Efficient simulations of tubulin-driven axonal growth.

This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman-Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g. its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.

Measurement of vascular water transport in human subjects using time-resolved pulsed arterial spin labelling.

Most approaches to arterial spin labelling (ASL) data analysis aim to provide a quantitative measure of the cerebral blood flow (CBF). This study, however, focuses on the measurement of the transfer time of blood water through the capillaries to the parenchyma (referred to as the capillary transfer time, CTT) as an alternative parameter to characterise the haemodynamics of the system. The method employed is based on a non-compartmental model, and no measurements need to be added to a common time-resolved ASL experiment. Brownian motion of labelled spins in a potential was described by a one-dimensional general Langevin equation as the starting point, and as a Fokker-Planck differential equation for the averaged distribution of labelled spins at the end point, which takes into account the effects of flow and dispersion of labelled water by the pseudorandom nature of the microvasculature and the transcapillary permeability. Multi-inversion time (multi-TI) ASL data were acquired in 14 healthy subjects on two occasions in a test-retest design, using a pulsed ASL sequence and three-dimensional gradient and spin echo (3D-GRASE) readout. Based on an error analysis to predict the size of a region of interest (ROI) required to obtain reasonably precise parameter estimates, data were analysed in two relatively large ROIs, i.e. the occipital lobe (OC) and the insular cortex (IC). The average values of CTT in OC were 260 ± 60 ms in the first experiment and 270 ± 60 ms in the second experiment. The corresponding IC values were 460 ± 130 ms and 420 ± 139 ms, respectively. Information related to the water transfer time may be important for diagnostics and follow-up of cerebral conditions or diseases characterised by a disrupted blood-brain barrier or disturbed capillary blood flow.

Effects of red blood cells with reduced deformability on cerebral blood flow and vascular water transport: measurements in rats using time-resolved pulsed arterial spin labelling at 9.4 T.

BACKGROUND: Our aim was to introduce damaged red blood cells (RBCs) as a tool for haemodynamic provocation in rats, hypothesised to cause decreased cerebral blood flow (CBF) and prolonged water capillary transfer time (CTT), and to investigate whether expected changes in CBF could be observed and if haemodynamic alterations were reflected by the CTT metric. METHODS: Damaged RBCs exhibiting a mildly reduced deformability were injected to cause aggregation of RBCs. Arterial spin labelling (ASL) magnetic resonance imaging experiments were performed at 9.4 T. Six datasets (baseline plus five datasets after injection) were acquired for each animal in a study group and a control group (13 and 10 female adult Wistar rats, respectively). For each dataset, ASL images at ten different inversion times were acquired. The CTT model was adapted to the use of a measured arterial input function, implying the use of a realistic labelling profile. Repeated measures ANOVA was used (alpha error = 0.05). RESULTS: After injection, significant differences between the study group and control group were observed for relative CBF in white matter (up to 20 percentage points) and putamen (up to 18-20 percentage points) and for relative CTT in putamen (up to 35-40 percentage points). CONCLUSIONS: Haemodynamic changes caused by injection of damaged RBCs were observed by ASL-based CBF and CTT measurements. Damaged RBCs can be used as a tool for test and validation of perfusion imaging modalities. CTT model fitting was challenging to stabilise at experimental signal-to-noise ratio levels, and the number of free parameters was minimised.