One of the advantages of arterial spin labeling (ASL) over other techniques for measuring perfusion is the possibility of accurate quantification. Blood perfusion and arterial transit time (time taken for blood to travel from the labeling region to tissue voxel) can be estimated.

We start with the basic difference images (control – label), in which the signal is dependent on perfusion. However, a number of other factors contribute to the difference signal, and these need to be taken into account to provide an accurate estimate of perfusion.

Details of the acquisition protocol can cause unwanted signal in the difference image that is unrelated to perfusion, for example, magnetization transfer differences between label and control images. Likewise, some true perfusion signal can be missed, for example, the passage of nonlabeled blood due to the restricted spatial extent of labeling. For the purposes of this chapter, it is assumed that the signal in the difference image contains contributions from all perfusing blood, and only from perfusing blood (i.e., ignoring the nonperfusion and missed perfusion contributions described above).

The difference signal can be collected at either a single time point after labeling or at multiple time points, as shown in Figure 30.1. This time is often referred to as the inversion time or the postlabeling delay time.

As an alternative to the kinetic modeling described above, a model-free approach can be used.¹⁵ The philosophy behind model-free perfusion quantification is that, instead of prior assumptions about bolus shape and the tissue’s residue function, the actual bolus or arterial input function is measured along with the tissue signal. This allows for extraction of the tissue residue function and thereby perfusion by means of deconvolution, a concept extensively used in dynamic contrast-agent based methods.¹⁶ A requirement is that temporal information of both the arterial signal as well as the tissue signal exists. In general, the tissue concentration of a tracer in the voxel under observation as a function of time can be described by the following convolution integral:

where, C_t(t) is the tissue concentration, f_t the tissue flow, C_a(t) is the arterial tracer concentration entering the voxel, and R(t) is the residue function describing the fraction of tracer molecules remaining in the voxel after time t (i.e., the difference between arterial influx and venous outflow at each point in time). C_a(t) is also called the arterial input function (AIF). This definition naturally implies that R(t) must start with 100% of the arriving tracer available at the beginning (R(t = 0) = 1) and that this amount of tracer subsequently decreases toward zero as the tracer washes out of the observed voxel through the venous outlet. The term f_tR(t) can therefore be found by deconvolving C_t(t) by C_a(t) and the tissue’s flow F_t subsequently found from f_tR(t = 0) due to the aforementioned property of the residue function being 1 at t = 0. The neat property of this deconvolution procedure is that no prior assumptions about the residue function are required, making it model free as long as both the arterial signal feeding the voxel and the actual tissue signal are measured.

Note that for arterial spin labeling, these tracer concentrations are essentially magnetization differences between the “control” and “label” experiments seen over time. If we look at Equation 9, it can be seen that the tissue concentration, ΔM(t), is described by the same convolution integral as shown in Equation 10. Here, ΔM(t) is the result of the convolution of the arterial signal, M_a(t), with the combined residue function r(t) and m(t). The additional term m(t) is added to account for the fact that that our magnetic labeled tracer decays over time. This is contrary to gadolinium-based perfusion methods, where the tracer mass remains constant during the entire experiment. We do not have conservation of “tracer mass” in our ASL experiment. Nevertheless, the same properties apply to r(t)m(t) as for R(t) that r(0)m(0) = 1. The perfusion, f, can therefore be found in a similar manner by deconvolution on a voxel-by-voxel basis.

The extraction of the information needed for this procedure, ΔM(t) and M_a(t), requires a bit more than what is measured by most standard available ASL sequences. Traditionally, only a single inversion time point ΔM(TI) after labeling is imaged and perfusion is estimated by assuming the characteristics of M_a(t), r(t), and m(t). The inversion time TI is chosen such that the bolus will have enough time to clear from the arterial compartment such that only the tissue perfusion is measured. For the model-free approach, multiple time points are needed, and this is typically achieved using a fast Look-Locker–based approach to ensure feasible scan times. A caveat of a multiple time point acquisition is that the arterial blood would not have had time to leave the arterial compartment when short TIs are used, meaning that instead of only measuring the tissue contribution, ΔM(t), it is ΔM(t) + M_a(t) · aBV, which is actually measured (Fig. 30.6). Here, aBV is the arterial blood volume fraction (not to be confused with total blood volume) in the measured voxel. However, the vascular contribution can be eliminated from the signal by the use of vascular crusher gradients. They are essentially bipolar diffusion-encoding gradients that dephase the signal from labeled spins moving faster than a preset velocity threshold.¹⁷ Spins moving perpendicular to the crusher gradient direction will not be dephased and therefore crushing in multiple directions is performed and averaged to keep the arterial contribution at a
minimum. Note that venous signal can be neglected as by the time the label arrives here it will have fully decayed. This means that a crushed multiple time point experiment measures the tissue signal, ΔM(t), and a noncrushed experiment measures ΔM(t) + M_a(t) · aBV, thereby allowing the extraction of the arterial signal M_a(t) · aBV from the subtraction of the two experiments. Weighting M_a(t) by aBV is done to get the concentrations right as the spins are located in the 1% to 2% blood volume. We will call this the fractional arterial input function fAIF(t) = M_a(t) · aBV. However, for absolute flow quantification, it is AIF(t) = M_a(t), which is needed (Equations 6 through 8) and therefore scaling with aBV is necessary. The aBV can be estimated by comparing the area under the measured fAIF(t) curve with the area under the calculated curve for M_a(t), given in Equation 8, provided the T₁ relaxation time of blood, the equilibrium magnetization of arterial blood M_a⁰, the labeling efficiency α, and the bolus duration τ are known.

A sequence that takes advantage of this is the quantitative STAR labeling of arterial regions (QUASAR) implementation,^15,18 which interleaves both crushed and noncrushed control-label pairs at multiple time points. After the separation of ΔM(t) and M_a(t), the flow is found by deconvolution, typically using the singular value decomposition method, along with some regularization to keep the solution sensible.¹⁶ The presence of added acquisition and physiologic noise in the signal often makes the matrix inversion, which is part of the deconvolution, an ill-posed problem.

An advantage of the multiple time point acquisition and in particular the interleaved acquisition of crushed and noncrushed data is the added information available in addition to the blood flow. From Figure 30.6 it can be seen that we have information about the arterial transit time (t_a). From the time the bolus arrives at the voxel, at t_a, it travels farther through smaller and smaller vessels toward the capillary network. The time it takes to reach vessels with flow velocities less than the preset crusher velocity can be measured as the upslope of the crushed experiment. We could call this the microvascular transit time (t_m). Because the fractional arterial input function is measured on a voxel-by-voxel basis, then we can also extract the arterial blood volume, aBV, simply by integrating the area under fAIF(t) and correct it for the T₁ decay of arterial blood¹⁵:

During the blood’s passage through the vasculature, it is exposed to resistance from the vasculature itself. As a result, the labeled bolus will get dispersed or blurred during its passage of the vascular tree and the farther or the narrower vessels the bolus has to traverse, the more dispersed it becomes. Therefore, different regions have different degrees of dispersion, and the effect is known to worsen especially in patients with vascular disease. By assuming some patterns of dispersion, such as the ones proposed by Hrabe et al.,¹⁹ one can investigate the amount of dispersion in different brain regions. An example of such a dispersion map fitted from the M_a(t) maps is shown in Figure 30.7.²⁰ It should be noted that t_a, t_m, aBV, and the dispersion maps all can be extracted without the need of deconvolution, but rather using simple subtraction, integration, fitting, and slope detection algorithms. The results of the deconvolution, r(t)m(t), also include information about the kinetic properties r(t) of the system
in addition to cerebral blood flow (CBF). However, the relaxation properties m(t) are mixed up with it so the interpretation is not straightforward. Future studies will need to be done to investigate the clinical usefulness of this information.