Work

General perturbative approach to the diffusion equation in the presence of absorbing defects: frequency-domain and time-domain results

Year: 2011

Type: conference-paper

Abstract: In this work, based on our previously proposed perturbation theory for the diffusion equation, we present new theoretical results in time and frequency domains. More specifically, we have developed a fourth order perturbation theory of the diffusion equation for absorbing defects. The method of Padé Approximants is used to extend the validity of the proposed theory to a wider range of absorbing contrasts between defects and background medium. The results of the theory are validated by comparisons with Monte Carlo simulations. In the frequency domain, the discrepancy between theoretical and Monte Carlo results for amplitude (AC) data are less than 10% up to an absorption contrast of Δμa ≤ 0.2 mm-1, whereas the discrepancy of phase data is less than 1° up to Δμa ≤ 0.1 mm-1. In the time domain, the average discrepancy is around 2-3% up to Δμa ≤ 0.06 mm-1. The proposed method is an effective and fast forwardproblem solver that has the potential to find general applicability in a number of situations.

Source: Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

DOI: 10.1117/12.876943

Authors: Angelo Sassaroli, Fabrizio Martelli, Sergio Fantini

Institutions: Tufts University, University of Florence

Language: English

Topic: Optical Imaging and Spectroscopy Techniques

Subfield: Radiology, Nuclear Medicine and Imaging

Field: Medicine

Domain: Health Sciences

Open Access status: bronze

Funders: European Commission, National Institutes of Health, National Institute of Neurological Disorders and Stroke

Awards: G2973790809, Non-invasive imaging of brain function and disease by pulsed near infrared light, Biological Mechanism of Fast Near-Infrared Signals in Peripheral Nerves