Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.

Prevalence and prognostic significance of secondary lymphedema following breast cancer

Background The adverse consequences of lymphedema following breast cancer in relation to physical function and quality of life are clear; however, its potential relationship with survival has not been investigated. Our purpose was to determine the prevalence of lymphedema and associated upper-body symptoms at 6 years following breast cancer and to examine the prognostic significance of lymphedema with respect to overall 6-year survival (OS). Methods and Results A population-based sample of Australian women (n=287) diagnosed with invasive, unilateral breast cancer was followed for a median of 6.6 years and prospectively assessed for lymphedema (using bioimpedance spectroscopy [BIS], sum of arm circumferences [SOAC], and self-reported arm swelling), a range of upper-body symptoms, and vital status. OS was measured from date of diagnosis to date of death or last follow-up. Kaplan-Meier methods were used to calculate OS and Cox proportional hazards models quantified the risk associated with lymphedema. Approximately 45% of women had reported at least one moderate to extreme symptom at 6.6 years postdiagnosis, while 34% had shown clinical evidence of lymphedema, and 48% reported arm swelling at least once since baseline assessment. A total of 27 (9.4%) women died during the follow-up period, and lymphedema, diagnosed by BIS or SOAC between 6–18 months postdiagnosis, predicted mortality (BIS: HR=2.5; 95% CI: 0.9, 6.8, p=0.08; SOAC: 3.0; 95% CI: 1.1, 8.7, p=0.04). There was no association (HR=1.2; 95% CI: 0.5, 2.6, p=0.68) between self-reported arm swelling and OS. Conclusions These findings suggest that lymphedema may influence survival following breast cancer treatment and warrant further investigation in other cancer cohorts and explication of a potential underlying biology.