Jesper Folsted Kallehauge^{1}

Post-processing and modeling of DCE time curves allow for reducing a vast amount of data into a set of parametric maps related to the underlying tissue properties: Permeability, Perfusion, compartmental composition etc. Multiple steps and methods are involved in reaching this point with possible pitfalls resulting in potential misinterpretation of the acquired data. Participants should come away from this seminar understanding these steps and how choices made during data acquisition influence what can sensibly be extracted from the data.

- Understand the necessary image processing steps to successfully extract useful parameters from the DCE experiment (signal to concentration conversion, extraction of input function, selection of model etc)
- Understand how DCE separates itself form other perfusion methods.
- Understand what underlying assumptions that are made during the analysis
- Understand what key experimental-parameters drive model-parameter robustness

The T1 weighted DCE experiment is closely related to the T2/T2* weighted DSC experiment. However the DCE experiment may also contain information about the exchange of contrast between extracellular-extravascular space (EES) and the vascular compartment. For this to happen, the DCE experiment is often performed longer than 5 minutes in order to capture the reflux of contrast agent back into the vascular space from the EES. The use of pre-experimental estimation of the T1 relaxation is not a necessary step for the subsequent analysis however it will improve the robustness of the quantitative parameters essential in multicentre studies. The baseline T1 allows for conversion of the signal into contrast agent concentration given certain assumptions. Similar to The DSC experiment, where the effect of T1 are assumed negligible, here the T2* effects are assumed negligible and are thus not taken into the signal to concentration conversion.

Once the DCE experiment has successfully been performed a number of options are available for the analysis: uptake-classification, semi-quantitative and quantitative. The latter is by far the most demanding and potentially most rewarding. The quantitative methods require a measured or assumed baseline T1 map covering the same volume as the DCE experiment. It also requires a measured or assumed supply of contrast agent into tissue of interest; commonly referred to as the Arterial Input Function (AIF). The correct extraction of the AIF is particularly challenging [1,2] and may introduce large uncertainties in final results. Once this is in place the choice of response model needs to be carefully chosen. Generally, a simple mono-exponential decay would be a good choice, since this assumes a well-mixed one compartment model. However be aware that when choosing a model you have already set a number of assumptions up which your data does not necessarily support. There are a number of key experimental parameters: temporal resolution, Contrast-to-Noise ratio, experiment duration and prior knowledge of the tissues tracer kinetics [3] that are useful when choosing form a wide range of potential models [4]

Once the choice of model (or sets thereof) has been made then the model fitting to the acquired data can begin. This minimization problem can again be performed following different strategies. For many of the non-linear models there also exists a linear version [5,6,7] that is simpler to solve, with no requirements to starting guesses but with a potential parameter bias due to the transformation of the noise. The linear models tend to perform well under good noise condition (high CNR) while their non-linear counterparts are more stable under noisier conditions (low CNR) [6]. For the non-linear models the optimization is often performed using gradient descent methods Levenberg-Marquart or Variational Bayes [8]. When applying multiple model fits of different complexity with the aim to determine which model is best describing the data it is good practice to start with the simplest model and only add complexity incrementally if this improves the fit [4].

[1] FF Simonis, A Sbrizzi, E Beld, JJ Lagendijk,CA van den Berg. Improving the arterial input function in dynamic contrast enhanced MRI by fitting the signal in the complex plane. Magnetic resonance in medicine 76(4):1236-45

[2] F Calamante. Arterial input function in perfusion MRI: a comprehensive review. Progress in nuclear magnetic resonance spectroscopy 74, 1-32

[3] R Luypaert, S Sourbron, S Makkat, J de Mey. Error estimation for perfusion parameters obtained using the two‐compartment exchange model in dynamic contrast‐enhanced MRI: a simulation study. Phys Med Biol 2010;55:6431–6443.

[4] SP Sourbron, DL Buckley. Tracer kinetic modelling in MRI: estimating perfusion and capillary permeability. Phys Med Biol 2012;57:R1–R33.

[5] K Murase. Efficient method for calculating kinetic parameters using T1-weighted dynamic contrast-enhanced magnetic resonance imaging. Magnetic resonance in medicine 51(4), 858–862.

[6] JF Kallehauge, S Sourbron, B Irving, K Tanderup, JA Schnabel, MA Chappell. Comparison of linear and nonlinear implementation of the compartmental tissue uptake model for dynamic contrast‐enhanced MRI. Magnetic resonance in medicine 77 (6), 2414-2423

[7] D Flouri, D Lesnic SP Sourbron. Fitting the two-compartment model in DCE-MRI by linear inversion. Magnetic resonance in medicine 76(3), 998–1006.

[8] MA Chappell, AR Groves, B Whitcher, MW Woolrich. Variational Bayesian inference for a nonlinear forward model. IEEE Transactions on Signal Processing, 2009