Brian Sweetman

A mathematical model of blood, cerebrospinal fluid and brain dynamics

Using first principles of fluid and solid mechanics a comprehensive model of human intracranial dynamics is proposed. Blood, cerebrospinal fluid (CSF) and brain parenchyma as well as the spinal canal are included. The compartmental model predicts intracranial pressure gradients, blood and CSF flows and displacements in normal and pathological conditions like communicating hydrocephalus. The system of differential equations of first principles conservation balances is discretized and solved numerically. Fluid–solid interactions of the brain parenchyma with cerebral blood and CSF are calculated. The model provides the transitions from normal dynamics to the diseased state during the onset of communicating hydrocephalus. Predicted results were compared with physiological data from Cine phase-contrast magnetic resonance imaging to verify the dynamic model. Bolus injections into the CSF are simulated in the model and found to agree with clinical measurements.

The Postsynaptic Density Protein PSD‐95 Differentially Regulates Insulin‐ and Src‐Mediated Current Modulation of Mouse NMDA Receptors Expressed in Xenopus Oocytes

Abstract : The NMDA subtype of glutamate receptor is physically associated with the postsynaptic density protein PSD‐95 at glutamatergic synapses. The channel activity of NMDA receptors is regulated by different signaling molecules, including protein tyrosine kinases. Because previous results have suggested a role for protein kinase C (PKC) in insulin potentiation of NMDA currents in oocytes, the effects of coexpression of PSD‐95 on insulin and PKC potentiation of NMDA currents from these receptors were compared. Another primary objective was to determine if PSD‐95 could enable Src to potentiate currents from NR2A/NR1 and NR2B/NR1 receptors expressed in Xenopus oocytes. The results show opposite effects of PSD‐95 coexpression on Src and insulin modulation of NR2A/NR1 receptor currents. Src potentiation of mouse NR2A/NR1 currents required PSD‐95 coexpression. In contrast, PSD‐95 coexpression eliminated insulin‐mediated potentiation of NR2A/NR1 receptor currents. PSD‐95 coexpression also eliminated PKC potentiation of NR2A/NR1 receptor currents. PSD‐95 may therefore play a key role in controlling kinase modulation of NR2A/NR1 receptor currents at glutamatergic synapses.

Normal and Hydrocephalic Brain Dynamics: The Role of Reduced Cerebrospinal Fluid Reabsorption in Ventricular Enlargement

CINE phase-contrast MRI (CINE-MRI) was used to measure cerebrospinal fluid (CSF) velocities and flow rates in the brain of six normal subjects and five patients with communicating hydrocephalus. Mathematical brain models were created using the MRI images of normal subjects and hydrocephalic patients. In our model, the effect of pulsatile vascular expansion is responsible for pulsatile CSF flow between the cranial and the spinal subarachnoidal spaces. Simulation results include intracranial pressure gradients, solid stresses and strains, and fluid velocities throughout the cranio-spinal system. Computed velocities agree closely with our in vivo CINE-MRI CSF flow measurements. In addition to normal intracranial dynamics, our model captures the transition to acute communicating hydrocephalus. By increasing the value for reabsorption resistance in the subarachnoid villi, our model predicts that the poroelastic parenchyma matrix will be drained and the ventricles enlarge despite small transmantle pressure gradients during the transitional phase. The poroelastic simulation thus provides a plausible explanation on how reabsorption changes could be responsible for enlargement of the ventricles without large transmantle pressure gradients.

Three-dimensional computational prediction of cerebrospinal fluid flow in the human brain

A three-dimensional model of the human cerebrospinal fluid (CSF) spaces is presented. Patient-specific brain geometries were reconstructed from magnetic resonance images. The model was validated by comparing the predicted flow rates with Cine phase-contrast MRI measurements. The model predicts the complex CSF flow patterns and pressures in the ventricular system and subarachnoid space of a normal subject. The predicted maximum rostral to caudal CSF flow in the pontine cistern precedes the maximum rostral to caudal flow in the ventricles by about 10% of the cardiac cycle. This prediction is in excellent agreement with the subject-specific flow data. The computational results quantify normal intracranial dynamics and provide a basis for analyzing diseased intracranial dynamics.

A Computational Model of Cerebral Vasculature, Brain Tissue, and Cerebrospinal Fluid

Abstract The dynamics of cerebral blood flow and its role in maintaining homeostasis of the central nervous system (CNS) is of high clinical relevance. A mechanistic understanding of intracranial dynamics may lead to greater insight of cerebrovascular disorders and how cerebral blood flow is controlled. Computational models of the cerebral vasculature can assist neurosurgeons in diagnosis and risk assessment of surgical intervention for specific patients. To this end, computer models of cerebral vasculature which capture hemodynamic properties of the human vasculature are constructed using modern medical imaging combined with automatic vessel generation techniques. The artificially generated cerebral networks enable realistic simulation of blood flow and pressure distribution throughout the entire brain. These studies permit a quantitative analysis of cerebral hemodynamics and may lead to fundamental understanding of complex dynamics and control mechanisms like autoregulation and functional hyperemia.

Modeling and Design of Distributed Systems; Methods and Algorithms

Abstract Mathematical programming techniques to predict cerebrospinal fluid (CSF) flow fields and drug transport in the human brain are presented. In addition, advantageous use of distributed mathematical models to accelerate design and development of a novel volume sensor for hydrocephalus treatment is demonstrated. CSF flow in the brain can be measured analytically in three dimensions, but quantitative interpretation requires a distributed inversion problem. In the example of a volume sensor, medical imaging and rigorous mathematical analysis lead to optimal sensor design and optimal placement for highest sensitivity. Finally, prediction of drug transport in the brain leads to improved treatment options for patients suffering from neurodegenerative disorders such as Parkinsons and Alzheimers. Infusion parameters such as flow rate and drug catheter position need to be optimized in three dimensions to achieve maximal therapeutic thresholds in the desired target area of the soft brain tissue. This example constitutes a three dimensional design problem with partial differential equation constraints. Our systematic modeling approach may improve the simulation and design of disease treatment options.