- Signal decay in diffusion weighted imaging experiments is governed by different effects such as diffusion, perfusion, and restricted diffusion whose influences vary with the b-values. As a result, more complex models than the popular mono-exponential model have been investigated to fit the measured data and compute diffusion parameters.

- In the Intravoxel Incoherent Model (IVIM), both diffusion and perfusion effects contribute to signal decay and can be estimated by means of a bi-exponential model or variants thereof.

- The selection of the b-values for the image acquisition has a strong influence on the accuracy and precision of the estimated diffusion parameters. Strategies to optimize the acquisition for clinical routine depending on the tissue properties and the selected model will be presented.

Radiologists, scientists, and clinicians interested in quantitative diffusion MRI and optimizing acquisition and processing methods for clinical applications.Participants will learn about the basics of quantitative diffusion mapping (models and fitting techniques), about pitfalls associated with parameter estimation, and strategies to optimize acquisition and processing of diffusion imaging data.

Measurements of the apparent diffusion coefficient (ADC) provide useful information on cell processes such as growth, swelling, necrosis, apoptosis, or reorganization [1]. In oncology, the ADC has the potential to serve as early biomarker of treatment success, tumor recurrence, and treatment outcome [2-3]. However, diffusion sequences are sensitive not only to pure molecular diffusion, but also to microscopic translational motions due to blood perfusion [4]. In highly perfused organs such as the liver, the perfusion effect can lead to a significant overestimation of ADC if a conventional mono-exponential model is applied for computation [5]. Differentiation between perfusion and diffusion effects can be performed by means of alternative models, as proposed in the intravoxel incoherent motion (IVIM) approach [4]. For example, the IVIM model has been applied successfully in the abdomen [6] and in the prostate [7] to separate perfusion and diffusion components.

Optimal selection of b-values is an essential part of diffusion weighted imaging in order to (a) eliminate systematic errors (bias) due e.g. to perfusion and noise and (b) to maximize the precision of the ADC estimates for a given scan time [8]. In this talk, the effect of perfusion and b-value selection on the accuracy and precision of ADC estimates will be discussed on the basis of the IVIM model. A Monte Carlo simulation framework will be presented as an example approach to determine which combination of model and b-value sampling is best adapted to a given perfusion regime.

The IVIM diffusion model consisting of fast and slow decay components was introduced in [4] to take into account all types of incoherent motion present contributing to signal attenuation observed with diffusion MR imaging, such as blood microcirculation in the capillary networks (perfusion), and not only molecular diffusion [9]. According to the IVIM approach, the signal decay as a function of the b-value can be described as:

$$S(b)=S_0\cdot\left(f\cdot e^{-b\cdot D^\star} + (1-f)\cdot e^{-b\cdot D} \right)$$

where $$$S(b)$$$ is the signal intensity measured at a b-value of $$$b$$$, $$$S_0$$$ is the theoretical signal intensity for b-value of 0 sec/mm², $$$f$$$ is the (T1-, T2-weighted) volume fraction of incoherently flowing blood in the tissue, $$$D^\star$$$ is the perfusion-related pseudo-diffusion coefficient, representing incoherent microcirculation within the voxel, and $$$D$$$ is the apparent diffusion coefficient representing pure molecular diffusion [10]. A simplified version of the bi-exponential IVIM model, originally proposed in [4], can also be considered in which the perfusion term is modeled solely by a Dirac function and is assumed to vanish for all non-zero b-values. This simplified IVIM model, which has shown promise to optimize acquisition efficiency of diffusion images in liver examination [11], allows the estimation of the perfusion fraction, but requires a careful selection of the b-values.

More recently, extensions of the IVIM model have been proposed to take into account the curvature of the signal attenuation that becomes apparent at high b-values, where the assumption of free-diffusion does not hold anymore as the motion of the water molecules is hindered by obstacles such as cell membranes, fibers, or macromolecules [9]. An example of these is the kurtosis model [12, 13]:

$$S(b)=S_0\cdot\left(f\cdot e^{-b\cdot D^\star} + (1-f)\cdot e^{-b\cdot D +(b \cdot D)^2 \cdot K / 6} \right)$$

where the kurtosis parameter $$$K$$$ primarily gives empirical information on the degree of diffusion non-Gaussianity and is not specific on tissue properties.

The complex signal decay observed in body diffusion experiments, as a result of perfusion effect and non-Gaussian diffusion is one of the reasons behind the high variability of mean ADC values reported in the literature. Indeed, applying the simple mono-exponential model associated with Gaussian diffusion to fit data closer to a bi- or tri-exponential decay as encountered in body applications results in a high variability of the fitted parameters as a function of the selected b-value sampling scheme. This variability is mainly due to systematic over- or under-estimation of the diffusion parameter as a result of model mismatch and therefore manifests itself even when comparing ADC values averaged over a region-of-interest.

Mathematically, this effect can be described by analyzing the accuracy (i.e. the systematic, mean error) and the precision (i.e. the standard deviation) of the estimated parameters as a function of the (hypothesized) diffusion process, of the fitting model, of the b-values selected for image acquisition, and of the noise level. In order to take into account the noise properties specific to magnitude MR images, non-linear maximum-likelihood estimation algorithms using the family of non-central Chi distributions (e.g. the Rician distribution) can be applied to obtain numerical estimates with minimal bias and optimal precision [14].

Monte Carlo simulations have been successfully applied to numerically assess accuracy and precision of fitting algorithms under different model hypotheses. For example, in the case of IVIM, simulations of a bi-exponential diffusion process were performed to compute mean and standard deviation of ADC estimates for a perfusion regime as encountered in the liver [11]. To account for the in vivo variability of perfusion parameters, $$$f$$$ and $$$D^\star$$$ were treated in the simulations as random variables with a uniform distribution and Gaussian noise was added to the simulated complex data prior to computation of magnitude signal.

In practice, quantitative diffusion methods based on models such as IVIM and kurtosis require multiple b-value acquisition to separate the contributions of the different effects, which increases scan time, and therefore is prone to motion artifacts and patient discomfort. As a consequence, optimal selection of the b-value sampling scheme is an important issue to obtain accurate parameter estimates with optimal precision in a given scan time. The problem of optimal b-value selection was addressed for selected perfusion regimes, such as encountered in the prostate [15] or in the kidney [16], or globally for a range of diffusion and perfusion parameters [8].

Here, we present an optimization approach based on Monte Carlo simulations, in which the systematic error of the diffusion parameters is forced to remain below a pre-defined threshold and the standard deviation of the diffusion parameter estimates is minimized. This constrained minimization problem has the advantage that it can be applied to obtain optimal b-value sampling schemes for any type of diffusion model, and to ensure that, within the boundaries of the model assumption, acquisition and estimation will result in unbiased estimators with maximal precision.

Examples of application to derive optimal b-values for liver, kidney, and prostate diffusion protocols will be given for the full bi-exponential and simplified IVIM models. Especially, it can be shown than the simplified IVIM model can lead to higher precision of diffusion parameter estimates than the full bi-exponential IVIM model when used in conjunction with optimized b-values [17].

The high variability of diffusion coefficient estimates observed in practice is an important obstacle for the wide application of quantitative diffusion acquisition protocols in routine clinical body applications. IVIM diffusion imaging represents a step towards a more accurate assessment of “pure” tissue diffusivity by minimizing the effect of tissue perfusion and reduces the variability of the ADC estimate with respect to the acquisition protocol. While the use of diffusion models beyond mono-exponential, such as IVIM and kurtosis, in combination with non-linear fitting algorithms and optimized b-values may help, a high SNR and a large number of b-values are necessary to obtain precise estimates [18]. Hence, these advanced quantitative diffusion techniques are also associated with longer acquisition times. As a result, patient discomfort and other effects such as motion may compromise their acceptance and clinical validity. More pragmatic approaches, that do not rely on model assumptions such as the “signature index” [9], have also been proposed recently to overcome the above mentioned limitations.Careful selection of the b-values for in vivo measurements of diffusion parameters with IVIM and other non-Gaussian diffusion models is required to obtain non-biased parameter estimates with maximal precision for a given acquisition time. The proposed methodology, which performs Monte Carlo simulations over a range of model parameters, allows selecting a suitable sampling scheme targeted to the relevant perfusion regime. Results showed that b-value sampling schemes designed to minimize noise propagation can significantly outperform common sampling schemes such as regular distributions of b-values. Interestingly, it was found that the simplified IVIM model can provide equivalently accurate estimates in a more time-efficient manner than the full bi-exponential IVIM model, provided the b-values are optimally chosen.