A stochastic differential equation analysis of cerebrospinal fluid dynamics

<p>Abstract</p> <p>Background</p> <p>Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data.</p> <p>Methods</p> <p>The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP.</p> <p>Results</p> <p>The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise.</p> <p>Conclusions</p> <p>Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.</p

Low levels of amyloid-beta and its transporters in neonatal rats with and without hydrocephalus

<p>Abstract</p> <p>Background</p> <p>Previous studies in aging animals have shown that amyloid-beta protein (Aβ) accumulates and its transporters, low-density lipoprotein receptor-related protein-1 (LRP-1) and the receptor for advanced glycation end products (RAGE) are impaired during hydrocephalus. Furthermore, correlations between astrocytes and Aβ have been found in human cases of normal pressure hydrocephalus (NPH) and Alzheimer's disease (AD). Because hydrocephalus occurs frequently in children, we evaluated the expression of Aβ and its transporters and reactive astrocytosis in animals with neonatal hydrocephalus.</p> <p>Methods</p> <p>Hydrocephalus was induced in neonatal rats by intracisternal kaolin injections on post-natal day one, and severe ventriculomegaly developed over a three week period. MRI was performed on post-kaolin days 10 and 21 to document ventriculomegaly. Animals were sacrificed on post-kaolin day 21. For an age-related comparison, tissue was used from previous studies when hydrocephalus was induced in a group of adult animals at either 6 months or 12 months of age. Tissue was processed for immunohistochemistry to visualize LRP-1, RAGE, Aβ, and glial fibrillary acidic protein (GFAP) and with quantitative real time reverse transcriptase polymerase chain reaction (qRT-PCR) to quantify expression of LRP-1, RAGE, and GFAP.</p> <p>Results</p> <p>When 21-day post-kaolin neonatal hydrocephalic animals were compared to adult (6–12 month old) hydrocephalic animals, immunohistochemistry demonstrated levels of Aβ, RAGE, and LRP-1 that were substantially lower in the younger animals; in contrast, GFAP levels were elevated in both young and old hydrocephalic animals. When the neonatal hydrocephalic animals were compared to age-matched controls, qRT-PCR demonstrated no significant changes in Aβ, LRP-1 and RAGE. However, immunohistochemistry showed very small increases or decreases in individual proteins. Furthermore, qRT-PCR indicated statistically significant increases in GFAP.</p> <p>Conclusion</p> <p>Neonatal rats with and without hydrocephalus had low expression of Aβ and its transporters when compared to adult rats with hydrocephalus. No statistical differences were observed in Aβ and its transporters between the control and hydrocephalic neonatal animals.</p

Venous hemodynamics in neurological disorders: an analytical review with hydrodynamic analysis.

Venous abnormalities contribute to the pathophysiology of several neurological conditions. This paper reviews the literature regarding venous abnormalities in multiple sclerosis (MS), leukoaraiosis, and normal-pressure hydrocephalus (NPH). The review is supplemented with hydrodynamic analysis to assess the effects on cerebrospinal fluid (CSF) dynamics and cerebral blood flow (CBF) of venous hypertension in general, and chronic cerebrospinal venous insufficiency (CCSVI) in particular.CCSVI-like venous anomalies seem unlikely to account for reduced CBF in patients with MS, thus other mechanisms must be at work, which increase the hydraulic resistance of the cerebral vascular bed in MS. Similarly, hydrodynamic changes appear to be responsible for reduced CBF in leukoaraiosis. The hydrodynamic properties of the periventricular veins make these vessels particularly vulnerable to ischemia and plaque formation.Venous hypertension in the dural sinuses can alter intracranial compliance. Consequently, venous hypertension may change the CSF dynamics, affecting the intracranial windkessel mechanism. MS and NPH appear to share some similar characteristics, with both conditions exhibiting increased CSF pulsatility in the aqueduct of Sylvius.CCSVI appears to be a real phenomenon associated with MS, which causes venous hypertension in the dural sinuses. However, the role of CCSVI in the pathophysiology of MS remains unclear

Benign external hydrocephalus: a review, with emphasis on management

Benign external hydrocephalus in infants, characterized by macrocephaly and typical neuroimaging findings, is considered as a self-limiting condition and is therefore rarely treated. This review concerns all aspects of this condition: etiology, neuroimaging, symptoms and clinical findings, treatment, and outcome, with emphasis on management. The review is based on a systematic search in the Pubmed and Web of Science databases. The search covered various forms of hydrocephalus, extracerebral fluid, and macrocephaly. Studies reporting small children with idiopathic external hydrocephalus were included, mostly focusing on the studies reporting a long-term outcome. A total of 147 studies are included, the majority however with a limited methodological quality. Several theories regarding pathophysiology and various symptoms, signs, and clinical findings underscore the heterogeneity of the condition. Neuroimaging is important in the differentiation between external hydrocephalus and similar conditions. A transient delay of psychomotor development is commonly seen during childhood. A long-term outcome is scarcely reported, and the results are varying. Although most children with external hydrocephalus seem to do well both initially and in the long term, a substantial number of patients show temporary or permanent psychomotor delay. To verify that this truly is a benign condition, we suggest that future research on external hydrocephalus should focus on the long-term effects of surgical treatment as opposed to conservative management