Cerebral Perfusion

2.3.1 Physiology

Cerebral perfusion is a rather general expression, specifying the process of blood delivery from the arteries to the capillary bed of tissue, supplying nutrients as glucose and oxygen.

To cover the nutrition consumption of the brain, 15 % of the total cardiac output of blood is delivered to the head [28]. Within the brain, perfusion is heterogeneous depending on the local construction of the vascular network (vessel radii, length and number) and the blood velocity (Figure 2.4).

Figure 2.4: Schematic illustration of a capillary bed figured as an artery (red), vein (blue) and the capillaries (magenta) with typical vessel radii and blood velocities [29]. Adapted from [Fig. 2.2 A in 28] Figure 2.2 A.

Cerebral Perfusion

In simplified terms, the biological tissue consists of cells, vessels and the extracellular-extravascular space (EES). Considering a defined tissue volume in brain, the volume belonging to vessels is the cerebral blood volume (CBV), the volume of arterial blood, that is delivered per minute to the considered tissue, represents the cerebral blood flow (CBF) and the time the blood needs to travel through the capillary bed on average is called mean transit time (MTT). These three parameters are linked by the central volume principle [28]:

𝑀𝑀𝑇𝑇𝑇𝑇= 𝐶𝐶𝐶𝐶𝐶𝐶

𝐶𝐶𝐶𝐶𝐶𝐶 ^(2.6)

In general, CBV is stated in ml per 100 g tissue, CBF in ml per 100 g tissue and per minute and MTT in seconds. In some applications, CBV is determined in percent as a volume fraction. This can be assumed to be equivalent to ml per 100 g because the mass density of tissue is close to 1 g/ml [28]. Typical perfusion values in healthy human brain are different for gray and white matter (Table 2.1). Values in Table 2.1 represent empirical data for healthy brain and alter for example under stress, inflammation or hypoxia.

Table 2.1: Typical perfusion parameter values in healthy brain: cerebral blood volume (CBV) in % or ml/100 g, cerebral blood flow (CBF) in ml/100 g/min and mean transit time (MTT) in s.

+ [30], * [28]

gray matter⁺ white matter⁺ normal brain^*

CBV 5.2 ± 1.2 2.7 ± 0.5 4.0

CBF 55.0 ± 12.0 22.0 ± 5.0 50.0

MTT 5.6 ± 2.0 7.2 ± 3.0 6.0

2.3.2 Imaging Perfusion: Pharmacokinetic Modeling and Curve Characterization

Since the 1980s, it is possible to image hemodynamic parameters [31]. The first techniques were xenon-enhanced computed tomography (XeCT) and PET. With technical improvement, also single photon emission computer tomography (SPECT), MRI and dynamic perfusion CT (PCT) became reliable for perfusion imaging [31, 32].

All these techniques need a specially labeled imaging agent for visualization. The underlying technology determines the kind of labeling. For PET imaging the injection of a positron-emitting radionuclide (¹⁸Fluor, ¹⁵Oxygen) is necessary. In MRI the injected agent contains paramagnetic (gadolinium) or superparamagnetic (iron oxide) particles.

An alternative is arterial spin labeling, where the blood water is used as an endogenous tracer that is magnetically labeled using radiofrequency pulses [33]. Even though in

principle the image analysis is similar for all techniques, this work focuses on dynamic methods using MRI and PET.

In biochemical and physiological imaging the aim of labeling is to have an agent that behaves metabolically equivalent to the unlabeled substance. The agent’s physical and biochemical properties, as size, coating, bonding behavior or metabolization, define its distribution volume in tissue. In the case of perfusion imaging, two types of agents are commonly used: mainly diffusible (e.g. labeled water) and mainly intravascular agents (e.g. superparamagnetic iron oxide particles).

Freely diffusible tracers distribute homogeneously over the complete tissue volume, taking some time until blood and tissue concentrations reach equilibrium. During this time, the concentration is mainly determined by the delivered arterial tracer concentration, which is proportional to the CBF. Contrary, a completely intravascular tracer only distributes within vessels with a fast venous clearance. In this case, the concentration of the tracer is primarily determined by the distribution volume, which allows a robust measurement of CBV. In fact, mixed forms are typically present [28].

The theory of tracer kinetics includes plenty of models. Most of them define the tissue as a combination of individual subsystems, called compartments [34]. A general description of the tracer distribution in tissue (concentration over time) can be mathematically expressed by a convolution:

𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡 =� 𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶^𝑡𝑡 𝑝𝑝(𝑤𝑤^′) 𝑅𝑅(𝑤𝑤 − 𝑤𝑤^′)𝑑𝑑𝑤𝑤^′ =

0 𝐶𝐶𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝑝𝑝(𝑤𝑤)∗ 𝑅𝑅(𝑤𝑤) ^(2.7)

This relation between the arterial input of the tracer, determined as concentration in blood plasma (𝐶𝐶𝑝𝑝), and the tissue concentration (𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡) is only valid if the blood flow (𝐶𝐶𝐶𝐶𝐶𝐶) is constant over time and each molecule of the agent has the same possibility to distribute over the volume at time 𝑤𝑤 [28]. All kinetic properties of the agent are condensed in the residue function 𝑅𝑅(𝑤𝑤). This function describes the probability that a molecule of the agent that entered the voxel at time 𝑤𝑤 = 0 is still there at time 𝑤𝑤 =𝑤𝑤^′. Figure 2.5 shows ideal residue functions of three possible tracer behaviors, which are described in the following. One common kinetic model is the two-compartment model that consists of one vessel and one tissue compartment. Therefore, it is often referred to as one-tissue compartment model. Within each compartment, the contrast agent (CA) is assumed to be freely diffusible. This absence of spatial concentration gradients specifies a well-mixed compartment and the corresponding residue function is represented by the dotted curve in Figure 2.5 [34].

An alternative to the standard two-compartment model is the tissue homogeneity model [35]. It adopts the EES as a compartment and assumes validity of the plug-flow model within the capillary bed. The main difference between compartment and plug-flow models lies in the concentration evolution of the agent. In compartments the

Cerebral Perfusion

concentration changes over time and is uniform over the volume. Using a plug-flow model, an additional concentration gradient along the capillaries is allowed. The adiabatic approximation of the tissue homogeneity model [36] assumes a slow change of the EES concentration relative to the fast change of concentration in the intravascular space. It approximates the tissue homogeneity model best for weakly vascularized or slow indicator exchange regimes and allows a separation of the dynamic time course in a fast vascular phase and a slow extravasation phase [13, 37]. For intravascular tracers modeled with plug-flow, all tracer particles have identical velocity and trajectories through the capillaries. Hence, only a single transit time exists and the residue function is represented by a box (solid line, Figure 2.5). The capillary transit time 𝑇𝑇_𝑐𝑐 therefore equals the MTT.

If the capillary bed allows multiple transit times, 𝑅𝑅(𝑤𝑤) behaves like the dashed curve [28].

Figure 2.5: Ideal residue functions R(t) for three different systems: freely diffusible agent and intravascular agent with a single and multiple capillary transit times.

For all of these models, the relation between the MTT of the agent and 𝑅𝑅(𝑤𝑤) is given by [37]:

𝑀𝑀𝑇𝑇𝑇𝑇=� 𝑅𝑅(𝑤𝑤)𝑑𝑑𝑤𝑤^∞

0

(2.8)

In PET, common tracers for perfusion quantification are ¹⁵O, C¹⁵O² and H²¹⁵O. They are freely diffusible and allow quantification of CBF using two-compartment models [34, 38]. Most other tracers have a specific binding mechanism or metabolism behavior.

Using a suitable model assumption, the vascular space, i.e. CBV, is included as a fitting parameter. In the simplest form, CBV is the ratio between 𝐶𝐶_{𝑡𝑡𝑡𝑡𝑡𝑡} and 𝐶𝐶_𝑝𝑝 at equilibrium.

This ratio specifies the volume of blood that contains the same activity as 1 ml of tissue [38].

For intravascular tracers, e.g. MRI contrast agents in brain, the distribution volume can be assumed equivalent to the blood volume. Combining the central volume principle (Eq. (2.6)), Eq. (2.7) and Eq. (2.8) it follows [28]:

𝐶𝐶𝐶𝐶𝐶𝐶= ∫ 𝐶𝐶₀^∞ 𝑡𝑡𝑡𝑡𝑡𝑡(𝑤𝑤) 𝑑𝑑𝑤𝑤

∫ 𝐶𝐶₀^∞ 𝑝𝑝(𝑤𝑤) 𝑑𝑑𝑤𝑤 ^(2.9) This equation holds under the assumption of a fast bolus injection, whereby the concentration rapidly reaches zero level after the first passage of CA through the vasculature.

In reality, for bolus experiments a second peak, the recirculation term, follows. This recirculation is partly caused by the second passage of CA through the brain. The greater contribution to this phenomenon is due to CA that first circulates through kidneys, thyroids and lymph nodes before it reaches the brain [39]. The recirculation term can confound the determination of perfusion parameters, especially if acquisition time is short. However, because the effect is the same in the arterial input and the tissue, its impact on CBV should be small [40]. More problematic is the definition of the arterial input function (AIF). Imaging specific problems (partial volume effects (PVE), selection of appropriate voxels) and problems due to physiological properties (dispersion or delay between arteries and regional tissue) make perfusion estimation complex. To avoid AIFs, reference region models [38, 41] or summary parameters can be used as alternatives [42].

Using a bolus injection, signal-time curves of the first pass of the tracer allow a rather simple extraction of curve shape characteristics (summary parameters). Such parameters are the time-to-peak (TTP), peak height, arrival time and washout or signal recovery.

Their stability enables a fast assessment of perfusion abnormalities, i.e. delayed perfusion via TTP. Widely used in MRI is the area under the curve (AUC). Under the assumption that the area of the AIF is constant for all voxels, a direct proportionality to CBV exists.

However, an absolute quantification of hemodynamic parameters is impossible without an AIF.

The advantage of PET is the possibility to convert signal (decays per second) directly to absolute concentration. In MRI several indirect mechanisms contribute to the signal complicating the conversion of signal to concentration and thus absolute quantification (section 2.4).