Low-cost, smartphone-based instant three-dimensional registration system for infant functional near-infrared spectroscopy applications

Significance To effectively apply functional near-infrared spectroscopy (fNIRS)/diffuse optical tomography (DOT) devices, a three-dimensional (3D) model of the position of each optode on a subject’s scalp and the positions of that subject’s cranial landmarks are critical. Obtaining this information accurately in infants, who rarely stop moving, is an ongoing challenge. Aim We propose a smartphone-based registration system that can potentially achieve a full-head 3D scan of a 6-month-old infant instantly. Approach The proposed system is remotely controlled by a custom-designed Bluetooth controller. The scanned images can either be manually or automatically aligned to generate a 3D head surface model. Results A full-head 3D scan of a 6-month-old infant can be achieved within 2 s via this system. In testing on a realistic but static infant head model, the average Euclidean error of optode position using this device was 1.8 mm. Conclusions This low-cost 3D registration system therefore has the potential to permit accurate and near-instant fNIRS/DOT spatial registration

Mapping quantum-classical Liouville equation: projectors and trajectories

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.Comment: 4 figure