Inversion Recovery

Config name: model: inversion_recovery BIDS suffix; IRT1 Method family; T1 Relaxometry Acquired volumes; 9 Fit granularity; voxelwise

Fits the longitudinal relaxation time T1 from a series of inversion-recovery images acquired at different inversion times. The magnitude signal is modelled as an exponential recovery with a free amplitude and offset, which together absorb imperfect inversion efficiency, so no assumption about a perfect 180° pulse is needed. T1 is recovered by a grid search over the configured range followed by a local zoom refinement.

Signal model¶

S(\mathrm{TI}) = a\,\exp\!\left(-\mathrm{TI}/T_1\right) + b

(1)

Symbol	Quantity	Unit
`T1`	Longitudinal relaxation time	s
`a`	Recovery amplitude (absorbs inversion efficiency)	—
`b`	Signal offset	—

What the model reads¶

A series of 9 volumes indexed by InversionTime. Volumes are matched to these identities by value, so reordering the acquisition yields an identical fit.

#	InversionTime
1	0.35
2	0.5
3	0.65
4	0.8
5	0.95
6	1.1
7	1.25
8	1.4
9	1.7

Where the protocol comes from¶

In a BIDS dataset these values are resolved for you:

Protocol parameter	Source	Key	Resolved
`InversionTime`	sidecar field	`InversionTime`	per volume
`RepetitionTime`	sidecar field	`RepetitionTime`	whole collection

Inputs¶

Figure 1:The 9 acquired volumes, each labeled with the identity the model reads it by.

Figure 2:Auxiliary maps and the mask applied to this fit.

Outputs¶

Map	BIDS suffix	Unit	Fit bounds	Fitted
`T1`	`T1map`	s	unbounded … unbounded	free

Output
`b`
`a`
`res`
`idx`

Figure 3:Fitted maps for one example subject.

Usage¶

BIDS

Without BIDS

Simulation

Browser

The acquisition comes from the sidecars, so recipes/bids/irt1_config.yaml carries only algorithm options:

model: inversion_recovery

# BIDS input: InversionTime is read from the JSON sidecars via the model's
# protocol_schema(), so the inversion-time list is NOT declared here.

# Algorithm options (always used; not BIDS metadata).
method: magnitude
t1_range:
  start: 0.001
  stop: 5.0
  step: 0.001
zoom:
  iterations: 2
  points: 21

# BIDS mask selection — disambiguates which mask in the dataset to apply.
mask:
  desc: brain

qmrust fit --bids-dir ds-mydata \
  --config recipes/bids/irt1_config.yaml --output-dir out

Fitted maps are written as BIDS derivatives:

out/derivatives/qmrust/sub-01/anat/
  sub-01_T1map.nii.gz
  sub-01_T1map.json

No sidecars, so recipes/non-bids/irt1_config.yaml declares the acquisition itself:

model: inversion_recovery

# non-BIDS: protocol from this file; mask via --mask
# All times are in seconds (BIDS/SI).
inversion_times:
- 0.350
- 0.500
- 0.650
- 0.800
- 0.950
- 1.100
- 1.250
- 1.400
- 1.700
repetition_time: 2.5

# Algorithm options (always used; not BIDS metadata).
method: magnitude
t1_range:
  start: 0.001
  stop: 5.0
  step: 0.001
zoom:
  iterations: 2
  points: 21

qmrust fit --data data.nii.gz --mask mask.nii.gz \
  --config recipes/non-bids/irt1_config.yaml \
  --output-dir out

See Fitting without BIDS.

model: inversion_recovery

# Simulation: the acquisition comes from this file, as for every non-BIDS
# recipe. All times are in seconds (BIDS/SI).
inversion_times:
- 0.350
- 0.500
- 0.650
- 0.800
- 0.950
- 1.100
- 1.250
- 1.400
- 1.700
repetition_time: 2.5

method: magnitude
t1_range:
  start: 0.001
  stop: 5.0
  step: 0.001
zoom:
  iterations: 2
  points: 21

# Ground truth: white matter at 3 T. The IR signal is a + b*exp(-TI/T1), so a
# is the recovered magnetization and b is close to -2a for a full inversion.
sim:
  params: { T1: 0.9, a: 500.0, b: -1000.0 }
  noise: { type: rician, snr: 100.0 }
  seed: 0
  trials: 100
  sweep: { param: T1, start: 0.3, stop: 2.5, steps: 10 }
  distributions:
    T1: { mean: 0.9, std: 0.15 }

qmrust sim signal       --config recipes/sim/irt1_sim.yaml --output signal.json
qmrust sim single-voxel --config recipes/sim/irt1_sim.yaml --output sv.json
qmrust sim sensitivity  --config recipes/sim/irt1_sim.yaml --output sens.json
qmrust sim montecarlo   --config recipes/sim/irt1_sim.yaml --output mc.json

See Simulation.

The same core, compiled to WebAssembly:

import init, { fit_volume } from './pkg/qmrust_wasm.js';
await init();
const maps = fit_volume(configYaml, data, [nx, ny, nz, nt],
                        JSON.stringify(volumeIds), mask, '{}');

Try it on real data in the playground, or read Browser & wasm.

Figure 4:One voxel’s measured data with the model’s forward signal at the fitted parameters. The curve is computed by the same Rust code that does the fitting.

Implementation¶

model.rs — the Model implementation: measurement contract, protocol schema, BIDS outputs.
fit.rs — the numerical fit.
config.rs — configuration and validation.

Every default materialized, as qmrust dump-config prints it.

model: inversion_recovery
inversion_times:
- 0.35
- 0.5
- 0.65
- 0.8
- 0.95
- 1.1
- 1.25
- 1.4
- 1.7
method: magnitude
t1_range:
  start: 0.001
  stop: 5.0
  step: 0.001
zoom:
  iterations: 2
  points: 21
repetition_time: 2.5

References¶

Barral et al. (2010)

References¶

Barral, J. K., Gudmundson, E., Stikov, N., Etezadi-Amoli, M., Stoica, P., & Nishimura, D. G. (2010). A robust methodology for in vivo T1 mapping. Magnetic Resonance in Medicine, 64(4), 1057–1067.