3D Reconstruction of neuronal activity using diamond nitrogen-vacancy magnetometry
We propose an algorithm to solve the reconstruction problem of detecting action potentials in a network of neurons with simulated diamond nitrogen-vacancy magnetometry. We highlight the advantage of axon hillock currents based signatures in simplifying the inverse problem.
Nitrogen-vacancy defect centers (NVC) in diamonds allow pico-tesla sized magnetic field detection at ambient temperatures and fine temporal resolution. Barry and colleagues demonstrated the capacity of NVCs to sense the magnetic field associated with action potentials (AP) in a worm axon. APs are the currency for virtually all neural computation and communication. Simultaneous AP measurement from multiple single-neurons underlies the challenge in developing brain activity mapping techniques. Barry and colleagues’ work propelled the possibility of NVC sensors probing mammalian neural AP magnetic fields (APMF). We estimated mammalian cortical APMFs and found they may fall within the range of the next-generation NVC sensors. Detailed theoretical solutions of simplified axon-like core-conductor models were long known (1 ,2 , 3), along with experimental evidence of SQUID based measurements of APMF of frog sciatic nerve. The above body of work helped build the forward problem of determining magnetic field from axonal currents and also provided approaches to solving the inverse problem, albeit in simplified scenarios. For a realistic and viable technique of brain neural activity mapping based on APMFs much advancement and in multiple areas are required: improvement of NVC sensitivity, enhancement of APMFs and developing solutions to the inverse problem for determining the axonal currents for real pyramidal mammalian neurons with complex structures in a volume of tissue. One should be able to spatiotemporally reconstruct the activity of a network of neurons at single cell resolution. As a first step towards solving the inverse problem which has non unique solutions that cannot be reached analytically, we first sought if any structure in the neuron can provide unique signatures in the associated magnetic field allowing neuronal spike detection, ignoring the same in other segments of the neuron. Exact propagation of axonal currents, then, would not need tracking. Our search pointed to the high ion channel density in the axon hillock. In a segmented model of a realistic pyramidal neuron, we found approximately two orders higher axonal currents through the axon hillock segments as compared to the other regions during APs. Also, a bidirectional current flow associated with the axon hillock region unlike anywhere else on the neuron provided a unique signature. The above allowed the reconstruction problem to be simplified to detecting current propagation in a localized, ~10μms area. For AP detection in space and time, we formulated a linear inverse problem, where we consider the experimental simulated maps to be a linear combination of elements of apriori known dictionary containing axon hillock AP signatures of different neurons located in a 3D volume. Smith and Lewicki’s work on sparse coding of natural sounds, provided a potential method - matching pursuit algorithms in decomposition of sparse linear combinations and we obtained results that allowed reasonable AP detection efficiency. For details on all the above please read the paper. Better methods to improve the detection efficiency can of course be developed, and something worth pursuing. However, sustained efforts of the community in the coming years, are needed to make NVC based brain mapping a reality.
This post has been written with inputs and editing from the corresponding authors of the paper - Dr. Kasturi Saha, Assistant Professor, Indian Institute of Technology Bombay and Dr. Sharba Bandyopadhyay, Assistant Professor, Indian Institute of Technology Kharagpur.