in Medvedyeva et al. [Phys. Rev. B 62, 14531(2000)] is confirmed for all dynamic models used, implying that this finite-size scaling behaviors in the vicinity of the Kosterlitz-Thouless transition are quite robust.Comment: 7 pages, 4 pictures, accepted in Physica

Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks

It is shown from computer simulations that the current-voltage ($I$-$V$) characteristics for the two-dimensional XY model with resistively-shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I$-$V$ exponent $a$ can be determined to good precision. This determination supports the conclusion $a=z+1$, where $z$ is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. {\bf 78}, 4324 (1997)].Comment: 6 pages, to appear in PR

Langevin Simulations of Two Dimensional Vortex Fluctuations: Anomalous Dynamics and a New IVIV-exponent

The dynamics of two dimensional (2D) vortex fluctuations are investigated through simulations of the 2D Coulomb gas model in which vortices are represented by soft disks with logarithmic interactions. The simulations trongly support a recent suggestion that 2D vortex fluctuations obey an intrinsic anomalous dynamics manifested in a long range 1/t-tail in the vortex correlations. A new non-linear IV-exponent a, which is different from the commonly used AHNS exponent, a_AHNS and is given by a = 2a_AHNS - 3, is confirmed by the simulations. The results are discussed in the context of earlier simulations, experiments and a phenomenological description.Comment: Submitted to PRB, RevTeX format, 28 pages and 13 figures, figures in postscript format are available at http://www.tp.umu.se/~holmlund/papers.htm

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio

Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio

Fluiddynamiska principer för analys av intrakraniellt tryck och dess reglering : för tillämpning inom rymdmedicin och hydrocefalus

Intracranial pressure (ICP) is an important component of the fluid dynamic environment of the brain and plays a central role with regards to the maintenance of normal cerebral blood flow and neuronal function. However, many regulatory mechanisms controlling the ICP are still poorly understood. One major gap in knowledge in this regard is the mechanism behind the postural/gravitational control of ICP. This is partly due to the fact that most ICP investigations are performed with the patients in a supine or recumbent position. Since most people spend 16 hours a day in an upright position, understanding these mechanics is highly motivated. Also spurring research on this topic is the increasing number of reports of the spaceflight-associated neuro-ocular syndrome (SANS) found in astronauts after prolonged exposure to weightlessness (i.e. microgravity), where evidence suggests that a disrupted balance between ICP and intraocular pressure (IOP) may be an underlying cause. Understanding how ICP is regulated with respect to posture could therefore provide important insight into the alterations introduced by microgravity, where postural effects are removed, and how to improve the safety of astronauts who are susceptible to this syndrome. Here on earth, disturbances in the ICP or cerebrospinal fluid (CSF) dynamics are associated with the development of chronic neurological diseases. One particular disease of interest is communicating hydrocephalus, where the cerebral ventricles are enlarged despite the absence of macroscopic CSF flow obstructions. A common finding in these patients is that of altered pulsatile flow in the CSF. The overall aim of this thesis was to utilize fluid dynamic principles to describe and validate potential regulatory mechanisms behind postural changes in ICP and causes of ventriculomegaly. The thesis is based on four scientific papers (paper I—IV). A postural dependency of the IOP-ICP pressure difference was verified by simultaneous measurements of ICP (assessed through lumbar puncture) and IOP (measured with an Applanation Resonance Tonometer) (paper I). Based on these measurements, a 24-hour average of the IOP-ICP pressure difference at the level of the eye was estimated for the state of microgravity, predicting a reduced pressure difference in space compared with that on earth. A hypothesis where postural changes in ICP are described by hydrostatic effects in the venous system, and where these effects are altered by the collapse of the internal jugular veins (IJVs) in more upright positions, was evaluated (paper II and III). Using ultrasound data, it was shown that the venous hydrostatic pressure gradient was balanced by viscous pressure losses in the collapsed IJVs to uphold a near atmospheric pressure at the level of the neck in the upright posture (paper II). A full evaluation of the hypothesis was then performed, based on simultaneous assessment of ICP, central venous pressure (through a PICC-line) and venous collapse in 7 postures of upper-body tilt in healthy volunteers (paper III).The proposed description could accurately predict the general changes seen in the measured ICP for all investigated postures (mean difference: -0.03±2.7 mmHg or -4.0±360 Pa). Pulsatile CSF flow-induced pressure differences between the ventricles and subarachnoid space were evaluated as a source for ventriculomegaly in communicating hydrocephalus (paper IV). The pressure distributions resulting from the pulsatile CSF flow were calculated using computational fluid dynamics based on MRI data. The estimated pressures revealed a net pressure difference (mean: 0.001±0.003 mmHg or 0.2±0.4 Pa, p=0.03) between the ventricles and the subarachnoid space, over the cardiac cycle, with higher pressure in the third and lateral ventricles. In conclusion, the results of this thesis support venous hydrostatics and jugular venous collapse as key governing factors in the postural/gravitational control of ICP. Furthermore, a postural dependency of the IOP-ICP pressure difference was demonstrated, providing a potential explanation for how an imbalance between the pressure of the eye and brain can be introduced in microgravity. Computational fluid dynamic analysis revealed that the altered pulsations in communicating hydrocephalus generate a pressure gradient within the CSF system. However, the gradient was small and additional effects are probably needed to explain the ventriculomegaly in these patients.