 Calculates a apparent diffusion coefficient (ADC) map based on diffusion weighted images. At least two images with different b-values are required. An optional mask can also be provided to limit the calculations to a region of interest.

Two methods can be used in the calculation of the ADC map; a linear (fast) method and a nonlinear (slower) method. Typically both methods give good results but the linear method involves taking the logarithm of a signal before fitting parameters and will therefore not treat noise optimally. Consequently, for lower signal-to-noise ratio data the nonlinear method is to be preferred. The estimation is based on a signal equation

$\begin{equation} S_i = S_0 e^{-b_i ADC}, ~~~i = 1, 2, ...,n \label{#eq:nonlin} \tag{1} \end{equation}$

where $$i$$ is an index over $$n$$ images acquired with different b-values.

An ADC map in units [$$\text{mm}^2/\text{s}$$] and a signal map that contains all weighting except that caused by diffusion are produced.

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## Inputs

#### B-Value Series

A time-series of images acquired with at least two different b-values.

MetaData: Requires that the field BValue is present in the metadata with one value per time frame.

Type: Image4DFloat, Required, Single

An (optional mask) that specifies which pixels to analyse.

Type: Image4DBool, Optional, Single

## Outputs

The ADC map in units $$\text{mm}^2/\text{s}$$. (Provided that the b-values are given in $$\text{s}/\text{mm}^2$$.)

Type: Image4DFloat

#### Signal

The weighting due to everything except diffusion, i.e. $$S_0$$ in equation (1).

Type: Image4DFloat

## Settings

#### Method 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 using a logarithm to yield a linear system of equations

$\begin{equation} \ln{S_i} = \ln{S_0} - b_i ADC, ~~~i = 1, 2, ...,n. \end{equation}$

The ADC values and $$S_0$$ are then obtained using linear regression.

NOTE: The nonlinear model fit is in beta-stage and may exhibit some unexpected behavior.

Values: Linear, NonLinear

1. Bernstein, K. F. King, and X. J. Zhou, Handbook of MRI Pulse Sequences. Amsterdam: Elsevier Academic Press, pp. 830 - 53, 2004.