Modelling of axonal fields in the optic nerve for direct MR detection studies
A number of studies have now shown that direct detection of neuronal firing by MRI may be possible. The optic nerve carries all visual information from the eye to the brain and is a particularly promising target for these measurements. However, it has been assumed that the effects of axonal firing may not be detectable, as a single firing event produces a bipolar waveform of around 1ms duration whose effects should cancel on MR. A simulation of the magnetic modulation which could feasibly be produced by the optic nerve over an extended period and with different firing rates has been developed. The HodgkinHuxley equations were calculated for an array of model ganglion cell axons which were assumed to act as voltage to pulse frequency converters. Dependence of the modulating waveform on relative action potential firing start time was investigated. Although the simulated waveforms were bipolar at the beginning, during the period of MR acquisition the different frequencies combine to produce a largely positive waveform. The simulation included only contrast luminance changes and not color, spatial correlations or other more sophisticated processing in the retina. A gradient echo sequence was used at 3T to create images for analysis by the ghost reconstructed alternating current estimation (GRACE) method from phantoms subject to current modulation by the actual modelled axonal waveforms. The optic nerve was also imaged using the same method during visual stimulus by a strobe light in adult human volunteers at 3T. Analysis of digitized video recordings of eye locations during strobe stimulation outside the magnet showed no correlation with the applied strobe frequency over the short duration of the scans. Images of the optic nerves at an echo time of TE=39ms had weak but significant first harmonic ghosts in locations consistent with the applied stimulus as calculated from GRACE theory in just two out of thirteen studies on 10 volunteers and a detection rate of only 15% providing no clear evidence for direct detection in these experiments.
grace ghost reconstructed alternating current estimation te echo time (ms) tr repeat time (ms) mr magnetic resonance lgn lateral geniculate nucleus hh hodgkinhuxley 3t 3tesla usa united states of america im membrane current cm membrane capacitance dv/dt rate of change of voltage with time ina sodium ion current ik potassium ion current icl chloride ion current vna sodium ion voltage vk potassium ion voltage vcl chloride ion voltage gna sodium ion channel conductance gk potassium ion channel conductance gcl chloride ion channel conductance ms/cm2 milli-siemens per square centimetre ?f/cm2 micro-farads per square centimetre mv milli-volts m n h gating parameters dm/dt dn/dt dh/t rate of change of gating parameters ?m ?n ?h empirical functions of voltage v ?h empirical functions of voltagev ?? phase change of mr signal ? gyromagnetic ratio b(t) modulating axonal magnetic field ?0 permeability of free space i(t) axonal current fm frequency of axonal current ts sampling time r distance ?s ghost distance from object s mr signal jn nth bessel function ? summation t time ? modulation index 2d two dimensional slt slice thickness (mm) fov field of view (mm) nex number of excitations d-a digital to analogue ?s micro second fa flip angle pc personal computer ?a micro amp nt nano-tesla b0 main magnetic field snr signal to noise ratio m male f female roi region of interest hz hertz db decibel t1 longitudinal relaxation time (ms) sense sensitivity encoding fps frames per second epi echo planar imaging bold blood oxygen level dependent