From a24b9adf478346129da64b600a3aa8bfee9f2588 Mon Sep 17 00:00:00 2001 From: Mathieu Boudreau Date: Thu, 3 Oct 2024 13:25:16 -0300 Subject: [PATCH] Add more figure links --- 2 T1 Mapping/1-1 Inversion Recovery/03-IR_DataFitting.md | 2 +- .../1-1 Inversion Recovery/04-IR_BenefitsAndPitfalls.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/2 T1 Mapping/1-1 Inversion Recovery/03-IR_DataFitting.md b/2 T1 Mapping/1-1 Inversion Recovery/03-IR_DataFitting.md index 51967b0..3f089f5 100644 --- a/2 T1 Mapping/1-1 Inversion Recovery/03-IR_DataFitting.md +++ b/2 T1 Mapping/1-1 Inversion Recovery/03-IR_DataFitting.md @@ -13,7 +13,7 @@ numbering: Several factors impact the choice of the inversion recovery fitting algorithm. If only magnitude images are available, then a polarity-inversion is often implemented to restore the non-exponential magnitude curves ([](#irPlot2)) into the exponential form ([](#irPlot1)). This process is sensitive to noise due to the Rician noise creating a non-zero level at the signal null. If phase data is also available, then a phase term must be added to the fitting equation {cite:p}`Barral2010-qm`. [Equation 1.3](#irEq3) must only be used to fit data for the long TR regime (TR > 5T1), which in practice is rarely satisfied for all tissues in subjects. -Early implementations of inversion recovery fitting algorithms were designed around the computational power available at the time. These included the “null method” {cite:p}`Pykett1983`, assuming that each T1 value has unique zero-crossings (see Figure 2), and linear fitting of a rearranged version of [Equation 1.3](#irEq3) on a semi-log plot {cite:p}`Fukushima1981`. Nowadays, a non-linear least-squares fitting algorithm (e.g. Levenberg-Marquardt) is more appropriate, and can be applied to either approximate or general forms of the signal model ([Equation 1.3](#irEq3) or [Equation 1.1](#irEq1)). More recent work {cite:p}`Barral2010-qm` demonstrated that T1 maps can also be fitted much faster (up to 75 times compared to Levenberg-Marquardt) to fit [Equation 1.1](#irEq1) – without a precision penalty – by using a reduced-dimension non-linear least squares (RD-NLS) algorithm. It was demonstrated that the following simplified 5-parameter equation can be sufficient for accurate T1 mapping: +Early implementations of inversion recovery fitting algorithms were designed around the computational power available at the time. These included the “null method” {cite:p}`Pykett1983`, assuming that each T1 value has unique zero-crossings (see [](#irPlot1)), and linear fitting of a rearranged version of [Equation 1.3](#irEq3) on a semi-log plot {cite:p}`Fukushima1981`. Nowadays, a non-linear least-squares fitting algorithm (e.g. Levenberg-Marquardt) is more appropriate, and can be applied to either approximate or general forms of the signal model ([Equation 1.3](#irEq3) or [Equation 1.1](#irEq1)). More recent work {cite:p}`Barral2010-qm` demonstrated that T1 maps can also be fitted much faster (up to 75 times compared to Levenberg-Marquardt) to fit [Equation 1.1](#irEq1) – without a precision penalty – by using a reduced-dimension non-linear least squares (RD-NLS) algorithm. It was demonstrated that the following simplified 5-parameter equation can be sufficient for accurate T1 mapping: ```{math} :label: irEq4 diff --git a/2 T1 Mapping/1-1 Inversion Recovery/04-IR_BenefitsAndPitfalls.md b/2 T1 Mapping/1-1 Inversion Recovery/04-IR_BenefitsAndPitfalls.md index d8ab18d..6a0582f 100644 --- a/2 T1 Mapping/1-1 Inversion Recovery/04-IR_BenefitsAndPitfalls.md +++ b/2 T1 Mapping/1-1 Inversion Recovery/04-IR_BenefitsAndPitfalls.md @@ -16,7 +16,7 @@ The conventional inversion recovery experiment is considered the gold standard T * It offers a wide dynamic range of signals ([up to `-kM0`, `kM0`]), allowing a number of inversion times where high SNR is available to sample the signal recovery curve {cite:p}`Fukushima1981`. * T1 maps produced by inversion recovery are largely insensitive to inaccuracies in excitation flip angles and imperfect spoiling {cite:p}`Stikov2015`, as all parameters except TI are constant for each measurement and only a single acquisition is performed (at TI) during each TR. -One important protocol design consideration is to avoid acquiring at inversion times where the signal for T1 values of the tissue-of-interest is nulled, as the magnitude images at this TI time will be dominated by Rician noise which can negatively impact the fit under low SNR circumstances (Figure 6). Inversion recovery can also often be acquired using commonly available standard pulse sequences available on most MRI scanners by setting up a customized acquisition protocol, and does not require any additional calibration measurements. For an example, please visit the interactive preprint of the ISMRM Reproducible Research Group 2020 Challenge on inversion recovery T1 mapping {cite:p}`Boudreau2023`. +One important protocol design consideration is to avoid acquiring at inversion times where the signal for T1 values of the tissue-of-interest is nulled, as the magnitude images at this TI time will be dominated by Rician noise which can negatively impact the fit under low SNR circumstances ([](#irPlot5)). Inversion recovery can also often be acquired using commonly available standard pulse sequences available on most MRI scanners by setting up a customized acquisition protocol, and does not require any additional calibration measurements. For an example, please visit the interactive preprint of the ISMRM Reproducible Research Group 2020 Challenge on inversion recovery T1 mapping {cite:p}`Boudreau2023`. :::{figure} #fig2p6cell