Keywords

1 Introduction

Hemodynamic information of the cerebrovascular system is useful to determine criteria of normality and diagnose, study, and follow-up on the treatment progress of cerebrovascular diseases, such as arteriovenous malformations, cerebral ischemia, and moyamoya disease [1]. In particular, variations in the arterial transit time (ATT) in the brain are related to hemodynamic impairment caused by cerebrovascular diseases [2].

Different imaging modalities are currently available to acquire blood flow data of the cerebrovascular system. For example, digital subtraction angiography [3], four-dimensional computed tomography angiography [4], four-dimensional arterial spin labeling magnetic resonance angiography (4D ASL MRA) [5], and others can be used for this purpose.

One common approach to analyze the blood flow data contained in the images is to estimate blood flow parameters using mathematical models, which need to be fitted to the observed signal for each voxel of the dataset containing the hemodynamic information. The model describes the expected behavior of the temporal signal of the selected imaging modality, considering the main modality-specific phenomena affected. The values of the required blood flow parameters can be calculated based on the continuous mathematical model fitted to the discrete temporal signal intensity curve.

The accuracy of the blood flow parameters estimation is usually limited by the temporal resolution of the acquired images and the amount of noise in the dataset [6]. Additionally, depending on the modality, other factors, such as labeling duration in case of 4D ASL MRA, can also affect the accuracy of the estimations. In this context, the present work focuses on the estimation of the ATT in six 4D ASL MRA datasets of a flow phantom, acquired with literature values of labeling duration and temporal resolution.

2 Four-Dimensional Arterial Spin Labeling Magnetic Resonance Angiography

4D ASL MRA is a medical imaging modality, which can simultaneously acquire blood flow and morphological data of the cerebrovascular system [5]. Instead of requiring the administration of an external contrast agent, 4D ASL MRA uses the water contained in blood as intrinsic contrast agent. During the acquisition, a radio-frequency (RF) pulse is applied to the base of the neck of the subject, parallel to the plane containing the main feeding arteries of the brain. The RF pulse inverts the magnetization of blood flow in the region where it is applied. The duration of the RF pulse (\(\tau \)) determines if the cerebrovascular system will be imaged as it fills with labeled blood or as it flushes out. In particular, labeling durations of 300 ms [1] and 1000 ms [7] have been proposed in the literature.

Once the magnetically labeled blood flows into the imaging region, it is imaged at different time points, which depend on the temporal resolution (r) of the 4D ASL MRA dataset. Control images are also acquired when no labeled blood is present in the imaged region of the brain. As a result, a 4D ASL MRA dataset is comprised of a set of control and labeled pairs of images. The subtraction of corresponding control and labeled image pairs allows the removal of most signal originating from other non-vascular structures. Thus, the final result contains the signal of magnetically labeled blood flowing through the brain and some residual noise [1]. Figure 1 shows maximum intensity projections of 60 contiguous slices of the control, labeled, and subtracted images of three time-points of a 4D ASL MRA dataset of the brain of a human subject, acquired with a labeling time of 300 ms and temporal resolution of 120 ms.

Fig. 1.
figure 1

Maximum intensity projections of 60 contiguous slices of control, labeled, and subtracted images of a 4D ASL MRA dataset of the brain of a human subject, acquired at three time-points: 440 ms, 680 ms, and 920 ms.

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3 Blood Flow Parameter Estimation

The blood flow data contained in 4D ASL MRA datasets can be analyzed by fitting a mathematical hemodynamic model to the observed signal S(v, t) of each vascular voxel v at time t. In particular, Okell et al. [7] designed a model for this specific image modality that takes into account the main acquisition phenomena of 4D ASL MRA datasets. The model is presented in Eq. 1.

$$\begin{aligned} S(v, t)= & {} \int _{t-\delta _t-\tau }^{t-\delta _t} A(v) dt_d D(v, t_d) T(\delta _t, t_d) R(t) \end{aligned}$$
(1)
$$\begin{aligned} D(v, t_d)= & {} \left\{ \begin{array}{ll} s(\Gamma (1+ps))^{-1}\exp (-st_d)(st_d)^{ps} &{} \text{ if } st_d> 0, ps > -1 \\ 0 &{} \text{ otherwise } \end{array} \right. \end{aligned}$$
(2)
$$\begin{aligned} T(\delta _t, t_d)= & {} \exp (-(\delta _t + t_d)/T_{1b}) \end{aligned}$$
(3)
$$\begin{aligned} R(t)= & {} \cos (\alpha )^{(t-t_0)/TR}\sin (\alpha ) \end{aligned}$$
(4)

In Eq. 1, the signal S(v, t) is expressed as a function of the relative volume of labeled blood A(v) flowing through a voxel and the signal decay due to different factors, which include the dispersion of labeled blood before reaching the analyzed voxel \(D(v, t_d)\), the \(T_1\) relaxation of magnetically labeled blood \(T(\delta _t, t_d)\), and the application of imaging pulses R(t). The arterial transit time (ATT), represented by \(\delta _t\), is one of the most important blood flow parameters that can be estimated using this mathematical function, the labeling duration \(\tau \) is an acquisition parameter set by the user, and the additional time delay \(t_d\) caused by the dispersion of labeled blood is the integration variable.

The signal decay due to dispersion of labeled blood is described in Eq. 2. It corresponds to a distribution that depends on the blood flow parameters sharpness s and time-to-peak p. The decay caused by \(T_1\) relaxation of the labeled blood is shown in Eq. 3. It includes the longitudinal relaxation time of blood \(T_{1b}\), which is approximately 1664 ms in a magnetic field of 3T [8]. Finally, Eq. 4 presents the formula of the signal decay due to imaging pulses applied to the labeled blood before it reaches voxel v, where \(\alpha \) is the flip angle, TR is the repetition time, and \(t_0\) corresponds to the time when the first imaging pulse is applied.

Optimization algorithms are commonly used to fit the described mathematical model to the signal contained in a 4D ASL MRA dataset. This work uses the multi-scale parameter search (MSPS) algorithm because it has been shown to yield good results in general benchmarks and medical applications [9].

4 Materials and Methods

4.1 Data Acquisition

Six 4D ASL MRA datasets of a flow phantom with a fluid delivered through a simple pipe at constant flow rate were acquired during the experiments. The pipe was filled with a fluid composed of \(36\%\) (vol.) glycerine in water, which is commonly used as a blood analog with similar viscosity [10]. The fluid was circulated at constant flow rate of 3.34 mL/s and average speed of 161.7 cm/s using a peristaltic pump (Sorin Group Deutschland GmbH, Munich, Germany). The pipe was fixated using sandbags and a bottle containing 1 L of demineralized water to represent other tissues, as suggested and used in previous studies [11].

The six 4D ASL MRA datasets were acquired on a Philips Achieva 3T MRI (Philips Healthcare, Best, The Netherlands). Each dataset contains pairs of volumetric control and labeled images, acquired using Look-Locker and Sensitivity Encoding (SENSE) to speed up the acquisition process. Each volumetric image contains 120 slices with 224 \(\times \) 224 voxels. The voxel size is 0.94 \(\times \) 0.94 \(\times \) 1.0 mm\(^3\). Additional acquisition parameters include a T1-Turbo Field Echo (TFE) scan with a TFE factor of 16, SENSE factor of 3, TR/TE values of 7.7/3.7 ms, flip angle of 10\(^{\circ }\), and half scan factor of 0.7. Figure 2 shows maximum intensity projections of the images of a 4D ASL MRA dataset of the described flow phantom, acquired with labeling time (\(\tau \)) of 300 ms and temporal resolution (r) of 120 ms.

Fig. 2.
figure 2

Maximum intensity projections of subtracted images of a 4D ASL MRA dataset of a flow phantom containing a mixture of glycerine and water at time points 320 ms, 560 ms, and 800 ms. This dataset was acquired using a labeling time (\(\tau \)) of 300 ms and temporal resolution (r) of 120 ms.

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The 4D ASL MRA datasets of the flow phantom were acquired in six scenarios, with different values for the labeling duration \(\tau \) and temporal resolution r, in order to evaluate their effect on the estimation accuracy of the ATT. The values of \(\tau \) and r were selected according to experiments reported in the literature [1, 7], as detailed in Table 1. The time at which the first imaging pulse \(t_0\) is applied is also indicated, together with the number of images in a dataset n.

Table 1. Labeling duration (\(\tau \)), temporal resolution (r), first imaging pulse time (\(t_0\)), number of images in a dataset n, and average absolute error (AAE) when estimating the arterial transit time in each evaluated scenario. The acquisition parameters are selected according to experiments reported in [1] (scenarios 1 to 3) and [7] (scenarios 4 to 6). The lowest AAE is in bold.
Full size table

4.2 Evaluation Method

Due to the variation of speed along the cross-sectional area of the pipe due to laminar flow, this work considers only the ATT values estimated at voxels of the centerline of the pipe, also referred to as skeleton. The pipe is segmented in the 4D ASL MRA datasets using a simple thresholding algorithm, followed by removal of small components that correspond to noise. The skeleton of the resulting segmentation is calculated using a skeletonization algorithm available in the Insight Toolkit framework (ITK) [12]. For each voxel contained in the skeleton, the ATT is estimated by fitting the blood flow model presented in Eq. 1 to the observed signal.

The ground-truth values for the ATT at each voxel v of the skeleton of the pipe are calculated by dividing the length of the centerline path from the extreme of the pipe to the voxel L(v) by the average speed S of the water and glycerine mixture delivered by the pump, as it is presented in Eq. 5. The estimated and ground-truth values for the ATT along the skeleton are compared using the average absolute error (AAE). In order to enrich the comparison, the acquisition time of a dataset in each scenario is also recorded.

$$\begin{aligned} ATT(v)= & {} L(v) / S \end{aligned}$$
(5)

5 Results

The AAE between the ground-truth and estimated values for the arterial transit time (ATT) along the pipe skeleton and the acquisition time in each one of the six scenarios is presented on Table 1. It can be noticed that the AAE decreases when the labeling duration is increased for each pair of scenarios with the same temporal resolution: 1 vs. 4, 2 vs. 5, and 3 vs. 6. Additionally, the AAE increases when the temporal resolution is decreased in sets of scenarios with the same labeling duration: 1 vs. 2 vs. 3 or 4 vs. 5 vs. 6. The lowest AAE of 42.34 ± 21.69 ms is reached in Scenario 4, when the longest labeling time and highest temporal resolution are used. Nevertheless, Scenario 4 is also the case that requires the longest acquisition time of 16 min.

6 Discussion and Conclusion

The present paper evaluated the influence of the labeling duration (\(\tau \)) and temporal resolution (r) on the arterial transit time (ATT) estimation accuracy. Labeling duration and temporal resolution are important acquisition parameters of 4D ASL MRA datasets and ATT is the most important blood flow parameter associated with hemodynamic impairment in the brain caused by cerebrovascular diseases.

The experiments were conducted in a controlled environment, using a flow phantom containing a mixture of glycerine and water, circulated at a constant flow rate. During the experiments, it was observed that the average absolute error (AAE) decreases when longer labeling times (\(\tau \)) and higher temporal resolution (r) are used to acquire a 4D ASL MRA dataset. Consequently, the most accurate results, with the lowest AAE, are achieved when the longest \(\tau \) of 1000 ms and the highest r of 60 ms are used.

Nevertheless, the scenario with the longest \(\tau \) and the highest r is also the one leading to the longest acquisition time of 16 min. Depending on the specific application, long acquisition times are often associated with more motion artifacts or are simply clinically not feasible [13]. Thus, this trade-off between accuracy of the ATT parameter estimation and acquisition time has to be considered when designing the 4D ASL MRA datasets in research or clinical applications.

In terms of limitations, this work represents an initial evaluation of the estimation of blood flow parameters in 4D ASL MRA datasets in a real physical setting, under controlled conditions. Further analysis would be required to translate the obtained conclusion to human subjects. In vivo acquisitions would include additional challenges, such as motion artifacts, other sources of noise, additional acquisition parameters to be optimized, and more complex vascular geometries. Nevertheless, it is expected that this simplified scenario, using a pipe containing a fluid similar to blood, can support clinicians and physicists optimizing 4D ASL MRA sequences for clinical studies or routine diagnosis.