MRI Sequence Documentation: Inversion Recovery (IR)

Overview

The Inversion Recovery (IR) sequence is a spin-echo–based experiment designed to characterize longitudinal relaxation (T1). The sequence applies an inversion pulse followed by a variable inversion time (TI) before excitation and signal acquisition. By sweeping TI and measuring the signal amplitude at a fixed echo time, the T1 relaxation constant can be estimated.

This sequence is intended for non-imaging experiments and produces time-domain signals that are later analyzed using a dedicated reconstruction and fitting routine.

---

Sequence Description

The sequence performs a sweep over inversion times between two user-defined limits. For each inversion time, a complete spin-echo experiment is executed.

Key characteristics:

• Logarithmic sampling of inversion times
• Robust spoiling using crusher gradients along all axes
• Fixed echo time (TE) for consistent signal sampling
• Averaging across multiple scans for improved SNR

---

Sequence Steps

1. Inversion Pulse
   A 180º RF pulse inverts the longitudinal magnetization.

2. Spoiler / Crusher Gradients
   Strong gradient crushers are applied along x, y, and z to eliminate residual transverse magnetization, particularly important at short inversion times.

3. Inversion Delay (TI)
   A variable delay allows partial T1 recovery before excitation. TI is swept between tInv0 and tInv1.

4. Excitation and Refocusing
   A 90º excitation pulse is followed by a 180º refocusing pulse to form a spin echo.

5. Signal Acquisition
   The signal is acquired around the echo center using a fixed acquisition window.

---

Parameters

• Sequence name: Name of the sequence. Default: InversionRecovery
• To MaRGE: Enable sending data to MaRGE
• Number of scans: Number of repetitions per inversion time
• Echo time (ms): Time between excitation and echo center
• Repetition time (ms): Time between consecutive inversion experiments
• Inversion time, Start (ms): Initial inversion time
• Inversion time, End (ms): Final inversion time
• Number of steps: Number of inversion times sampled
• Larmor frequency (MHz): System operating frequency
• RF excitation amplitude (a.u.)
• RF refocusing amplitude (a.u.)
• RF excitation time (µs)
• RF refocusing time (µs)
• nPoints: Number of acquired points per echo
• Acquisition time (ms): Duration of the readout window
• Shimming: Static field offsets applied along x, y, z
• Crusher gradient amplitude (mT/m): Spoiler gradient strength
• Crusher gradient time (µs): Duration of crusher gradients
• Crusher gradient delay (µs): Delay before crusher application

---

Inversion Time Sweep

The inversion time vector is generated automatically:

• Values are logarithmically spaced between tInv0 and tInv1
• The number of points is defined by nSteps
• The vector is stored internally and used both during acquisition and analysis

This improves sensitivity to short T1 values while preserving coverage of long relaxation times.

---

SequenceRun

The sequenceRun method:

• Generates the inversion time sweep
• Builds RF and gradient waveforms
• Executes the sequence for all inversion times and scans
• Handles oversampling and FIR decimation
• Stores all acquired data and metadata in the mapVals dictionary

---

Output and Results

The Inversion Recovery experiment produces complex time-domain echo signals acquired at different inversion times. A dedicated analysis routine processes these signals to extract quantitative T1 information.

The final outputs include:

• Estimated T1 relaxation time
• Equilibrium magnetization amplitude
• Plots of signal vs inversion time and full echo train evolution

---

Sequence Analysis

The analysis is performed by an external function that operates directly on the saved .mat raw data file.

Analysis Workflow

1. Data Loading
   Raw data and acquisition parameters are loaded from the .mat file.

2. Signal Averaging
   Data is reshaped to [nScans, nSteps, nPoints] and averaged across scans.

3. Echo Sampling
   The signal amplitude is extracted at the center of the echo

4. T1 Fitting
   The signal evolution as a function of inversion time is fitted to a mono-exponential inversion recovery model: S(TI) = | M · (1 − 2 · exp(−TI / T1)) |

5. Quality Assessment
   Correlation between experimental data and fitted curve is computed.

6. Visualization

   • Signal amplitude vs inversion time (with fitted curve)
   • Full echo train evolution (absolute, real, imaginary components)

---

Raw Data

• acqTime: Acquisition window duration (ms)

• bw: Acquisition bandwidth (Hz)

• samplingPeriod: Receiver sampling period (s)

• data: Decimated and concatenated complex signal for all inversion times and scans

• irTimeVector: Inversion times used in the experiment

• nScans: Number of scans per inversion time

• nSteps: Number of inversion times

• nPoints: Number of acquired points per echo

• echoTime: Echo time (ms)

• repetitionTime: Repetition time (ms)

• larmorFreq: Larmor frequency (MHz)

• rfExAmp: Excitation RF amplitude (a.u.)

• rfExTime: Excitation RF pulse duration (µs)

• rfReAmp: Refocusing RF amplitude (a.u.)

• rfReTime: Refocusing RF pulse duration (µs)

• crusherAmp: Crusher gradient amplitude (T/m)

• crusherTime: Crusher gradient duration (µs)

• crusherDelay: Crusher gradient delay (µs)

• gradRiseTime: Gradient rise time (µs)

• gSteps: Number of gradient steps used for trapezoids

• scanTime: Approximate total experiment duration

• seqName: Sequence identifier

• T1: Longitudinal relaxation time obtained from mono-exponential inversion recovery fitting (ms).

• M1: Fitted equilibrium magnetization scaling factor from inversion recovery analysis.

---

Notes

• T1 fitting assumes a mono-exponential inversion recovery model.
• The absolute value of the signal is used to avoid phase-related sign ambiguities.
• Sequence acquisition and analysis are decoupled, enabling offline processing and batch analysis.
• The analysis routine returns both numerical results and plotting instructions for visualization.