29. DCE MRI Model Analysis

29.1. Compartmental modeling

DCE MRI analysis is required to relate measured data to the parameters of the tissue or organ of interest. These parameters have been increasingly used in individualized medicine for disease diagnostics, treatment planning, and predicting and monitoring response to treatment.

Compartmental modeling provides fully quantitative physiological parameters. Compartmental models represent tissues and organs as combinations of uniform, instantly mixed compartments. Models usually require a vascular input function (IF) driving the system. The input function is usually the concentration of contrast in a vessel feeding the tissue of interest. Some models require more than one IF, such as the liver models, which may have two IFs, arterial and portal venous, reflecting the hepatic blood supply.

In FireVoxel, several compartmental models are available under Dynamic Analysis > Calculate Parametric Map for the analysis of compatible DCE MRI data.

The following describes two-compartment Tofts models (regular and extended), widely used for analyzing DCE MRI in cancer and other diseases:

Model 8: Tofts two-compartment exchange model {k-trans, Ve} : 1IF (single input function);

Model 9: Modified Tofts two-compartment exchange model {k-trans, Ve, Va} : 1IF.

29.2. Tofts Model

The two-compartment tracer kinetic models describe the scenario, in which intravenously injected contrast agent enters the bloodstream, and (in body tissues) distributes throughout the vasculature and the EES, with bidirectional exchange between the vascular compartment and the EES compartment across the vessel walls (Fig. 29.1).

Tissue compartments in Tofts model

Fig. 29.1 Contrast in tissue exchanges between vascular and EES compartments.

The extended Tofts model [Tofts1999] predicts the contrast concentration as a function of time in the tissue of interest C_{t}(t) fed by a blood vessel with the plasma concentration C_{p}(t):

(29.1)C_{t}(t) &= v_{p}C_{p}(t) + K^{\text{trans}}\int_{0}^{t}{C_{p}(\tau)
\exp( - k_{\text{ep}}(t - \tau))d\tau}

The concentration in the vascular compartment is considered to be the same as the concentration in the feeding vessel, which serves as the arterial input function (AIF). The model parameters include the vascular volume fraction v_{p} (unitless), the volume transfer constant K^{\text{trans}} (measured in mL/min/mL - mL/min per mL of tissue) and the rate constant k_{\text{ep}} = K^{\text{trans}}/v_{e} (1/min), where v_{e} (unitless) is the fractional EES volume.

The regular Tofts model ignores the contribution of the vascular compartment, when the vascular volume fraction is small (v_{p} \ll 1), which may be an appropriate approximation for tissues that are not highly vascularized:

(29.2)C_{t}(t) &= K^{\text{trans}}\int_{0}^{t}{C_{p}(\tau)
\exp( - k_{\text{ep}}(t - \tau))d\tau}

In the body, the volume transfer constant K^{\text{trans}} typically reflects a combination of tissue perfusion (blood flow, F in Fig. 29.1) and vessel wall permeability (leakiness). In contrast, in the brain with mostly intact blood-brain barrier (BBB), where low molecular weight GBCAs mostly intravascular, K^{\text{trans}} is mostly a measure of vascular permeability, which is low in healthy brain and may be elevated in areas of injury or tumors, where BBB may be disrupted. The rate constant k_{\text{ep}} describes the rate of the contrast washout from EES back into the vasculature.

The Tofts model parameters scale with the AIF and, as a result, are sensitive to the AIF errors. Special care must be exercised to ensure robust measurements of the Tofts model parameters and their intrapatient repeatability in longitudinal studies. Users are urged to consider the issues that may affect the reliability of the AIF measurements in their experiments.

FireVoxel offers the Image Derived Input Function tool for mostly automatic derivation of the AIF as well as a tool for the cardiac output based correction of the AIF to minimize the signal-to-concentration errors (Cardiac Output Measurement and Correction). These commands are also available under the Dynamic Analysis main menu tab.

29.3. Performing DCE MRI model analysis

1. Load images. Load dynamic (4D) images into FireVoxel and save them as a FireVoxel document. See Open Images for general information on opening images in FireVoxel and Loading DWI data for examples of loading 4D datasets. See Save for saving documents.

2. Determine the input function. The input function (signal or concentration vs time) for model analysis must be saved in a text file with two columns of data: (1) time and (2) signal intensity (or concentration). The input function may be obtained manually, from an ROI drawn in a blood vessel, or using another method, such as FireVoxel’s Image Derived Input Function.

3. Segment the tissue or organ of interest (if needed). This step will create one or more ROI layers. Name these layers clearly to help identify modeling results. If model analysis is performed only for a tissue or organ of interest, the corresponding portion of the image must be segmented. Segmentation can be performed manually, by drawing an ROI, or using commands under the ROI menu (see ROI), or via automatic segmentation (such as Segmentation 3D (EdgeWave)).

4. Enter precontrast tissue T10 value. For each ROI layer, specify T10 for the corresponding tissue or organ. Open Layer Control and select an ROI layer to be the active layer. Click Attributes in the lower right corner of the Layer Control panel. A dialog (Tissue attributes) will appear to enter the T10-value (in seconds). Click OK. Repeat this step for each ROI layer for which modeling will be performed. Modeling is currently implemented only for a fixed T10. Model analysis using voxel-by-voxel matched T10-map is under development.

5. Open Calculate Parametric Map dialog. Select Dynamic Analysis > Calculate Parametric Map. This opens Parametric Map Calculation for Dynamic Experiment dialog, where the user can configure the parameters of model analysis.

6. Use Model dropdown menu and and select Model 8 (regular Tofts model) or Model 9 (extended Tofts model).

7. Load the input function. Under Input function, click Load to browse for file and select the previously saved AIF text file. Alternatively, Paste to load AIF data from clipboard. Click View to preview the AIF curve. Click Attributes and enter the blood precontrast T10 (in seconds).

8. Set up the AIF signal-to-concentration conversion (if needed). If the AIF data are signal intensity, it needs to be converted to contrast concentration. Under Input function, click Concentration to open the Concentration Conversion dialog and enter the required parameters for blood/plasma. If appropriate, enter the hematocrit value under Hct to obtain plasma concentration. If the AIF data are already converted to concentration, but not corrected for hematocrit, use Concentration Conversion, select No conversion, and enter the hematocrit value. Click OK to close the Conversion dialog and return to Calculate Parametric Map.

9. Set up the tissue signal to concentration conversion. Click Tissue Concentration to open Concentration Conversion and enter the conversion parameters for tissue of interest. Note: Hematocrit correction is not necssary for tissue.

10. Set hyperparameters and select output parameters, described below (see Hyperparameters and outputs for Tofts model.

11. Select the fitting option: Process All, Process ROI Only, Process ROI as a single curve. See Fitting options and Results described for DWI.

29.3.1. Hyperparameters and outputs for Tofts model

Hyperparameters (the same set for Models 8 and 9):

K-trans max (1/min) – Maximum allowed value of K^{\text{trans}}.

Ve max – Maximum value of EES fractional volume ve.

Max arterial delay (sec) – Maximum time interval between the bolus arrival time and the tissue concentration rise (IS THIS CORRECT?)

Optimization depthADD DETAIL

Use L1\L2 residual metric – Default, 2. The choice of L1 or L2 norm to compute the residual. L2 norm is the default for the output residual.

Use balanced solution (0\1) – Default, 1. ADD DETAIL.


Ktrans – Volume transfer constant K^{\text{trans}} (1/min).

Ve – EES volume fraction V_{\text{e}} (unitless).

Va (only for Model 9 (extended Tofts model)) – Vascular volume fraction V_{\text{p}} (unitless).

Arterial_delay – Time interval between the bolus arrival time and the tissue concentration rise.

Residual – Goodness of fit measure, expressed as L1 or L2 norm, as selected under Hyperparameters (L2 by default).


Tofts PS, Brix G, Buckley DL, et al. Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols. J Magn Reson Imaging. 1999; 10(3):223-32. PMID: 10508281 https://www.ncbi.nlm.nih.gov/pubmed/10508281

Yankeelov TE, Cron GO, Addison CL, et al. Comparison of a reference region model with direct measurement of an AIF in the analysis of DCE-MRI data. Magn Reson Med. 2007;57(2):353-61. PMID: 17260371 https://www.ncbi.nlm.nih.gov/pubmed/17260371