### Abstract

Propagation of errors, in conjunction with the theoretical signal equation for spoiled gradient echo pulse sequences, is used to derive a theoretical expression for uncertainty in quantitative variable flip angle T_{1} mapping using two flip angles. This expression is then minimized to derive a rigorous expression for optimal flip angles that elucidates a commonly used empirical result. The theoretical expressions for uncertainty and optimal flip angles are combined to derive a lower bound on the achievable uncertainty for a given set of pulse sequence parameters and signal-to-noise ratio (SNR). These results provide a means of quantitatively determining the effect of changing acquisition parameters on T_{1} uncertainty.

Original language | English (US) |
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Journal | Physics in Medicine and Biology |

Volume | 54 |

Issue number | 1 |

DOIs | |

State | Published - Jan 7 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Radiology Nuclear Medicine and imaging
- Radiological and Ultrasound Technology

### Cite this

**Uncertainty in T1 mapping using the variable flip angle method with two flip angles.** / Schabel, Matthias; Morrell, Glen R.

Research output: Contribution to journal › Article

*Physics in Medicine and Biology*, vol. 54, no. 1. https://doi.org/10.1088/0031-9155/54/1/N01

}

TY - JOUR

T1 - Uncertainty in T1 mapping using the variable flip angle method with two flip angles

AU - Schabel, Matthias

AU - Morrell, Glen R.

PY - 2009/1/7

Y1 - 2009/1/7

N2 - Propagation of errors, in conjunction with the theoretical signal equation for spoiled gradient echo pulse sequences, is used to derive a theoretical expression for uncertainty in quantitative variable flip angle T1 mapping using two flip angles. This expression is then minimized to derive a rigorous expression for optimal flip angles that elucidates a commonly used empirical result. The theoretical expressions for uncertainty and optimal flip angles are combined to derive a lower bound on the achievable uncertainty for a given set of pulse sequence parameters and signal-to-noise ratio (SNR). These results provide a means of quantitatively determining the effect of changing acquisition parameters on T1 uncertainty.

AB - Propagation of errors, in conjunction with the theoretical signal equation for spoiled gradient echo pulse sequences, is used to derive a theoretical expression for uncertainty in quantitative variable flip angle T1 mapping using two flip angles. This expression is then minimized to derive a rigorous expression for optimal flip angles that elucidates a commonly used empirical result. The theoretical expressions for uncertainty and optimal flip angles are combined to derive a lower bound on the achievable uncertainty for a given set of pulse sequence parameters and signal-to-noise ratio (SNR). These results provide a means of quantitatively determining the effect of changing acquisition parameters on T1 uncertainty.

UR - http://www.scopus.com/inward/record.url?scp=58149267823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149267823&partnerID=8YFLogxK

U2 - 10.1088/0031-9155/54/1/N01

DO - 10.1088/0031-9155/54/1/N01

M3 - Article

VL - 54

JO - Physics in Medicine and Biology

JF - Physics in Medicine and Biology

SN - 0031-9155

IS - 1

ER -