# T1 Estimation

Calculates a T1 map using the variable flip angle (VFA) method. The input must be a multi-channel image, where each volume has an associated flip angle (FA), however more images are advised if a larger range of T1 values are expected. Flip angle (FA) and repetition time (TR) are detected automatically and it is required that the TR is the same in all images.

In addition to the images with varying flip angle, a B1 map can also be provided to improve the accuracy, in particular at high field strengths. The B1 map represents a scaling of FA, hence value 1 indicates that the nominal FA is achieved. An optional mask can also be provided to limit the calculations to a region.

Produces a T1 map in the same units as TR, and a $$S_0$$ map which is a proton and $$T2^*$$-weighted image. The parameter values are obtained by fitting the data to equation (1) directly or a linearized version of the of equation (1)[1]:

$$$S_i = \frac{S_0(1-e^{-TR/T1})\sin(FA_i \cdot B1)}{1-\cos(FA_i \cdot B1)e^{-TR/T1}},~~~~i = 1, 2, ...,n ~~~~~~~(1) \label{eq:sample}$$$

where $$n$$ is the number of images used.

## Inputs

#### Dataset

An image or a list of images (for batch processing) where channel dimensions are used for the different flip angles. At least two volumes are needed and they should have the same $$TR$$ and echo time.

Type: Image, List, Required, Single

#### B1

B1 correction map(s). A value of $$1$$ indicates that that the actaual flip angle is at the nominal value. A single 3D volume should be provided for all flip angles.

Type: Image, List, Optional, Single

Mask(s) used to confine the region in which the signal model is fitted.

## Outputs

#### T1

The estimated $$T1$$ parameter map.

Type: Image

#### S0

The estimated $$S_0$$ parameter map.

Type: Image

## Settings

### Configure

#### Algorithm Selection

Use a linearized or a nonlinear fitting model. When selecting a nonlinear model, equation (1) is fit directly with a square loss term. In the linearized case the data is transformed to yield a system of linear equations.

Values: Linear, NonLinear

#### Batch Size Integer

The number of voxels that are computed per batch. This is a trade-off between performance and memory consumption.

### Configure NonLinear

#### Tolerance Float

The threshold change in the objective function. Changes smaller than this value imply that the fitting has converged.

#### Max Iterations Integer

Maximum number of iterations.

#### Return Convergence Map Boolean

Output a binary mask, where all true voxels have converged in the fit. This can be used to exclude voxels that did not converge.

#### Repetition Time Source Selection

Select the $$TR$$-value source for the calculation. The $$TR$$-values can be taken from the metadata, or can be supplied as an input Numeric Array.

#### Flip Angle Source Selection

Select the FA source for the calculation. The FA values can be taken from the metadata, or can be supplied as an input Numeric Array.

#### Repetition Time Tag Text

The $$TR$$-value tag name in the metadata.

#### Flip Angle Tag Text

The FA tag name in the metadata.

## References

[1] H. L. M. Cheng and G. A. Wright, “Rapid high-resolution T1 mapping by variable flip angles: Accurate and precise measurements in the presence of radiofrequency field inhomogeneity,” Magn. Reson. Med., vol. 55, no. 3, pp. 566–574, 2006.