INTRODUCTION

Neuronal firing generates an action potential traveling down axon and across synapses for communication among neurons. Traveling action potentials generate electric current in the axon (~2ms in duration) and in the postsynaptic dendrites (~10–100ms in duration). These currents produce electric and magnetic fields detectable by scalp electroencephalography (EEG) and magnetoencephalography (MEG), respectively^1,2. However, scalp EEG and MEG detect the fields relatively far away (~20mm) from firing sources, and have difficulty to locate firing sources and thus limit their sensitivity to slow, easily-synchronized postsynaptic currents in a large area^1,3-5. Here we propose to use local quantum sensing ⁶ and detect magnetic fields related to both fast (action potential) and slow (postsynaptic) neuronal currents with high temporal resolution and high spatial localization of firing sources.

THEORY

The quantum sensors in our method are local endogenous nuclear spins of proton (¹H) inside neurons, with two quantum states, |0> and |1>, in a static external magnetic field B₀ provided by MRI scanner. Target magnetic field, B_n(r,t), to be measured at location r and time t in the brain is induced by electric currents, {I_n(r,t), r in ΔV}, generated by firing neurons nearby (<1mm in distance) ^7-9. The sensing process is electromagnetic interaction of these nuclear spins at superposition state (achieved by an exciting RF pulse) with the target magnetic field (Fig. 1). During sensing period, nuclear spins accumulate an extra phase φ(r,t) (Eq. 1) and encode it in the free induction decay (FID), s(t), in Eq. 2. Spins' states are read-out by RF receive coils placed around the head during data acquisition of the FID signal from the spin ensemble in a coil-specific investigation volume, ΔV, of magnetization density ρ(r) and effective transverse relaxation constant T₂*(r) (Eq. 2). A phase difference at a sampling interval Δt is calculated for an estimate of the firing field z-component B_n,z (Eq. 3). The firing magnetic field, although very small (~0.1 nT) above the scalp^1,7-9, is large enough (~18–363 µT) inside axons (~0.2–2.0 µm in diameter) in the brain to generate a measurable change in local resonance frequency as large as 15.5 kHz for proton (¹H) MRI.
Eq. [1]. $$$ φ(r,t)=φ(r,TE)+γ∫_{TE}^t B_{n,z} (r,τ) dτ $$$.
Eq. [2]. $$$ s(t)=∫_{∆V} c(r) ρ(r) e^{-t/T_2^* (r)} e^{-jφ(r,t)} dr⁡ $$$
Eq. [3]. $$$ B ̃_{n,z} (t)=(1/γ)dφ/dt≈(1/γ) phase[s(t) s^* (t+∆t)]/(∆t) $$$, s.t. spatially uniform B_n,z across ∆V.

METHOD

Computer simulations and human studies were performed to determine the accuracy of qsLNF measurements and to show its feasibility in vivo. There were 40 FID signals acquired on four healthy subjects (age 28.0±5.4 years, 3 male and 1 female). All study subjects were provided the informed consent for the study. The FID signals were acquired at resting state using vendor’s pulse sequence AdjFre on a 3T scanner (Prisma, Siemens), with a standard head/neck array coil (16 out of 20 channels were used). The investigation volumes in the brain were defined by individual coil images (Fig. 2). The FID readout time is 100ms at a sampling interval of 0.0977ms, with TE=15ms and flip angle=10º. A custom-developed software in MATLAB R2021a (MathWorks, Natick, MA) was used to analyze the raw data, including a 3-point smoothing before and after the phase calculation in Eq. 3.

RESULTS

The computer simulations in Fig. 3 showed a very high accuracy of the qsLNF measurements, with an error of <0.7% for the action potentials and <1.9% for the postsynaptic currents under a typical SNR=250. The human study in Fig. 4 presented a quiet resting state, only recording one postsynaptic firing (20ms long, 0.26µT intensity). In contrast, the subject in Fig. 5 showed an active rest state, with massive action potential firings (1.5–2.0ms long, 20–40µT intensity) from the prefrontal lobes and occipital lobes.

DISCUSSION

The results in Figs. 2–5 showed the feasibility of our method that was based on quantum sensing of local neuronal firings. Proton (¹H) nuclear spins, serving as intrinsic micro quantum sensors, exist inside neuons and thus have higher sensitivity to neuronal firings than scalp EEG and MEG above the skull. However, the estimates of neuronal magnetic field in Eq. 3 is prone to partial volume effect and needs to be further addressed. The sensing volume, passively defined by coil sensitivity in this study, needs to be reduced in size or actively defined by single-voxel excitation. The dynamic range of quantum sensing for magnetic field was restricted by sampling interval, ∆t, as seen in the design of simulation model for action potentials in Fig. 3a. To increase the dynamic range, ∆t needs to be decreased.

CONCLUSION

The presented data of computer simulations and human studies supported our proposed idea for the quantum sensing of local neuronal firing via proton (¹H) MRI. The qsLNF has the potential to non-invasively record neuronal firings of both fast action potentials and slow postsynaptic currents in the brain through continuous acquisition of FID signals. In principle, this idea can be extended to the deep brain and other body parts.

Acknowledgements

This work was financially supported in part by the NIH RF1 AG067502 and the General Research Fund of the Department of Radiology. This work was also performed under the rubric of the Center for Advanced Imaging Innovation and Research (CAI2R, www.cai2r.net), an NIBIB Biomedical Technology Resource Center (NIH P41 EB017183).

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