The role of fractional calculus in modeling biological phenomena: A review

Translational motion in solution, either diffusion or fluid flow, is at the heart of chemical and biochemical reactivity. Nuclear Magnetic Resonance (NMR) provides a powerful non-invasive technique for studying the phenomena using magnetic field gradient methods. Describing the physical basis of measurement techniques, with particular emphasis on diffusion, balancing theory with experimental observations and assuming little mathematical knowledge, this is a strong, yet accessible, introduction to the field. A detailed discussion of magnetic field gradient methods applied to Magnetic Resonance Imaging (MRI) is included, alongside extensive referencing throughout, providing a timely, definitive book to the subject, ideal for researchers in the fields of physics, chemistry and biology.

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NMR Studies of Translational Motion

Anomalous diffusion expressed through fractional order differential operators in the Bloch–Torrey equation

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure

A novel tensor distribution model for the diffusion-weighted MR signal

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the meansquare displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal Communication

An electronic position guidance device is configured to attach to a medical device having a first end configured for percutaneous insertion and a second end configured to remain exterior to a patient's skin. The device includes an orientation attachment configured to detect an orientation and a position of the medical device, a processor configured to receive orientation and position information from the orientation attachment and determine a degree to which an actual insertion angle of the medical device deviates from a target angle and/or a degree to which an actual insertion depth of the medical device deviates from a target insertion depth, a display configured to visually convey to a user, in real-time via graphic, text and/or color, the orientation and the position of the medical device, and a speaker configured to audibly convey to the user, in real-time via sound, the orientation and the position of the medical device.

Electronic position guidance device with real-time auditory and visual feedback

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Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal Communication

Electronic position guidance device with real-time auditory and visual feedback